J. Chem. Soc., Furaday Trans. I, 1982, 78, 1555-1560 Structural Analysis of Molten LiBr BY HIDEO OHNO* AND KAZUO FURUKAWA Molten Materials Laboratory, Division of Nuclear Fuel Research, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 3 19- 1 1, Japan AND KAZUO IGARASHI AND JUNICHI MOCHINAGA Department of Synthetic Chemistry, Faculty of Engineering, Chiba University, Chiba-shi 260, Japan Received 3rd July, 1981 The structure of molten LiBr has been studied by X-ray diffraction analysis and compared with that generated by computer simulation. The position of the first peak in the correlation function g(r) was found to be 0.265 nm by experiment; this value is slightly higher than that obtained by computer simulation (0.24 nm). The coordination number of the first nearest-neighbour was 3.8, which is in good agreement with the value estimated from Furukawa's relationship.Levy et a1.l have studied the structure of molten LiBr by the X-ray diffraction method and reported that the coordination number of the nearest Li-Br pair was 5.2. On the other hand, Furukawa2 has reported that the first coordination number of molten alkali-metal halides, n,, can be evaluated from a proportional relationship using the experimental values of other quantities. His estimated value of n, was ca. 4. Since the n, value gives us information about the molten structure comparable with that obtained from the position of the first peak, r,, of the radial distribution function (r.d.f.), precise values are desirable. In the present study, the r.d.f.of molten LiBr was determined by X-ray diffraction and the results are compared with those reported previous1y.l EXPERIMENTAL Experimental procedures and analysis of observed intensities are identical to those described in our previous paper.3 X-ray diffraction measurements were performed on a 8-8 X-ray diffractometer having a curved graphite crystal in the path of the diffracted beam. Mo Ka (A = 0.071 07 nm) radiation diffracted at the free surface of the melt was then monochromatized. The observable range of scattering angle (0) was 3 < < 35, corresponding to the range 9.3 < Q/nm-l < 101.4 (Q = 4 nssinO/A). The slit systems used were go-+' and lo-lo for low (3 < S/O < 15) and high (12 < S/" < 35) scattering angles, respectively. The minimum total count per datum point at intervals of 0.25O was accumulated to lo4 at low scattering angles and to 2 x lo4 at high scattering angles.The temperature of the melt was controlled at 570 f 5 "C throughout the measurements. The observed intensities were corrected for polarization and absorption in the melt in the usual manner. The background was subtracted from the measured intensities, so that the difference between the scaling factors derived both by the high-angle region method and by 15551556 STRUCTURAL ANALYSIS OF MOLTEN LiBr the method of Krogh-Moe and Norman was within 0.02%. The r.d.f., D(r), the correlation function, g(r), and the reduced intensity Q * i(Q) are given by the following expressions: g(r) = 1 +X(Km)2/(27t2gor) JoQmax Q.i(Q)sin(rQ)dQ (1) D(r) = 4nr2g0g(r) (2) i(Q> = s(Q)- 1 (3) m m and where po is the number of stoichiometric units per unit volume (lo3 nmP3), Km the effective electron number in the atom m,f,(Q) the independent atomic scattering intensity and I,C,Oh(Q) the total coherent intensity.The parameters used in the analysis are given in table 1. The sample (of analytical reagent grade) was dehydrated by heating at 500 OC under continuous evacuation for ca. 24 h and then purified argon gas was bubbled into the melt for a few hours. TABLE PA PARAMETERS USED IN THE CALCULATION OF THE R.D.F. OF MOLTEN LiBr ~~ ~ ~~ temperaturePC 570 density/ lo3 kg m-3 2.516 effective electron number: K,i 2.168 KBr 35.832 Po 0.017 47 Qmaxlnm-’ 100 RESULTS A N D DISCUSSION Fig. 1 shows the observed reduced intensity curve Q - i(Q) of molten LiBr at 570 OC.The r.d.f., D(r), the function D(r)/r, and correlation function, g(r), are shown in fig. 2. The experimental numerical structure values, Q - i(Q), S(Q) and g(r) are given in tables 2 and 3, respectively. Levy et a1.l have reported an rl value in D(r) of 0.268 nm. The rl value depends on the choice of D(r), D(r)/r and g(r), and the rl values from these three curves obtained in this work are 0.269, 0.267 and 0.265 nm, respectively, as shown in fig. 3. The rl value in D(r) obtained is in good agreement with that reported by Levy et a2.l Computer simulation by Monte Carlo (MC) or molecular dynamics (MD) has been applied to many molten alkali-metal halide+ and the structural properties reported are in good agreement with those derived from experiments by X-ray and neutron diffraction.We have previously concluded that rl values of the r.d.f. of molten alkali-metal halides calculated by computer simulation are always shorter than those found from experiments6 Lantelme et al.’ have carried out a computer simulation by molecular dynamics for molten LiBr and gave an rl value of 0.24 nm for g(r), which is slightly lower than that for g(r) obtained by X-ray diffraction (0.265 nm). The difference (0.025 nm) exceeds the experimental uncertainty, which is < 0.0 1 nm. As discussed previously,6 this small difference seems to be due to the non-spherical deformation of the electron shell in the area where ions are in contact with each other, and the polarization of the ion in the model employed in computer simulations has not sufficiently been takenH.OHNO, K . FURUKAWA, K. IGARASHI A N D J. MOCHINAGA 1557 i . 5 i c 0.5 h 01 . o 01 v .- - 0.5 - { 0 I I I I I I I 1 I I I 1 I I I I 2 4 6 0 10 Q/ 10 nm-' FIG. 1.-Reduced intensity curve of molten LiBr at 570 O C . 3 , "0 , Oi2 , 0,.4 , 0,6 I 0,8 , 1 .[ r/nm FIG. 2.-The functions D(r), D(r)/r and g(r) for molten LiBr at 570 O C .1558 STRUCTURAL ANALYSIS OF MOLTEN LiBr 0 25 0 28 r/nm FIG. 3.-First-peak positions of D(r), D(r)/r and g(r) for molten LiBr: (a) D(r), 0.269 nm; (b) D(r)/r, 0.267 nm; (c) g(r), 0.265 nm. TABLE 2.-NUMERICAL VALUES OF THE STRUCTURE Q . i(Q) AND S(Q) OF MOLTEN LiBr AT 570 O C a 1.0 -0.841 1.1 -0.904 1.2 -0.962 1.3 -0.985 1.4 -0.984 1.5 -0.721 1.6 -0.071 1.7 0.728 1.8 1.354 1.9 1.558 2.0 1.289 2.1 0.709 2.2 0.083 2.3 -0.367 2.4 -0.571 2.5 -0.594 2.6 -0.555 2.7 -0.524 2.8 -0.493 2.9 -0.406 3.0 -0.225 3.1 0.031 3.2 0.294 3.3 0.489 3.4 0.576 3.5 0.556 3.6 0.455 3.7 0.302 3.8 0.121 3.9 -0.066 4.0 -0.230 0.159 0.178 0.198 0.242 0.297 0.519 0.956 1.428 1.753 1.820 1.645 1.338 1.038 0.840 0.762 0.762 0.787 0.806 0.824 0.860 0.925 1.010 1.099 1.148 1.169 1.159 1.126 1.082 1.032 0.983 0.943 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 -0.344 -0.391 -0.378 - 0.328 - 0.264 -0.196 -0.1 18 - 0.022 0.088 0.192 0.264 0.289 0.270 0.221 0.161 0.099 0.036 - 0.026 - 0.079 -0.113 -0.122 -0.1 13 - 0.098 - 0.089 - 0.088 - 0.088 - 0.077 - 0.052 -0.016 0.019 0.045 0.916 7.2 0.907 7.3 0.912 7.4 0.925 7.5 0.941 7.6 0.957 7.7 0.975 7.8 0.995 7.9 1.018 8.0 1.038 8.1 1.052 8.2 1.055 8.3 1.051 8.4 1.041 8.5 1.029 8.6 1.018 8.7 1.006 8.8 0.996 8.9 0.987 9.0 0.981 9.1 0.980 9.2 0.982 9.3 0.984 9.4 0.986 9.5 0.986 9.6 0.987 9.7 0.989 9.8 0.992 9.9 0.998 10.0 1.003 1.006 0.056 0.058 0.055 0.053 0.05 1 0.051 0.049 0.045 0.035 0.019 - 0.002 - 0.02 1 - 0.033 - 0.036 - 0.033 - 0.029 - 0.03 1 - 0.038 - 0.042 - 0.036 -0.019 0.003 0.021 0.030 0.027 0.020 0.013 0.009 0.006 1.008 1.008 1.007 1.007 1.007 1.007 1.006 1.006 1.004 1.002 0.999 0.997 0.996 0.996 0.996 0.997 0.996 0.996 0.995 0.996 0.998 1 .ooo 1.002 1.003 1.003 1.002 1.001 1.001 1.001 a Q is in units of lo-' nm-l.H.OHNO, K . FURUKAWA, K. IGARASHI A N D J. MOCHINAGA 1559 into account.The effect would be relatively large in a molten salt composed of ions of different charge densities such as LiBr and LiI. The n, value gives us comparable information about the molten structure as does the r1 value. The following three methods have usually been used to determine n, values3 (a) symmetrical rg(r), (b) symmetrical rzg(r) and (c) integration to the first minimum in D(r). Usually, although not always, these methods will result in progressively higher numerical values, i.e. (nl)a < (n,), < (nl)c. The experimental n, values of molten LiBr obtained in this work for methods (a) and (c) are 3.8 and 4.1, respectively; these are smaller than that reported by Levy et a1.l (5.2). However, the n, value in this experiment is close to the results from computer simulation, 4.27.' The reason for the discrepancy between this work and the results of Levy et al.is due to the non-negligible amount of ghost below r = 0.2 nm present in the latter case; this will affect the n, value. The first coordination number can also be evaluated from the following proportional expression2 n:alc = n,( Vz/ V 3 ( r : / r 3 3 where Vz and V$ are the molar volumes of the solid and liquid at the melting point, rs and ri are the nearest-neighbour distances of the Li-Br pair in the solid and liquid, respectively, and n, is the coordination number of the nearest Li-Br pair in the solid. Using the following values, V$ = 28.03 x m3 mol-l, rs = 0.285 nm, r: = 0.265 nm and n, = 6, one obtains nfalc = 3.9. Thus, as in all (6) m3 mol-l, Vd = 34.3 1 x TABLE 3.-NUMERICAL VALUES OF THE STRUCTURE g(r) OF MOLTEN LiBr AT 570 *Ca 0.21 -0.012 0.22 0.027 0.23 0.130 0.24 0.283 0.25 0.440 0.26 0.541 0.27 0.544 0.28 0.450 0.29 0.307 0.30 0.189 0.31 0.164 0.32 0.264 0.33 0.477 0.34 0.763 0.35 1.069 0.36 1.356 0.37 1.599 0.38 1.783 0.39 1.897 0.40 1.935 0.41 1.896 0.42 1.792 0.43 1.647 0.44 1.487 0.45 1.336 0.46 1.205 0.47 1.094 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 1 .ooo 0.920 0.855 0.808 0.776 0.757 0.745 0.736 0.733 0.738 0.753 0.778 0.807 0.835 0.859 0.881 0.902 0.925 0.950 0.977 1.005 1.035 1.066 1.099 1.128 1.150 1.160 0.75 0.76 0.77 0.78 0.79 0.80 0.8 1 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.9 1 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 .oo 1.157 1.146 1.131 1.116 1.101 1.085 1.064 1.039 1.012 0.988 0.969 0.956 0.948 0.943 0.938 0.934 0.93 1 0.93 1 0.935 0.941 0.949 0.959 0.970 0.982 0.994 1.005 a r is in units of nm.1560 STRUCTURAL ANALYSIS OF MOLTEN LiBr molten alkali-metal halides except LiI,2 the n, value of molten LiBr estimated from eqn (6) is in reasonable agreement with the experimental value obtained by X-ray diffraction analysis.CONCLUSIONS (I) The position of the first peak in correlation function g(r) was obtained as 0.265 nm, a slightly higher value than that obtained by computer simulation (0.24 nm). (2) The coordination number of the first nearest-neighbour was found to be 3.8, in good agreement with that calculated from Furukawa's relationship. H. A. Levy, P. A. Agron, M. A. Bredig and M. D. Danford, Ann. N . Y. Acad. Sci., 1960,79, 762. K. Furukawa, Discuss. Faraday Soc., 1962, 32, 51. H. Ohno and K. Furukawa, J . Chem. SOC., Faraday Trans. I , 1978, 74, 795. M. J. L. Sangster and M. Dixon, Adv. Phys., 1976, 25, 247. L. V. Woodcock, Advance in Molten Salt Chemistry, ed. J. Braunstein, G. Mamantov and G. P. Smith (Plenum Press, New York, 1975). K. Furukawa and H. Ohno, 3rd Int. Symposium on Molten Salts (The Electrochemical Society, Princeton, N.J., 1980), extended abstracts, vol. 80-2, p. 1587; Proc. 3rd Int. Symposium on Molten Salts (The Electrochemical Society, Princeton, N.J., 1981), vol. 81-9, p. 36. ' F. Lantelme, P. Turq and P. Sochofield, J. Chem. Phys., 1977, 67, 3869; F. Lantelme and P. Turq, Mol. Phys., 1979, 38, 1003. C. J. Pings, Physics of Simple Liquids, ed. H. N. V. Temperley, J. S. Rowlinson and G. S. Rushbrooke (North Holland, Amsterdam, 1968), chap. 10. (PAPER 1/1058)