New Approach for Evaluating Lattice‐Configurational Thermodynamic Properties
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11.A multicomponent treatment would pose no problem except a lack of simplicity that would unnecessarily encumber the common application to one‐component systems.
12.With such a periodic system the energy between particles separated by one or more periodic boundaries should be included, but must obviously be properly weighted in arriving at the mean energy per period.
13.That is, for central forces two particles do not interact except when they are in the same unit or in adjacent units.
14.In this and subsequent partial differential equations the constancy of temperature is implied.
15.For the so‐called hard‐core lattice fluid, for which and limited to the values zero and infinity, is the probability that the end configuration will be such as to permit adding thereto a unit having any configuration of class i.
16.Equation (14) is a reminder, incidentally, that is the same for every configuration class having a given value of s, though the individual (and hence the also) usually have differences arising from Eq. (4).
17.Suppose the number of layers of sites in the primary unit is f and Since all layers in the lattice interior are equivalent, each must have the same mean density, even though it be identified as a particular layer of the unit. In some such cases this fact readily provides, in addition to Eq. (17), additional independent relations which are consistent with and can conveniently supplant an equal number of relations derived from Eq. (14) for the purpose of solving for the values of
18.The computer time for solving the resulting matrix of coefficients is proportional to the cube of this number.
19.In this case except where both are zero.
20.These two limiting values, which must apply for all three types of lattice, were obtained empirically by monotonic extrapolation of (3b), but are consistent with the other five methods of extrapolation within their limits of uncertainty. In the calculation of the finite results for (3), each pair of infinitely long rows equidistant from the center may be treated as belonging to a single group, since their individual densities will then obviously be equal by symmetry. It is also obvious that the properties for or 2 are identical for (1), (2), and (3).
21.With, in addition, special methods of extrapolation of critical properties not considered here.
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