Technological Aspects of Corrosion Control in Metallic Systems

The Pennsylvania State University

The Graduate School

Department of Materials Science and Engineering

TECHNOLOGICAL ASPECTS OF CORROSION CONTROL IN METALLIC SYSTEMS

A Dissertation in

Materials Science and Engineering

by

Matthew Logan Taylor

2012 Matthew Taylor

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

December 2012

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The dissertation of Matthew Taylor was reviewed and approved* by the following:

Digby D. Macdonald1

Distinguished Professor of Materials Science and Engineering

Dissertation Advisor

Chair of Committee

James H. Adair1

Professor of Materials Science and Engineering, Bioengineering and Pharmacology

Michael A. Hickner1

Assistant Professor of Materials Science and Engineering

Mirna Urquidi-Macdonald1

Professor of Engineering Science & Mechanics

Bernard Normand2

Professor of Materials Science and Engineering

Special Member

Damien Feron3

Professor of Nuclear Science and Technology

Special Member

Gary L. Messing1

Distinguished Professor of Ceramic Science and Engineering

Head, Department of Materials Science and Engineering

*Signatures are on file in the Graduate School

1 The Pennsylvania State University

2 Institut National des Sciences Appliquées de Lyon


3 Institut National des Sciences et Techniques Nucléaires

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ABSTRACT

Three corrosion control technologies were investigated, including the effect of nitrogen

on the passivity of chromium in sulfate solutions, possible issues associated with the use of

amines in steam turbine environments and the microstructure of naval advanced amorphous

coatings.

Nitrogen (N) is a minor alloying element commonly used to increase the strength of

steels by stabilizing the austenite phase. Nitrogen has been found to improve the corrosion-

resistance of stainless steels, although the mechanism which confers this protection is under

debate. An atomistic model is proposed which explains the incorporation of nitrogen into the

passive films of chromium-based alloys and predicts the effects of such incorporation on the

passive film behavior. The model is conceptualized through a novel use of the Hume-Rothery

rules of solid solution, for which only one possible substitution of N into the Cr2O3 lattice was

found to be compatible with all four “rules”; coordination number, electronegativity, ionic radius

mismatch and valency. Four crystallographic defect reactions are proposed; one at the metal/film

interface, where N(3-) occupies an oxygen vacancy and three subsequent reactions with H+ at the

film/solution interface where the nitrogen defect evolves into ammonia. Rate constants are

derived and reported for the reactions using the method of partial charge transfer. Using the

Solute Vacancy Interaction Model as a guide, it is proposed that the negatively charged nitrogen

defects would have electrostatic interactions with the positively charged oxygen vacancies and

metal interstitials, and the resulting complexes should reduce the transport of these defects.

Consequently, the Point Defect Model rate constants are affected, correctly predicting that N

defects should reduce both the passive film thickness, and the steady state current density, as has

been observed in nitrogen-bearing alloys and nitrided stainless steels. Physical vapor deposited

chromium + nitrogen (0, 6.8 and 8.9 at.%N) coatings were investigated as a model system, to test

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the model. Because Cr passive films have been observed to be generally n-type semiconductors,

an impedance function containing a n-type Faradaic impedance was constructed and optimized to

electrochemical impedance spectra for the model system at pH 4,7 and 10 1M sulfate solution at

30°C. An apparent deviation from theory was observed, however. The n-type model predicted

steady state currents which were independent of potential, while the observed current densities

had a positive correlation with potential. Mott-Schottky analysis revealed that the test potentials

were within the n-p transition and p-type potential range, which resolves the apparent deviation.

Despite this difficulty, however, the impedance model produced reasonably accurate results,

calculating current densities to within one order of magnitude of the measured steady state

currents where anodic currents were available and passive film thicknesses on the order of 1-2

nm.

Various amines are commonly used to inhibit corrosion in thermal power generation

systems, including steam turbines, by increasing the pH. However, during the shutdown phase of

the power plant, it is possible for these inhibitors to concentrate and cause corrosion of the turbine

rotor. The effect of two ammine inhibitors (monoethanolamine and dimethylamine) on the

passivity of ASTM A470/471 steel is investigated in a simulated turbine environment at pH 7,

and temperatures of 95°C and at 175°C. Potentiodynamic scans and potentiostatic measurements

revealed that the steel depassivated with high (0.1M) concentrations of monoethanolamine, in

combination with acetate. Because the steel depassivated at low potentials and at neutral pH, it is

unlikely to be acid or transpassive depassivation. The proposed mechanism for this depassivation

is resistive depassivation, whereby the potential drop incurred by the precipitated outer-layer robs

the barrier layer of the passive film of the potential required to maintain a finite film thickness.

This effect was observed at both 95°C and 175°C and was found to destroy the metal at an

alarming rate. This observation was made in tandem with modeling of the amine concentrations

found in steam turbines during operation and shutdown. Monoethanolamine has a lower vapor

v

pressure than water during turbine dryout conditions, meaning that it will tend to concentrate,

along with acetate, while dimethylamine evaporates. Because the monoethanolamine

concentrations during operation were three orders of magnitude lower than the least concentrated

experiment in this work, but equal to the most concentrated conditions in this work during

shutdown, it is likely that the corrosion damage attributed to this mechanism occurs only during

shutdown. It is recommended that monoethanolamine be evaluated for exclusion from use as an

inhibitor in thermal power systems containing ASTM A470/471 steel.

High velocity oxy-fuel (HFOV) coatings are employed in maritime environments to

protect against corrosion and wear. The performance of such coatings is dominated by flaws in

the microstructure, such as porosity, delamination and secondary phases. A nondestructive

evaluation technique that is capable of determining the quality of a HVOF coating was

developed, based on electrochemical impedance spectroscopy (EIS). The EIS measurement was

correlated to the microstructure observed via scanning electron microscopy (SEM). Because a

transmission line model was unable to provide discriminatory information, a convenient

mathematical impedance function was constructed, with two separated time constants defined by

constant phase elements, with time constants for a “fast” and a “slow” process. When the

parameters of this model is optimized to the impedance data, a microstructure-time constant

relationship emerges. It was found that for the “fast” time constant, all values below 0.15s

belonged to delaminated specimens, while all values above 0.30 belonged to hermitic samples.

For samples with “fast” time constants between 0.15 and 0.30, a measure of the microstructure

can be comparatively inferred, with lower values for both the “fast” and “slow” time constant

corresponding to higher porosity.

Enabling the impedance studies above is a new software package for fitting complicated

impedance functions of up to 50 parameters to complex impedance data, developed specifically

for this work. The curve-fitting software utilizes differential evolution, an evolutionary algorithm

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which is relatively new to the field of impedance modeling, enabling the operator to obtain high

quality fits without the need for excellent starting guesses, taking trial and error out of the curve-

fitting process and vastly improving the man-hour efficiency involved in optimizing complicated

impedance functions such as the Faradaic impedance of the Point Defect Model.

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TABLE OF CONTENTS

LIST OF FIGURES ......................................................................................................... ix LIST OF TABLES ........................................................................................................... xvii ACKNOWLEDGEMENTS ............................................................................................. xviii

Chapter 1 History and Philosophy of Corrosion Control ....................................................... 1

The Pre-History of Metals ................................................................................................ 3 The Cost of Corrosion ...................................................................................................... 4 Technological Corrosion Control ..................................................................................... 4

Chapter 2 The Effect of Nitrogen on the passivity of pure Chromium .................................. 6

Background and Theory ................................................................................................... 6 The Point Defect Model of the Passive State (PDM)....................................................... 8

Chapter 3 Complex Function Optimization for One Independent Variable by

Differential Evolution ...................................................................................................... 19

The Challenge .......................................................................................................... 19 Differential Evolution .............................................................................................. 24 The Tool ................................................................................................................... 28

Mott-Schottky Analysis ................................................................................................... 30 The Solute Vacancy Interaction Model ............................................................................ 32 The Hume-Rothery Rules of Solid Solution .................................................................... 33 The Location of Nitrogen in the metal-oxide lattice ........................................................ 34

The Electronic State of Nitrogen in the passive film ............................................... 38 Proposed Point Defect Reactions for Nitrogen ................................................................ 40

Reaction N1: Incorporation of Nitrogen into the Barrier Layer................................ 41 Reaction N2,N3 and N4: Production of Surface Amines ........................................... 41

Derivation of the Reaction Rate Constants Using the Method of Partial Charges ........... 41 For Reaction N1: ....................................................................................................... 42 For Reaction N2: ....................................................................................................... 44 For Reaction N3: ....................................................................................................... 44 For Reaction N4: ....................................................................................................... 45

Derivation of Rate Constants ........................................................................................... 45 Nitrogen-Interstitial Interaction ................................................................................ 47

Experimental: Microstructural Characterization of Cr +N Physical Vapor Deposition

Coatings .................................................................................................................... 49 Experimental: Electrochemical Measurements ........................................................ 58 Electrochemical Method .......................................................................................... 61

Results and Analysis ........................................................................................................ 61 Potentiodynamic Polarizations ................................................................................. 61 Mott-Schottky Analysis: Agreement with Proposed Model .................................... 66 Potentiostatic Current Contour Mapping ................................................................. 69

The Optimization of Model Parameters to Impedance Data ............................................ 71 The Validation of Impedance Data .......................................................................... 74

viii

Validation of Impedance Data via the Use of Confidence Bands ............................ 76 Results: Impedance Model Optimization ......................................................................... 79

Barrier Layer Thickness ........................................................................................... 82 Conclusions and Suggestions for Further Study .............................................................. 85

Chapter 4 Resistive Depassivation of ASTM 470/471A Rotor/Disc Steel in Aqueous

Amine Environments at Elevated Temperatures .............................................................. 86

Introduction ...................................................................................................................... 86 Amine background: Dimethylamine (DMA) ................................................................... 89 Amine Background: Monoethanolamine (ETA) .............................................................. 89 Thermodynamics of the Iron-Water System .................................................................... 91 The features of a cyclic polarization Curve ..................................................................... 94 The features of a potentiostatic polarization curve .......................................................... 97 A note on reference electrode potentials .......................................................................... 99 A note on the thickness of passive films and modes of depassivation ............................. 100 Experimental .................................................................................................................... 102 Low Temperature (95°C) Testing .................................................................................... 102 High Temperature (175°C) Testing ................................................................................. 106 Cyclic Polarization ........................................................................................................... 108 Predicted Corrosion Rates based on the linear polarization resistance ............................ 114 Potentiostatic Polarization ................................................................................................ 116 Visual observations .......................................................................................................... 119 Electrochemical Impedance Spectroscopy (EIS) ............................................................. 120 Discussion / Conclusions ................................................................................................. 121

Chapter 5 Characterization of Naval Advanced Amorphous Coatings (NAAC)................... 125

Introduction ...................................................................................................................... 125 Experimental .................................................................................................................... 126 SEM Imaging ................................................................................................................... 129

B-plate detail. ........................................................................................................... 133 J-plate Detail ............................................................................................................ 134

Experimental .................................................................................................................... 136 Impedance Modeling ........................................................................................................ 138 Discussion ........................................................................................................................ 140 Conclusions ...................................................................................................................... 141

Chapter 6 .................................................................................................................................. 142

Final Conclusions and Suggestions for Future Work .............................................................. 142

Bibliography ............................................................................................................................ 143

Appendix A: Cr+N EIS Curve Fits .......................................................................................... 147

Appendix B: Potentiostatic Curves for ASTM 470/471A Steel with Various

Concentrations of Amines ................................................................................................ 157

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LIST OF FIGURES

Figure 1: Cartoon of PDM Reaction 1: Consumption of metal vacancies at the metal/film

interface ............................................................................................................................ 10

Figure 2: Cartoon of PDM Reaction 2: Injection of metal interstitials at the metal/film

interface ............................................................................................................................ 10

Figure 3:Cartoon of PDM Reaction 3: Generation of oxygen vacancies at the metal/film

interface (grows the film into the metal, away from the f/s interface) ............................. 11

Figure 4:Cartoon of PDM Reaction 4: Generation of metal vacancies at the film/solution

interface ............................................................................................................................ 11

Figure 5:Cartoon of PDM Reaction 5: Dissolution of metal interstitials at the

film/solution interface ...................................................................................................... 11

Figure 6:Cartoon of PDM Reaction 6: Consumption of oxygen vacancies at the

film/solution interface ...................................................................................................... 12

Figure 7:Cartoon of PDM Reaction 7: Dissolution of the passive film at the film/solution

interface (Shrinks film thickness towards the m/f interface) ............................................ 12

Figure 8: Localized Passivity Breakdown due to the Condensation of Vacancies: 1. A

vacancy condensate forms, locally eliminating the m/f interface. 2. The film

continues to shrink everywhere due to reaction 7, but grow only in regions where the

interface exists. 3. The film undergoes mechanical rupture, presenting a small

anode in an occluded area, where pitting corrosion initiates. .......................................... 14

Figure 9: Single mode fitness function y, for parameter x ....................................................... 20

Figure 10: Multi-modal fitness function y, for parameter x..................................................... 20

Figure 11: Multi-modal fitness function y for parameter x, with one global solution and

many local solutions ......................................................................................................... 21

Figure 12: Fitness function Z for parameters x and y with one optimal solution .................... 22

Figure 13: Multi-modal Fitness function Z for parameters x and y ......................................... 22

Figure 14: Multi-modal fitness function z for parameters x and y with one global

optimum and many local optima ...................................................................................... 23

Figure 15: Visualization of an arbitrary solution vector in a solution Space bounded by

the limits for three parameters; p1,p2 and p3 ................................................................... 25

Figure 16: Concatenation of a complex impedance spectrum into a real-valued list .............. 28

x

Figure 17: Unit Cell of Cr2O3 (corundum structure) in various projections drawn with

Crystal Maker software[38] ............................................................................................. 35

Figure 18: XPS investigation of Cr+N PVD coatings[41]. 1) Pure Cr 2)Cr+N,

approximately 10%N. 3) CrN. Three peaks are observed, CrN (red), Cr2N (Blue)

and Amine (Green). All three peaks correspond to N in a similar electronic state to

(3-) .................................................................................................................................... 39

Figure 19: Effect on Diffusivity of Cation Interstitials by Nitrogen Alloying Fraction .......... 48

Figure 20: XRD Pattern and Fit for Pure Cr PVD coating showing Cr110(44.4°) and

Cr200 (64.4°) reflections .................................................................................................. 50

Figure 21:XRD Pattern and Fit for 6.8%N Cr PVD coating showing Cr110(44.4°) and

Cr200 (64.4°) reflections .................................................................................................. 51

Figure 22: XRD Pattern and Fit for 9.8% N Cr PVD coating showing Cr110(44.4°) and

Cr200 (64.4°) reflections .................................................................................................. 51

Figure 23: Williamson-Hall Plot for Cr+N PVD coatings. The slope of each line is

proportional to the strain by a constant value, C. The y-intercept is proportional to

quotient of the wavelength and the thickness by a constant value, K. ............................. 52

Figure 24: Strain and Grain Diameter of Cr PVD coatings for various concentrations of N

as calculated from XRD peak broadening, assuming C=5 and K=0.9 ............................. 52

Figure 25: Tabulated XRD spectra of various Cr+N Phases[44] and Pure Cr vs. Nitrided

Cr [45] .............................................................................................................................. 53

Figure 26: Comparison of XRD peak locations observed in this study with literature

values [45]. Dashed lines: Expected peak locations. Black circles: Peak locations

observed in this study. ...................................................................................................... 54

Figure 27: SEM micrograph of the texture of the pure Cr PVD coating ................................. 55

Figure 28: SEM Micrograph of a Pure Cr particle embedded in a pure Cr PVD coating ........ 55

Figure 29: SEM micrograph of a void in the pure Cr PVD coating ....................................... 56

Figure 30: SEM Micrograph of a 6.8% N / Cr PVD coating, illustrating the texture of the

coating and the presence of Cr+N particles ..................................................................... 56

Figure 31: SEM micrograph illustrating a Cr+N particle embedded in the Cr + 6.8% N

PVD coating ..................................................................................................................... 57

Figure 32: SEM Micrograph featuring a Cr+N particle sitting on the surface of the Cr +

6.8% N PVD coating ........................................................................................................ 57

Figure 33: SEM micrograph of a Cr+N particle embedded in the Cr + 8.9% N PVD

coating .............................................................................................................................. 58

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Figure 34:SEM micrograph of a void in the Cr + 8.9% N PVD coating ................................. 58

Figure 35: Pourbaix Diagram for the Cr-Water system at 28°C Calculated with HSC

Chemistry 5.11[47] .......................................................................................................... 60

Figure 36: Kinetic Phase Stability Diagram for Alloy X in acidic, 6.25M NaCl at 50°C

[48] ................................................................................................................................... 60

Figure 37: Overview of potentiodynamic scans of PVD coatings at 30°C in Sulfate

solution at pH 4,7 and 10, for compositions 0 at.%, 6.8 at.% and 8.9 at.% N. ................ 62

Figure 38: Potentiodynamic scans at pH 4............................................................................... 63

Figure 39: Potentiodynamic Scan at pH 10 ............................................................................. 64

Figure 40: Potentiodynamic scan at pH 7 for 6.8 and 8.9% N samples, with the

potentiostatic currents superimposed. .............................................................................. 65

Figure 41: Mott-Schottky Analysis for Cr PVD coatings with 0% and 8.9% N at pH 4 and

7 ........................................................................................................................................ 66

Figure 42: Mott-Schottky Plot for 0% and 8.9% N, pH 10 ..................................................... 67

Figure 43: Acceptor density in the p-type potential range as a function of pH ....................... 68

Figure 44: Flat-band potentials estimated from mott-schottky analysis as a function of pH ... 68

Figure 45: Donor density in the n-type potential range as a function of pH ............................ 69

Figure 46: Flat Band Potential in the n-type potential range as a function of pH .................... 69

Figure 47: Measured Current Density E-pH Contour Map for 0%N ....................................... 70

Figure 48: Measured Current Density E-pH Contour Map for 9.8% N ................................... 71

Figure 49: Impedance Circuit. Rs: Solution Resistance. Rdl: Charge Transfer Resistance.

Cdl: Double Layer Capacitance. Zw: Warburg Diffusion Element. ZF: Faradaic

Impedance. Zg: Geometric Impedance ............................................................................. 72

Figure 50: Checking the ratio of impedance for smoothness ................................................... 75

Figure 51: Representative Confidence Bands as calculated by Ellis2; 105 trials, +/- 5%

parameter values .............................................................................................................. 76

Figure 52: Representative confidence bands for phase angle (green), |Z| (purple), Z’(red)

and Z’’(blue) after the exclusion of the final 8 points of the spectrum, which fell

outside of the initial confidence band (Figure 51). .......................................................... 77

Figure 53: Representative Impedance Spectrum Optimized with PDM .................................. 80

xii

Figure 54:Steady State Current Densities at pH 10 for 0% and 8.9% N measured and

calculated ......................................................................................................................... 80

Figure 55: Steady State Current Densities at pH 7 for 0% and 8.9% N measured and

calculated ......................................................................................................................... 81

Figure 56: PDM calculated steady state barrier layer thicknesses for pure Cr ........................ 82

Figure 57:PDM calculated steady state barrier layer thicknesses for 8.9% N ......................... 83

Figure 58: Barrier Layer Thickness as Estimated by a parallel plate capacitor assumption

for pure Cr ........................................................................................................................ 83

Figure 59:Barrier Layer Thickness as Estimated by a parallel plate capacitor assumption

for 8.9% N ........................................................................................................................ 84

Figure 60: Cartoon Interpretation of the thermodynamics of corrosion. ................................. 88

Figure 61: Environmentally defined regimes of potential and pH ........................................... 88

Figure 62: “Ball-and-stick” structure of dimethylamine. Hydrogen is silver, carbon is

black, and nitrogen is blue. .............................................................................................. 89

Figure 63:“Ball-and-stick” structure of monoethanolamine. Hydrogen is silver, carbon is

black, nitrogen is blue, and oxygen is red. ....................................................................... 90

Figure 64: Three ethanolamine molecules coordinated octahedrally to one iron atom ........... 91

Figure 65: Pourbaix Diagram for the Iron-water system at 95°C, 1 atm. potentials vs. the

Standard Hydrogen Electrode (SHE). .............................................................................. 93

Figure 66: Pourbaix diagram for the Iron-water system at 175°C, 300 psia. potentials vs.

theStandard Hydrogen Electrode (SHE). ......................................................................... 93

Figure 67: Three cyclic polarization curve cases for a spontaneously active metal ................ 95

Figure 68: Typical shape of a potentiostatic current density vs. time curve ............................ 97

Figure 69: Shape of a pit nucleating and repassivating with time under potentiostatic

control .............................................................................................................................. 98

Figure 70: Nucleation and growth of a stable pit under potentiostatic control ........................ 98

Figure 71: Bar of ASTM A470/471 from which the specimens were machined. .................... 103

Figure 72. Sample configuration for the 95 oC experiments: Cylindrical metal sample set

in low thermal expansion epoxy casting with PTFE tube jacketing a copper

conductor .......................................................................................................................... 104

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Figure 73: High temperature annular sample holder prototype with luggini-probe, stirring

funnel, mounting options for two samples and fluroelastomer o-rings ............................ 107

Figure 74: Schematic of the apparatus used to carry out the corrosion experiments at

175°C. .............................................................................................................................. 108

Figure 75: Potentiodynamic Scans at 95C for various concentration of amine inhibitors at

pH7. DMA: Dimethylamine. ETA: Ethanolamine......................................................... 109

Figure 76: 0.01M ETA at 175°C (#19) .................................................................................... 113

Figure 77: 0.1M DMA at 175°C (#27) .................................................................................... 113

Figure 78: 0.001M DMA at 175°C. (#16) ............................................................................... 113

Figure 79: Cyclic polarization at 175°C, with 0.1M ETA (#20) ............................................ 114

Figure 80: Current vs. Potential at 95° C. Numbered series correspond to Appendix B. ....... 117

Figure 81: Current density vs. Potential at 175° C. Numbered series correspond to

Appendix B. ..................................................................................................................... 117

Figure 82: Visual inspection of ASTM A470/471 coupon (a) before and (b) after

polarization tests in 0.1M ETA at 95°C. This test was repeated to verify the

incredible corrosion rates observed. ................................................................................. 119

Figure 83: Visual observations of the specimen surfaces after exposure to simulated

phase transition zone electrolytes containing three concentrations of DMA and ETA

at 95°C for several days, polarized at values within the quasi-passive range for each. ... 120

Figure 84: Schematic of the dependence of the barrier layer thickness as a function of

increasing current or specific resistance of the outer layer. ............................................. 123

Figure 85: Manufacture of HVOF coating ............................................................................... 126

Figure 86: Sectioning Schematic ............................................................................................. 126

Figure 87: Plate “B” following sectioning and electrochemical testing .................................. 128

Figure 88: Plate “F” following sectioning and electrochemical testing ................................... 128

Figure 89: Plate “H” following sectioning and electrochemical testing .................................. 128

Figure 90: Plate “J” following sectioning and electrochemical testing ................................... 129

Figure 91: Electrochemical Measurement Locations ............................................................... 129

Figure 92: Normal orientation B-plate HVOF coating SEM image at 100x ........................... 130

Figure 93: Normal orientation F-plate HVOF coating SEM image at 100x ............................ 131

xiv

Figure 94: Normal orientation H-plate HVOF coating SEM image at 100x ........................... 131

Figure 95: Normal orientation J-plate HVOF coating SEM image at 100x ............................ 131

Figure 96: B plate 100x magnification SEM ........................................................................... 132

Figure 97: F Plate 100x magnification SEM. .......................................................................... 132

Figure 98: H Plate 100x magnification SEM ........................................................................... 132

Figure 99: J Plate 100x magnification SEM ............................................................................ 132

Figure 100: B plate, location 1 interface detail 900x magnification SEM ............................... 133

Figure 101: B Plate, location 1 3000x defect detail magnification SEM. ................................ 133

Figure 102: B Plate, location 1 interface detail 800x magnification SEM .............................. 134

Figure 103: B Plate, location 2 1500x interface detail magnification SEM ............................ 134

Figure 104: J plate, location 3 coating detail 120x magnification SEM .................................. 134

Figure 105: J Plate, location 3 defect detail 450x magnification SEM – note cracks .............. 134

Figure 106: J Plate, location 3 800x crack detail magnification SEM ..................................... 135

Figure 107: J Plate, location 2 5000x crack detail magnification SEM ................................... 135

Figure 108: F plate preparation ................................................................................................ 136

Figure 109: Nyquist Plot for plate B HVOF ............................................................................ 137

Figure 110: Nyquist Plot for plate F HVOF ............................................................................ 137

Figure 111: Nyquist Plot for plate H HVOF ............................................................................ 138

Figure 112: Nyquist Plot for plate J HVOF ............................................................................. 138

Figure 113: Mathematically Convenient Impedance Circuit with Two Time Constants ........ 139

Figure 114: Microstructure - Impedance map .......................................................................... 141

Figure 115:Optimized Impedance Spectrum for 0%N, pH 10, 0.072VSHE .............................. 147

Figure 116:Optimized Impedance Spectrum for 0%N, pH 10, 0.06 VSHE ............................... 148


Figure 118: Optimized Impedance Spectrum for 0%N, pH 10,0.26 VSHE ............................... 149

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Figure 119: Optimized Impedance Spectrum for 0%N, pH 10, 0.36 VSHE .............................. 149

Figure 120:Optimized Impedance Spectrum for 0%N, pH 10, 0.46 VSHE .............................. 150


Figure 122: Optimized Impedance Spectrum for 8.9%N, pH 7,0.06 VSHE ............................. 151






Figure 128: Optimized Impedance Spectrum for 8.9%N, pH 10,0.16 VSHE ........................... 154





Figure 133: (#01): 95 C 0.001M ETA/ 0.05M Acetate, pH 6.86 ............................................. 157

Figure 134: (#05): 95 °C 0.1M ETA/ 0.19M Acetate, pH 7.40 ............................................... 158

Figure 135: (#04): 95 °C 0.01M ETA/ 0.097M Acetate, pH 6.70 ........................................... 158

Figure 136: (#08): 175 C 0.001M ETA/ 0.11M Acetate, pH 7.01 ........................................... 159

Figure 137: (#09): 95 °C 0.001M NH4OH/ 0.098M Acetate, pH 10.59 .................................. 159

Figure 138: (#21): 175 °C 0.001M NH4OH/0.1M Acetate, pH 6.26 ....................................... 160

Figure 139: (#23): 95 °C 0.1M ETA/ 0.098M Acetate, 6.49 ................................................... 160

Figure 140: (#26): 95 °C 0.001M DMA/ 0.107M Acetate, pH 6.94........................................ 161

Figure 141: (#25): 95 °C 0.01M DMA/ 0.098M Acetate, pH 7.00.......................................... 161

Figure 142: (#24): 95 °C 0.1M DMA/ 0.098M Acetate,pH 6.94............................................. 162

Figure 143: (#27): 175 °C 0.1M DMA/ 0.0978M Acetate, pH 7.00........................................ 162

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Figure 144: (#16): 175 C 0.001M DMA/ 0.107M Acetate, pH 6.96 ....................................... 163

Figure 145: (#14): 95 °C 0.001M NH4OH/ 0.001M Acetate, pH 5.07 .................................... 164

Figure 146: (#18): 95 °C 0.001M ETA/ 0.0001M Acetate,pH 9.64 ........................................ 164

Figure 147: (#19): 175 °C 0.01M ETA/ 3.46x10-5

M Acetate, pH 6.98 ................................... 165

Figure 148: (#20): 175 °C 0.001M NH4OH/ 0.001M Acetate, pH 4.51 .................................. 165

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LIST OF TABLES

Table 1: The Transport and Reactions of Point Defects for the PDM ..................................... 9

Table 2: Atomic Radius Data for Cr-O-N system [39] Light Shading: most likely anion

substitute pair. Heavy Shading: Most likely cation substitute pair / octahedral

interstitial substitution ...................................................................................................... 36

Table 3: Hume-Rothery Rule Summary. Heavy borders indicate matching CN. Green

cells indicate radius mismatch <7.5%. Orange cells indicate radius mismatch <15%.

Red cells indicate radius mismatch >0.15%. Bold text indicates the solute radius

exceeds the solvent radius. Gray shading indicates species known to exist in Cr2O3 ..... 36

Table 4: Discrepancy of Pauling Electronegativy for Cr, O and N. Green cells indicate an

electronegativity mismatch <15%. Orange Cells Indicate a mismatch <60% and red

cells indicate a mismatch >60% ....................................................................................... 37

Table 5: Exponential coefficients for rate constants ki of nitrogen defect reactions ................ 46

Table 6: Resistivities of Barrier Layers ................................................................................... 84

Table 7. Characteristics of polarization regions for an iron-based alloy in aqueous

solution. ............................................................................................................................ 96

Table 8: Summary of polarization behavior of ASTM A470/471 in the presence of amine

inhibitors. ......................................................................................................................... 110

Table 9: Summary of corrosion rates and passive current densities for ASTM A470/471

in the presence of dimethylamine in simulated phase transition zone of a low

pressure steam turbine at pH 7. ........................................................................................ 112

Table 10: Resistance Curve Fitting Values, 95° C................................................................... 118

Table 11: Resistance Curve Fitting Values, 175°C.................................................................. 119

Table 12: Polishing scheme ..................................................................................................... 127

xviii

ACKNOWLEDGEMENTS

This document serves to chronicle and share the knowledge developed over a protracted

campaign of academic research. It would have been impossible without the help and support of

many people. Thank you especially to my family, friends and colleagues. I would also like to

acknowledge the generosity of the organizations that have funded in part my graduate studies,

including The Embassy of France, Siemens Plant Chemistry, the U.S. Department of Energy and

Alphasense Deleware. Thank you also to my esteemed scientific research advisors both past and

present; Digby Macdonald4, Bernard Normand

5, Preet Singh

6, Glen Mcmillion

7, Naresh

Thadhani6 and Kenneth Sandhage

6. You have all contributed in no small way to my development

as a scientist and as a professional. I would also like to thank the many people who have taught

and encouraged me during this work, especially Patrick Reed4, James Bellows and Omar Rosas-

Comacho4. Finally, I would like to acknowledge the undergraduate students that I have had the

distinct honor of teaching and mentoring, especially Jason Strull7, Daniel Seong

4 and Adam

Haavisto4, for I have found that I learn the best when I am teaching others.

Vast quantities of data were collected during the course of this particular work and I

could not have done it without the help of two tireless and talented undergraduate research

assistants; Daniel Seong4 and Adam Haavisto

4. In addition, substantial contributions were made

4 The Pennsylvania State University


6 Georgia Institute of Technology

7 University of Nevada, Reno

8 Ecole Nationale Supérieure des Mines de Saint-Etienne

xix

by Nicolas Mary5 and Maria Klimkiewicz

4 in assistance with the collection of various SEM, EDS

and XRD data.

Sincere thanks are also well deserved to my colleagues bridging the gap between Penn

State University and INSA de Lyon by translating various critical documents into the French

language, most notably Jean Geringer8. Many thanks are owed to Andrew Nelson for the creation

of gencurvefit and his willingness to add additional features at my request which enabled certain

advanced aspects of Ellis2. Thank you also to Jacob Bolton who assisted me with some computer

science issues during the early development of Ellis.

1

Chapter 1

History and Philosophy of Corrosion Control

Broadly defined, corrosion is the deleterious result of the interaction between a material and its

environment. Corrosion damage can be the result of chemical, electrochemical, or mechanical

interactions, or as a combination of those effects. For the purpose of this dissertation, only the most

common form of corrosion, electrochemical corrosion will be considered, for which the primary loss of

metal through anodic dissolution is impeded by the formation of a passive film on the metal’s surface.

Obviously, materials placed in a benign environment are likely to have a longer working lifetime

than those placed in an aggressive one. Perhaps not so obvious, however, is that the entire terrestrial

environment of planet earth is thermodynamically hostile towards practically all native-state metals, as it

is rich in both oxygen and water. There are enormous benefits in terms of free energy for converting

metals back into oxides and dissolved ions, as evidenced in the industrial use of metals, for instance, the

use of aluminum as rocket propellants, magnesium as an emergency fire-starting material and in the case

of thermites, as a fuel for high temperature welding, etc. Despite the tremendous driving force for such

reactions, our infrastructure is built out of machines that rely on such materials for structural purposes.

The fact that reactive metals remain usable as engineering materials is due largely in part to a

phenomenon known as “passivity”, whereby a thin barrier of defective oxide forms on the surface of the

metal, hermetically sealing it off from the aggressive environment. Faraday’s paradoxical experiment in

1831 spurred his hypothesis that iron formed a protective passive film under oxidizing conditions,

protecting it from strong nitric acid while it corroded when exposed to dilute nitric acid. Faraday made

this postulate in a scientific age before such rudimentary concepts such as pH and the dissociation of ionic

salts in water to form electrolytes were fully understood. The phenomenon of passivity is pervasive and

general to reactive metals. For instance, aluminum forms an optically transparent film of sapphire on its

surface, explaining the cloudy appearance of aluminum metal. Scratching away this film reveals the

2

highly reflective metal underneath, but the rate of reaction that forms the film is fast enough that one can

observe the shiny metal clouding over in a matter of seconds. Intentionally growing this film to a

microscopic thickness under an applied potential (anodization) results in a honeycomb shaped columnar

structure, which provides significant corrosion and scratch resistance exterior to the passive film below.

These barrier films, however remarkable, are not thermodynamically stable in general and are metastable

at best. Hence, their tenuous existence is governed by the kinetics of formation and dissolution, not

simply the thermodynamic prediction of their existence [1].

Because not all material systems are deployed in a benign environment, corrosion control is an

important facet of durable engineering. The natural terrestrial environment that enables human life is not

the only environment aggressive towards metallic systems. As we push the boundaries of technology, yet

more aggressive locales where metals must be used are discovered or created, from deep-sea

environments to highly aggressive industrial conditions. Despite having control over the design and

operation of their systems, engineers are still tackling issues of corrosion control on a continuous basis in

industrial, maritime and energy applications.

Advancements in engineering technology are often stymied without sufficient scientific

understanding of the fundamental mechanisms that dominate the material system of application and

metallic systems are no exception. In order to understand the current state of affairs in the battle against

corrosion, and to chart and navigate the challenges that lie ahead, it is of paramount importance to

understand how we got here in the first place. Human history has been punctuated by advances in

technology, all of which were enabled by advances in materials science, from the iron age to the age of

steel, silicon, space age materials and beyond. To quote a popular truism, “the stone age certainly did not

end because we ran out of rocks”, rather, it was the invention of smelting ores that led to the first alloys

(bronze) and the subsequent foundation of our metals-based civilization.

3

The Pre-History of Metals

Today, it is possible to place an order for a high performance alloy that is available off-the-shelf,

mechanically and thermally processed to produce a myriad of different microstructures. However, metals

were not always solid engineering materials, especially on a geological time scale. Before they were

metals, the metallic elements in the earth’s crust were bound up in oxides and before they were oxides,

they were dissolved cationic species. This is presented in in general terms, of course, and in order of

oxidation state, but it illustrates a fine point about the history of terrestrial metals and their relationship

with the environment; it is a bitter and ancient struggle. During the infancy of the planet earth, circa four

billion years ago, a large fraction of world’s supply of engineering metals was found in aqueous solution

in a vast, anoxic, prehistoric ocean. Chemoautotrophs began producing oxygen prior to the advent of

photosynthesis, but it was the solar energy source which enabled the massive quantities of oxygen

required to create the 21 vol. % oxygen environment which both sustains life and is the atmosphere into

which we impress our engineering structures. The first photosynthesizers began converting the outgassing

carbon dioxide from the earth’s crust into oxygen, and combined with H2S gas as a hydrogen source,

produced the hydrocarbons from which almost all life on earth was later constructed. However, oxygen

gas was not yet released into the atmosphere in great quantities because it was immediately bound up with

dissolved metals (mostly iron) in the ocean and precipitated as solid oxides such as red hematite and black

magnetite, deposited on the sea floor in alternating banded structures forming a large quantity of the iron

ores we rely upon.

Because of this precipitation effect, it would take approximately 1.5 billion years before any

appreciable oxygen partial pressure would be seen in the atmosphere.

Producing such metals from oxides formed during the previous four billion years means an uphill

battle in the face of the thermodynamic driving force for metals in terrestrial environments to return to the

oxide, hydroxide or dissolved state. It is readily observed, therefore, that the desire to battle corrosion

involves a struggle against one of the greatest forces of nature: thermodynamics. To a student of

4

chemistry, no scientific concept is more elegant, predictive, or absolute as thermodynamics. On a

geological time scale, it appears that the machinations of any thermodynamically unstable civilization will

be forever lost. As the most disruptive force in this balance, scientists and engineers we seek to subvert

the natural order and build a durable metals-based civilization in the face of the absolute sovereignty of

thermodynamics.

The Cost of Corrosion

It is not only the desire to enter new and more aggressive environments or to meet grand

challenges such as the long-term storage of nuclear waste that drives the progress of corrosion science.

The direct cost of corrosion in the United States was estimated at 3.1% of Gross Domestic Product (GDP)

in 1998, accounting only for materials and services required to replace damaged facilities[2]. This

estimate does not include the associated costs such as lost productivity, human health costs and the cost of

environmental damages following a corrosion-related disaster. Adjusting for the 2012 GDP and these

ancillary costs, the total estimated cost of corrosion for the United States economy alone is approaching

one trillion dollars per year, about 6.5% of GDP[3]. A large fraction of this cost is avoidable and gives

further utility to the industry of corrosion control, from which various technologies have been produced to

combat the ever-present and costly effects of corrosion.

Technological Corrosion Control

Scientists and engineers have developed many technologies for combatting corrosion, for

instance, metallurgical design and selection, mechanical design such as electrical isolation of dissimilar

metals, elimination of crevices, the application of organic coatings, metallic coatings, ceramic coatings,

the use of corrosion inhibitors, anodization, and cathodic protection. Because the approaches used in the

field are sufficiently diverse, this monograph will consider three of these technologies(minor alloying

5

elements, inhibitors and metallic coatings). Specifically, the characterization of metallic coatings used in

maritime applications, the effect of nitrogen as an alloying agent in stainless steels, and the deleterious

effects of certain inhibitors in low pressure steam turbine environments. Binding together these diverse

topics is the concept of passivity and its study using electrochemical impedance spectroscopy (EIS). The

analysis of EIS data is sufficiently difficult that a new software package was developed in order to tackle

the problem, known as Ellis2. The development of this software is possibly the most important hallmark

of this work, because it makes previously intractable problems more accessible, and seeks to promote the

use of the Point Defect Model of the passive state as an immediately usable tool instead of an esoteric

theory.

6

Chapter 2

The Effect of Nitrogen on the passivity of pure Chromium

Background and Theory

Both historically and practically, chromium (Cr) is the principle alloying agent chosen for

corrosion-resistant steels, because of its ability to form a nano-thin, hermetic passive film of Cr2O3,

enabling passive behavior under a wide range of conditions that normally would not yield passivity for an

alloy lacking Cr. The threshold for a steel obtaining a “stainless” designation is 10.5 at.%, established

first by German scientists Monnartz and Borchers in 1907. The first chromium-bearing steel alloys were

proposed by French scientist Berthier in 1820. The first patented stainless steel alloy contained 30-35%

Cr (Woods and Clark, 1871), however, it wasn’t until the advent of the thermite purification process

invented by Hans Goldschmidt in 1889 that chromium could be produced in sufficiently purities to be

used in an engineering scale alloy. Subsequently, in 1918, the first patented application of a stainless

steel was filed by Harry Brearley, for use in table cutlery. Since that time, the use of stainless steels has

expanded to practically all fields where corrosion resistance is of high importance, such as power

generation, chemical processing, surgical implements and implants, food preparation, airframes,

architectural features, and heavy machinery. There are many different varieties of stainless steel,

differentiated primarily by Cr and carbon (C) content and the addition of other minor alloying elements

such as Molybdenum (Mo) and Tungsten (W), which protect against localized corrosion.

Carbon content is an exceedingly important factor for determining the corrosion resistance of a

stainless steel. In 1874, French scientist French scientist Brustlein first recognized high carbon content in

stainless steel as detrimental to corrosion performance, identifying in a need for low carbon content

stainless steels. Traditional steels contain some quantity of carbon for stabilizing austenite, hence

enhancing the steel’s strength, exhibiting far superior mechanical properties over pure iron. Reducing the

C content leads to a reduction in hardness, which is often rectified by the addition of Ni, also an austenite

7

stabilizer. Nitrogen (N) is another austenite stabilizer and can be used in addition to, or in substitution of

C as a strengthening element[4]. The addition of small quantities of N can produce high hardness alloys

otherwise unachievable without the inclusion of Ni, which is expensive and has associated health and

environmental hazards. One weakness of Cr as an alloying agent in carbon-bearing steels is the tendency

to form chromium carbide precipitates, depleting Cr from the surrounding metal, especially at the grain

boundaries, leading to passivity breakdown and pitting near the precipitates. For this reason, low-carbon

steels such as 316L were developed. However, carbon is the principal austenite stabilizer and reducing

the carbon content leads to a lower strength steel. Using nitrogen (N) as an alloying agent in place of

carbon avoids the precipitation of carbides, as well as reducing the possibility for decarburization in the

presence of hydrogen. It should be noted that the inclusion of too much nitrogen can lead to chromium

nitride precipitates which are detrimental to passivity in the same Cr depletion mechanism seen with

chromium carbides, with the advantage that decarburization effects and the need for Ni is avoided. The

solubility of N in pure Cr is around 13 at.%, however, sensitization of N bearing alloys has been reported

under stress corrosion cracking (SCC) conditions for compositions as low as 6 at.% N [5,6]. There have

also been efforts to produce N-saturated (up to 24 at. %N) austenite without the formation of CrN through

the use of low temperature plasma nitriding [7]. The inclusion of nitrogen often results in benefits to the

corrosion resistance of the stainless steel (for instance, a general lowering of passive current densities and

hence general corrosion rates, along with enhanced resistance to pitting) [8]. However, the mechanism

for this benefit is currently under discussion. One hypothesis for this effect is the generation of ammonia,

which serves to regulate the local pH, preventing acid depassivation. Another, compatible argument

addresses the evolution of the phases making up the outer layer of the passive film and the evolution of

the underlying metal composition and microstructure [7]. However, this hypothesis does not directly

address the exact role of nitrogen within the barrier layer lattice and therefore cannot fully account for the

beneficial action of N in Cr alloys with regards to steady state conditions. Previous attempts to

incorporate nitrogen into the Point Defect Model framework were inconclusive and therefore not formally

8

presented by Macdonald and co-workers. It is the intention of this work to systematically determine the

mechanism by which nitrogen acts on the passive film to enhance the passivity of stainless steels.

Passive film thickness has been postulated to contribute to passivity breakdown through the

build-up of electrostrictive stresses. It has been observed [9–11] that both nitrided and carburized

stainless steels exhibit thinner passive films than untreated samples, and that the samples with thinner

passive films exhibited superior pitting protection. Enhanced pitting resistance is explained in these cases

by chemo-mecahnical action brought about by long wavelength thickness perturbations during film

growth, reducing the strain energy density in the film arising from both electrostrictive stresses and

intrinsic stresses caused by inhomogeneities during the formation of the passive film [12]. The same

studies found a critical thickness required for pitting to be approximately 3nm, and films thinner than this

critical value did not pit in the presence of 0.6M NaCl, while those with thicker films were found to pit

readily. A dependence on the film thickness with potential was observed, however, the film thickness is

determined by the applied potential, meaning that segregation of the thickness effect from the potential

effect was not possible. Additionally, no atomic-scale model was proposed to account for the mechanism

of film thinning with increasing nitrogen content.

The Point Defect Model of the Passive State (PDM)

The Point Defect Model of the passive state (PDM) is a deterministic, atomic scale kinetic model

that describes the formation and maintenance of passive films formed on metals. The PDM originated in

1981 [13] and has undergone several revisions since that time [14–17]. Each revision of the model was

evolutionary, addressing new empirical observations and revising the model in order to overcome

shortcomings in the previous generation. This work is presented in the same spirit of previous revisions,

seeking to explain a previously unaddressed aspect of passive film kinetics. The PDM models passive

films through the action of point-defect reactions on the external (film/solution; f/s) and internal

(metal/film; m/f) interfaces of the passive film. Also critical to the success of the PDM is the transport of

9

point defects such as vacancies and interstitials across the barrier layer. Due to the high concentration of

such defects (on the order of 1020

cm-3

), the PDM predicts that the passive film should behave as a highly-

doped, defective semiconductor.

The PDM defines seven point-defect generation and annihilation reactions occurring at the

interfaces of the barrier layer. Reactions 1-4 occur at the m/f interface and Reactions 3-7 occur at the f/s

interface, summarized here using Krӧger-Vink notation:

Table 1: The Transport and Reactions of Point Defects for the PDM

Metal/film interface Transport Film/solution interface

(1) →

⇐

→

(2)

(3) →

⇒

→

(4)

(5) →

⇒

→ (6)

→

(7)

Metal vacancies are consumed in Reaction 1, producing a number of electrons equal to the

oxidation state of the metal in the metal oxide, corresponding to the charge of the vacancy, χ. These

vacancies are generated in Reaction 4 by the ejection of metal cations from the oxide, taking on a charge

of Γ ion the outer layer/aqueous phase. (Γ-χ) electrons are produced, where χ is the charge of the metal

cation in the oxide. Reaction 2 describes the incorporation of metal cations into interstitial sites in the

metal-oxide crystal, again producing electrons equal to the oxidations state. The interstitials diffuse to the

f/s interface where they are ejected from the barrier layer in Reaction 5, in similar fashion to Reaction 4.

Reaction 3 is a lattice non-conservative reaction, serving to grow the film into the metal, producing an

oxygen vacancy in tandem with a new occupied metal site on the oxide lattice and χ electrons. Thus,

Reaction 3 serves to extend the barrier layer lattice into the metal. Reactions 1,2 and 3 also produce metal

vacancies within the metal. Due to the dimensional disparity between a passive film (1-6 nm) and the

metal substrate, which has a bulk dimension, it is assumed that the metal can accommodate sufficient

oxygen vacancies, such that they do not diffuse into the oxide. For conceptual purposes, the seven PDM

reactions are illustrated in the following cartoons:

10

Figure 1: Cartoon of PDM Reaction 1: Consumption of metal vacancies at the metal/film interface

Figure 2: Cartoon of PDM Reaction 2: Injection of metal interstitials at the metal/film interface

11

Figure 3:Cartoon of PDM Reaction 3: Generation of oxygen vacancies at the metal/film interface (grows the

film into the metal, away from the f/s interface)

Figure 4:Cartoon of PDM Reaction 4: Generation of metal vacancies at the film/solution interface

Figure 5:Cartoon of PDM Reaction 5: Dissolution of metal interstitials at the film/solution interface

12

Figure 6:Cartoon of PDM Reaction 6: Consumption of oxygen vacancies at the film/solution interface

metal)

Figure 7:Cartoon of PDM Reaction 7: Dissolution of the passive film at the film/solution interface (Shrinks

film thickness towards the m/f interface)

Negatively charged defects are transported from the f/s interface to the m/f interface, where they

are consumed, while positively charged defects are transported from the m/f interface to the f/s interface,

where they are also consumed.

13

There are two lattice non-conservative reactions; Reaction 3, which serves to grow the film into

the metal and Reaction 7 which serves to thin the film through dissolution of the oxide. If there were only

one lattice non-conservative reaction, the film would either grow to an infinite thickness, or shrink away

to nothing. However, passivated metals have been observed to maintain finite thickness passive films,

necessitating no less than two opposing lattice non-conservative reactions in order to maintain a finite

steady state film thickness. The steady state film thickness and steady state currents are predicted from

the rates of reactions, as defined in “The Faradic Impedance” section.

Pitting

The PDM predicts localized passivity breakdown to be controlled by the metal vacancy flux[14]. Should

the flux of metal vacancies from the f/s interface to the m/f interface exceed the flux of metal vacancies

into the metal from the film through Reactions 1-3, a 2-d vacancy condensate forms (Figure 8). Because

this condensate eliminates the local m/f interface, Reaction 3 will not occur and the film will not grow in

this region. However, the film will recede in all locations at the f/s interface due to Reaction 7, serving to

thin the film above the condensate with respect to the otherwise healthy passive film in all other locations.

Finally, the film mechanically fails, resulting in the exposure of a microscopic anode in the presence of an

otherwise passive metal, which acts as a very large cathode, providing sufficient current to initiate and

perpetuate a pit or the nucleus may repassivate resulting in a “metastable” pitting event. Evidence for this

mechanism of pitting has been obtained through experiments concerning solid and liquid gallium [18,19],

where it was found that pitting did not occur in the liquid-metal case, because the metal vacancies could

not accumulate at the metal/film interface.

14

Figure 8: Localized Passivity Breakdown due to the Condensation of Vacancies: 1. A vacancy condensate

forms, locally eliminating the m/f interface. 2. The film continues to shrink everywhere due to reaction 7, but

grow only in regions where the interface exists. 3. The film undergoes mechanical rupture, presenting a

small anode in an occluded area, where pitting corrosion initiates.

The PDM also predicts that thinner passive films are more protective against localized passivity

breakdown, but not due to electrostrictive stresses. Both the thickness and the occurrence of pitting

depend on potential. The PDM predicts a constant electric field strength through the film. Because a

thinner film has a greater potential drop across the metal/film interface and hence a higher rate of metal

vacancy annihilation (Reaction 4), the breakdown potential is predicted to be more positive, and therefore

the film will be more resistive to pitting.

The Faradaic Impedance

PDM rate constants are often used to predict long-term corrosion rates [20–22]. Currently, such

rate constants must be determined by measuring the impedance of the passive film and optimizing a

deterministic impedance model containing the Faradaic impedance.

Englehardt derived an expression for the Faradaic impedance for an n-type passive film [23],

which is used in this work without modification. The Faradaic impedance considers seven reactions,

three (1,2,3) at the metal/film interface, at L=x and four (4,5,6,7) at t the film/solution interface, at L=0.

15

Reactions 1,2,4,5 and 6 are lattice-conservative, while Reactions 3 and 7 are lattice non-conservative and

their rates are used to calculate the film thickness. Reaction 6 includes no electron transfer, so it does not

contribute to the Faradaic impedance or to the current density. The assumption of n-type character

ignores any current contribution from Reaction 1.

The standard rate constants are defined in the following way:

(8)

The standard reaction rate constants, are defined in accordance to activated complex theory.

The exponential coefficients ai (1/V), bi (1/cm) and ci , with their expressions being derived from the

method of partial charge transfer (MPC).

(9) (10) (11)

(12) (13) (14)

(15) (16) (17)

(18) (19)

(20) (21)

(22) (23)

(24) (25)

α is the polarizability of the barrier layer/outer layer (solution) interfaces and defines the impact

of the applied voltage on the voltage drop across that interface and ranges between 0 and 1. αi are the

transfer coefficients, which in the MPC define the position of the activated complex for each reaction

along the reaction coordinate and also vary from 0 to 1. T is the temperature in the Kelvin, F is Faraday’s

constant, and R is the gas constant in Joules per Kelvin mol. In the n-type potential region, it is assumed

that the dominant defects are metal interstitials and oxygen vacancies, so Reactions 1 and 4 are ignored.

However, in the transition region, and the p-type region, all seven reactions must be considered for the

Faradaic impedance. As previously stated, χ is the oxidation state for the metal in the passive film. Γ is

16

the oxidation state for the metal cation in solution. In the specific case of Cr metal forming a Cr2O3

barrier film, χ = 3 and Γ = 3. At high anodic potentials, it is possible to produce Γ = 6 hexavalent

chromium cations through the following reaction:

→ (26)

This reaction also implies that the film would become a p-type semiconductor, due to the

formation of metal vacancies as the dominating defect as has been observed in chromium oxide, as seen

in Alloy 22 and in stainless steels at high potentials[22,24]. The current from this reaction adds to the

steady state current density and is detectable as a function of increasing potential, in contrast to the

normal form of Reaction 4;

→

(27)

for which no net electrons are produced, because Γ = χ and the steady state current in the passive region is

predicted to be independent of potential.

For yet higher, transpassive potentials, the following reaction occurs, leading to depassivation:

→

(28)

The standard rate constants are calculated as a function of potential and electronic field strength from k°°

(29)

(30)

(31)

(32)

(33)

(34)

17

The steady state thickness is calculated from Reactions 3 and 7 (the lattice non-conservative

reactions), with the exception that if Lss evaluates to a value less than zero (which is nonphysical), Lss is

set to 0 by the fitting algorithm.

(

)

(35)

The current generated due to vacancies is calculated:

(

) (36)

The concentration of available hydrogen is calculated from the bulk pH;

The current at x=L (the metal/film interface) is calculated:

(37)

The current due to interstitial ejection:

(38)

The steady state current is calculated, which is also used to calculate the diffusivity of defects

after the fit.

(39)

(40)

Ω is the molar volume of the oxide per mol of cation, here assumed to be 15 cm3/mol [20].

Solving for the derivatives of concentration, a solution to the differential equation for defect

motion is introduced (r1,r2).

( √

) (41)

( √

) (42)

(43)

18

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

(52)

Finally, the admittance is calculated by summing the differentials:

(53)

The inverse of which is the Faradaic impedance:

(54)

19

Chapter 3

Complex Function Optimization for One Independent Variable by Differential

Evolution

The Challenge

Historically, the Point Defect Model (PDM) parameter optimization has been carried out with a

combination of gradient-based optimization methods, such as the Levenberg-Marquardt algorithm [25].

These methods work by calculating a numerical gradient of the fitness function, generally X2 error, in the

location of the starting guess. If the fitness function is a measurement of the error, the algorithm then

chooses the direction of steepest descent, changes/updates the starting guess by some user-defined step

size, and repeats this process; seeking to minimize that error until no further minimizations are possible.

At this point, the algorithm stops, and reports the optimized values. A covariance matrix can also be

calculated, providing a confidence interval for the fit. A number of problems can cause this method to

fail, for instance discontinuities in the function which will cause the derivative to fail, however, the most

likely issue is the possibility of becoming “stuck” in a local optimum, instead of the global optimum.

For an arbitrary fitness function y, for a single parameter x, shown in Figure 9, any starting guess

for x will result in an optimization to the global minimum at x = 2.5, because there is only one global

solution and the derivative at any point directs the algorithm in the correct direction (i.e., as in Newton’s

method).

20

Figure 9: Single mode fitness function y, for parameter x

If the function has a multiplicity of solutions, the situation shown in Figure 10can arise:

Figure 10: Multi-modal fitness function y, for parameter x

In this case, there are many possible minima in error, each with its own value for x, and they are

all equally valid. The solution produced by the fitting algorithm will be controlled entirely by the location

of the starting guess, with each solution being equally valid from a mathematical standpoint, but not

explicitly correct from the physical standpoint of the given model. For many models, the situation

depicted in Figure 11 is more likely:

21

Figure 11: Multi-modal fitness function y for parameter x, with one global solution and many local solutions

In this scenario, there is one global minimum, at x = 4.3, which has the lowest error of all of the

local solutions. The fitness function at x = 4.3 has a very similar value to that at x = 5.8, however, it is the

global minimum in error. In this case, the starting position must lie on the interval between x = 3.5 and x

= 5.1, otherwise the global optimum will not be reached. The operator may not be able to distinguish

between the optima at x = 4.25 and x = 5.9, and may inadvertently choose the wrong solution, because the

fit appears very good and may choose to accept the inferior solution, not knowning about the existence of

a better one. The situation becomes somewhat more complicated when dealing with more than one

parameter. For instance, a fitness function with two parameters and a universally reached minimum is

displayed in Figure 12, in analogy to Figure 9:

22

Figure 12: Fitness function Z for parameters x and y with one optimal solution

In this case, the starting guess is inconsequential. The solution will always optimize to the global

minimum because the direction of the most negative derivative at all points on the surface (x,y) point

towards this particular solution.

However, solution spaces are rarely so easily optimized. In analogy to the situation in Figure 10,

we can obtain a two parameter solution space with many equally optimal solutions, known as a multi-

modal surface:

Figure 13: Multi-modal Fitness function Z for parameters x and y

23

And of course, by analogy with Figure 11, a fitness function with two parameters can have many

locally optimized solutions, with only one global optimum, as shown in Figure 14:

Figure 14: Multi-modal fitness function z for parameters x and y with one global optimum and many local

optima

Visualizing higher order fitness function spaces becomes difficult, owing to the fact that the

solution space exists as a n-dimensional hypervolume, where n is the number of varying parameters, but

by analogy, such spaces exist and can contain many optima, and possibly one global solution.

Impedance models containing the Point Defect Model, for instance, can have solution spaces

from 15 to 30 parameters (15 in this study, although Ellis2 has been used successfully with 29

parameters), depending on the assumptions made and the accompanying impedance elements. The

Faradaic impedance from the PDM also contains exponential functions, which can cause problems, due to

the extremely large values that they can produce, causing problems for derivative methods and

fundamentally exceeding the capabilities of 64-bit floating point numbers. Generally, these extreme

values do not control the value of the impedance, as the final result in the limit works out to an easily

handled number analytically, but they cause a challenge in terms of programming, because they can be

generated when sampling the solution space, causing the algorithm to crash. Transmission line models

suffer from the same issues, due to the hyperbolic sine and cosine functions, which can also produce very

large values. For any algorithm failure, or unacceptable solution, the operator has to begin the curve

24

fitting process again, with a new set of starting guesses. For these reasons, optimizing PDM parameters

has been a laborious, time-consuming issue, further confounding researchers attempting to use it and

requiring a large time investment. In many past studies, only a subset of the available data was fit.

Differential Evolution

Differential evolution is a hybrid of two mathematical search methods, so-called "evolutionary

strategies" (ES) and "genetic algorithms" (GA), which seeks to optimize the parameters for a given model

by mimicking nature’s process of evolution through survival of the fittest. Biological evolution is capable

of searching a solution space containing a staggering number of possibilities. The human genome for

instance contains approximately 3.2 billion base pairs of nucleic acids, for which there are four

possibilities (G,T,C,A), resulting in a solution space that would require 43,200,000,000

bits of data in order to

enumerate, or 101,700,000

. The world's digital data storage capabilities are currently on the order of 1021

bits, illustrating what a serious challenge evolution really is. Even with all of the world's computing

resources, one could not hope to enumerate all possibilities for analysis. And even when testing one

billion possibilities per second (which would require an impressive supercomputing cluster), it would take

on the order of 102,000,000

years to test all possible combinations. Therefore, nature MUST rely on the

process of evolution in order to obtain new and viable sequences of DNA. To put things in perspective,

most calculations in the laboratory are performed with 64-bit real floating point numbers. So for each 64-

bit parameter in a given solution vector, there are 264

, or 1.8 x 1019

possible values. For a solution vector

N units long, there are (1019

)n possibilities, so for a model like the PDM, with 20 parameters, there are

10380

possible combinations, clearly less than required for evolution of a viable creature, but still requiring

3x10363

years of computations testing one billion vectors per second to enumerate all possible solutions.

Consider a vector of n parameters for a given model sm= [p0,p1,p2,...,pn], known as a solution

vector, with user-defined limits. The limits define the edges of a "hypervolume" containing the set of all

25

possible solutions within those boundaries, as illustrated in Figure 15. (not all solutions in the

hypervolume are necessarily feasible solutions).

Figure 15: Visualization of an arbitrary solution vector in a solution Space bounded by the limits for three

parameters; p1,p2 and p3

This hypervolume is also known as the "Search space". It is possible to reduce the size of the

hypervolume, and hence reduce the difficulty of obtaining the global solution by constraining the

parameters within tighter limits. If prior information is known about a system, for instance, a good

estimate of certain parameters, the operator may wish to perform such constraints to speed up the

optimization.

A "generation" containing a "population" of m "individuals" is randomly selected, for instance pg

[s0. s1 s2 … sm]. Each member of the population is evaluated and tested for fitness. Next, “selection” is

performed. The "least fit" individuals are deleted, other individuals are chosen at random to mutate,

changing part or all of their solution vectors randomly. The "best fit" individuals exchange information to

produce "daughter" individuals in a process known as “crossover”. Finally, the eliminated individuals are

replaced with new, totally random (within the hypervolume) “stranger” solutions. The daughter solutions

express properties of the parent individuals, tending the overall solution towards better fitness, while

X Axis

Y A

xis

p1

p2

p3

Limits

(p3)

Limits (p1)

Lim

its (p

2)

solut io

n vector

26

exploring the familiar space within the population. The process of selection; the removal of low

performing solutions, effectively discards parts of the solution space that are unlikely to provide better

fitness than those of the daughter solutions. The mutation and replacement processes prevent the

algorithm from becoming stuck in a local minimum by constantly introducing new locations in the

solution space to test. This process is more efficient than a purely random exploration of the solution

space, which, as stated earlier, can be immense. As the fit progresses, it is possible for the newly

introduced solutions to interact with the daughter solutions if their fitness is high enough, or to replace

them if they are the most fit vectors in the population. In this way, the mutants and strangers serve an

important purpose of mitigating local optima in favor for global optima. This process is repeated many

times until no further improvement in fitness is observed or the predetermined number of generations of

evolution is reached.

Analogous (“electrical equivalent”) circuits are often used by researchers to model the impedance

behavior of passive and corroding systems. For the most part, non-physical analogs are employed for this

purpose because they are easy to manipulate and understand. However, they are not based on first-

principles modeling and do not afford physical meaning apart from an implied one. These circuits can

also suffer from degeneracy (multiple circuits can fit equally well to a given data set), requiring the

operator to choose the most appropriate circuit. A great advantage of such models is that they present

very small solution spaces (2-7 dimensional spaces), which can be easily searched using trial and error

and gradient based methods. Because the solution space of the Point Defect Model is a 15-30

dimensional hypervolume containing a multi-modal optimal surface of solution vectors, it is highly

unlikely to obtain a fit solution corresponding to a global minimum in error using gradient-based

methods, unless either a near-perfect starting guess is employed or sufficient, inefficient trial-and-error is

performed to obtain such a starting guess. Because of this inherent difficulty, the PDM is hard for

researchers to use in their own work, often resulting in attempts at using the PDM to be either discarded,

or of accepting a generally poor fit quality. Indeed, the screening criteria used for determining the quality

of a fit with such methods is often done entirely by “eye” and is therefore highly subjective. It is also

27

highly likely, even with a large number of random samples of starting guesses, to obtain a fit whereby

there are no alternative solutions with superior agreement.

As previously noted, excellent starting guesses must be provided to a gradient-based

algorithm in order to obtain a satisfactory fit, meaning the solution must be known prior to attempting a

curve-fit. A solution can often be estimated through geometrical means when the system is simple and

frequency-complete. However, with a physical model such as a transmission line, or the Point Defect

Model, this approach is particularly difficult and in many cases intractable. Fits are often done by using,

as the initial guesses for the parameter values, the results of prior optimizations when changing only one

independent parameter in a series of experiments (e.g., the passive film formation potential).

Improving the fit over subsequent trials with a gradient-based optimization method was generally

accomplished by trial-and-error starting guesses input by the user, or by utilizing a linear grid-based set of

starting conditions, evaluating the goodness of fit and choosing the best result. Furthermore, the all-

inclusive Point Defect Model has up to 30 parameters, meaning that due to software limitations, many

assumptions were required in order to formulate the problem to fit in order to reduce the number of

parameters to the limit of the software, generally, 10 parameters, resulting in an incomplete search space,

which, depending on the assumptions, could affect the scientific conclusion of the fit. Differential

evolution suffers from none of these issues.

The only advantage of gradient methods is that they are extremely fast. Now that the

computational power of desktop computers has outpaced this hurdle, it is necessary to take a new

approach for optimizing physico-chemical models, such as the PDM, on experimental impedance data.

To this end, software has been developed and is currently being used by researchers at Penn State to fit

impedance data to a degree of quality never before seen.

The earliest known attempt to fit impedance data with a genetic algorithm dates from 1998.

VanderNoot and Abrahams attempted to fit an analogous circuit with two constant phase elements

representing diffusion and double layer capacitance, resulting in a 6-dimensional solution space. Even

with the relatively slow computers of the time (100 MHz 486 processors), there was little difficulty in

28

finding good fits without the need to restart the search[26]. Although differential evolution had been

invented in 1997 [27], it was not employed at the time, although there are only a few differences between

the algorithms. As recently as 2006, a 7-parameter analogous circuit had been fit to impedance data using

an evolutionary strategy [28], with allowances for the use of a gradient method to do a final polishing step

(also known as a hybrid algorithm, a concept which was followed up on recently [29], although it was

concluded that a genetic algorithm was not appropriate for use as it required too much time to process).

The Tool

Ellis2[30,31] is a software package developed for the optimization of complex functions of one

variable. It is particularly geared towards fitting impedance models, although other types of complex

functions should be easily adaptable to the Ellis2 framework. Ellis2 relies on Igor Pro[32], a wave-based

data analysis system and gencurvefit [33], an implementation of the differential evolution algorithm,

originally developed to fit neutron scattering data [34]. One challenge addressed by Ellis lies in fitting

complex data. Complex numbers do not lend well to commercially available curve fitting codes. Ellis2

operates on a complex data set by converting it to a set of real values through concatenating the real and

imaginary values of impedance, as illustrated in Figure 16. Ellis2 automatically handles this special data

type, producing complex values in the final impedance calculation and the user should never be aware of

it.

Figure 16: Concatenation of a complex impedance spectrum into a real-valued list

29

In previous optimization schemes, only one part of the impedance (real or imaginary) was fit at

any given time, giving rise to situations where an excellent fit was obtained for one of the parts, usually

the imaginary, and a poor fit for the other part. This also necessitated the separation of the entire

impedance function into the real and imaginary parts, which was a technical challenge, because the

resulting equations were very large. Mcmillion [21] attempted to mitigate this issue by feeding the results

from the imaginary curve fit as starting values for the real curve fit, and iterating until no further

improvement was made. Ellis2, however, operates upon both parts simultaneously, such that the fit is

consistent. However, unless the magnitudes of the values stored in Z’ and Z’’ are “symmetric”, there is

still an opportunity for the larger part to control the curve fit. In order to deal with this issue, Ellis2

includes an option to weight the fitness function by the reciprocal of the function values to help alleviate

situations where one part of the impedance is much “larger” than the other one, which is common for

chromium alloys such as Alloy-22. By using reciprocal weighting, the error values are treated as equally

valuable at all points in the function; this can be thought of as a type of normalization, whereby the larger

data values (typically at low frequency) are unable to hijack the fitting algorithm. It is likely that the

historical issues with PDM fitting to the phase angle is due to this fact, because the phase angle is

computed as a combined function of Z’ and Z’’, while the curve fit was controlled disproportionally by

Z’’. Weighting of the fitness function leads to faster optimizations in general, and an improvement in

agreement with the phase angle.

Basic Operation of Ellis2

1. Load data (usually accomplished by pasting data into the provided table from another

program, such as Excel)

2. “treat” data: Convert frequency spectrum from Hz to rads/s or normalize the impedance to the

surface area (optional)

3. Apply weighting (optional)

30

4. Run the setup function for the chosen impedance function. This generates the table of limits

and tells Ellis2 which function to use. Ellis contains a library of built-in functions, but it is

highly suggested to write your own, for your specific situation.

5. Adjust limits – the default limits for the chosen function may be too large or too small for the

given application. Adjust limits accordingly by typing into the table of limits

6. Adjust holds – sometimes, a parameter must be held constant during a curve fit. Good

examples include the applied voltage, temperature and pH. 1 = held. 0 = varied.

7. Display Graphs – Gives a visual impression of how the fit is progressing and the path of the

parameters through the solution space

8. Check and adjust algorithm parameters. Some optimizations benefit from changing the

algorithm parameters, such as the population size, number of iterations, mutation and

crossover coefficients, tolerance, etc.

9. Initiate the fit. The operator can watch the fit progress in real-time, along with the fitness

function value and the values of the various fit parameters plotted as a function of the number

of generations of optimization.

Starting guesses are required due to a software dependency, but they not used. Rather, the limits

of the solution space are the more critical values. For further, more detailed information about

the operation of Ellis, please see the Ellis2 user manual [30].

Mott-Schottky Analysis

As mentioned previously, the PDM predicts the passive film to be a highly-doped, defect

semiconductor. Previous studies have used Mott-Schottky analysis [35] to determine the semiconductor

nature of the passive film and to estimate the concentration of the dominant charge carrier. The analysis

assumes that the passive film capacitance is a sum of two series capacitances, the space charge

31

capacitance attributed to the passive film material and the Helmholtz capacitance attributed to the ionic

double layer. The Helmholtz capacitance is assumed (and generally found to be) much larger than the

space charge capacitance, approximating the total capacitance measured to be dominated by the space-

charge capacitance:

(55)

Considering the inverse square of this capacitance and assuming a parallel plate geometry, the

following Mott-Schottky relationship is derived:

(

)

(56)

where E is the applied potential, Efb is the flat-band potential, kB is the Boltzman constant, T is the

absolute temperature in Kelvin, q is the charge of the electron for the n-type case, or the charge of the

hole, for the p-type case, ε is the dielectric constant, εo is the permittivity of free space, Nq is the number

of charge carriers (either donors or acceptors).

has a linear relationship with potential, with the slope

of

and the intercept on the potential axis giving the flat-band potential,

. The

quantity,

, tends to be small at room temperature, so the flat band potential is generally estimated by

the intercept alone. According to the PDM, the passive current density is independent of potential for n-

type films, but varies exponentially for p-type films. Chromium is generally observed to be n-type in the

passive region, much like the passive film on iron; this is attributed to a high concentration of interstitials.

However, at higher potentials, a transition from n-type to p-type is observed, due to the oxidation of

Cr(III) to Cr(VI) upon ejection of cations from the film and the concomitant generation of cation

vacancies, which act as electron acceptors as described in (26).

32

The Solute Vacancy Interaction Model

The solute-vacancy interaction model (SVIM) [36] has been previously used to account for the

protection of stainless steels against the onset of pitting corrosion. The SVIM is a natural product of the

Point Defect Model, postulating that minor alloying elements substitute on metal vacancies on the passive

film lattice, such that the difference in oxidation state from that of the occupied site results in an immobile

positively charged defect, for instance in the following reaction:

→

(57)

The positively charged defect will then form complexes with negatively charged defects (cation

vacancies) already present in the film, immobilizing them, as in the following complex with a metal

vacancy:

→ [

] (58)

The equilibrium constant for this reaction can be calculated from ion-pairing theory, as is

commonly applied to ion pairing in solution:

[

]

[ ][

]

(59)

If the complex is immobile, then the diffusivity of metal vacancies will be severely reduced, affording

protection to the alloy against pitting by the mechanism illustrated in Figure 8, because the condensation

of metal vacancies requires vacancy flux to the interface to exceed that of the flux away from the interface

into the metal. This has the effect of raising the critical pitting potential and explains why small additions

of Mo and W are able to significantly enhance the critical pitting potential of stainless steels[36]

The effect on diffusivity can be calculated as a function of alloying agent concentration [33]:

33

[

(

)

(

)] (60)

where D is the diffusivity of the defect, here a cation vacancy, with no interacting solute present, nA and

nV are the solute and vacancy concentrations respectively and α is defined below [33]:

(61)

The SVIM was originally used to explain the effect on the diffusivity of metal vacancies, as

outlined above. Reducing the diffusivity of metal vacancies and reducing the concentration of free,

mobile cation vacancies results in reduced pitting potentials, but has no effect on the steady state passive

film thickness or the steady state current density. This issue is dealt with below after first specifying the

conditions that must be met for substitution of a highly-charged solute on the cation sublattice of the film.

The Hume-Rothery Rules of Solid Solution

The Hume-Rothery rules[37] predict the likelihood of solubility for two metals in an alloy. In

this treatment, the meaning of “solubility” and “ability to substitute” are interchangeable, which is a fair

assumption considering that a phase of solid solution is defined as a solvent matrix containing substituted

atoms of solute. There are four main criteria to determine solubility, also known as “rules”.

1. Atomic Size Rule: The ratio of the difference in atomic radii must be no more than 15%

(

)

(62)

2. Crystal Structure Rule: The two metals should have the same crystal structure prior to

alloying. Here, this rule is interpreted as agreement in coordination number, which is

34

derived from the electronic structure of the atoms considered and dictates the most

“comfortable” geometry within the crystal.

3. Valency Rule: A metal prefers to dissolve a metal of the same valence, and will dissolve

only metals of higher valence with some difficulty and those with lower valences not at

all

4. The Electronegativity Rule: Soluble atoms should have equal electro-negativities. A

greater mismatch in electronegativity indicates a lower possibility for solid solution.

The Location of Nitrogen in the metal-oxide lattice

Using the PDM and the SVIM as a framework, it is postulated that the protective action of N

stems from its incorporation substitutionally into oxygen vacancies in the passive film, creating a

negatively charged “nitrogen defect”. This defect consequently, forms complexes with positively charged

defects, immobilizing them. Interfering with the transport of the charged point defects, which control the

existence of such passive films leads to an alteration of the steady state current density and thickness.

Because the nitrogen defect is predicted to be negatively charged with respect to the lattice, it will interact

electrostatically with positively charged point defects such as cation interstitials and oxygen vacancies, in

a manner similar to the effect of minor alloying elements such as Mo, as previously shown in the solute-

vacancy interaction model (SVIM)[14,36].

Modeling the role of Nitrogen in the passive film requires defect reactions to be written that

describe the incorporation of nitrogen at the metal/film interface and the subsequent dissolution of

nitrogen at the film/solution interface. The location, coordination number and oxidation state of N within

the passive film must first be determined, in order to propose the correct set of reactions. For instance,

the properties of N substituting on the oxygen sublattice would have vastly different effects from N

substituting on the metal sublattice, or as an interstitial.

35

Figure 17: Unit Cell of Cr2O3 (corundum structure) in various projections drawn with Crystal Maker

software[38]

In order to propose a set of defect reactions to account for the behavior of nitrogen bearing

passive films, one must first consider the possible location of the nitrogen atoms within the crystal lattice

of the passive film. If the assumption is made that similar atoms can substitute freely for one another,

then possible substitution pairs may be screened with the the Hume-Rothery criteria as described

previously. Cr2O3 assumes as corundum structure, as illustrated in Figure 17. The unit cell is

rhombohedral, space group R c and can be thought of as a hexagonal close-packed (HCP) structure with

2/3 of the octahedral sites filled with Cr atoms. Possible oxidation states, coordination numbers, electron

structures, crystallographic and ionic radii for Cr, O and N are tabulated in Table 2.

36

Table 2: Atomic Radius Data for Cr-O-N system [39] Light Shading: most likely anion substitute pair. Heavy

Shading: Most likely cation substitute pair / octahedral interstitial substitution

Atom Ox. State Structure Radius (Crystal) Radius (Ionic) CN

O 2- 2P 6 1.21 Å 1.35 Å 2

O 2- 2P 6 1.22 Å 1.36 Å 3

O 2- 2P 6 1.24 Å 1.38 Å 4

O 2- 2P 6 1.26 Å 1.40 Å 6

O 2- 2P 6 1.28 Å 1.42 Å 8

N 3- 2P 6 1.32 Å 1.46 Å 4

N 3+ 2S 2 0.30 Å 0.16 Å 6

N 5+ 1S 2 0.44 Å -0.104 Å[sic] 3

N 5+ 1S 2 0.27 Å 0.13 Å 6

Cr 2+ 3D 4 0.87 Å 0.73 Å 6

Cr 2+ 3D 4 0.94 Å 0.80 Å 6

Cr 3+ 3D 3 0.755 Å 0.615 Å 6

Cr 4+ 3D 2 0.55 Å 0.41 Å 5

Cr 4+ 3D 2 0.69 Å 0.55 Å 6

Cr 5+ 3D 1 0.485 Å 0.345 Å 4

Cr 5+ 3D 1 0.63 Å 0.49 Å 6

Cr 5+ 3D 1 0.71 Å 0.57 Å 8

Cr 6+ 3P 6 0.40 Å 0.26 Å 4

Cr 6+ 3P 6 0.58 Å 0.44 Å 6

From the data presented in Table 2, the radius mismatch is computed for each possible pairing.

The results are collected in Table 3, which addresses Hume-Rothery rules 1,2 and 3.

Table 3: Hume-Rothery Rule Summary. Heavy borders indicate matching CN. Green cells indicate radius

mismatch <7.5%. Orange cells indicate radius mismatch <15%. Red cells indicate radius mismatch >0.15%.

Bold text indicates the solute radius exceeds the solvent radius. Gray shading indicates species known to exist

in Cr2O3

Species O(2-) O(2-) O(2-) O(2-) O(2-) Cr(2+) Cr(2+) Cr(3+) Cr(4+) Cr(4+) Cr(5+) Cr(5+) Cr(5+) Cr(5+) Cr(6+)

CN 2 3 4 6 8 6 6 6 5 6 4 6 8 4 6

Radius 1.12 1.22 1.24 1.26 1.28 0.87 0.94 0.755 0.55 0.69 0.485 0.63 0.71 0.4 0.58

N(3-) 4 1.32 0.09 0.08 0.06 0.05 0.03 0.52 0.40 0.75 1.40 0.91 1.72 1.10 0.86 2.30 1.28

N(3+) 6 0.30 0.75 0.75 0.76 0.76 0.77 0.66 0.68 0.60 0.45 0.57 0.38 0.52 0.58 0.25 0.48

N(5+) 3 0.44 0.64 0.64 0.65 0.65 0.66 0.49 0.53 0.42 0.20 0.36 0.09 0.30 0.38 0.10 0.24

N(5+) 6 0.27 0.78 0.78 0.78 0.79 0.79 0.69 0.71 0.64 0.51 0.61 0.44 0.57 0.62 0.33 0.53

37

If nitrogen was in the (5+) state, one could imagine substitution on the Cr cation sublattice with a

coordination number of 6. However, the difference in ionic radius in this case is about 60%, well beyond

the Hume-Rothery limit of 15%, making such a substitution highly unlikely. It is also hypothetically

possible for N to substitute on interstitial sites. HCP has both octahedral and tetrahedral interstitial

locations. The octahedral interstices are geometrically identical to the Cr sites, which implies that N

would also have a 60% radius mismatch in the octahedral interstitial. The tetrahedral sites would require

a coordination number of 4, which corresponds to N(3-). However, the tetrahedral interstitial sites are also

too small to accommodate N(3-). From Rules 1-3, it is clear that the most likely substitution is N(3-) on

to a vacant O(2-) site. It shares the same valence (2p6), yielding the same coordination number and a

similar atomic radius, with only 6% mismatch.

Rule 4 cannot be considered so precisely, because the exact values of electronegativity for each

oxidation state are presently unknown. The literature indicates, however, that the electronegativity is not

strongly dependent on oxidation state, which is possibly the reason that no extensive tables exist apart for

the few elements (Ti, Pb), for which there is a strong dependence. The Pauling electronegativity for Cr, O

and N[40] are presented in Table 4.

Table 4: Discrepancy of Pauling Electronegativy for Cr, O and N. Green cells indicate an electronegativity

mismatch <15%. Orange Cells Indicate a mismatch <60% and red cells indicate a mismatch >60%

Element Solvent→ Cr O N

Solute↓ Electronegativity 1.66 3.44 3.04

Cr 1.66 0.0% -51.7% -45.4%

O 3.44 107.2% 0.0% 13.2%

N 3.04 83.1% -11.6% 0.0%

Table 4 reveals a further mismatch for nitrogen to substitute onto the Cr lattice and compatibility

with the oxygen sublattice. Clearly, the difference in electronegativities between N and O or Cr is large;

over 83% substituting N for Cr, but only -11.6% substituting N for O. N is therefore more suitable for

38

substitution with O than with Cr. The Hume-Rothery rules are used here in an unorthodox screening

procedure, in that they were originally intended for use only with metals. However they are used as a

guideline for determining what the most likely substitution would be. The most likely substitution is N(3-

) on the oxygen sublattice, as it obeys all four of the Hume-Rothery rules. Because the only metal oxide

considered in this study is Cr2O3, it remains to be seen if N would substitute on the cation sublattice or

interstitial sites for films composed of other metal oxides, such as iron oxides, where nitrogen may also

enhance passivity. The same technique outlined above can be easily applied to any metal system, such as

Fe or Ni. Because of the result of this exploration, the only substitution to be considered from here on

will be N(3-) for O(2-).

The Electronic State of Nitrogen in the passive film

Further evidence for nitrogen occupying a (3-) state within the film is provided in XPS data from

the literature on Cr+N physical vapor deposition (PVD) coatings [41]. In the figure below, “Sample 1” is

a pure Cr sample, and “Sample 2” contains a quantity of N similar to that used in the present study.

“Sample 3” is a purposefully created CrN coating with approximately 1:1 stoichiometry, as reported

during XPS.

39

Figure 18: XPS investigation of Cr+N PVD coatings[41]. 1) Pure Cr 2)Cr+N, approximately 10%N. 3) CrN.

Three peaks are observed, CrN (red), Cr2N (Blue) and Amine (Green). All three peaks correspond to N in a

similar electronic state to (3-)

If the XPS peaks are due to N in the passive film and not in the metal, all three peaks detected for

N1s correspond to N in the (3-) state, which is in line with the Hume-Rothery analysis presented above.

If the XPS measurement is detecting the metal coating, which is likely, then Cr2N and CrN peaks are

meaningless in terms of oxidation state in the coating, as those phases are interstitial solutions (FCC Cr

with all octahedral interstitials occupied by N for CrN and Hexagonal Cr with 6 N-occupied octahedral

interstices per unit cell for Cr2N). The NIST[42] database of N1s binding energies agrees with the CrN

peak, but not with the Cr2N peak, which is about 0.55eV off. Therefore, it is possible that the binding

observed was not Cr2N, but N in the (3-) state within the passive film, because Cr2N would require two

things that are not present. First, it would require a 2:1 stoichiometry, which was not observed. The

reported stoichiometry is approximately 5.7:1. Secondly, it would require the peak to be in the proper

position. The NH3/NH4+ peak corresponds well to ammonia absorbed on silicon substrates, however it is

very faint. In summary, although they do not directly implicate N(3-) occupying an oxygen lattice site,

the XPS observations currently available in the literature report N in the (3-) state in the passive film, and

do not rule out N(3-) on the oxygen lattice.

40

Proposed Point Defect Reactions for Nitrogen

The following reactions are written in Krӧger-Vink notation, where the subscript denotes the

location of the species and the superscript indicates the charge with respect to the oxide crystal. For

instance, an oxygen in an oxygen site would have zero charge with respect to the lattice and be written

OO, while a vacancy on the oxygen lattice would be written , indicating a charge of (2+) with respect to

the lattice. Defect reactions must be written such that lattice sites, charge, and mass are all conserved,

except in the case of a lattice non-conservative reaction, such as oxide dissolution from the Point Defect

Model, noting that charge and mass must still be conserved in that case. The proposed reactions are

electroneutral, in accordance with the conservation of mass and lattice sites. Lattice non-conservative

reactions are possible and in fact required by the PDM, however, N is not predicted to participate in any

non-conservative reactions. Because oxygen is always in the 2- oxidation state in an oxide passive film,

the proposed reactions are independent of the metal with which the nitrogen is alloyed. Traditionally, OO

would be written , with x indicating neutrality with respect to the crystal, but this causes confusion

with the notation used in the Point Defect Model, so the convention of no superscript in the case of

neutrality is used here.

As outlined previously, nitrogen can only enter the oxygen vacancies if it is in the (3-) oxidation

state, where its valence is identical to O(2-), which should yield the same coordination number (4 in this

case). Further, the atomic radii for O(2-) and N(3-) are very similar; around 1.3Å. The difference in

atomic radii is 6.5%, which is well within the Hume-Rothery limit of 15% for substitutional solid

solution. Additionally, the electronegativities are similar, offering further argument for the compatibility

of N (3-) substitution into an oxygen vacancy.

41

Reaction N1: Incorporation of Nitrogen into the Barrier Layer

Reaction N1 takes place at the metal/film interface and involves moving a nitrogen atom from the

metal into a waiting oxygen vacancy. Here, N is written in the (3-) oxidation state, as is supported by the

theoretical hypothesis in the previous section. N remains in the (3-) state, but occupies a vacancy of (2+)

charge, yielding a net charge of (1-) with respect to the lattice.

(N1)

↔

(63)

The mobility of such nitrogen substitutions should be far less than that of the oxygen vacancies

occupying the lattice, therefore, it can be assumed that once they are created, they are effectively

immobile, creating a constant concentration profile, where the concentration of N substitutions is the

same everywhere except for the film/solution interface. This would be quite different were the N atoms

to inject into the lattice at interstitial sites.

Reaction N2,N3 and N4: Production of Surface Amines

Reactions N2, N3, and N4 take place at the film/solution interface and involves single additions of

hydrogen ion to create an amine surface species and finally solvated ammonia in reaction N4

(N2)

↔ (64)

(N3)

↔

(65)

(N4)

↔

(66)

Derivation of the Reaction Rate Constants Using the Method of Partial Charges

The method of partial charges (MPC) was employed here to determine the reaction rate constants

for each defect reaction, after [43]. MPC stands on the postulate that a transition state is achieved

between the initial and final states, representing a nonequilibrium state at the maximum in the Gibbs

42

energy, popularly known as the “Gibbs energy of activation”. F is Faraday’s constant, 96485 C/mol. The

brackets in the following transition equations and the corresponding shaded columns refer to the transition

state. In the subsequent equations, α can be thought of as the extent of reaction, or a measure of the

position of the activated complex along the “reaction coordinate” between the initial state of the reaction

and the final state, such that when α is zero, the activated complex is indistinguishable from the initial

state, and when alpha equal to one, the activated complex is indistinguishable from the final state, and for

all other values of α between 0 and 1, the activated complex lies somewhere between the initial and final

states.

For Reaction N1:

(67)

[

]

Species

Location Metal film Metal Film Film Film

Potential

Standard

Energy (elec)

The free energy change for the transition state is:

(68)

The chemical component is calculated:

(69)

(70)

43

Combining like terms

(71)

Factoring out

(72)

For which we can identify the standard Gibbs energy change,

,

yielding

(73)

The electronic component is calculated by subtracting the initial state from the nonequilibrium

state:

(74)

(75)

Combining like terms

(76)

(77)

And rearranging to express in terms of , the potential drop across the metal/film

interface,

(78)

And therefore,

(79)

An identical treatment yields the free energy relationship for the film/surface reactions

44

For Reaction N2:

[

]

Species

Location Film Solution Film Solution Film Film

Potential

Standard

Energy (elec)

(80)

(81)

(82)

For Reaction N3:

[ ]

Species

Location Film Solution Film Solution Film Film

Potential

Standard

Energy (elec)

(83)

(84)

(85)

45

For Reaction N4:

[

]

Species

Location Film Soln Film Solution Film Solution Film Soln

Potential

Standard

Energy (elec)

(86)

(87)

(88)

Derivation of Rate Constants

Due to the nonzero result of the method of partial charge, it is evident that the rate of reaction

depends partly on potential. With this in mind, the electrochemical rate constants, kN1,kN2,kN3 and kN4 are

derived after the method given in [43]

(

)

(

) (89)

(

)

(90)

Substituting

and

⁄

(

)

(

⁄

)

(91)

Defining , ,

46

(

)

⁄

(92)

And defining ,

(

)

⁄

(93)

The remaining constants, k2N,k3N and k4N are derived and organized in the same manner.

(

)

⁄

(94)

(95)

(

)

⁄

(96)

(97)

(

)

⁄

(98)

(99)

The results are collected in the following table:

For i=(N1,N2,N3,N4), (100)

and (

)

⁄

(101)

Table 5: Exponential coefficients for rate constants ki of nitrogen defect reactions

i ai bi ci

N

N1

N

N2

N

N3

N

N4

47

The nonzero result implies that the rate of these proposed reaction should vary with potential,

however, with the number of transferred electrons being zero, the Faradaic impedance should be

unaffected directly. As will be explained, the Faradaic impedance and other properties of the film will be

affected by this result indirectly, through electrostatic interactions between the nitrogen defects and

oppositely charged point defects in the film.

Nitrogen-Interstitial Interaction

For the model proposed herein, nitrogen is theorized to substitute on the oxygen sublattice,

obtaining a charge of (-1) with respect to the lattice. The solute vacancy interaction model introduced

previously can be used to predict the consequences of such substitutions on the behavior of the passive

film. Because the charge is negative, it is expected that N would instead interact with positively charged

defects, such as oxygen vacancies and metal interstitials, forming the following possible complexes:

For oxygen vacancies:

[

]

(102)

For which the equilibrium constant is calculated after equation (59):

[

]

[ ][

]

(103)

For metal cation interstitials:

[

( ) ] (104)

And its equilibrium constant:

[

( ) ]

[ ][

]

(105)

where q is a stoichiometric coefficient and quantities in brackets are concentrations of crystallographic

species in the passive film. Interactions of this type should serve to reduce the rates of Reactions 3 and 6

through the immobilization of oxygen vacancies and Reactions 2 and 5 through the immobilization of

48

metal interstitials. It is possible to calculate the effect of such complexes on the diffusivity of cation

interstitials by Equations (60) and (61), assuming that the number of cation interstitials is approximately

7x1020

[20] and that every available nitrogen atom enters an oxygen vacancy. Figure 19 illustrates a first

approximation of the effect of nitrogen alloying on the diffusivity of metal interstitials, showing a

decrease of approximately one order of magnitude with 9 at.% N.

Figure 19: Effect on Diffusivity of Cation Interstitials by Nitrogen Alloying Fraction

The steady state thickness and current equations predicted by PDM can provide a check on the

empirical data available for such passive films, most notably reduced current densities (and hence general

corrosion rates) and thinner passive film thicknesses for nitrogen bearing stainless steels.

First, the film thickness is considered:

10

8

6

4

2

Diffu

siv

ity o

f ca

tio

n in

ters

titia

ls (

cm

2s

-1)x

10

-17

86420

Nitrogen Alloying Fraction, atomic %

49

(

)

(106)

In the case of a Cr passive film at potentials below the transpassive potential, (Γ-χ) = 0, meaning

that a7 = 0 and the equation reduces to

(

(

)

) (107)

It is now obvious that the first term will always be positive under anodic polarization (V>0),

leaving the second term to determine the passive film thickness. is predicted to be unaffected by a

reduction in the flux of oxygen vacancies, however, both and α3 would be affected. A reduction in

either of these values would result in a thinner film by increasing the value of the second term. An

increase in α would also decrease Lss. A local increase in pH due to the consumption of H+ ions through

Reactions N2-N4 would serve to increase the film thickness, but should only have a major effect at low pH

in the bulk solution.

The steady state current,

(108)

will increase with an increase of Γ, such as seen at high potentials and high pH values, due to the

formation of hexavalent chromium. F is a positive constant, yielding two rate constants, k2 and k7 to

determine the total current density. k2 is predicted to decrease due to the reduction in flux of metal

interstitial defects due to the interaction of the solute with the interstitials, which combines with an

increased pH, reducing the value of the second term to further reduce current densities

Experimental: Microstructural Characterization of Cr +N Physical Vapor Deposition Coatings

Physical vapor deposition by Argon (Ar) sputtering an ultra-pure Cr target was used to generate 5

micron thin coatings of pure chromium on silica glass substrates. Silica glass was the chosen substrate, in

order to avoid galvanic coupling with the base material. The composition of the samples was varied by

50

controlling the nitrogen gas flow rate during deposition, resulting in two alloys, one of 6.8 at% nitrogen

and one of 8.9%, as measured and reported by the manufacturer. Both of these compositions were below

the theoretical saturation limit of nitrogen in chromium of 13 at.%, which would result in a CrN1-x phase

and it was the goal of the PVD process to avoid a secondary phase, while tightly controlling the

composition of the coating with high purity.

X-Ray Diffraction (XRD) studies were carried out in order to verify that the coatings were of a

single phase of pure Cr with varying amounts N in solid solution. Two characteristic peaks were

observed, the [200] reflection, at approximately 64.3 in degrees 2 theta, and [110] at approximately 45

degrees. It is important to note, however, that the difference in degrees 2 theta between a Cr+N solid

solution and CrN second phase is relatively small; approximately one degree for both peaks. Using a

Lorentzian peak fit, Figure 20-Figure 22 are obtained, illustrating the difference in diffraction between

pure Cr and Cr+N solid solutions. The peak locations did not vary, but the peaks were seen to broaden

with increasing N content.

Figure 20: XRD Pattern and Fit for Pure Cr PVD coating showing Cr110(44.4°) and Cr200 (64.4°) reflections

100

80

60

40

20

0

60504030

2Theata (Degrees)

2010

0-10-20

80604020

0

Cr 110: 44.4o

Cr 200: 64.4o

51

Figure 21:XRD Pattern and Fit for 6.8%N Cr PVD coating showing Cr110(44.4°) and Cr200 (64.4°)

reflections

Figure 22: XRD Pattern and Fit for 9.8% N Cr PVD coating showing Cr110(44.4°) and Cr200 (64.4°)

reflections

Peak broadening was observed in the XRD patterns with increasing nitrogen content. A

Williamson-Hall Plot was constructed in order to estimate the effect on grain size and strain. However,

only two peaks were observed for each sample, so this result is presented cautiously and is not intended to

draw a strong conclusion.

150

100

50

0

60504030

2Theta (degrees)

-40-20

020

160120

8040

0

Cr 110: 44.4o

Cr 200: 64.4o

52

Figure 23: Williamson-Hall Plot for Cr+N PVD coatings. The slope of each line is proportional to the strain

by a constant value, C. The y-intercept is proportional to quotient of the wavelength and the thickness by a

constant value, K.

The Williamson-Hall plot is used to deconvolve the peak broadening observed in XRD data into

two parts, one part due to grain size, and the second part accounted for in terms of lattice strain. The

following plot illustrates general trends observed across the samples, as a function of N content, assuming

the following values for the scaling constants K = 0.9 and C = 5:

Figure 24: Strain and Grain Diameter of Cr PVD coatings for various concentrations of N as calculated from

XRD peak broadening, assuming C=5 and K=0.9

3x10-3

2

1

0

B c

os(t

heta

)

2.01.51.00.50.0

4 sin(theta)

0% N 6.8%N 8.9% N

2000

1500

1000

Avera

ge G

rain

Dia

mete

r (A

ngstr

om

s)

86420

180x10-6

160

140

Str

ain

Strain Linear fit - Strain

Grain Diameter Linear fit - Grain Diameter

53

The average grain diameter was estimated to decrease with increasing N content, while the strain

increased slightly, although it appears to be more or less constant. Introducing N into the Cr lattice may

induce some strain, due to atomic size mismatch, although it is impossible to tell if this is the effect

observed in the XRD patterns, since the sample size is small and only two reflection peaks were observed.

Comparison of this data to literature observations of CrxN phases indicates that the phase detected

is most likely pure Cr with solid solution of N. For example, the figure below provides patterns that do

not match any of the XRD patterns observed, except for the [200] and [110] reflections of pure Cr.

Figure 25: Tabulated XRD spectra of various Cr+N Phases[44] and Pure Cr vs. Nitrided Cr [45]

The peak locations are consistent with Cr, and not CrN. It is theoretically possible that small

zones of CrN exist but they are likely to be an insignificant fraction of the observed XRD signal and

therefore are undetectable, due to the relatively close overlap of the Cr peak. A first order approximation

for 10 at.% N reveals that should the entirety of the nitrogen content be bound up in nitrides, the present

phases by atomic fraction would be 11% CrN and 89% Cr. Assuming an equal sensitivity to both phases,

54

the CrN signal would be easily hidden in the peak broadening. Possibly, the peaks could be resolved via

XPS, but would require a longer time period for measurement than was taken in this study. The expected

peak locations in Figure 26 are taken from Figure 25 above [45] and show good agreement with Cr, but at

least a 1° deviation from the expected location of CrN peaks.

Figure 26: Comparison of XRD peak locations observed in this study with literature values [45]. Dashed

lines: Expected peak locations. Black circles: Peak locations observed in this study.

The coatings were examined via scanning electron microscopy (SEM), revealing a somewhat less

than flat surface, which is characteristic of PVD coatings. The coatings were not found to be free of

micro-scale defects, with occasional large (3 micron diameter) particles (Figure 28) and a few voids

exposing the glass substrate. Energy dispersive X-ray spectroscopy (EDS) revealed the inclusions to be

identical to the surrounding material. EDS was also used to positively identify the holes by the

appearance of both silicon and oxygen signals and the absence of Cr.

55

Figure 27: SEM micrograph of the texture of the pure Cr PVD coating

Figure 28: SEM Micrograph of a Pure Cr particle embedded in a pure Cr PVD coating

56

Figure 29: SEM micrograph of a void in the pure Cr PVD coating

For the coating with 6.8% N, the same type of precipitates and voids are observed. It would be

advantageous to verify that they are not CrN precipitates. However, N is a “light” element, and is

therefore difficult to resolve with EDS. The quantification of N varied widely, even measuring the same

spot multiple times, yielding inconclusive results. N was undetectable via EDS on the Pure Cr PVD

coatings, as expected. At 6.8% N, N was detected at approximately 1.3% in the bulk, which is far lower

than expected.

Figure 30: SEM Micrograph of a 6.8% N / Cr PVD coating, illustrating the texture of the coating and the

presence of Cr+N particles

57

Figure 31: SEM micrograph illustrating a Cr+N particle embedded in the Cr + 6.8% N PVD coating

Figure 32: SEM Micrograph featuring a Cr+N particle sitting on the surface of the Cr + 6.8% N PVD coating

The texture for the PVD coatings containing N was a bit “finer” than that of the pure Cr slide,

which is probably due to manufacturing variables. For the 8.9% N sample, N was observed with EDS

between 5 and 7%. Holes were again observed, and again, there was no discernible difference in

composition between the coating and the large particles.

58

Figure 33: SEM micrograph of a Cr+N particle embedded in the Cr + 8.9% N PVD coating

Figure 34:SEM micrograph of a void in the Cr + 8.9% N PVD coating

With the coatings examined microscopically, electrochemical experiments were carried out.

Experimental: Electrochemical Measurements

Due to the razor-thin thickness dimension of the coating, classical metallographical polishing was

not carried out. Instead, the specimens were tested in the as-received condition. Experiments were

carried out in a typical temperature controlled “flat” cell at 28°C, controlled by a recirculating thermostat.

59

Electrolytes are composed of 0.1M Na2SO4 salt and distilled water, which has a natural pH of about 7,

then adjusted to pH 4 or 10 by the addition of dilute H2SO4 or NaOH respectively. Electrolytes were

continuously deoxygenated using flowing high purity Ar or N2 as a sparge gas. Reference electrodes

were saturated mercury sulfate electrodes, with a nominal potential of 0.0 VSSE / 0.65 VSHE. Ag/AgCl and

Calomel electrodes were avoided due to the possibility of chloride contamination. Luggin probes were

not used due to the geometry of the cell, resulting in a somewhat high solution resistance (approximately

30-60 Ωcm2). Because the currents measured are very small (due to the high polarization resistance,

expected to be between 105 and 10

7 Ω cm

2), the deviation of potential measurements due to

uncompensated IR drop is expected to be negligible[46]. The counter electrode was a platinum mesh. A

silicone washer was used as a water-tight seal at the interface between the electrolyte and the specimen,

exposing approximately 0.71 cm2 of surface area. The pH and potentials examined were chosen such that

they lie within the Cr2O3 phase field and should therefore spontaneously form Cr2O3 oxide as a barrier

layer. A Pourbaix, or potential-pH diagram was constructed to illustrate the experimental space. The

Pourbaix diagram is a thermodynamic construction based on the Nernst equation, which predicts the

thermodynamically stable species at a given pH and potential, holding temperature, concentration of

dissolved ions and pressure constant[1]. In the following diagram, the solid black lines indicate

equilibrium reactions between the adjacent species and the dashed blue lines outline the region within

which water is stable. Below the water line, hydrogen will be produced, and above it, oxygen will be

produced, providing the basis for electrolysis of water on opposing, oppositely charged electrodes.

Raising the potential sufficiently high enough at any potential within the Cr2O3 phase field will result in

Cr entering the 6+ oxidation state (shown here as Cr2O7 (2-) and CrO4 (2-)) causing passivity breakdown.

It is evident from the negatively sloped phase field boundary lines that the potential for the formation of

Cr 6+ is lower at higher pH.

60

Figure 35: Pourbaix Diagram for the Cr-Water system at 28°C Calculated with HSC Chemistry 5.11[47]

The preceding Pourbaix diagram does not indicate any information about the kinetic stability of

the passive film, which is the domain of the Point Defect Model. Kinetic phase stability diagrams have

been proposed by Macdonald[15] but they are not as readily calculated as the Pourbaix diagrams. A

kinetic phase stability diagram is available for “alloy X”, (Figure 36) which is a chromium based alloy, in

acidic conditions at 50°C, with 6.25M NaCl, however it is specific to those conditions and not readily

applied here.

Figure 36: Kinetic Phase Stability Diagram for Alloy X in acidic, 6.25M NaCl at 50°C [48]

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Cr - H2O - System at 28.00 C

C:\HSC5\EpH\Cr38.iep pH

Eh (Volts)

CrH

Cr2O3

Cr(+3a)

Cr(+2a)

CrO4(-2a)Cr2O7(-2a)

Cr(OH)4(-a)

ELEMENTS Molality Pressure

Cr 1.000E+00 1.000E+00

61

Electrochemical Method

The general procedure of electrochemical testing was to mount the sample in the sample holder,

fill the cell with electrolyte, insert the reference electrode and begin sparging with intert gas while heating

the cell. During this process, the electrolyte is brought up to temperature and oxygen is removed from the

system, while measuring the open circuit potential. Once the open circuit potential has stabilized (this can

take 24-48 hours), a potentiodynamic scan is performed. The sample is allowed to rest until the same

open circuit potential value is again reached, upon which time an automated computer program takes over

control of the cell, measuring an impedance spectrum at the open circuit potential and then controlling the

potential potentiostatically at -0.5VSSE, stepping at 0.1V increments in the positive direction every three

hours, measuring the impedance in the middle of each step. In this way, the entire passive range is

examined systematically.

Results and Analysis

Potentiodynamic Polarizations

The current response behavior was measured while sweeping the potential in the positive

direction from just beneath the open circuit potential. In some cases, N alloying was found to be

beneficial, especially at high pH, while at lower pH, it was found to be detrimental, in the sense that the

passive current density was decreased and increased, respectively. In the following figures, the

displacement in the corrosion potential is likely due to the various states of the passive films that existed

on the samples prior to testing, because the samples were tested in the as-received condition, due to the

impossibility of polishing such a thin coating without destroying it. The results are displayed in the

following four figures. The overview figure (Figure 37) exhibits the differences in open circuit potentials

between samples polarized at different pH values. Also evident is the passive range, which is not entirely

62

vertical, but is extensive for all samples, spanning a potential range of over 1V. 6.8% N samples

exhibited a much lower transpassive potential than either 9.8%N or pure chromium samples.

Figure 37: Overview of potentiodynamic scans of PVD coatings at 30°C in Sulfate solution at pH 4,7 and 10,

for compositions 0 at.%, 6.8 at.% and 8.9 at.% N.

63

As shown in Figure 38, at pH 4, the nitrogen containing sample exhibited higher currents along

the entire passive range, but no difference was seen in the transpassive range.

Figure 38: Potentiodynamic scans at pH 4

As shown in Figure 39, at pH = 10, a clear advantage of N alloying was seen, with lower current

densities all along the passive range and a slightly improved transpassive potential. The 6.8%N sample

curiously exhibited a higher current density at all potentials in the passive range and a lower transpassive

64

potential. The potentiostatic results shown in the same figure for 0%N and 8.9%N show the same trend,

with a general reduction in current densities for higher quantities of nitrogen.

Figure 39: Potentiodynamic Scan at pH 10

-0.6

-0.4

-0.2

0.0

0.2

0.4

Po

ten

tia

l, V

SH

E

10-9 10

-7 10-5 10

-3

Current Density (A cm2)

0% N pH 10 6.8% N pH 10 8.9% N pH 10

0% N pH 10 (static) 8.9% N pH 10 (static)

65

No potentiodynamic scan was measured for pure chromium at pH = 7, but two nitrogen bearing

samples can be compared, showing that the lower N content sample had a lower current density, as shown

in Figure 40. In addition, the potentiodynamic current values at pH = 7 are also shown, illustrating the

reduction in current densities measured for the high nitrogen sample.

Figure 40: Potentiodynamic scan at pH 7 for 6.8 and 8.9% N samples, with the potentiostatic currents

superimposed.

The results of the potentiodynamic scans are curious and appear to show the opposite effect intended by

including N in the alloy. However, the potentiostatic measurements revealed a different story, as

articulated below.

66

Mott-Schottky Analysis: Agreement with Proposed Model

Mott-Schottky analysis was performed by measuring the impedance at a frequency of 5 kHz

across a range of potentials, and then calculating the capacitance as . Passive

chromium and its alloys are generally observed to be n-type in the passive region[20,22,49]. However, at

higher potentials, there is a clear transition from n-type (positive slope) to p-type (negative slope)

behavior and then finally, to transpassive behavior. It was observed that the potentiostatic polarizations

and impedance measurements were performed at potentials within the p-n transition area and the p-type

potential range, instead of in the n-type potential range. In Figure 41 and Figure 42, the n-type, p-type

and transpassive potential regimes are demarcated with vertical black lines. A linear regression was

performed for each semiconductor region, from which the carrier density and flat-band potential was

calculated.

Figure 41: Mott-Schottky Analysis for Cr PVD coatings with 0% and 8.9% N at pH 4 and 7

67

Figure 42: Mott-Schottky Plot for 0% and 8.9% N, pH 10

In the n-type region, the slope is positive, indicating that the dominant defect is positively

charged, and is likely to be metal cation interstitials ( ) and to a lesser extent, oxygen vacancies

.

In the p-type potential region, the slope is negative, indicating that the dominant defect is negatively

charged, corresponding to metal vacancies( ) and to a lesser extent, substitutional nitrogen

defects . A dependence on pH of the density of charge carriers was observed, with a higher

concentration at lower pH. Assuming a dielectric constant of 30 for Cr2O3 [50], the carrier densities were

calculated independently for the n and p-type regions for the linear part of those curves. The flat-band

potential was also estimated from the same relationship, neglecting the temperature term. Both

estimations are displayed in Figure 43 and Figure 44, respectively.

68

Figure 43: Acceptor density in the p-type potential range as a function of pH

The acceptor density is effectively indistinguishable between samples and exhibits a negative

trend with increasing pH.

Figure 44: Flat-band potentials estimated from mott-schottky analysis as a function of pH

The effect on the flat-band potential by N in the p-type region is difficult to interpret, [51,52];

however, it appears that the flat-band potential for the N-bearing passive film is less affected by a change

in the bulk pH (9 mV/pH) than the N-free film (17.6 mV/pH) (Figure 44). This could be due to the

presence of Reactions N2-N4, which can potentially increase the pH on the electrode surface.

The same trend is observed in the n-type region, with the exception that there is a discernible

difference in donor density at low pH. One possible explaination for this observation is the action of

400x1018

300

200

100

NA c

m-3

108642

pH

0%N (p-type) 8.9%N (p-type)

0.88

0.86

0.84

0.82

0.80

0.78

Po

ten

tia

l, V

SH

E

10864

pH

Efb 8.9%N (p-type)

Efb 0%N (p-type)

69

reaction N4, which would be increased at a lower pH, resulting in the generation of oxygen vacancies at

the film/solution interface.

Figure 45: Donor density in the n-type potential range as a function of pH

Figure 46: Flat Band Potential in the n-type potential range as a function of pH

Potentiostatic Current Contour Mapping

Potentiostatic currents were measured at six potentials for each pH value. These values are

plotted in E-pH space and a contour map is interpolated between them, as shown in figure Figure 47 and

Figure 48. The steady-state currents revealed significantly improved pitting properties (lower current

6x1021

5

4

3

2

1

ND. cm

-3

10864

pH

0%N (n-type) 8.9%N (n-type)

-7

-6

-5

-4

-3

-2

-1

Efb

, V

SH

E

10864

pH

Efb 0%N (n-type)

Efb 8.9%N (n-type)

70

density and higher potentials required to initiate pitting) for samples containing N. In comparison to the

Pourbaix diagram derived earlier in Figure 35, it is not terribly surprising that the general trend for steady

state currents was to increase from potential up to high potential, with no discernible trend related to pH,

with the highest current densities observed at the highest potential at pH 10, due to the downward sloping

equilibrium line. For the regions, within which negative currents are seen, the currents observed are

generated by the cathodic reactions taking place on the surface, and do not correlate to the corrosion rate.

Unfortunately, as shown by Mott-Schottky analysis, these potentials are the region for which Cr behaves

as an n-type semiconductor.

Figure 47: Measured Current Density E-pH Contour Map for 0%N

The current density map for 8.9 at% N-bearing samples revealed an identical trend, with the

exception that the current densities are generally lower, especially at high potential and pH.

0.6

0.4

0.2

0.0

Po

ten

tia

l, V

SH

E

10864

pH

800

600 600

500 400

300

200

100

20

20 20

10 9 8 7 7 6

6 6 4 4 4

3 3 3 2 2 2

1 0.5

0.5 0

0

0% N

Current Density, nA/cm2

Measured Point

71

Figure 48: Measured Current Density E-pH Contour Map for 9.8% N

The same data is presented with the potentiodynamic curves reported in Figure 39 and Figure 40.

The Optimization of Model Parameters to Impedance Data

In order to model the impedance of the passive film, the system was spatially reduced into one

dimension, perpendicular to the film, with area normalizing of the impedance to yield units of Ωcm2. As

shown in Figure 49 and expressed in Equation (109), the impedance function is serially divided into three

parts. The solution impedance is composed only of the resistance of the solution. The electrical double

layer is modeled by a resistor (charge transfer resistance) and capacitor (double layer capacitance) in

parallel. Finally, the passive film is modeled with the Faradaic impedance, defined by the Point Defect

Model, a Warburg transport element to describe the motion of the point defects (cation vacancies, oxygen

vacancies, and metal interstitials), and a geometric impedance, which models the dielectric and resistive

0.6

0.4

0.2

0.0

Po

tential, V

SH

E

10864

pH

500 350 300 250 200

150 100

50 20

20

10 9 9 9

8 7 6

5 4 4

3 2

1 0.5

0.5

0

0

8.9%N

Current Density, nA/cm2

Measured Point

72

properties of the film and scales with the film thickness, as calculated by the PDM and expressed by

Equation (54).

Figure 49: Impedance Circuit. Rs: Solution Resistance. Rdl: Charge Transfer Resistance. Cdl: Double Layer

Capacitance. Zw: Warburg Diffusion Element. ZF: Faradaic Impedance. Zg: Geometric Impedance

The impedance function which was optimized onto the data set is of the form:

(109)

Values for each impedance element indicated in Equation (109) are defined as follows: Rs is the

solution resistance; the resistance between the reference and working electrode. Rct and Cdl correspond to

the charge transfer resistance and capacitance of the electronic double layer directly outside the passive

film, Zw is the Warburg semi-infinite transport impedance, corresponding to the diffusion/migration of

defects within the passive film. Zg is the geometric impedance, which accounts for both permittivity and

resistivity of the passive film material. Zg is a function of Lss, which is calculated during the composition

of ZF . ZF , Zg and ZW all depend upon frequency. ω is the angular frequency, in radians per second,

(ω=2πf, where f is the frequency in Hz) and j is the imaginary constant ( √ ).

The Warburg semi-infinite transport impedance is defined[53]

√ (110)

73

where the Warburg coefficient, σw has units of

√ . The diffusivity of the defects can be calculated from

the Warburg coefficient, the polarizability, the electronic field strength, and the steady state current,

although this information is not used during the curve fit [53]:

(111)

where D is the diffusivity of the defect within the film.

The geometric impedance, Zg is a constant phase element of the form

(

)

(112)

where Q is calculated from n, the resistivity ρ, and the permittivity Ɛ. n is a fit parameter and represents

the degree of dispersion of dielectric permittivity and resistivity and varies between 0 and 1. In practice,

Q is fit as a parameter, and then the resistivity is calculated, after the fact, as a check on the model. The

resistivity is expected to be similar to a heavily doped semiconductor, on the order of mΩ or higher.

(113)

g is a numerically evaluated, and is a dimensionless value that varies as a function of n [54].

(114)

The CPE behaves as a pure capacitor when the exponent α = 1, g = 1 and

. The CPE

behaves as a pure resistance and is independent of frequency, when the exponent α = 0 for which, g =

3.88 and

. Its expected behavior is to be mostly capacitive in character, with a value

between 0.5 and 1.

74

The electronic conductance (115) considered in Zg is calculated from k2, k3, χ, and the diffusivities

of various charge carriers after the method of Bojinov, assuming that DO=Di=10-11

cm2s

-14 [55] and De is

the diffusivity of the electron, 2x10-11

cm2s

-1.

(115)

In this way, the geometric impedance is now coupled to the calculation of the Point Defect Model

and these results can be used as a check on the validity of the optimization.

The Validation of Impedance Data

Several methods were employed during this study to validate the impedance spectra.

1. Hysteresis: The impedance spectrum is measured from high to low frequency, and then

immediately measured from low to high frequency. Any hysteresis in the resulting curve

should be interpreted as instability of the system at that particular frequency although

inconsistencies tend to be systemic and mostly expressed at low frequency, where the

measurement takes the longest time to accomplish.

2. Inspection of |

| vs. ω for smoothness: Problem frequencies will appear as spikes in

the data, for instance, this plot of the impedance of a standard reference cell and data

provided by the potentiostat manufacturer, as shown below, illustrates this method :

75

Figure 50: Checking the ratio of impedance for smoothness

A visual inspection of this graph reveals that the data is “smooth” between about 3 kHz and

0.1 Hz. Particularly bad points should be discarded or otherwise penalized prior to

performing an optimization. In this simple case, it is unlikely that the result would be

strongly affected by the noise observed at high and low frequency. However, the inflection

point, seen in this graph at approximately 20 Hz, is generally not observed for highly resistive

systems, such as pure Cr, making the extreme frequencies yet more important. It is important

to note that the interference observed by this method did not appear using the same

manufacturer’s Kramers-Kronig transform software. A better validation can be performed

with confidence bands, as outlined in the following section.

3. Kramers-Kronig transforms [56–59]that thansform the impedance data between the real and

imaginary axes. The K-K transforms are derived from Cauchy’s theorem for causality, which

is the principal underpinning of modern scientific philosophy, and they test for compliance of

1

10

100

1000

|Z'/Z

''|

10-2

10-1

100

101

102

103

104

105

106

Frequency, Hz

Measured Theoretical

76

the system with the linearity, causality, stability, and finiteness constraints of linear systems

theory. Many EIS instrument vendors now supply programs for performing K-K transforms.

Validation of Impedance Data via the Use of Confidence Bands

Impedance data can be screened for validity through the calculation of confidence bands. A

covariance matrix is calculated at the end of all Ellis2 curve fits in order to determine the 95% confidence

interval for each parameter. It is possible for this calculation to fail numerically, and produce a set of

standard deviations that are all equal to zero. In this case, Ellis2 calculates a variation at the user’s

request, for instance +/- 5%. A large number of solution vectors are then chosen from a uniform random

distribution within this interval and impedance curves are calculated. The maxima and minima of the

calculated impedances are taken as the edges of the confidence band. A representative confidence band is

displayed in Figure 51.

Figure 51: Representative Confidence Bands as calculated by Ellis2; 105 trials, +/- 5% parameter values

102

103

104

Imp

ed

an

ce (

Oh

ms)

10-1

100

101

102

103

104

105

Angular Frequency (2PiHz)

100

101

102

103

104

105

Ima

gin

ary

Im

pe

da

nce

(O

hm

s)

Real Impedance Imaginary Impedance

Confidence Band (real) Confidence Band (Imaginary)

77

The points at high frequency falling outside of the confidence band were excluded from a second

curve fit, whereupon a new confidence band was calculated, and all of the points fell within the band.

Figure 52: Representative confidence bands for phase angle (green), |Z| (purple), Z’(red) and Z’’(blue) after

the exclusion of the final 8 points of the spectrum, which fell outside of the initial confidence band (Figure 51).

The optimization of PDM model parameters with respect to empirical impedance data has always

been a “hard” problem. In the past, the state-of-the-art fitting technique involved the use of Levenberg-

Marquadt gradient based curve fitting, also known as complex nonlinear least squares (CNLS) curve

fitting. Such techniques are easily applied to intuitive systems such as the Randles cell, because they

require excellent starting guesses in order to operate without failure. Applying this technique to the

optimization of a PDM model, which can have upwards of 20-30 fitting parameters is a daunting task,

indeed, for a number of reasons. In order to overcome the limitations of previous efforts, a software

-80

-60

-40

-20

0

Pha

se A

ng

le (D

eg

ree

s)

10-1

100

101

102

103

104

105

Frequency (Radians / sec)

102

103

104

105

Mo

dulu

s,

|Z| (O

hm

s)

-300x103

-200

-100

0

100

Imp

ed

an

ce,

(Ohm

s)

-50

0

%

2-2-6

%

-0.8-0.40.0 º

pH:10 ESHE:0.56 NaN%N Iss:16.07nA Lss:1.263nm X2:5.0135

78

package, named Ellis (and now Ellis 2 [31]) was developed and discussed earlier. Ellis2 uses an

evolutionary algorithm known as “Differential Evolution” (DE) to obtain excellent curve fits even when

high quality starting guesses are unknown. The general operation of differential evolution is as follows:

1. Propose an objective function, a fitness function, and a set of limits for each model

parameter. The limits create a hypervolume within which allowed solution vectors exist.

2. Randomly generate a population of solution vectors within the coefficient limits (here a

proposed solution to the impedance function)

3. Test these vectors through the objective function (here the impedance function) and rank

them according to some fitness metric (here, X2 error)

4. Delete those vectors resulting in the worst fit result.

5. Add new random vectors and randomly mutate members of the previous generation

6. Allow those vectors with high fitness to reproduce, exchanging information to produce

“daughter” vectors.

7. Repeat steps 2-6 for each generation until a stopping condition is met (number of generations,

convergence, etc.)

The advantages of using Ellis2 over other fitting packages for this purpose are manifold:

1. The fit function is complex, as opposed to fitting the real or imaginary parts discretely and

separately. Experience has shown that it is impossible to obtain a solution that fits well to

one axis, but not the other.

2. The fit can be weighted by the reciprocals of the data values, meaning that large impedance

values cannot hijack the fit, as has happened in the past. This results in vast improvements to

the phase angle results, which have been historically poor.

3. Logic can be incorporated into the impedance function. For instance, if Lss is calculated to be

a negative value for a given solution vector, then it should be set to zero for the purposes of

calculating further steps dependent on Lss.

79

4. Causes of crashing with other fitting packages have been worked-around. One such issue is

the limitations of 64-bit floating point numbers. The largest number possible in such a

system is approximately 10308

. The PDM contains exponential functions which have the

ability to exceed this value. Analytically, this is not a problem, but during numerical

evaluation, it can cause a crash. Ellis2 checks for such points and sets them equal to zero.

This seems appropriate, because such problems occur only at high frequencies. Another issue

that is avoided is that of the singular matrix error, which plagues users of the Levenberg-

Marquardt method. Differential evolution does not require a derivative, so discontinuities are

not an issue.

Results: Impedance Model Optimization

In all, 56 Cr and Cr-N alloys in contact with acidic (H2SO4) and basic (NaOH) 1M Sulfate

(Na2SO4) solutions were collected and fit. A representative fit is shown in Figure 53, and the full set of

optimized spectra can be found in Appendix A.

-400x103

-200

0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_3_1

80

Figure 53: Representative Impedance Spectrum Optimized with PDM

The model parameters optimized during the curve fits was used with Equation (35) to generate

the following figures comparing the steady state potentiostatic data previously displayed in Figure 47 and

Figure 48, in order to compare the model output to the measured currents.

Figure 54:Steady State Current Densities at pH 10 for 0% and 8.9% N measured and calculated

1

10

100

1000

Cu

rre

nt

de

nsity,

nA

/cm

2

0.50.40.30.20.1

Applied Potential, VSHE

Imeas0% N pH 10

Icalc 0% N pH 10

Imeas8.9% N pH 10

Icalc 8.9% N pH 10

81

Figure 55: Steady State Current Densities at pH 7 for 0% and 8.9% N measured and calculated

The current densities, while agreeing on the order of magnitude, were not correct with respect to

the trend of current with potential. The model used was for an n-type film, which predicted current

densities independent of potential, while the Mott-Schottky analysis revealed that the measured potentials

are within the n-p and p-type potential regions. Deriving a p-type Faradaic impedance would likely

rectify this discrepancy. Another discrepancy is the apparent prediction of the model that nitrogen

bearing samples should have higher current densities in all cases. This is likely also due to the model

being for an n-type film. The n-type model was used because n-type films were expected, but analysis of

the data has revealed that the measurements require the all-inclusive PDM to interpret properly.

0.01

0.1

1

10

Curr

en

t d

en

sity,

nA

/cm

2

0.50.40.30.20.1

Applied Potential, VSHE

Imeas 0% N pH 7

Imeas 8.9% N pH 7

Icalc 0% N pH 7

Icalc 8.9% N pH 7

82

Barrier Layer Thickness

The barrier layer thickness can also be predicted by PDM, and gives good agreement to physical

measurements of the barrier layer as measured by ellipsometry in other studies[60]. The optimized PDM

parameters were used to calculate the steady state film thickness and plotted in contour maps of pH and

potential.

Figure 56: PDM calculated steady state barrier layer thicknesses for pure Cr

0.5

0.4

0.3

0.2

0.1

Po

ten

tia

l, V

SH

E

10864

pH

1.3

1.3

1.3

1.25

1.2

5

1.25

1.25

1.2

5

1.2

1.2

1.15

1.1

5 1.15

1.1

5

1.1

1.1

1.05

1 0.95

0%NL, nmCalculated, PDM

Measured Points

0.5

0.4

0.3

0.2

0.1

Po

ten

tia

l, V

SH

E

10864

pH

1.3

1.3

1.25

1.2

1.15

1.1

5

1.1 1.1

1.1

1.0

5

1.05

1

1

1

1 1

1

1

0.9

5

0.95

0.9

0.9

0.9

0.9 0.9

0.8

5

0.85

0.8

0.75

0.7

5

0.7

8.9%NL, nmCalculated, PDM

Measured Points

83

Figure 57:PDM calculated steady state barrier layer thicknesses for 8.9% N

The barrier layer can also be estimated assuming a dielectric constant of 30 and the impedance at

5kHz. A high frequency is chosen for the capacitance calculation, because the non-solution resistance

contribution to impedance is almost entirely imaginary at that point and, therefore, is behaving in a purely

capacitive mode.

Figure 58: Barrier Layer Thickness as Estimated by a parallel plate capacitor assumption for pure Cr

0.5

0.4

0.3

0.2

0.1

Po

ten

tia

l, V

SH

E

10864

pH

3.6 3

.4

3.2

3

3

2.8

2.8

2.8

2

.6

2.6

2.6

2.4

2.4

2.4

2.2

2

.2

2

1.8

1

.8

1.6

1

.6

0%NL, Calculated, PPC at 5 kHz

Measured Points

84

Figure 59:Barrier Layer Thickness as Estimated by a parallel plate capacitor assumption for 8.9% N

Unfortunately, no direct measurement of the barrier layer thickness was possible with the

equipment available at the time of the experiment. However, both calculations yield values that are

within reason for a barrier layer, usually 1-6 nm and indicate thinner films at lower pH, as indicated by

PDM.

In addition, the resistivity of the barrier layer was calculated for each sample type from (113).

The resistivities tended to be around 1 mΩ cm, which is in agreement with the passvive film being a

highly defective (doped) semiconductor material. The averages for each sample are tabulated below.

Table 6: Resistivities of Barrier Layers

Sample Resistivity,

mΩ cm

Pure Cr 1.6

Cr + 6.8% N 0.64

Cr + 8.9% N 1.5

0.5

0.4

0.3

0.2

0.1

Po

ten

tia

l, V

SH

E

10864

pH

4 3

.5

3.5

3

3

2.5

2.5

2

.5

2.5

2

2

2

2

1.5

1

.5

1.5

8.9%NL, Calculated, PPC at 5 kHz

Measured Points

85

Conclusions and Suggestions for Further Study

A theoretical basis for the incorporation of nitrogen into chromium passive films compatible with

the Point Defect Model of the passive state has been presented, and tested through the use of specially

prepared PVD coatings and analyzed using the Point Defect Model. It is predicted that the incorporation

of N would affect transport of oppositely charged point defects, as suggested in the solute-vacancy

interaction model. During the experimental portion of this work, PDM was found to be in very good

agreement with pure Cr samples, but was less predictive with the Cr+N samples. However, the order of

magnitude for barrier layer thicknesses and passive current densities remained correct, possibly due to the

incorporation of a physically modeled constant phase element which takes into account the dielectric

constant and resistivity of the barrier layer material. It is recommended that this work be continued.

Specificially, the nitrogen effect could be further explored through the use of advanced surface techniques

to positively identify the electronic state and crystallographic location of N in the passive film. Such

investigations would lend a higher degree of certainty to the model, or possible require the model to be re-

thought. A major problem to be overcome is the implementation of a n-p type Faradaic impedance for

use with the data collected here. The lack of agreement between the measured steady state currents and

the model prediction is entirely due to the assumption of an n-type semiconductor passive film, while the

Mott-Schottky analysis revealed that the potentials investigated were in fact n-p and p-type in character.

Once a more appropriate Faradaic impedance is derived, it should be possible to easily optimize the data

using Ellis2, which was developed for this work. Further upgrades to Ellis2 are planned, including a

more accessible batch-processing dialog, and the production of instructional videos intended to help those

new to impedance optimization get a head start.

86

Chapter 4

Resistive Depassivation of ASTM 470/471A Rotor/Disc Steel in Aqueous Amine

Environments at Elevated Temperatures

Introduction

The typical materials of fabrication of low pressure steam turbines are Type 403 SS or Al-6X for

blades and ASTM A470/471 for disks and rotors. These materials were chosen largely for their

mechanical properties (strength and stiffness, for efficiencies in power generation) rather than for their

corrosion resistance. Over the past several decades, many blade failures (Type 403 SS) and disk failures

(ASTM A470/471) have been experienced, often with catastrophic results, beginning with the spectacular

failure at Hinkley Point B nuclear station in the United Kingdom in 1979. Since then, inspection of

operating turbines revealed many cracks in disks and rotors and to a lesser extent, blades in operating

turbines[61,62]. In interpreting these failures, it must be recognized that both Type 403 SS and ASTM

A470/471 are hard, high strength materials and hence are highly susceptible to hydrogen embrittlement

(HE) and hydrogen-induced cracking (HIC).

ASTM A470/471 steel is a low-alloy steel that comprises mostly Iron (typical composition is:

0.05-0.3 wt% C; 0.02 wt% Si; 0 – 01.0 wt% Mn; 8-14 wt% Cr; 0.3-3 wt% Mo; 2-5% V;0.01-0.5 wt%

Ni;0.01-0.05 wt% Nb; 0.001-0.08 wt% N; 0.001-0.02 wt% B). As indicated, ASTM A470/471 steel has

very small quantities of nickel, chromium, molybdenum, and vanadium, but the chromium content does

not exceed the requisite 13% for the alloy to be considered a stainless steel. As previously mentioned,

ASTM A470/471 steel is used to fabricate rotor discs and shafts for steam turbines used in thermal power

generation. The chemical environment of such turbines is high pressure steam, nominally derived from

ultra-pure water, but in reality containing various steam-phase impurities (e.g., acetic acid) and inhibitors

or pH-regulating compounds (e.g., amines) that are used for corrosion control.. The various amines are

introduced as corrosion inhibition additives, such as ammonia, dimethylamine, and monoethanolamine.

87

These amines are effective primarily by moderating (increasing) the pH in the transition phase zone

condensate. Thus, the purpose of such additives is to regulate the pH of the system into the basic regime,

avoiding the regime where solvated iron ions are the stable phase and free corrosion can occur, and to

push the corrosion potential to sufficiently low values that the passivity of the metal is unlikely to be

disturbed. The logic underlying this assumption is based on the Pourbaix diagram for iron, where at

higher potentials, the iron is passivated, that is, coated by an ultra-thin layer of iron oxide that is both

tenacious and protective, while at low pH, the metal freely corrodes. However, the rationale, based on the

Pourbaix diagram is in some ways faulty, because passivity is a kinetically-controlled phenomenon, not a

wholly thermodynamically controlled process, as postulated by Pourbaix [1]. There is, however, an

undeniable causality between the thermodynamics and the apparent behavior of the kinetics. In the

kinetic interpretation of passivity, the protective film exists on the steel surface, because the rate of film

formation at zero film thickness is greater than the rate of dissolution. Under these circumstances, the

nm-thin passivating barrier layer of magnetite exists on the steel surface as a metastable entity and

passivity exists. If the conditions change (e.g., lowering of pH) such that the rate of film formation at

zero film thickness becomes less than the rate of dissolution, the barrier layer of the passive film can no

longer exist, even as a meta-stable phase. In that case, corrosion resistance is greatly reduced and any

remaining resistance may be due to the resistive, precipitated outer layer only. This mechanism gives rise

to “acid depassivation”. The formation of magnetite (Fe3O4) as a metastable phase, and hence the

acquisition of corrosion resistance, generally requires an oxidizing environment to raise the corrosion

potential above that stipulated by extrapolation of the Fe/Fe3O4 equilibrium line into the Fe2+

stability

region at low pH and potential (See Figure 65). These conditions do not exist in a steam turbine under

normal operation and hence an iron-based alloy, such as ASTM A470/473 is not expected, or found, to be

corrosion resistant, particularly if the pH falls below 5.5. Nevertheless, we will use Pourbaix diagrams

throughout this report to interpret the corrosion behavior of ASTM A470/471 in reducing environments.

88

Figure 60: Cartoon Interpretation of the thermodynamics of corrosion.

Attributed to Marcel Pourbaix.

Figure 61: Environmentally defined regimes of potential and pH

The Pourbaix diagram can be thought of as consisting of four quadrants (Figure 36),

which are defined by the environment. The environment may be either oxidizing or reducing,

and acidic or basic. Dissolved oxygen, as we know, controls the electrochemical potential of the

system, however, other oxidizing agents can also do the same job, for instance, ferric ions may

89

drive the potential in the positive (oxidizing) direction. In addition, the presence of carbon

dioxide can increase the potential by decreasing pH.

Amine background: Dimethylamine (DMA)

Figure 62: “Ball-and-stick” structure of dimethylamine. Hydrogen is silver, carbon is black, and

nitrogen is blue.

Verbatim entry from NACE Corrosion survey:

“(CH3)2NH, B.P. 7 C, is very water-soluble. It is non-corrosive except to copper and chromium-free nickel

alloys in the presence of dissolved oxygen.” [63]

Amine Background: Monoethanolamine (ETA)

90

Figure 63:“Ball-and-stick” structure of monoethanolamine. Hydrogen is silver, carbon is black,

nitrogen is blue, and oxygen is red.

Monoethanolamine (2-aminoethanol, CAS 141-43-5), , has been historically known to

react with iron[64,65]. The NACE corrosion survey database contains the following

compatibility chart for monoethanolamine with various alloys:

Verbatim entry:

“HO C2H4 NH2 has corrosion characteristics of both alcohols and aliphatic amines, M.P. 11 C. Dissolved

oxygen will cause severe corrosion of copper and chromium-free nickel alloys.” [63]

Of particular note are aluminum, copper and zinc alloys, which are highly susceptible to

direct corrosion by the amine, because of the formation of amino-cation complexes that destroy

the barrier layer of the passive film, thereby inducing depassivation. Because of the susceptibility

of zinc, any alloys containing zinc, such as galvanized steels and brass, should also be avoided.

Most other alloys exhibit very low corrosion rates; less than 2 mils per year, (mpy), unless studied

at very high concentration and/or temperature.

The handling guide for ethanolamines from Dow chemical summarizes the practical

knowledge of chemical compatibility of ethanolamine with its container alloys, empirical

confirmation of which is found in the NACE corrosion database. Storing pure monoethanolamine

in steel containers at any temperature results in a brown discoloration of the monoethanolamine,

due to the formation of a tris-complex of three monoethanolamine molecules octahedrally

coordinated to one iron atom[66] (Figure 64).

91

Figure 64: Three ethanolamine molecules coordinated octahedrally to one iron atom

Despite the apparent reactivity of iron with monoethanolamine, the formation of the

water insoluble, tris complex is not considered to be a hazard, because the corrosion rate is

extremely low.

The mechanism preventing corrosion in ASTM 470 / 471A steels is postulated to be the

formation of the passive layer protecting the steel from further oxidation. In order to study the

effect of various amine (nitrogen containing) inhibitors (ethanolamine, dimethylamine, and

ammonia) on the viability of such a passive film and the resulting passivity, we must examine the

thermodynamics, kinetics, and electrochemical properties of the film and the surface.

Thermodynamics of the Iron-Water System

The thermodynamics of the aqueous iron system is well-described by the Nernst Equation

(116).. The phase diagram depending on pH and potential is derived after the methods outlined

by Pourbaix in the 1960’s [1] to reveal the Pourbaix diagram (or Eh-pH diagram).

(116) QnF

RTEE o ln

92

where Q is the reaction quotient (ratio of the product of the activities of the species on the right

hand side of the half-cell reaction divided by the product of the species on the left side, with the

half cell reaction being written in the reduction sense). With the activities of all other species

being constant, the Nernst equation describes the equilibrium potential, E, as a function of pH

(via the relationship between hydrogen ion activity and pH, defined as pH = -Log(aH+)), for a

particular equilibrium reaction. T is the absolute temperature, in Kelvin. R is the gas constant,

8.134 J/(mol K), n is the number of equivalents of electrons exchanged in the reaction, and E° is

the standard potential of the reaction at some standard state, in this case, pH=0 (aH+ = 1)

Modern thermodynamics software was used (Outokumpu HSC Chemistry 5.1) [47] to

produce the following E-pH diagrams for iron at 95°C and 175°C, Figure 65 and Figure 66,

respectively. The solid black lines indicate equilibrium reactions and divide the fields of pH and

potential that contain stable species. The blue lines represent the upper and lower stability limits

for water. At potentials above the upper line, oxygen is evolved while potentials below the

bottom blue line result in hydrogen evolution. Phase fields indicate the thermodynamically stable

iron containing species across a range of potential and pH.

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Fe - H2O - System at 95.00 C

C:\HSC5\EpH\Fe95.iep pH

Eh (Volts)

Fe

Fe2O3

Fe3O4

Fe(+2a)


Fe 1.000E+00 1.000E+00

93

Figure 65: Pourbaix Diagram for the Iron-water system at 95°C, 1 atm. potentials vs. the Standard

Hydrogen Electrode (SHE).

Figure 66: Pourbaix diagram for the Iron-water system at 175°C, 300 psia. potentials vs.

theStandard Hydrogen Electrode (SHE).

According to the Pourbaix diagram, at the temperatures studied (95° and 175°C), any pH

above 5 will not experience active corrosion, that is, no Fe ionic species are stable at any

potential. Therefore, the mode of corrosion will be via the formation of various oxides of iron

(red hematite, α-Fe2O3 or black maghemite, γ -Fe2O3, at high potentials or black magnetite, γ-

Fe3O4 at low potentials). The oxidation state for iron in Fe2O3 is iron (III). The average oxidation

state of iron in magnetite is 8/3, which is greater than 2, but is less than 3. Magnetite is

sometimes considered as hematite with the addition of FeO; wüstite, where the oxidation state for

Fe is Fe (II). Increasing the potential should convert Fe to a higher oxidation state, which is why

Fe2O3 appears at higher potentials than Fe3O4. Note that FeO is unstable at the temperatures

studied, so it does not appear on the diagram. Also, Fe3O4 is often considered as FeO·Fe2O3, a

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Fe - H2O - System at 175.00 C

C:\HSC5\EpH\Fe175.iep pH

Eh (Volts)

Fe

Fe2O3

Fe3O4Fe(+2a)

FeO2(-a)


Fe 1.000E+00 8.742E+00

94

spinel, in which the divalent and trivalent ions are present on the cation sublattices or as

interstitials. Thus,for the purpose of describing diffusion of point defects in such a lattice, the

divalent iron can be thought of as being an interstitial and the trivalent iron as being fixed in the

lattice [67].

The effect of temperature in this case on the thermodynamics of the system and hence the

Pourbaix diagram is a shifting of equilibrium boundaries to more negative potentials. The effect

is very subtle, but it intensifies with increasing pH. As shown in Figure 66, at higher

temperatures, the stable species over a wide range of potentials above pH=13.4 becomes Ferrate

(III) ion (Iron (III) dioxide –ion), which is an aqueous oxy-anion.

The features of a cyclic polarization Curve

Cyclic polarization is a potentiodynamic technique, wherein the potential is swept

upwards from a value below the open circuit potential, which is identified as the corrosion

potential in an electrochemical corrosion cell. Upon reaching a limiting potential or current, the

controller then sweeps back in the negative direction until a negative current is again observed.

Figure 67 summarizes the types of cyclic polarization curves observed in this study.

95

Figure 67: Three cyclic polarization curve cases for a spontaneously active metal

Case I is for a material that exhibits a passive range from Point d to Point e. Point c

indicates the activation region where the electron flow measured is used to create the initial

formation of the passive film. Negative hysteresis is observed in the return sweep after Point f

(dashed line), which indicates the surface has immediately repassivated when returned from the

transpassive state. Case II is a material that is susceptible to pitting. Upon polarizing past Point

e, the material is transpassive, however, unlike Case I, sweeping in the reverse direction results in

a positive hysteresis, indicating an unprotected surface. The material is not protected by a passive

film until the potential is driven below Point g, the repassivation potential. Case III is a purely

active metal. The limiting current density seen beyond Point c is simply due to transport

limitations. If this electrode were placed in a high flow situation, for instance, as a rotating disc

electrode, the current density could go much higher.

96

Table 7. Characteristics of polarization regions for an iron-based alloy in aqueous solution.

Range Point Meaning

~50 mV negative to OCP a-b Cathodic region (current negative here)

OCP (Ecorr) b-d Active (anodic)

Activation Peak

Passive Region Begins d-e Passive Region

Transpassive Region Begins e-f Transpassive Region

New OCP Beyond f Reverse scan (cathodic)

Repassivation Potential

Cyclic polarization techniques contain several pieces of key data needed to make

predictions about corrosion rate in the specified conditions; The Tafel region is the linear portion

of the curve near Point b and can be used to estimate the polarization resistance of the alloy in the

absence of a passive film, to give its free corrosion rate by determining the corrosion current.

The same region may be used to extrapolate Tafel information which should corroborate the

polarization resistance measurements. Finally, the passive current density (the current density

seen in Region d-e) can be used to directly predict the corrosion rate of the passive alloy.

Tafel slopes can be measured from the potentiodynamic chart as the linear portion of the

Tafel region (the region where the current passes through zero, at the corrosion potential, Ecorr).

The intersection of the anodic and cathodic Tafel sloped lines will give the corrosion potential

and the corrosion current (icorr). The corrosion current calculated in this manner should be close

to the value calculated through the polarization resistance method. The corrosion currents are

then related to corrosion rate by way of Faraday’s law, which give the direct relationship between

current and material loss, hence, with geometrical factors included, the corrosion rate in mils per

year may be calculated.

For actively corroding materials, these methods work rather well, however, the corrosion

rates for “passive” materials are more appropriately estimated using the passive current density,

ipass (the current shared from (d) to (e) in the above charts) [68].

97

The features of a potentiostatic polarization curve

Potentiostatic polarization involves maintaining a constant potential on the electrode

surface and measuring the resulting current as a function of time. In general, as shown in Figure

68, a current decay curve will be observed, approaching some steady state current density, iss.

The slope of the curve can also be positive, depending on the mechanism of the reaction,

approaching iss, however, here it is drawn only as a negatively sloped function.

Figure 68: Typical shape of a potentiostatic current density vs. time curve

Pits can be observed electrochemically during potentiostatic polarizations with passivity

breakdown appearing as “spikes” on the decaying current. These spikes commonly are of the

form of a sharp increase corresponding to breakdown of the film followed by a gradual relaxation

lasting from milliseconds to seconds as the breakdown site repassivates. The typical shape of a

meta-stable pit repassivating is shown in Figure 69, while a stable pit, or possibly a crevice

nucleation is shown schematically in Figure 70.

98

Figure 69: Shape of a pit nucleating and repassivating with time under potentiostatic control

Figure 70: Nucleation and growth of a stable pit under potentiostatic control

Because repassivating (metastable) pits are fairly common and benign, due to their short

lifetime and hence small penetration depth, they are not of general concern and are common

features of potentiostatic curves and in the passive range of potentiodynamic polarization curves.

Pit penetration depth is far greater for a stable pit, because it becomes autocatalytic and self-

sustaining, and given enough time and a sufficiently large cathode surface to drive the anodic

processes occurring within the pit, it will penetrate the entire thickness of the afflicted part.

Because of this, localized (pitting or crevice) corrosion is an important feature to monitor. In this

99

study, however, it is difficult to produce samples that are perpetually immune to crevice corrosion

due to experimental difficulties encountered at high temperature and polarizing to high enough

potential will cause pitting corrosion on practically all passive materials. Note, also, that pitting

itself indicates a passive film is present, requiring the passive surface as the cathode and the pit as

the anode. Lacking enough external cathode will stop the propagation of a pit, but with a

potentiostat capable of providing as many electrons as are "requested" by the system, this

limitation is not seen. Independent coupons of small size, however, may not be able to support

the propagation of deep pits.

A note on reference electrode potentials

All potentials are measured in a relative sense; that is, there is no absolute scale for

potential. As such, a reference potential must be used in order to compare results from one

measurement to another. This is especially important in corrosion science, as opposed to for

instance, battery technology, because the thermodynamics of corrosion are controlled by

potential. For experiments at 95°C, a saturated calomel electrode (SCE), kept at room

temperature is used and at 175°C, a Tungsten / Tungsten oxide electrode (W/WO3) is used. The

W/WO3 electrode has a potential characterized by the following equation, derived from the

Nernst equation:

117

Where is 0.013 V. This reference electrode potential indeed varies with pH, but that

is taken care of during calculations and the standard potential is available from previous work

through calibration [69].

pHF

RTEE o

WWOW 303.23/

o

WE

100

A note on the thickness of passive films and modes of depassivation

The thickness of a passive film has a direct relationship to the applied potential. Thus,

the Point Defect Model (PDM) predicts that the barrier layer thickness increases linearly with

increasing potential, which is a ubiquitous observation in the field of passivity. For iron the

barrier layer typically varies in thickness from 1 -3 nm over the passive range. However, there is

no limit to the thickness of the outer layer as it forms by hydrolysis of iron cations being diffusing

through the barrier layer and so long as the transmission continues the outer layer will continue to

grow ad infinitum. The thick rust that is commonly seen on “rusted” iron is the outer layer and,

in some cases, it may exceed a centimeter in thickness. Because the outer layer is formed by

precipitation, it is porous and does not represent a significant barrier to the transmission of iron

ions that originate at the metal/barrier layer interface by the oxidation of the metal. Accordingly,

the outer layer normally does not result in inhibition of corrosion, but the IR potential drop across

the outer layer, in the case where the current flows to a remote cathode, may be such that the

barrier layer is destroyed and the surface becomes depassivated. This form of depassivation was

predicted theoretically by the PDM and, apart from the present work on turbine steels, it has been

detected in the corrosion of carbon steel in acidified CO2-containing brine [60]. It is important to

note that a thicker passive film (barrier layer) does not indicate that it offers superior corrosion

protection. So long as the thickness of the film is finite, that is non-zero, the corrosion current

will be a constant value for a metal, such as iron, whose passive film exhibits n-type electronic

character[70]. This is easily visualized in the cyclic polarization plot, where the “passive

potential region”, (d-e) for case I above, is a region in which the current is constant for any

change in potential within that region. The steady state thickness will vary within that region as a

function of potential, as noted above, but the corrosion rate will remain constant.

101

Should the kinetics of the system dictate that the film thickness is less than zero for the

given potential, then there will be no passive film and the corrosion rate is expected to increase

and. ultimately, be controlled by the outer layer [17,71].

There are several modes of depassivation known. Driving the potential to a high enough

value results in so-called transpassive-depassivation, resulting from enhanced, potential mediated

film dissolution, due to a change in oxidation state of the cation in the film upon passing into the

solution. Dissolving the passive film by reducing the pH will result in acid depassivation,

because the dissolution rate of the barrier layer to increase with CH+n, where CH+ is the

concentration of hydrogen ion at the barrier layer/outer layer (solution) interface The third mode

of depassivation is tentatively known as Resistive Depassivation (RD), and is a prediction of the

PDM [15], for which physical evidence has never been studied before, although it is postulated to

occur in the corrosion of carbon steel gas transmission lines containing small amounts of CO2-

acidified brine (NaCl solution). It is our postulate that we are witnessing such a mode of

depassivation in this system, possibly because the amines result in the formation of a resistive

outer layer (amines are typical “filming” inhibitors) and because amines are capable of chelating

dissolved iron species, thereby enhancing the dissolution rate of the barrier layer. Other modes of

depassivation include microbially-influenced corrosion (MIC), particularly in the presence of a

resistive biofilm and forms of mechanically-mediated corrosion, such as erosion-corrosion (or

flow-induced corrosion), fretting corrosion due to frictional contact between surfaces, and particle

impact corrosion, all of which involve mechanical factors in enhancing the rate of destruction of

the barrier layer. MIC is clearly an example of RD, but has only just been recognized as being so

(subsequent to the present work). In all cases, depassivation occurs, because the dissolution rate

of the barrier layer exceeds the film growth rate at the metal/barrier layer at zero film thickness

[17].

102

Experimental

This section describes the experimental techniques and procedures used to investigate the

corrosion of ASTM A470/471 in simulated phase transition environments containing

dimethylamine (DMA) or ethanolamine (ETA). The experiments were mostly electrochemical in

nature and were designed to measure the rate of corrosion and the impedance of the interface.

The three techniques employed are potentiodynamic polarization, potentiostatic polarization, and

electrochemical impedance spectroscopy (EIS). During the course of this study, we collected a

tremendous volume of EIS data on the expectation that we could interpret the data in terms of the

Point Defect Model as we have previously done for other passive metals and alloys [16,72].

However, our experiments indicate that the barrier layer does not exist and that the corrosion rate

is controlled by the resistive, precipitated outer layer, as predicted theoretically [73]. We are

currently deriving impedance expressions for various iron dissolution reaction mechanisms;

however, the results were not available at the time of preparation of the report. Even if they were,

the current data indicate resistive control of the current, presumably due to the resistive outer

layer and hence the dissolution mechanism may not have significant impact on the impedance. In

that case, it may be impossible to obtain information on the dissolution mechanism.

Low Temperature (95°C) Testing

The low temperature experiments (95°C) were performed using conventional

electrochemical cells, because the temperature is below the boiling temperature of the solution.

Accordingly, the system did not need to be pressurized to suppress boiling and hence solvent loss.

Furthermore, conventional, saturated calomel reference electrodes could be used, by maintaining

the electrode at ambient temperature and connecting it to the call at elevated temperature by a

103

non-isothermal KCl solution bridge. This arrangement results in a thermal liquid junction

potential (TLJP) and a corresponding Soret (thermal diffusion) potential, which is estimated to be

a few millivolts. No correction was made for the TLJP.

Figure 71: Bar of ASTM A470/471 from which the specimens were machined.

Initial samples of ASTM A470/471 steel were obtained from Siemens Corporation as 25-

mm diameter bar stock (Figure 71). The nominal composition was provided as “26 NiCrMoV14-

5” with a designation of UWU-No. 4231. Subsequent samples bear no such designation markers.

The bar was sectioned into 3/8” thick cylinders and tapped for electrical connection to copper

wire conductors.

Reliable high temperature aqueous corrosion testing is difficult, especially because of

crevice corrosion caused by the mismatch in thermal expansion coefficients between mounting

epoxies and metal samples. Epoxies tend to expand more than metals and will de-bond from the

metal, creating an aggressive crevice condition. Crevice corrosion is a form of localized

corrosion and is much more severe than the general corrosion taking place on the sample surface,

making it difficult to measure bulk corrosion properties without the addition of a significant

signal from the crevice. For this reason, a chemical resistant, low thermal expansion epoxy was

chosen, EP30LTE (Master Bond Inc.), which has a linear thermal expansion coefficient (CTE) of

12x10-6

in/in°C. Standard epoxies have coefficients around 5 – 10 times this value. In fact,

104

certain epoxies have expansion coefficients 20 times this value. Steel, however, has a CTE of 13

x10-6

, with stainless steels ranging between 14-18 x10-6

. Because the epoxy has a lower or

equivalent CTE than the metal, the tendency will be for the metal to expand into the epoxy with

compressive force, thus eliminating any possible crevice. Other researchers have tried [20,74] to

eliminate crevice corrosion in high temperature aqueous experiments through the use of

Microstop™ electroplating lacquer as a secondary boundary for the edge of the sample. This

technique is successful for test conditions below about 60 °C, which is the melting point of the

lacquer; however, it will flow and contaminate the test solution at temperatures exceeding the

melting point of the lacquer.

Hollow polytetrafluoroethylene (PTFE), (Teflon™) rod was used to support the epoxy

mounted sample and copper rod, because of the tendency for glass to break when mounted in the

strong epoxy and then heated (again, due to the high coefficient of thermal expansion; the CTE of

glass is about ½ that of the epoxy used. The PTFE rod has a notch cut by belt sander in the neck

to give an added security notch for the epoxy to flow into. Despite the high CTE of Teflon, about

10 times that of the epoxy, Teflon is very damage tolerant and will not fracture, but rather,

compress into the epoxy, forming a yet tighter seal.

Figure 72. Sample configuration for the 95 oC experiments: Cylindrical metal sample set in low

thermal expansion epoxy casting with PTFE tube jacketing a copper conductor

Epoxy

PTFE Tube

Copper conductor

Sample

105

As shown in Figure 17, the sample is attached to a threaded copper rod jacked in PTFE

rod and then cast with the epoxy in a custom casting cup made from a modified metallography

cup and Teflon thread tape. No casting lubricant is used.

The epoxy is cured at 95°C for two hours in a vacuum oven, drastically reducing the

curing time required at ambient temperatures. A slight vacuum (5-15 inches Hg) is pulled on the

samples during this time to discourage porosity formed by residual gas bubbles.

Samples were polished using wetted Silicon carbide metallographic papers in the

following scheme: 240-300-600-800-1200 grit, and then mirror finished using either 5 micron

alumina powder, or 1 micron diamond paste. For certain samples, 60-grit sandpaper was used as

a precursor to remove turning marks or other large blemishes left over from the machine shop.

The finished surface generally includes a few, minute scratches. It was observed that samples left

in the atmosphere would exhibit pitting corrosion after a few days, and polished samples would

exhibit pitting corrosion if left slightly damp for about an hour or so, likely due to differential

aeration. Mounted and polished samples are then placed into the test chamber for

electrochemical testing.

All electrochemical testing at 95°C was carried out in deaerated electrolytes under

flowing, bubbling Argon atmosphere at a slight positive pressure. This is important because the

potential of the system is controlled by oxygen content in the electrolyte. Even very small

oxygen content can change the system behavior and hence, the results. The positive argon

pressure maintains a constant force preventing oxygen contamination over long periods of time,

such as those used to carry out the experiment (5 – 14 days).

106

High Temperature (175°C) Testing

Previous work [74] made use of a sample holder that was fabricated out of PTFE.

Although this seems like a good idea due to the electrical insulating and chemically inert

properties of PTFE, the material itself tends to flow at high temperatures and does not protect the

electronic connection to the working electrode, and tends to create a crevice environment on the

edges of the sample. A new sample holder was designed to utilize fluoro-elastomer coated o-

rings to protect the electronic connection and avoid the massive crevice situation caused by the

all-PTFE sample holder. The design of the sample holder is shown in Figure 73. It is an annular

design with a funnel at the top, which rests below the impeller inside of the autoclave, facilitating

the constant flow of test solution through the annular sample. Two samples are mounted within

the sample holder; one which is electrically connected to the potentiostat, and the other which is

left without an electrical connection as an open circuit test coupon.

107

Figure 73: High temperature annular sample holder prototype with luggini-probe, stirring funnel,

mounting options for two samples and fluroelastomer o-rings

108

The testing rig is complicated to operate, as illustrated in Figure 74, with many possible

points of failure, however, when it works, it works well.

Figure 74: Schematic of the apparatus used to carry out the corrosion experiments at 175°C.

Apart from the use of the autoclave and special reference and counter electrodes, the

procedure is identical to that at 95°C.

Cyclic Polarization

At 95°C and pH 7, it is apparent that there is an effect of inhibitor concentration on the

potentiodynamic behavior of the alloy, as shown by the potentiodynamic curves collected in

Figure 75:

109

Figure 75: Potentiodynamic Scans at 95C for various concentration of amine inhibitors at pH7.

DMA: Dimethylamine. ETA: Ethanolamine

For high concentrations of ethanolamine (0.1M) at both 95 and 175°C, a purely active,

depassivated metal behavior was observed. For all other samples, a quasi-passive behavior was

seen. It is called quasi-passive, because the current densities are much higher than those observed

in traditionally passive films and are likely not controlled by the rates of surface reactions, but by

transport limitation through the precipitated outer layer and the interaction of the metal with the

absorbed amines.

In the case of monoethanolamine, increasing concentrations of amine leads directly to

depassivation evident in the above charts. At a low concentration, negative hysteresis is seen

from potentials up to +600mVSHE, indicating that the material remains passive up to the

maximum potential scanned. A concentration of 0.01M ethanolamine yields a positive hysteresis

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6P

ote

ntia

l, V

(S

HE

)

10-7

10-6

10-5

10-4

10-3

10-2

Current Density, A/cm2

0.001M ETA 0.01M ETA 0.1M ETA 0.1M DMA 0.001 DMA 0.001M ETA / 0.0001M Acetate

110

loop, indicating a repassivation potential (-300 mV SHE) following transpassive behavior. This

indicates that the passive layer may be removed by polarizing in the transpassive region but will

not be able to form in previously passive regions of potential space until it is polarized back

below the repassivation potential.

Table 8: Summary of polarization behavior of ASTM A470/471 in the presence of amine inhibitors.

0.0001M

Acetate

/0.001M

Ethanolamine

0.001M

Ethanolamine

0.01M

Ethanolamine

0.1M

Ethanolamine

Description Purely Passive Behavior

Purely passive behavior / high corrosion currents. May not have gone transpassive.

Depassivating behavior with a repassivation potential of -0.3V SHE

Purely Active Behavior with high corrosion currents. Depassivated.

Corrosion Rate by Rp

0.39 25 28.5 189

Passive Current Density (microamperes)

2.3-5.6 600-700 240-300 N/A. At potentials in the “passive region”, (10

4 or higher)

It is interesting to note that the passive current for 0.01 and 0.001M ETA were not

identical, with the higher concentration yielding a lower current. The mechanism for this is

currently unclear, but may have to do with other components of the system, such as sodium

acetate or acetic acid. Acetate also appears to have an effect on the system performance, but only

in the presence of ethanolamine as seen in Figure 75, using a very small concentration of acetate

appears to result in a less aggressive condition. Previous work by Maeng and Macdonald [75,76]

has shown that acetic acid is deleterious to turbine steel corrosion, resulting in enhanced

dissolution and inhibiting stress corrosion cracking by blunting the crack tip and, in hind-sight,

possibly in depassivation.

111

In the case of dimethylamine, a different picture emerges. The passive currents are lower

than for ethanolamine by several hundred microamperes. The corrosion potentials are all

relatively the same as for ethanolamine. The 0.01M case of DMA is unique and likely caused by

some sort of experimental artifact, such as a defect in the epoxy-metal interface, which initiated

crevice corrosion on the sample. It appears to share the same oxidation peak as the other two

concentrations, at approximately -900 mV vs SHE, but then becomes highly active and does not

exhibit a passivity region.

Repassivating pits are visible in the passivation region for DMA, but not for ETA (Figure

75). This could be due to differences in scan rate, however, repassivating pits, and negative

hysteresis in the cyclic polarization scan is an indication of a more protective passive film, which

is not as susceptible to stable pitting.

It is unlikely that the corrosion potentials were affected by the amine concentration,

because they are offset by the same amount as the oxidation peak around -500mV SHE.

Oxidation and reduction peaks will occur at the same potential relative to SHE, so the shift in

corrosion potentials is likely due to a small variation in reference electrode. Shifts in the

reference electrode, however, have been observed in our lab as much as 5 mV.

Note that while the corrosion potentials for this work are similar to those measured by the

previous investigator [74], the potentiodynamic curves are markedly different. Previous work

shows a massive oxidation peak followed by a much lower current passive region, while this

work reveals a much smaller activation region. One possible reason for this is the decreased

polarization rate for the current work, but it is more likely to be due to the large crevice formed

by the PTFE sample holder used at 175°C.

112

Table 9: Summary of corrosion rates and passive current densities for ASTM A470/471 in the

presence of dimethylamine in simulated phase transition zone of a low pressure steam turbine at pH

7.

0.001M Dimethylamine 0.01M Dimethylamine 0.1M Dimethylamine

Description Purely passive behavior Anomalous active

behavior

Purely passive behavior

Corrosion Rate by

Rp (mpy)

16 8 10

Passive current

density

(microamperes)

25-64 28-120 22-48

The high current, totally active corroding metal results for high concentrations of ETA

were astounding. Physical evidence of heavy corrosion on the sample and repeats of the test with

identical results have confirmed the phenomena.

Interpretation of the high temperature potentiodynamic scans is difficult, however it is

immediately obvious that higher current densities are observed after normalizing for the

difference in surface area. Figure 76-Figure 78 show a negative hysteresis with respect to the

reverse potential scan, indicating that the material is protecting itself somehow. Shockingly, even

with a constant flow rate, the current densities come to a plateau, mimicking passive behavior.

113

Figure 76: 0.01M ETA at 175°C (#19)

Figure 77: 0.1M DMA at 175°C (#27)

Figure 78: 0.001M DMA at 175°C. (#16)

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0

Po

ten

tial

, V

(SH

E)

Current Density A/cm²

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0

Po

ten

tial

, V

(SH

E)


-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0

Po

ten

tial

, V

(SH

E)


114

At high temperature, currents are again much higher for the ETA Case than the DMA

case. Corrosion rates are yet higher than those at low temperature, which is to be expected due to

the temperature enhancement of the kinetics.

Figure 79: Cyclic polarization at 175°C, with 0.1M ETA (#20)

The potentiodynamic results at high temperature followed much the same trend as those

at low temperature; high concentrations of ETA resulted in what appears to be total

depassivation.

Predicted Corrosion Rates based on the linear polarization resistance

Polarization resistance can be a good indicator of corrosion rate, from Ohm’s law; V=IR.

By measuring the linear response about the corrosion potential (point where the current switches

from negative to positive in a positive potential sweep), we can find the polarization resistance as

the slope of the line. This resistance is then used with the corrosion potential to predict the

corrosion current, using the Stern-Geary equation [68]. Because the corrosion reactions involve

electron transfer, we can directly measure corrosion rate by measuring the corrosion current and

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1E-7 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+0

Po

ten

tial

, V

(SH

E)


115

invoking Faraday’s law. This technique is accurate only for a freely corroding metal, however.

In the case of passive materials, the passive current density, indicated in the following diagram, is

of more interest. This is the current density, independent of potential, which is expected to

control the corrosion rate of a passive metal once a passive film has been formed.

Utilizing the built-in analysis software on our potentiostat, corrosion rates were

calculated via the polarization resistance method before any long-term polarization has begun.

Where applicable, the corrosion rate was also measured at the end by the same technique. The

data are summarized in the following table, in mm per year (mpy). (The conversion from

mils/year to mm/year is 0.0254.)

Table 5. Summary of corrosion rates of ASTM A470/471 in the presence of amines.

0.001M Dimethylamine 0.01M Dimethylamine 0.1M Dimethylamine

Description Purely passive behavior Anomalous active

behavior

Purely passive behavior

Corrosion Rate by

Rp (mpy)

16 8 10

Passive current

density

(microamperes)

25-64 28-120 22-48

A corrosion rate of 5 mpy (0.127 mm/yr) is generally considered to be “good” for most

systems. For a few high temperature cases, the corrosion rate appears to have gone to

astronomically high values. This is likely due to localized crevice corrosion or to an artifact

associated with the apparatus, because major damage was not observed on the coupon itself.

Another method of estimating corrosion rates is to assume that the material will be

passive in the long term and consider the passive current density of the system. The problem with

116

using that method in this case is that the passive current densities are in general higher than the

corrosion current densities. That is, active corrosion is continuing to happen in the potential

region that “looks” like passivity. This is possibly because the film is very “low quality” or

porous and is not protecting the surface, other than to provide some transport limitations or

surface area restrictions. These films should not be considered to be protective.

Potentiostatic Polarization

During potentiostatic polarization, in which the potential increases in a step-wise manner,

the current density is measured every 10 seconds, for eight hours per potential step. There is a lot

of information contained in the potentiostatic data, including pitting frequency, the nucleation of

stable pits, and the current density observed at a specific potential.

Corrosion rates in this study appear to be controlled by active metal dissolution at the

solution/metal interface. No passive layer exists, and the current limitations seen are due to

transport limitations of the porous precipitated outer layer. This is demonstrated by the linear

relationship between potential and current density for 95°C (Figure 80) and at 175°C (Figure 81).

117

Figure 80: Current vs. Potential at 95° C. Numbered series correspond to Appendix B.

Figure 81: Current density vs. Potential at 175° C. Numbered series correspond to Appendix B.

118

Note that creation of these figures required omission of pitting or crevice currents.

The slope of the linear fit is exactly 1/R and the corrosion currents can be expressed by

Ohm's Law

(118)

Where i is the current density, A is the surface area of the sample and V is the potential.

Because of this relationship, the corrosion rate can be predicted fairly well at all potentials in the

range if the potential is known. The resistance of the interfaces can be calculated through a

simple slope calculation, and normalized to 1 cm2 surface area to yield the specific resistance,

with higher specific resistances indicating lower steady state corrosion rate.

Table 10: Resistance Curve Fitting Values, 95° C

No. Slope Intercept Fit R (cm2*Ω)

1 0.0005 0.0001 0.9779 2000

5 0.0165 0.0053 0.9927 61

4 0.0009 0.0002 0.9698 1100

9 1.00E-06 3.00E-07 0.943 1000000

23 0.0045 0.0045 0.9713 220

25 -0.0005 0.0004 0.8928 -2000

24 4.00E-05 0.0002 0.136 25000

14 0.0009 0.0004 0.9855 1100

RAVi

1

119

Table 11: Resistance Curve Fitting Values, 175°C

No. Slope Intercept Fit R (cm2*Ω)

8 0.0569 0.0343 0.9956 18

21 0.0024 0.0003 0.9562 420

27 7.00E-07 9.00E-07 0.8998 1400000

16 3.00E-04 4.00E-06 0.8233 3300

19 0.0078 0.0037 0.9391 130

20 0.0009 5.00E-05 0.8867 1100

Visual observations

Samples were photographed after removal from the test chamber. All samples exhibited

some visible degree of corrosion including visible pits, crevice corrosion, and in some extreme

cases (figure), grain boundary attack and grain lift-out.

Figure 82: Visual inspection of ASTM A470/471 coupon (a) before and (b) after polarization tests in

0.1M ETA at 95°C. This test was repeated to verify the incredible corrosion rates observed.

120

0.001M DMA (#1) 0.01M DMA (#4) 0.1M DMA (#5)

0.001M ETA (#26) 0.01M ETA (#25) 0.1M ETA (#24)

Figure 83: Visual observations of the specimen surfaces after exposure to simulated phase transition

zone electrolytes containing three concentrations of DMA and ETA at 95°C for several days,

polarized at values within the quasi-passive range for each.

Note the voluminous corrosion product on the surfaces; this is postulated to be the

precipitated, porous outer layer composed of both iron oxides and absorbed amines. The deposits

were not adherent and tended to slough off when the samples were removed, which may explain

why the resistive outer layer fails to build up in such quantity during flow conditions.

Electrochemical Impedance Spectroscopy (EIS)

Impedance is a powerful tool for investigating the reaction mechanisms that govern the

kinetic stability of passive films within the Point Defect Model. However, it is only an effective

investigation tool if the impedance is high enough that the Faradaic impedance, that is, the

121

impedance established due to electron transfer/mass transfer at the interface is sufficiently large

that it dominates over resistances, such as that arising from the precipitated outer layer, in

determining the total impedance. If this condition is not fulfilled, the Faradaic impedance cannot

be “seen”. During the study of electrochemical reactions at the metal/oxide and oxide/solution

interfaces and the transport of defects across the barrier layer, the impedances due to these

processes is normally sufficiently high to dominate the overall impedance. With depassivated

systems, however, the interfacial impedance is due to active metal dissolution and not due to a

passive film and hence is likely to be low in comparison with the resistance of the outer layer.

The maximum values of impedance measured at any frequency in this study was far too low for

the Faradaic impedance to be sensed. A significant body of impedance data have been collected,

but a method of deconvolving the Faradaic impedance from the electronic resistance and barrier

layer capacitance is not currently known. Therefore, while the impedance data are included in the

digital appendix, however, they are not discussed in depth here.

Discussion / Conclusions

The cyclic polarization curves for ASTM A470/471 steel in dilute monoethanolamine

and dimethylamine solutions both exhibit the shape expected for passivity, however, the current

densities are too high to be considered truly “passive”. For example, passive current densities for

fully passive systems are expected to be on the order of 10-9

A/cm2 to 10

-6 A/cm

2. Currents in the

microampere range are borderline passive, but the measured currents in this study are 10-5

A/cm2

to 10-2

A/cm2. The limiting quasi-passivity current density seen could be due to transport limited

phenomena, which could be investigated using a rotating disc electrode. Due to the fact that there

is an activation peak, however, it is more likely that it is due to the outer layer of magnetite

(Fe3O4) or maghemite (γ-Fe2O3), visible to the naked eye as black deposits, which is in the form

122

of a low-quality, highly porous and disordered non-protective layer. While higher currents could

be due to active crevice corrosion, this is not likely the case in the cyclic polarization because

current becomes independent of potential above the activation potential.

In many, but possibly not all cases, it has been observed that alloy ASTM A470/471 is

not a passive metal in the specific amine environments tested. This is due to a new mode of

depassivation predicted by the Point Defect Model and is a consequence of the potential drop

across the outer layer of the sample. The theory describing potential drop across the outer layer

causing depassivation in metals is discussed in an earlier section in detail.

To reiterate, we note that the voltage drop across a layer of material is defined by ohm’s

law, V = IR (resistive control). If the total current measured by the potentiostat is I and the

resistance of the outer layer is Rol, defined by the resistivity of the outer layer material and

configuration (porosity, etc.), rho and the geometric configuration (A: Surface area, Lol: Outer

layer thickness), we can draw the following conclusions: If the net current through, or impedance

of the outer layer, is too high (or both are too high), then the barrier layer of the passive film

cannot exist, because, according to the Point Defect Model, the barrier layer thickness is

controlled by potential at the barrier layer/outer layer interface. This potential, Vbl/ol = Vapp –IRol,

is a function of the current flowing to a remote cathode and by the resistance of the outer layer.

Thus, if I and Rol are sufficiently large, Vbl/ol may become too small to maintain the barrier layer

and the surface becomes depassivated. This does not mean that current will flow unimpeded,

since the surface is still covered by the porous outer layer, but the expectation is that the corrosion

rate will be significantly higher than that for the fully passive state in which the barrier layer is

present.

123

Figure 84: Schematic of the dependence of the barrier layer thickness as a function of increasing

current or specific resistance of the outer layer.

One corroborating piece of evidence that depassivation occurs via IR drop is the

discrepancy between the high temperature and low temperature data for ethanolamine. There is

an additional difference between the two experiments apart from the temperature; the high

temperature sample is kept under a state of constant flow by the impeller in the high temperature

rig, which tends to mechanically remove the precipitated outer layer, passing it as particulate into

the pressure relief valve of the apparatus. If the outer layer is as loosely attached as we have

observed at low temperature, the tendency would be for the outer layer to be swept away with the

flow, reducing the resistance it provides and keeping the IR-drop to a minimum, thus reducing the

corrosion rate by allowing the passive film to form. We must reiterate, however, that we are

hesitant to call anything measured in this study “passive”, simply because the corrosion rates are

so high.

Modeling of amine concentrations in various stages of the steam-side of a power station

[77] was performed in tandem with this study, and although that study indicates that the expected

124

concentrations of amines during operation was far below what was prepared in the laboratory,

during shutdown, all constituents of the solution will evaporate rapidly, except for

monoethanolamine, which, having a very low vapor pressure, will concentrate in the residual

moisture, theoretically to levels high enough to depassivate the steel. This effect is likely a major

contributor to the corrosion damage seen in turbine systems where amines in general, and

specifically, monoethanolamine is employed.

125

Chapter 5

Characterization of Naval Advanced Amorphous Coatings (NAAC)

Introduction

NAACs are a form of high velocity oxy-fuel (HVOF) coating, which are employed in

maritime environments for their exceptional corrosion and wear resistance. One particular

application is the coating of the top deck surface of aircraft carriers. The texture of the HVOF

coating provides a naturally high friction and high-durability surface enhancing safety of on-deck

personnel and enhancing the ability of aircraft wheels to grip what would otherwise be a slick

surface. The advantage of using a HVOF coating over for instance embedded abrasive particles

such as employed in other non-slip surfaces is found in its far superior durability and corrosion

resistance. The performance of a HVOF coating is entirely controlled by its microstructure. If

the coating is porous, it will not provide a hermetic seal against the salt water environment and

risks spallation upon impact due to delamination between the coating and the metal substrate. In

addition, there is a disadvantage in terms of corrosion resistance if the coating is not sufficiently

amorphous due to the existence of preferred crystallographic orientations and grain boundaries

(and other inhomogeneity) where corrosion is likely to initiate.

126

Figure 85: Manufacture of HVOF coating

Experimental

Samples were received as 12”x6” steel plates with high velocity oxidizing fuel coatings.

Plates were sectioned using electrical discharge machining (EDM) with a brass wire electrode

into eight 3”x3” squares for electrochemical testing and 6 triangular pieces for SEM analysis

from the corners, according to Figure 86. Individual pieces were marked on the uncoated side

using a vibrating tool with the sample designation prior to cutting.

Figure 86: Sectioning Schematic

The SEM pieces were chosen to provide three faces parallel to the same axis in case of a

non-isotropic microstructure[78].

127

SEM samples were mounted in profile in phenolic resin for polishing and then polished

according to the following table, adapted from a published recipe for preparing metallographic

samples composed of ductile substrates with hard coatings[79].

Table 12: Polishing scheme

Step Abrasive Rating Platter RPM

Duration Direction Sample rpm

Water Force

1 SiC 240 grit 250 10 min (to flat)

Contra 40 On 5 lbs.

2 SiC 600 grit 250 5 min Contra 40 On 5 lbs.

3 Diamond on Diamat cloth

1μm 250 6 min Contra 40 off 5 lbs.

4 α-alumina on final-A cloth

.05 μm 130 6 min Contra 40 off 4 lbs.

Samples were then cleaned ultrasonically for 10 minutes in room temperature deionized

water, rinsed in either ethanol or isopropyl alcohol and hot-air-dried. No chemical or

electrochemical etching was performed prior to observation.

A Hitachi S3500N scanning electron microscope (SEM) was used to obtain all of the

electron micrographs. Specific SEM settings for individual micrographs can be read from the

black bar in each figure but are generally captured with 20keV accelerating voltage and a 15mm

working distance, which is the optimal accelerating voltage and working distance for the energy

dispersive x-ray spectroscopy (EDS) detector that was used.

The sample plates were photographed in order to document the location of each

electrochemical measurement. The following figures document these photographs.

Electrochemical measurement sites can be seen as red-brown stains, and some residual salts (as

were seen in the case of a leak) appear as white-yellow marks. The triangular missing sections

were taken for microscopy purposes.

128

Figure 87: Plate “B” following sectioning and electrochemical testing

Figure 88: Plate “F” following sectioning and electrochemical testing

Figure 89: Plate “H” following sectioning and electrochemical testing

129

Figure 90: Plate “J” following sectioning and electrochemical testing

The above figures are summarized in Figure 91, below.

Figure 91: Electrochemical Measurement Locations

SEM Imaging

SEM images were captured normal to the coating surface, revealing that the exterior

morphology cannot be used to discriminate between the plates. Figure 92-Figure 95 illustrate the

130

exterior morphology, which reveals microcracking and unmelted metal particles on the surface,

and there is no apparent difference between the plates.

Figure 92: Normal orientation B-plate HVOF coating SEM image at 100x

131

Figure 93: Normal orientation F-plate HVOF coating SEM image at 100x

Figure 94: Normal orientation H-plate HVOF coating SEM image at 100x

Figure 95: Normal orientation J-plate HVOF coating SEM image at 100x

132

Images of each plate were captured in profile at 100x to give a representative overview of

the microstructural morphology (Figure 96-Figure 99). Note that Figure 97 has been rotated 180°

for consistency with the other images and that the interface is very hard to see due to contrast

limitations. The images are oriented with the plastic mounting material at the top, the coating in

the middle and the steel substrate at the bottom.

Figure 96: B plate 100x magnification SEM Figure 97: F Plate 100x magnification SEM.

Figure 98: H Plate 100x magnification SEM Figure 99: J Plate 100x magnification SEM

133

Detail images of the defects were also captured, illustrating the interface delamination

and porosity issues

B-plate detail.

Note that these images are oriented 180 degrees with respect to the previous micrographs.

Figure 100: B plate, location 1 interface detail

900x magnification SEM

Figure 101: B Plate, location 1 3000x defect

detail magnification SEM.

134

Figure 102: B Plate, location 1 interface detail

800x magnification SEM

Figure 103: B Plate, location 2 1500x interface

detail magnification SEM

J-plate Detail

Figure 104: J plate, location 3 coating detail 120x

magnification SEM

Figure 105: J Plate, location 3 defect detail 450x

magnification SEM – note cracks

135

Figure 106: J Plate, location 3 800x crack detail

magnification SEM

Figure 107: J Plate, location 2 5000x crack detail

magnification SEM

In general, the J plate has somewhat light porosity and microcracking while the B plate

exhibits a medium porosity with some adhesion problems at the plate-coating interface, and the H

plate exhibits a severe porosity with further issues at the coating-plate interface. Plate B was

intended by the manufacturer to be a “pristine” sample, against which to compare the other

defective coatings. However, the B plate received contained a large amount of defects, as

evidenced by SEM imaging and electrochemical testing. The F plate image above was taken

from the middle-left region of plate F, where the coating is highly defect free. The right side of

plate F contained the following defect formers: oil, o-ring lubricant and sea water, arranged as

shown in Figure 108:

136

Figure 108: F plate preparation

Because this information was not provided at the outset of the investigation, some

confusion was raised concerning the identity of the plates and the significant scatter in the EIS

data. However, thanks to Figure 70 and a careful examination of the SEM evidence, the true

defect profile of the coatings was determined, and the EIS data was then interpretable.

Experimental

Impedance spectra were collected at open circuit potential at room temperature under

anoxic conditions. An EG&G three-electrode flat cell was used, with a calomel reference

electrode (0.244V vs. SHE). As shown in Figure 109-Figure 112, to the human eye, behavior

varied across plates without much of a discernible pattern.The designation of each curve, for

instance “B3-1” refers to the first EIS spectrum collected at location 3 on plate B, as indexed in

137

Figure 91. Because of the aforementioned scatter in the data, a diamond core-drill was used to

extract SEM samples from each location where EIS was measured. Unfortunately, this method

resulted in cracking the microstructure, however, the general microstructure is visible in each

image, as shown in Figure 114.

Figure 109: Nyquist Plot for plate B HVOF

Figure 110: Nyquist Plot for plate F HVOF

-700

-600

-500

-400

-300

-200

-100

0

Z''

(Oh

ms)

25002000150010005000

Z' (ohms)

B3-1 B3-2 B6-1 B6-2 B7-1

138

Figure 111: Nyquist Plot for plate H HVOF

Figure 112: Nyquist Plot for plate J HVOF

Impedance Modeling

A non-physical analog circuit was constructed with two time constants produced by two

constant phase elements in parallel with resistors, as indicated in Figure 113:

-700

-600

-500

-400

-300

-200

-100

0

Z''

(Ohm

s)

25002000150010005000

Z' (Ohms)

J1-1 J1-2 J1-3 J4-1 J4-2 J5-1 J6-1 J6-2

139

Figure 113: Mathematically Convenient Impedance Circuit with Two Time Constants

The impedance is defined:

(119)

Where the complex impedance, Z is in Ohms , R1 and R2 are resistors in ohms, Q1 and Q2

are the coefficients of the constant phase elements, in S/s, i is the complex constant, ω is the

angular frequency in radians/s, and n is a unitless exponent ranging between 0 (pure resistor

behavior) to 1( pure capacitor behavior). The time constants are calculated by multiplying the

capacitance in Farads by its parallel resistance in Ohms, producing a time constant, whose units

are seconds; the inverse of which is Hz, which is the frequency at which the process is occurring.

Because Q is only a pure capacitance at n=1, the capacitance must be calculated;

(120)

And therefore,

(121)

Because of the additive property, it is impossible to differentiate mathematically between

the two time constants; indexes 1 and 2 can be interchanged without changing the value of the

total impedance. Therefore, a convention must be made once the curve fits have been performed.

The larger τ value will be named the “slow” process and the smaller value will be named the

“fast” process.

140

It was theorized from the outset that a transmission line such as that developed by

Macdonald[80] for corrosion and later enhanced by Bisquert[81–83] could be used to model a

cylindrical pore, however, the transmission line model, while it was excellent at fitting the data,

failed to yield sufficient information to discriminate between measurements, likely due to over-

determination of the model and the inherent differences between the model assumption of a

cylindrical pore and the rather chaotic and diverse microstructures encountered in this study.

The aforementioned Ellis2 software developed out of necessity during this course

of study was used to fit the impedance data. The error of the fitness function was weighted using

the reciprocal of the impedance values at each frequency, yielding a better fit result to the un-

weighted case. Finally, time constants were calculated as in (121) for each impedance spectrum

and plotted in Figure 114.

Discussion

Tabulating and graphing the time constants from the impedance curve fits revealed an

impedance – microstructure relationship that can be used as a sensor to determine the quality of a

coating. If the “fast” time constant is determined to be above 0.35, it is likely that the coating is

hermetic, while a value less than 0.15 indicates a delaminated specimen, likely due to the

exposure of the substrate material to the solution. For intervening values of the “fast” time

constant, a combination of the “Fast” and “Slow” time constants are inversely correlated to

increasing porosity, as indicated by the black arrow. The “fast” and “slow” processes are linked

in terms of porosity the middle range (from 0.15 to 0.30 seconds) because of the surface area

exposed for each morphology varies.

141

Figure 114: Microstructure - Impedance map

Conclusions

It was indeed possible to derive a relationship between the impedance and the

microstructure, albeit, one that is not physically modeled. Although this result may not be of

much academic interest, it can be adapted into service as a sensor for nondestructively

determining the local quality of a HVOF coating. Systematic preparation of ideally defective

microstructures and the indexing of impedance measurements with a quantitative microstructural

142

measurement would provide a more quantitative correlation and improve the sensor’s value

tremendously. The major draw-back to this type of a sensor is the time required to make and

analyze individual measurements; about 30 minutes is required to collect each spectrum down to

0.1 Hz. Employing a multiple-frequency EIS measurement technique could reduce the amount of

time required for each measurement, however, it is a far-cry from an ideal sensor in that respect.

Chapter 6

Final Conclusions and Suggestions for Future Work

In conclusion, three technologies for corrosion prevention were investigated during the

course of this work. The effect of nitrogen on the passivity of chromium-bearing alloys was

modeled by examining the possible substitutional crystallographic defects that would occur with

the introduction of nitrogen to the Cr2O3 passive film, identifying N(3-) substituting on the

oxygen vacancy to be the most likely possibility. With the location of N in the film identified, a

set of defect reactions was proposed to account for the ingress of nitrogen into the passive film at

the metal/film interface and its subsequent evolution to ammonia at the film/solution interface.

The rate constants for these reactions were derived by the method of partial charge transfer and

reported. Considering the effects on other point defects within the film, in the framework of the

Point Defect Model of the passive state and the solute vacancy interaction model, the proposed

model correctly predicted that nitrogen bearing passive films should be both thinner and exhibit

lower steady state current densities in comparison to films bearing no nitrogen.

143

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147

Appendix A: Cr+N EIS Curve Fits

Figure 115:Optimized Impedance Spectrum for 0%N, pH 10, 0.072VSHE

-2.0x106

-1.0

0.0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_0

148

Figure 116:Optimized Impedance Spectrum for 0%N, pH 10, 0.06 VSHE


-1.5x106

-1.0

-0.5

0.0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_1

-1.5x106

-1.0

-0.5

0.0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_2

149

Figure 118: Optimized Impedance Spectrum for 0%N, pH 10,0.26 VSHE

Figure 119: Optimized Impedance Spectrum for 0%N, pH 10, 0.36 VSHE

-1.2x106

-0.8

-0.4

0.0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_3

-600x103

-400

-200

0

200

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_4

150



-200x103

-100

0

100

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_5

40x103

20

0

-20

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-80

-60

-40

-20

0

Phase A

ngle

(Degre

es)

-60

0

x10

3

-300

x10

3

11 -1-1 -3-3

00_10_6

151

Figure 122: Optimized Impedance Spectrum for 8.9%N, pH 7,0.06 VSHE


-400x103

-200

0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_1

-400x103

-200

0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_2

152



-400x103

-200

0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_3

-400x103

-300

-200

-100

0

100

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_4

153



-200x103

-100

0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_5

-80x103

-40

0

40

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-60000

-50000 11 -1-1 -3-3

98_7_6

154



-0.8x106

-0.4

0.0

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_10_2

-800x103

-600

-400

-200

0

200

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

106

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_10_3

155



-600x103

-400

-200

0

200

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

104

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_10_4

-200x103

-100

0

100

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

105

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_10_5

156


40x103

20

0

-20

Impedance, (O

hm

s)

10-1

100

101

102

103

104

105


102

103

104

Modulu

s, |Z

| (O

hm

s)

-1.2

-0.8

-0.4

0.0

Phase A

ngle

(Degre

es)

-10

10

x10

3

-100

x10

3

11 -1-1 -3-3

98_10_6

157

Appendix B: Potentiostatic Curves for ASTM 470/471A Steel with Various

Concentrations of Amines

All potentials are versus standard hydrogen reference potential. All currents are total

current, and not current densities. The number listed in parenthesis in the figure caption is the

index number for the experiment, as indicated in Figure 80and Figure 81.

Figure 133: (#01): 95 C 0.001M ETA/ 0.05M Acetate, pH 6.86

158

Figure 134: (#05): 95 °C 0.1M ETA/ 0.19M Acetate, pH 7.40

Figure 135: (#04): 95 °C 0.01M ETA/ 0.097M Acetate, pH 6.70

159

Figure 136: (#08): 175 C 0.001M ETA/ 0.11M Acetate, pH 7.01

Figure 137: (#09): 95 °C 0.001M NH4OH/ 0.098M Acetate, pH 10.59

160

Figure 138: (#21): 175 °C 0.001M NH4OH/0.1M Acetate, pH 6.26

Figure 139: (#23): 95 °C 0.1M ETA/ 0.098M Acetate, 6.49

161

Figure 140: (#26): 95 °C 0.001M DMA/ 0.107M Acetate, pH 6.94


162

Figure 142: (#24): 95 °C 0.1M DMA/ 0.098M Acetate,pH 6.94


163

Figure 144: (#16): 175 C 0.001M DMA/ 0.107M Acetate, pH 6.96

164


Figure 146: (#18): 95 °C 0.001M ETA/ 0.0001M Acetate,pH 9.64

165

Figure 147: (#19): 175 °C 0.01M ETA/ 3.46x10-5

M Acetate, pH 6.98


166

VITA

Matthew Logan Taylor

Matthew Taylor was born in Albuquerque, New Mexico on June 27th, 1982. His early life was

very rich with learning, as his father is an engineer, and his mother is an artist. As a voracious reader with

an experimental mind, it was curiosity of the world, both past and present, and the way things work that

characterized his early life. He spent his early years in San Angelo, Texas before moving to Atlanta,

Georgia where he graduated from Parkview high school, captaining both the Science Olympiad team and

the state champion DOE science bowl quiz team in 2000. He earned a bachelor’s of science degree in

materials science and engineering from the Georgia Institute of Technology in 2004. While at Georgia

Tech, he had his first taste of real laboratory work, studying high strain rate phenomena under the

instruction of Naresh Thadhani, learning how to operate an ancient Hitachi SEM, trigger high speed

cameras and oscilloscopes, and make ultrasonic measurements and the joy of getting his hands dirty

fabricating parts for experimental apparatus in the machine shop and cleaning up the copious exploded

debris generated from each experiment. For his senior thesis, he and two other partners developed an

apparatus to test the efficacy of a sol-gel technique to coat diatom frustules with titania and carbon for use

as a water-cracking UV-photo-catalyst under the supervision of Ken Sandhage. During his undergraduate

years, Matthew sang in the chamber choir, most notably performing the role of “Death” in Distler’s

“Totentanz” during a performance in Spivey Hall. In early 2005, he moved to Reno, Nevada, beginning

his graduate career studying the hydrogen permeation and impedance properties of alloy-22, a high nickel

alloy intended for use in protecting nuclear waste from the environment. During his time at UNR, he

mentored an undergraduate research assistant, Jason Strull, who is currently pursuing a PhD in chemical

engineering. After one year studying nonaqueous corrosion of pipeline steels at The Georgia Institute of

Technology under the direction of Preet Singh, and instructing a high-school student studying corrosion,

Matthew transferred to The Pennsylvania State University to perform the studies described in the

document above. During the course of his education at Penn State, mentored by Digby Macdonald, he

was afforded a wonderful opportunity to study at INSA de Lyon in France under the instruction of

Bernard Normand for one year. It is his sincerest hope to enkindle the romance of science for future

generations and leverage the fruits of scientific discovery for the benefit of mankind.

Documents

Technological Aspects of Corrosion Control in Metallic Systems