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EXAFS studies of Negative Thermal Expansion
Zincblende structurePhD student Naglaa
AbdelAllTutors Prof. Giuseppe Dalba
Prof. Paolo Fornasini
Email n.fathy_at_science.unitn.it
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Overview

• Negative thermal expansion (NTE) in crystals
• ? Thermal Expansion of zincblende structure

• Short introduction to EXAFS
• ? comparison with Bragg diffraction

• Experimental results on Ge, CuCl and CdTe of
  the 1st Coordination shell
• interatomic distances
• thermal factors
• the local origin of NTE in Zincblende crystals

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Solids generally expand when heated, a courious
example
The Sears tower in Chicago, USA grows by 15 cm in
the summer!
Standing at 442 m and 110 stories high.
There are however exceptions solids that
contract when heated!
Examples
Crystalline Silicon at low temperature
ZrW2O8 beetwen 0.31050 K!
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Expansion coefficient of zincblende structure
Grüneisen function g
Thermal Expansion coefficient

• NTE in Zincblende crystals has been attributed
  to a low-frequancy transverse a coustic
  modes with negative Gruneisen functions.

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NTE - phenomenological mechanism
Barrera, Bruno, Allan, Barron - J. Phys.
Condens. Matter 17, R217 (2005)
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Why EXAFS?

• Local origin of NTE ? phenomenological
  explanations,
• BUT
• lack of experimental data!

• EXAFS
• ? sensitive to selected bond lengths
• parallel relative motion
• Through a comparison with Bragg diffraction
• perpendicular relative motion
• and correlation

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• Short introduction to EXAFS
• ? comparison with Bragg diffraction

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Measurements performed at ESRF (Grenoble)
BM29 (EXAFS in CdTe)
BM08 GILDA (EXAFS in CuCl)
The experimental goal is measure the absorption
coefficient as function of energy, and extract
information from oscillations
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EXAFS .VS. Diffraction
EXAFS
Diffraction
plane waves
photo-electron spherical wave

• long-range sensitivity
• atomic positions
• atomic thermal factors

• short-range sensitivity
• inter-atomic distances
• relative displacements

• Structural probe

• By EXAFS it is possible to extract original
  information about local structural and
  vibrational dynamics

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EXAFS .VS. Diffraction(I) Bond distances
Perpendicular MSRD
Fornasini et al., Phys. stat. sol. (b) 1-7 (2008)
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EXAFS .VS. Diffraction(II) Thermal factors
Relative thermal motion
Absolute thermal motion
Variance
Average distance
First and second cumulant of EXAFS also contain
original information about the local dynamics!
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• Experimental results on Ge, CdTe and CuCl of the
  1st Coordination shell
• interatomic distances
• thermal factors
• the local origin of NTE in Zincblende structure

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Thermal expansion 1-st shell
Lattice thermal expansion
Bond-stretching effect
Tension effect
CuCl
CdTe
Ge
Present work
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Mean square relative displacements 1st shell
8.6
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Perpendicular-parallel anisotropy of relative
vibration
2 For perfect isotropy
more negative expansion is associated to a
stronger ratio g /
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MSRDs
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Einstein models for MSRDs Effective force
constants
effective stiffness of the nearest-neighbor bond
70Ge CdTe CuCl
k (ev/Å2) 8.5 3.76 1.4 k? (ev/Å2) 2.9 0.9 0.3 ? k / k? 2.9 4.17 4.7
bond-stretching force
bond-bending force
Anisotropy parameter

• Stronger NTE corresponds to
• - Smaller value of k , say to a looser bond.
• - Larger anisotropy of relative vibrations.

1 perfect isotropy
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Conclusions

• Crystallographic NTE (Bragg diffraction)
• ? positive 1st shell bond expansion (EXAFS)

• Larger NTE
• stronger anisotropy of relative thermal
  vibrations
• high / ratio
• ? tension mechanism

• EXAFS of NTE in Zincblende structures
• ? The relative perpendicular vibration are
  related to the tension mechanism and to
  transverse acoustic modes which are considered
  responsible for NTE .

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Thank You