Iron melting curve with a tricritical point

Solidification as a first order phase transition is described in the Landau theory by the same equation as tricritical phenomena. Here, the solidification or melting temperature against pressure curve is modelled to end at a tricritical point. The model gives the phase transition temperature's dependence on pressure up to the quadratic term with a definite expression for the coefficients. This formula is expected to be generally valid for pure materials having melting curves with dT/dP approaching zero at very high P. Excellent experimental agreement is obtained for iron, the material having the most high pressure data which rather accurately determines the value of the coefficient defining the curvature. The geophysically interesting iron solidification temperatures at the Earth's core pressures are obtained. In addition, the general formulae for entropy change, latent heat and volume contraction in solidification are found and calculated for iron as functions of pressure and temperature.Comment: 17 pages, 6 figure

Melting and Solidification Study of Indium and Bismuth Nanocrystals Using Reflection High-Energy Electron Diffraction

As technology begins to utilize nanocrystals for many chemical, biological, medical, electrical, and optoelectrical applications, there is a growing need for an understanding of their fundamental properties. The study of melting and solidification of nanocrystals is of interest to fundamental understanding of the effect of reduced size and crystal shape on the solid-liquid phase transition. Melting and solidification of as-deposited and recrystallized indium and bismuth nanocrystals were studied using reflection high-energy electron diffraction (RHEED). The nanocrystals were thermally deposited on highly oriented 002-graphite substrate at different deposition temperatures. The growth dynamics of the nanocrystals was studied using in situ RHEED while the morphology and size distributions were studied using ex situ real image technique (atomic force microscopy (AFM) or scanning electron microscopy (SEM)). RHEED observation during deposition showed that 3D nanocrystals of indium are directly formed from the vapor phase within the investigated temperature range, 300 K up to 25 K below the bulk melting point of indium. On the other hand, bismuth condensed in the form of supercooled liquid droplets at temperatures above its maximum supercooling point, 125 K below the bulk melting point of bismuth. Below the maximum supercooling point, bismuth condensed in the solid phase. Post deposition real images showed that the formed nanocrystals have morphologies and size distributions that depend on the deposition temperature, heat treatment, and the amount of the deposited material. As-deposited nanocrystals are found to have different shapes and sizes, while those recrystallized from melt were formed in similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting and solidification of the nanocrystals. Melting started early before the bulk melting point and extended over a temperature range that depends on the size distribution of the nanocrystals. Nanocrystals at the lower part of the distribution melt early at lower temperatures. With the increase in temperature, more nanocrystals completely melt with the thickness of the liquid shell on the remaining crystals continuing to grow. Due to size increase after melting, recrystallized bismuth nanocrystals showed a melting range at temperatures higher than that of as-deposited. However, recrystallized indium nanocrystals showed an end melting point nearly equal to that of-the recrystallized ones except for the 1.5-ML film which showed an end melting point ∼10 K higher than that of as-deposited

Melting and Solidification Study of As-Deposited and Recrystallized Bi Thin Films

Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting and solidification of the crystallites. Melting started at temperatures below the bulk melting point of Bi, T0=544.5 K, and extended over a temperature range that depended on the size distribution of the crystallites. The as-deposited 1.5 ML film started to melt at T0-50 K and melted completely at T0-20 K. For films with higher coverage, the size distribution was observed to spread over a wider range with a larger mean value, resulting in a shift in the melting temperature range towards higher temperatures. Due to the shift in size distribution to higher values upon recrystallization, the recrystallized Bi crystallites showed a melting temperature range higher than that of the as-deposited crystallites. For the investigated conditions, all films were completely melted below or at T 0 of Bi. The characteristic film melting point, defined as the temperature at which the film melting rate with temperature is the fastest, showed a linear dependence on the reciprocal of the average crystallite radius, consistent with theoretical models. Of these models, the surface-phonon instability model best fits the obtained results. During solidification, the Bi films showed high amount of supercooling relative to T0 of Bi. The amount of liquid supercooling was found to decrease linearly with the reciprocal of the average crystallite size. © 2006 American Institute of Physics. [DOI: 10.1063/1.2208551

Structural disjoining potential for grain boundary premelting and grain coalescence from molecular-dynamics simulations

We describe a molecular dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain-coalescence in solidification. The method is applied in a comparative study of (i) a Sigma 9 120 degress twist and (ii) a Sigma 9 {411} symmetric tilt boundary in a classical embedded-atom model of elemental Ni. Although both boundaries feature highly disordered structures near the melting point, the nature of the temperature dependence of the width of the disordered regions in these boundaries is qualitatively different. The former boundary displays behavior consistent with a logarithmically diverging premelted layer thickness as the melting temperature is approached from below, while the latter displays behavior featuring a finite grain-boundary width at the melting point. It is demonstrated that both types of behavior can be quantitatively described within a sharp-interface thermodynamic formalism involving a width-dependent interfacial free energy, referred to as the disjoining potential. The disjoining potential for boundary (i) is calculated to display a monotonic exponential dependence on width, while that of boundary (ii) features a weak attractive minimum. The results of this work are discussed in relation to recent simulation and theoretical studies of the thermodynamic forces underlying grain-boundary premelting.Comment: 24 pages, 8 figures, 1 tabl

Quantum thermodynamics at critical points during melting and solidification processes

We systematically explore and show the existence of finite-temperature continuous quantum phase transition (CTQPT) at a critical point, namely, during solidification or melting such that the first-order thermal phase transition is a special case within CTQPT. Infact, CTQPT is related to chemical reaction where quantum fluctuation (due to wavefunction transformation) is caused by thermal energy and it can occur maximally for temperatures much higher than zero Kelvin. To extract the quantity related to CTQPT, we use the ionization energy theory and the energy-level spacing renormalization group method to derive the energy-level spacing entropy, renormalized Bose-Einstein distribution and the time-dependent specific heat capacity. This work unambiguously shows that the quantum phase transition applies for any finite temperatures.Comment: To be published in Indian Journal of Physics (Kolkata

Effect of degassing addition on the solidification of nickel aluminum bronze

The effect of degassing agent addition on the solidification of Nickel Aluminum Bronze was investigated. The complex relationship between the development of the alloy solidification and its thermal analysis in Nickel Aluminum Bronze was obtained by using data logger. This experiment describes the characterization of thermal analysis in Nickel Aluminum Bronze which was interpret using solidification cooling curve. With this method, the differences of temperature points during solidification were clearly evidenced. The results show a solidification cooling curve directly affected by percentage of degassing agent added in molten Nickel Aluminum Bronze alloy. There is distribution of temperature point after solidification from melting. As for degassing treatment, higher degassing addition on the Nickel Aluminum Bronze decreased the solidification temperature point

Measuring kinetic coefficients by molecular dynamics simulation of zone melting

Molecular dynamics simulations are performed to measure the kinetic coefficient at the solid-liquid interface in pure gold. Results are obtained for the (111), (100) and (110) orientations. Both Au(100) and Au(110) are in reasonable agreement with the law proposed for collision-limited growth. For Au(111), stacking fault domains form, as first reported by Burke, Broughton and Gilmer [J. Chem. Phys. {\bf 89}, 1030 (1988)]. The consequence on the kinetics of this interface is dramatic: the measured kinetic coefficient is three times smaller than that predicted by collision-limited growth. Finally, crystallization and melting are found to be always asymmetrical but here again the effect is much more pronounced for the (111) orientation.Comment: 8 pages, 9 figures (for fig. 8 : [email protected]). Accepted for publication in Phys. Rev.

Analysis of acoustic emission during the melting of embedded indium particles in an aluminum matrix: a study of plastic strain accommodation during phase transformation

Acoustic emission is used here to study melting and solidification of embedded indium particles in the size range of 0.2 to 3 um in diameter and to show that dislocation generation occurs in the aluminum matrix to accommodate a 2.5% volume change. The volume averaged acoustic energy produced by indium particle melting is similar to that reported for bainite formation upon continuous cooling. A mechanism of prismatic loop generation is proposed to accommodate the volume change and an upper limit to the geometrically necessary increase in dislocation density is calculated as 4.1 x 10^9 cm^-2 for the Al-17In alloy. Thermomechanical processing is also used to change the size and distribution of the indium particles within the aluminum matrix. Dislocation generation with accompanied acoustic emission occurs when the melting indium particles are associated with grain boundaries or upon solidification where the solid-liquid interfaces act as free surfaces to facilitate dislocation generation. Acoustic emission is not observed for indium particles that require super heating and exhibit elevated melting temperatures. The acoustic emission work corroborates previously proposed relaxation mechanisms from prior internal friction studies and that the superheat observed for melting of these micron-sized particles is a result of matrix constraint.Comment: Presented at "Atomistic Effects in Migrating Interphase Interfaces - Recent Progress and Future Study" TMS 201