1
Investigation of Structural, thermodynamics and dynamics of Alkali- metal disilicate glasses via molecular dynamics simulation
Hamid Peyman 1, Saman Alavi 2, M. H. Kowsari 1 and Bijan Najafi 1
1 Department of Chemistry, Isfahan University of Technology, Isfahan, Iran.
Email: [email protected], [email protected] & [email protected]
2Department of Chemistry, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada.
Email: [email protected]
Silicates are multi-functional materials which are important in optical and biomedical applications and dominant in geological environments. For this reason they are of interest to variety of scientific communities.
In this work, we have used molecular dynamics simulations to study the structural, thermodynamic, and dynamical properties of alkali-metal disilicates with the formula M2Si2O5 over a wide range of temperature and pressure conditions. The model potential used in these simulations is based on that of Vessal et al. [1]. The MD calculations were performed for sodium and potassium silicates in the temperature and pressure ranges from 250 to 1000 K and 1.01325 bar to 100 kbar, respectivley. The time step for the simulations was 1 × 10-3 ps and the systems were equilibrated for a minimum of 60,000 time steps. We have obtained the partial radial distribution functions (RDFs) for all ion pairs and the total RDF over a wide temperature range for sodium and potassium disilicate glasses. The results for sodium disilicate glass at 1000 K and 100 kbar are presented in Fig. 1.
14
12
Si-O 10
8
O-O Si-Si
6
4 Na-Si
Na-Na 2
0
0 20 40 60 80 100 120 140 160 180
r / A
Figure 1. Partial RDF for Na2Si2O5 at 1000 K and 100 kbar
The increase of the molar enthalpy (Hm) with temperature is shown in Fig. 2. The
g (r)
Na-O
2
molar enthalpy is linear and the slope yields the average heat capacity at constant pressure, Cp,m, in the whole temperature range,
Hm = (Hm,298 – 298 Cp,m) + Cp,mT (1)
The molar heat capacity Cp,m and correlation coefficient R2 for sodium and potassium disilicate glasses are as follows: (0.2798 kJ.K-1mol-1,1.000 for sodium disilicate glass) and (0.2758 kJ.K-1mol-1,0.998 for potassium disilicate glass).
-32100
-32200
-32300
-32400
-32500
-32600
-32700
200 300 400 500 600 700 800 900 1000 1100
T / K
Figure 2. Correlation plots of themolar enthalpy as a function of absolute temperature (p = 1 bar)
The linear thermal expansion coefficient (alin) of sodium and potassium disilicate glasses can be evaluated from the variations of the lattice parameter with temperature and pressure as follows:
alin = 1/a(T0) [6a(T)/6T]p , (2)
where a(T0) is the lattice parameter at room temperature. The calculated results for sodium and potassium disilicate glasses are shown in Fig. 3.
1.009 1.008 1.007 1.006 1.005 1.004 1.003 1.002 1.001 1 0.999 0.998
200 300 400 500 600 700 800 900 1000 1100
Temperature (K)
Figure 3. Calculated linear thermal expansion coefficient of Na2Si2O5 as a function of temperature at 1 bar.
K2Si2O5
Na2Si2O5
alin (K-1) Hm / kJ mol-1
3
Both sodium and potassium disilicates glasses show excellent agreement with the form of the Parsafar and Mason equation of state for solids [3],
P(V/V0)2=A0+A1(V0/V) +A2(V0/V)2. (3)
Finally we obtained the mean-square displacement (MSD) for sodium and potassium ions as a function of temperature in range 1000 – 2000 K. The oxygen and silicon atoms are covalently bonded and do not show appreciable diffusion. Fig.4 shows the MSD obtained for sodium ions. The slope of the linear portions of these curves is proportional to the diffusion coefficient of Na+. As it was expected, the diffusion coefficient of Na+ is greater than K+.
225 200 175 150 125 100 75 50 25
0
0 5 10 15 20 25 30 35 40 45 50
t / ps
Figure 4 . A plot of mean square displacement (in Å2) as a function of time for sodium atoms in sodium disilicate glass.
Refrences:
1- B. Vessel, M. Amini, D. Fincham, and C. R. A. Catlow, Philos. Mag. B 60, 753 (1989)
2- M. L. Wolf, J. R. Walker, and C. R. A. Catlow , Solid State Ionics 13, 33 (1984).
3- G. Parsafar, E.A. Mason, Phys. Rev. B 49 (1994) 3049-3060
2000 K
1800 K
1600 K
1400 K
1200 K 1000 K
MSD
4
