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First-principles molecular dynamics studies of liquid and glasses

First-principles molecular dynamics studies of liquid and glasses. Carlo Massobrio Institut de Physique et Chimie des Matériaux Strasbourg (France) (CNRS-Univ. L. Pasteur ). Short and intermediate range order structural properties in disordered network-forming

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First-principles molecular dynamics studies of liquid and glasses

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  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) Short and intermediate range order structural properties in disordered network-forming materials: AX2, An 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 Old Strasbourg: "Petite France"

  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) Short and intermediate range order structural properties in disordered network-forming materials: AX2, An 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 Liquid GeSe2 at 1100 K

  3. Our model: essential features First principles molecular dynamics Density functional theory: best with GGA…!! (case of GeSe2) Periodic cell, Plane waves basis sets Norm conserving pseudopotentials How do we deal with space and time limitations..? Typical size of the periodic boxes: L=15-20 Å (N=120,144) kmin < 0.4 Å-1 kFSDP 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: GeSe2: for each LC, 22 ps down to T=600K and 22 ps at T=300 K Computer code: norm-conserving version of ultra-soft FPMD written by A. Pasquarello (Lausanne) (PRL 69, 1982 (1992), PRB 47, 10142 (1993))

  4. Two issues of methodology: • Role of the generalized gradient approximation (GGA) • within density functional theory (case of liquid GeSe2) • (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 GeSe2) GGA LDA Ionic character of bonding enhanced: GGA brings the FSDP together with the predominant occurrence of a tetrahedral order.

  6. Two issues of methodology: • Role of the generalized gradient approximation (GGA) • within density functional theory (case of liquid GeSe2) • (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. R c sinkr = [ ] ò - 2 1 (r) 1 + r g 4 π dr S r αβ αβ kr - ( ) = a å ik R R i j β e S ij αβ N N α β Two ways are available to calculate the structure factors… Extent of correlations responsible of the FSDP Total S(k) for a given L= 15.7 Å Real space (solid line) Reciprocal space (dotted line): our approach The FSDP becomes clearly discernible for Rc in between 6 and 10 Å

  8. FSDP FSDP For point charges (classical MD): no FSDP in SCC charge-charge structure factor Scc/cgecse= SZZ Liquid GeSe2: a prototype case I.T. Penfold and P.S. Salmon, PRL 67, 97(1991) Total S(k) Scc/cge cse = 1+cgecse(Sgege-Sgese) +cgecse(Ssese-Sgese) FSDP in both total and Scc structure factors

  9. SNN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 SGeGe and Scc Note: LDA (dotted line) inaccurate!!!

  10. dGeGe = 2.7 0.1 Å dGeGe (exp) = 2.33 0.03 Å Liquid GeSe2 Ngege Ngese Nsege Nsese 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 Liquid GeSe2 is a highly defective tetrahedral network, with miscoordinations and homopolar bonds

  11. Amorphous GeSe2 Liquid vs amorphous (dotted line) High statistics required: about 500 ps (quench+relaxation) Results from a single quench “true” (chain-like) homopolar Ge-Ge bonds are found CM and Alfredo Pasquarello, unpublished

  12. Understanding the origins of the FSDP in the concentration-concentration structure factor Scc Liquid (l) GeSe2 • Two approaches: • Look for analogies and differences with other systems (SiO2, SiSe2,GeSe4) • Exploit statistical mechanics on relevant configurations of l-GeSe2

  13. Si(0) Si(1) Amorphous SiSe2 Si(2) Enhanced chemical order Exp. CMD nsisi nsise nsesi nsese 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% Massimo Celino and CM, PRL 64, 125502 (2003)

  14. Understanding the origins of the FSDP in the concentration-concentration structure factor Scc Liquid (l) GeSe2 • Two approaches: • Look for analogies and differences with other systems (SiO2, SiSe2,GeSe4) • Exploit statistical mechanics on relevant configurations of l-GeSe2

  15. How to calculate Scc and Szz structure factors Scc= cacx[1+cacx((SAA-SAX)+(SXX-SAX))] ziionic charges (Ge= 4, Se =6) POINT-LIKE CHARGE (PLC) MODEL No FSDP in Szz (charge neutrality on IRO scales) (CM and Alfredo Pasquarello PRB 68, 020201 (2003)) What is the behavior of Scc for systems having in common the FSDP in the total S(k)..??

  16. Correlation between FSDP in Scc and chemical disorder Case I: perfect chemical order: l-SiO2 (theory) Case II: small deviations from chemical order: a-SiSe2 (theory) Case III: large deviations from chemical order: l-GeSe2 (theory)

  17. Disordered networks: 3 classes of systems identified (CM, Massimo Celino and Alfredo Pasquarello PRB 70, 174202 (2004)) Perfect network (case I, l-SiO2 ): charge neutrality does not require any local variation of the concentration: FSDP absent in Scc Intensity of FSDP in Scc Case II Moderate chemical disorder (case II): Occurrence of different valence states Variations of concentration induce FSDP in Scc Ex: l-GeSe4, a-SiSe2, l-GeSe2 (exp) Case III Case I Chemical disorder Chemical disorder High chemical disorder (case III) : FSDP in the total S(k) but FSDP absent(or very small) in Scc Ex: l-GeSe2 (theory)

  18. Understanding the origins of the FSDP in the concentration-concentration structure factor Scc Liquid (l) GeSe2 • Two approaches: • Look for analogies and differences with other systems (SiO2, SiSe2,GeSe4) • Exploit statistical mechanics on relevant configurations of l-GeSe2

  19. DFT underestimates the height of the FSDP in Scc Average value liquid GeSe2 Idea: look at the time behavior

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

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

  22. 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…!!!

  23. Striking correlation between the number of Ge* subunits and the height of the FSDP in Scc Link with chemical disorder:number n of Ge and Ge* n-fold coordinated n 1 2 3 4 5 Ge 0.2 5.3 22.4 60.9 10.8 Ge* 1.6 10.5 30.0 41.6 16.5 « Superatoms Ge* » are more defective than Ge CM and Alfredo Pasquarello, PRB 2007

  24. 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

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