Email: n.fathy@science.unitn.it

1. “EXAFS studies of Negative Thermal Expansion Zincblende structure”PhD student: Naglaa AbdelAllTutors: Prof. Giuseppe Dalba Prof. Paolo Fornasini Email: n.fathy@science.unitn.it

2. 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

3. 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 0.3÷1050 K!

4. (cubic symmetry) 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.

5. Bond-stretching effect Tension effect POSITIVE contribution NEGATIVE contribution NTE - phenomenological mechanism Barrera, Bruno, Allan, Barron - J. Phys.: Condens. Matter 17, R217 (2005)

6. 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

7. Short introduction to EXAFS  comparison with Bragg diffraction

8. 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

9. k0 k1 EXAFS .VS. Diffraction EXAFS Diffraction Structural probe photo-electron spherical wave plane waves • long-range sensitivity • atomic positions • atomic thermal factors • short-range sensitivity • inter-atomic distances • relative displacements • By EXAFS: it is possible to extract original information about local structural and vibrational dynamics

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

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

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

13. Thermal expansion: 1-st shell EXAFS XRD Lattice thermal expansion Bond-stretching effect Tension effect CdTe CuCl Ge M. Vaccari et al. Phys. Rev. B75, 184307(2007) G. Dalba et al. Phys. Rev. Lett.82, 4240 (1999) [Present work]

14. Mean square relative displacements: 1st shell 6 8.6 11 Perpendicular-parallel anisotropy of relative vibration =2 : For perfect isotropy “…more negative expansion is associated to a stronger ratio g = ^ / || …”

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

16. Einstein models for MSRDs: Effective force constants effective stiffness of the nearest-neighbor bond 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

17. 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 .

18. Thank You