Melting line of nickel monoaluminide

Harmonic cell models (HCMs) are shown to predict the melting line of the Lennard-Jones (LJ) but not the sublimation line. In addition, even for the melting line, the HCMs are found to be physically unrealistic for inverse power potential systems near the hard-sphere limit, and for the Weeks-Chandler-Andersen system at extremely low temperatures. Despite this, the HCM accurately predicts the LJ mean-square displacement (MSD) from molecular-dynamics (MD) simulations along both lines after simple scaling corrections, to include the effects of anharmonicity and correlated dynamics of the atoms, are applied. Single caged atom molecular dynamics and Monte Carlo simulations provide further quantitative characterization of these additional effects, which go beyond harmonicity. The melting indicator and a modification of the cell model in a similar form are shown to be approximately constant along the melting line, which indicates an isomorph. The less well studied LJ sublimation line is shown not to be an isomorph, yet it still can be represented analytically very accurately by the relationship k_{B}T=aρ^{4}+bρ^{2}, where a and b are constants (k_{B} is Boltzmann's constant, T is the temperature, and ρ is the number density). This relationship has been found previously for the melting line, but the two constants have opposite signs for the sublimation and melting lines. This simple formula is also predicted using a nonharmonic static lattice expression for the pressure. The probability distribution function of the melting factor indicates departures from harmonic or Gaussian behavior in the lower wing. Nevertheless, the mean melting factor is shown to follow a simple MSD Debye-Waller factor dependence along both the melting and sublimation lines. This work combining HCM and MD simulations provides a comparison of the melting and sublimation lines of the LJ system, which could provide the foundations for a more unified statistical mechanical description of these two solid boundary lines.

We have measured the phase behavior of a binary mixture of like-charged colloidal spheres with a size ratio of Γ=0.9 and a charge ratio of Λ=0.96 as a function of particle number density n and composition p. Under exhaustively deionized conditions, the aqueous suspension forms solid solutions of body centered cubic structure for all compositions. The freezing and melting lines as a function of composition show opposite behavior and open a wide, spindle shaped coexistence region. Lacking more sophisticated treatments, we model the interaction in our mixtures as an effective one-component pair energy accounting for number weighted effective charge and screening constant. Using this description, we find that within experimental error the location of the experimental melting points meets the range of melting points predicted for monodisperse, one-component Yukawa systems made in several theoretical approaches. We further discuss that a detailed understanding of the exact phase diagram shape including the composition dependent width of the coexistence region will need an extended theoretical treatment.

This study is devoted to the impurity concentration–temperature phase diagram of a substance (A) contain-ing an impurity (B) and featuring a liquid–liquid phasetransition A1 A2, which is manifested by a sharpchange in the short-order structure of the α solutionbased on component A. This transition is caused byvariation of the solution composition or temperatureand results in a phase separation, which is basically dif-ferent from the usual separation of a liquid into the αsolution based on the main component A and a β solu-tion based on impurity B. Intersection of the two-phaseregion of phase separation in a liquid α solution with atwo-phase region of the liquid–solid system leads tonew, previously unknown binary phase diagrams, thetypes of which can be established using thermody-namic analysis.1. INTRODUCTIONThere are many simple substances exhibiting pres-sure-induced first-order phase transitions in the liquidstate at the melting line on the phase diagram. Anexhaustive review of the corresponding experimentaldata can be found in [1]. These transitions are mani-fested by a sharp change in characteristics of the localstructure of the melt, such as the average interatomicdistance and coordination number, and are accompa-nied by anomalous variation of their physical propertiesboth in the pretransition state and immediately on thephase transition line [1–3]. On the temperature–pressure plane of thermody-namic variables, the first-order phase transition linebegins at the triple point on the melting line (featuringthe coexistence of the two types of liquids and the crys-tal) and is usually terminated by the point of the sec-ond-order phase transition, which was predicted as the“structural boiling” point by Katayama et al. [4]. Thisphase transition line can also be terminated at the pointof intersection with the line of liquid–gas phase transi-tion or with the line of another liquid–liquid phase tran-sition that originates either at the melting line (as, e.g.,in bismuth) or at the liquid–gas equilibrium line [5]. Inthe latter case, the phase diagram exhibits a triple pointin the region of liquid states.In order to describe the phase diagrams of pure sub-stances on the pressure–temperature plane, with contin-uation of the phase transition line to the region of liquidstates and termination at the “structural boiling” point,we have developed a model that was described in [6–9].There is a natural question as to how the structuraltransformation in a pure melt will be influenced by anadditional thermodynamic factor—the presence of asecond component (impurity) in the system—that is, bythe passage to the binary system. The aim of this studywas to elucidate this question.2. A TWO-PHASE REGION ON THE CONCENTRATION–TEMPERATURE DIAGRAMLet us consider a phase transition in a liquid solutionrepresenting a melt of the main component A. Consid-ering the concentration of impurity B as a preset exter-nal parameter and assuming that it is not redistributedbetween phases, we would obtain a line on the temper-ature–concentration diagram (similar to that on thepressure–temperature diagram), which terminates atthe “structural boiling” point ( T

We propose a general approach for determining the entropy and free energy of complex systems as a function of temperature and pressure. In this method the Fourier transform of the velocity autocorrelation function, obtained from a short (20 ps) molecular dynamics trajectory is used to obtain the vibrational density of states (DoS) which is then used to calculate the thermodynamic properties by applying quantum statistics assuming each mode is a harmonic oscillator. This approach is quite accurate for solids, but leads to significant errors for liquids where the DoS at zero frequency, S(0), remains finite. We show that this problem can be resolved for liquids by using a two phase model consisting of a solid phase for which the DoS goes to zero smoothly at zero frequency, as in a Debye solid; and a gas phase (highly fluidic), described as a gas of hard spheres. The gas phase component has a DoS that decreases monotonically from S(0) and can be characterized with two parameters: S(0) and 3Ng, the total number of gas phase modes [3Ng→0 for a solid and 3Ng→3(N−1) for temperatures and pressures for which the system is a gas]. To validate this two phase model for the thermodynamics of liquids, we applied it to pure Lennard-Jones systems for a range of reduced temperatures from 0.9 to 1.8 and reduced densities from 0.05 to 1.10. These conditions cover the gas, liquid, crystal, metastable, and unstable states in the phase diagram. Our results compare quite well with accurate Monte Carlo calculations of the phase diagram for classical Lennard-Jones particles throughout the entire phase diagram. Thus the two-phase thermodynamics approach provides an efficient means for extracting thermodynamic properties of liquids (and gases and solids).

Using computer simulations we study the phase behaviour of hard spheres with repulsiveYukawa interactions and with the repulsion set to zero at distances larger than adensity-dependent cut-off distance. Earlier studies based on experiments and computersimulations in colloidal suspensions have shown that the effective colloid–colloid pairinteraction that takes into account many-body effects resembles closely this truncatedYukawa potential. We present a phase diagram for the truncated Yukawa system bycombining Helmholtz free energy calculations and the Kofke integration method. Comparedto the non-truncated Yukawa system we observe (i) a radical reduction of the stability ofthe body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the facecentred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly anyshift of the (FCC) melting line when compared with the (BCC) melting line forthe full Yukawa potential for sufficiently high salt concentrations, i.e. truncationof the potential does not affect the location of the solid–fluid line but replacesonly the BCC phase with the FCC at the melting line. We compare our resultswith earlier results on the truncated Yukawa potential and with results fromsimulations where the full many-body Poisson–Boltzmann problem is solved.

Our understanding of the three basic states of matter (solids, liquids, and gases) is based on temperature and pressure phase diagrams with three phase transition lines: solid-gas, liquid-gas, and solid-liquid lines. There are analytical expressions P(T) for the first two lines derived on a purely general-theoretical thermodynamic basis. In contrast, there exists no similar function for the third, melting, line (ML). Here, we develop a general two-phase theory of MLs and their analytical form. This theory predicts the parabolic form of the MLs for normal melting, relates the MLs to thermal and elastic properties of liquid and solid phases, and quantitatively agrees with experimental MLs in different system types. We show that the parameters of the ML parabola are governed by fundamental physical constants. In this sense, parabolic MLs possess universality across different systems.

Natural lipids with nutritional or therapeutic benefits that also provide desired texture, melting and organoleptic appeal (mouthfeel, skin feel) are difficult to procure for the food and cosmetics industries. Natural Astrocaryum pulp oil (AVP) and kernel fat (AVK) from Guyana were blended without further modification to study the potential of extending the physical functionality of the blends beyond that of crude AVK and AVP. An evaluation of non-lipid components by ESI-MS indicated twenty-four (24) bioactive molecules, mainly carotenoids (90%), polyphenols (9%) and sterols (1%) in AVP, indicating important health and therapeutic benefits. Only trace-to-negligible amounts of these compounds were detected in AVK. The thermal transition phase behavior, solid fat content (SFC), microstructure and textural properties of five AVP/AVL blends were used to construct phase diagrams of the AVK/AVP binary system. Binary phase diagrams constructed from the cooling and heating DSC thermograms of the mixtures and description of the liquidus line indicated a mixing behavior close to ideal with a tendency for order, with no phase separation. Melting onsets, solid fat content and measurements of solid-like texture all predictively increased with increasing AVK content. The descriptive decay parameters obtained for SFC, crystal size, hardness, firmness and spreadability were similar and predictive and indicate the way the binary system structure approaches that of a liquid or a functional solid. The bioactive content of the blends was accurately calculated; the work provides a blueprint for the blending of AVP and AVK to deliver targeted bioactive content, stability, spreadability, texture, melting profile, organoleptic appeal and solid content. SFCs at 20 °C ranged from 9.1% to 39.1%, melting onset from −17.5 °C to 27.8 °C, hardness from 0.1 N to 3.5 N and spreadability from 3.3 N·s to 147.1 N·s; indicating a useful dynamic range of physical properties suitable for bioactive oils to bioactive butters.

It is generally assumed that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models have also suggested that compressed hydrogen may form an unusual two-component (protons and electrons) metallic fluid at low temperature, or possibly even a zero-temperature liquid ground state. The existence of these new states of matter is conditional on the presence of a maximum in the melting temperature versus pressure curve (the 'melt line'). Previous measurements of the hydrogen melt line up to pressures of 44 GPa have led to controversial conclusions regarding the existence of this maximum. Here we report ab initio calculations that establish the melt line up to 200 GPa. We predict that subtle changes in the intermolecular interactions lead to a decline of the melt line above 90 GPa. The implication is that as solid molecular hydrogen is compressed, it transforms into a low-temperature quantum fluid before becoming a monatomic crystal. The emerging low-temperature phase diagram of hydrogen and its isotopes bears analogies with the familiar phases of 3He and 4He (the only known zero-temperature liquids), but the long-range Coulomb interactions and the large component mass ratio present in hydrogen would result in dramatically different properties.

Context: Drug dispersed in a polymer can improve bioavailability; dispersed amorphous drug undergoes recrystallization. Solid solutions eliminate amorphous regions, but require a measure of the solubility.Objective: Use the Flory–Huggins Theory to predict crystalline drugs solubility in the triblock, graft copolymer Soluplus® to provide a solid solution.Materials and methods: Physical mixtures of the two drugs with similar melting points but different glass forming ability, sulfamethoxazole and nifedipine, were prepared with Soluplus® using a quick technique. Drug melting point depression (MPD) was measured using differential scanning calorimetry. The Flory–Huggins Theory allowed: (1) interaction parameter, χ, calculation using MPD data to provide a measure of drug–polymer interaction strength and (2) estimation of the free energy of mixing. A phase diagram was constructed with the MPD data and glass transition temperature (Tg) curves.Results: The interaction parameters with Soluplus® and the free energy of mixing were estimated. Drug solubility was calculated by the intersection of solubility equations and that of MPD and Tg curves in the phase diagram.Discussion: Negative interaction parameters indicated strong drug–polymer interactions. The phase diagram and solubility equations provided comparable solubility estimates for each drug in Soluplus®. Results using the onset of melting rather than the end of melting support the use of the onset of melting.Conclusion: The Flory–Huggins Theory indicates that Soluplus® interacts effectively with each drug, making solid solution formation feasible. The predicted solubility of the drugs in Soluplus® compared favorably across the methods and supports the use of the onset of melting.

<p>Carbonates appear to be one group of the main carbon-bearing minerals in the Earth’s interior. Inclusions of carbonates in diamonds of lower mantle origin support the assumption that they are present even in the Earth’s lower mantle. Although the carbonates’ phase diagrams have been intensively studied, their stability in presence of mantle silicates at deep mantle conditions (>25 GPa) remains unclear. Furthermore, the carbonate inclusions show a high REE enrichment. This raises questions on the distribution of trace elements between carbonates and silicates and on the possible role of carbonates as trace element carrier in the Earth’s mantle.</p><p>Numerous studies show that magnesite is likely to be the major solid carbonate carried by subduction into the Earth’s lower mantle. We investigated the stability of MgCO<sub>3</sub> in presence of mantle silicates and the Fe, Sr and La partitioning in high-pressure and high-temperature experiments. One set of experiments was conducted with multi-anvil presses at BGI, Bayreuth, at conditions ranging from 24 GPa to 30 GPa and 2000 K. The investigated reaction is between natural magnesite and (Mg,Fe)SiO<sub>3</sub>-glasses doped with either Sr or La. Preliminary data from the multi-anvil press at 24 GPa and 2000K show the onset of carbonate melting which is consistent with the previous study of the melting curve in the enstatite-magnesite system [1]. Decomposition of MgCO<sub>3</sub> is not observed, in contrast to experiments using magnesite and SiO<sub>2</sub> as starting materials [2], suggesting that MgCO<sub>3</sub> is stable at these conditions in the presence of silicates phases. The silicate glass react to bridgmanite (Mg,Fe)SiO<sub>3</sub> as well as stishovite SiO<sub>2</sub> and magnesiowüstite (Mg,Fe)O. The Fe-Mg partitioning coefficient between bridgmanite and magnesite calculated in this study is ~2 and in agreement with previous experiments at similar conditions [3].<br>Laser-heated diamond anvil cell (LH-DAC) experiments were performed at University of Potsdam [4] at conditions 30 to 40 GPa and 1800 to 2300 K. The run products were characterized in-situ at high-pressure by XRD and XRF mapping at the P02.2 beamline at PETRA III. Our data show a transformation of the starting silicate glass into bridgmanite. We also observed stishovite and magnesiowüstite in the center of the hotspot where the temperature had reached >2000 K. In this case, the presence of magnesiowüstite might be the result of MgCO<sub>3 </sub>decomposition at higher temperature. Additional TEM analyses on the post-mortem sample will allow us to further characterize the different phases present in the laser-heated hotspot.</p><p>[1] Thompson et al. (2014) Chemistry and mineralogy of the earth’s mantle. Experimental determination of melting in the systems enstatite-magnesite and magnesite-calcite from 15 to 80 GPa. American Mineralogist 99(8-9), 1544-1554.<br>[2] Drewitt et al. (2019) The fate of carbonate in oceanic crust subducted into Earth’s lower mantle. EPSL 511, 213-222<br>[3] Martinez, et al. (1998). Experimental investigation of silicate-carbonate system at high pressure and high temperature. Journal of Geophysical Research: Solid Earth, 103(B3), 5143-5163.<br>[4] Spiekermann et al. (2020). A portable on-axis laser heating system for near-90° X-ray spectroscopy: Application to ferropericlase and iron silicide. Journal of Synchrotron Radiation. (accepted)</p>

We investigate the existence of a [ital T]=0 quantum melting transition in the vortex system of a type-II superconductor. We find that homogeneous high-resistance thin films are good candidates for the observation of this effect. We calculate both the continuous dislocation-mediated melting line [ital B][sub [ital m]][sup [ital d]]([ital T]) as well as the first-order melting line [ital B][sub [ital m]][sup [ital G]]([ital T]) driven by Gaussian fluctuations and present the resulting [ital H]-[ital T] phase diagram. At low temperatures the melting line [ital B][sub [ital m]][sup [ital G]] extrapolates to a value below the upper critical field, resulting in a quantum liquid state in the region [ital B][sub [ital m]][sup [ital G]][lt][ital B][lt][ital H][sub [ital c]2].

A temperature-size (T-N) phase diagram is derived for Na clusters of up to N\ensuremath{\sim}1000 atoms. It is based on first-order pseudopotential calculations and the Lindemann criterion for melting. It contains three regions of stability: (1) a liquid (jellium) phase at temperatures above the melting line ${\mathit{T}}_{\mathit{M}}$(N); (2) a phase related to the body-centered-cubic structure at temperatures below the melting line; and (3) a close-packed structure at very low temperatures and sufficiently large N. The melting line drops to ${\mathit{T}}_{\mathit{M}}$(N)=0 for N65. The phase diagram reduces asymptotically to the known phases of Na as N\ensuremath{\rightarrow}\ensuremath{\infty}, including the known martensitic transformation at T\ensuremath{\approxeq}5 K.

The first part of this thesis presents a first-order pseudopotential calculation at T=O of the total energy of small sodium clusters of size N<800. The calculation is based on a local-pseudopotential scheme and local-density correlation and exchange. A temperature-size (T-N) phase-diagram is then derived using the T=O results and Lindemann's criterion for melting. The phase-diagram contains three regions of stability: (1) a liquid (jellium) phase at temperatures above the melting line T{sub M}(N) where cluster-stability occurs at electronic magic numbers: (2) a phase related to complete geometrical shells of body-centered-cubic structure at temperatures below the melting line; and (3) a close-packed structure at very low temperatures and sufficiently large N. The melting line drops to T{sub M}(N)=O for N<65, where electronic magic numbers are stable even at T=O. The phase diagram reduces asymptotically to the known phases of sodium as N{yields}{infinity}, including the known martensitic transformation at T{approximately}5 K. The second and the last part of this thesis consists of a study of small-cluster many-body systems by means of an on-site local'' chemical potential which allows the continuous variation of local electron-density. This method yields a criterion to distinguish particular features of a small cluster that are likely to survive in the large-N thermodynamic limit from those discontinuities that arise only from finite-size effects.

The first part of this thesis presents a first-order pseudopotential calculation at T=O of the total energy of small sodium clusters of size N<800. The calculation is based on a local-pseudopotential scheme and local-density correlation and exchange. A temperature-size (T-N) phase-diagram is then derived using the T=O results and Lindemann`s criterion for melting. The phase-diagram contains three regions of stability: (1) a liquid (jellium) phase at temperatures above the melting line TM(N) where cluster-stability occurs at electronic magic numbers: (2) a phase related to complete geometrical shells of body-centered-cubic structure at temperatures below the melting line; and (3) a close-packed structure at very low temperatures and sufficiently large N. The melting line drops to TM(N)=O for N<65, where electronic magic numbers are stable even at T=O. The phase diagram reduces asymptotically to the known phases of sodium as N→∞, including the known martensitic transformation at T~5 K. The second and the last part of this thesis consists of a study of small-cluster many-body systems by means of an on-site ``local`` chemical potential which allows the continuous variation of local electron-density. This method yields a criterion to distinguish particular features of a small cluster that are likely to survive in the large-N thermodynamic limit from those discontinuities that arise only from finite-size effects.

We present measurements of dc and ac complex resistivities for thick amorphous $(a\ensuremath{-}){\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ films. Both the resistivities and the derived vortex-glass-transition line ${B}_{g}(T)$ exhibit the decreased temperature T dependence below about 0.1 K. We have proved experimentally that this feature is intrinsic, not resulting from the simple heating effects. We have interpreted this as a sign of a crossover from temperature dominated to quantum driven fluctuations. In the limit $\stackrel{\ensuremath{\rightarrow}}{T}0,$ the ${B}_{g}(T)$ line is T independent and extrapolates to a field ${B}_{g}(0)$ lower than the upper critical field ${B}_{c2}(0)$ at $T=0,$ indicative of the presence of the quantum-vortex-liquid phase in the region ${B}_{g}(0)&lt;B&lt;{B}_{c2}(0).$ We show that the $T=0$ phase diagram for the thick films is markedly different from that for the thin films, which is mainly attributed to the different strength of quantum fluctuations between three dimensions and two dimensions. Also, we discuss the difference between the shape of the ``melting line'' at low T observed in thick amorphous films and single-crystal layered superconductors.