Experimental determination of thermodynamic characteristics of smithsonite

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

doi:10.1016/j.jct.2012.02.028

Cited by 3 publications

(7 citation statements)

References 10 publications

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“…As examples experimental data of heat capacities of carbonates [ 2 , 3 ], molybdates [ 4 – 8 ], hollandites [ 9 ], molybdenum trioxide [ 17 ], and a zeolitic polymorph of SiO 2 , faujasite [ 12 ], are analyzed by the Debye–Einstein fit approach according to Eq. ( 1 ).…”

Section: Resultsmentioning

confidence: 99%

“…The following characteristic temperatures and pre-factors are obtained when applying the Debye–Einstein integral (Eq. ( 1 )) to the heat capacity data of smithsonite [ 3 ], see Table 3 .…”

Section: Resultsmentioning

confidence: 99%

“…Advanced calorimetric techniques (e.g., by means of a relaxation method instrument [ 1 ]) allow for heat capacity measurements at very low temperatures. Recently, heat capacities of various minerals and compounds (e.g., carbonates [ 2 , 3 ], molybdates [ 4 – 8 ] and Sr-, Rb-, and Cs-substituted barium aluminotitanate hollandites [ 9 ]) were determined and the derived thermodynamic functions were reported. Thermodynamic data as provided in Bissengaliyeva et al [ 2 , 3 ] are required to describe the formation of lead and zinc carbonates occurring in the oxidation zones of sulfide ore deposits.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, heat capacities of various minerals and compounds (e.g., carbonates [ 2 , 3 ], molybdates [ 4 – 8 ] and Sr-, Rb-, and Cs-substituted barium aluminotitanate hollandites [ 9 ]) were determined and the derived thermodynamic functions were reported. Thermodynamic data as provided in Bissengaliyeva et al [ 2 , 3 ] are required to describe the formation of lead and zinc carbonates occurring in the oxidation zones of sulfide ore deposits. In addition, theoretical investigations may be assisted by these data when Pb 2+ ions have to be removed from aqueous solution [ 10 , 11 ].…”

Section: Introductionmentioning

confidence: 99%

“…Heat capacity measurements and the derived thermodynamic functions are essential for further thermochemical calculations. Currently, heat capacities at temperatures in the range of almost absolute zero to 300 K are fitted by several cubic splines [ 2 , 3 ] or by more theory-based fitting approaches discriminating low-, mid-, and high-temperature ranges [ 6 , 9 ]. A combination of Debye–Einstein and Schottky functions are used to fit the temperature-dependent heat capacity data [ 4 , 12 ] with individual coefficients depending on the temperature region.…”

Section: Introductionmentioning

confidence: 99%

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Low temperature heat capacities and thermodynamic functions described by Debye–Einstein integrals

Gamsjäger

Wießner

2018

Monatsh Chem

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Thermodynamic data of various crystalline solids are assessed from low temperature heat capacity measurements, i.e., from almost absolute zero to 300 K by means of semi-empirical models. Previous studies frequently present fit functions with a large amount of coefficients resulting in almost perfect agreement with experimental data. It is, however, pointed out in this work that special care is required to avoid overfitting. Apart from anomalies like phase transformations, it is likely that data from calorimetric measurements can be fitted by a relatively simple Debye–Einstein integral with sufficient precision. Thereby, reliable values for the heat capacities, standard enthalpies, and standard entropies at T = 298.15 K are obtained. Standard thermodynamic functions of various compounds strongly differing in the number of atoms in the formula unit can be derived from this fitting procedure and are compared to the results of previous fitting procedures. The residuals are of course larger when the Debye–Einstein integral is applied instead of using a high number of fit coefficients or connected splines, but the semi-empiric fit coefficients keep their meaning with respect to physics. It is suggested to use the Debye–Einstein integral fit as a standard method to describe heat capacities in the range between 0 and 300 K so that the derived thermodynamic functions are obtained on the same theory-related semi-empiric basis. Additional fitting is recommended when a precise description for data at ultra-low temperatures (0–20 K) is requested.Graphical abstract

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Low temperature heat capacities and thermodynamic functions described by Debye–Einstein integrals

Gamsjäger

Wießner

2018

Monatsh Chem

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Heat capacities and standard entropies and enthalpies of some compounds essential for steelmaking and refractory design approximated by Debye-Einstein integrals

Ogris

Gamsjäger

2021

Calphad

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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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Experimental determination of thermodynamic characteristics of smithsonite

Cited by 3 publications

References 10 publications

Low temperature heat capacities and thermodynamic functions described by Debye–Einstein integrals

Low temperature heat capacities and thermodynamic functions described by Debye–Einstein integrals

Heat capacities and standard entropies and enthalpies of some compounds essential for steelmaking and refractory design approximated by Debye-Einstein integrals

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

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