First-principles molecular dynamics studies of liquid and glasses

Carlo MassobrioInstitut de Physique et Chimie des MatériauxStrasbourg (France) (CNRS-Univ. L. Pasteur)

Old Strasbourg: "Petite France"

Short and intermediate rangeorder structural propertiesin disordered network-formingmaterials: AX2, An X(1-n)

A=Ge, Si , X=Se

Current Challenges in Liquid and Glasses ScienceCosener’s House, Abingdon, United Kingdom, 10-12/1/2007

First-principles molecular dynamics studies of liquid and glasses

Carlo MassobrioInstitut de Physique et Chimie des MatériauxStrasbourg (France) (CNRS-Univ. L. Pasteur)

Liquid GeSe2 at 1100 K

Short and intermediate rangeorder structural propertiesin disordered network-formingmaterials: AX2, An X(1-n)

A=Ge, Si , X=Se

Current Challenges in Liquid and Glasses ScienceCosener’s House, Abingdon, United Kingdom, 10-12/1/2007

Our model: essential featuresFirst principles molecular dynamicsDensity functional theory: best with GGA…!! (case of GeSe2)Periodic cell, Plane waves basis setsNorm conserving pseudopotentials

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 relaxationEx: GeSe2: 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..?

Two issues of methodology:

1) 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))

Correlation between structure and bonding properties:role of the GGA in DFT (case of liquid GeSe2)

Ionic character of bonding enhanced:GGA brings the FSDP together with the predominant occurrence ofa tetrahedral order.

LDA

GGA

Two issues of methodology:

1) 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))

Total S(k) for a given L= 15.7 Å

drkr

sinkr

αβ

Rc4παβ ][ 1(r)gr1S

2

ij

)(e R jβRiik

βααβ

NNS

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 Rc in between 6 and 10 Å

Extent of correlations responsible of the FSDP

FSDPFSDP

I.T. Penfold and P.S. Salmon, PRL 67, 97(1991)

Scc/cge cse = 1+cgecse(Sgege-Sgese)

+cgecse(Ssese-Sgese)

Liquid GeSe2: a prototype case

FSDP in both total andScc structure factors

Scc/cgecse = SZZ

For point charges (classical MD): no FSDP in SCC

charge-charge structure factorezz

)rr(ik ji

vji,j

vi

Total S(k)

Note: LDA (dotted line) inaccurate!!!

SNNStot

“…the distribution of the FSDP weigthsin the partials is different in theory andexperiments..” (PRB 64, 144205 (2001))

Reduced intensity of FSDP in SGeGe and Scc

dGeGe (exp) = 2.33 0.03 Å

dGeGe = 2.7 0.1 ÅLiquid GeSe2

Theory 0.04 3.76 1.88 0.37Exp 0.25 3.5 1.75 0.23CON 0 4 2 0 RCN 2 2 1 1

CON chemically ordered networkRCN random covalent network

Ngege Ngese Nsege Nsese

Liquid GeSe2 is a highly defective tetrahedral network, withmiscoordinations and homopolar bonds

Amorphous GeSe2

High statistics required:about 500 ps (quench+relaxation)Results from a single quench

“true” (chain-like)homopolar Ge-Ge bondsare found

Liquid vs amorphous (dotted line)

CM and Alfredo Pasquarello, unpublished

Understanding the origins of the FSDP in theconcentration-concentration structure factor Scc

Liquid (l) GeSe2

Two approaches: 1) Look for analogies and differences with other systems (SiO2, SiSe2, GeSe4)2) Exploit statistical mechanics on relevant configurations of l-GeSe2

Amorphous SiSe2

Enhanced chemical order

nsisi nsise nsesi nsese

Theory 0.06 3.89 1.94 0.10CON 0 4 2 0RCN 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)

Understanding the origins of the FSDP in theconcentration-concentration structure factor Scc

Liquid (l) GeSe2

Two approaches: 1) Look for analogies and differences with other systems (SiO2, SiSe2, GeSe4)2) Exploit statistical mechanics on relevant configurations of l-GeSe2

How to calculate Scc and Szz structure factors

Scc= cacx[1+cacx((SAA-SAX)+(SXX-SAX))]

e)s()r(drdsS)sr(ik

ttzz

zi ionic charges (Ge= 4, Se =6)

)r()rr(z)r( eit ii

POINT-LIKE CHARGE (PLC) MODEL

S)cc(S ccba

PLCzz

1 ezz)rr(ik ji

vji,j

vi

i it )rr(z)r( vi

No FSDP in Szz

(charge neutralityon IRO scales)(CM and Alfredo PasquarelloPRB 68, 020201 (2003))

What is the behavior of Scc

for systems having in common the FSDPin the total S(k)..??

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)

Disordered networks: 3 classes of systems identified

Moderate chemical disorder (case II): Occurrence of different valence statesVariations of concentration induce FSDP in Scc

Ex: l-GeSe4, a-SiSe2, l-GeSe2 (exp)

Perfect network (case I, l-SiO2 ): charge neutrality does not require any local variation of the

concentration: FSDP absent in Scc

High chemical disorder (case III) :FSDP in the total S(k) but FSDP absent(or very small) in Scc

Ex: l-GeSe2 (theory)

Intensity of FSDP in Scc

Case I

Case II

Chemical disorder

Case III

Chemical disorder

(CM, Massimo Celino and Alfredo PasquarelloPRB 70, 174202 (2004))

Understanding the origins of the FSDP in theconcentration-concentration structure factor Scc

Liquid (l) GeSe2

Two approaches: 1) Look for analogies and differences with other systems (SiO2, SiSe2, GeSe4)2) Exploit statistical mechanics on relevant configurations of l-GeSe2

liquid GeSe2Idea: look at the time behavior

DFT underestimates the height of the FSDP in Scc

Average value

Proposal:We select configurations belonging totwo sub-trajectories:« low » when FSDP in Scc lower than average« high » when FSDP in Scc higher than average

Intermediate range orderas expressed through the Ge-Ge structure factor: much better agreement for the trajectory « high »..!!!

By using the samescheme, we comparethe two sets of Bhatia-Thorntonstructure factors

« low » « high »

Note : the NNs are very close: both sets yield very good total structure factors

Comparing an extensive listof structural properties(coordination numbers, rings topology, g (r) )the results on the two trajectoriesare 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 numberof Ge* subunits

Warning: 1 and 2 form a Ge*, 2 and 3 do not…!!!

Striking correlation between the number of Ge* subunitsand 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 5Ge 0.2 5.3 22.4 60.9 10.8Ge* 1.6 10.5 30.0 41.6 16.5

« Superatoms Ge* » aremore defective than Ge

CM and Alfredo Pasquarello, PRB 2007

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 toIPCMSCNRSIDRIS (France), CINES (France) CSCS (Switzerland)Computer centers

Work in collaboration withAlfredo Pasquarello(early stages: Roberto Car)

on Si-Se systemsMassimo Celino