scholarly journals Зависимость поверхностной энергии от температуры и давления для макро- и нанокристалла

2021 ◽  
Vol 63 (9) ◽  
pp. 1415
Author(s):  
М.Н. Магомедов
Keyword(s):  
High Pressures ◽  
Interatomic Potential ◽  
Nanocrystal Size ◽  
Surface Shape ◽  
Thermoelastic Properties ◽  
Specific Surface Energy ◽  
Lennard Jones ◽  
Different Temperatures ◽  
Derivatives Of ◽  
Good Agreement

Based on the RP-model of a nanocrystal, an analytical method is developed for calculating the specific surface energy (), isochoric and isobaric derivatives of the  function with respect to temperature, and isothermal derivatives of the  function with respect to pressure and density. It is shown that the method is applicable for both macro-and nanocrystals with a given number of atoms and a certain surface shape. To implement this method, the parameters of the Mie–Lennard-Jones paired interatomic potential were determined in a self-consistent way based on the thermoelastic properties of the crystal. The method was tested on macrocrystals of 15 single-component substances: for 8-FCC crystals (Cu, Ag, Au, Al, Ni, Rh, Pd, Pt) and for 7-BCC crystals (Fe, V, Nb, Ta, Cr, Mo, W). The calculations were made at different temperatures and showed good agreement with the experimental data. Using the example of FCC-Rh, the change in surface properties with a decrease of the nanocrystal size along the isotherms of 10, 300, 2000 K is studied. It is shown that at high pressures and low temperatures, there is a region where the  function increases at an isomorphic-isothermal-isobaric decrease in the nanocrystal size. As the temperature increases, this area disappears.

scholarly journals Изучение свойств сплава золото-железо в макро- и нанокристаллических состояниях в различных P-T-условиях

2020 ◽  
Vol 62 (12) ◽  
pp. 2034
Author(s):  
М.Н. Магомедов
Keyword(s):  
Surface Energy ◽  
Specific Surface ◽  
Interatomic Potential ◽  
State Equation ◽  
Specific Surface Energy ◽  
Lennard Jones ◽  
Pressure Region ◽  
Substitution Alloy ◽  
Fe Substitution ◽  
Good Agreement

For a disordered fcc-Au-Fe substitution alloy, the parameters of the Mie–Lennard-Jones pairwise interatomic potential are determined. Based on these parameters, the concentration dependencies of lattice properties for the macrocrystal of this alloy are calculated. Calculations of 20 properties of macrocrystals fcc-Au, fcc-Fe and fcc-Au0.5Fe0.5 are showed good agreement with experimental data. Using the RP-model of the nanocrystal, the state equation P(v, T; N) and baric dependences of both lattice and surface properties of the fcc-Au0.5Fe0.5 alloy are calculated. Calculations were performed at temperatures T = 100, 300 and 500 K for both a macrocrystal (N = Macro) and a cubic nanocrystal with N = 306 atoms. It is shown that with an isothermal-isobaric (P = 0) decrease in the size of a nanocrystal, its the Debye temperature, elastic modulus, and specific surface energy decrease, while its the specific volume, thermal expansion coefficient, specific heat capacity, and Poisson's ratio increase. At low temperatures in a certain pressure region, the specific surface energy increases at an isothermal-isobaric decrease in the number of atoms in the nanocrystal. As the temperature increases, this pressure region disappears.

Crystal Dynamics of Rubidium. II. Anharmonic Calculations of the Phonon Self-Energy and the Heat Capacity

1973 ◽  
Vol 51 (24) ◽  
pp. 2564-2586 ◽  
Author(s):  
J. R. D. Copley
Keyword(s):  
Heat Capacity ◽  
Interatomic Potential ◽  
Thermal Strain ◽  
Large Degree ◽  
Self Energy ◽  
Lattice Heat Capacity ◽  
Crystal Dynamics ◽  
Derivatives Of ◽  
Transverse Branch ◽  
Good Agreement

We have made anharmonic calculations of phonon frequency shifts and widths, the thermal strain, and the lattice heat capacity for solid rubidium. The calculations were performed using an interatomic potential derived from the work of Price, Singwi, and Tosi. The calculated shifts are in reasonable agreement with experiment, except in the case of the Σ4 transverse branch in the [ζζ0] direction, where there are definite indications that the calculation disagrees with experiment. The calculated thermal strain is ~15% too high at intermediate temperatures. On the other hand, the calculated anharmonic contributions to the heat capacity are in good agreement with experiment at intermediate temperatures, but are 10 to 20% too low near the melting temperature. The anharmonic contributions are sensitive to the third and fourth derivatives of the potential, owing to the large degree of cancellation between the cubic and quartic terms. Furthermore there is evidence that higher order anharmonic terms may be significant.

scholarly journals Метод определения параметров парного межатомного потенциала

2020 ◽  
Vol 62 (7) ◽  
pp. 998
Author(s):  
М.Н. Магомедов
Keyword(s):  
Experimental Data ◽  
Thermal Expansion ◽  
Interatomic Potential ◽  
Coefficient Of Thermal Expansion ◽  
State Equation ◽  
Zero Temperature ◽  
Thermoelastic Properties ◽  
Lennard Jones ◽  
Sublimation Energy ◽  
Potential Parameters

Disadvantages of methods known from the literature for determining 4 parameters of the paired interatomic potential of Mie-Lennard-Jones in relation to crystals are indicated. A new method is proposed for determining the parameters of this potential from the thermoelastic properties of the crystal. In this method the parameters are determined by the best coincidence of calculated values with experimental data: 1) of the sublimation energy of the crystal at zero temperature (T = 0 K) and pressure (P = 0); 2) of coefficient of thermal expansion and isothermal elastic modulus, which were measured at P = 0 and T = 300 K; 3) of the dependence of the isotherm T = 300 K state equation from volume of P(300 K, V). The method was tested on iron and gold and showed good results. By this method also were determined the interatomic potential parameters for refractory metals: Nb, Ta, Mo, and W. The results obtained also made it possible to determine more precisely such properties of these metals as the sublimation energy, the Debye temperature, and the surface energy.

scholarly journals BARIC DEPENDENCE OF LATTICE PROPERTIES FOR DIAMOND

2018 ◽  
Vol 59 (9) ◽  
pp. 57
Author(s):  
Makhach N. Magomedov
Keyword(s):  
Experimental Data ◽  
Thermal Expansion ◽  
Elastic Modulus ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Interatomic Potential ◽  
State Equation ◽  
Relative Volume ◽  
Lennard Jones ◽  
Good Agreement

Based on the pairwise interatomic potential of Mi-Lennard-Jones and the Einstein's model of crystal the state equation P(V/V0, T) and the baric dependencies of the lattice properties for diamond were obtained. The calculations were performed along two isotherms: T = 300 and 3000 K and until to P = 10000 kbar (i.e. until to the relative volume V/V0 = 0.5). The baric dependencies for the following properties were obtained: isothermal elastic modulus, isochoric and isobaric heat capacities and thermal expansion coefficient. Good agreement with experimental data was obtained.

Multicanonical Molecular Dynamics Simulation Study of the Liquid-Solid and Solid-Solid Transitions in Lennard-Jones Clusters

2011 ◽  
Author(s):  
Toshihiro Kaneko ◽  
Kenji Yasuoka ◽  
Ayori Mitsutake ◽  
Xiao Cheng Zeng
Keyword(s):  
Molecular Dynamics ◽  
Heat Capacity ◽  
Transition Temperature ◽  
Peak Position ◽  
Temperature Curve ◽  
Dynamics Simulation ◽  
Lennard Jones ◽  
Dynamics Simulations ◽  
First Time ◽  
Good Agreement

Multicanonical molecular dynamics simulations are applied, for the first time, to study the liquid-solid and solid-solid transitions in Lennard-Jones (LJ) clusters. The transition temperatures are estimated based on the peak position in the heat capacity versus temperature curve. For LJ31, LJ58 and LJ98, our results on the solid-solid transition temperature are in good agreement with previous ones. For LJ309, the predicted liquid-solid transition temperature is also in agreement with previous result.

scholarly journals Experimental and Numerical Buckling Analyses of Laminated Composite Plates under Temperature Effects

2010 ◽  
Vol 19 (4) ◽  
pp. 096369351001900 ◽  
Author(s):  
Emin Ergun
Keyword(s):  
Composite Plate ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Buckling Load ◽  
Fibre Reinforcement ◽  
Stacking Sequence ◽  
Laminated Composite Plates ◽  
Different Temperatures ◽  
Good Agreement

The aim of this study is to investigate, experimentally and numerically, the change of critical buckling load in composite plates with different ply numbers, orientation angles, stacking sequences and boundary conditions as a function of temperature. Buckling specimens have been removed from the composite plate with glass-fibre reinforcement at [0°]i and [45°]i (i= number of ply). First, the mechanical properties of the composite material were determined at different temperatures, and after that, buckling experiments were done for those temperatures. Then, numerical solutions were obtained by modelling the specimens used in the experiment in the Ansys10 finite elements package software. The experimental and numerical results are in very good agreement with each other. It was found that the values of the buckling load at [0°] on the composite plates are higher than those of other angles. Besides, symmetrical and anti-symmetrical conditions were examined to see the effect of the stacking sequence on buckling and only numerical solutions were obtained. It is seen that the buckling load reaches the highest value when it is symmetrical in the cross-ply stacking sequence and it is anti-symmetrical in the angle-ply stacking sequence.

Temperature Dependence of Hole Impact Ionization Coefficient in 4H-SiC Photodiodes

2009 ◽  
Vol 615-617 ◽  
pp. 311-314 ◽  
Author(s):  
W.S. Loh ◽  
J.P.R. David ◽  
B.K. Ng ◽  
Stanislav I. Soloviev ◽  
Peter M. Sandvik ◽  
...  
Keyword(s):  
Phonon Scattering ◽  
Impact Ionization ◽  
Positive Temperature Coefficient ◽  
Positive Temperature ◽  
Different Temperatures ◽  
Ionization Coefficients ◽  
Increasing Temperature ◽  
The Impact ◽  
Good Agreement ◽  
Ionization Rates

Hole initiated multiplication characteristics of 4H-SiC Separate Absorption and Multiplication Avalanche Photodiodes (SAM-APDs) with a n- multiplication layer of 2.7 µm were obtained using 325nm excitation at temperatures ranging from 300 to 450K. The breakdown voltages increased by 200mV/K over the investigated temperature range, which indicates a positive temperature coefficient. Local ionization coefficients, including the extracted temperature dependencies, were derived in the form of the Chynoweth expression and were used to predict the hole multiplication characteristics at different temperatures. Good agreement was obtained between the measured and the modeled multiplication using these ionization coefficients. The impact ionization coefficients decreased with increasing temperature, corresponding to an increase in breakdown voltage. This result agrees well with the multiplication characteristics and can be attributed to phonon scattering enhanced carrier cooling which has suppressed the ionization process at high temperatures. Hence, a much higher electric field is required to achieve the same ionization rates.

Theoretical Assessment of Compressibility Factor of Gases by Using Second Virial Coefficient

2018 ◽  
Vol 73 (2) ◽  
pp. 121-125
Author(s):  
Bahtiyar A. Mamedov ◽  
Elif Somuncu ◽  
Iskender M. Askerov
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Compressibility Factor ◽  
Analytical Approximation ◽  
Accurate Evaluation ◽  
Numerical Examples ◽  
Lennard Jones ◽  
Theoretical Assessment ◽  
Good Agreement

AbstractWe present a new analytical approximation for determining the compressibility factor of real gases at various temperature values. This algorithm is suitable for the accurate evaluation of the compressibility factor using the second virial coefficient with a Lennard–Jones (12-6) potential. Numerical examples are presented for the gases H2, N2, He, CO2, CH4 and air, and the results are compared with other studies in the literature. Our results showed good agreement with the data in the literature. The consistency of the results demonstrates the effectiveness of our analytical approximation for real gases.

scholarly journals Anharmonic Self-Consistent Theory of Crystals. II. The 2d and 3d Quartic Crystal Models

1994 ◽  
Vol 49 (6) ◽  
pp. 663-670
Author(s):  
S. Sh. Soulayman ◽  
C. Ch. Marti ◽  
Ch. Ch. Guilpin
Keyword(s):  
Helmholtz Free Energy ◽  
Equations Of State ◽  
Three Dimensional ◽  
Inert Gases ◽  
Thermoelastic Properties ◽  
Consistent Theory ◽  
Jones Potential ◽  
Lennard Jones ◽  
2D And 3D ◽  
Strong Anharmonicity

Abstract In this paper we apply the method developed in part I for describing the crystalline state of two and three dimensional inert gases. For strong anharmonicity of fourth order, the equations of state of these gases are obtained. This way we calculate the thermoelastic properties of two and three dimensional argon, krypton and xenon using the Lennard-Jones potential. The corrections to the Helmholtz free energy and thermodynamic properties due to quantum effects are considered. The results are compared with the available experimental data.

Rheological Properties of Tomato Concentrate

2008 ◽  
Vol 4 (7) ◽  
Author(s):  
Manish Dak ◽  
Radha Charan Verma ◽  
S N A Jaaffrey
Keyword(s):  
Rheological Properties ◽  
Absolute Temperature ◽  
Power Law Model ◽  
Arrhenius Model ◽  
Rotational Viscometer ◽  
Consistency Coefficient ◽  
Flow Behaviour Index ◽  
Different Temperatures ◽  
Wide Gap ◽  
Good Agreement

Rheological properties of tomato concentrate were evaluated using a wide-gap rotational viscometer (Brookfield Engineering Laboratories: Model LVDV-II) at different temperatures of 20, 30, 40, 50, and 60oC, at concentration of 18, 12.18 and 8.04 % total solids, and at appropriate shear rate(1-100 RPM). The power law model was fitted to the experimental results. The values of flow behaviour index (n) were found less than unity (0.23 to 0.82) at all the temperature and the concentration indicating shear-thinning (pseudoplasticity) behaviour of the concentrate. The correlation between the observed consistency coefficient ranging from 0.09 to 65.87 Pa.sn and the inverse absolute temperature has been exhibited by Arrhenius model. Consistency coefficient increased exponentially with increase in the concentration. Statistical model was used for prediction of the consistency coefficient as a function of temperature and concentration which showed a good agreement (r2=0.99) between experimental and theoretical values. The magnitude of activation energy were found to be in the range of 8.6 to 14.08 kJ/mol.K.

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