MINISTRYOFEDUCATION
ANDTRAINING
VIETNAMACADEMY
OFSCIENCEANDTECHNOLOGY
GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY
-----------------------------
CU SY THANG
STUDY OF THE THERMODYNAMIC PARAMETERS AND
CUMULANTS OF SOME MATERIALS BY ANHARMONIC
XAFS METHOD
SUMMARY OF MATERIAL SCIENCE DOCTORAL THESIS
Ha Noi - 2020
MINISTRYOFEDUCATION
ANDTRAINING
VIETNAMACADEMY
OFSCIENCEANDTECHNOLOGY
GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY
-----------------------------
CU SY THANG
STUDY OF THE THERMODYNAMIC PARAMETERS
AND CUMULANTS OF SOME MATERIALS BY
ANHARMONIC XAFS METHOD
SUMMARY OF MATERIAL SCIENCE DOCTORAL THESIS
Major: Electronic material
Code: 9 44 01 23
Supervisor: Prof. Dr. Sc. Nguyen Van Hung
Dr. Le Quang Huy
Ha Noi - 2020
1
INTRODUCTION
The X-ray Absorption Fine Structure (XAFS) spectroscopy
techniqueisamodernandhighprecisionmethodtobeusedinthe
structuraldeterminationofmaterials.Ingeneral,thismethodisused
to fit the theoretical and experimental spectra to extract data or
parametersfromtheXAFSspectra.
AnharmonicCorrelatedEinsteinModel(ACEM)[9]isoneofthe
efficiency theoretical methods [7] used to study thermodynamic
parameters of XAFS spectra. Anharmonic effective interaction
potential in ACEM has been built. In which Morse potential is
assumedtodescribethesingle-pairatomicinteraction.Byusingthis
effectivepotential,theACEMhasnotonlyovercomethelimitations
ofusingsinglebondpotential[8]butalsosimplifiedthemany-body
systemproblembacktothesimpleone-dimensionalsystemproblem
withthecontributionofmany-bodyeffectsthroughconsiderationof
theinteractionofneighboringatoms.
Manypreviousstudies[10-25]showedthatthenumericalresults
of the ACEM were good agreement with the experimental data as
wellasthoseobtainedvaluesbyothermethodsforseveraldifferent
structuralmaterials,...However,mostofthe studiesfocused onthe
thermodynamic parameters, especially the cumulants of the XAFS
spectra without concerning the anharmonic contribution of the
second cumulant as well as the anharmonic contribution to XAFS
phase and amplitude components. Debye-Waller factor or the
second-order cumulant is an important thermodynamic parameter
that characterizes the decrease XAFS amplitude. The relationship
between the second-order cumulant and other thermodynamic
parametersandXAFSphaseandamplitudeneedstobecontinuously
studied,consideredinmoredetailandcomprehension.Therefore,I
2
choose the research topic: "Study of thermodynamic parameters
and cumulants of some materials by anharmonic XAFS method".
1. Target of thesis
Todevelopamethodthatcansimplifythedeterminationofthe
thermodynamic parameters and XAFS spectra which base on the
second-order cumulant only. In particular, this method can be
applied for both theoretical calculations and experimental
measurementsintheXAFSmethod.
2. Subject and Scope of the thesis:
Subject:
-Thermodynamicparameters,XAFScumulants,XAFSspectra,and
theirFouriertransformmagnitudes.
- Materials: Diamond crystals (Si, Ge), fcc crystals (Cu), hcp
crystals(Zn).
Scope:
- Models and theoretical methods of XAFS: focus on anharmonic
correlated Einstein model using anharmonic effective potential in
whichMorsepotentialis assumedtodescribethesinge-pairatomic
interaction.
3. Study methods
Theoretical method:
-UsingtheanharmoniccorrelatedEinsteinmodel.
-Usingtheanharmoniceffectiveinteractionpotentialmethod.
Experimental method: Study on documents, the configuration of
XAFS spectroscopy experimental station, the scanning process of
XAFS spectra as well as data processing methods at Synchrotron
LightResearchInstitute-Thailand.
Numerical calculation Program and XAFS spectra data processing
and analysis software
-UsingMatlab2014software,Demeter9.0.25software.
3
4. Main contents of the thesis
- Study and establish the expressions of thermodynamic
parameters and the Debye-Waller factor of the XAFS spectra of
materialsdependingonthetemperature.
- Study and establish a relationship between the anharmonic
contribution of the second-order cumulant and the Debye-Waller
factorofXAFSspectraofmaterialsdependingontemperature.
- Study and establish a relationship between the Debye-Waller
factor and anharmonic contribution of the XAFS phase and
amplitudeofmaterialsdependingontemperature.
- Analyze and evaluate constructed theoretical calculations as
well as evaluating the agreement between theoretical results and
obtained experimental values from Synchrotron Light Research
Institute - Thailand and other theoretical methods or measurements
forfcc(Cu)andhcp(Zn)structuralmaterials.
CHAPTER 1. OVERVIEW OF XAFS DEBYE-WALLER
FACTOR
1.1. Fundamentals of XAFS
1.1.1. Simple physical description of XAFS
X-ray absorption fine structure is the final state of interference
between photoelectric waves emitted from absorption atoms and
scatteringwavesbyneighboringatoms.
1.1.2. XAFS equation

2 2
2 2 / ( )
2
0
2
( )
(k) sin 2 (k)
j j
k R k
j j
j j
jj
S N e e f k kR
kR
(1.14)
1.1.3. XAFS Debye-Waller factor
-Thefactor
2 2
2
j
k
e
in(1.14)haveformedas
w+i
e
iscalledXAFS
Debye-Wallerfactor[29].