Low-temperature heat capacity and thermodynamic functions of natural chalcanthite

Bissengaliyeva, Мira R.; Bekturganov, N. S.; Gogol, Daniil B.; Taimassova, Shynar T.

doi:10.1016/j.jct.2017.03.026

Cited by 2 publications

(2 citation statements)

References 49 publications

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“…Calorimetric measurements of heat capacity data for various crystalline solids have been extensively reported in the literature (see e.g., [ 2 , 10 , 22 , 23 , 24 , 25 , 26 ]). These measurements cover a temperature range from ultra-low temperatures, such as

, up to

or slightly higher temperatures.…”

Section: Literature Data and Theorymentioning

confidence: 99%

“…Some sets of model parameters used to fit low temperature heat capacity measurements are purely empirical (see, e.g., [ 1 , 2 , 3 , 4 ]), other parameters are at least partly motivated by theory, e.g., following the Debye–Einstein approach [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ]. A Debye–Einstein integral to describe heat capacities of several compounds is introduced by Kelley and King [ 5 ].…”

Section: Introductionmentioning

confidence: 99%

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Extended Regression Analysis for Debye–Einstein Models Describing Low Temperature Heat Capacity Data of Solids

Gamsjäger,

Wiessner

2024

Entropy

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Heat capacity data of many crystalline solids can be described in a physically sound manner by Debye–Einstein integrals in the temperature range from 0K to 300K. The parameters of the Debye–Einstein approach are either obtained by a Markov chain Monte Carlo (MCMC) global optimization method or by a Levenberg–Marquardt (LM) local optimization routine. In the case of the MCMC approach the model parameters and the coefficients of a function describing the residuals of the measurement points are simultaneously optimized. Thereby, the Bayesian credible interval for the heat capacity function is obtained. Although both regression tools (LM and MCMC) are completely different approaches, not only the values of the Debye–Einstein parameters, but also their standard errors appear to be similar. The calculated model parameters and their associated standard errors are then used to derive the enthalpy, entropy and Gibbs energy as functions of temperature. By direct insertion of the MCMC parameters of all 4·105 computer runs the distributions of the integral quantities enthalpy, entropy and Gibbs energy are determined.

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