Isothermal Elastic Moduli Research Articles

Study on Thermodynamic Properties and Elastic Deformation of Full-Heusler Alloys Co2TaGa and Co2VGa by Statistical Moment Method

Heusler alloy is a ferromagnetic alloy based on the Heusler phase. It is an intermetallic alloy between metallic and non-metallic elements that can be non-ferromagnetic and has a BCC crystal structure. This paper presents the theory of thermodynamics and elastic deformation of full-Heusler A2BC alloy with BCC structure built on the basis of statistical moment method (SMM). The paper presents numerical results for the temperature and pressure dependence of the mean nearest neighbor distance between two atoms, the density, the volume, the thermal expansion coefficient, the isotherm and adiabatic compressibilities, the isothermal elastic modulus, the heat capacities at constant volume and pressure, Young’s modulus, the bulk modulus, longitudinal and transverse wave velocities of alloys Co2TaGa and Co2VGa when using the coordination sphere method and the Mie–Lennard-Jones pair interaction potential. Some SMM calculation results agree well with available ab initio calculation results.

Thermodynamic and elastic properties of tungsten and tungsten silicide

We present thermodynamic and elastic theory for BCC metal and binary interstitial alloy established by the statistical moment method (SMM) and perform numerical calculations for the silicon concentration, pressure and temperature dependences of nearest neighbor distance, volume, thermal expansion coefficient, heat capacities at constant volume and at constant pressure, Debye temperature, Gruneisen parameter, isothermal elastic modulus, bulk modulus, shearing modulus, elastic constants and longitudinal wave velocity for W and WSi under temperature up to 3600 K, pressure up to 100 GPa and silicon atom concentration up to 5%. The SMM numerical calculations for W are compared with experiments and other calculations. The SMM calculated results for WSi are predictive, orienting experimental results in the future.

Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method

We built a model and proposed a theory about the thermodynamic properties of face-centered cubic (FCC) binary interstitial alloy’s thin films based on the statistical moment method and performed numerical calculations for AuSi (gold silicide). First, the statistical moment method (SMM) calculations for the thermodynamic properties of Au are compared with reported experiments and calculations that show a good agreement between the calculations in this paper and earlier studies. Additionally, the SMM calculations for thermodynamic properties of AuSi alloy films are performed, which show that the thermal expansion coefficient, the specific heat at constant volume, and the specific heat at constant pressure increases, while the isothermal elastic modulus decreases with increasing temperature and increasing interstitial atom concentration. Furthermore, when the number of layers reaches 100, the thermodynamic properties of the film are similar to those of the bulk material. The achieved theoretical results for AuSi films are novel and can be useful in designing future experiments.

Ideal and limiting strength of a Lennard-Jones crystal at temperatures lower than the melting line endpoint temperature: molecular dynamics simulation

ABSTRACT The conditions of stability of a stretched face-centered cubic (FCC) crystal against infinitesimal and finite changes in the state parameters have been considered at temperatures lower than that of the endpoint of the melting line [V.G. Baidakov, S.P. Protsenko. Phys. Rev. Lett. 95 015701 (2005)]. Molecular dynamics simulation has been used to calculate effective isothermal elastic moduli, average lifetimes, the work of formation of a critical nucleus and the nucleation rate close to the boundary of the limiting stretching of a Lennard-Jones FCC crystal. States in which the isothermal bulk elastic modulus K is equal to zero, with the shear moduli and being nonzero, have been achieved. It is shown that at K < 0 the crystal retains thermodynamic stability. The kinetics of the phase decay of a Lennard-Jones crystal beyond to the line K = 0 has been investigated. It has been found that the decay proceeds by the nucleation mechanism, through the formation and growth of new-phase nuclei. As distinct from small stretchings, at the boundary of limiting ones the nucleus has a form close to spherical.

Метод определения параметров парного межатомного потенциала

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.

Stress heterogeneities and failure mechanisms induced by temperature and pore-pressure increase in volcanic regions

We study the strain and stress fields produced by temperature and pore pressure increases within and outside a Thermo-Poro-Elastic (TPE) inclusion (the source region), embedded within a medium (the matrix) in isothermal drained conditions. This model is suitable to describe a crustal region in a volcanic environment pervaded by hot pressurized fluids released by an underlying magma chamber. After introducing the pertinent constitutive relations, a formal solution for the displacement field is provided in terms of the Green's function for an elastic medium with drained isothermal elastic moduli, employing a generalization of Eshelby (1961) procedure. If an unbounded medium is considered, a displacement potential can be introduced, obeying the Laplace equation within the source region and the Poisson equation within the matrix. If a spherically symmetric source region is considered, simple analytical solutions are obtained for the displacement, the strain and the stress fields, showing that thrust faulting mechanisms are promoted within the source region while normal faulting mechanisms prevail in the embedding matrix. Employing reasonable numerical values for the thermo-poro-elastic parameters, suitable to describe highly porous sedimentary rock, strain and stress variations are found to be significant even for moderate changes of temperature and pore pressure. Variations of the Coulomb failure function are high in the TPE region and are strongly dependent on the friction coefficient and pore pressure. Application of these results to the 1982-84 and 2011-13 unrest episodes at Campi Flegrei caldera (Italy) suggests that an oblique dike intrusion across a previously unfaulted TPE region took place with a mixed tensile-thrust dislocation mechanism in both events, as previously inferred from accurate inversion of geodetic data.

Dependence of the Elastic Modulus on the Size and Shape of an Argon Nanocrystal

The isothermal dependences of the lattice properties of a nanocrystal on its the size and shape are investigated using the nanocrystal RP model which contains both lattice vacancies and delocalized (diffusing) atoms. A Gibbs surface model is proposed in which a part of the cells is vacant and a part of the atoms are in the delocalized state. The model takes into account that a part of the atoms on the Gibbs surface are delocalized in the bulk manner and the others, on the surface manner. The calculations are performed for argon atoms, which interact by means of the Mie‒Lennard‒Jones pairwise potential. The state equation (P) and the isothermal elastic modulus (B) for argon macro- and nanocrystals along the isotherm T = 10 K are calculated. The calculated data for the macrocrystal are shown to agree well with the experimental data. The isochoric and isobaric dependences of the Debye temperature Θ, the first (γ) and second (q) Gruneisen parameters, the specific surface energy σ, and the functions B and B'(P) = (∂B/∂P)T on the nanocrystal size and shape are studied. It is shown that the Θ, q, σ, B, and B '(P) functions decrease with an isomorphic-isobaric decrease in the nanocrystal size, while the γ value increases. However, in the case of an isomorphic-isochoric decrease in the nanocrystal size, the modulus of elasticity of argon increases. Upon a deviation of the nanocrystal shape from the energy-optimal shape (for the RP(vac) model it is cube), the size dependences of these functions are enhanced.

Размерная зависимость упругих свойств нанокристалла аргона

AbstractThe state equation ( P ) and isothermal elastic modulus ( B ) are calculated for argon macro- and nanocrystals at T = 10 K using in the framework the RP(vac)-model of nanocrystal. The isochoric and isobaric (at P = 0) dependences of the Debye temperature (Θ), of the first (γ) and second ( q ) Grüneisen parameters, as well as the specific surface energy (σ), B and B '( P ) = (∂ B /∂ P )_ T , are studied as the functions of size and shape of the nanocrystal. As shown, the isothermally isobaric decrease in nanocrystal size is accompanied by a decrease in functions Θ, q , σ, B and B '( P ) and by an increase in the γ parameter. However, the elastic modulus rises in the case of the isothermally isochoric decrease in the nanocrystal size. When the nanocrystal deviates from its most energetically optimal shape (a cube for the RP(vac)-model), the size dependences of these functions become more noticeable.

Size Dependence of Elastic Properties of Argon Nanocrystals

The state equation (P) and isothermal elastic modulus (B) are calculated for argon macro- and nanocrystals at T = 10 K using in the framework the RP(vac)-model of nanocrystal. The isochoric and isobaric (at P = 0) dependences of the Debye temperature (Θ), of the first (γ) and second (q) Gruneisen parameters, as well as the specific surface energy (σ), B and B'(P) = (∂B/∂P)T, are studied as the functions of size and shape of the nanocrystal. As shown, the isothermally isobaric decrease in nanocrystal size is accompanied by a decrease in functions Θ, q, σ, B and B'(P) and by an increase in the γ parameter. However, the elastic modulus rises in the case of the isothermally isochoric decrease in the nanocrystal size. When the nanocrystal deviates from its most energetically optimal shape (a cube for the RP(vac)-model), the size dependences of these functions become more noticeable.

Molecular Simulations Shed Light on Potential Uses of Ultrasound in Nitrogen Adsorption Experiments.

Nitrogen adsorption is one of the main characterization techniques for nanoporous materials. The experimental adsorption isotherm provides information about the surface area and pore size distribution (PSD) for a sample. In this work we show that additional insight into PSD can be gained when the speed of sound propagation through a sample is measured during nitrogen adsorption experiment. We analyzed published experimental data on ultrasound propagation through a nanoporous Vycor glass sample during nitrogen adsorption experiment. Next, we calculated the change of the longitudinal and shear moduli of the sample as a function of relative vapor pressure. From this, we show that the shear modulus of the sample does not change upon filling the pores, evidencing that adsorbed nitrogen at 77 K has zero shear modulus, similarly to a bulk liquid. The longitudinal modulus of the sample behaves differently: it changes abruptly at the capillary condensation and keeps gradually increasing thereafter. We performed Monte Carlo molecular simulations to predict the compressibility of adsorbed nitrogen and then calculated the longitudinal modulus of the nitrogen-saturated Vycor using the Gassmann equation. Our theoretical predictions nicely matched the longitudinal modulus derived from the experimental data. Additionally, we performed molecular simulations to model nitrogen adsorbed in silica pores of sizes ranging from 2 to 8 nm. We found that the isothermal elastic modulus of adsorbed nitrogen depends linearly on the inverse pore size. This dependence, along with the proposed recipe for probing the modulus of adsorbed nitrogen, sets up the grounds for extracting additional information about the porous samples, when the nitrogen adsorption is combined with ultrasonic experiments.

BARIC DEPENDENCE OF LATTICE PROPERTIES FOR DIAMOND

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.

Variations in thermal properties of diamond under isothermal compression

State equation P(V/V 0, T) and baric dependences of thermal properties of diamond have been obtained without any fitting parameters from the interatomic pair Mie–Lennard-Jones potential and the Einstein model of a crystal. Calculations have been performed along two isotherms (at T = 300 and 3000 K) up to P = 10000 kbar = 1000 GPa, i.e., to a relative volume of V/V 0 = 0.5. The baric dependences have been obtained for the following characteristics: isothermal elastic modulus B T and B'(P), isochoric heat capacity C v and C v ' (P), isobaric heat capacity C p ; thermal expansion coefficient α p and α p ' (P); and specific surface energy σ, as well as its derivatives σ'(P) and σ'(T). It is shown that for P → ∞, functions B T (P) and σ(P) vary linearly, functions B'(P), α p (P), C v (P), C p (P) and σ'(P) tend to constants, while functions α p '(P), C v '(P), and difference C p (P)–C v (P) tend to zero. Good agreement with experimental data has been demonstrated.

A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172-180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473-2480, 2005; Hale et al. in Soft Matter 5:3603-3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528-540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature.

Thermophysical properties of carbon nanotubes in toluene under high pressure

It investigates the thermophysical properties and the equation of state of single-walled carbon nanotubes in liquid toluene. The equation of state is established for the investigated system. It analyzes the dependence of its constants on temperature and characteristics of the structure. Numerical values of isothermal elastic modulus are obtained as functions of pressure. It is found that the addition of carbon nanotubes in toluene caused the increase of the energy of molecular interaction in the investigated system.

On the Gibbs conditions of stable equilibrium, convexity and the second-order variations of thermodynamic potentials in nonlinear thermoelasticity

The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the convexity or concavity properties of all thermodynamic potentials in relation to each other, and to derive the relationships between the specific heats at constant stress and deformation, and between the isentropic and isothermal elastic moduli and compliances. The comparison with the derivation based on the classical thermodynamic approach is also given.

Temperature dependences of relaxation time, adiabatic and isothermal elastic moduli in ZnSe:Ni and ZnSe:Cr crystals obtained in an ultrasonic experiment

Theory of ultrasonic absorption and dispersion, based on the Zener equation, was used for constructing the equations, those made it possible to restore the temperature dependences of relaxation time, adiabatic and isothermal elastic moduli on the basis of experimental data on the temperature dependences of ultrasound absorption and phase velocity. This method was used for processing the experimental results obtained in single crystals of ZnSe:Ni and ZnSe:Cr.

Elastic moduli calculation and instability in structure I methane clathrate hydrate

The thermal expansion of structure I clathrate hydrates with empty cages and with enclathrated methane molecules has been calculated from 5 to 270 K using the lattice dynamics approach within the quasiharmonic approximation. The temperature dependence of several elastic properties, namely the dynamical, adiabatic and isothermal elastic moduli, are calculated. The dynamical and thermodynamical stability of the crystals are investigated according to the Born stability criteria. Methane hydrate is unstable against small homogeneous deformations near the melting transition at normal pressure. For the empty hydrate lattice, a thermodynamical instability was found to occur at significantly higher temperature. The theoretical results are compared with new thermal expansion data on methane hydrate and results from a previous molecular dynamics study.

Kinetics of Network Re-Formation in Hydrolytic Degraded AFR700B Polyimide Resin

Dynamic mechanical spectrometry was used to investigate the network formation processes during the high-temperature isothermal post-cure of virgin and hydrolytic degraded AFR700B resin. Upon exposure to hydrolytic conditions, a significant degradation in physical and mechanical properties of newly developed high-temperature PMR type polyimide resins (AFR700B) was observed. In this study we are particularly interested in the kinetics and the controlling mechanism of the network formation and re-formation processes at the high-temperature post-cure stage. In situ viscoelastic experiments were performed at a temperature of 400 °C. At this temperature the curing of polymer resin continues, thus the isochronal elastic modulus increases as the curing time increases. Furthermore, it was possible to perform a time–curing time superposition using these isothermal elastic modulus curves. This time–curing time shift-rate is then used as a direct measure of the kinetics of polyimide network formation. Interestingly, in this study we found that the time–curing time shift-rate for the hydrolytic degraded samples was identical to the time–curing time shift-factor of virgin ‘ascured’ formulated samples. This observation does not necessarily imply that the chemistry of polyimide network formation is the same, but instead that the controlling mechanism of network formation must be identical.

Generalized Anderson-Grüneisen parameters for non-cubic solids

General thermoelastic equations are developed relating the temperature and the stress derivatives of the effective isothermal elastic moduli of an orthorhombic crystal which is subjected to a purely extensional deformation parallel to the crystallographic axes. When the stress is hydrostatic, these equations are used to obtain finite strain expressions for the generalized isothermal Anderson-Grüneisen parameters of a crystal with orthorhombic or higher elastic symmetry. The expressions are derived in terms of the second-order elastic constants and compliances, the third-order elastic constants and the Grüneisen parameters. Theoretical values of the five independent isothermal Anderson-Grüneisen parameters are then calculated for two hexagonal metals (Mg and Zn). Finally, a relation between the adiabatic and isothermal Anderson-Grüneisen parameters is given which generalizes that previously obtained in the case of cubic crystals.

On phase transitions involving internal strain

This is an analysis of continuous phase transitions at body centred tetragonal configurations of nonlinearly elastic monatomic crystals. The aim is to assess the implications of molecular theory with regard to a thermoelastic description of the transitions by means of a prototype calculation which models a change in invariance of the constitutive equation. As a by-product of the investigation, the status of the Cauchy-Born hypothesis becomes evident. The most striking result is that the isothermal elastic moduli suffer a finite discontinuity precisely at the transition point.