Thermodynamic and Experimental Study of the Mg-Sn-Ag-In Quaternary System

Phase equilibria in the Mg-rich region of the Mg-Sn-Ag ternary system were determined by quenching experiments, differential scanning calorimetry, electron probe micro-analysis, and X-ray diffraction techniques. No ternary compounds were found in the studied isothermal sections. A critical evaluation of the available experimental data and a thermodynamic optimization of the Mg-Sn-Ag-In quaternary system were carried out using the calculation of phase diagrams method. The modified quasichemical model in the pair approximation was used for the liquid solution, which exhibits a high degree of short-range order. The solid phases were modeled with the compound energy formalism. All available and reliable experimental data were reproduced within experimental error limits. A self-consistent thermodynamic database was constructed for the Mg-Sn-Ag-In quaternary system, which can be used as a guide for Mg-based alloys development.     

On the Quaternary System Ti-Fe-Ni-Al

The homogeneity ranges of the Laves phases and phase relations concerning the Laves phases in the quaternary system Ti-Fe-Ni-Al at 900 °C were defined by x-ray powder diffraction (XPD) data and electron probe microanalysis (EPMA). Although at higher temperatures the Laves phase forms a continuous solid solution, two separate homogeneity fields of TiFe₂-based (denoted by λ_Fe) and Ti(TiNiAl)₂-based (denoted by λ_Ni) Laves phases appear at 900 °C. The relative locations of Laves phases, G phase, Heusler phase, and CsCl-type phase as well as the associated tie-tetrahedra were experimentally established in the quaternary for 900 °C and presented in three-dimensional (3D) view. Furthermore, a partial isothermal section TiFe₂-TiAl₂-TiNi₂ was constructed, and a connectivity scheme, derived for equilibria involving Laves phases in the Ti-Fe-Ni-Al quaternary system at 900 °C was derived. As a characteristic feature of the quaternary phase diagram, the solid solubility of fourth elements in both the TiFe₂-based and Ti(NiAl)₂-based Laves phases is limited at 900 °C and is dependent on the ternary Laves phase composition. A maximum solubility of about 8 at.% Ni is reached for composition Ti_33.3Fe_33.3Al_33.4. Structural details have been evaluated from powder x-ray and neutron diffraction data for (i) the Ti-Fe-Ni ternary and the Ti-Fe-Ni-Al quaternary Laves phases (MgZn₂-type, space group: P6₃/mmc) and (ii) the quaternary G phase. Atom site occupation behavior for all phases from the quaternary system corresponds to that of the ternary systems. For the quaternary Laves phase, Ti occupies the 4f site and additional Ti (for compositions higher than 33.3 at.%Ti) preferably enters the 6h site. Aluminum and (Fe,Ni) share the 6h and the 2a sites. The compositional dependence of unit cell dimensions, atomic coordinates, and interatomic distances for the Laves phases from the quaternary system is discussed. For the quaternary cubic G phase, a centrosymmetric as well as a noncentrosymmetric variety was observed depending on the composition: from combined x-ray and neutron powder diffraction measurements Ti_33.33Fe_13.33Ni_10.67Al_42.67 was found to adopt the lower symmetry with space group .     

Mg-Zn-Al三元系富镁角335°C等温截面(英文)

采用平衡合金法,利用X射线衍射、扫描电镜及能谱分析,系统地研究了Mg-Zn-Al三元系富镁角335°C的平衡相组成及其成分。从实验上证实,α-Mg固溶体并不与Mg32(Al,Zn)49(τ)三元金属间化合物或q准晶相平衡,而仅与一个三元化合物Al5Mg11Zn4(φ)相平衡。获得了φ相在335°C的整个成分范围,即:52.5%~56.4%Mg、13.6%~24.0%Al、19.6%~33.9%Zn(摩尔分数)。Al在Mg Zn相中的固溶度远大于在Mg7Zn3相中的固溶度,其最大值可达8.6%Al(摩尔分数)。Al和Zn可以同时固溶在α-Mg固溶体中。     

Al-Fe-Si、Al-Mn-Si与Al-Fe-Mn-Si体系热力学描述的更新

采用Calphad方法对Al-Fe-Mn-Si四元系及其子体系进行热力学评估。首先，通过考虑文献中最新的实验研究结果以及对部分三元化合物应用新的热力学模型，修正Al-Fe-Si三系的热力学描述，显著地改善了整个成分范围内、尤其是富Al角的液相面投影图。随后，对三元化合物a-AlMnSi和β-AlMnSi采用新的模型，精修Al-Mn-Si体系富Al角的热力学描述。然后，通过模拟a-AlMnSi相在Al-Fe-Mn-Si体系中的固溶度，优化Al-Fe-Mn-Si四元系富Al角的热力学描述。在优化时，对a-AlMnSi作特殊考虑并加入限制条件，以确保其不会在Al-Fe-Si三元系中变得稳定。最后，将所获得的热力学描述加入TCAL数据库，通过一系列的相平衡计算与凝固模拟、以及与商业铝合金的实验数据的比较，对所获得的热力学描述进行全面的验证。更新后的TCAL数据库能够可靠地预测Al-Fe-Si基与Al-Fe-Mn-Si基合金中的相形成。     

Phase Relations in the System CaO-Fe2O3-Y2O3 at 1273?K and Compatibility Between Y1?xCaxFeO3?0.5x and Stabilized Zirconia

Phase relations in the system CaO-Fe₂O₃-Y₂O₃ in air (( P_\textO2 P_{{{\text{O}}_{2} }} /P°) = 0.21) were explored by equilibrating samples representing eleven compositions in the ternary at 1273 K, followed by quenching to room temperature and phase identification using XRD. Limited mutual solubility was observed between YFeO₃ and Ca₂Fe₂O₅. No quaternary oxide was identified. An isothermal section of the phase diagram at 1273 K was constructed from the results. Five three-phase regions and four extended two-phase regions were observed. The extended two-phase regions arise from the limited solid solutions based on the ternary oxides YFeO₃ and Ca₂Fe₂O₅. Activities of CaO, Fe₂O₃ and Y₂O₃ in the three-phase fields were computed using recently measured thermodynamic data on the ternary oxides. The experimental phase diagram is consistent with thermodynamic data. The computed activities of CaO indicate that compositions of CaO-doped YFeO₃ exhibiting good electrical conductivity are not compatible with zirconia-based electrolytes; CaO will react with ZrO₂ to form CaZrO₃.     

Phase equilibria in Mg-rich corner of Mg–Ca–RE (RE=Gd,Nd) systems at 400 °C

The phase equilibria in Mg-rich corner of Mg–Ca–Gd and Mg–Ca–Nd ternary systems at 400 °C were determined through the equilibrated alloy method by using XRD, SEM, EPMA and DSC. Partial isothermal sections in Mg-rich corner of Mg–Ca–Gd and Mg–Ca–Nd ternary systems at 400 °C were constructed from 13 alloys. A three-phase region of α–Mg, Mg₄₁RE₅ and Mg₂Ca was determined in both ternary systems. It is formed by a similar ternary eutectic reaction L→α-Mg+Mg₂Ca+Mg₄₁RE₅ at 499.6 °C and 505.6 °C, respectively. It is found that the maximum solubility of Ca in Mg₅Gd is 3.68% (molar fraction) and 3% of Gd can be dissolved in Mg₂Ca in the Mg–Ca–Gd system at 400 °C. While in the Mg–Ca–Nd system the maximum solubility of Ca in Mg₄₁Nd₅ is 3.57% and 1.24% of Nd can be dissolved in Mg₂Ca at 400 °C. Other three-phase equilibria existing in Mg-rich corner of Mg–Ca–Gd system are α-Mg+Mg₅Gd+T and Mg₅Gd+Mg₂Ca+T and the three-phase equilibrium in Mg-rich corner of Mg–Ca–Nd system is Mg₃Nd+Mg₂Ca+ Mg₄₁Nd₅.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Investigation of the Mg-Rich Part of the Mg-Dy-Sm Phase Diagram

Constitution of the Mg-rich part of the ternary phase diagram of Mg with two rare-earth metals, Mg-Dy-Sm was experimentally investigated for the first time using optical and scanning electron microscopy (SEM) with electron probe microanalysis (EPMA), x-ray diffraction and differential thermal analysis. In equilibrium with Mg solid solution only two solid phases were found, each of them being the riches by Mg compound in the respective binary systems, Mg₂₄Dy₅ and Mg₄₁Sm₅. Each of these compounds can also dissolve some other rare-earth metal. There is significant combine solubility of Dy and Sm in Mg solid solution, which decreases with lowering temperature. In the studied part of the Mg-Dy-Sm system one invariant four-phase equilibrium of L + (Mg₂₄Dy₅) ? (Mg) + (Mg₄₁Sm₅) exists, which takes place at 535 °C. A number of isothermal partial sections and one temperature-composition section of the Mg-Dy-Sm phase diagram were constructed.     

The Y–Cu–Mg system in the 0–66.7 at.% Cu concentration range: The isothermal section at 400 °C

Synthesis and characterization of about fifty alloys were performed in order to construct the isothermal section of the Y–Cu–Mg ternary system at 400 °C in the 0–66.7 at.% Cu concentration range. Scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDXS) and X-ray powder diffraction (XRPD) techniques were used to examine microstructures, identify phases and define their compositions and crystal structures. Phase equilibria in the investigated compositional region are characterized by the absence of extended ternary solid solutions and by the presence of at least ten ternary phases. Crystal structures of the previously reported Y₂Cu₂Mg, Y₅Cu₅Mg₈, Y₅Cu₅Mg₁₃, Y₅Cu₅Mg₁₆ and YCuMg₄ phases were confirmed. A ternary phase with homogeneity range around the YCu₄Mg stoichiometry was found, crystallizing in the cF24--MgCu₄Sn structure type; at 400 °C this phase coexists with a ternary solid solution based on the binary Laves phase Cu₂Mg, which dissolves about 5 at.% Y. The equiatomic YCuMg phase was also found to exist: from the analysis of X-ray powder patterns it is suggested to crystallize in the hP9--ZrNiAl structure type (a = 0.74449(4) nm, c = 0.39953(2) nm). Two other stoichiometric ternary phases were detected, of approximate compositions Y₂₅Cu₁₈Mg₅₇ and Y₁₃Cu₉Mg₇₈, whose crystal structures are still unknown. In the Mg-rich region, a ternary phase forms characterized by a large homogeneity region.     

TerQuat: Approximate prediction of ternary and quaternary phase diagrams comprising stoichiometric phases

The TerQuat method is an easy-to-use tool for a first prediction of ternary and quaternary phase diagrams. A number of simplifications (only stoichiometric compounds; Δ_fG° can be approximated by the Miedema model, ΔH_Miedema, data) allows the user to get an impression of a ternary or quaternary system with only a minimum of knowledge about the system, namely a list of existing compounds. Stable tie lines are calculated by comparison of the Gibbs energy of reaction of all possible reactions between four phases in the ternary. In the quaternary system, all the competing two- and three-phase equilibria are compared with each other, and a list of stable equilibria is generated. In addition, the intersections of stable two- and three-phase equilibria with a user specified plane in the tetrahedron can be calculated and plotted. This enables a simple generation of a space model for the visualization of the quaternary system. This paper was presented at the International Phase Diagram Prediction Symposium sponsored by the ASM/MSD Thermodynamics and Phase Equilibria Committee at Materials Week, October 21-23,1991, in Cincinnati, Ohio. The symposium was organized by John Morral, University of Connecticut, and Philip Nash, Illinois Institute of Technology.     

Phase equilibria on the ternary Mg–Mn–Ce system at the Mg-rich corner

Three isopleths at the Mg-rich corner of Mg–Mn–Ce ternary system were investigated via thermal analysis, SEM/EPMA and XRD. A ternary eutectic reaction was observed at 1 wt.% Mn and 23 wt.% Ce and 592 °C. A solid-solution type ternary intermetallic compound, (Mg,Mn)₁₂Ce, was observed with 0.5 at% solid solubility of Mn in the tetragonal Mg₁₂Ce. With the aid of thermodynamic modeling and experiments, a revised phase diagram for the binary Mg–Ce system and the isopleths of 0.6, 1.8 and 2.5 wt.% Mn were proposed up to 25 wt.% Ce.     

Phase equilibria of the long-period stacking ordered phase in the Mg–Ni–Y system

Phase equilibria in the Mg-rich Mg–Ni–Y system at 300, 400 and 500 °C have been experimentally investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), differential scanning calorimetry (DSC), electron probe micro-analyzer (EPMA) and transmission electron microscopy (TEM). The results show that a long-period stacking ordered (LPSO) phase with 14H structure is thermodynamically stable in the Mg–Ni–Y system in a wide temperature range, but it dissolves varying from 492 to 559 °C depending on the alloy composition. The equilibrium 14H phase has a very limited solid solution range, and can be nearly regarded as a ternary stoichiometric compound with a formulae as Mg₉₁Ni₄Y₅. The isothermal sections of the Mg-rich Mg–Ni–Y system at 300, 400 and 500 °C have been finally established, and a eutectic reaction, Liquid ↔ α-Mg + 14H + Mg₂Ni, has been determined occurring at 492 °C with a liquid composition about Mg_84.8Ni_12.0Y_3.2.