Three-phase Field Research Articles

The melting diagram of the Ti–Dy–Si system in the Ti–Ti 5Si 3–Dy 5Si 3–Dy region

The phase equilibria in the Ti–Ti 5Si 3–Dy 5Si 3–Dy part of the Ti–Dy–Si system were studied by DTA, X-ray diffraction, metallography and EPMA. The melting diagram, isopleths at 5Si, 65Ti and 65Dy, and a reaction scheme were constructed. The solidus surface is characterized by the following three-phase fields: 〈β-Ti〉 + 〈Ti 5Si 3〉 + 〈TiDySi〉, 〈β-Ti〉 + 〈TiDySi〉 + 〈α-Dy〉, 〈TiDySi〉 + 〈α-Dy〉 + 〈Dy 5Si 3〉, and 〈Ti 5Si 3〉 + 〈TiDySi〉 + 〈Dy 5Si 3〉. The first two fields form via U-type equilibria, L + 〈Ti 5Si 3〉 ⇄ 〈β-Ti〉 + 〈TiDySi〉 and L + 〈β-Ti〉 ⇄ 〈TiDySi〉 + 〈α-Dy〉, at 1320 and 1170 °C, respectively. The third three-phase field results from an invariant eutectic four-phase equilibrium, L ⇄ 〈TiDySi〉 + 〈α-Dy〉 + 〈Dy 5Si 3〉, at 1157 ± 6 °C. The fourth one is the result of a P-type equilibrium, L + 〈Ti 5Si 3〉 + 〈Dy 5Si 3〉 ⇄ 〈TiDySi〉. The temperature of the latter was estimated to be within the interval 1650–1700 °C.

Crystallization of polymer-derived SiC/BN/C composites investigated by TEM

The crystallization behavior of two polymer-derived Si/B/C/N ceramics with similar compositions lying close to the three-phase field BN + SiC + C was investigated by (high-resolution) transmission electron microscopy. The materials were high-temperature mass stable up to T = 2000 °C. During thermolysis at 1050 °C a homogeneous amorphous solid formed. SiC crystallization started at about 1400 °C. Further annealing to higher temperatures up to 2000 °C led to formation of microstructures composed of SiC crystals embedded into a structured BNC x matrix phase. With increasing temperature, both the size of the crystallites and the ordering of the matrix phase increased.

Precipitation of Gamma-Prime and Gamma-Double Prime Coherent Phases in Three-Phase Ni-V-Si Alloys

Phase separation of γ (A1) supersaturated solid solution into A1, γ’ (L12) and γ” (D022) phases was investigated in two Ni-rich Ni-V-Si ternary alloys by means of transmission electron microscopy. When the alloys are annealed at 1073K, two different sequences of the phase separation are observed, depending on the chemical composition of the alloy: In Ni-17.0at%V-6.9at%Si alloy (A) at the D022 corner of three-phase field, first many D022 particles precipitate aligning along the <110> direction of the matrix and the so-called chessboard pattern is observed, followed by the formation of L12 phase at the interface between D022 and A1 phases. In Ni-12.1at%V-11.3at%Si alloy (B) at the L12 corner of the Gibbs triangle, cuboidal L12 particles precipitate arranging along the <100> direction, and then D022 phase is formed. As the phase separation proceeds, a selective growth/formation of the third phase (L12 in the alloy A, D022 in the alloy B) occurs: In the alloy A, L12 phase grows into D022 particle inside along the diagonal direction of D022 cube which is parallel to the a-axis of D022 tetragonal phase. In the alloy B, D022 forms on the {100} cube face of cuboidal L12 particle, arranging the c-axis of D022 perpendicular to the {100} cube face of L12 phase. As a result of such a selective growth/formation, the first phase D022/L12 is split off into two particles, which results in the formation of laminated structure consisting of D022 and L12 phases. The selective growth/formation is considered to occur so as to maintain the less elastic strain state.

Tillage and N Application Rates Affect on Corn and Soybean Yields and NO3-N Leaching Losses

Long-term assessment of NO3-N leaching losses to subsurface drainage tile water from different tillage systems and N application rates can help mitigate the environmental concerns of production agriculture. A three-phase field study was conducted to investigate the impact of two tillage systems (chisel vs. no-till) and different N application management systems on flow-weighted NO3-N concentrations and leaching losses to tile water. The study was conducted at Iowa State University's Northeastern Research Center, near Nashua, Iowa, from 1990 to 1992, 1993 to 1998, and 2001 to 2005. N application rates of 202 and 168 kg-N ha-1 during the first and third phases and low N rates of 135 and 110 kg-N ha-1 during the second phase were applied to continuous corn (CC) and rotated corn (CS), respectively, for both tillage systems. Rotated corn plots had significantly (p = 0.05) higher corn grain yields and lower NO3-N leaching losses than CC plots for both tillage systems. On the average, higher flow-weighted NO3-N concentrations were observed during the first phase (20.7 mg L-1), followed by the third phase (18.7 mg L-1) and the second phase (10.5 mg L-1) due to higher N application rates. Chisel plowing increased corn grain yields and resulted in almost equivalent NO3-N leaching losses to tile water compared with the no-till system. Effects of a wet year after dry years and low plant N uptake in some years elevated NO3-N concentrations to as high as 32.8 mg L-1 in 1990, 12.5 mg L-1 in 1995, and 24.5 mg L-1 in 2004. Fall-applied manure and chisel plowing had significantly higher NO3-N concentrations of 27 mg L-1 compared with 17.7 mg L-1 from no-till and spring-applied manure. These results suggest that low N application rates applied during the second phase with chisel plowing can be a viable option. Proper N credit, however, needs to be assessed for N pool buildup after dry years as a result of mineralization processes to minimize the offsite transport of NO3-N leaching losses to tile water.

Effect of the annealing temperature on the long-range order in the B2 phase of the Ti-Al-Nb(Zr,Mo) alloy

Investigation has been performed of changes in the degree of long-range order (LRO) upon annealing in a temperature range of 1000–1150°C for 1 h in the cubic B2 phase of the Ti-28.2% Al-13.2% Nb-1.2% Zr-0.86% Mo alloy. The calculation carried out using X-ray diffraction data showed that the degree of LRO in the B2 phase in the three-phase field (O + α2 + B2, T = 1000°C) is 0.36. Structure of the B2-phase regions with a low degree of LRO was studied using transmission electron microscopy. Temperature ranges suitable for thermomechanical treatment of the alloy have been determined.

Enthalpy and Gibbs energy of formation of dysprosium dicarbide

The equilibrium CO(g) pressures have been determined over the univariant three-phase field DyO 1.5(s)–C(s)–DyC 2(s) by means of the dynamic effusion MS method, in the temperature range 1360–1590 K. The carbide phase was generated in situ by the carbothermic reduction of the oxide using a quadrupole mass spectrometer, the effusion pressure of carbon monoxide was monitored. The enthalpy of the carbothermic reduction reaction was calculated by second- and third-law methods. By combining the appropriate thermal functions and enthalpies of other constituents from standard thermodynamic tables, the enthalpy of formation of the dicarbide at 298 K has been calculated. The Gibbs energy of formation of the dicarbide in this temperature range has also been calculated. The recommended values of enthalpy and Gibbs energy of formation of DyC 2(s) at 298 K are −(131 ± 19) kJ mol −1 and −(165 ± 6) kJ mol −1, respectively.

Study of three-phase equilibrium in the Nb-rich corner of Nb–Si–Cr system

The full understanding of the Nb–Si–Cr ternary system is important for the development of Nb silicide based composites, which show great potential for high temperature applications. There was, however, disparity in experimental observations of phase equilibrium in the vicinity of the Nb-corner. Two kinds of three-phase equilibrium, Nb ss+C14+αNb 5Si 3 and Nb ss+CrNbSi+αNb 5Si 3, in the Nb corner of the Nb–Si–Cr system have been reported in the literature. This work aims to clarify the three-phase equilibrium near the Nb-corner, by studying phase equilibrium in the Nb–18Si–15Cr ingot. Such a composition was chosen with the assistance of CALPHAD calculations to avoid unnecessary load of work. The alloy ingot was prepared by clean melting followed by heat treatment at 1000 and 1500 °C. The C14 Laves phase formed in all the samples and was stable at both temperatures. The results confirmed that Si has the effect of stabilising the C14 Laves phase down to at least 1000 °C. The three-phase equilibrium Nb ss+C14+αNb 5Si 3, instead of Nb ss+CrNbSi+αNb 5Si 3, was observed in this work. The current work demonstrates that ingot metallurgy is necessary to check the reliability of the information obtained about the ternary and higher-order phase diagrams, especially for the regions where the exact phase boundaries are in question. The investigation of the selected alloy was greatly helpful to clarify the confusion of the three-phase field near the Nb corner in the Nb–Si–Cr ternary system. The work confirmed the CALPHAD prediction of phase equilibrium near the Nb corner, showing the power to combine phase diagram predictions with experimental work for cost effective alloy development.

Experimental determination of the activity-composition relations and phase equilibria of H 2O-CO 2-NaCl fluids at 500°C, 500 bars

An understanding of the activity-composition ( a-X) relations and phase equilibria of halite-bearing, mixed-species supercritical fluids is critically important in many geological and industrial applications. We have performed experiments on H 2O-CO 2-NaCl fluids at 500°C, 500 bar, to obtain accurate and precise data on their a-X relations and phase equilibria. Two kinds of experiments were performed. First, H 2O-CO 2-NaCl samples were reacted at fixed activities of H 2O = 0.078, 0.350, 0.425, 0.448, 0.553, 0.560, 0.606, 0.678, 0.798, 0.841, and 0.935 to define the tie lines of known H 2O activity in the halite-vapor and vapor-brine fields. Results indicate that fluids with all but the last of these H 2O activities lie in the vapor-halite two-phase region and that a fluid with a H 2O = 0.841 has a composition close to the three-phase (vapor + brine + halite) field. A second set of experiments was performed to determine the solubility of NaCl in parts of the system in equilibrium with halite. Data from these experiments suggest that the vapor corner of the three-phase field lies at H 2O contents above X H 2O = 0.58 and X NaCl = 0.06, and below X H 2O = 0.75 and X NaCl = 0.06, which is a significantly more H 2O-rich composition than indicated by existing thermodynamic models.

Contribution to the knowledge of the Cu–Sn–Zn system for compositions close to brass alloys

The effect of tin content in the equilibrium phases of the Cu–Zn-based alloys, within the range of chemical compositions with interest to brass producers is described. For this purpose, ternary alloys with copper contents between 55.4 and 67.5wt.% and tin contents up to 5.30wt.% have been studied. The chemical composition of each alloy has been determined by X-ray fluorescence spectrometry (XRF). Isothermal homogenization, followed by rapid cooling, has been employed to determine the equilibrium phases at different temperatures. The homogenized alloys have been observed by scanning electron microscopy and the respective chemical analysis of the phases determined by electron probe microanalysis (EPMA). The statistical analysis of the obtained results enable to correlate the chemical composition of equilibrium phases with temperature. The chemical composition of the three-phase field, for the studied temperatures, has also been determined.

The 430 °C Isothermal Section of the Al—4Mg—Sc—Zr Quaternary System in the Al‐Rich Range.

Abstract The 430 °C isothermal section of the Al–4Mg–Sc–Zr quaternary system in the Al-rich range has been determined by means of equilibrium alloys with the use of microstructural, X-ray diffraction analysis, and electron probe microanalysis. There coexist three single-phase fields, two two-phase fields and one three-phase field. It is established that the Al3Sc1−0.5Zr0−0.5 phase with L12 structure and Al3Zr1−0.8Sc0−0.2 with DO23 structure are in equilibrium with the α-solid solution, Zr being dissolved in Al3Sc, further substituting for about 50 at.% Sc whilst Sc is present in the phase Al3Zr and the maximum substitution for Zr is about 20 at.% Zr.

The 430 °C isothermal section of the Al–4Mg–Sc–Zr quaternary system in the Al-rich range

The 430 °C isothermal section of the Al–4Mg–Sc–Zr quaternary system in the Al-rich range has been determined by means of equilibrium alloys with the use of microstructural, X-ray diffraction analysis, and electron probe microanalysis. There coexist three single-phase fields, two two-phase fields and one three-phase field. It is established that the Al 3Sc 1−0.5Zr 0−0.5 phase with L1 2 structure and Al 3Zr 1−0.8Sc 0−0.2 with DO 23 structure are in equilibrium with the α-solid solution, Zr being dissolved in Al 3Sc, further substituting for about 50 at.% Sc whilst Sc is present in the phase Al 3Zr and the maximum substitution for Zr is about 20 at.% Zr.

Enthalpy and Gibbs energy of formation of samarium dicarbide

Enthalpy and Gibbs energy of formation of SmC 2 have been determined between 1420 and 1650 K by measuring the CO(g) partial pressure over the invariant SmC 2(s)–SmO 1.5(s)–C(s) three-phase field. The equilibrium CO pressure over the three-phase field was deduced from the effusion pressure by the dynamic effusion MS method. The Gibbs energy of formation of SmC 2(s) in the entire temperature range was deduced from the Gibbs energy of the reaction, SmO 1.5(s) + 3.5 C(s)=SmC 2(s) + 1.5 CO(g), and by taking the Gibbs energy functions of the other constituents from literature. The recommended Gibbs energy of formation of SmC 2 at 298 K is −(98 ± 7) kJ mol −1. The enthalpy of formation of SmC 2(s) was derived from the enthalpy of reaction and the enthalpies of formation of SmO 1.5(s) and CO(g) taken from literature. The third-law enthalpy of formation of SmC 2(s) at 298 K is −(85 ± 8) kJ mol −1.

The microstructure of an Fe-Mn-Si-Cr-Ni stainless steel shape memory alloy

The microstructure and phase stability of the Fe-15Mn-7Si-9Cr-5Ni stainless steel shape memory alloy in the temperature range of 600 °C to 1200 °C was investigated using optical and transmission electron microscopy, X-ray diffractometry (XRD), differential scanning calorimetry (DSC), and chemical analysis techniques. The microstructural studies show that an austenite single-phase field exists in the temperature range of 1000 °C to 1100 °C, above 1100 °C, there exists a three-phase field consisting of austenite, δ-ferrite, and the (Fe,Mn)3Si intermetallic phase; within the temperature range of 700 °C to 1000 °C, a two-phase field consisting of austenite and the Fe5Ni3Si2 type intermetallic phase exists; and below 700 °C, there exists a single austenite phase field. Apart from these equilibrium phases, the austenite grains show the presence of athermal ɛ martensite. The athermal α′ martensite has also been observed for the first time in these stainless steel shape memory alloys and is produced through the γ-ɛ-α′ transformation sequence.

Ni-based bulk metallic glass formation in the Ni–Nb–Sn and Ni–Nb–Sn–X (X=B,Fe,Cu) alloy systems

Refractory Ni-based bulk metallic glasses are formed in the three-component Ni–Nb–Sn system near a ternary eutectic composition located within the three-phase field bounded by the three intermetallics Ni3Nb, Ni6Nb7 (μ-phase), and Ni2NbSn (BiF3-type). Bulk amorphous alloys of composition Ni60Nb40−xSnx with 3<x<9 were prepared by injection-casting the molten alloys into copper models. X-ray diffraction and differential scanning calorimetry studies show the cast strips to be fully amorphous up to thicknesses from 0.5 to 3 mm as x is varied. Maximum glass-forming ability (GFA) observed when x is between 6 and 7. These refractory bulk amorphous alloys exhibit high glass transition temperatures 881<Tg<895 K, a large, stable, undercooled liquid region with ΔT=Tx−Tg, at ∼40–60 K, very high Vickers hardness (VH∼1000–1280 Kg/mm2), and estimated yield strengths in the range of 3 to 3.8 GPa. The effects of small quaternary additions of B and Fe on the GFA of the ternary alloys are also reported.

Quantitative analysis of the effect of the binder phase composition on grain growth in WC-Co sintered materials

Microstructural evolution of WC-Co materials with different compositions and WC grain sizes is discussed from SEM observations and quantitative image analyses of intercept length distributions in the WC phase. Effect of the C/W ratio in the binder phase and of V- or Cr-dopants is particularly studied. Microstructural coarsening is shown to be more rapid and less abnormal when the C/W ratio is increased in the two-phase field {WC + liquid} and up to the three-phase field {WC + C + liquid}. The V-dopant does not completely suppress this effect. The composition dependence of the liquid stability—analysed from the calculated Gibbs energies of the phases—could explain the trend of the experimental results.

Microstructures and phase equilibria of the transition metal corner in the Rh–Al–C and Ir–Al–C ternary systems

The isotherms of the Rh–Al–C and Ir–Al–C ternary systems were determined at 1373 K for the transition metal rich corner. It has been revealed that the three-phase field consisting of primary solid solution of a transition metal, B2 type intermetallic compound and graphite extends over a very wide compositional range in these two alloy systems. There exists no carbide in related transition metal rich regions. The phase constitution in the Rh–Al–C and Ir–Al–C ternary alloys prepared by arc melting is basically the same as that by spark plasma sintering (SPS) except the presence of Al2O3 particles. The reaction scheme and liquidus surface projection in the transition metal corner of the Rh–Al–C and Ir–Al–C ternary systems were estimated by deliberating on the solidification sequence, as-cast microstructures and invariant reactions on the binary edges.

High temperature phase relationships in (Y,Nd)-123 superconducting oxides: the Y2BaCuO5–Nd4Ba2Cu2O10–Ba3Cu5Ox system

The quasi-ternary phase diagram of the Y2BaCuO5 (Y-211), Nd4Ba2Cu2O10 (Nd-422) and Ba3Cu5Ox (‘035’) system has been constructed in the vicinity of the peritectic temperature of YBa2Cu3O6+δ (Y-123) under air. The extent of the YxNd1−x+yBa2−yCu3O6+δ [(Y,Nd)-123ss] and liquid two-phase field is found to reduce with increasing temperature and tend towards the Nd-enriched region of the phase diagram via the emergence of a three-phase field of the ‘(Y,Nd)-123ss + (Y,Nd)-211ss + liquid’, followed by a ‘(Y,Nd)-211ss + liquid’ two-phase field. Furthermore, it is found that RE/Ba substitution in (Y,Nd)-123ss solid solution is significantly suppressed under reduced pO2, limiting the stable field of formation of (Y,Nd)-123ss within the Y-123 and Nd-123 binary section of the phase diagram. This is in contrast with the wide composition and temperature stable region observed in the ‘Y-123 + Nd-123 + Nd-213’ quasi-ternary system under air.

Phase Diagram Studies in the System Tl2O3-BaO-CaO-CuO-Ag

The phase relations within the system Tl2O3–BaO–CaO–CuO including Ag have been studied with emphasis on the high-temperature superconducting phases TlBa2Ca2Cu3O8.5 (1223 phase), Tl2Ba2Ca2Cu3O10 (2223 phase), TlBa2CaCu2O6.5 (1212 phase), and Tl2Ba2CaCu2O8 (2212 phase) at 890°C in an oxygen atmosphere. 1223 has been found to be in equilibrium with a liquid phase that is Tl poor. 2223 and 2212 exhibit varying Tl/(Ba + Ca) ratios. The three-phase field 1223 + 2223 + 2212 has been identified. The results of this study emphasize that multiphase samples can be prepared which consist of three superconducting phases, each exhibiting a critical temperature of 100 K or above.

Tie-lines and mixing properties of solid solutions in the system CaO-SrO-PbO-O at 1100 K

Phase relations in the system CaO-SrO-PbO-O2 at 1100 K have been determined by equilibrating samples with different compositions in air, oxygen, or evacuated ampoules for 7 days and characterizing quenched specimens by optical and scanning electron microscopy, energy-dispersive analysis of x-rays (EDX), and x-ray diffraction (XRD). There is a solid-state miscibility gap in the pseudo-binary system CaO-SrO, and continuous solid solubility between Ca2PbO4 and Sr2PbO4 at 1100 K. Substitution of Ca for Sr occurs only to a limited extent (∼2 mol.%) in SrPbO3. The calcium-rich solid solutions (Ca1−y Sr y )2PbO4 characterized by y≤0.255 are in equilibrium with PbO in air; compositions with y≥0.255 coexist with (Ca1−z Sr z )PbO3. There is a three-phase region involving the two monoxide solid solutions (Ca1−x Sr x )O on either side of the miscibility gap with x=0.24 and 0.71 and (Ca1−y Sr y )2PbO4 with y=0.96. Accurately determined are the locations of tie-lines between the solid solutions. Attainment of equilibrium was checked by the conventional tie-line rotation technique. The excess Gibbs energy of mixing of the solid solution with orthorhombic structure is obtained by an analysis of tie-line data; for the mixing of one mole of Ca and Sr represented by (Ca1−y Sr y )Pb0.5O2, ΔG E=y(1−y) [15,840−2950 y] J/mol. The thermodynamic properties suggest the onset of immiscibility in this solid solution below 884 (±5) K. The miscibility gap is asymmetric with a critical composition at y=0.43 (±0.02). Inside the triangle (Ca1−y Sr y )Pb0.5O2−(Ca1−z Sr z )PbO3−PbO, a small liquid-phase region is present close to the PbO corner, surrounded by three two-phase fields. Each corner of the approximately triangular liquid-phase region is associated with a three-phase field.

Solid State Cells with Buffer Electrodes for Measurement of Chemical Potentials and Gibbs Energies of Formation: System Ca–Rh–O

The isothermal section of the phase diagram for the system Ca–Rh–O at 1273 K has been determined by equilibrating 12 compositions in the ternary and identifying phases present in quenched samples by optical microscopy, powder X-ray diffraction (XRD), and energy-dispersive analysis of X rays (EDX). One ternary compound, CaRh2O4, was found to be stable. It coexists with CaO and metallic Rh. All the alloy compositions are in equilibrium with CaO. The standard Gibbs energy of formation of CaRh2O4 and the oxygen chemical potential corresponding to the three-phase field Rh+CaO+CaRh2O4 were determined using novel designs of solid state cells incorporating yttria-stabilized zirconia as the electrolyte: Pt–Rh, CaO+CaRh2O4+Rh/(Y2O3)ZrO2/Rh+Rh2O3, Pt–Rh,Pt–Rh, CaO+CaRh2O4+Rh/(Y2O3)ZrO2/O2(0.1 MPa),Pt–Rh. Buffer electrodes were introduced between reference and working electrodes to dissipate the electrochemical flux of oxygen through the solid electrolyte caused by the difference in chemical potential of oxygen at the electrodes. Polarization of the electrodes was prevented by the use of buffer electrodes. For the reaction 2Rh+CaO+32O2→CaRh2O4,ΔG°=32ΔμO2=−493,340+288.67T (±285) J/mol. The Gibbs energy of formation of the interoxide compound from the component binary oxides is β-Rh2O3+CaO→CaRh2O4,ΔG°=−101,670+10.6T (±290) J/mol. Using the Neumann–Kopp rule to estimate the heat capacity of CaRh2O4, the standard enthalpy of formation and standard entropy of the compound at 298.15 K are evaluated as −1142.3(±2) kJ/mol and 103.2(±2) J/mol·K, respectively.