scholarly journals Изменение свойств алмаза из -=SUP=-13-=/SUP=-C при изотермическом сжатии

2019 ◽  
Vol 89 (6) ◽  
pp. 882
Author(s):  
М.Н. Магомедов
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Equation Of State ◽  
Pair Potential ◽  
Atomic Interaction ◽  
Natural Isotopic Composition ◽  
Capacity Surface ◽  
Derivatives Of

AbstractThe parameters of atomic interaction pair potential for ^13C diamond have been determined from experimental data on the ratio of Raman frequencies for isotopically different diamonds. Based on these parameters, an equation of state and baric dependences of ^13C diamond lattice properties at 300 K have been calculated. Specifically, the Debye temperature; the first, second, and third Grüneisen parameters; elastic modulus; thermal expansion coefficient; heat capacity; surface energy; and pressure derivatives of these parameters along a 300 K isotherm have been determined. The results have been compared with available data for diamond having a natural isotopic composition, i.e., for ^12.01C.

scholarly journals INFLUENCE OF SIZE AND PRESSURE ON THE TEMPERATURE DEPENDENCIES OF THERMODYNAMIC PROPERTIES OF PLATINUM

2021 ◽  
pp. 465-474
Author(s):  
Сергей Петрович Крамынин
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Equation Of State ◽  
Surface Energy ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Interatomic Interaction ◽  
Isobaric Heat Capacity ◽  
Temperature Dependences

Основываясь на параметрах парного потенциала межатомного взаимодействия Ми-Леннард-Джонса для Pt, и используя RP-модель нанокристалла, изучены температурные, барические и размерные зависимости следующих свойств: модуля упругости, коэффициента теплового расширения, изобарной теплоемкости и поверхностной энергии. Расчет уравнения состояния Pt показал хорошее согласие с экспериментом. Уравнение состояния было рассчитано вдоль пяти изотерм: T = 300, 1300, 1500, 1700, 1900 К. Впервые с единых позиций выполнены расчеты температурных зависимостей указанных свойств Pt в диапазоне от 0 K до 1500 K вдоль изобар 0 и 50 ГПа. Расчеты указанных зависимостей проведены как для макро-, так и для нанокристалла кубической формы из 306 атомов. Показано, что при изобарно-изотермическом уменьшении размера нанокристалла Pt происходит уменьшение значений модуля упругости и поверхностной энергии, а значения коэффициента теплового расширения и изобарной теплоемкости увеличиваются на исследуемом интервале температур. Based on the parameters of the pair interatomic interaction potential of the Mie-Lennard-Jones for Pt, and using the RP-model of the nanocrystal, the temperature, pressure and size dependencies of the following properties are studied: elastic modulus, thermal expansion coefficient, isobaric heat capacity, and surface energy. The calculation of the equation of state showed good agreement with experiment. The equation of state was calculated along five isotherms: T = 300, 1300,1500, 1700, 1900 K. For the first time, calculations of the temperature dependences of the above properties of Pt in the range from 0 to 1500 K along 0 and 50 GPa isobars were performed from a unified standpoint. Calculations of these dependencies were carried out for both macro- and cubic nanocrystals of 306 atoms. It is shown that with an isobaric-isothermal decrease in the nanocrystal size, the values of the elastic modulus and surface energy decrease, while the values of the thermal expansion coefficient and isobaric heat capacity increase over the investigated temperature range.

scholarly journals Analysis of Equation of State for Carbon Nanotubes

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jeewan Chandra ◽  
Pooja Kapri Bhatt ◽  
Kuldeep Kholiya
Keyword(s):  
Experimental Data ◽  
Carbon Nanotubes ◽  
Thermal Expansion ◽  
Carbon Nanotube ◽  
Equation Of State ◽  
Compression Behavior ◽  
Nanotube Bundles ◽  
The Individual

Compression behavior of carbon nanotube bundles and individual carbon nanotubes within the bundle has been studied by using the Suzuki, Shanker, and usual Tait formulations. It is found that the Suzuki formulation is not capable of explaining the compression behavior of nanomaterials. Shanker formulation slightly improves the results obtained by the Suzuki formulation, but only usual Tait’s equation (UTE) of state gives results in agreement to the experimental data. The present study reveals that the product of bulk modules and the coefficient of volume thermal expansion remain constant for carbon nanotubes. It has also been found that the individual carbon nanotubes are less compressible than bundles of carbon nanotubes.

Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
Author(s):  
Ivan Cibulka ◽  
Lubomír Hnědkovský ◽  
Květoslav Růžička
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Equilibrium Data ◽  
State Behaviour ◽  
Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

scholarly journals Изменение свойств железа при ОЦК-ГЦК-фазовом переходе

2021 ◽  
Vol 63 (2) ◽  
pp. 191
Author(s):  
М.Н. Магомедов
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Coefficient Of Thermal Expansion ◽  
Pair Potential ◽  
Specific Surface Energy ◽  
Pressure Derivative ◽  
Lennard Jones ◽  
Crystal Properties ◽  
Fcc Phase

Using the previously developed method for calculating crystal properties based on the Mie–Lennard-Jones pair potential, the thermodynamic properties of the BCC and FCC phases of iron at the temperature of the polymorphic BCC-FCC phase transition are calculated. 23 properties of iron and their changes during the BCC-FCC transition are calculated. Calculations have shown that properties such as the Gruneisen parameter, the coefficient of thermal expansion, and the heat capacity practically do not change during the BCC-FCC transition. The elastic modulus, specific entropy, Poisson's ratio, and specific surface energy change in the same way as the molar volume, i.e. within 1%. The Debye temperature and its pressure derivative decrease at the BCC-FCC transition in the same way as the distance between the centers of the nearest atoms increases, i.e. within 2-3%. Based on the analysis of experimental data known from the literature, it is shown that even relatively accurately measured parameters such as the coefficient of thermal expansion and elastic modulus are measured with an error exceeding the values of jumps in these parameters at the BCC-FCC transition. It is indicated that amorphization or nanostructuring of a certain portion of iron during the BCC-FCC transition can contribute to changes in the properties of iron during this phase transition.

scholarly journals The Triple Product Rule is Incorrect

2021 ◽  
Vol 1 (2) ◽  
pp. 1-3
Author(s):  
Igor Stepanov*
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Isothermal Compressibility ◽  
Chain Rule ◽  
Triple Product ◽  
Product Rule ◽  
Capacity Ratio ◽  
The Difference ◽  
The Relationship ◽  
Derivatives Of

The triple product rule, also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, relates the partial derivatives of three interdependent variables, and often finds application in thermodynamics. It is shown here that its derivation is wrong, and that this rule is not correct; hence, the Mayer's relation and the heat capacity ratio, which describe the difference between isobaric and isochoric heat capacities, are also untrue. Also, the relationship linking thermal expansion and isothermal compressibility is wrong. These results are confirmed by many experiments and by the previous theoretical findings of the author.

Thermomechanical properties and equation of state for the γ-polymorph of hexahydro-1,3,5-trinitro-1,3,5-triazine

RSC Advances ◽  
2014 ◽  
Vol 4 (78) ◽  
pp. 41491-41499 ◽  
Author(s):  
Kartik Josyula ◽  
Rahul Rahul ◽  
Suvranu De
Keyword(s):  
Thermal Expansion ◽  
Elastic Modulus ◽  
Equation Of State ◽  
Thermomechanical Properties ◽  
Continuum Modeling ◽  
Tensor Equation ◽  
Material Information ◽  
Elastic Modulus Tensor

This work predicts the elastic modulus tensor, equation of state, and coefficients of thermal expansion at all stable thermodynamic states for γ-RDX. The work provides substantial material information for continuum modeling of RDX.

scholarly journals THE SIZE DEPENDENCIES OF PROPERTIES OF MO-W ALLOY OF EQUIATOMIC COMPOSITION

2020 ◽  
pp. 128-135
Author(s):  
Сергей Петрович Крамынин
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Surface Energy ◽  
Expansion Coefficient ◽  
Coefficient Of Thermal Expansion ◽  
Interatomic Interaction ◽  
Isobaric Heat Capacity ◽  
Substitution Alloy ◽  
Capacity Surface ◽  
Thermal Volume Expansion

Основываясь на параметрах парного потенциала межатомного взаимодействия Ми-Леннард-Джонса для Mo и W были рассчитаны параметры потенциала для сплава замещения Mo - W эквиатомного состава. Получены размерные зависимости для уравнения состояния, модуля упругости, коэффициента теплового расширения, изобарной теплоемкости, поверхностной энергии и производной поверхностной энергии по температуре. Также получены температурные зависимости коэффициента теплового расширения изобарной теплоемкости для макро- и нанокристаллов сплава Mo - W. Было показано, что температурная зависимость коэффициента теплового объемного расширения для нанокристалла лежит выше, чем зависимость для макрокристалла, также обнаружено, что с уменьшением размера уменьшается модуль упругости, коэффициент теплового объемного расширения возрастает, а удельная поверхностная энергия нанокристалла сплава Mo - W уменьшается. Based on the parameters of the Mie-Lennard-Jones pair-wised potential of the interatomic interaction for Mo and W , the potential parameters for an equiatomic Mo - W substitution alloy were calculated. Size dependences for the equation of state, modulus of elasticity, coefficient of thermal expansion, isobaric heat capacity, surface energy and surface energy temperature derivative were obtained. Temperature dependencies of coefficient of thermal expansion and isobaric heat capacity for macro- and nano-crystals of Mo - W alloy were also obtained. It was shown that the temperature dependence of the thermal expansion coefficient for a nanocrystal is higher than that for a macrocrystal. It was also found that with a decrease in size, the elastic modulus decreases, the thermal volume expansion coefficient increases, and the specific surface energy of the alloy nanocrystal Mo - W decreases.

scholarly journals The Triple Product Rule is Incorrect

2021 ◽  
pp. 1-3
Author(s):  
Igor Stepanov ◽  
Keyword(s):  
Heat Capacity ◽  
Thermal Expansion ◽  
Isothermal Compressibility ◽  
Chain Rule ◽  
Triple Product ◽  
Product Rule ◽  
Capacity Ratio ◽  
The Difference ◽  
The Relationship ◽  
Derivatives Of

The triple product rule, also known as the cyclic chain rule, cyclic relation, cyclical rule or Euler’s chain rule, relates the partial derivatives of three interdependent variables, and often finds application in thermodynamics. It is shown here that its derivation is wrong, and that this rule is not correct; hence, the Mayer’s relation and the heat capacity ratio, which describe the difference between isobaric and isochoric heat capacities, are also untrue. Also, the relationship linking thermal expansion and isothermal compressibility is wrong. These results are confirmed by many experiments and by the previous theoretical findings of the author.

AB INITIO THERMODYNAMICS OF ZINC-BLENDE ZnS, ZnSe

2011 ◽  
Vol 25 (32) ◽  
pp. 4553-4561 ◽  
Author(s):  
HUAN-YOU WANG ◽  
HUI XU ◽  
JU-YING CAO ◽  
MING-JUN LI
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Thermal Expansion ◽  
Constant Pressure ◽  
Local Density ◽  
Linear Thermal Expansion ◽  
Plane Wave Method ◽  
Temperature Range ◽  
Zinc Blende ◽  
Good Agreement

The density function perturbation theory (DFPT) is employed to study the linear thermal expansion and heat capacity at constant pressure (with the quasiharmonic approximation). The calculations are performed using a pseudopotential plane wave method and local density approximation for the exchange-correlation potential. The calculated results of linear thermal expansion coefficient and heat capacity at constant pressure for zinc-blende ZnS , ZnSe are compared with the available experimental data in a wide temperature range. Generally, in low-temperature range, they have good agreement. However, in high-temperature range, due to anharmonic effect and other reasons, lead to larger errors for these properties between the theoretical results and available experimental data.

Equation of state for liquid water

2006 ◽  
Vol 4 ◽  
pp. 186-199
Author(s):  
R.I. Nigmatulin ◽  
R.Kh. Bolotnova
Keyword(s):  
Experimental Data ◽  
Heat Capacity ◽  
Equation Of State ◽  
Liquid Water ◽  
Specific Volume ◽  
High Pressures ◽  
Internal Heat ◽  
Heat Energy ◽  
Grüneisen Coefficient ◽  
Gruneisen Coefficient

The equation of state for water (EOSW) in Mi–Gruneisen form with Born–Mayer potential for densities less, than 1 g/cm^3 is developed. The equation is applicable to moderate and high pressures (up to 2·10^12 Pa), in particular, to explosive and static pressures in the range of densities from 0.7 to 3.8 g/cm^3 . The equation for the Gruneisen coefficient that depends not only on the specific volume but also on the temperature is received. The proposed method by the experimental data for dependencies on specific volume and temperature the heat capacity and isochoric temperature coefficient of pressure increase allows to calculate the Gruneisen coefficient and the internal heat energy.

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