XRD Excercises

8/9/2019 XRD Excercises

1/23

X-ray diffraction exercises

Dr. Sharon Mitchell and Prof. Javier Pérez-Ramírez

Institute for Chemical and Bioengineering, ETH Zurich, Switzerland

E-mail: [email protected] • http://www.perez-ramirez.ethz.ch

Characterization of catalysts and surfaces Thermal methods


2/23

a) b)

c) d)

b

a

Problem 1

Introduction to thermal analysis X-ray diffraction excercises

Using the 2D lattice given below draw planes corresponding to a) (010) b) (200), c) (110),

and d) (120).


3/23

Problem 2


The diffraction pattern of copper metal was measured with X-ray radiation of wavelength of

1.315 Å. The first order Bragg diffraction peak was found at an angle 2 of 50.5°. Calculate the

d-spacing between the diffracting planes in the copper metal.

Bragg’s law n=2dsin = 1.315 Å.

2 = 50.5°

= 25.25°

d = /2sin

d = 1.54 Å

Note: In order to calculate the d-spacing using Excel, theta must be in radians.


4/23


5/23

Problem 3


n / radians 2 /

1 0.183 10.52 0.372 21.33 0.576 33.0

4 0.813 46.65 1.139 65.2


6/23

Problem 4


The quality of the experimental pattern shown below is very poor and only the strongest

reflections are visible. Why might the signal to noise ratio be so low? If this is due to a bad data

collection strategy, how might this be improved?

Intensity of simulated pattern isarbitrary, scaled for ease of visualization cannot directlycompare intensities withexperimental pattern.

Why is it important to obtain agood signal to noise ratio?

What factors contribute to an

experimental pattern?


7/23

Problem 4


1) Sample. 2) Background 3) Noise

+ +

Crystallinity/disorder

Quantity

Multiple phases

Amorphous

Particle size

Variation of intensity

with Bragg angle.

Detector dependent

e.g. Bragg-Brentano

geometry greater

divergence of X-ray beam

at higher 2 .

Incident beam

Fluctuations in intensity of

incident X-rays.

Inelastic scattering /

absorbance.


8/23

Problem 4


How could we improve the data collection strategy?

Sample preparation: Flat sample surface.

Ensure sample fully

illuminated by incident X-ray

beam.

Instrumental: Ensure incident beam monochromatic.

Focusing of incident and diffracted beam using slits.

Choice of wavelength.

Higher incident beam intensity (synchrotron).

Measurement parameters:

Reduction of step size.

Increased collection time.

Mo Kα (= 0.71073 Å) and Cu Kα (= 1.54178 Å) most

common laboratory X-ray sources. What influence does

have on diffraction pattern?


9/23

Problem 4


Mo Kα (= 0.71073 Å) and Cu Kα (= 1.54178 Å) most common laboratory X‐ray

sources. What influence does have on diffraction pattern?

Shorter less absorption Mo preferred for strongly absorbing samples.

Shorter reflections closer together (Bragg relationship). more reflections are

observable for 2


10/23

Problem 5


Figure 1 shows the X-ray diffraction pattern of nanocrystalline silicon (n-Si) which exhibits

significant line broadening with respect to that of bulk silicon (shown for comparison). Data

was collected using Cu Kα radiation, = 1.54178 Å.

i) Describe what factors might contribute to the line

broadening. How could this data be used to

estimate the size of the nano-crystallites?

Bobs = B instr + Bsample = B instr + Bsize + Bstrain

Binstr

-Dependent on experimental set up

e.g. Monochromaticity of incident

beam, beam divergence etc.

-Direct relationship with θ .

- Determined by measurement of

suitable reference.

Bsample = Bsize + Bstrain

-Crystals have finite size (not infinitely periodic)

Bsize

Lattice imperfections (e.g. vacancies, substitutions,

dislocations) Bstrain


11/23

Problem 5





i) Describe what factors might contribute to the line

broadening. How could this data be used to

estimate the size of the nano-crystallites?

Bobs = B instr + Bsample = B instr + Bsize + Bstrain

Scherrer equation relates peak width to crystalline domain size

Bstrain Frequently assumed to have the following dependence:

Bstrain(2θ ) = 4 · ε0 ·tanθ

• Possible to gain information about sample if instrumental

parameters are known.

Bsize 1/cosθ

Bstrain tanθ

cos2

L

K B

size

K = Scherrer constant, L = apparent ‘size’ of the crystalline domain / ÅB = Full width half maximum /°

λ = Wavelength / Å

ε0 =Δd/d


12/23

Problem 5





cos

2 L

K B

size

cos size B

K L

Assuming K = 0.89 (i.e. for spherical crystalline domains).

Then the size of the crystalline domains perpendicular to (331), L(331) = 1.6 Å.

ii) For the reflection at 2 = 76.452°, the FWHM, B, is

found to be 1.0886° after correction for instrumental

contributions. Using the Scherrer equation estimate

the size of the nano-crystalline domains.


13/23

Problem 5





iii) Why might the size you calculated differ from the average

particle size observed by electron microscopy?

• Size of crystalline domain might not be clear from electron

microscopy studies.

• Crystalline domainsize may not behomogeneous.

Gives average value perpendicular to reflection

studied. May not be the same in all directions.

• Inaccuracies based on calculation e.g. incorrect

estimation of instrumental / strain broadening etc.

• Crystalline domains may not be

spherical.


14/23


15/23


In an effort to design catalysts for the CO2 reforming of methane, Co-Ce1−xZrxO2 catalysts with various ratiosof Ce/Zr were prepared by the co-precipitation method from the corresponding metal nitrates. Ce(NO3)3·6H2O,

Zr(NO3)4·5H2O and Co(NO3)2·6H2O in stoichiometric ratios. The CoO content was fixed at 16 wt.%. The PXRD of

the materials obtained is shown in Figure A. The PXRD patterns of the 4 crystalline phases, cubic fluorite

structure of CeO2, the cubic and tetragonal phases of ZrO2 and the catalytic phase Co3O4 identified by theauthors are shown in Figure B.

N. Wang, W. Chu, L. Huang, T. Zhang, J. Natural Gas Chem. 19 (2010), 117.

Co3O4

i) Comparing the reflections in Figure B, what are the

best reflections:

a) to identify the presence of each phase?b) to differentiate between the tetragonal and cubic

forms of ZrO2.

Problem 6

• To assign diffraction patterns of multi-phase materials

easiest to identify the most intense reflections first.• Reflection should not overlap with that of another

possible phase.• If a phase is present all reflections should be present, but weaker reflections

may not be visible if signal to noise ratio is low.


16/23


Problem 6

ii) Based on the information in Figure B, assign the reflections in Figure A as far as you can.

In an effort to design catalysts for the CO2 reforming of methane, Co-Ce1−xZrxO2 catalysts with various ratiosof Ce/Zr were prepared by the co-precipitation method from the corresponding metal nitrates.

Ce(NO3)3·6H2O, Zr(NO3)4·5H2O and Co(NO3)2·6H2O in stoichiometric ratios. The CoO content was fixed at 16

wt.%. The PXRD of the materials obtained is shown in Figure A. The PXRD patterns of the 4 crystalline

phases, cubic fluorite structure of CeO2, the cubic and tetragonal phases of ZrO2 and the catalytic phaseCo3O4 identified by the authors are shown in Figure B.

Co3O4and CeO2, ZrO2


17/23


Problem 6

iii) Are any reflections unaccounted for? What might be the origin of these reflections?

Circled reflectionsunaccounted for inreported phaseassignment

In an effort to design catalysts for the CO2 reforming of methane, Co-Ce1−xZrxO2 catalysts with variousratios of Ce/Zr were prepared by the co-precipitation method from the corresponding metal nitrates.





18/23


Problem 6

iv) By looking at the variation in peak broadening, what can we tell about the variation in crystallinity withcomposition?





• Narrowest reflections observed for single phase oxides (e.g. CeO2 or

ZrO2).• Assuming identical synthesis conditions in all cases this is unlikely

to be due to large differences in crystal domain size as time for

crystal growth would be equivalent Greater crystallinity.

• At intermediate compositions (solid solutions of Co-Ce1−xZrxO2 ) thereflections are broadened.

• Substitution of Zr into the CeO2 lattice or vice versa causes

imperfections in the infinite lattice (due to differing size) strain

broadening.


19/23


Problem 6

v) At which composition might the catalytic Co3O4 phase have the smallest crystallite size?





• Content of CoO during coprecipitation is fixed at 16 wt.%.

• Extent of incorporation into the Ce1−xZrxO2 structure dependent on

the phase diagram and on the relative rates of precipitation of the

crystalline components.

• Reflections of Co3O4 phase most intense for materials with high

ZrO2 contents. (larger) crystalline domains of Co3O4.

• Assuming that all Co(NO3)2·6H2O is precipitated the smallest

reflection observed for CeO2:ZrO2 = 4:1 probably smallest

crystallite size.


20/23


Problem 7The (hydrothermal) reaction of MgO and Al2O3 is a green chemistry route for the preparation of hydrotalcite, alayered metal hydroxide and commonly used precursor for the preparation of Mg xAlO a well known solid base

catalyst. The PXRD patterns compared below show the PXRD patterns of the materials obtained following

hydrothermal reaction under three different conditions: 1) Reaction in conventional oven at 100°C, 2) reaction

in a microwave oven at 100°

C and 3) Reaction in a microwave oven at 180°

C. Each reaction was undertakenfor 120 minutes with equivalent quantities of MgO, Al2O3, and H2O.

S. Mitchell, I.R. Baxendale, W. Jones, Green Chem. 10 (2008), 629.

• Same reflections observed in both diffraction patterns No

variation in phase selectivity with heating method.

• Reflections in the material obtained by conventional heating

broader than those observed in the material prepared using

microwave irradiation.

• Use of microwave irradiation larger crystallite size/ higher

crystallinity.

Improved heating (rapid and homogeneous faster

nucleation and growth?

i) Comparing the PXRD pattern of the materials obtained under conditions 1 and 2, what can we say about the

influence of the heating method (conventional or microwave oven) on the reaction?


21/23


Problem 7The (hydrothermal) reaction of MgO and Al2O3 is a green chemistry route for the preparation of hydrotalcite, alayered metal hydroxide and commonly used precursor for the preparation of Mg xAlO a well known solid base

catalyst. The PXRD patterns compared below show the PXRD patterns of the materials obtained following

hydrothermal reaction under three different conditions: 1) Reaction in conventional oven at 100°C, 2) reaction

in a microwave oven at 100°

C and 3) Reaction in a microwave oven at 180°

C. Each reaction was undertakenfor 120 minutes with equivalent quantities of MgO, Al2O3, and H2O.

ii) By comparison of the reaction under conditions 2 and 3, what can we determine about the influence of

temperature on the materials obtained?

• New reflections observed on increasing the temperature

to 180°C.

Change in phase selectivity. New phase formed at high

temperature (e.g. thermal stability).

• Although similar in appearance closer observation shows

that some reflections shifted to higher diffraction angles,some to lower and some remain in the same position.

Structural differences in materials obtained at 100 and

180°C.


22/23


Problem 7iii) The layers in hydrotalcite may stack with different arrangements leading to ‘polytypes’ which may beidentified by PXRD. The positions and relative intensities of the reflections expected for the two most common

arrangements (A and B) are summarized in the table below. Try to confirm if hydrotalcite was formed in any of

the reactions and if so in which polytype.Polytype A Polytype B

(hkl) 2 / ° Intensity 2 / ° Intensity

(003) 11.6 Strong 12.1 Strong(006) 23.3 Strong 24.2 Strong

(101) ‐ ‐ 34.2 Medium(012) 34.9 Strong ‐ ‐(104) ‐ ‐ 37.9 Strong(015) 39.3 Medium ‐ ‐

(107) ‐ ‐

45.0 Weak(108) 46.8 Medium ‐ ‐(1010) 53.0 Weak 54.0 Weak(110) 60.7 Medium 60.7 Medium(113) 62.1 Medium 62.2 Medium

• Polytype A formed at 100°

C.• At 180°C predominant phase formed is polytype B.

• Some reflections corresponding to polytype A also

observed.


23/23


Problem 7iv) This data was collected using monochromated Cu Kα radiation (λ = 1.5418 Å). Using the Bragg relationship(n λ = 2dsin ) calculate the d-spacing associated with the (003) reflection of hydrotalcite.

• For the (003) reflection 2 = 11.6°.

• d=n λ/2sin

• d=7.63 Å.

How does this relate to the lattice parameter, c ,for this hydrotalcite?

c = 3*d = 22.88 Å.

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