Calculated Melting Curve Research Articles

Molecular dynamics study of melting and fcc-bcc transitions in Xe.

We have investigated the phase diagram of Xe over a wide pressure-temperature range by molecular dynamics. The calculated melting curve is in good agreement with earlier experimental data. At a pressure of around 25 GPa and a temperature of about 2700 K we find a triple fcc-bcc liquid point. The calculated fcc-bcc boundary is in nice agreement with the experimental points, which, however, were interpreted as melting. This finding suggests that the transition from close-packed to bcc structure might be more common at high pressure and high temperature than was previously anticipated.

Numerical prediction of the melting curve of n-octane

We compute the melting curve of n-octane using Molecular Dynamics simulations with a realistic all-atom molecular model. Thermodynamic integration methods are used to calculate the free energy of the system in both the crystalline solid and isotropic liquid phases. The Gibbs–Duhem integration procedure is used to calculate the melting curve, starting with an initial point obtained from the free energy calculations. The calculations yield quantitatively accurate results: in the pressure range of 0–100 MPa, the calculated melting curve deviates by only 3 K from the experimental curve. This deviation falls just within the range of uncertainty of the calculations.

Melting curve for argon calculated from pure theory

The melting curve of argon is determined from non-equilibrium molecular dynamics simulations performed in the NPH ensemble. The interatomic interactions are described by an ab initio pair potential constructed by Woon. Clusters of vacancy defects in the otherwise perfect fcc cyrstal are created prior to the melting simulations in order to provide nucleation sites for melting. The calculated melting curve is in good agreement with experimental measurements, suggesting that many-body and quantum effects are negligible for this property.

High Pressure and High Temperature Equation-of-State of Gamma and Liquid Iron

ABSTRACTShock-wave experiments on pure iron preheated to 1573 K were conducted in the 17–73 GPa range. The shock-wave equation of state of γ-iron at an initial temperature of 1573 K can be fit with us = 4.102 (0.015) km/s + 1.610(0.014) up with ρo = 7.413±0.012 Mg/m3 We obtain for γ-iron's bulk modulus and pressure derivative the values: 124.7±1.1 GPa and 5.44±0.06, respectively.We present new data for sound velocities in the γ- and liquid-phases. In the γ-phase, to a first approximation, the longitudinal sound velocity is linear with respect to density: Vp = −3.13 (0.72) + 1.119(0.084) p(units for Vp and p are km/s and Mg/m3, respectively). Melting was observed in the highest pressure (about 70–73 GPa) experiments at a calculated shock temperature of 2775±160 K. This result is consistent with a previously calculated melting curve (for ε-iron) which is close to those measured by Boehler [1] and Saxena et al. [2]. The liquid iron sound velocity data yields a Grüneisen parameter value of 1.63±0.28 at 9.37±0.02 Mg/m3 at 71.6 GPa. The quantity γρ is 15.2±2.6 Mg/m3, which agrees with the uncertainty bounds of Brown and McQueen [3] (13.3–19.6 Mg/m3). Based on upward pressure and temperature extrapolation of the melting curve of γ-iron, the estimated inner core-outer core boundary temperature is 5500±400 K, the temperature at the core-mantle boundary on the outer core side is 3930±630 K.

First-order melting and dynamics of flux lines in a model for YBa2Cu3O7- delta.

We have studied the statics and dynamics of flux lines in a model for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, using both Monte Carlo simulations and Langevin dynamics. The lines are assumed to be flexible but unbroken in both the solid and liquid states. For a clean system, both approaches yield the same melting curve, which is found to be weakly first order with a heat of fusion of about 0.02${\mathit{k}}_{\mathit{BT}\mathit{m}}$ per vortex pancake at a field of 50 kG. The time-averaged magnetic field distribution experienced by a fixed spin is found to undergo a qualitative change at freezing, in agreement with NMR and muon spin resonance experiments. The calculations yield, not only the field distribution in both phases, but also an estimate of the measurement time needed to distinguish these distributions: We estimate this time as \ensuremath{\ge}0.5 \ensuremath{\mu}sec. The magnetization relaxation time in a clean sample slows dramatically as the temperature approaches the mean-field upper critical field line ${\mathit{H}}_{\mathit{c}2}$(T) from below. Melting in the clean system is accompanied by a proliferation of free disclinations and a simultaneous disappearance of hexatic order. Just below melting, the defects show a clear magnetic-field-dependent two- to three-dimensional crossover from long disclination lines parallel to the c axis at low fields, to two-dimensional ``pancake'' disclinations at higher fields. Strong point pins produce an energy varying logarithmically with time. This lnt dependence results from slow annealing out of disclinations in disordered samples. Even without pins, the model gives subdiffusive motion of individual pancakes in the dense liquid phase, with mean-square displacement proportional to ${\mathit{t}}^{1/2}$ rather than to t as in ordinary diffusion. The calculated melting curve and many dynamical features agree well with experiment. \textcopyright{} 1996 The American Physical Society.

Melting of a self-complementary DNA minicircle: Comparison of optical melting theory with exchange broadening of the nuclear magnetic resonance spectrum

Melting curves are calculated for the 16-base-pair duplex DNA sequence 5′ GTATCCGTACGGATAC 3′ linked on the ends by TTTT single-strand loops. The equilibrium statistical thermodynamic theory of DNA melting is modified to include effects of end-loops on the melting transition. An excellent fit of the experimental melting curve in 0.2 m-NaCl is obtained using two adjustable parameters, one for end-loop formation and the other for formation of the complete 40-base single-strand loop. The best-fit calculated melting curve permits evaluation of these parameters. The free energy to close a TTTT end-loop is 2.12 kcal/mol (1 cal = 4.184 J). A TTTT end-loop or hairpin loop is significantly more stable than an internal loop of comparable size sandwiched between two helical regions, even after allowing for the different stacking contributions. Reasons for this increased stability are presented. The loop free energy of the 40-base single-strand open minicircle is evaluated to be +1.27 kcal/mol, thus favoring the melting of two end-loops into the large open minicircle. The present results are compared with those of others for d(T-A) oligomers. The sequence TTTT forms a more stable end-loop, or hairpin, than TATA by about 2.0 kcal/mol. Theoretical rate constants for the proton-transfer step in the standard hydrogen-exchange model are calculated by extending the theory of diffusion-controlled reactions to take account of the electrostatic potential of the DNA. The predicted ratios of rate constants for different pairs of catalysts exchanging an A · T proton agree satisfactorily with the available experimental data for a 14-base-pair linear duplex, which confirms the diffusion-control of the proton-transfer step. Data presented here for the 16 base-pair duplex of the minicircle are consistent with catalysis-limited exchange in which the proton-transfer step is likewise diffusion-controlled. Under catalysis-limited conditions, the imino proton exchange rates are predicted from the catalytic rate constants, prevailing buffer catalyst concentrations, and the equilibrium constants to form the unstacked open state of optical melting theory. The observed exchange rates of the A · T base-pairs show no sign of the strong predicted end-melting trend, and exceed the predicted values by factors of 10 to 400. Moreover, the succession of “melting” in the nuclear magnetic resonance line-broadening deviates from that predicted by optical melting theory. In particular, the central base-pairs (T · A(8) and A · T(9) are out of order by 25 deg.C. These and other considerations indicate that the solvent-accessible open state of the standard model for imino proton exchange is most probably not identical with the unstacked open state of optical melting theory. Considerations concerning the recently reported exchange in the absence of added catalyst (AAC) indicate that the structures and kinetics of the solvent-accessible open states may differ for A · T base-pairs in certain locales, as well as A · T pairs in different duplex DNAs. AAC exchange is inferred to be much less important for many DNAs, including ours, than for others, and to be much more important in poly[d(A-T)] · poly[d(A-T)].

Melting curve and Grüneisen coefficient for aluminum

The Lindeman law and a model for the volume dependence of the Grüneisen coefficient generalizing previous current theories are used to calculate the melting curve of aluminum at high pressure. In this model, the Grüneisen coefficient depends on a parameter p specific for the investigated material. Agreement between the calculated melting curve and experimental results involves a negative value of p for aluminum. This result confirms previous determinations of p from shock-wave data and also from the pressure dependance of the elastic moduli determined by ultrasonic measurements.