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Based on the delocalized of melting criterion, a relatively simple analytical (i.e., without computer simulation) method for calculating the Lindemann ratio is proposed. It is shown that for classical single-component solids (in which the melting point (T m) is greater than the Debye temperature (Θ): T m /Θ > 1.5), the Lindemann ratio is determined only by the packing coefficient of the structure. Calculations for various structures of classical solids (both crystalline and amorphous) showed good agreement with the estimates of other authors. For quantum single-component crystals (in which T m /Θ < 0.4), the Lindemann ratio is determined not only by the crystal structure, but also by the Θ/ T m function. Therefore, when passing from the classical to the quantum area, the T m (Θ) function changes its functional dependence. It was shown that for quantum crystals, the Lindemann ratio decreases with increasing pressure along the melting line. For quantum nanocrystals, the Lindemann ratio increases with an isobaric decrease in a nanocrystal size. At this, the more noticeably the shape of the nanocrystal deviates from the energy-optimal shape, the greater the sized increase in the Lindemann ratio. Therefore, the use of the Lindemann criterion to study the melting of quantum crystals (as they tried to when studying the melting of atomic metallic hydrogen) showed incorrect results. The dependence of the Lindemann ratio (LE) on the ratio of the melting point (Tm) to the Debye temperature (Θ) for various structures of solid. [Display omitted] • Lindemann ratio, which can be applied to classical and quantum solids is proposed. • Lindemann ratio (LR) for crystalline and amorphous classical solids is calculated. • For quantum crystals the LR decreases at the pressure increase along the melting line. • For quantum nanocrystals the LR increases with the decrease in the nanocrystal size. • It is incorrect to use the Lindemann criterion to the melting of quantum crystals. [ABSTRACT FROM AUTHOR]

In this work we present new analytical (i.e., without computer modeling) method for calculating the dependence of the nanocrystal melting temperature both on pressure and on the size (number of atoms N) and surface shape of the nanocrystal. This method is based on the paired Mie – Lennard-Jones interatomic interaction potential, and takes into account the dependence of both the state equation and other lattice properties on the size and shape of the nanocrystal. For the first time, the dependences of the melting temperature on the pressure P , size N , and shape f of the nanocrystal were obtained. Calculations have been performed for gold, platinum and iron. It is shown that at any pressure, the melting point T m (P , N , f) decreases both with an isomorphic-isobaric (f , P – const) decrease in the number of N atoms, and with an isomeric-isobaric (N , P – const) deviation of the nanocrystal shape from the energy-optimal shape. It is shown that the value of the baric derivative of the melting temperature T m ′(P) for a nanocrystal at low pressures is greater, and at high pressures less than the T m ′(P) value for a macrocrystal. At this, the dependence of the T m ′(P) function on the nanocrystal size is insignificant, i.e., at constant N-f -arguments, the baric dependences T m (P , ∞) and T m (P , N , f) are practically parallel. It is indicated how this method can be applied for experimental evaluation of the pressure under which a nanocrystal is located in a refractory matrix. • Method for calculate T m (P) dependence on size and nanocrystal shape was developed. • The T m (P) dependences were calculated for cub and rod Au nanocrystal of 306 atoms. • The T m (P) decreases inatoms number decrease, or inshape deviationofoptimal ones. • Baric derivative of T m (P) for nano at low P big and at high P less than for macro. • Method can evaluate of P under which a nanocrystal located in a refractory matrix. [ABSTRACT FROM AUTHOR]

It was shown that the Clausius-Clapeyron relation (CCR) determines only the maximum possible slope of the first-order phase transition (PT-1) line in the temperature-pressure coordinates. This conclusion follows from the fact that the real PT-1 it is an irreversible process. An inequality has been obtained that generalizes the CCR to the case of irreversibility at PT-1: the Clausius-Clapeyron inequality (CCI). It is indicated that the CCI passes into equality (i.e., into the CCR) only in the case of reversible PT-1. Analysis of experimental data for various types of PT-1 showed the implementation of CCI in most cases. Herewith, the deviation from the CCR is the more noticeable, the greater the volume change in PT-1. It was found that deviations of experimental data from the CCR correlate with the presence of phase-transition radiation in PT-1. This makes it possible to use the value of the deviation from the CCR for thermodynamic indication of the probability of observing phase-transition radiation at PT-1 in various substances. A method has been proposed for estimating the irreversibility PT-1 value, based on the magnitude of the deviation from the CCR. The obtained CCI has been generalized to the case of the presence of an external homogeneous magnetic (or electric) field acting on the two phases of matter in equilibrium. • An inequality generalizing the CCR for an irreversible phase transition is obtained • The deviations from the CCR in the various experimental works were indicated • Deviation from the CCR is more, the greater of volume change in phase transition • Deviations from the CCR correlate to the presence of phase-transition radiation • The results were generalized for the case of an external magnetic or electric field [ABSTRACT FROM AUTHOR]

In this work we present new analytical (i.e., without computer modeling) method for calculating the dependence of the melting temperature (T m) on pressure (P) for a single-component crystal. The method is based on the paired four–parameter Mie–Lennard-Jones interatomic interaction potential, and the delocalized criterion of melting. This method was used to calculate the baric dependences of the melting temperature T m (P) and its pressure derivative T m ′(P) for gold, platinum and niobium in the pressure range: P = 0–1000 GPa. It has been shown that the dependences calculated by this method for gold and platinum are in better agreement with experimental data than the dependences obtained by computer modeling methods: the molecular dynamics simulations and the ab initio Z-method calculations. For niobium, the calculated T m (P) dependence turned out to be steeper, i.e. the T m ′(P) values turned out to be greater than the experimental data obtained in [D. Errandonea et al. Communications Materials 1 , 1 (2020)]. It has been indicated that this deviation can be caused both by a decrease in the Lindemann parameter with an increase in pressure, and by the redistribution of electrons in the s-to-d orbitals during compression of transition metals with a bcc structure. Furthermore, the discrepancy may also be due to the highly-correlated chain-like self-diffusion, which is inherent in bcc metals before melting. • A method for calculating the baric dependence of melting temperature is proposed. • A new delocalized melting criterion was used for calculating of T m (P) up to 1 TPa. • The method was used to calculate the T m (P) and T m ′(P) dependences for Au, Pt, Nb. • The T m (P) dependences for Au and Pt are in good agreement with experimental data. • For Nb the calculated T m (P) dependence lie higher than obtained by Errandonea et al. [ABSTRACT FROM AUTHOR]

Based on the previously proposed model of paired covalent bond, the reasons for the brittleness for covalent crystals have been studied. It is shown that the brittleness of a covalent crystal is due to the "duplicity" of the paired interatomic interaction potential for elastic (reversible) and plastic (irreversible) deformation. This leads to the fact that the specific surface energy during plastic deformation of a covalent crystal is more than two times less than the specific surface energy during elastic deformation. Therefore, with a small deformation of a covalent crystal, it is energetically more advantageous to create a surface by breaking than by elastic stretching it. It is shown that the brittle-ductile transition temperature for single-component covalent crystals has an upper limit: T BDT / T m < 0.45, where T m is the melting temperature. • The paired interatomic interaction potential for a covalent bond is "two-faced". • Surface energy at plastic deformation of a covalent crystal is less than at elastic. • Create the surface in a covalent crystal is favorable by rupture than by stretch. • Brittleness of a covalent crystal is due to the interatomic potential "duplicity". • The brittle-ductile transition temperature for covalent crystals has an upper limit. [ABSTRACT FROM AUTHOR]

The parameters of the electroneutral vacancy formation and self-diffusion of atoms in iron have been calculated by the analytical method based on the paired four-parameter Mie–Lennard-Jones interatomic interaction potential. For the first time, all activation process parameters were calculated within the framework of a single method: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The isobaric temperature dependences of the indicated activation parameters for bcc and fcc iron structures from T = 10 K–1810 K along two isobars: P = 0 and 10 GPa were calculated. It is shown that, at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region is negative. In the high temperature region, a good agreement has been obtained with the experimental estimates of activation parameters for different iron structures known from the literature. It is shown that at the α-γ transition temperature (1184 K), the activation parameters decrease during the isobaric transition from the bcc to the fcc structure. At the γ-δ transition temperature (1667 K), the activation parameters increase during the isobaric transition from the fcc to the bcc structure. With increasing pressure, the jumps magnitude for the Gibbs energy and the enthalpy of the activation process increases, and for the entropy and volume of the activation process decreases. Temperature dependences of the enthalpy of vacancy formation (curves 1 and 2) and self-diffusion (curves 3 and 4). Solid lines 1 and 3 are isobars P = 0, dashed lines 2 and 4 are isobars P = 10 GPa. [Display omitted] • A new analytical method for calculating the activation parameters in Fe is proposed. • Activation parameters of Fe is calculated from 10 to 1810 K for P = 0 and 10 GPa. • Activation parameters in α-Fe, γ-Fe, and δ-Fe have been studied by a single method. • At α-γ transition the activation parameters decrease, and at γ-δ transition – increase. • Changes in activation parameters with increasing pressure have been studied. [ABSTRACT FROM AUTHOR]

Based on calculations of the activation process parameters (vacancy formation and self-diffusion) for gold at the temperature range T = 10–1330 K, the correlations of the activation process parameters s i (T) ∼ h i (T) and s i (T) ∼ v i (T), along two isobars. P = 0 and 24 GPa, are studied. Here h i is the enthalpy, s i is the entropy, and v i is the volume of the activation process, i.e. for the formation of an electroneutral vacancy (i = v) or for the self-diffusion of atoms (i = d). It is shown that if, during isobaric heating, an energy less than a certain value (h i < h si) is required to create a defect (vacancy or diffusing atom), or if the resulting defect has a volume less than a certain value (v i < v si), then this defect has a negative entropy, i.e. this defect orders the crystal. However, if a larger energy value is required to create a defect (h i > h si) or this defect has a noticeable volume (v i > v si), then this defect has a positive entropy, i.e. this defect disorders the crystal. It is shown that at a low concentration of defects, they order the crystal, and only starting from a certain concentration (X si) does the defect formation entropy pass into the positive region, where defects disorder the crystal. The changes in the functions of h si , v si , and X si with increasing pressure are studied. Dependence of entropy on the logarithm of the defect formation probability for gold. The two upper curves are for the atom self-diffusion process, and the two lower curves are for the vacancy formation process. Solid curves are isobars P = 0, dashed curves are isobars P = 24 GPa. [Display omitted] • Correlations of entropy on enthalpy and on volume of activation process are studied. • If the defect creating energy is small h < h s , then such a defect orders the crystal. • If a small volume v < v s is needed for a defect, such a defect orders the crystal. • If the concentration of defects is low X < X s , they order the crystal. • The changes of hs , vs , and Xs functions with increasing pressure has been studied. [ABSTRACT FROM AUTHOR]