XAFS Data Analysis using LCF / PCA · − 3+Mn − 4+Mn 6520 6540 6560 6580 6600 0.0 0.4 0.8 1.2 1.6 2.0 Normalized Absorption Coefficient Energy (eV) V-XAFS series from an in-situ

XAFS Data Analysis using LCF / PCA

NSLS XAFS Short Course Nov 13-15, 2014

1. A XAFS of a sample of multi-component 2. Good knowledge on the sample & each component 3. Need to quantify fractions

− Mn2+

− Mn3+

− Mn4+

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V-XAFS series from an in-situ reaction 1. XAFS series show systematic change 2. Little information on the process or distinct

reaction phases. 3. Need to understand kinetics and composition

Mn-XAFS spectrum from a sample

LCF vs. PCA

LCF: Linear Composition Fitting PCA : Principal Component Analysis

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• A Factor Analysis Method • Applied to a series of XAFS • Obtain number of distinct phases in

this group of spectra • Advantages:

– No prior knowledge is required – Detect the intermediate, if applied to

in-situ reaction; assuming complete reaction.

• Requirements: – Large # of spectra – Data point # > spectrum # – Good data quality, minimum noise as

possible – Data are collected and processed in

the same manner.

• A Specification Method – Applied to an spectrum for a sample – Quantify the composition for the

sample of multi-component. • Advantages:

– Straightforward implementation – Applicable to both single spectrum

& XAFS series • Requirements:

– Good knowledge on the sample(s) and the references

– Good reference spectra: • Experiment • data processing

Same condition to the sample

NSLS XAFS Short Course, Nov 13-15, 2014

Software and Packages

Freeware: • DAthena – B. Ravel http://bruceravel.github.com/demeter/

• SixPack – S. Webb: http://home.comcast.net/~sam_webb/sixpack.html

Distribution Permission / Purchase Option: • XAMath – S. R. Wasserman (Mathematica 4. & above) • WinXAS – T. Ressler: http://www.winxas.de/


Result: Fe2+/Fe3+ fractions


Data One Spectrum (XANES, EXAFS)

Least Square Fitting

Linear Combination Fitting

Reference Spectra

Result Fraction

of Each Component

LCF analysis: fits data to LC of spectra of Fe2+ and Fe3+

Determine the Fraction of Each Component that can be combined to reproduce the experimental spectrum within statistical error

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Energy (eV)

001 002 003 004 005 006 007

Fe K-edge

0.5C Charge

Result: Fe2+/Fe3+ fractions

2.5

3.0

3.5

4.0

4.5

5.0

0.0 0.2 0.4 0.6 0.8 1.00.0

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0.4

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0.8

1.0 LiFePO4

FePO4

X in Li1-xFePO4

Frac

tion

of L

iFeP

O 4 or F

ePO 4

0.5 C Charge

Fe2+

Fe3+

1 2 3 4 5 6 7

Mix

ing

frac

tion

Fe2+

Fe3+

Single data group

Sequence: Batch mode

data

data


A

B

LCF in DAthena

E

A) Load Data B) Display C) LCF setup D) Actions

E) LCF Results

D C

Principal Component Analysis


Original Data XAFS series

Linear Algebra

• Principal components • Mathematical constructs

derived original data • Each component is unique

Abstract Standards

PCA Mathematical Matrix

Vector = Spectrum

Target Transformation Real Standards

• Examine each standard • Reproduce spectra

Determine the number of components that can reproduce a series of experimental spectra within statistical error.

PCA: Algorithm

Singular value decomposition (SVD) algorithm – Matrix: [D] = m x n ( m: row; n: column; m ≥ n) – [D] = [E] x [V] x [W]t

– Eigenvectors: Columns of [E]

– Eigenvalues: Diagonal elements of [V]


mnmm

n

n

n

XXX

XXXXXXXXX

............

..

..

..

21

33231

22221

11211

mnmm

n

n

n

eee

eeeeeeeee

............

..

..

..

21

33231

22221

11211

nnv

vv

v

...0......0..0..00..0

33

22

11

nnn

n

n

ww

wwwwww

.............

..

..

1

22221

11211

= x x

D E V W = x x t

Ressler, Environ. Sci. Technol. 2000, 34, 950

m x n n x n n x n

PCA: Data Requirement & Selection

[D] = m x n XAFS data Data points in each spectrum : m Number of spectra n


• Number of data points are larger than numbers of XAFS spectra • All XAFS spectra are interpolated to the same energy grid • Number of spectra are larger than number of principal components

XAFS data requirement

data

A

D B

F

C

A) Load Data B) Display C) PCA setup D) PCA results E) Actions F) Target Transformation


DAthena PCA Demo

Demeter © Bruce Ravel

E

PCA 1. PCA + LCF 2. PCA + FEFF Fit

Applications

• Mixed phases: – Environmental Science – Biomedical Science

• Sequential processes: – Chemical Transformation – Catalysis – Battery


LCF

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Combined PCA and LCF

in-situ battery lithiation

Experiment: Real-time lithiation of V-based battery material

XANES data: 1. Pre-edge change 2. Edge shift 3. Above-edge & EXAFS


• Maximum number of components equals the number of original spectra – Data reconstructed using all components reproduce exactly the

original spectra. • Principal components contain real spectra features • Other components: data noises & errors

PCA: Components

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0

1

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6

A

Row Numbers5460 5480 5500 5520 5540 5560-0.7

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AU

Energy (eV)

1 2 3 4

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Eige

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Component #NSLS XAFS Short Course, Nov 13-15, 2014

Scree Plots

PCA: Principal Components • Contains the spectra features • Can reproduce the data • Determined by:

- Eigen-values - Error Analysis - Reproduction of data

Eigen Value # 1: 36.679264 # 2: 0.294768 # 3: 0.024383 # 4: 0.001016 # 5: 0.000139

Component 1 ~ 4

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data

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data fit residual

2-compent fit

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3 Component fit

0.0000

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0.0006

0.0008

0.0010

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Resid

ual

Residual using 3 components

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0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

Resid

ual

Capacity

Residual using 2 components

Data Reproduction

• Examine reproduction by using varied number of components – Original data vs. Reproduced spectrum – Reproduction residuals

• Very useful for intermediate detection in a multiple-phase reaction


2-compoent fits and residuals 3-component fits and residuals

A reaction involving 3 phases

Target Transformation

• Examine the standards • A correct standard can be fitted by principal components

– Determine whether a selected standard is legitimate – Eliminate impossible standards


Wrong Standard Reasonable Standard


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Starting Phase Intermediate Phas Ending Phase

Mixin

g Fra

ction

# Li

Obtain Mixing Fractions - Composition of a sample. - Indicate reaction dynamics of a chemical change

LCF: Mixing Fractions

Conclusion for Analysis: 1. Relates the mixing fraction with inserted Li# 2. Only need to analyze data for 3 reaction phases to understand the

chemical compositions and structures

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Combined PCA & FEFF Fit

Experiment: quick XAFS @ Cu Ke-edge on reduction/re-oxidation of 20% Cu/CeO2

Reduction at 200oC • XANES (8959 ~ 9059 eV) showing structural evolution • No isosbetic points

17 Q. Wang, et al. J. Chem. Phys., 129, 234502 (2008).


in-situ catalysis

Reproduction: determine Intermediate

18 NSLS XAFS Short Course, Nov 13-15, 2014

3-component fit: • Presence of Intermediate

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Resid

uals

(a.u.

)

Reaction time t(s)

1)()()( =++ tztytx

)()()()()()(),( EtzEtyEtxtE PIR χχχχ ++= t = t* 𝒚 𝒕 = 𝟏

Intermediate Phase

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0.008

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Resid

uals

(a.u.

)

Reaction time t (s)

t=t*

2-component fit: • Uneven residual 660< t <900s • Intermediate phase

FEFF fit to EXAFS of Intermediate

19 NSLS XAFS Short Course, Nov 13-15, 2014

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k2χ(

k), Å

-2

k, Å-1

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A Intermediate phase:extracted by PCA

FEFF

)(223)3(eff2

20 22

)(342sin)()( kRk

iiiii

ii

iii eekkkRkfkR

nSk λσδσχ −−

+−=

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FT M

agni

tude

إ ,-3

Data Fit

B

r,Å

Intermediate Analyzed by FEFF

NCu-O = 2.2 ± 0.5

NCu-Cu = 5.8±3.5

RCu-O = 1.86 ±0.02 Å

RCu-O = 3.07 ±0.02 Å

Conclusion for Analysis: 1. intermediate is detected. 2. Reaction dynamics is elucidated by applying PCA followed by LCF. 3. Intermediate structure was determined by combined use PCA and FEFF fit.

Cu2O

2

12

1.85 Å

3.02 Å

Summary

NSLS XAFES Short Course, Nov 13-15, 2014

• LCF and PCA are important speciation and quantification methods applied to XAFS spectra

• LCF: – simple and straight forwards – require knowledge of number and types of references.

• PCA: – mathematically accurate – no priori assumption for standards – requires additional information to relate the mathematical vectors

to physically meaningful spectra. • Combined use of PCA and LCF would provide insights on reactions • Broadly applied in a variety of research fields

Some References

• B. Ravel, “http://bruceravel.github.io/demeter/ • S.R. Wasserman, et al . “EXAFS and principal component analysis: a new shell game” , J . Synchrotron Rad. (1999) 6, 284 • A. I. Frenkel, et al. “Phase speciation by extended x-ray absorption fine structure spectroscopy “ , J. Chem. Phys. (2002) 116, 1473193 • S. Beauchemin et al., “Principal component analysis approach for modeling sulfur K-XANES spectra in humic acids”, Soil. Sci. Soc.Am.J. (2002) 66,83. • T. Ressler et al., “Quantitative speciation of Mn-bearing particulates emitted from autos burning mcp-Mn gasolines using XANES spectroscopy”, Environ. Sci. Technol., (2000) 34, 950.


XAFS Data Analysis using LCF / PCA · − 3+Mn − 4+Mn 6520 6540 6560 6580 6600 0.0 0.4 0.8 1.2 1.6 2.0 Normalized Absorption Coefficient Energy (eV) V-XAFS series from an in-situ

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