“EXAFS studies of Negative Thermal Expansion Zincblende structure” PhD student : Naglaa AbdelAll Tutors: Prof. Giuseppe Dalba Prof. Paolo Fornasini

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 1 st 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… ZrW 2 O 8 beetwen 0.3÷1050 K! Crystalline Silicon at low temperature Standing at 442 m and 110 stories high.

Expansion coefficient of zincblende structure (cubic symmetry) 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 Macroscopic Expansion Positive contribution Negative contribution

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

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 k0k0 k1k1 plane wavesphoto-electron spherical wave  long-range sensitivity  atomic positions  atomic thermal factors  short-range sensitivity  inter-atomic distances  relative displacements Diffraction EXAFS Structural probe

EXAFS.VS. Diffraction (I): Bond distances Perpendicular MSRD Fornasini et al., Phys. stat. sol. (b) 1-7 (2008) Bragg diffraction “Apparent” bond length distance between average positions EXAFS “True” bond length average inter-atomic distance (a) (b)

EXAFS.VS. Diffraction(II) : Thermal factors EXAFS Mean square relative displacements Bragg diffraction Absolute mean square displacements First and second cumulant of EXAFS also contain original information about the local dynamics! Average distance Variance Relative thermal motion Absolute thermal motion

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

Thermal expansion: 1-st shell M. Vaccari et al. Phys. Rev. B 75, (2007) G. Dalba et al. Phys. Rev. Lett. 82, 4240 (1999) CuCl CuCl Ge CdTe EXAFS XRD Lattice thermal expansion Bond-stretching effect Tension effect [Present work]

Mean square relative displacements: 1 st shell Perpendicular-parallel anisotropy of relative vibration =2 : For perfect isotropy “…more negative expansion is associated to a stronger ratio  =  / || …”

MSRDs : “…NTE is connected to anisotropy of relative, rather than absolute, thermal vibrations …” XRD : MSDs Isotropic EXAFS: MSRD Anisotropic

Einstein models for MSRDs: Effective force constants = 1 : perfect isotropy 70 Ge CdTe CuCl k || (ev/Å 2 ) k  (ev/Å 2 ) ξ = k || / k  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 1 st shell bond expansion (EXAFS) Larger NTE:  stronger anisotropy of relative thermal vibrations  high  / || ratio  tension mechanism

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