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Notes for Contributors

Rao, B Jayachander

Mahapatra, S

On the Electronic Nonadiabatic Effects in the H + H<SUB>2</SUB> Reaction Dynamics

Indian J. Phys. 81(11) 1113 (2007) 
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Diffusion and Mobility Driven Instabilities in a Reaction-Diffusion System : A Review

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Jangid, R A

Dielectric Dispersion and Relaxation Studies of Some Pure Nicotinates and their Ternary Mixtures at a Single Microwave Frequency and Temperature 36.5°C

Rai, S B

Singh, Shiv Kumar

Optogalvanic Detection of NaNe and Na<SUB>2</SUB> in a Hollow Cathode Lamp

Nath, P P

Joarder, R N

5V0t€ 
Indian J. Phys. 82(7) 913-917(2008) 
A note on the dynamical structure of liquid LiNa alloy 
PPNath^andRNJoarder 
department of Engineering Physics, Bengal Institute of Technology, Kolkata-700 150, India 
Department of Physics, Jadavpur University, Kolkata-700 332, India 
E-mail rnjoarder@yahoo co in 
Received 28 June 2007, accepted 16 April 2008 
Abstract : The dynamical structure factors of liquid LiNa alloy are calculated in the visco-elastic approximation 
using static properties like effective pair potential and static structure factors The results are compared with 
inelastic neutron scattering (INS) and molecular dynamics (MD) simulation results The specific features are 
discussed It is clearly shown that the effect of the concentration variation on the dynamical structure is small 
though the corresponding effect on the static structure is quite large 
Keywords : Dynamical structure, ordering potential, visco-elastic approximation. 
PACS Nos. : 61 20, 61 25 Mv, 63 50 
Based on the modified Young-Hoshino (MYH) potential for Li and simple Ashcroft 
model for Na, the successful calculation of Bhatia-Thornton (B-T) static structure 
factors and the thermodynamic properties of liquid LiNa system at different 
concentrations [1] and thereafter the dynamical properttos like diffusion constants [2], 
we are tempted to see the applicability of this model for the calculation of dynamical 
structure factors of this system at different concentrations. This is important because, 
as pointed out by Sinn et al [3], the precise measurements of the dynamical structure 
factors provide a stringent test of the inter-atomic interactions. For instance, the results 
of dynamical structure factors for liquid Li obtained with neutral pseudo-atom method 
[4] compare well with their experimental data, whereas Ashcroft's empty core model 
appears to be inadequate. Evidently the choice of the model potential is important. 
The liquid LiNa alloy is a typical phase separating (ps) system whose 
stoichiometric composition (Cy = 0.61) is also the null alloy composition in neutron 
diffraction. The total static structure factor, S(g) reduces to concentration-concentration 
w 
'Corresponding Author © 2008 IACS 
914 P P Nath and R N Joarder 
structure factor, SJqWq.^ and is dominated by a strong small angle scattering with 
subsequent weak oscillations [1]. The system possesses a typical ordering potential. 
It is therefore interesting to see if these features in the ordering potential and static 
structure factor have appreciable effects on the dynamical structure. 
For binary liquid alloy in the effective medium approximation (EMA) [5] we use 
the concept of Wigner-Seitz sphere treating them as a pseudo one component system 
with mean potential (<f>Jr) s </>NN(r)), obtainable from component pair potentials and 
the pure component parameters are replaced by effective values. For dynamical 
structure factor, S(g,u;) we consider visco-elastic approximation [6]. The visco-elastic 
model is simplest one to use and has been applied to a number of systems with 
reasonable success. It gives a method for connecting dynamical properties to static 
properties like liquid structure factor and effective pair potential. The method is based 
on phenomenological analysis of time correlation function and principal advantage is 
that it provides unified treatment of a wide variety of transport coefficients. In the 
model stress correlation functions can be related to intermediate dynamic scattering 
function and expression for S(qtJ) can be conveniently obtained. Thus, S(q,u>) is given 
by 
0 / s 1 T(q)v?hq2lu,2L(q)-u,20(q)) 
S(qtu) = - T L — — * - y (1) 
n§vrlq)iLjz-u>l(q)j\ +\u;2-uj*(q)} J 
with 
7 ^ = ^> /K(9) -^o(q) ) , Vo(q) = v*q/y[S(q) (2) 
where vm is the thermal velocity and uL{q) is the longitudinal frequency of the 
associated wave. S(q), the total structure factor for LiNa alloy can be obtained in the 
low order perturbation theory using appropriate pseudopotentials [1J. For uL(q) we 
follow Bhatia-Singh calculation procedure [7] primarily intended for amorphous systems. 
The relations can be extended to liquids and mixtures with some modifications. For 
liquid, the parameters 0 and 6 of the first and the second derivatives of the effective 
pair potential are related and the modified dispersion relations for liquid can be 
obtained [7]. 
We consider LiNa liquid alloy at T= 725 K and ionic density, p * 0.031083 A"*. 
In Figure 1 we show the calculated S(q) and S^tf/cuC^ at three different 
concentrations. The general features of the experimental (neutron) S(q) curves [8J are 
represented reasonably well by our model potentials as shown in our previous paper 
(Ref. [1] of this paper) for c^ = 0.61. The agreement with other curves is similar. For 
Cu » 0.61, S(q) based on MD simulation [9] has also similar features. In the model, 
A note on the dynamical structure of liquid LiNa alloy 915 
Figure 1. LiNa liquid alloy, structure factors vs. q: S(q) , Scdq)/^^ at (a) q_, = 0.3 (origin shifted by 
1.0) (b) CL, * 0.61 (null alloy) (origin shifted by 0.5) (c) cu = 0.8. 
at CL, = 0.61, S(q) and Scc(q)/cLicr4a are almost indistinguishable while for Cy = 0.3 and 
cu = 0.8 they are very different in their features. The calculated uL(q) (not shown) 
appears in some respect similar to that of pure liquid Li. 
The dynamical structure factors have been obtained for three g-values, q = 0.8, 
1.2 and 1.5 A*"1 and the results are shown in Figure 2. The results when compared 
with MD simulation results [10], we find reasonably good agreement for q = 0.8 and 
1.2 A""1. The experimental, INS data [11] are also shown and there is some 
agreement. The agreement is reasonable in the sense that the viscoelastic model is 
an appropriate model and no calculation even on liquid metals e.g. Li, Rb etc. could 
yield better agreement [12] with MD/experimental results. Further LiNa is a phase 
separating non-simple alloy where the application of the model is surely approximate. 
In this connection it is also to be noted that when the experimental, INS data is 
integrated over u to give the static S(q), the obtained results show some discrepancies 
with experimental S(q) result [10] while MD data give a better agreement. Evidently, 
the experimental (INS), S(q,u;) data are somewhat lower. We have also done 
calculations for qj = 0.3 and 0.8, to see the concentration dependence of S(q,u;). At 
q = 0.8 and 1.2 A"1, the effect of concentration on S(<J^ ;) is small while at q = 1.5 
A"1 the effect is significant. 
Though the total static structure factors are different considerably with 
concentration at these ^values S(q,J) are not affected much. Again at lower 
concentration, S(q,v) are mostly lower at q = 0.8 and 1.2 A"*1 while this trend is almost 
reversed at q = 1.5 A"1. At q = 1,5 A"1, however, our calculated S(qta;) are relatively 
not in good agreement with MD as well as INS results. Anyway, it is clear that though 
the effect of concentration is enormous on static structure factor and ordering 
potential, it is less prominent on dynamical structure factor. The possible explanation 
916 
P P Nath and R N Joarder 
Figure 2. S(q,u) vs. u{u; in p s_f) for liquid LiNa alloy for (a) q = 0.8 A"1, (b) 1 2 A-' and (c) 1.5 A-1 
Calculated — (at 0 61 Li concentration), (at 0.3 Li concentration) and (at 0.8 Li concentration), MD 
simulation result ooo and experimental result ••• both at 0.61 Li concentration 
may be as follows. S(q,u) in the explored (q,u) region decreases monotonically as 
function of u with no side peak. At null alloy (q., = 0.61), S[q,u) is entirely given by 
ScdQ'U) which therefore follow the same pattern of S(q,u>). Though SNfAq,u>) shows 
side peak [10] its contribution to S(q,u>) is very small at CJJ = 0.3 and 0.8. Again, like 
Scdq) (Figure 1 except at q -» 0), Scc{qtuj) is also expected to be not strongly 
concentration dependent. So it is expected that S(q,o;) is only weakly dependent on 
concentration. The concentration dependence is however prominent at larger 
Li-concentration and larger q-values. In case of static structure, however, the SNN(q) 
and ScdQ) have basic differences in shape. While SNtj(q) has a pattern more like that 
of pure Li or Na with a large first peak, Scdq) has a small double peak with low-q 
region changing enormously with concentration and this shoots up at CL, = 0.61. This 
difference in SN^q) and SCM structure {SM is very small at all q) is responsible 
for large change in S{q) with concentration. Further, the overall features of S(q,u;) 
curves are that unlike pure liquid Li, no side peaks revealing the existence of 
propagating sound modes are present. 
A note on the dynamical structure of liquid LiNa alloy 917 
Acknowledgment 
One of the authors (RNJ) acknowledges with thanks, the financial support from CSIR, 
New Delhi (India). 
References 
[1] P P Nath, S Sarkar and R N Joarder Indian J. Phys. 77A 609 (2003) 
[2] P P Nath and R N Joarder Indian J. Pure and Appl. Phys. 43 180 (2005) 
[3] S Sinn, F Sette, U Bergmann, Ch Halcoussis, M Krisch, R Verbeni and E Burkel Phys. Rev. Lett. 781715 
(1997) 
[4] M Canales, L E Gonzalez and J A Padro Phys. Rev. E50 3656 (1994) 
[5] A Pratap, D Bhandari, N S Saxena and M P Saxena Indian J. Pure Appl. Phys. 33 601 (1995) 
[6] K Hoshino, H Ugawa and M Watabe J. Phys. Soc. Jpn. 61 2182 (1992) 
[7] A B Bhatia and R N Singh Phys. Rev. B31 4751 (1985) 
[8] H Ruppersberg and W Knoll Z. Naturforsch a32 1374 (1977) 
[9] M Canales, D J Gonzalez, L E Gonzalez and J A Padro Phys. Rev. E58 4747 (1998) 
[10] N Anento, J Casas, M Canales, D J Gonzalez, L E Gonzalez and J A Padro J. Non-Cryst. Sol. 250 348 
(1999) 
[11] PRGartrell-Mills, RLMcGreevyand WVanderLugtPhysicaB154 1 (1988) 
[12] J Cases, D J Gonzalez and L E Gonzalez Phys. Rev. B60 10094 (1999); J P Hansen and IR McDonald 
Theory of Simple Liquids (London : Academic Press) (1986) 


A Note on the Dynamical Structure of Liquid LiNa Alloy

Sinha, Santanu

Santra, S B

Finite-Size-Scaling Theory for Anisotropic Percolation Models

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