“EXAFS studies of Negative Thermal Expansion

Zincblende structure”

PhD student: Naglaa AbdelAll

Tutors: Prof. Giuseppe Dalba Prof. Paolo Fornasini

Email: n.fathy@science.unitn.it

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