(Santoro, 1974). The existence of twins in RbPb (MnO2)2 are, therefore, quite possible, and anyone working with single crystals of the compound should be aware of it. e. Studies of the Geometrical Properties of Lattices It has been shown (Santoro and Mighell, 1970) that in some lattices more than one cell is based on the shortest three noncoplanar translations. Gruber (1973) has shown that, at most, five different cells of this type may exist in the same lattice. For identification purposes, it is necessary to describe a crystal in terms of only one of these cells and the special conditions of reduction theory provide a way to make such selection. On the other hand, there are cases in which it is useful to find and relate to one another all of the cells based on the shortest trans lations, and the B-matrix algorithm represents a simple procedure to study this type of problem. As an example, let us consider the lattice studied by Gruber (loc. cit.) and described by the cell As we require only the equality of cell edges, only the equations need to be satisfied and the required values of the elements B. are Bij restricted to integers for which |B| = 1. The algorithm finds the five different cells in agreement with those found by Gruber. In the previous section only a few examples of the application of the algorithm have been illustrated. Many more cases could have been given. The method represents a practical tool to study inter- and intralattice relationships, and for this reason it is particularly suited to carry out research on the published crystallographic data now collected in the NBS Crystal Data File and JCPDS Powder Data File. Applications of the procedure, underway or planned for the future, comprise cross-referencing of the single-crystal and powder data files, routine identification and registration procedures, and a systematic study of twinning, especially to clarify the relationship between the geometrical and structural aspects of twins. 1. Santoro, A. and Mighell, A. D., Acta Cryst. A 28, 284-287, (1972). 2. Cassels, J. W. S., "An Introduction to the Geometry of Numbers," 3. Delaunay, B., Z. F. Kristall. 84, 109-149, (1933). 4. 5. Santoro, A. and Mighell, A. D., Acta Cryst. A 26, 124-127, (1970). 6. Visser, J. W., J. Appl. Cryst. 2, 89-95, (1969). 7. DeCamp, W. H., Acta Cryst. B 32, 2257-2258, (1976). 8. Santoro, A., Acta Cryst. A 30, 224-231, (1974). 9. Gruber, B., Acta Cryst. A 29, 433-440, (1973). 10. 11. Donnay, J. D. H. and Ondik, H. M., Crystal Data Determinitive Tables, Swarthmore, PA., (1972). International Center for Diffraction Data, Morris, M. C., Mc Murdie, H. F., Evans, E. H., Paretzkin, B., THERMAL RELAXATION IN A LIQUID UNDER SHOCK COMPRESSION D. H. Tsai (Thermal Physics Division) and S. F. Trevino (Energetic Materials Division, LCWSL, ARRADCOM, Dover, NJ) We have carried out a molecular-dynamical study of the shock compression of a dense three-dimensional liquid. Our system consists of 7200 12 particles interacting through a Lennard-Jones potential 4€[(0/4) 1 = (o/r)6] with ɛ and σ adjusted to simulate argon. The range of inter action extends to about 2.5 o. The particles form a filament with a cross-section of 9.9 σ x 9.9 σ and a length of 170 σ. The undisturbed portion of the filament is maintained at equilibrium throughout the calculation. Shock compression is initiated by causing the filament to move with a mass velocity of -U in the longitudinal direction along the P Z axis toward the origin, and to collide with its image through a mirror plane located at Z=0. The boundary conditions in the transverse (X-Y) directions are assumed to be periodic. We calculate the response of the filament under these initial and boundary conditions by solving numerically the classical equations of motion for all the particles in the filament. From the positions and velocities of all the particles as functions of time we calculate the profiles of mass density, energy density, kinetic temperature and stress components, and thus obtain an atomistic description of the shock compression process in a dense liquid system under fully nonequilibrium conditions. We have two main objectives in this investigation. First, we wish to compare these results for the discrete model of a dense liquid system 1 with the results for a continuum model. The continuum model usually assumes that local equilibrium exists in the shock profile, even within the thickness of the shock front where conditions change most rapidly. Second, we wish to study the thermal relaxation process in the dense liquid following the passage of the shock front and to compare this relaxation process with that obtained earlier2 in a crystalline solid under similar condition of shock compression. and Dremin 3 In addition, the recent work of Klimenko has just come to our attention. These authors have also made molecular dynamical calculations of the shock compression of liquid argon. Their system is similar to ours, and it would be interesting to compare their results with ours. We have completed two calculations in which the initial configurations of the uncompressed liquid (subscript 1) were different, but both corresponded to the same equilibrium conditions as follows: 0.85/03, = p. Ꭲ. 1.16 ε/k, P. = 3.18 €/03 with = 120 k and σ = 0.3405 nm. 1 = 1 in a fcc crystal of argon at is the atomic mass of argon. = U is Р 9.46/c/m is the longitudinal sound velocity zero pressure and zero temperature and m P 1 U is then approximately 300 m/s. In his study of the continuum solution based on the Navier-Stokes description of strong shock waves in a liquid, Hoover has also obtained one set of solutions under conditions similar to ours. We compare our results with his as follows (subscript 2 refers to conditions at the high pressure side of the shock front profile; p, P and T in proper units; U is shock front velocity): S *Disagreement here is due to slight differences in the cutoff of the Lennard-Jones potential and in the treatment of the correction term beyond the cutoff. See D. H. Tsai, J. Chem. Phys. 70, 1375 (1979). Our values are the "best" average values taken from a number of time steps between T = 140 and 160 at the end of the calculation, where t is measured in d/C, d being the interplanar spacing of the fcc argon at zero pressure and zero temperature. By this time, the shock front profile is essentially steady. However, additional data would be useful for reducing the fluctuation in the data. We obtain a shock front thickness of 14.9 o as compared with 17.6 σ obtained by Hoover. The two profiles are qualita- ness. Our results are also in qualitative agreement with the results of 3 Klimenko and Dremin. For example, we also find a marked difference in the longitudinal and transverse components of the kinetic temperature within the thickness of the shock front. However, we have allowed the shock wave to propagate considerably farther than the Russian authors did, by a factor of 4 or 5, so that we may also investigate the energy relaxation process behind the shock front. Р Figure 1 shows the average kinetic temperature profile from three time steps near T = 160, at U = 0.2 C 2 C. In this case the temperature rise immediately following the shock front is 15% higher than that in the trailing portion farther behind. Here we ignore that part of the profile adjacent to the mirror plane at Z=0 where the boundary conditions introduce some disturbance to the system. The corresponding pressure profile gives a uniform pressure over the entire profile. The corresponding mass density immediately following the shock front is 1% lower than that in the region farther behind. The conservation of energy (and of momentum) for the entire calculation is better than 0.5%. These considerations indicate that the temperature difference in figure 1 is real and not an artifact of the numerical computation. If this is indeed so, this result is in harmony with our understanding of the thermal relaxation process in a crystalline solid2, i.e., in a dense system under shock compression, equilibration of thermal energy in the shock profile is slower than the equilibration of momentum |