Thermodynamics of equilibrium alkali plasma. Simple and accurate analytical model for non-trivial case

Мокшин, А. В.; Mirziyarova, Diana A.

doi:10.1016/j.physleta.2021.127819

Cited by 4 publications

(3 citation statements)

References 32 publications

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“…For implicit (“hidden”) correlations between different parameters, it is quite natural and often feasible that the parameters do not appear in the resulting correlation relation as single additive terms, but in the form of combinations (products or ratios). For example, in contrast to the methodology of artificial neural networks, this is most clearly manifested in the method of joint accounting for arguments using the Kolmogorov–Gabor polynomial [ 37 , 38 , 39 ]:

which determines the relationship of a parameter y with the parameters

,…

,… In the obtained model of the artificial neural network, the appearance of the parameter

, together with the individual parameters

and

, directly indicates that the Arrhenius crossover temperature

correlates not only with the absolute values of the melting and glass transition temperatures for different systems, but also with their ratio. This result is fully consistent with the theoretical description of crystallization rate characteristics of supercooled melts within the reduced temperature scale

and universal scaled relations [ 9 , 30 ].…”

Section: Regression Model For Arrhenius Crossover Temperaturementioning

confidence: 99%

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

2023

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The Arrhenius crossover temperature, TA, corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below TA. The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates. In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T. The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature TA and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature TA was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature Tg, the melting temperature Tm, the ratio of these temperatures Tg/Tm and the fragility index m were applied as input parameters. It has been established that the temperatures Tg and Tm are significant parameters, whereas their ratio Tg/Tm and the fragility index m do not correlate much with the temperature TA. An important result of the present work is the analytical equation relating the temperatures Tg, Tm and TA, and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature TA for a large class of materials, regardless of their compositions and glass-forming abilities.

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which determines the relationship of a parameter y with the parameters

,…

,… In the obtained model of the artificial neural network, the appearance of the parameter

, together with the individual parameters

and

, directly indicates that the Arrhenius crossover temperature

and universal scaled relations [ 9 , 30 ].…”

Section: Regression Model For Arrhenius Crossover Temperaturementioning

confidence: 99%

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

2023

View full text Add to dashboard Cite

show abstract

“…For implicit ("hidden") correlations between different parameters, it is quite natural and often feasible that the parameters do not appear in the resulting correlation relation as single additive terms, but in the form of combinations (products or ratios). For example, in contrast to the methodology of artificial neural networks, this is most clearly manifested in the method of joint accounting for arguments using the Kolmogorov-Gabor polynomial [37,38,39]:…”

Section: Regression Model For Arrhenius Crossover Temperaturementioning

confidence: 99%

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

Galimzyanov,

Doronina,

Mokshin

2023

Preprint

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The Arrhenius crossover temperature, T A , corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below T A . The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates.In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T . The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature T A and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature T A was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature T g , the melting temperature T m , the ratio of these temperatures T g /T m and the fragility index m were applied as input parameters. It has been established that the temperatures T g and T m are significant parameters, whereas their ratio T g /T m and the fragility index m do not correlate much with the temperature T A . An important result of the present work is the analytical equation relating the temperatures T g , T m and T A , and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature T A for a large class of materials, regardless of their compositions and glass-forming abilities.

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“…Alkali metals have been studied using velocity auto correction function and power spectrum [44]. Owing to the scientific and technological importance, in recent years, numerous theoretical and experimental studies on alkali metals have been made [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].…”

mentioning

confidence: 99%

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

Arumugam¹,

Ramasamy²

2023

Phys. Scr.

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The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid - vapour critical – point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS, which satisfactorily describes the properties of alkali metals, differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy have been derived. In all these cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. Hence, it has been established that the parameters of at any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the fluid properties other than the liquid-vapour critical point.

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Thermodynamics of equilibrium alkali plasma. Simple and accurate analytical model for non-trivial case

Cited by 4 publications

References 32 publications

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

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