Multidimensional geometric aspects of the solid–liquid transition in simple substances
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6.We designate the average calculated temperature with T. according to custom, rather than with the more consistent but unusual
7.See Ref. 2, p. 363.
8.To see this, write as the canonical conflgurational average Integrate the numerator by parts, discarding the surface term which vanishes in the thermodynamic limit, to find In our units, See Sec. 6.10 of Ref. 2 for the traditional application of this equality to the development of the Wigner‐Kirkwood quantum‐mechanical corrections to classical thermodynamics.
9.This generalization has been exploited in another context. See S. Hess, Physica A 127, 509 (1984).
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11.As noted in the Introduction, in the harmonic regime is identical with the root‐mean square displacement of the coordinates from the static crystal lattice, and increases with See Ref. 2, p. 365.
12.One quantitative test of how well fits the data is given by the Pearson test, where and where is the sample size and is the number of bins of Roughly, fits the data if See, for example, B. L. van der Waerden, Mathematical Statistics (Springer, New York, 1969), Chap. 11. In our calculations, and the number of bins of increasing with temperature (adjusted so that nearly all bins contain at least five samples). At is less than one‐half so is an excellent fit to the data while at is several times
13.For similar results with other potentials, see F. H. Stillinger and T. A. Weber, J. Chem. Phys. 80, 4434 (1984);
13.T. A. Weber and F. H. Stillinger, J. Chem. Phys. 81, 5089 (1984)., J. Chem. Phys.
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18.The error in estimating due to the finite size of the system has been claimed to be of order See W. G. Hoover, S. G. Gray, and K. W. Johnson, J. Chem. Phys. 55, 1128 (1971).
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22.F. H. Stillinger and T. A. Weber, J. Chem. Phys. 81, 5095 (1984).
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