Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The two-parameter Debye model   When analyzing thermodynamic and kinetic properties of crystals whose
anisotropy is not large and the considered effects do not relate to the
existence of singled-out directions in crystals, one may use a more simple
model of an isotropic medium with a good accuracy, after having chosen its
parameters in an optimal way. Based on the quantum mechanical description it is
shown that the method of approximation of the moduli of elasticity of a crystal
by the model of an isotropic medium, proposed earlier in [2], follows from the
requirement of the minimal difference between the free energies of a crystal
and an approximating isotropic medium. The two-parametric Debye model is
formulated, which, in contrast to the standard model where the average speed of
phonons is introduced, takes into account the existence in an isotropic medium
of both longitudinal and transverse phonons. The proposed model contains,
except the Debye energy, an additional dimensionless parameter and,
consequently, the law of corresponding states for the heat capacity being
characteristic of the standard model does not hold. With taking account of the
two phonon branches the structure of the density of phonon states proves to be
more complex as compared to the standard model and has a singularity that
resembles Van Hove singularities in real crystals. As an example, an
application of the two-parametric Debye theory to such crystals of the cubic
system as tungsten, copper, lead is considered. It is shown that the
calculation of the low-temperature heat capacity of these crystals by means of
the approximated moduli of elasticity within the framework of the
two-parametric model leads to a considerably better agreement with experiment
than in the case of the standard Debye model.

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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn