1. First-principles molecular dynamics studies of liquid and glasses Carlo Massobrio Institut de Physique et Chimie des Matériaux Strasbourg (France) (CNRS-Univ. L. Pasteur) Old Strasbourg: "Petite France" Short and intermediate range order structural properties in disordered network-forming materials: AX 2, A n X (1-n) A=Ge, Si, X=Se Current Challenges in Liquid and Glasses Science Cosener’s House, Abingdon, United Kingdom, 10-12/1/2007

2. First-principles molecular dynamics studies of liquid and glasses Carlo Massobrio Institut de Physique et Chimie des Matériaux Strasbourg (France) (CNRS-Univ. L. Pasteur) Liquid GeSe 2 at 1100 K Short and intermediate range order structural properties in disordered network-forming materials: AX 2, A n X (1-n) A=Ge, Si, X=Se Current Challenges in Liquid and Glasses Science Cosener’s House, Abingdon, United Kingdom, 10-12/1/2007

3. Our model: essential features First principles molecular dynamics Density functional theory: best with GGA…!! (case of GeSe 2 ) Periodic cell, Plane waves basis sets Norm conserving pseudopotentials k min < 0.4 Å -1 k FSDP  1 Å -1 (intermediate range order scales) Length of equilibrium trajectories : Liquids : up to 100 ps (significant sampling ensured by diffusion) Glasses : Quench of uncorrelated liquid configurations (LC) followed by structural relaxation Ex: GeSe 2 : for each LC, 22 ps down to T=600K and 22 ps at T=300 K Typical size of the periodic boxes: L=15-20 Å (N=120,144) Computer code: norm-conserving version of ultra-soft FPMD written by A. Pasquarello (Lausanne) (PRL 69, 1982 (1992), PRB 47, 10142 (1993)) How do we deal with space and time limitations..?

4. Two issues of methodology: 1)Role of the generalized gradient approximation (GGA) within density functional theory (case of liquid GeSe 2 ) (CM, Alfredo Pasquarello, Roberto Car, JACS 121, 2943 (1999)) 2) System size and periodicity: are they compatible with IRO..? (CM, Alfredo Pasquarello, Roberto Car, PRB 64, 144205 (2001))

5. Correlation between structure and bonding properties: role of the GGA in DFT (case of liquid GeSe 2 ) Ionic character of bonding enhanced: GGA brings the FSDP together with the predominant occurrence of a tetrahedral order. LDA GGA

6. Two issues of methodology: 1)Role of the generalized gradient approximation (GGA) within density functional theory (case of liquid GeSe 2 ) (CM, Alfredo Pasquarello, Roberto Car, JACS 121, 2943 (1999)) 2) System size and periodicity: are they compatible with intermediate range order (IRO) distances...? (CM, Alfredo Pasquarello, Roberto Car, PRB 64, 144205 (2001))

7. Total S(k) for a given L= 15.7 Å dr kr sinkr αβ R c 4π ][ 1(r) g r 1 S 2        ij )( e R jβ R i ik βα αβ NN S  Two ways are available to calculate the structure factors… Real space (solid line) Reciprocal space (dotted line): our approach The FSDP becomes clearly discernible for R c in between 6 and 10 Å Extent of correlations responsible of the FSDP

8. FSDP I.T. Penfold and P.S. Salmon, PRL 67, 97(1991) S cc /c ge c se = 1+c ge c se (S gege - S gese ) +c ge c se (S sese - S gese ) Liquid GeSe 2 : a prototype case FSDP in both total and S cc structure factors S cc /c ge c se = S ZZ  For point charges (classical MD): no FSDP in S CC charge-charge structure factor Total S(k)

9. Note: LDA (dotted line) inaccurate!!! S NN  Stot “… the distribution of the FSDP weigths in the partials is different in theory and experiments..” (PRB 64, 144205 (2001)) Reduced intensity of FSDP in S GeGe and S cc

10. d GeGe (exp) = 2.33  0.03 Å d GeGe = 2.7  0.1 Å Liquid GeSe 2 Theory 0.04 3.76 1.88 0.37 Exp 0.25 3.5 1.75 0.23 CON 0 4 2 0 RCN 2 2 1 1 CON chemically ordered network RCN random covalent network N gege Ngese N sege N sese Liquid GeSe 2 is a highly defective tetrahedral network, with miscoordinations and homopolar bonds

12. Amorphous GeSe 2 High statistics required: about 500 ps (quench+relaxation) Results from a single quench “true” (chain-like) homopolar Ge-Ge bonds are found Liquid vs amorphous (dotted line) CM and Alfredo Pasquarello, unpublished

13. Understanding the origins of the FSDP in the concentration-concentration structure factor S cc Liquid (l) GeSe 2 Two approaches: 1)Look for analogies and differences with other systems (SiO 2, SiSe 2, GeSe 4 ) 2)Exploit statistical mechanics on relevant configurations of l-GeSe 2

14. Amorphous SiSe 2 Enhanced chemical order n sisi n sise n sesi n sese Theory 0.06 3.89 1.94 0.10 CON 0 4 2 0 RCN 2 2 1 1 Si(0) 26% 48% 30% Si(1) 52% 46% 61% Si(2) 22% 6 % 9% Exp. CMD Si(1) Si(2) Si(0) Massimo Celino and CM, PRL 64, 125502 (2003)

15. Understanding the origins of the FSDP in the concentration-concentration structure factor S cc Liquid (l) GeSe 2 Two approaches: 1)Look for analogies and differences with other systems (SiO 2, SiSe 2, GeSe 4 ) 2)Exploit statistical mechanics on relevant configurations of l-GeSe 2

16. How to calculate S cc and S zz structure factors S cc = c a c x [1+c a c x ((S AA -S AX )+(S XX -S AX ))] z i ionic charges (Ge= 4, Se =6) POINT-LIKE CHARGE (PLC) MODEL No FSDP in S zz (charge neutrality on IRO scales) (CM and Alfredo Pasquarello PRB 68, 020201 (2003)) What is the behavior of S cc for systems having in common the FSDP in the total S(k)..??

17. Correlation between FSDP in S cc and chemical disorder Case I: perfect chemical order: l-SiO 2 (theory) Case II: small deviations from chemical order: a-SiSe 2 (theory) Case III: large deviations from chemical order: l-GeSe 2 (theory)

18. Disordered networks: 3 classes of systems identified Moderate chemical disorder (case II): Occurrence of different valence states Variations of concentration induce FSDP in S cc Ex: l-GeSe 4, a-SiSe 2, l-GeSe 2 (exp) Perfect network (case I, l-SiO 2 ): charge neutrality does not require any local variation of the concentration: FSDP absent in S cc High chemical disorder (case III) : FSDP in the total S(k) but FSDP absent(or very small) in S cc Ex: l-GeSe 2 (theory) Intensity of FSDP in S cc Case I Case II Chemical disorder Case III Chemical disorder ( CM, Massimo Celino and Alfredo Pasquarello PRB 70, 174202 (2004))

19. Understanding the origins of the FSDP in the concentration-concentration structure factor S cc Liquid (l) GeSe 2 Two approaches: 1)Look for analogies and differences with other systems (SiO 2, SiSe 2, GeSe 4 ) 2)Exploit statistical mechanics on relevant configurations of l-GeSe 2

20. liquid GeSe 2 Idea: look at the time behavior DFT underestimates the height of the FSDP in S cc Average value

21. Proposal: We select configurations belonging to two sub-trajectories: « low » when FSDP in S cc lower than average « high » when FSDP in S cc higher than average Intermediate range order as expressed through the Ge-Ge structure factor: much better agreement for the trajectory « high »..!!!

22. By using the same scheme, we compare the two sets of Bhatia-Thornton structure factors « low »« high » Note : the NNs are very close: both sets yield very good total structure factors

23. Comparing an extensive list of structural properties (coordination numbers, rings topology, g (r) ) the results on the two trajectories are very close… Where does the difference come from..? Number of Ge in two fourfold rings (chains of edge-sharing tetrahedra): Ge* units The trajectory « high » has a higher number of Ge* subunits Warning: 1 and 2 form a Ge*, 2 and 3 do not…!!!

24. Striking correlation between the number of Ge* subunits and the height of the FSDP in S cc Link with chemical disorder: number n of Ge and Ge* n-fold coordinated n12345 Ge0.25.322.460.910.8 Ge*1.610.530.041.616.5 « Superatoms Ge* » are more defective than Ge CM and Alfredo Pasquarello, PRB 2007

25. Structural studies of disordered network-forming materials: quantitative AND predictive power of first-principles molecular dynamics at short and intermediate range-order distances Ge-Se based systems: challenging and stimulating for DFT approaches Many thanks to IPCMS CNRS IDRIS (France), CINES (France) CSCS (Switzerland) Computer centers Work in collaboration with Alfredo Pasquarello (early stages: Roberto Car) on Si-Se systems Massimo Celino