Зависимость Поверхностной Энергии От Температуры И Давления Для Макро- И Нанокристалла

A new analytical (i.e., without computer modeling) method for calculating the dependence of the melting temperature (Tm) of a single-component crystal on pressure (P) is proposed. The method is based on the delocalization melting criterion and does not contain fitting constants. The baric dependences of the melting temperature Tm(P) and its pressure derivative Tm(P) for gold, platinum and niobium in the pressure range: P = 0 – 1000 GPa were calculated by this method. It was shown that the dependences calculated by this method for gold and platinum agree better with the experimental data than the dependences obtained by computer simulation methods. For niobium, the calculated dependence Tm(P) turned out to be steeper, i.e., the value Tm(P) turned out to be larger than in the experiment. It was indicated that this discrepancy might be due both to a decrease in the Lindemann parameter with increasing pressure and to a redistribution of electrons on the s-d-orbitals during compression of transition metals with a BCC structure.

Section: золотоunclassified

Section: платинаunclassified

See 1 more Smart Citation

Изменение Температуры Плавления Металлов С ростом Давления

Магомедов¹

2023

“…Кроме этого, было необходимо в рамках данного метода расчета самосогласованно определить все четыре параметра межатомного потенциала (33). Эти задачи были решены в [26][27][28], где был разработан аналитический метод расчета свойств однокомпонентного кристалла, который не содержит вакансий и делокализованных атомов. Именно на основе этого метода в [28] были определены параметры межатомного потенциала для 15 однокомпонентных металлов.…”

Section: расчеты уравнения состояния и свойств кристалла золотаunclassified

Изменение Параметров Образования Вакансий И Самодиффузии В Кристалле С Температурой И Давлением

Magomedov¹

2022

Self Cite

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T = 10 K to 1330 K along two isobars P = 0 and 24 GPa. 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 has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T = 0 K were discussed.

“…Температурная зависимость удельной поверхностной энергии (a), ее производной по температуре (b), и ее производной по давлению (c) для ГЦК-Au вдоль изобар 0, 24, 60 GPa 300 и 1337 K. Однако, как это было показано в[59], параметры межатомного потенциала (3), которые были использованы в[55] дают малые значения модуля упругости и параметра Грюнайзена, чем экспериментальные. Поэтому в дальнейшем в[29] и в данной работе были использованы более корректные параметры потенциала из(13).…”

unclassified

Изучение свойств ГЦК-Au в широком диапазоне температур и давлений

Магомедов¹

2022

The properties of the FCC of the gold crystal were calculated using an analytical method (without computer modeling) in the temperature range: T = 10 – 1337 K and pressures: P = 0 – 110 GPa. The following properties were calculated: state equation, Debye temperature, first and second Gruneisen parameters, elastic modulus (BT), thermal expansion coefficient (p), isochoric (Cv) and isobaric (Cp) heat capacity, specific surface energy. Derivatives of these properties also have been calculated both by temperature along three isobars and by pressure along three isotherms. The obtained results showed good agreement with the other authors results. It was shown that there is a certain temperature TB in which the product pBT does not change during the crystal compression. At T > TB, the pBT function increases, and at T < TB, it decreases with an increase in pressure. For FCC-Au has been received TB =132 K. Показано, что изотермы производной модуля упругости по давлению B(P) пересекаются в точке: P = 21.58 GPa, B(P) = 7.43. It was shown that the isotherms of the baric derivative of elastic modulus B(P) intersect at the point: P = 21.58 GPa, and B(P) = 7.43. At P < 21.58 GPa, the B(P) function increases, and at P > 21.58 GPa, it decreases with increasing temperature. It was shown that the isotherm of the baric derivative of the isochoric heat capacity Cv(P) has a minimum, and the isotherm of the baric derivative of the isobaric heat capacity Cp(P) has both a minimum and a maximum. Based on the obtained dependencies, some approximations, which are used to calculate the properties of the crystal under high P-T conditions, have been analyzed.