Isothermal Section Of Phase Diagram Research Articles

Critical Evaluation and Thermodynamic Re-Optimization of the Si-P and Si-Fe-P Systems.

Thermodynamic modeling of the Si-P and Si-Fe-P systems was performed using the CALculation of PHAse Diagram (CALPHAD) method based on critical evaluation of available experimental data in the literature. The liquid and solid solutions were described using the Modified Quasichemical Model accounting for the short-range ordering and Compound Energy Formalism considering the crystallographic structure, respectively. In the present study, the phase boundaries for the liquidus and solid Si phases of the Si-P system were reoptimized. Furthermore, the Gibbs energies of the liquid solution, (Fe)3(P,Si)1, (Fe)2(P,Si)1, and (Fe)1(P,Si)1 solid solutions and FeSi4P4 compound were carefully determined to resolve the discrepancies in previously assessed vertical sections, isothermal sections of phase diagrams, and liquid surface projection of the Si-Fe-P system. These thermodynamic data are of great necessity for a sound description of the entire Si-Fe-P system. The optimized model parameters from the present study can be used to predict any unexplored phase diagrams and thermodynamic properties within the Si-Fe-P alloys.

Phase equilibrium in the system Y-Ni-In at 870 K

Interaction of the components in Y ‑ Ni ‑ In system was investigated by X-ray powder methods and isothermal section of phase diagram was constructed at 870 K in full concentration range. The samples were synthesized in an arc-furnace on a water-cooled Cu-plate under an argon atmosphere and annealed in silica tubes at 870 K for one month. The phase analysis was performed by X-ray powder diffraction method. Twelve ternary compounds, namely YNi 9 In 2 (YNi 9 In 2 -type structure), Y 1-1 . 40 Ni 4 In 1-0 . 60 (MgCu 4 Sn-type structure), YNiIn 2 (MgCuAl 2 -type structure), Y 4 Ni 11 In 20 (U 4 Ni 11 Ga 20 -type structure), YNi 1 . 00-0 . 50 In 1 . 00-1 . 50 (ZrNiAl-type structure), Y 2 Ni 2 In (Mn 2 AlB 2 -type structure), Y 2 Ni 1 . 78 In (Mo 2 FeB 2 -type structure), Y 5 Ni 2 In 4 (Lu 5 Ni 2 In 4 -type structure), Y 11 Ni 4 In 9 (Nd 11 Pd 4 In 9 -type structure), Y 12 Ni 6 In (Sm 12 Ni 6 In-type structure), Y 13.84 Ni 3.19 In 2.97 (Lu 14 Co 3 In 3 -type structure), ~Y 3 Ni 0.05 In 0.95 (AuCu 3 -type structure) exist in the Y ‑ Ni ‑ In system at the temperature of annealing. Compound Y 3 Ni 2.26 In 3.74 exists at higher temperature. The substitution of Ni for In was observed for YNi 1.00-0.50 In 1.00-1.50 and In for Y in the case of Y 1-1,40 Ni 4 In 1-0,60 compound. Besides, yttrium can enter the structure of NiIn (CoSn-type) leading to formation of including-subtraction type solid solution, which is stable for 0 ‑ 8 at. % Y. The composition of this solid solution can be described by the formula Y 0-0 . 16 NiIn 1-0 . 93 . The inclusion of yttrium and indium atoms in position (2 e ) with the simultaneous exclusion of a small amount of indium atoms from position (1 a ) takes place in the homogeneity range of this solid solution. The character of component interaction in the ternary Y ‑ Ni ‑ In system is similar to other related ternary system R ‑ T ‑ In ( R – rare earth of the yttrium subgroup). The common feature of all these systems is the existence of large number isotypical ternary compounds, the formation of homogeneity range for compounds with ZrNiAl and including-subtraction type solid solutions based on the binary compound NiIn. Keywords: yttrium, indium, nickel, phase equilibria, ternary compound, crystal structure.

Topology of subsolidus sections of phase diagrams of quaternary reciprocal systems without solid solutions

A problem of constructing subsolidus isobaric–isothermal sections of phase diagrams of quaternary reciprocal systems with constant-composition compounds and limited solid solutions was considered. Relations between the topological characteristics of such sections were derived. Their topological classification was proposed. An algorithm for constructing sections using the theory of finite graphs was developed. A problem of enumerating sections for diagrams with a given set of classification characteristics was solved.

Analytic Approach to Alloys Thermodynamics: Ternary Cu-Ga-Ni system

In this paper are presented the results of the calculation of thermodynamic properties in liquid state for ternary Cu-Ga-Ni alloys using the newest version of general solution model. Calculation was carried out in temperature interval 1473-2073 K, along 3 cross sections from corner of each metal, with ratios between two other metals 1:3, 1:1 and 3:1. Partial and integral molar thermodynamic properties in liquid phase for the Cu-Ga-Ni ternary system are determined, presented and discussed. Calculated data is compared with data available from literature and good agreement between these two sets of data was observed. Additionally, isothermal section of phase diagram at 298 K is calculated using Thermo-Calc software and presence of eleven different phases is detected. Presented thermodynamic data for the Cu-Ga-Ni alloys could be useful for the further assessment of this system and its phase diagram as well as for completing thermodynamic description of these alloys.

Thermodynamics and characterization of shape memory Cu–Al–Zn alloys

The thermodynamic properties and the microstructure, hardness and electrical conductivity of shape memory alloys (SMAs) belonging to ternary Cu–Al–Zn system were studied by Muggianu model and experiment, respectively. The isothermal section of phase diagram at 293 K was calculated using Thermo-Calc software. Experiments were conducted by X-ray diffraction, light optic microscopy, scanning electron microscopy with energy dispersive X-ray spectrometry, hardness and electrical conductivity measurements. The calculated values of thermodynamic properties indicate that Cu shows good miscibility with Al and Zn in all investigated alloys. The microstructural analysis of samples reveals that the structure consists of large and polygonal grains.

Interpretation and calculation of first-melting projections of phase diagrams

The first-melting projection of the phase diagram of a ternary or higher-order system shows the temperature at which a liquid phase first appears upon heating at any given composition in a system at thermodynamic equilibrium. In most systems, first-melting projections are identical to solidus projections. It is shown that they obey the same well-known topological rules as isothermal sections of phase diagrams. Hence, their interpretation is straightforward. Only in systems with catatectic invariants or retrograde solid solubility do exceptions to these rules occur, and then only over limited composition regions. In these regions the first-melting and solidus projections are not identical. In such cases it is preferable to plot the first-melting projection which is always single-valued at all compositions. A general algorithm for calculating first-melting projections thermodynamically is outlined.

Calculation of Fe–B–V ternary phase diagram

The phase equilibria of the Fe–B–V ternary system are studied experimentally and theoretically in this paper. Phase diagram of the system was modelled by CALPHAD method. Boron was modelled as an interstitial element in the FCC and BCC solid solutions. The calculations of isothermal sections of phase diagram are compared with our experimental results at 903 and 1353K and with available literature experimental data. New ternary phase (with chemical composition 28Fe32V40B in at.%) was found in 67Fe–18B–15V alloy [in at.%]. Further experimental studies for the determination of exact nature of the ternary phase including crystallographic information are necessary.

Interactions in the NdF3-Nd2O3-MF2 (M = Ba, Sr) systems

Isothermal anneals (at 873 K) and powder X-ray diffraction were used to study isothermal sections of phase diagrams of the NdF3-Nd2O3-MF2 (M = Ba, Sr) systems. In studying the NdF3-Nd2O3-BaF2 system, classical solid-phase synthesis was supplemented with mechanochemical activation of feedstock mixtures or BaF2 activated with gaseous hydrogen fluoride was used. In both systems, a solid solution with the fluorite structure based on MF2 and NdOF phases, a solid solution with the tysonite structure based on NdF3, and an ordered fluorite-related phase Ba4Nd3F17 were found. The NdOF-based solid solutions were shown to have polymorphism: βtrig ai αcub at ≈800 K; a new trigonal phase of these solid solutions has been discovered. The effect of a dimensional factor \(\left( {R_{Ba^{2 + } } > R_{Sr^{2 + } } } \right)\) on phase formation and unit cell parameters of the solid solutions was traced.

A ternary linear compound T 2 and its phase equilibrium relationships in Mg–Zn–Nd system at 400 °C

The composition and the crystal structure of the phases in the alloys of Mg–Zn–Nd system at 400 °C have been studied by scanning electron microscopy (SEM), electron probe microanalysis (EPMA), X-ray diffraction (XRD) and selected area electron diffraction (SAED) of transmission electron microscopy (TEM). The phase equilibrium relationships have been identified. As a result, a linear ternary compound T 2 phase has been identified. The general chemical formula of T 2 phase is (Mg, Zn) 11.5Nd and the crystal structure of that is C-centered orthorhombic. As the results, the other three ternary compounds T 1 phase, T 3 phase and T 4 phase have also been identified. The partial isothermal section of phase diagram of Mg–Zn–Nd system at 400 °C has been established.

Phase relationships in the Ho–Mn–Ti ternary system at 773 K

The isothermal section of phase diagram of the Ho–Mn–Ti ternary system at 773 K has been investigated mainly by X-ray powder diffraction analysis with the aid of differential thermal analysis in this work. The existence of eight binary compounds HoMn 2, Ho 6Mn 23, HoMn 12, Mn 5Ti, Mn 2Ti, βMnTi, αMnTi and Mn 15Ti 85 has been confirmed in this system. At 773 K, the maximum solid solubility of Ti in αMn is about 8 at.%Ti. The homogeneity range of Mn 2Ti extends from about 31 at.% to 39 at.% Ti. The maximum solid solubility of Ho in Mn 2Ti phase is about less than 1 at.% Ho. The existence of solid solubility of other phases was not observed. No ternary compounds were found in this ternary system. At 773 K, the isothermal section of phase diagram of Ho–Mn–Ti ternary system consists of 11 single-phase regions, 19 two-phase regions and 9 three-phase regions.

Phase relationships in the Er–Mn–Ti ternary system at 773 K

The Phase relationship in the Er–Mn–Ti ternary system at 773 K has been investigated by X-ray powder diffraction analysis with the aid of differential thermal analysis and optical microanalysis techniques in this work. The existence of eight binary compounds Mn 15Ti 85, αMnTi, βMnTi, Mn 2Ti, Mn 5Ti, ErMn 12, Er 6Mn 23 and ErMn 2 has been confirmed at 773 K in this system. The maximum solid solubility of Ti in Mn is about 8 at%Ti. The homogeneity range of Mn 2Ti extends from about 31 at% to 39 at% Ti. The maximum solid solubility of Er in Mn 2Ti phase is about less than 1 at% Er. No ternary compounds were found in this ternary system at 773K. At 773 K, the isothermal section of phase diagram of Er–Mn–Ti ternary system consists of 11 single-phase regions, 19 two-phase regions and 9 three-phase regions.

The 773 K isothermal section of the ternary phase diagram of the Nd–Ni–Ti

The isothermal section of the phase diagram of the Nd–Ni–Ti ternary system at 773 K has been investigated by X-ray powder diffraction, DTA, optic microscopy and scanning electron microscopy techniques. It consists of 13 single-phase regions, 23 two-phase regions and 11 three-phase regions. At 773 K, the maximum solid solubilities of Ti in Ni, NdNi 5, Nd 2Ni 7, NdNi 3 and NdNi 2 are about 7, 3, 3, 3 and 2 at.% Ti, respectively. The existence of any ternary compounds was not observed.

Yb–Ni–P system

The interaction between the components in the Yb–Ni–P system has been investigated by means of X-ray phase and structure analyses and the isothermal section of phase diagram of the system at 870 K has been constructed. Four earlier known compounds, YbNi 2P 2, Yb 2Ni 12P 7, Yb 6Ni 20P 13 and YbNi 4P 2, and three new phosphides Yb 5Ni 19P 12, ∼YbNi 11P 4 and ∼YbNi 2P have been identified at 870 K. Besides that, single crystals of two new compounds, Yb 9Ni 26P 12 and YbNi 5P 3, have been obtained using the tin flux technique.

873 K Isothermal section of phase diagram for YFeTi ternary system

For Y-Fe-Ti ternary system, a ternary compound, Fe{sub 10.8}Ti{sub 1.2}Y, was observed by Mooij et al. in the alloys with composition Fe{sub 12{minus}x}Ti{sub x}y homogenized and equilibrated at 1123 K for 2--3 weeks. Additionally, a new ternary compound R{sub 3}(Fe,Ti){sub 29} (for R = Sm or Nd) has excited interest of research recently. The present work was also intended to determine whether or not this phase can exist for R = Y at the considered temperature range.