Theoretical Melting Curve Research Articles

Revisiting the melting curves of vanadium and niobium metals under pressure

The Lindemann criterion is adjusted to revisit melting curves of vanadium and niobium metals under pressure thanks to the statistical moment method (SMM) in statistical mechanics. The equation-of-state and atomic mean-square displacement in SMM approach are applied to implement numerical calculations for vanadium and niobium metals up to 250 GPa and 150 GPa, respectively. The obtained theoretical melting curves are compared with results of previous experiments and molecular dynamics (MD) simulations where possible to check the theory. We expose that our theoretical melting line of vanadium is overall in good agreement with previous results determined by in situ X-ray diffraction (XRD) and diffuse scattering signals using synchrotron XRD together with shock experiments up to pressure 250GPa. For niobium, our melting curve follows very well with those of recent experimental XRD data as well as ab initio Z method up to 124 GPa. However, we also observe the difference of classical MD simulation results from SMM calculations at pressure below 2.5 GPa. This research enriches the high-pressure melting point database as well as provides a relatively simple approach with low computational cost to estimate high-pressure melting points of materials.

Experimental and theoretical confirmation of an orthorhombic phase transition in niobium at high pressure and temperature

Compared to other body-centered cubic (bcc) transition metals, Nb has been the subject of fewer compression studies and there are still aspects of its phase diagram which are unclear. Here, we report a combined theoretical and experimental study of Nb under high pressure and temperature. We present the results of static laser-heated diamond anvil cell experiments up to 120 GPa using synchrotron-based fast x-ray diffraction combined with ab initio quantum molecular dynamics simulations. The melting curve of Nb is determined and evidence for a solid-solid phase transformation in Nb with increasing temperature is found. The high-temperature phase of Nb is orthorhombic Pnma. The bcc-Pnma transition is clearly seen in the experimental data on the Nb principal Hugoniot. The bcc-Pnma coexistence observed in our experiments is explained. Agreement between the measured and calculated melting curves is very good except at 40–60 GPa where three experimental points lie below the theoretical melting curve by 250 K (or 7%); a possible explanation is given.

High pressure melting curve of osmium up to 35 GPa

The melting curve of osmium (Os) has been determined up to 35 GPa and 5800 K using a laser heated diamond anvil cell facility. Al2O3 was used as the thermal insulator and pressure transmitting medium. Melting was detected by the laser speckle method, and spectroradiometric technique was employed for determination of melting temperature. The measured melting curve has been compared with available theoretical melting curves. The Simon-Glatzel fit to the experimental data agrees reasonably well with the recently reported theoretical melting curve using Z-method. The melting slope of the measured melting curve is 58.0 K/GPa at P = 0.1 MPa. The melting line of Os is seen to cross that of W around 6 GPa, making it the most refractory metal. The density dependence of Grüneisen parameter [γ(ρ)] has also been determined analytically, using the experimentally obtained melting slope.

Compression and phase diagram of lithium hydrides at elevated pressures and temperatures by first-principles calculation

High pressure and high temperature properties of AB (A = 6Li, 7Li; B = H, D, T) are comprehensively investigated with first-principles methods. It is found that H−sublattice features in the low-pressure electronic structure near the Fermi level of LiH are shifted to that dominated by the Li+ sublattice under compression. The lattice dynamics are studied in quasi-harmonic approximation, from which the phonon contribution to the free energy and the isotopic effects are accurately modelled with the aid of a parameterized double-Debye model. The equation of state (EOS) obtained matches perfectly with available static experimental data. The calculated principal Hugoniot is also in accordance with that derived from shock wave experiments. Using the calculated principal Hugoniot and the previous theoretical melting curve, we predict a shock melting point at 56 GPa and 1923 K. In order to establish the phase diagram for LiH, the phase boundaries between the B1 and B2 solid phases are explored. The B1–B2-liquid triple point is determined at about 241 GPa and 2413 K. The remarkable shift in the phase boundaries with isotopic effect and temperature reveal the significant role played by lattice vibrations. Furthermore, the Hugoniot of the static-dynamic coupling compression is assessed. Our EOS suggests that a precompression of the sample to 50 GPa will allow the shock Hugoniot to pass through the triple point and enter the B2 solid phase. This transition leads to a discontinuity with 4.6% volume collapse—about four times greater than the same B1–B2 transition at zero temperature.

Ab initiomelting curve of osmium

The melting curve of osmium up to a pressure $P$ of 500 GPa is obtained from an extensive suite of ab initio quantum molecular dynamics (QMD) simulations using the Z method. The ab initio $P=0$ melting point of Os is $3370\ifmmode\pm\else\textpm\fi{}75$ K; this range encompasses all of the available data in the literature and corroborates the conclusion of J. W. Arblaster [Platinum Metals Rev. 49, 166 (2005)] that the melting temperature of pure Os is $3400\ifmmode\pm\else\textpm\fi{}50$ K and that the 3300 K typically quoted in the literature is the melting point of impure Os. The $T=0$ equation of state (EOS) of Os and the $P$ dependence of the optimized $c/a$ ratio for the hexagonal unit cell, both to pressures $\ensuremath{\sim}900$ GPa, are obtained in the ab initio approach as validation of its use. Although excellent agreement with the available experimental data ($P\ensuremath{\lesssim}80$ GPa) is found, it is the third-order Birch-Murnaghan EOS with ${B}_{0}^{\ensuremath{'}}=5$ rather than the more widely accepted ${B}_{0}^{\ensuremath{'}}=4$ that describes the QMD data to higher pressures, in agreement with the more recent experimental EOS by Godwal et al. The theoretical melting curve of Os obtained earlier by Joshi et al. is shown to be inconsistent with our QMD results, and the possible reason for this discrepancy is suggested. Regularities in the melting curves of Os and five other third-row transition metals (Ta, W, Re, Pt, Au) could be used to estimate the currently unknown melting curves of Hf and Ir.

On equation of state, elastic, and lattice dynamic stability of bcc bismuth under high pressure: Ab-initio calculations

First principles calculations have been carried out using density functional theory based Vienna Ab-initio Simulation Package to analyze the elastic and lattice dynamic stability and determine the equation of state of bismuth in bcc phase. The 0 K isotherm has been determined from total energy calculations. The 300 K isotherm obtained after adding thermal corrections to 0 K isotherm compares well with experimental data. The elastic stability of the bcc phase examined from 0 GPa to 220 GPa suggests that this phase is elastically stable throughout this pressure range. The calculated phonon spectra of bcc phase suggest that this phase will be unstable lattice dynamically at ambient pressure but it will attain lattice dynamic stability at ∼8 GPa (the pressure around which this phase gets stabilized energetically). Further, from theoretically calculated elastic moduli, we have derived the volume dependent Gruneisen parameter and used this in Lindemann melting rule to determine the pressure effect on the melting point, i.e., the melting curve. The Hugoniot of bismuth has been generated from 0 K isotherm after adding thermal corrections in conjunction with Rankine-Hugoniot relation. The theoretical Hugoniot and melting curve yielded the shock induced melting pressure to be ∼23.1 GPa with corresponding melting temperature of ∼1333 K, in reasonable agreement with the experimental value of 18–28 GPa.

Correction to “Pressure‐volume‐temperature relations in MgO: An ultrahigh pressure‐temperature scale for planetary sciences applications”

[1] In the paper “Pressure‐volume‐temperature relations in MgO: An ultrahigh pressure‐temperature scale for planetary sciences applications” by Zhongqing Wu, Renata M. Wentzcovitch, Koichiro Umemoto, Baosheng Li, Kei Hirose, and Jin‐Cheng Zheng (Journal of Geophysical Research, 113, B06204, doi:10.1029/2007JB005275, 2008), on Figure 4 two theoretical melting curves by Belonoshko and Dubrovinsky [1996] and Strachan et al. [1999] are switched; that is, the dotted line is from Belonoshko and Dubrovinsky [1996] and the heavy dashed line is from Strachan et al. [1999].

Pressure induced phase transition in tin: Ab-initio calculations

First principles total energy calculations as a function of unit cell volume have been performed on α (diamond structure), β (double bct), bct, bcc and hcp structures of tin. The comparison of total energies of these structures at various volumes suggests high pressure structural transitions of α → β → bet → bct at pressures of ~ 0.15 GPa, 2.7 GPa and 28 GPa. Also, 300 K isotherm upto maximum pressures of ~ 400 GPa has been determined for this metal. Using theoretical isotherm, shock Hugoniot of tin has been derived. Further, theoretically evaluated volume dependent Gruneisen parameter in conjunction with Lindeman melting law has been used to determine the pressure dependent melting of tin. The intersection of the theoretical melting curve with theoretically determined temperature rise with shock pressure reveals that this metal will melt at shock pressure of ~ 38 GPa (temperature ~ 1428 K) in good agreement with experimental value of 39 GPa (1550+100 K).

First-principles study of the relations between the elastic constants, phonon dispersion curves, and melting temperatures of bcc Ta at pressures up to1000GPa

The possibility to relate analytically elastic shear modulus to melting temperature in the framework of Lindemann melting criterion is investigated here in the particular case of the body-centered cubic phase of tantalum, which is identified as a problematic case. Equation of state, elastic constants, and full phonon dispersion curves (PDCs) are first gathered for a wide pressure range using density functional theory and its perturbation within the generalized gradient approximation. A global fair agreement is found with previous experimental studies. Anomalies in PDCs tend to disappear with compression. Various equivalent Debye temperatures ${\ensuremath{\theta}}_{\mathrm{D}}(n)$ are then deduced and compared for increasing compression. The initial Debye model for atomic vibration is found to stand well above $120\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. Under this pressure a possibly significant difference up to 10% is found between elastic Debye temperature ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}3)$ and ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}2)$ required in Lindemann melting criterion. As for all the theoretical melting curves proposed in the past, the one found here using ${\ensuremath{\theta}}_{\mathrm{D}}(\ensuremath{-}2,V)$ completely overpasses the melting curve established by static measurements in diamond anvil cells, but agrees well with the shock melting experiment available. This fact is extensively discussed in terms of evolution of PDCs and explaining hypotheses to be tested in the future are proposed.

Evaluation of denaturing gradient gel electrophoresis in the detection of 16S rDNA sequence variation in rhizobia and methanotrophs

The ability of denaturing gradient gel electrophoresis (DGGE) technique to resolve 16S rDNA products generated from two different collections of bacteria using universal 16S primers was investigated. Alignments of 16S rDNA sequences of known species of rhizobia and methanotrophs were performed in order to determine the genetic variations within a 200 bp product obtained with PCR primers which amplify the 16S rRNA encoding genes from Eubacteria. Theoretical DNA melting curves were obtained with the Melt87 program and found to correlate with the ability to resolve fragments by DGGE. In the case of the rhizobia, the inability of DGGE analysis to resolve the PCR products from closely related species was in accordance with the low polymorphism observed amongst the sequences in the amplified area. In the case of the methanotrophs, the PCR products were surprisingly difficult to resolve given the high degree of sequence polymorphism of the amplified area in some distantly related species. The difference in sequence divergence within the two groups members allowed therefore to scale the resolution ability of the DGGE technique.

The melting curve of iron at the pressures of the Earth's core from ab initio calculations

The solid inner core of the Earth and the liquid outer core consist mainly of iron1 so that knowledge of the high-pressure thermodynamic properties of iron is important for understanding the Earth's deep interior. An accurate knowledge of the melting properties of iron is particularly important, as the temperature distribution in the core is relatively uncertain2,3,4 and a reliable estimate of the melting temperature of iron at the pressure of the inner-core boundary would put a much-needed constraint on core temperatures. Here we used ab initio methods to compute the free energies of both solid and liquid iron, and we argue that the resulting theoretical melting curve competes in accuracy with those obtained from high-pressure experiments. Our results give a melting temperature of iron of ∼6,700 ± 600 K at the pressure of the inner-core boundary, consistent with some of the experimental measurements. Our entirely ab initio methods should also be applicable to many other materials and problems.

Evaluation of denaturing gradient gel electrophoresis in the detection of 16S rDNA sequence variation in rhizobia and methanotrophs

The ability of denaturing gradient gel electrophoresis (DGGE) technique to resolve 16S rDNA products generated from two different collections of bacteria using universal 16S primers was investigated. Alignments of 16S rDNA sequences of known species of rhizobia and methanotrophs were performed in order to determine the genetic variations within a 200 bp product obtained with PCR primers which amplify the 16S rRNA encoding genes from Eubacteria. Theoretical DNA melting curves were obtained with the Melt87 program and found to correlate with the ability to resolve fragments by DGGE. In the case of the rhizobia, the inability of DGGE analysis to resolve the PCR products from closely related species was in accordance with the low polymorphism observed amongst the sequences in the amplified area. In the case of the methanotrophs, the PCR products were surprisingly difficult to resolve given the high degree of sequence polymorphism of the amplified area in some distantly related species. The difference in sequence divergence within the two groups members allowed therefore to scale the resolution ability of the DGGE technique.

Comparison of Experimental with Theoretical Melting of the Yeast Genome and Individual Yeast Chromosome Denaturation Mapping Using the Program Meltsim

AbstractThe yeast S. cereviseae represents the first eukaryotic organism whose genome has been entirely sequenced as a result of the Human Genome Project(1). In this report we demonstrate the good agreement between an experimental high resolution melting curve of total nuclear S. cereviseae DNA and the theoretical melting calculated for the complete yeast DNA genome (12,067,277 bp: Saccharomyces Genome Database) by the statistical thermodynamics program MELTSIM, parameterized for long DNA sequences(2,3). The experimental and theoretical melting curves are both fairly symmetrical and possess nearly identical Tmvalues. Calculated melting of coding and flanking DNA regions indicates that flanking DNAs are more (A+T)-rich than coding sequences and account for the earliest melting DNA. Calculated melting curves of the 16 individual yeast chromosomes are very similar and with few exceptions exhibit symmetric melting curves. MELTSIM was also used to calculate a theoretical denaturation map of Chromosome III DNA. The agreement between MELTSIM calculated and experimental melting data demonstrates our ability to accurately simulate long DNA sequence melting in complex eukaryotic genomes, whose sequences are becoming increasingly available for study in public databases. This has important consequences for the understanding of sequence dependent energetic properties of DNA in their biological sequence context and also for their potential use in biomaterials applications.

Thermal transition of plasmid pBR322 closed circular, open circular and linear DNAs

Thermal transitions of pBR322 closed circular (cc), open circular (oc) and linear (l) DNAs have been measured by calorimetry. Six or eight peaks were observed for l and oc DNAs in 0.1 × SSC and 1 × SSC buffer solutions in the temperature ranges 67–84°C and 82–97°C, respectively, while ccDNA showed one broad peak at 103°C. Thermal reversibility was excellent for 1DNA and good for ocDNA but the DSC curve of ccDNA at the consequent second heating was quite different from that of the first run. The morphological changes induced by heating cc and ocDNAs have been examined by electrophoresis of the preheated samples. ccDNA which was heated above 75°C was found to be converted partly to ocDNA, the amount of ocDNA increasing with increasing temperature. The DSC curve of lDNA in 0.1 × SSC has been deconvoluted to a 24-state transition, and thermodynamic functions for the multistep transitions have been estimated; the results are discussed in comparison with its theoretical melting curve and its genetic map.

Polymer melting: heating rate effects on DSC melting peaks

The effect of heating rate on DSC peak shape has been investigated using Gray's model. Theoretical DSC melting curves for small samples with sharp transition temperatures were created and compared with DSC melting curves from pure indium samples. Good agreement was found between theoretical curves and experimental indium DSC peaks. As heating rate increases, there is an increase in both peak height and the time necessary for the sample to catch up with the programmed temperature. For pure indium samples the slope of the leading edge of the first half-peak shows no variation with increase in heating rate when plotted versus temperature. With increasing heating rate the melting peak appears narrower when heat flow is plotted versus time, and broader when plotted against temperature. Peak height dependence on heating rate was found to be somewhat more noticeable at lower heating rates than at higher rates. However, samples formed from a mixture of polyethylene (PE) and indium powder had melting curves that are quite different from those of pure indium. Significant variation in the slope of the first half-peak with heating rate results from changes in thermal resistance from sample surface to the interior. This information helps develop our understanding of, and aids in interpreting, ordinary DSC results.

High-pressure melting temperatures of uranium: Laser-heating experiments and theoretical calculations.

The melting temperatures of uranium have been measured to 45 GPa with an inert Ar pressure medium in a diamond-anvil cell using a spatially resolved laser-heating system. The temperature was measured within 1.4 \ensuremath{\mu}m at the center of laser-heating spot using reflecting optics, and the melting was visually observed as the material flows forming a microchannel and/or by a shape change in the edge of the sample. Theoretically, the melting curve has also been calculated to 100 GPa via \ensuremath{\gamma}(bcc) solid and liquid free energies derived from generalized pseudopotential theory. The calculated melting temperatures agree well with the experimental measurements. It is also found that the theoretical melting curve obeys a Lindemann scaling law for solid densities up to about 25.5 g/${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, corresponding to 100 GPa in pressure.

Theoretical Melting Curves of Alkali Halides

Abstract An analysis of the melting curves of alkali halides is given. The study is based on the Improved Unsymmetrized Self-Consistent Field Method (IUSCFM) for strongly anharmonic crystals with complex lattice and the energy, entropy and Ross’s criterions in calculating the melting curves of alkali halides. The anharmonicities up to sixth order have been taken into consideration. The energy criterion was proven to be the most correct one along the melting curves of the high pressure modification (CsCl structure) while the entropy and Ross's criterions lead to a little better agreement with experiment than the energy criterion when dealing with rocksalt structure. Calculations of the melting curves of KCl and CsCl are compared with the experimental results.

Helix–Coil transition of plasmid dna by adiabatic differential scanning microcalorimetry

AbstractAdiabatic differential scanning microcalorimetry, which provides curves of the heat capacity vs temperature, was carried out for the DNA of plasmid pJL3‐TB5 (5277 base pairs in length). The calorimetry curve shows nine peaks ranging from 81 to 96°C in 1 × SSC buffer at a heating rate of 0.25°C, due to the stepwise helix–coil transition of the DNA along the molecular chain. The theoretical melting curve, which can be constructed by calculation from the entire nucleotide sequence of the plasmid DNA by the helix–coil transition theory, is then compared with the calorimetry curve. The two curves resemble each other remarkably well, particularly when a parameter for the methylated adenine residues at GATC sites by Dam methylase is used appropriately. This allows us to assign each peak in the calorimetry curve to the melting of the respective regions of the plasmid DNA sequence. The local stability of the helix–coil transition along the DNA chain is closely related to the functional regions coded by pJL3‐TB5, such as genes, transcriptional promoters, and particular sites generated by recombination of two different sequences in vivo and in vitro.

Comparative analysis of purity determination methods using a differential scanning calorimeter

Comparative analysis of several methods for purity determination using DSC is presented. This is based on a mathematical model including the construction of theoretical melting curves for two-component systems and the calculation of recorded melting curves with the help of a set of equations describing the formation of a DSC output signal. It is shown that the true accuracy of purity determinations in the range of impurity concentrations ¯x=0.005–0.02 does not exceed 30–50%.

Electron microscopy of the melting of sequenced DNA.

AbstractDifferential melting curves (DMCs) of DNAs pA03 and pBR322 in solutions of different ionic strength (0.02 and 0.2M Na+) were obtained. A previously developed procedure of glyxal fixation of partially denatured DNA molecules at temperatures within the melting range was used to construct electron‐microscopic melting maps for pBR322 and pAO3 plasmid DNA and for the replicative form of bacteriophage ϕX174 DNA, allowing the melting of these DNA molecules to be followed in solutions of low (0.1 × SSC) and high (1 × SSC) ionic strength. In spite of the fact that the melting was at nonequilibrium at the low ionic strength, the melting maps for the two kinds of solutions practically coincided. Experimental data are compared with theoretical calculations based on the Fixman‐Freire algorithm. The conclusion is that the melting pattern of these DNAs is, on the whole, correctly described by the theory, although there are appreciable differences between the theoretical and experimental differential melting curves. We have also determined the relation between the melting temperature of a region and its GC content, with allowances made for the boundary conditions of melting in 0.1 × SSC and 1 × SSC solutions, and have analyzed the theoretical shape of peaks of the DMCs.