{Molecular dynamic simulation study of molten cesium} J. Serb. Chem. Soc. 82 (6) 681–694 (2017) UDC 546.36:544.27:536.7+544.022: JSCS–4996 532.11:66.09.001.57 Original scientific paper 681 Molecular dynamic simulation study of molten caesium SAEID YEGANEGI1*, VAHID MOEINI2 and ZOHREH DOROODI2 1Department of Physical Chemistry, University of Mazandaran, Babolsar, Iran and 2Department of Chemistry, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran (Received 25 July 2016, revised 5 January, accepted 8 February 2017) Abstract: Molecular dynamics simulations were performed to study thermo- dynamics and structural properties of expanded caesium fluid. Internal pres- sure, radial distribution functions (RDFs), coordination numbers and diffusion coefficients have been calculated at temperature range 700–1600 K and pres- sure range 100–800 bar. We used the internal pressure to predict the metal– –non-metal transition occurrence region. RDFs were calculated at wide ranges of temperature and pressure. The coordination numbers decrease and positions of the first peak of RDFs slightly increase as the temperature increases and pressure decreases. The calculated self-diffusion coefficients at various tempe- ratures and pressures show no distinct boundary between Cs metallic fluid and its expanded fluid where it continuously increases with temperature. Keywords: metal–non-metal transition; MD simulation; internal pressure; RDF. INTRODUCTION Molten Cs has been attracted considerable attention for its novel properties which makes it potentially useful in the systems which need heat pipe, lubricants and coolants at high temperature. Also, it is used in space and nuclear power technology.1–4 Experimental and theoretical investigations show that a moment- ous amount of clustering takes place in the region of the metal-nonmetal tran- sition, when the density decreases below 1.3 g cm–3.5–7 The design and develop- ment of technological applications of Cs, as a kind of new engineering material, needs a precise knowledge of the structural and dynamical features of alkali metal fluids. The metal–non-metal transition for alkali metals occurs close to critical point,8 but does not coincide with it.9 Because of the experimental difficulty at high pressure and temperature (the critical point of liquid- vapor transitions for Cs is Tc = 1924 K, pc = 9.25 MPa and dc = 0.38 g cm–3),10 the simulation can be used as a valuable method to study metallic fluids. One of the early efforts to study the structure of liquid metals was * Corresponding author. E-mail: yeganegi@umz.ac.ir doi: 10.2298/JSC160725018Y 682 YEGANEGI, MOEINI and DOROODI performed in 195211 and the first momentous molecular dynamics (MD) simul- ation for Cs was performed in 2001.12 The diffusion and shear-viscosity coef- ficients and velocity auto correlation function have been reported for Na, K, Rb and Cs near the melting point.13–15 The simple but useful expressions for the relationship between structural and surface properties of liquid metals have been presented by employing the hard-sphere description near the melting point.16,17 Also, MD simulations have been performed to calculate the structural and trans- port properties of liquid alkali metals by using reformed Morse potential near the melting point.18 The embedded atom method potentials have been calculated for the alkali metals along the melting line of the metal and the discrepancy between the simulated energy, and the actual energy of the metal at high temperatures has been discussed.19 Recently, thermodynamic quantities of the alkali metals20 and their cluster size distributions21 have been studied based on the static crystalline properties and using ab initio potential respectively. Gupta proposed a semi-empirical potential to study the metallic fluids by molecular dynamics.22 The Gupta potential function has been applied success- fully by many researchers to describe the structure and energy of Pb23, Ni, Ag, Au24 and Cu–Au, Al, Zn and Cd clusters.25 Also, Gupta potential has been used to study the melting of Na and Cs clusters in order to investigate the effects of the geometric and electronic magic numbers on the melting temperature as a function of cluster size.26–28 The electronic structure of alkali metal fluids strongly depends on the ther- modynamic state of the system. When Cs fluid expands, two transitions can occur, liquid–vapour and metal–non-metal one.9 In fact, a high-density liquid metal is a conductor, while it becomes a non-metal insulator when turned into low-density vapour. Near the critical point the transition from a liquid metal to a non-metal takes place.29 This transition implies that the nature of the particle interactions must change dramatically, from metallic to a van der Waals-type interaction.30 The particle interactions in dense alkali metals are dominated by the Coul- omb potential, whereas the interactions in the nonmetallic phase are weak van der Waals forces. It is suggested that there is a relationship between rapid vari- ation in the conductivity and density.31 The metal–non-metal transition can be investigated by comparing the measured electrical conductivity with the value calculated from the nearly-free-electron theory (NFE). This theory is often used to describe metallic behaviour and is valid when the mean free path of the con- duction electron is much larger than the average distance between neighbouring atoms in the liquid. It has been shown that the nearly-free electron theory pro- vides a good account of the conductivity for Cs for densities higher than 1.3 g cm–3.29–31 According to this theory, the transition begins at 1.3 g cm–3 for Cs, which is exactly the density around which the deviation from the linear isotherm THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 683 regularity (LIR) is observed.5,32 Keshavarzi et al.32 demonstrated that the metal– –non-metal transition is surely neither first nor second order, and it can occur separately or simultaneously with the liquid–vapour transition (LVT). In other words, the metal–non-metal transition proceeds gradually, which is indicated by some changes in liquid properties such as lower conductivity than that predicted by NFE theory,29,30 deviation of density from the LIR predictions for a single phase.5,32 There has been an increasing interest in the study of internal pressure in the elucidation of thermodynamic properties of metallic fluids.5 A general method of calculating the internal pressure is based on the thermodynamic equation of state: i T V E p p T p V T ∂ ∂   = = −   ∂ ∂    (1) E is the internal energy, [ ]/ TE V∂ ∂ is the internal pressure and [ ]/ VT p T∂ ∂ is usually called the thermal pressure.33–35 According to the statistical mechanics, the total internal energy E of a fluid is the sum of potential energy, U, and the kinetic energy, K. It is assumed that any kinetic energy contribution to the inter- nal energy will vanish on taking the derivative, since the temperature is held constant.36 The potential energy can be divided into two parts, attractive UA and repulsive UR parts37 and inserting into Eq. (1) gives: ( ) ( )A R i i,A i,R , ,N T N T U K U U p p p V V    ∂ + ∂ + = = = +      ∂ ∂    (2) Where pi,A is the attractive internal pressure (positive) and pi,R is the repulsive internal pressure (negative). As the density is raised at constant temperature, the repulsive pressure becomes predominant, and therefore, internal pressure dec- reases. On the other hand, the reason is that the resultant forces under low pres- sure conditions are attractive, and as the pressure increases, the repulsive forces become predominant. Although some approximate approaches exist, there is no definite way to distinguish the metallic and non-metallic states. Moeini5 has shown that linear regularity of simple fluid can be applied successfully for predicting the metal– –non-metal transition in alkali metals. Based on this assumption they showed that internal pressure of expanded Cs versus density has a maximum around 1.3 g cm–3 or 0.097 L mol–1, when before reaching this density some properties such as local contraction, electrical conductivity and magnetic susceptibility show significant changes.5,9,29,30,31 Internal pressure, as well as density, of molten metal can be used to recog- nize the metal–non-metal transition of an expanded metallic fluid.32,33 The goal of this paper is the study of the pressure dependence of internal pressure of Cs fluid 684 YEGANEGI, MOEINI and DOROODI by the molecular dynamics (MD) simulations to recognize the initiation of metal–non-metal transition from the bulk fluid up to the expanded fluid. MD simulations were performed near metal-nonmetal transition by using Gupta pot- ential. In the present work, up to our knowledge, we demonstrate the first study to calculate internal pressure by performing classical molecular dynamics. We used the internal pressure in order to predict metal–non-metal transition and also we study the structural and dynamical properties from bulk up to creating exp- anded fluid of Cs by calculation of radial distribution function, coordination number and diffusion coefficient. SIMULATION DETAILS We have used Gupta potential to describe the interactions in Cs fluid. Based on this pot- ential, the energy between particles can be written as a sum of Born-Mayer-type repulsive and many-body attractive energies as:38 2 0.5 0 0 exp( 1) exp[ 2 ( 1 ]ij ij j i j i r r E A p B q r r≠ ≠    = − − − − −       (3) where rij is distance between i and j atoms and r0 is the equilibrium nearest-neighbour distance in the bulk fluid. The parameters p and q represent the repulsive interaction and the attractive interaction ranges, respectively. The Gupta potential parameters for Cs used in this work are: A = 0.02054 eV, B = 0.24218 eV, p = 9.62, q = 1.45 and r0 = 9.44 a.u. 24 Cs and other alkali metals are simple metals, meaning that the Fermi surface of these metals is spherical. They are generally considered to be monatomic simple liquids.39,40 In all our molecular dynamic simulations, we have used 428 Cs atoms initially placed in a bcc array replicated in xyz directions. All MD simulations were performed using DL-POLY-2.18 prog- ram.41 Internal pressure and radial distribution function (RDF) were calculated at wide ranges of temperature (700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500 and 1600 K) and pressure (100, 200, 300, 400, 500, 600, 700 and 800 bar). At each temperature for the lowest pressure, 428 atoms were placed in the simulation cell then NPT (constant particle number, pressure and temperature) simulation was conducted for 5ns with the Berendsen method using 1 and 3 ps as the thermostat and barostat relaxation times to reproduce the experimental density.42 The equations of atomic motion was integrated using the Verlet velocity algorithm43 with a time step of 0.005 ps and cut off distance of 12.0 Å. The diffusion coefficients were calculated by NVT MD simulations and Berendsen thermostat for 10 ns time steps where 2 ns steps were discarded as equilibration. RESULTS AND DISCUSSION Internal pressure The calculated total energy and density are presented and compared with experimental densities42 in Table I. The deviations expressed in percent from experimental values are shown in Fig. 1. Our simulations underestimate Cs den- sity for temperatures higher than 900 K while overestimating it for lower tempe- ratures. Large deviation at high temperatures and low pressures can be attributed THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 685 to the lack of sufficient accuracy of the proposed potential energy function to describe the atomic interactions. Also, the large fluctuation in density due to the formation and destruction of varying size Cs clusters at low pressure and high temperatures can be the cause for the observed large deviations. TABLE I. Calculated total energy, E, calculated density, dcal, and experimental density, dexp, of Vargaftik et al.42 for Cs fluid at different pressures, p, and temperatures, T p / bar E / J mol-1 dcal / g cm -3 dexp / g cm -3 p / bar E / J mol-1 dcal / g cm -3 dexp / g cm -3 T = 700 K T = 800 K 100 –559.263 1.662 1.626 100 –530.899 1.579 1.57 200 –561.786 1.685 1.643 200 –534.217 1.606 1.588 300 –564.169 1.706 1.659 300 –537.114 1.630 1.605 400 –566.366 1.727 1.675 400 –539.684 1.653 1.622 500 –568.235 1.747 500 –542.02 1.675 600 –569.917 1.765 1.704 600 –544.053 1.695 1.654 700 –571.529 1.783 700 –546.062 1.715 800 –572.931 1.800 800 –547.838 1.733 T = 900 K T = 1000 K 100 –502.372 1.496 1.515 100 –473.167 1.410 1.457 200 –506.437 1.526 1.533 200 –478.377 1.446 1.477 300 –509.965 1.554 1.552 300 –482.886 1.479 1.497 400 –513.026 1.579 1.570 400 –486.624 1.508 1.516 500 –516.04 1.604 500 –490.082 1.534 600 –518.563 1.627 1.604 600 –493.05 1.559 1.554 700 –520.759 1.648 700 –495.993 1.584 800 –522.955 1.669 800 –498.4 1.606 T = 1100 K T = 1200 K 100 –443.097 1.321 1.397 100 –412.117 1.229 1.335 200 –449.943 1.365 1.419 200 –420.458 1.280 1.361 300 –455.387 1.402 1.441 300 –427.654 1.325 1.385 400 –460.106 1.435 1.463 400 –433.355 1.363 1.409 500 –464.195 1.466 500 –438.284 1.397 600 –467.863 1.494 1.504 600 –442.49 1.428 1.454 700 –471.017 1.519 700 –446.228 1.456 800 –473.914 1.544 800 –449.639 1.483 T = 1300 K T = 1400 K 100 –378.87 1.127 1.272 100 –343.006 1.017 1.204 200 –390.388 1.193 1.301 200 –359.057 1.102 1.240 300 –399.103 1.245 1.328 300 –370.038 1.164 1.271 400 –406.182 1.289 1.354 400 –378.706 1.216 1.299 500 –412.093 1.328 500 –385.809 1.260 600 –417.163 1.363 1.404 600 –391.673 1.298 1.354 700 –421.509 1.394 700 –396.79 1.332 800 –425.364 1.423 800 –401.323 1.364 T = 1500 K T = 1600 K 100 –302.376 0.888 1.131 100 –251.747 0.724 1.052 200 –325.694 1.005 1.175 200 –290.344 0.902 1.108 686 YEGANEGI, MOEINI and DOROODI TABLE I. Continued p / bar E / J mol-1 dcal / g cm -3 dexp / g cm -3 p / bar E / J mol-1 dcal / g cm -3 dexp / g cm -3 T = 1500 K T = 1600 K 300 –340.413 1.083 1.211 300 –309.362 0.997 1.149 400 –351.02 1.142 1.244 400 –322.469 1.067 1.187 500 –359.314 1.191 500 –332.609 1.123 600 –366.02 1.233 1.305 600 –340.553 1.170 1.256 700 –372.188 1.272 700 –347.352 1.212 800 –377.188 1.306 800 –353.193 1.249 Fig. 1. Relative deviations of calculated densities from the experimental values42 from Table I for Cs at temperature range 700–1600 K. Internal energy is generally represented by a cubic expression in the density by allowing the coefficients to depend on temperature.34 We have used a similar expression in terms of volume rather than density: 2 30E E aV bV cV= + + + (4) where V = V(p,T) and a, b and c are constants characteristic of a particular sub- stance. The fitting parameters a, b and c can be determined by fitting E versus V at constant temperature over the whole pressure range. Fitted parameters are shown in Table II, while coefficients of determination (R2) for all of fittings were nearly 1. After the seminal work of Parsafar34 many researcher used the equation U = U(V) for obtaining the equation of state and some linear regularities (LIR).36 Up to our knowledge, we obtained for the first time the coefficients of U = U(V) by fitting the calculated internal energies to volume. The obtained coefficients are strongly depended on temperature, which shows the dependence of the inter- particle interaction to the thermodynamic sate of the Cs. The calculated internal energy from Eq. (4) and the simulated one depicted good agreement in Fig. 2. The internal pressure can be obtained by the straightforward differentiation of internal energy with respect to volume at constant temperature. THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 687 TABLE II. Fitted parameters of equation 4, a, b, c at different temperatures T T / K a / kJ mol-1 m-3 b / 107 kJ mol-1 m-6 c / 1012 kJ mol-1 m-9 700 –3.71 675.07 394.49 800 0.19 –24.95 23.36 900 –0.96 175.57 –93.48 1000 –0.21 52.18 –26.18 1100 –0.34 71.57 –36.16 1200 –0.34 69.14 –34.43 1300 –0.09 32.16 –16.59 1400 0.07 10.44 –6.78 1500 0.15 –0.52 –2.08 1600 0.23 –9.53 1.40 Fig. 2. Calculated (symbols) and simulated (lines) internal energies vs. volume for Cs. The resulting internal pressures, pi, versus molar volume are shown in Fig. 3. It shows that at 700–1000 K, internal pressure, pi, increases with molar volume, Vm, but for 1300–1600 K, it decreases with molar volume. The isotherms of 1100 and 1200 K in Fig. 3 show maxima at about 0.093 and 0.094 L mol–1 (1.43 and 1.41 g cm–3), respectively. Our results are in agreement with previous experi- mental and theoretical results5,6,44,45 which showed that the internal pressure had a maximum at 1.3 g cm–3 (0.097 L mol–1) at 1350 K. It is well known that liquid Cs at high densities shows characteristics typical of a nearly free electron (NFE) metal.6,31,44,46 However, when the density is reduced below about 1.3 g cm–3 or the temperature is increased up to 1350 K, the quantitative changes begins to develop. Under this condition, the measured electrical conductivity is lower than the NFE value31 and the magnetic susceptibility47 and density fluctuation48 inc- rease. These changes indicate that the metal–non-metal transition is developing and that it is strongly dependent on the thermodynamic state.29–31 The failure of the 688 YEGANEGI, MOEINI and DOROODI 0.6 1.0 1.4 1.8 2.2 2.6 0.06 0.09 0.12 0.15 0.18 p i / M Pa Vm / L mol-1 700 K 800 K 900 K 1000 K 1100 K 1200 K 1300 K 1400 K 1500 K 1600 K Fig. 3. Calculated internal pressure pi isotherms for Cs at temperature range 700–1600 K. NFE theory reflects, most probably, cluster formation and the increased imp- ortance of soft potential.5,6,31,45 It is revealed that for molar volumes higher than Vmax the attractive force becomes predominant and it has strong influence on the determination of internal energy and internal pressure.6,32,48,49 Marcus50,51 has shown that the internal pressure of water (contrary to most liquids, except liquid metals) increases with the temperature and exhibit a maximum at 446.15 K. He has explained this behaviour in terms of gradual change in the nature of binding between water molecules. Likewise, the maximum in internal pressure vs. molar volume in Fig. 2 can be understood in terms of two different bindings in the mol- ten alkali metals.32 At the low molar volumes (high pressures and low tempe- ratures), where the measured conductivity and thermodynamic state of the system agrees well with predictions from the NFE theory and the LIR, respect- ively,5,6,27,32 the system is in a monoatomic state with a delocalized electron cloud over the entire system. In this state, increasing the molar volume further (dec- reasing pressure) leads to a smaller repulsion between ions and negative repul- sive internal pressure, pi,R, which tend to increases the internal pressure. As can be seen from Fig. 2 at 700 K, the internal pressure increases steadily with the increasing the molar volume. Further increasing of the molar volume leads to clustering, where the electrons tend to be shared between atoms within a cluster, resulting in a molecular or polyatomic structure with an insignificant conduct- ivity. Therefore, there are two different types of bindings in the system, the metallic bonding between atoms within clusters and van der Waals attractions between clusters. Formation of clusters diminish the metallic bonding then dec- reases the attraction energy over the system where this decreases the attractive internal pressure, pi,A. Keshavarzi et al.32 have shown that this transition is neither first nor second order but occurs gradually in the expanded molten Cs. The max- THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 689 imum of internal pressure in Fig. 3 is the point where the electron delocalization over the entire system breaks down by clustering and the system composed of the metallic and non-metallic parts. The extrapolation of results of a rather small system to bulk fluid must be done carefully. In order to check the size dependency of our results, especially the location of Vmax, the internal pressures versus molar volume at 1100 K were reproduced for a larger system with 856 Cs atoms in Fig. 4 and compared with that of a smaller system. Figure 4 revealed that the density for a larger system is shifted slightly toward smaller molar volume but the location of the maximum remains nearly unchanged. So, one can conclude that the value of Vmax is inde- pendent of the system size. 2.050 2.070 2.090 2.110 2.130 0.080 0.085 0.090 0.095 0.100 0.105 p i / M Pa Vm / L mol-1 856 Cs 428 Cs Vmax Fig. 4. Calculated internal pressure, pi, for 428 (black square) and 856 Cs atoms (grey triangle) at 1100 K. Fluid structure We calculated radial distribution functions (RDFs) of the expanded Cs in whole studied temperature and pressure ranges using Gupta potential. The posi- tions of the first peak of RDFs, namely rmax, have been analysed. It slowly rises from 4.98 Å at low temperature and high pressure, to 5.03 Å at high temperature and low pressure. The RDFs at temperature range 700–1600 K and 500 bar pres- sure are plotted as an example in Fig. 5. It shows that the intensity of the first and second peak of RDFs reduced and overspread as temperature increases. The coordination number, N, up to the first minimum of RDFs for Cs fluid is plotted in Fig. 6 at the studied temperature and pressure ranges. The calculated coordination number generally decreases with temperature, from 12 to 7, but its variations are strongly depends on the thermodynamic state of the system. The variations of the coordination number at high temperature and low pressure are more pronounced than in the low temperature and high pressure. 690 YEGANEGI, MOEINI and DOROODI 0 0.4 0.8 1.2 1.6 2 2 4 6 8 10 12 14 R D F r / Å 700 K 800 K 900 K 1000 K 1100 K 1200 K 1300 K 1400 K 1500 K 1600 K Fig. 5. Radial distribution functions (RDFs) for Cs at p = 500 bar at temperatures from 700 to 1600 K. 6 8 10 12 600 800 1000 1200 1400 1600 1800 N T / K 800 700 600 500 400 300 200 100 Fig. 6. The calculated coordination number (N) of Cs at temperatures from 700 to 1600 K and pressures from 100 to 800 bar. The comparison of snapshots of the system at low and high temperatures in Fig. 7 shows that, as the system expands, the average nearest neighbour-distance (rmax) remains nearly constant while the average coordination number decreases. This observation agrees well with the findings of Hensel30 explained based on the formation of Cs clusters. The average coordination number decreases because of an increase in the number of atoms on the surface of clusters.30 This calculations are in good agreement with the results of previous studies.7,29,47 Our study shows that in high temperature, when non-metallic properties are prevailing, the coor- dination number of Cs fluid is less than 11, while it is larger than 11 for Cs fluid with metallic properties at lower temperature. THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 691 Fig. 7. Snapshots of the simulation ensemble at: a) T = 700 K and p = 800 bar and b) T = 1500 K and p = 100 bar. Self-diffusion coefficient The knowledge of diffusivities plays an important role in the investigation of liquid metals and fluids. Numerous experimental and theoretical diffusion coef- ficient data exist near melting point of Cs 13,14,16,18 and a few studies of liquid metals have been carried out at high temperature.29,52,53 However, for temperature and pressure ranges considered here, there is no reported diffusion coefficient for Cs fluid. The diffusion coefficients were calculated for some selected points around the maximum of the pi–Vm curve in Fig. 3 and reported in Table III. The state of Cs fluid for molar volumes lower and higher than Vmax were labelled M and EM, respectively. The state of the maximum points of pi–Vm isotherm curves at 1100 K and 400 bar are shown also in Table III. The entries in Table III were sorted based on the diffusion coefficient increment. The inspection of Table III shows that although there is not a definite boundary between metal and non- -metal regions, one can certainly predict that the compressed Cs fluid with dif- fusion coefficient less than 9.12×10–6 cm2 s–1 possess metallic characteristic and the expanded Cs with diffusion coefficient greater than 1.07×10–5 cm2 s–1 starts to show non-metallic characteristic. So one can suggest the diffusion coefficient as a simple factor to characterize the metallic state of Cs fluid. Calculated diffusion coefficients of metallic and non-metal Cs are different by one order of magni- tude, but the metal to non-metal transition takes place gradually in terms of dif- fusion coefficient. TABLE III. Calculated molar volume, Vm, coordination number, N, diffusion coefficient, D, and state of the Cs fluid designated as metal (M) or expanded metal (EM) around maximum point (MAX) of pi–Vm in Fig. 3 T / K p / bar Vm / L mol -1 N D / 106 cm2 s-1 State 700 800 0.074 12.83 3.96 M 700 600 0.075 12.51 4.14 M 800 100 0.084 12.08 6.07 M 692 YEGANEGI, MOEINI and DOROODI TABLE III. Continued T / K p / bar Vm / L mol -1 N D / 106 cm2 s-1 State 900 100 0.089 11.05 7.45 M 1100 800 0.086 11.99 8.55 M 1100 600 0.089 11.41 8.92 M 1000 200 0.092 11.07 9.07 M 1100 500 0.091 11.20 9.12 M 1100 400 0.093 10.58 9.45 MAX 1000 100 0.094 11.01 9.60 M 1100 300 0.095 10.73 10.19 EM 1200 800 0.090 11.52 10.45 M 1200 700 0.091 11.12 10.46 M 1200 600 0.093 11.11 10.65 M 1100 100 0.100 10.14 10.73 EM 1200 500 0.095 10.58 11.36 EM 1200 400 0.097 10.44 11.42 EM 1300 800 0.093 10.86 11.43 EM 1400 800 0.097 10.21 13.40 EM 1500 800 0.102 10.16 14.94 EM 1600 700 0.110 10.00 18.09 EM 1600 100 0.184 6.99 21.37 EM CONCLUSIONS We calculated density, internal pressure, RDFs and diffusion coefficients of Cs fluid using molecular dynamics and Gupta potential for wide ranges of pres- sure and temperature to investigate the metal–non-metal transition. The internal pressure of Cs fluid exhibits a pronounced maximum when the transition from metal to non-metal begins to develop. Our results showed that molten Cs with coordination number more than 11 exhibits metallic behaviour, while for the expanded fluid of Cs, with lower electrical conductivity than predicted by NFE theory, the coordination number is less than 11. The dynamical behaviour of Cs fluid was studied by the calculation of self-diffusion coefficients. Our results show that the diffusion coefficients of metallic Cs are smaller than those of the expanded fluid. It is shown that the diffusion coefficient can be used to charac- terize the metallic and non-metallic state of Cs fluid accurately, although it is not as accurate as internal pressure. И З В О Д СТУДИЈА СТОПЉЕНОГ ЦЕЗИЈУМА МОЛЕКУЛСКО-ДИНАМИЧКОМ СИМУЛАЦИЈОМ SAEID YEGANEGI1, VAHID MOEINI2 и ZOHREH DOROODI2 1 Department of Physical Chemistry, University of Mazandaran, Babolsar, Iran и 2Department of Chemistry, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran Урађене су симулације молекулском динамиком са циљем да се проуче термоди- намичка и структурна својства експандованог течног Cs. Унутрашњи притисак, функције радијалне расподеле (RDFs), координациони бројеви и коефицијенти дифузије израчу- THERMODYNAMICS AND STRUCTURAL PROPERTIES OF MOLTEN Cs FLUID 693 нати су у температурном опсегу 700–1600 K и опсегу притиска 100–800 bar. Користили смо унутрашњи притисак за предвиђање области појављивања прелаза метал–неметал. RDF су израчунате за широке области температуре и притиска. Координациони бројеви опадају, а положаји првог пика у RDF лагано расту са порастом температуре и са сма- њењем притиска. Израчунати коефицијенти самодифузије на различитим темпера- турама и притисцима не показују за Cs јасну границу између металног и експандованог течног стања, а континуално расту са температуром. (Примљено 25. јула 2016, ревидирано 5. јануара, прихваћено 8. фебруара 2017) REFERENCES 1. C. T. Ewing, J. P. Spann, J. R. 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