Papers by Keyword: Statistical Thermodynamics

Abstract: The paper features the mathematical model of analytical calculation of thermodynamic properties like viscosity, speed of sound and thermal conductivity for fluids in one and two-phase region (fluid-solid, fluid-gas) on the basis of statistical mechanics. For the calculation of thermal conductivity and viscosity for fluids will be presented Chung-Lee-Starling model Equations for the thermal conductivity are developed based on kinetic gas theories and correlated with the experimental data. The low-pressure transport properties are extended to fluids at high densities by introducing empirically correlated density dependent functions. These correlations use acentric factor, dimensionless dipole moment and an empirically determined association parameters to characterize molecular structure effect of polyatomic molecules. The calculation of thermodynamic properties for fluids was developed under the theory of statistical thermodynamics and statistical associated fluid theory. For the calculation of thermal conductivity of solids are the most important two contributions: the heat transport by electrons (el) and by phonons (ph). In our model we have made the assumption that heat transport by electrons and by phonons is independent and the thermal conductivity is than a sum of both terms.

Abstract: Theory for describing the conditions leading to dynamic recrystallization in FCC metals is introduced. The approach also describes stress-strain curves when this process occurs, and is unique in incorporating the effects of strain rate and temperature employing only physical parameters as input. The novelty of the approach stems from incorporating an incubation period in the equations describing the progress of dislocation density with strain; beyond such incubation dislocation free grains form. The energy barrier to ignite grain growth is expressed as a function of the strain energy stored on the material and a statistical entropy contribution due to the degrees of freedom available to a dislocation for annihilation. The incubation strain is obtained by performing an energy balance between the stored energy on the subgrain boundaries, the slip energy of boundary migration and the interfacial energy required for grain nucleation. The application of this work to pure Cu and Ni has lead to transition maps in temperature-strain rate space indicating the conditions for dynamic recrystallization occurrence.

Abstract: Theory for describing the conditions leading to dynamic recrystallization in FCC metals is introduced. The approach also describes stress-strain curves when this process occurs, and is unique in incorporating the effects of strain rate and temperature employing only physical parameters as input. The novelty of the approach stems from incorporating an incubation period in the equations describing the progress of dislocation density with strain; beyond such incubation dislocation free grains form. The energy barrier to ignite grain growth is expressed as a function of the strain energy stored in the material and a statistical entropy contribution due to the degrees of freedom available to a dislocation for annihilation. The incubation strain is obtained by performing an energy balance between the stored energy on the subgrain boundaries, the slip energy for boundary migration and the interfacial energy required for grain nucleation. The application of this work to Fe and Ni multicomponent alloys has lead to transition maps in temperature-strain rate space indicating the conditions for dynamic recrystallization occurrence.

Abstract: Within the framework of the lattice-statics and static fluctuation-waves’ methods, the available energiesof strain-induced interaction of interstitial–interstitial, interstitial–substitutional and substitutional–substitutional impurity atomic pairs are collected and analysed for f.c.c.-(Ni,Fe)–C solutionsallowing for discrete atomic structure of the host-crystal lattice. The lattice spacings, elasticity moduliand/or quasi-elastic force parameters of the host-crystal lattice, and concentration coefficients of thedilatation of solid-solution lattice due to the respective solutes are selected as the input numerical experimentaldata used. The above-mentioned interaction energies prove to have non-monotonically decreasing(‘quasi-oscillating’) and anisotropic dependences on discrete interatomic radius-vector, andthemselves are strong and long-range. In all f.c.c.-(Ni,Fe)-base solutions, there is strain-induced attractionin many co-ordination shells. In general, the strain-induced interaction between impurity atomsin γ-Fe is weaker than in α-Ni (but in some solid solutions, it may prove to be of the same order).The verification of applicability of the approximation of strain-induced interaction of impurities forf.c.c.-(Ni,Fe)–C alloys (by means of analysis of thermodynamic C activity and ‘short-range order’ parametersof C-atoms’ distribution revealed by Mössbauer spectroscopy) showed that it must be supplementedwith additional short-range (‘electrochemical’) repulsion in the first co-ordination shell.Nevertheless, in any case, the strain-induced interaction of impurity atoms must be taken into accountfor analysis of structure and properties of f.c.c.-(Ni,Fe)-base solutions.

Abstract: Using both the statistical-thermodynamics methods within the scope of the selfconsistent field approximation and the diffraction data on coherent (or diffuse) scattering of X-rays (or thermal neutrons) from (dis)ordered f.c.c.-Ni–Fe alloys of various compositions, the estimation of interatomic interactions (including their magnetic contribution) and their temperature– concentration dependences were obtained. Based on the static concentration-wave representation, the expressions for configuration free energies of L12-Ni3Fe-type permalloy, L10-NiFe-type elinvar and L12-Fe3Ni-type invar were analyzed, considering explicit expressions for configuration entropies of atomic and magnetic subsystems with their configuration internal energies. Phase diagram of a system at issue was plotted within the field of the presence of f.c.c.-Ni–Fe alloys; their phase boundaries, equilibrium (static) properties near critical points (order parameter, etc.), and possible microstructures developed by composition-controlled magnetic transitions and/or order–disorder constant-composition solid–solid phase transformations were discussed. The obtained results were compared with available experimental data.