1 Dynamical Processes in Glasses by Molecular Dynamics Simulations José Pedro Rino Universidade Federal de São Carlos, Departamento de Física GSIMCO - Grupo de Simulação Computacional

2 Outline Introduction What is molecular dynamics simulation. How to produce a glass Characterization. Properties Conclusions

3 Introduction Molecular Dynamics Motion of real molecules by molecular beam or Spectroscopic techniques Lattice dynamics (vibratory motion of atoms) Molecular mechanics (force field calculation) Molecular Dynamics simulation compute the motions of individual particles in a given model of solid, gas, liquid or glass.

4

5

6 Introduction Molecular Dynamics Simulation is a method to compute the simultaneous motions of all interacting particles, for a given model, of solid, gas, liquid or glass. Which are the necessary ingredient to calculate the trajectory of all particles of the system? We can ask: What can we get from the trajectories? Are the results reliable?

7 Consider a system How to describe the motion of each particle? At atomic scale we have to know the interactions : Nucleon – Nucleon Electron – Electron Electron – Nucleon SiO 2 (Li 2 O) x (SiO 2 ) 1-x B2O3B2O3 NaCl...

8 Example For the orbitals For the nuclei For instance – one water molecule 2 H atoms + 2 electrons 1 O atom + 6 electrons 8 orbitals 9 equations for the nuclei

9 M nucleous >> m electron Born-Oppenheimer The energy functional is approximated by a phenomenological function: But:

10 Classical M.D.  3N differential 2 nd order eq., not linear and coupled. Classical equations of motion  6N initial conditions.  Interaction Potential, , among particles. with

11 Classical M.D. What can we get? The integration of the 3N eq. of motion (N ≤ atoms) Phase space: coordinates and momenta of all particles.

12 Classical M.D. Phase space: coordinates and momenta of all particles. Statistical Mechanics Thermodynamics (E, c v, H, T, P, , …) Structural correlations (g(r), S(q), bond angles) Mechanical properties (C ij, G, B, …) Correlations in time (G(  ), R 2 (t), g(r,t), …)

13 Structural Correlations r r+dr Pair distribution function Coordination number Bond angle distribution

14 Structural Correlations CrystalLiquid/Glass Gas

15 Structural Correlations : a-SiO 2

16 Structural Correlations : ZnSe

17 Validation How do we know that we are describing the material? Comparison with experimental data.

18 Q is the wave vector I(Q) the intensity of the scattered radiation S(Q) the static structure factor. X-ray or particle beam sample detector For elastic scattering and Experimentally

19 Comparison Experiment-Simulation Experiment Simulation Reciprocal space Real space Related by a Fourier Transform

20 Structure Partial Static Structure Factor Static Structure Factor Pair Correlation Function or Pair Distribution Function

21 Glass Structure Atomic arrangement? Crystal ?Diffraction experiments

22 Structural arrangement Glass ?Cannot by Diffraction experiments BaO 2(SiO 2 ) But, with simulation we can.

23 Example a-SiO 2

24 Example BaO 2(SiO 2 ) Li 2 O 2(SiO 2 ) InSb

25 Example Crystal T=100K) Liquid (T=1000K) Amorphous T=300K) Recrystal. T=300K)

26 Structural Correlations : a-SiO 2

27 Structural Correlations : ZnSe

28  Ring of order m: - closest path connecting alternating Si-O bond - there are 2m Si-O ligações  For N atoms of Si with coordination 4: 6N rings Si Ring definition

29 Structural Correlations 3-fold ring – not planar

30 Solution of all equations of motions and  Temporal correlations  Chronology of events  structural correlations Again…

31

32

33 Solution of all equations of motions and  Temporal correlations  Chronology of events  structural correlations Again…

34 Temporal correlations – MSD & Diffusion Crystal Liquid

35 Temporal correlations – MSD & Diffusion Example: Li 2 Si 2 O 5 L.G.V.Gonçalves, J.P.Rino; J. Non-Cryst.Sol. 402, 91 (2014).

36 Temperature dependence of Diffusion constant Stokes-Einstein relation I. Avranov, J.Phys.:Cond Mat. 11, L267 (1999). J. Ziman in: Models of Disorder (Cambridge Univ. Press, 1979, p Na 2 O 2SiO 2

37 Breakdown of Stokes-Einstein relation I. Avranov, J.Phys.:Cond Mat. 11, L267 (1999). I.Avranov, J.Chem.Phys. 95, 4439 (1991). I.Avranov, J.Non-Cryst.Solids 262, 258 (2000). Temperature dependence of Diffusion and Viscosity are not the same NOT constant Stokes-Einstein relation not valid anymore.

38 …

39 Structural relaxation A.K. Schulz; J. Chim. Phys. Biol. 51, 324 (1954) Glycerol When  ~10 13 P → solid like → T g T g < T < T m Super cooled region Central quantity : structural or  -relaxation Maxwell relation: instantaneous shear modulus

40 Structural relaxation How to compute, using MD Relaxation time Viscosity

41 Viscosity Green-Kubo relation whereis the stress tensor Known all coordinates and momenta

42 Temporal Correlations Suitable definition of relaxation time for liquids ( A.J.Heuer, J.Phys.:Cond. Matter 20, (2008) Intermediate Scattering Function: At large times – fitted by stretched exponential function reciprocal vector - ~ first sharp diffraction peak

43 Metallic Glasses: Pd 45 Ni 55 and Pd 45 Pt 10 Ni K 1000K 800K Supercooled region 800 – 1000 K Ni relaxation time Intermediate scattering function

44 Structural relaxation or Maxwell model  and   same temperature dependence Pd 45 Ni 55 Pd 35 Pt 10 Ni55

45 …

46 Fractional Stokes-Einstein relation  = 1 SE relation  <1 spatial heterogeneity - GFA Since

47 VAF and VDofS W. Jin, P. Vashishta, R. Kalia, J.P. Rino; PRB. 48, 9359 (1993).

48 DoS InP a- BaO.2(SiO 2 )

49 Specific Heat Smaller density  more nanovoids At same T  higher C V Increase number of low-frequency phonons 

50 Summingup Classical Molecular Dynamics – Integration of Newton´s equations for N atoms All positions and momenta as a function of time: r (t) and p (t) Any results: o Structural characterization o Dynamical characterization o Thermal characterization o Mechanical Characterization o Chronological events Weakness  No electronic behavior  Which is the interatomic potential  Time scale extremely powerful technique

51 Fundação de Amparo à Pesquisa do Estado de São Paulo - Brasil Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil Acknowledgments Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil