Pressure Dependence Of Melting Temperature Research Articles

A reinterpretation of the results for melting curves of metals based on the force – Heat equivalence energy density principle

A phenomenological model for describing the melting of metals at high pressures has recently been formulated by Ma et al. using the force – heat equivalence energy density principle. This theory represents an alternative to the Lindemann law of melting. Ma et al. have derived a formulation for the pressure dependence of melting temperature using the Murnaghan approximation for the linear dependence of bulk modulus on pressure. Since this approximation has proven to be not accurate for solids at high pressures, we have revised the expressions obtained by Ma et al. using the third order Birch- Murnaghan equation of state and the usual Tait equation of state. The revised expressions are used to describe the melting curves for twenty metals viz. Al, Ti, V, Cr, γ-Fe, Co, Ni, Cu, Zn, Mo, Pd, Ag, Ta, W, Re, Ir, Pt, Au, Pb and U. We have thus presented a reinterpretation of previous results for melting using the method proposed by Ma et al.

Pressure dependence of the Grüneisen parameter and melting temperature of some metals

We have used a method for determining volume dependence of the Grüneisen parameter in the Lindemann law to study the pressure dependence of melting temperatures in case of 10 metals viz. Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn. The reciprocal gamma relationship has been used to estimate the values of Grüneisen parameters at different volumes. The results for melting temperatures of metals at high pressures obtained in this study using the Lindemann law of melting are compared with the available experimental data and also with the values calculated from the instability model based on a thermal equation of state. The analytical model used in this study is much simpler than the accurate DFT calculations and molecular dynamics.

Study of melting curves for some transition metals

Abstract The volume dependence of the Gruneisen parameter has been used to calculate the pressure dependence of melting temperature using Lindemann law. The volume dependence of the Gruneisen parameter for some transition metals viz, Cu, Ni, Pd, and Pt has been determined using Shanker reciprocal relationship between γ and the ratio of pressure and bulk modulus. In this study, volume dependence of the Gruneisen parameter for some transition metals using the Stacey and Davis formulations for infinite pressure. The results for γ have been found similar from both the formulations given by Shanker and Stacey-Davis. The values of melting temperature are calculated and different pressures and Equation of state compared with the available data reported in the literature.

Melting behaviour of the candidate minerals for planetary models

The discovery of super-Earths and extra solar giant planets has made high pressure physics relevant for determining the formation and composition of these planets.We have developed a model to determine the pressure dependence of melting temperature, Tm and the Debye temperature, ΘD of materials utilizing Grüneisen parameter, ξ and the bulk modulus, B as the basic ingredients. The formalism has been applied to estimate the pressure dependence of melting temperature and Debye temperature of one of the candidate minerals such as quartz (stishovite, SiO2). The pressure range used in the present study is 0-6000GPa commensurate with the interior pressures of giant exoplanets. The results show an excellent agreement with the available experimental and other theoretical results.

Thermal and physical properties of titanium oxide at high pressure

We have investigated the pressure dependence of the thermal and physical properties of titanium oxide (rutile) by utilizing the semi-empirical relation developed following the Lindemann's melting law. Grüneisen parameter and the bulk modulus are the basic inputs of the empirical relation. The formalism has been applied to estimate the pressure dependence of melting temperature, Debye temperature, viscosity, conductivity and diffusivity of rutile. The pressure range used in the present study is 0–20GPa. The results show that the properties of TiO2 as a function of pressure are close to linear at low pressures (P≤6.0GPa) but starts deviating from being linear for (P>6.0GPa). Similar trends are also exhibited for viscosity, thermal conductivity, and diffusivity.

A theoretical model to study melting of metals under pressure

On the basis of the thermal equation-of-state a simple theoretical model is developed to study the pressure dependence of melting temperature. The model is then applied to compute the high pressure melting curve of 10 metals (Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn). It is found that the melting temperature is not linear with pressure and the slope [Formula: see text] of the melting curve decreases continuously with the increase in pressure. The results obtained with the present model are also compared with the previous theoretical and experimental data. A good agreement between theoretical and experimental result supports the validity of the present model.

Melting of metals under pressure

Lindemann's formula of melting is extended in terms of bulk modulus and Grüneisen parameter to study the pressure dependence of melting temperature, Tm(P) of metals. The formalism is applied to study Tm(P) of noble and transition metals, di-, tri- and tetravalent (Ag, Au, Cu, Mn, Mg, Zn, CD, In, Pb and Al) metals over a wide range of pressures up to 12GPa. The computed melting temperatures of the metals under pressure using our semi-empirical relation is in good agreement with the experimental data.

Pressure Dependence of Melting Temperature of Iron at the Earth’s Core Conditions

A semi-empirical relation to compute the pressure dependence of the melting temperature, \(T_\mathrm{m}(P)\), is derived in terms of the bulk modulus, Gruneisen parameter, and their first derivative with pressure. It is used to compute \(T_\mathrm{m}(P)\) for iron for pressures ranging up to 350 GPa at conditions relevant to the Earth’s core. The computed results are in excellent agreement with the values obtained from first principle calculations.

Dominant factors affecting the pressure dependence of melting temperatures in homologous series of aliphatic polyesters

The pressure dependence of the melting temperature of six aliphatic polyesters belonging to two different homologous series, poly(x-succinate) and poly(x-adipate) having even number of methylene groups (2,4,6) in the alkylene segment (x) was investigated by high pressure differential thermal analysis (HP-DTA) up to 500MPa. The phase diagrams of these polyesters were newly determined except for poly(ethylene adipate). The dTm/dpo at atmospheric pressure was obtained from the quadratic equation and the trend of dTm/dpo with respect to the number of methylene groups in the monomer unit in each homologous series is discussed. Amorphous densities at 25°C, expansion and compressibility coefficients in the melt of these polyesters are also reported. The entropy of fusion (ΔSm), enthalpy of fusion (ΔHm), volume change on melting (ΔVm), conformational entropy (ΔSor) and volume entropy (ΔSv) were correlated with respect to the number of methylene groups in the alkylene segment. ΔVm and ΔSv displayed a similar trend as that of dTm/dpo while ΔSm, ΔSor and ΔHm showed an increasing trend. The influence of these parameters on dTm/dpo is discussed in the context of the Clapeyron equation.

On melting of B4C boron carbide under pressure

The pressure dependence of melting temperatures for boron carbide and B4C-carbon eutectic has been studied up to 8 GPa, and it was found that in both cases the melting curves exhibit negative slope (-13\pm6 K/GPa), that is indicative of higher density of the melt as compared to the solid phase.

Improving the understanding of the melting curve of tantalum at extreme pressures through the pressure dependence of fusion volume and entropy

Molecular dynamics simulations of the melting curve of tantalum for the pressure range 0–300GPa are reported. The calculated melting curve agrees well with shock wave measurements and other calculations, but disagrees strongly with the diamond anvil cell data at high pressure. Calculated results for the pressure dependence of the fusion volume and entropy show that the pressure dependence of melting temperature approximately followed the Clausius–Clapeyron relation, and the slope of melting curve is mainly due to the variation of fusion volume. Entropy change due to latent volume change in melting, ΔSV and change in the configuration, ΔSD were evaluated. It is found that they have similar trend as the overall entropy change in melting, and ΔSD is more dominant. Furthermore, the value of ΔSD at ambient pressure is close to Rln2 per mole, which is the specific value of ΔSD predicted by the Rln2 rule, while it decreases when pressure goes from 50 to 300GPa. The analysis of the pair distribution function at extreme pressure shows that the change of configuration on melting decreases with increasing pressure, which supports the pressure dependence of ΔSD.

Study of Melting Temperature of Metals: Pressure Dependence

The melting temperature of metals are studied using the statistical moment method, going the quasi-harmonic appromations. The melting temperature of metals are calculated as a function of the pressure. We discuss the pressure dependence of melting temperatures of Ce, Fe metals and compare the present results with those of the experimental results.

Defects induced melting in alkali halides

In the present paper we study the pressure dependence of melting of NaCl and CsCl crystals. A formulation has been presented for the pressure dependence of melting temperature on the basis of the vacancy model using the expression for the pressure dependence of the volume of Schottky defects from the Roy–Roy equation of state. Values of pressure derivatives of melting temperature have been calculated at elevated pressures to determine the rate of change of melting temperature with increase in pressures using the data of vacancy formation energy and effective volume of Schottky defects. The vacancy model revised in the present study takes into account the variation of bulk modulus with pressure, whereas in the Ksiazek and Gorecki model, it was treated constant. Results for pressure derivative of melting temperature are calculated for the solids under study. The melting curves have also been obtained and found to compare well with results based on molecular dynamics simulation and experimental data reported in recent literature.

Behavior of pressure dependence of melting temperatures in aromatic polyesters: Influence of polymer structure

AbstractThe thermal behavior of three aromatic polyesters in a homologous series, poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT) was studied under hydrostatic pressure up to 200 MPa by using a high pressure differential thermal analysis apparatus. Confining fluid high pressure dilatometer was used to establish the volume–temperature curves (in both solid and liquid regions) from which volume change on melting of these polyesters at atmospheric pressure was determined. Single endothermic peak was seen for PET and PTT, whereas PBT showed double peaks above 50 MPa. Pressure coefficient of melting temperature at atmospheric pressure (dTm/dp(0)), was obtained from the quadratic fit. The dTm/dp(0) for PTT was newly determined to be 0.445 KMPa−1, whereas for PET and PBT were 0.503 and 0.455 KMPa−1, respectively, comparable to reported values. The dTm/dp(0) exhibited the odd‐even behavior corresponding to odd and even number of methylene groups in the repeat unit. Enthalpy and entropy of fusion had the most influence on this coefficient. Entropy related to conformational and volume change were evaluated and the former was found to have a significant impact on the value of dTm/dp(0). © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1799–1808, 2009

Pressure dependence of melting temperature in alkali halides

We present an estimate of the pressure dependence of melting temperature in 16 alkali halides. We use the formulations due to Gilvarry and Lindemann, and due to Stacey and Davis for calculating the pressure derivative of melting temperature. The data for thermal expansivity, bulk modulus and the Grüneisen parameter used in calculations have been determined corresponding to melting temperature of alkali halides. The results obtained from the two models are compared with the available experimental data. It has been discussed that both of the quoted theories rely on the dislocation theory of melting, which gives a satisfactory description of the process of melting for alkali halides.

Pressure dependence of melting temperatures in branched polyethylene up to 2 GPa

The melting temperatures ( T m) of branched polyethylene (B-PE) have been measured over the pressure range up to 2 GPa by use of a high-pressure X-ray diffraction apparatus. The T m- P curve for B-PE is expressed as ( T m T m,0 ) c = (P + P 0) a where T m,0 is the T m at atmospheric pressure, c = 4.788, P 0 = 280.2 MPa and a = P 0 + 0.1 MPa. The T m of B-PE increases with increasing pressure monotonically, and T m = 310°C at 2 GPa. The X-ray diffraction peaks corresponding to the spacing d = 3.84 A ̊ for the (110) lattice plane of the orthorhombic B-PE crystal do not change with increasing temperature below 1.85 GPa but d values for the (200) lattice plane increase with increasing temperature. The thermal properties of a B-PE melt crystallized at various high pressures above 1.0 GPa have been measured at atmospheric pressure, and four endothermic peaks are observed for the sample melt crystallized at 800 MPa. The entropies of fusion ΔS F of B-PE and linear polyethylene (L-PE) at pressures up to 200 MPa have been determined based on the Clausius-Clapeyron equation and P- V- T data by O. Olabisi and R. Simha ( Macromolecules, 1975, 8, 206), and ΔS F for B-PE is much smaller than for L-PE.

Correlation between the equation of state and the pressure dependence of glass transition and melting temperatures in polymers and rare-gas solids

A correlation between the equation of state and the pressure dependence of the glass transition temperature T g in polymers such as polystyrene (PS) and poly (methyl methacrylate) (PMMA) and the pressure dependence of the melting temperature T m in polymers such as polyethylene (PE), in rare-gas solids such as argon (Ar) and in hydrogen (H 2) has been examined based on the experimental data by Simha, Zoller and Rehage for polymers and Cheng, Mills and Zha for rare-gas solids and an equation of state derived in a previous work. The volume-pressure relation at constant temperature for solid and liquid states is expressed by: V x(P 0, T)/V x(P, T)= A x(P + P x) m x where V x ( P 0, T) is the volume at constant pressure P 0 and temperature T, V x ( P, T) is the volume at P and T, P x is a function of temperature, m x is a constant and the subscript x means a state such as x = 1 for liquid and x = s for solid. It is found that values of P x change discontinuously with increasing temperature in the vicinity of T g, while m x changes discontinuously at T m where P x is continuous with respect to temperature. Values of F m,s defined by F m,s = 1 − V s (P m , 0) V s (P m , T m ) for a rare-gas solid such as Ar are calculated based on the experimental data and are around 0.09 for Ar, independent of pressure, where V s( P m, T m) is the volume of solid phase at T m. Values of F g defined by F g = 1 − V s (P g , T 0) V(P g ), T g ) at T g are 0.036-0.055 for PS and 0.018–0.036 for PMMA. A three dimensional P- V- T surface over the temperature region including T g and T m is established based on the experimental data.

On the equation for the pressure dependence of melting temperature

The Clausius-Clapeyron equation is used to show that the melting equation of Couchman and Reynolds (1976) is equivalent to a quadratic expression in P for Q/ Delta Vm, where Q is the latent heat of melting. Experimentally derived parameters are listed for eight elements, and predicted values of Q/ Delta Vm at atmospheric pressure are found to agree with experiment to within about +or-10%.

Tait equation for inorganic solids with applications to the pressure dependence of melting temperature

The original version of the Tait equation is proposed to represent the compression of certain inorganic solids and has been applied to a derivation of the pressure dependence of melting temperature.