Stable Isotopes: principles, integration and applications

Stable isotope

Long-l ived radioisotope

Short-l ived radioisotope

16

P2715

Si26Si2514

Al25Al24Al2313

Mg24Mg23Mg22Mg21Mg2012

Na23Na22Na21Na20Na1911

Ne22Ne21Ne20Ne19Ne18Ne1710

F21F20F19F18F17F169

O20O19O18O17O16O15O14O138

N19N18N17N16N15N14N13N12N117

C18C17C16C15C14C13C12C11C10C9C86

B17B15B14B13B12B11B10B9B85

Be14Be12Be11Be10Be9Be8Be7Be64

Li11Li9Li8Li7Li6Li53

He8He6He5He4He32

IsotopesTDH1

1211109876543210

Neutron Number (N)

S40S39S38S37S36S35S34S33S32S31S30S29

P39P38P37P36P35P34P33P32P31P30P29P28P27

Si36Si35Si34Si33Si32Si31Si30Si29Si28Si27Si26

Al34Al33Al32Al31Al30Al29Al28Al27Al26Al25

Mg32Mg31Mg30Mg29Mg28Mg27Mg26Mg25Mg24

Na33Na32Na31Na30Na29Na28Na27Na26Na25Na24Na23

Ne27Ne26Ne25Ne24Ne23Ne22

F25F24F23F22F21

O24O23O22O21O20

N21N20N19

C19C18

B17

24232221201918171615141312

Neutron Number (N)Neutron Number (N) http://www2.bnl.gov/CoN/

Prot

on N

umber

(Z)

Isobars

Isotopes

Isotones

Brief history

• By year 1800 ~39 elements were known • John Dalton “all matter is made of atoms” led to

hypothesis that equal volume of gas contain equal numbers of particles (Avogadro, 1811), or that atomic weights are multiples of the mass of H (Prout, 1815).

• 1870 Mendeleev related chemical properties with atomic weights producing the periodic table.

• Rayleigh and Ramsay discover Ar in 1894 and He in 1895, by using the periodic table predictions.

• By 1900, periodic table complete up to U. However, atomic weights of some elements did not increase with atomic # and Prout’s hypothesis was disproved. TW Richard (1900) first measure different atomic weights in Pb.

Brief history

• 1895-1897 discovery of X-rays, cathode rays (electrons) and Becquerel (1896) discovered the spontaneous emission of radiation by U.

• In 1914, Frederick Soddy, reworked Dalton’s hypothesis of atoms by stating that the place of an element in the periodic table can accommodate more than one atom. He called these atoms “isotopes” which means “same place”.

– Isotopes = Nuclides of a single element that have

different atomic weights

Brief history

• JJ Thomson used a modified “cathode ray tube” (first mass spectrometer) to measure the charge-to-mass ratio q/m (q/z) of gas particles (electrons). By 1913 identified the first isotopic masses of Neon (20 and 22).

JJ Thomson’s cathode ray tube, 1897

• In 1919 Aston’s mass spectrograph allowed to detect 212 of the 287 naturally occurring isotopes. Nobel prize 1922.

• It was 1932 when Chadwick discover the missing puzzle piece: neutrons. Isotope existence was explained.

Brief history

FW Aston’s photograph

plate, 1919. Elements

with same mass will hit

the same spot

Stable isotope

Long-l ived radioisotope

Short-l ived radioisotope

16

P2715

Si26Si2514

Al25Al24Al2313

Mg24Mg23Mg22Mg21Mg2012

Na23Na22Na21Na20Na1911

Ne22Ne21Ne20Ne19Ne18Ne1710

F21F20F19F18F17F169

O20O19O18O17O16O15O14O138

N19N18N17N16N15N14N13N12N117

C18C17C16C15C14C13C12C11C10C9C86

B17B15B14B13B12B11B10B9B85

Be14Be12Be11Be10Be9Be8Be7Be64

Li11Li9Li8Li7Li6Li53

He8He6He5He4He32

IsotopesTDH1

1211109876543210

Neutron Number (N)

S40S39S38S37S36S35S34S33S32S31S30S29

P39P38P37P36P35P34P33P32P31P30P29P28P27

Si36Si35Si34Si33Si32Si31Si30Si29Si28Si27Si26

Al34Al33Al32Al31Al30Al29Al28Al27Al26Al25

Mg32Mg31Mg30Mg29Mg28Mg27Mg26Mg25Mg24

Na33Na32Na31Na30Na29Na28Na27Na26Na25Na24Na23

Ne27Ne26Ne25Ne24Ne23Ne22

F25F24F23F22F21

O24O23O22O21O20

N21N20N19

C19C18

B17

24232221201918171615141312

Neutron Number (N)Neutron Number (N) http://www2.bnl.gov/CoN/

Prot

on N

umber

(Z)

Isobars

Isotopes

Isotones

• Around 1920, professor of physics A. J. Dempster of the University of Chicago developed a magnetic deflection instrument with direction focusing--a format later adopted commercially and still in use today. Dempster also developed the first electron impact source, which ionizes volatilized molecules with a beam of electrons from a hot wire filament. Electron impact ion sources are still very widely used in modern mass spectrometers. Many MS applications have derived from this design.

• The new model for the atom, and the neutron discovery led H.C. Urey to the discovery of Deuterium (and a job at U of Chicago), and to Urey’s measurements of isotope effects and isotope fractionation.

• The discovery came when Urey and Murphy measured that the mass of Hydrogen was about 0.02% heavier than 1 (earth abundance of 2H is 0.015%).

• A.O. Nier developed the first high precision mass spectrometer for stable isotopes.

Brief history

1940’s Nier type MS

Nucleosynthetic process Elements created

Big bang 1H, 4He, 2H, 3H (Li, B?)

Main sequence stars:

Hydrogen burning 4He

Helium burning 12C, 4He, 24Mg, 16O, 20Ne

Carbon burning 24Mg, 23Na, 20Ne

CNO cycle 4He

x-process (spallation)

& supernova (?) Li, Be, B

a-process 24Mg, 28Si, 32S, 36Ar, 40Ca

e-process 56Fe & other transition

s-process up to mass 209

r-process up to mass 254

Nucleosynthesis Schematic

Nucleosynthesis during the Big Bang

- initially, protons (1H) and neutrons

combine to form 4He, 2H (D), and 3He

via exothermic fusion reactions.

- some uncertainty about whether

some B, Be, and Li were created at

this stage

- H & He comprise 99% of

mass of universe

Nucleosynthesis during small star evolution

- star must form from gravitational

accretion of „primordial‟ H and He

- temperature ~ 107 after formation

- H-burning creates 4He from 1H,

longest stage of star (107 - 1010y)

- He-burning begins with formation

of Red Giant (T=108)

4He + 4He --> 8Be

8Be + 4He --> 12C

12C + 4He --> 16O and so on to 24Mg

- core contracts as He consumed,

a-process begins (T=109)

20Ne --> 16O + 4He

20Ne + 4He --> 24Mg and so on to 40Ca

For ‘small’ star, such as our Sun

Terrestrial Abundances of Stable Isotopes of Main Interest in Ecological Studies

Element Isotope Abundance Reference Ter. Range

(%) Std in ‰

Hydrogen 1H 99.985 V-SMOW δD= -450 to +50

2H 0.015

Carbon 12C 98.89 PDB δ13C= -120 to +10

13C 1.11

Nitrogen 14N 99.63 AIR δ15N= -20 to +30

15N 0.37

Oxygen 16O 99.759 V-SMOW δ18O= -50 to +40

17O 0.037 or PDB

18O 0.204

Sulfur 32S 95.00 CDT δ34S= -65 to +90

33S 0.76

34S 4.22 36S 0.014 V-SMOW: standard mean ocean water, Atomic Energy Commission, Vienna (2H/1H=0.00015595;

18O/16O=0.0020052); PDB: Pee Dee Belemnite in NC (13C/12C =0.0112372); AIR:Atmospheric Nitrogen (15N/14N=0.0036765); CDT: Canyon Diablo Troilite (34S/32S=0.0450451). Oxygen isotopes PDB (carbonates) or V-SMOW (water and silicates).

Nucleosynthesis during small star evolution (cont)

For ‘small’ star, such as our Sun

- odd # masses created by proton bombardment

- slow neutron addition (s-process) during

late Red Dwarf:

13C + 4He --> 16O + n 21Ne + 4He --> 24Mg + n

follows Z/N stability up to mass 209

Heavy element formation - the „s‟ and „r‟ processes

Neutron # (N)

Relative composition of heavy elements in sun very similar to “primordial”

crust (the carbonaceous chondrite), so we assume that solar system

was well-mixed prior to differentiation.

The abundance of the elements - our solar system

Stable isotope

Long-l ived radioisotope

Short-l ived radioisotope

16

P2715

Si26Si2514

Al25Al24Al2313

Mg24Mg23Mg22Mg21Mg2012

Na23Na22Na21Na20Na1911

Ne22Ne21Ne20Ne19Ne18Ne1710

F21F20F19F18F17F169

O20O19O18O17O16O15O14O138

N19N18N17N16N15N14N13N12N117

C18C17C16C15C14C13C12C11C10C9C86

B17B15B14B13B12B11B10B9B85

Be14Be12Be11Be10Be9Be8Be7Be64

Li11Li9Li8Li7Li6Li53

He8He6He5He4He32

IsotopesTDH1

1211109876543210

Neutron Number (N)

S40S39S38S37S36S35S34S33S32S31S30S29

P39P38P37P36P35P34P33P32P31P30P29P28P27

Si36Si35Si34Si33Si32Si31Si30Si29Si28Si27Si26

Al34Al33Al32Al31Al30Al29Al28Al27Al26Al25

Mg32Mg31Mg30Mg29Mg28Mg27Mg26Mg25Mg24

Na33Na32Na31Na30Na29Na28Na27Na26Na25Na24Na23

Ne27Ne26Ne25Ne24Ne23Ne22

F25F24F23F22F21

O24O23O22O21O20

N21N20N19

C19C18

B17

24232221201918171615141312

Neutron Number (N)Neutron Number (N) http://www2.bnl.gov/CoN/

Prot

on N

umber

(Z)

Isobars

Isotopes

Isotones

Terrestrial Abundances of Stable Isotopes of Main Interest in Ecological Studies

Element Isotope Abundance Reference Ter. Range

(%) Std in ‰

Hydrogen 1H 99.985 V-SMOW δD= -450 to +50

2H 0.015

Carbon 12C 98.89 PDB δ13C= -120 to +10

13C 1.11

Nitrogen 14N 99.63 AIR δ15N= -20 to +30

15N 0.37

Oxygen 16O 99.759 V-SMOW δ18O= -50 to +40

17O 0.037 or PDB

18O 0.204

Sulfur 32S 95.00 CDT δ34S= -65 to +90

33S 0.76

34S 4.22 36S 0.014 V-SMOW: standard mean ocean water, Atomic Energy Commission, Vienna (2H/1H=0.00015595;

18O/16O=0.0020052); PDB: Pee Dee Belemnite in NC (13C/12C =0.0112372); AIR:Atmospheric Nitrogen (15N/14N=0.0036765); CDT: Canyon Diablo Troilite (34S/32S=0.0450451). Oxygen isotopes PDB (carbonates) or V-SMOW (water and silicates).

Delta (δ) notations are referred to arbitrary standards

Atom %:

Delta (δ) notation vs. N standard (N2 air):

where,

Ion Source and Mass Separation

Isotope Mass Spectrometry

Sample

introduction

Ionization Minimize collisions, interferences

Separate

masses

Count ions Collect results

Nier-type

mass spec

Basic equations of mass spectrometry

21

2mv zV

2 /F mv R

F Bzv

2 /mv R Bzv

2 2/ / 2m z B R V

Ion‟s kinetic E function of accelerating voltage (V) and charge (z).

Centrifugal force

Applied magnetic field

balance as ion goes through flight tube

Fundamental equation of mass spectrometry

Combine equations to obtain:

Change „mass-to-charge‟ (m/z) ratio by

changing V or changing B.

NOTE: if B, V, z constant, then:

r m

Ion generation and focusing

Ionization occurs in the „source‟

Electron Ionization

Gas stream passes through beam of e-,

positive ions generated.

Thorium, tungsten or Rhenium filaments

Thermal Ionization Plasma: Gas stream passes through plasma

maintained by RF current and Ar.

Themal: Filament heated to ~1500C

Mass Analyzers - the quadrupole vs. magnetic sector

Quadrupole:

Changes DC and RF

voltages to isolate

a given m/z ion.

PRO: cheap, fast, easy

Magnetic Sector:

Changes B and V to focus

a given m/z into detector.

PRO: turn in geometry means

less „dark noise‟,

higher precision,

Examples of mass spec data output

You can scan in B or V to sweep masses

across a single detector.

OR

You can put different masses into

multiple cups without changing B or V.

Ex: B

Isotope ion Ratio Mass Spectrometers

Continuous Flow Dual Inlet

Sample Introduction Systems (aka “front ends”)

1) Gas source (lighter elements)

dual inlet - sample purified and measured with standard gas at identical conditions

precisions ~ ±0.005%

continous flow - sample volatized and purified (by EA or GC) and injected into

mass spec in He carrier gas, standards measured before and after,

precisions ~ 0.005-0.01%

2) Solid source (heavier elements)

TIMS - sample loaded onto Re filament, heated to ~1500°C, precisions ~0.001%

laser ablation - sample surface sealed under vacuum, then sputtered with laser

precisions ~0.01%?

3) Inductively coupled plasma (all elements, Li to U)

ICPMS - sample converted to liquid form,

converted to fine aerosol in nebulizer,

injected into ~5000K plasma torch

Popular combinations Gas source 1) Dual inlet isotope ratio mass spec (at UIC, VG-SIRA II; Lynch-Steiglitz and Cobb)

- O, C, H ratio analyses

2) Elemental analyzer IRMS (Costech-Delta+XL)

- N, C, S ratio analyses

3) Gas chromatograph IRMS (at UIC, Delta XP; New 4D-GC-MS: Pegasus 4D-LECO)

- compound-specific ratio analyses

Solid source 1) Thermal Ionization mass spec (multi-collector) (coming to UIC)

- heavy metals, organics

ICP

1) ICP quadrupole mass spec

- trace metal analysis

2) Single collector magnetic sector ICPMS

- higher-precision trace metal

analysis

3) Multi-collector ICPMS

- U/Th dating, TIMS

replacement

Micromass IsoProbe - MC-ICPMS

3) Dark Noise - detector will register signal even without an ion beam

- no vacuum is perfect

and

- no detector is perfect

- must measure prior to run, acceptable values = 3-10cpm

4) Detector “gain” - what is the relationship between the electronic signal recorded

by the detector and the number of ions that it has counted?

- usually close to 1 after factory testing

- changes as detector “ages”

- must quantify with standards

Cardinal rule of mass spectrometry:

Your measurements are only as good as your STANDARDS!

Standards (both concentration and isotopic) can be purchased from NIST

Hurdles in mass spectrometry (cont.)

Ex: NBS-19, O, C carbonate isotopic standard

Cardinal rule of mass spectrometry:

Your measurements are only as good as your STANDARDS!

Standards (both concentration and isotopic) can be purchased from NIST

Designing an analytical strategy for isotopic analysis

1. How much material do you have available for analysis?

- often set by external factors (no sample is unlimited)

2. What is the expected concentration of the isotopes of interest?

3. What is the error on the isotope ratio expected from counting statistics?

4. What are the other sources of error?

- blanks (know the sources of contamination and their isotopic signatures)

5. Is the expected/desired isotopic signal larger than the sum of all expected

errors?

yes? proceed

no? back to square one – can you use more sample? limit blanks? etc

6. What instrument will deliver you the required precision?

7. What particular sources of error are associated with this analysis technique?

- poor yield from sample injection to detection (lowers N)

- mass fractionation, abundance sensitivity, etc

8. Is the expected/desired isotopic signal larger than the sum of all expected

errors?

A review of terms

accuracy: how close the measurement is to a true value

precision: how well we can measure something analytically

Good science: quote values that are accurate within the precision

Systematic error: cannot be assessed by repeated measurements (ex?)

Random error: can be assessed by repeated measurements (ex?)

Internal error: measure ratio repeatedly, assess scatter (aka precision)

External error: compare measurements of standards with internal

errors to truth (aka accuracy)

Reducing systematic errors:

1) minimize systematic errors, add them to random errors

2) make sure systematic errors are small compared to random errors (<10%)

3) measure unknowns relative to a standard so systematic errors cancel out

* Different applications require different approaches (2 & 3 most popular in mass spec work)

Systematic error

Examples:

detector gain (only counts a fraction of signal, usually close to 1)

uncorrected blank or “memory”

wrong mass discrimination law assumed

spike calibration not accurate

How do you hunt for

systematic errors?

Random error

Counting Statistics:

problem of counting subset of a large set (sometimes the subset will reflect the

large set, sometimes over-estimate, sometimes under-estimate)

theoretical limit: 68% chance of being within of measured values

so need 10,000 realizations to get 1% error (at 68% confidence, or 1s)

1/ n

Internal error:

derives from imperfect measurement (collector noise, electronic noise, etc)

measure ratio repeatedly and use scatter to assess uncertainty

External error:

the ability to reproduce standards over many runs (why might this change long-term?)

measure standard repeatedly, over a very long time

cite as 2 s.d. and mention how many standards based on

Ex.: “External reproducibility was assessed with repeated measurements

of the NBS-19 carbonate standard, and is reported as ±0.05‰ (2 s.d., N=550).”

238U/235U ratios over typical multi-collector ICPMS run

1.40E+02

1.40E+02

1.40E+02

1.40E+02

1.40E+02

1.40E+02

0 50 100 150 200

Scan number

238U

/235U

Example – U isotope ratios in single run

Statistic

1) mean = 140.0833

2) standard deviation (1s) = 0.038

* variance = (s)2

3) standard error (1s) = 0.0027

4) relative standard error (1s) = 1.93 x 10-5

ix

N

21( )

1ix x

Ns

. .s eN

s

. .. . .

s er s e

238U/235U ratio

Fre

quency

ME

AN

-1s

+1

s

-2s

+2

s

0.9999994

0.9999366

0.9973002

0.9544997

0.6826895

CI range

The Gaussian, or “normal” distribution

21 1

exp22

G

xP

ss

Probability density equation: