Limiting Debye temperature behavior following from cryogenic heat capacity data for group-IV, III-V, and II-VI materials

Pässler, R.

doi:10.1002/pssb.200945158

Cited by 20 publications

(59 citation statements)

References 82 publications

(186 reference statements)

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“…Owing to this excessive simplification of the true state of affairs, Debye's heat capacity model [13] has been commonly found (see, e.g., Ref. [15] and numerous experimental and theoretical studies there cited) to be as a rule incapable of providing proper numerical simulations of given C p (T) data sets unless the fictitious cut-off energies were admitted to change, themselves, into complicated functions of lattice temperature, i.e., e D ! e D (T) ¼ k B Q D (T) (where the quantities Q D (T) play the role of suitably changing ''Debye temperatures'' [13,15]).…”

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confidence: 99%

“…This is in contrast to the commonly expected cubic asymptotes, C p (T ! 0) / T 3 [13][14][15], for limiting lattice heat capacities in solids. The latter can be, of course, obtained readily by adopting -as a principal alternative -some continuous functions [15] for low-energy tails of PDOS spectra that are tending to certain quadratic asymptotes in the zero phonon energy limit, g P (e !…”

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Representative hybrid model used for analyses of heat capacities of group‐IV, III–V, and II–VI materials

Pässler

2010

Physica Status Solidi (b)

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Characteristic non-Debye features inherent to the dispersionrelated hybrid model, which had been devised for the sake of physically adequate representations of isobaric heat capacities of semiconductor and wide band gap materials, are demonstrated and discussed in some detail. We perform least-meansquare fittings of low-and high-temperature C p (T) data sets that are available for group-IV materials (diamond, Si, Ge, 3C-SiC), III-V materials (BN, BP, BAs, AlN, AlP, AlAs, AlSb, GaN, GaP, GaAs, GaSb, InP, InAs, InSb), and II-VI materials (ZnO, ZnS, ZnSe, ZnTe, CdO, CdS, CdSe, CdTe). The simulations of the C p (T) data sets under study, particularly with respect to the cryogenic region, are graphically represented, and existing data deficiencies are discussed. Important by-products of the fittings are presented within the frame of Supporting Information (online at: www.pss-b.com). There are given in tabulated form the characteristic phonon energies, e P (m), for integral orders, m ¼ À2, À1, 0, 1, 2, and 4, including further dispersion-related parameters like average phonon temperatures, Q P , dispersion coefficients, D P , and high-temperature limiting values of Debye temperatures, Q Dh (1). Furthermore, basing on comprehensive calculations of the C p (T) dependences from absolute zero up to room temperature, we provide representative values of entropies, S p (T), enthalpies, H p (T) À H p (0), and Gibbs free energies, G p (T) À G p (0), for the frequently considered reference point, T r ¼ 298.15 K, the accurate knowledge of which is indispensable for possible high-temperature continuations of these standard thermodynamic functions within the frame of the commonly used thermo-chemical formalism.

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Representative hybrid model used for analyses of heat capacities of group‐IV, III–V, and II–VI materials

Pässler

2010

Physica Status Solidi (b)

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“…It then decreases, and after passing through a minimum at T ≈ Θ D (0)/10 starts to increase to a constant plateau at about T ≈ Θ D (0)/2, [2,3,8]. Therefore, it is often impossible to provide good fitting of Eq.…”

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confidence: 99%

“…Therefore, it is often impossible to provide good fitting of Eq. (1) to the given heat capacity data set with a single Debye temperature over the entire temperature range [3,8]. These non-Debye behaviors have been given in terms of C V /T 3 functions [9][10][11].…”

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New Kinetic Theory for Absorption and Emission Rates of Radiation and New Equations for Lattice and Electronic Heat Capacities, Enthalpies and Entropies of Solids: Application to Copper

Bozdoğan

2017

Acta Phys. Pol. A

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New equations, which have analytical solutions, for lattice and electronic heat capacities, entropies and enthalpies at constant volume and constant pressure were derived by using kinetic theory, Kirchhoff and Stefan-Boltzmann laws and Wien radiation density equation. These equations were applied to the experimental constant volume heat capacity data of copper. The temperature ΘV corresponding to 3R/2 was found to be 78.4 K for copper. Copper shows the dimensionality crossover from 3 to 2 at about 80 K. The ΘV (T ) is proportional to Debye temperature. The relationship between dimension and ΘV was given. Temperature dependence of Debye temperature and nonmonotonic behavior were discussed. The heat capacity and entropy values, predicted by the proposed models were compared with the values predicted by the Debye models. The results have shown that the proposed models fit the data better than the Debye models. Enthalpy equations derived in this study were compared with the polynomial model and a good fitting was obtained. The equation for the photon absorption equilibrium constant of copper was derived.

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Qualitatively Different Non‐Quartic Low‐Temperature Heat Capacity Behaviors due to Various Non‐Metallic Solids

Pässler

2019

Physica Status Solidi (b)

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Different non-quartic cryogenic heat capacity dependences can be unambiguously associated with the qualitatively different types of either sub-quartic or super-quartic regimes. The simplest way for a prompt association with one of these two alternative regimes is based on a couple of parameters controlling the straight-line tangents to the material-specific C(T)/T 3 curves in consideration. A representative non-Debye heat capacity formula is used for performing high-accuracy fittings of cryogenic heat capacity data sets, including reliable determinations of the material-specific temperature dependences of effective power function exponents. The cryogenic heat capacity dependences of the exemplary wide bandgap materials AgCl and LiI are found to show pronounced sub-quartic behaviors, whereas germanium and silicon are seen to pertain to the regime of super-quartic behavior. These results are in clear contrast to a hypothetical field-theoretical model published recently by Gusev [R. Soc. Open Sci. 2019, 6, 171285], which suggested an allegedly universal low-temperature behavior of quartic type. An unprecedented graphical distinction tool is introduced here, consisting in alternative C(T)/T 4 data representations, by means of which the qualitative differences between opposite non-quartic heat capacity behaviors for the materials under study have been visualized in rather pronounced form. A brief discussion is given of preliminary assessments of non-quartic cryogenic heat capacity behaviors for a larger variety of III-V, II-VI, and I-VII materials.

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Limiting Debye temperature behavior following from cryogenic heat capacity data for group-IV, III-V, and II-VI materials

Cited by 20 publications

References 82 publications

Representative hybrid model used for analyses of heat capacities of group‐IV, III–V, and II–VI materials

Representative hybrid model used for analyses of heat capacities of group‐IV, III–V, and II–VI materials

New Kinetic Theory for Absorption and Emission Rates of Radiation and New Equations for Lattice and Electronic Heat Capacities, Enthalpies and Entropies of Solids: Application to Copper

Qualitatively Different Non‐Quartic Low‐Temperature Heat Capacity Behaviors due to Various Non‐Metallic Solids

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