Unary Phases Research Articles

First-principles study on the stability of(R, Zr)(Fe, Co, Ti)12against 2-17 and unary phases(R=Y, Nd, Sm)

The stability of $(R,\phantom{\rule{0.16em}{0ex}}\mathrm{Zr}){(\mathrm{Fe}, \mathrm{Co}, \mathrm{Ti})}_{12}$ with a ${\mathrm{ThMn}}_{12}$ structure is investigated using first-principles calculations. We consider energetic competition with multiple phases that have the ${\mathrm{Th}}_{2}{\mathrm{Zn}}_{17}$ structure and the unary phases of $R$, Zr, Fe, Co, and Ti simultaneously by constructing a quinary energy convex hull. From the analysis, we list the stable phases at zero temperature, and show possible stable and metastable ${\mathrm{ThMn}}_{12}$ phases.

The third generation Calphad description of Al–C including revisions of pure Al and C

New descriptions of pure Al and liquid C were developed and used to describe the Al–C system for the third generation of Calphad databases. The stable phases of the elements are described with a single expression for the entire temperature range. The expression is based on the Einstein model and an important parameter is therefore the Einstein temperature. For the metastable phases, the difference in entropy between stable and metastable phases is used to calculate the Einstein temperature for the metastable allotrope. In this way we avoid breaking the third law of thermodynamics, which would be the consequence if the SGTE lattice stabilities were used. The liquid-amorphous phase for the pure substances and for the binary is described with the two-state model. For the pure substances, we introduce a zero-point entropy that is related to the entropy of melting. The heat capacity of the liquid of the pure substances approaches 3R at high temperatures if the electronic contribution is subtracted. The Al–C system has one stable carbide, Al4C3, which is described with a model equivalent to that used for the solid unary phases but with two Einstein functions. In Al–C, the FCC phase is stable and its metastable end-member, Al1C1, is described with a new model, here called the hybrid model, as it combines the Einstein model (giving the harmonic contribution) and the Neumann–Kopp relationship (adding the additional contributions) to describe the heat capacity. Its Einstein temperature is estimated and its formation energy is obtained from DFT calculations. The total energy of the end-members of the metastable phases BCC(Al1C3) and HCP(Al1C0.5) is calculated with DFT and their Einstein temperatures are estimated using the mass-effect model. The Al–C system was chosen because it is a simple system without magnetism and the results show that the proposed models can reproduce experimental information well. When only one temperature range is used to describe the solid phases, they may be re-stabilized at high temperatures and the recently presented equal-entropy criterion (EEC) is used to exclude solid phases with higher entropy than the liquid.

A fully automated approach to calculate the melting temperature of elemental crystals

The interface method is a well established approach for predicting melting points of materials using interatomic potentials. However, applying the interface method is tedious and involves significant human intervention. The whole procedure involves several successive tasks: estimate a rough melting point, set up the interface structure, run molecular dynamic calculations and analyze the data. Loop calculations are necessary if the predicted melting point is different from the estimated one by more than a certain convergence criterion, or if full melting/solidification occurs. In this case monitoring the solid–liquid phase transition in the interface structure becomes critical. As different initial random seeds for the molecular dynamic simulations within the interface method induce slightly different melting points, a few ten or hundred interface method calculations with different random seeds are necessary for performing a statistical analysis on these melting points. Considering all these technical details, the work load for manually executing and combining the various involved scripts and programs quickly becomes prohibitive. To simplify and automatize the whole procedure, we have implemented the interface method into pyiron (http://pyiron.org). Our fully automatized procedure allows to efficiently and precisely predict melting points of stable unaries represented by arbitrary potentials with only two user-specified parameters (interatomic potential file and element). For metastable or dynamically unstable unary phases, the crystal structure needs to be provided as an additional parameter. We have applied our automatized approach on fcc Al, Ni, dynamically unstable bcc Ti and hcp Mg and employed a large set of available interatomic potentials. Melting points for classical interatomic potentials of these metals have been obtained with a numerical precision well below 1 K.

Solidus Surface of the Mo–Fe–B System

The arc-melted Mo–Fe–B alloys with boron content up to ~41 at.% were studied after annealing at subsolidus temperatures by X-ray diffraction, differential thermal analysis, SEM/EMPA, and Pirani– Altertum technique for measurement of incipient melting temperatures. The partial solidus surface projection was constructed for the first time in the Mo–MoB1.0–FeB~0.8–Fe region using our own experimental and literature data. The Mo2FeB2 ternary compound has a two-phase equilibrium at subsolidus temperatures with each of the binary and unary phases from the constituent binary systems. The Mo2FeB2 phase has a wide homogeneity range for metal content: 14–27 at.% Fe. A three-phase α-MoB + β-MoB + Mo2B region exists close to the Mo–B side of the Gibbs composition triangle. In addition, a three-phase region composed by the Mo2FeB2 ternary compound and two iron modifications is shown to exist: BCC (δ-Fe) and FCC (γ-Fe). Another ternary compound, MoxFe3–xB, with molybdenum content of 1.3–2.0 at.% is present at subsolidus temperatures in two structural modifications: orthorhombic (Fe3C-type structure) and tetragonal (Ti3P-type structure). The intermetallic μ-(Mo6Fe7) phase in the Mo–Fe–B ternary system takes part in the three-phase equilibria on the solidus surface: σ-(MoFe) + μ-(Mo6Fe7) + Mo2FeB2 at 1375 ± ± 10°C, μ-(Mo6Fe7) + Mo2FeB2 + R-(Mo2Fe3) at 1340 ± 10°C, and σ-(MoFe) + μ-(Mo6Fe7) + R-(Mo2Fe3) at 1385 ± 10°C.

Embedded atom method potential for studying mechanical properties of binary Cu–Au alloys

We present an embedded atom method (EAM) potential for the binary Cu–Au system. The unary phases are described by two well-tested unary EAM potentials for Cu and Au. We fitted the interaction between Cu and Au to experimental properties of the binary intermetallic phases Cu3Au, CuAu and CuAu3. Particular attention has been paid to reproducing stacking fault energies in order to obtain a potential suitable for studying deformation in this binary system. The resulting energies, lattice constant, elastic properties and melting points are in good agreement with available experimental data. We use nested sampling to show that our potential reproduces the phase boundaries between intermetallic phases and the disordered face-centered cubic solid solution. We benchmark our potential against four popular Cu–Au EAM parameterizations and density-functional theory calculations.

Liquid-liquid equilibria for soft-repulsive particles: improved equation of state and methodology for representing molecules of different sizes and chemistry in dissipative particle dynamics.

Three developments are presented that significantly expand the applicability of dissipative particle dynamics (DPD) simulations for symmetric and non-symmetric mixtures, where the former contain particles with equal repulsive parameter for self-interactions but a different repulsive parameter for cross-interactions, and the latter contain particles with different repulsive parameters also for the self-interactions. Monte Carlo and molecular dynamics simulations for unary phases covering a wide range of repulsive parameters and of densities for single-bead DPD particles point to deficiencies of the Groot and Warren equation of state (GW-EOS) [J. Chem. Phys. 107, 4423 (1997)]. A revised version, called rGW-EOS, is proposed here that is significantly more accurate over a wider range of parameters/densities. The second development is the generalization of the relationship between the Flory-Huggins χ parameter and the repulsive cross-interaction parameter when the two particles involved have different molecular volumes. The third aspect is an investigation of Gibbs ensemble Monte Carlo simulation protocols, which demonstrates the importance of volume fluctuations and excess volumes of mixing even for equimolar symmetric mixtures of DPD particles. As an illustrative example, the novel DPD methodology is applied to the prediction of the liquid-liquid equilibria for acetic anhydride/(n-hexane or n-octane) binary mixtures.

Experimental study of phase relations in the U–Ti–Al ternary system

The phase relations in the ternary U–Ti–Al system were established for the whole concentration range for two temperatures, 923 K and 1123 K. They were derived from quenched samples annealed at 1123 K for about 500 h and at 923 K for about 720 h using X-ray powder diffraction, scanning electron microscopy and energy dispersive spectroscopic analysis. Only one ternary phase, the Al-rich compound, UTi2Al20, was found. It forms by a peritectic reaction at 1365(5) K, and remains stable at least down to 923 K. Based on single-crystal structure refinements, it was confirmed that it adopts the CeCr2Al20 structure type (cubic, Fm3¯d, n°227) with lattice parameter at room temperature, a = 14.634(1) Å. Unlike most of the isotypic aluminides, UTi2Al20 should be regarded as a line compound. At 1123 K, the isothermal section is characterized by the extended homogeneity ranges due to mutual exchange between U and Ti and between Ti and Al in the unary phases, whereas at 923 K, the mutual solubility between U and Ti was found null. Regarding the binary phases, only in the Laves phase, UAl2 (cubic-C15, MgCu2-type) such solubilities were observed with limits of about 2 at% of U by Ti and 5.5 at% of Al by Ti, at 1123 K. For the other binary compounds, the solubility of the third component was found negligible at both temperatures.

Physico-chemical characterisation of a new polymorph of caffeine

Caffeine is a widely used drug substance. Two polymorphic forms and one hydrate of caffeine are known. Thanks to scanning transitiometry, the curves pressure versus temperature, P = f(T), of the caffeine were plotted. A (temperature, pressure) unary phase diagram was deduced. It confirms the existence of a new polymorph of caffeine at low pressure synthesized by sublimation. Its identification and its physico-chemical properties were determined using a variety of experimental methods: X-ray powder diffraction, differential scanning calorimeter, thermogravimetric analysis, thermally stimulated current and electrochemical impedance.

Low pressure phases

A metastable form of γ-aminobutyric acid has been prepared by sublimation under vacuum. A theoretical unary phase diagram has been deduce from experimental thermal analysis. Aqueous solution of γ-aminobutyric acid (Gaba) prepared from commercial product (monoclinic) does not cross blood–brain barrier after intra peritoneal administration to mice, hence it displays no anticonvulsion activity. Therefore, we developed a polymorphic form, the solution of which presents such activity. In the present paper the preparation and the physico-chemical properties are reported.

A thermodynamic assessment of the Sb–Zn system

The thermodynamic assessment is made for the Sb–Zn system using the CALPHAD approach (calculation of phase diagram). The liquid phase, the intermediate compounds of SbZn, Sb 3Zn 4 (three modifications of ɛ, δ and δ′) and Sb 2Zn 3 (two modifications of η and ξ) and the terminal phases of rhombohedral-Sb and hcp-Zn are taken into consideration in this optimization. Liquid phase is described by a substitutional solution model with Redlich–Kister polynomials. The intermediate compounds are treated as stoichiometric. Two terminal phases are taken as unary phases according to literature. A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties are presented and compared with experimental data obtained from literature.

Contributions of Calorimetry for Cp Determination and of Scanning Transitiometry for the Study of Polymorphism

Importance of temperature-controlled scanning calorimetry for Cp measurements and of scanning transitiometry for simultaneous caloric and pVT analysis in studies of polymorphic systems is demonstrated. Three types of problems of importance in polymorphism of pharmaceutical substances are analyzed: (1) identification of an enantiotropic system with hindered multiphase transitions, with polymorphism in carbamazepine as an example; (2) role of heat capacity determination in understanding homogeneous nucleation, with polymorphism in progesterone as an example; (3) creating a (p,T) unary phase diagram over wide ranges of temperature and pressure, with application to the enantiotropic system of caffeine as an example.

Chemical potential shifts due to capillarity-unary systems

The effect of curvature on the chemical potential for two-phase unary systems at constant temperature, is usually given in the literature by the Gibbs-Thomson equation [1–6], μ β ( H ) = μ β ( H = 0 ) + 2 γ V β H where H is the local mean curvature of a β particle in equilibrium with an α matrix and V β , the molar volume of the β phase. It can be shown, based on the above equation, that the corresponding shift in chemical potential for the α phase is [1]: μ α ( H ) = μ α ( H = 0 ) Thus the usual form of the Gibbs-Thomson equation that appears in the literature is not rigorous and hence results in a violation of the condition for chemical equilibrium for a curved interface ( μ α ≠ μ β(H) ) assuming incompressibility and isotropic stresses in the case of the solid phases [7–9]. A rigorous derivation of the Gibbs-Thomson equation for unary two-phase systems at constant temperature is provided, that gives the correct equation for the chemical potential shift: μ β ( H ) = μ α ( H ) = μ β ( H = 0 ) + 2 γ H [ V α V β / ( V α − V β ) ] While the above equation can be approximated ( V α = G−V β≈V G ) in the case of a condensed-gas ( G) system to give the usual form of the Gibbs-Thomson equation, a similar approximation for a condensed-condensed system can result in a significant error in both the sign and magnitude of the shift. The corrected expression for the chemical potential shift has an inverse dependence on the difference in the molar volumes ( V α−V β ) between the two condensed phases. For solid ( S)-liquid ( L) equilibrium in certain systems the shift may be negative (e.g. V α = L < V β = S for Bi, Si, Ge) or even approach infinity (e.g. V α = L≈V β = S for carbon). A similar dependence is obtained for the pressure shifts in each phase. The present formulation is consistent with the Clausius-Clapeyron equation used to represent unary phase diagrams, which has the same dependence on the relative molar volume.

Studies on the viscosity of solutions of limited miscibility near the phase-separation temperature. Nitrobenzene— n-hexane and nitrobenzene— n-heptane

The viscosity coefficient η of nitrobenzene in n -hexane and n -heptane in the unary phase was measured as a function of concentration and temperature. The temperature range studied was T − T s ⩽ 7.5 K, where T s is the phase separation temperature. For the mixtures studied, the empirical expression for the temperature dependence of the viscosity of critical mixtures given by Debye et al. was verified.

The Derivation of Stable Unary Phase Diagrams Through the Use of Dual Networks

Unary phase diagrams of stable equilibria can be derived with the aid of Dual networks. For each basic form of these phase diagrams there exists a unique Dual network. In addition, the elements of the two are related by a one-to-one correspondence such that areas correspond to points and line intervals to line segments. Systems with up to 7 phases yield 86 different diagrams, all of which are presented here, together with the corresponding Dual networks. Solutions for 8 and 9 phases are tabulated. The results are helpful for deriving metastable diagrams and diagrams for more than one component.

The derivation of stable unary phase diagrams through the use of dual networks

Unary phase diagrams of stable equilibria can be derived with the aid of Dual networks. For each basic form of these phase diagrams there exists a unique Dual network. In addition, the elements of the two are related by a one-to-one correspondence such that areas correspond to points and line intervals to line segments. Systems with up to 7 phases yield 86 different diagrams, all of which are presented here, together with the corresponding Dual networks. Solutions for 8 and 9 phases are tabulated. The results are helpful for deriving metastable diagrams and diagrams for more than one component.