On the example of typical metals, it’s found that the activation energy of self-diffusion is above of the melting heat and below of vaporization heat. This corresponds to the existence of liquid-mobile particle class...On the example of typical metals, it’s found that the activation energy of self-diffusion is above of the melting heat and below of vaporization heat. This corresponds to the existence of liquid-mobile particle classification based on the concept of randomized particles. A formula for estimating the activation energy of self-diffusion by which it is approximately half of the heat of evaporation of the substance is recommended. We derive the temperature dependence for a fraction self-diffusion’s particles.展开更多
The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commen...The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the act展开更多
The significance of the work is determined by the need to develop a cluster theory of the liquid state of a substance in order to more deeply substantiate the viscosity, which is still expressed by empirical parameter...The significance of the work is determined by the need to develop a cluster theory of the liquid state of a substance in order to more deeply substantiate the viscosity, which is still expressed by empirical parameters within the framework of ideal ideas about the stratified flow of a liquid. According to the reference data on the dynamic viscosity of the melts for chlorides of the first group of the Periodic System, the approximating dependences in the form of cluster-associate and Frenkel’s models were constructed at various temperatures. The first model is based on taking into account the share of particles that cannot overcome the thermal melting barrier and thus serve to form virtual clusters and associates while preserving the structural motifs of the solid phase. In the framework of the cluster-associate viscosity model developed by the authors, these formations determine the melt viscosity and serve as flow units to which the energy of fluid motion is applied. The Frenkel’s model allows us to estimate the activation energy of fluidity. Calculations show that by comparing this energy with the degree of cluster association obtained in the framework of the cluster-associate model, a fairly close linear correlation is obtained, and the proportionality coefficient has the meaning of the activation energy per cluster. This energy does not go beyond the van der Waals energy of the unsaturated intermolecular bond characteristic of the interaction of particles in a liquid. This confirms the earlier established by the authors a similar pattern for melts of simple substances, based on the understanding of fluidity as a consequence of the destruction of cluster associates while preserving the clusters themselves.展开更多
The purpose of the research is to develop the temperature dependence of the dynamic viscosity for silver chloride. The data were calculated on the basis of a new cluster and associate equation, which was derived using...The purpose of the research is to develop the temperature dependence of the dynamic viscosity for silver chloride. The data were calculated on the basis of a new cluster and associate equation, which was derived using the concept of randomized particles. The calculated data are given in the temperature range from the melting point to the boiling point. The cluster and associate model is compared with the Frenkel’s equation in logarithmic coordinates, showing the mutual correspondence and complementarity of these models.展开更多
Using thermal barriers at the melting point?Hm and RTm,it is shown that the latter directly reflects the chaotic process,since it is equal to the kinetic energy reserve of chaotic(thermal)particle motions,and the firs...Using thermal barriers at the melting point?Hm and RTm,it is shown that the latter directly reflects the chaotic process,since it is equal to the kinetic energy reserve of chaotic(thermal)particle motions,and the first additionally takes into account the energy expenditure for overcoming the potential energy of the interconnection of particles,which is typical for inorganic compounds.Therefore,to determine the share of crystal-mobile particles responsible for the viscosity of the melt,the chaotization barrier of RTm should be used,since in the virtual clusters the potential binding energy is conserved,thereby compensating for the heat expense of breaking these bonds upon melting.Therefore,to analyze the share of crystal-mobile particles,it is necessary to use the formula of their share in the form:Pcrm=1-exp(-tm/t).On the basis of the distribution of clusters previously found by the authors in terms of the number of crystal-mobile particles included in them,it was shown that all non-single crystal-mobile particles are responsible for the viscosity,and for flowability all single particles,including crystal-mobile,liquid-mobile and vapor-mobile.This ensures the superiority of the share of single particles over the share of crystal-mobile particles arranged in non-single clusters at the melting point,and thereby the fluidity of the melt.Based on the share distribution of clusters in terms of the number of particles entering into them,the share of non-single clusters responsible for the viscosity of the melt is expressed as:Pct=p2crm=[1-exp(-Tm/T)2].The probabilistic meaning of the formation of clusters from non-single crystal-mobile particles is extended to the formation of associates,which made it possible to disclose the meaning of the second level of the exponential dependence of viscosity in the cluster and associate model:η=η1(T1/T)a2(T2/T)b,where the first level is responsible for the formation of clusters,and the second—for associates.This form corresponds to the physical hierarchy when combining crystal-展开更多
文摘On the example of typical metals, it’s found that the activation energy of self-diffusion is above of the melting heat and below of vaporization heat. This corresponds to the existence of liquid-mobile particle classification based on the concept of randomized particles. A formula for estimating the activation energy of self-diffusion by which it is approximately half of the heat of evaporation of the substance is recommended. We derive the temperature dependence for a fraction self-diffusion’s particles.
文摘The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the act
文摘The significance of the work is determined by the need to develop a cluster theory of the liquid state of a substance in order to more deeply substantiate the viscosity, which is still expressed by empirical parameters within the framework of ideal ideas about the stratified flow of a liquid. According to the reference data on the dynamic viscosity of the melts for chlorides of the first group of the Periodic System, the approximating dependences in the form of cluster-associate and Frenkel’s models were constructed at various temperatures. The first model is based on taking into account the share of particles that cannot overcome the thermal melting barrier and thus serve to form virtual clusters and associates while preserving the structural motifs of the solid phase. In the framework of the cluster-associate viscosity model developed by the authors, these formations determine the melt viscosity and serve as flow units to which the energy of fluid motion is applied. The Frenkel’s model allows us to estimate the activation energy of fluidity. Calculations show that by comparing this energy with the degree of cluster association obtained in the framework of the cluster-associate model, a fairly close linear correlation is obtained, and the proportionality coefficient has the meaning of the activation energy per cluster. This energy does not go beyond the van der Waals energy of the unsaturated intermolecular bond characteristic of the interaction of particles in a liquid. This confirms the earlier established by the authors a similar pattern for melts of simple substances, based on the understanding of fluidity as a consequence of the destruction of cluster associates while preserving the clusters themselves.
基金The work was carried out within the framework of the project AR05130844/GF for grant funding of the MES of Kazakhstan.
文摘The purpose of the research is to develop the temperature dependence of the dynamic viscosity for silver chloride. The data were calculated on the basis of a new cluster and associate equation, which was derived using the concept of randomized particles. The calculated data are given in the temperature range from the melting point to the boiling point. The cluster and associate model is compared with the Frenkel’s equation in logarithmic coordinates, showing the mutual correspondence and complementarity of these models.
文摘Using thermal barriers at the melting point?Hm and RTm,it is shown that the latter directly reflects the chaotic process,since it is equal to the kinetic energy reserve of chaotic(thermal)particle motions,and the first additionally takes into account the energy expenditure for overcoming the potential energy of the interconnection of particles,which is typical for inorganic compounds.Therefore,to determine the share of crystal-mobile particles responsible for the viscosity of the melt,the chaotization barrier of RTm should be used,since in the virtual clusters the potential binding energy is conserved,thereby compensating for the heat expense of breaking these bonds upon melting.Therefore,to analyze the share of crystal-mobile particles,it is necessary to use the formula of their share in the form:Pcrm=1-exp(-tm/t).On the basis of the distribution of clusters previously found by the authors in terms of the number of crystal-mobile particles included in them,it was shown that all non-single crystal-mobile particles are responsible for the viscosity,and for flowability all single particles,including crystal-mobile,liquid-mobile and vapor-mobile.This ensures the superiority of the share of single particles over the share of crystal-mobile particles arranged in non-single clusters at the melting point,and thereby the fluidity of the melt.Based on the share distribution of clusters in terms of the number of particles entering into them,the share of non-single clusters responsible for the viscosity of the melt is expressed as:Pct=p2crm=[1-exp(-Tm/T)2].The probabilistic meaning of the formation of clusters from non-single crystal-mobile particles is extended to the formation of associates,which made it possible to disclose the meaning of the second level of the exponential dependence of viscosity in the cluster and associate model:η=η1(T1/T)a2(T2/T)b,where the first level is responsible for the formation of clusters,and the second—for associates.This form corresponds to the physical hierarchy when combining crystal-
