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“ EXAFS studies of Negative Thermal Expansion Zincblende structure ” PhD student : Naglaa AbdelAll Tutors: Prof. Giuseppe Dalba Prof. Paolo Fornasini. Email: [email protected]. Overview. Negative thermal expansion (NTE) in crystals - PowerPoint PPT PresentationTRANSCRIPT
“EXAFS studies of Negative Thermal Expansion
Zincblende structure”
PhD student: Naglaa AbdelAll
Tutors: Prof. Giuseppe Dalba Prof. Paolo Fornasini
Email: [email protected]
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
Solids generally expand when heated, a courious example…
The Sears tower in Chicago, USA grows by 15 cm in the summer!
There are however exceptions: solids that contract when heated!Examples…
ZrW2O8 beetwen 0.3÷1050 K!
0 200 400 600 800 1000 1200-0.50
-0.25
0.00
0.25
0.50
Rel
ativ
e E
xpan
sion
(%)
Temperature [K]
Relative Thermal Expansion in ZrW2O
8
0 100 200 300-0.01
0.00
0.01
0.02
0.03
Rel
ativ
e E
xpan
sion
(%)
Temperature [K]
Relative Thermal Expansion in Crystalline Silicon
Crystalline Silicon at low temperature
Standing at 442 m and 110 stories high.
Expansion coefficient of zincblende structure
3 (cubic symmetry)
VCVT
Thermal Expansion coefficient Grüneisen function
NTE in Zincblende crystals has been attributed to a low-frequancy transverse a coustic modes with negative Gruneisen functions.
NTE - phenomenological mechanism
Barrera, Bruno, Allan, Barron - J. Phys.: Condens. Matter 17, R217 (2005)
Bond-stretching effect
POSITIVE contribution
Tension effect
NEGATIVE contribution
Why EXAFS?
Local origin of NTE phenomenological explanations, BUTBUT
… lack of experimental data!
EXAFS: sensitive to selected bond lengths parallel relative motion
Through a comparison with Bragg diffraction: perpendicular relative motion || and correlation
Short introduction to EXAFS comparison with Bragg diffraction
Measurements performed at ESRF (Grenoble)…
BM08 – GILDA
(EXAFS in CuCl)
BM29 (EXAFS in
CdTe)
The experimental goal is measure the absorption coefficient as function of energy, and extract information from oscillations
EXAFS .VS. Diffraction
By EXAFS: it is possible to extract original information about local structural and vibrational dynamics
k0
k1
plane wavesphoto-electron spherical wave
long-range sensitivity atomic positions atomic thermal factors
short-range sensitivity inter-atomic distances relative displacements
DiffractionEXAFS
Structural probe
EXAFS .VS. Diffraction(I): Bond distances
r R u
2
2R
Perpendicular MSRDFornasini et al., Phys. stat. sol. (b) 1-7 (2008)
R
r
Bragg diffraction
“Apparent” bond length
distance between average positions
R r b
r a
EXAFS
“True” bond length
average inter-atomic distance
r r b
r a
R
(a) (b)
EXAFS .VS. Diffraction(II): Thermal factors
cR
EXAFS
Mean square relative displacements
Bragg diffraction
Absolute mean square displacements
cR
First and second cumulant of EXAFS also contain original information about the local dynamics!
R
uRC
2
2*1
22 IIuC*
Average distance
Variance
Relative thermal motion Absolute thermal motion
Experimental results on Ge, CdTe and CuCl of the
1st Coordination shellinteratomic distances
thermal factors
the local origin of NTE in Zincblende structure
Thermal expansion: 1-st shell
0 100 200 300
0
2
4
6
8
10
12
14
XRD
EXAFS
1-st shell
Ther
mal e
xpan
sion
(1
0-3 Å
)
T (K)0 100 200 300
0
2
4
6
8
10
12
14
EXAFS
CuCl 1st shell
XRD
Ther
mal
exp
ansion
(1
0-3 Å
)
T (K)
M. Vaccari et al. Phys. Rev. B 75,184307(2007)
G. Dalba et al. Phys. Rev. Lett. 82, 4240 (1999)
0 100 200 300
0
2
4
6
8
10
12
14 Å Å Å
Ther
mal
exp
ansion
( 10
-3 Å
)
T (K )
XRD
EXAFS
CuClCuClGeGe CdTeCdTe
R r u
2
2R
EXAFSXRD
Lattice thermal
expansion
Bond-stretching effect
Tension effect
[Present work]
-10-8-6-4-2024
0 20 40 60 80 100 120
Thermal expansion coefficient
Ge COTE (e-6) Zhda
Ge COTE (e-6) White
Ge COTE(e-6) Sparks
Ge COTE(e-6) Carr
CuCl_COTE e-6 Barron
CdTe COTE (e-6) White
(1
0-6
K-1
)
T(K)
CuCl
CdTe
Ge
Mean square relative displacements: 1st shell
Perpendicular-parallel
anisotropy of relative vibration
2
2
||u
u
8.6 116
0 100 200 3000
2
4
6
8
10
||
CuCl 1st shell
MSRDs
(10
-2 Å
2)
T (K)0 100 200 3000
2
4
6
8
10
MSRDs (
10-2 Å
2)
T (K)
CdTe 1st shell
0
2
4
6
8
10
0 200 400 600
Ge 1st shell
T (K)
||
=2 : For perfect isotropy
“…more negative expansion is associated to a stronger ratio = / || …”
0 100 200 3000.00
0.02
0.04
0.06
0.08
Ge 1st shell
MSRDs (
10-2 Å
2)
T (K)0 100 200 300 400
MSRDs (1
0-2 Å
-2)
T (K)
/ 2
CdTe 1st - shell
MSRDs :
“…NTE is connected to anisotropy of relative, rather than absolute, thermal vibrations …”
XRD : MSDs Isotropic
EXAFS: MSRD Anisotropic
cR
Einstein models for MSRDs: Effective force constants
k||
k
T
u2
2 u||2
0 100 200 3000
2
4
6
8
MSRDs
(10
-2 Å
2)
T (K)
CdTe 1st shell
= 1 : perfect isotropy
70Ge CdTe CuCl
k|| (ev/Å2) 8.5 3.76 1.4
k (ev/Å2) 2.9 0.9 0.3
ξ = k|| / k 2.9 4.17 4.7
bond-bending force
bond-stretching force
Anisotropy parameter
effective stiffness of the nearest-neighbor bond
Stronger NTE corresponds to:
- Smaller value of k|| , say to a looser bond.
- Larger anisotropy of relative vibrations.
Conclusions
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 .
Crystallographic NTE (Bragg diffraction): positive 1st shell bond expansion (EXAFS)
Larger NTE: stronger anisotropy of relative thermal vibrations high / || ratio tension mechanism
Thank You