相图计算及其应用

综述相图计算方法的发展现状、相图热力学计算常用的相描述模型及常用的热力学计算软件,并以Cu–Fe–Mn和Fe–Mn–Ni体系为例重点介绍相图热力学计算在材料设计及制备中的应用。     

Calculation of the forming limit diagram

A mathematical model is presented to help understand sheet metal deformation during forming. The particular purpose of this model is to predict the forming limit diagram (FLD). The present model is an extension of a previous analysis by Jones and Gillis (JG)^[1] in which the deformation is idealized into three phases: (I) homogeneous deformation up to maximum load; (II) deformation localization under constant load; (III) local necking with a precipitous drop in load. In phase III, the neck geometry is described by a Bridgman-type neck. The present model extends the JG theory, which was applied only to the right-hand side (RHS) of the FLD. The main difference in treating the two different sides of the FLD lies in the assumptions regarding the width direction deformations. For biaxial stretching (the RHS), the minor strain rate is assumed to be homogeneous throughout the process. However, for the left-hand side (LHS) of the FLD in the critical cross section, the minor strain rate is taken to be proportional to major strain rate. This is a critical difference from the JG approach and permits the LHS to be computed with good accuracy. Another important difference between this and the JG analysis is a more realistic neck geometry. At the inception of phase III, JG matched the phase II sheet thickness at the center of the neck, that is, at its minimum cross section. Here, the phase III neck matches the phase II sheet thickness at its ends, that is, at its maximum cross section. Although this may seem a minor point, it greatly improves the geometrical concept involved. Both the actual neck geometry and the criterion for determining the limit strain are modified from the earlier analysis in order to agree more closely with actual press shop practice. Results from this analysis are compared with the experimental ones for aluminum-killed (AK) steel and three aluminum alloys. These results are also compared to other theoretical calculations of the forming limit for AK steel. It is apparent that the present model is best. Unlike the other types of analyses, the present model predicts the limiting strain states for several materials very accurately without any adjustable parameters. This is certainly an unprecedented result. Using the mathematical model, the effects of varying material properties are studied. The properties considered are the strain-hardening exponent,n, the strain-rate sensitivity parameter,m, and the plastic anisotropy ratio,r, The important influence of these material properties upon the formability (level of the FLD) is affirmed.     

On the iron-carbon phase diagram

Experimental results that are obtained by electron microscopy, X-ray diffraction, and carbide analysis and indicate the precipitation of carbon atoms clusters in a hypereutectoid steel during its annealing above the eutectoid temperature are presented. These results are compared to the reported data in order to construct a new Fe-C phase diagram, where cementite forms below the eutectoid temperature due to the tendency of the Fe-C system toward ordering and carbon unbound to iron precipitates above this temperature in the form of clusters or graphite particles due to the tendency of this system toward phase separation.     

On the Mn-MnS phase diagram

Using a DTA technique the melting point of pure MnS has been determined to 1655 ±5°C. The monotectic temperature in the Mn-MnS system was found to be 1570 ±5°C. With these new data a thermodynamic analysis of the Mn-MnS system was carried out applying a previously developed thermodynamic model.     

Low-temperature extension of the lehrer diagram and the iron-nitrogen phase diagram

Iron layers are nitrided in mixtures of ammonia and hydrogen at low temperatures, using a thin nickel caplayer as a catalyst. In the coordinate field of inverse temperature vs nitriding potential, we determined the boundaries between areas in which the α, γ′, or ε phases are in thermal equilibrium. Using these data, the Fe-N phase diagram is extended from 350 °C to 240 °C and extrapolated down to 200 °C. The α, γ′, and ε phases probably coexist in a triple point in the Lehrer diagram around 214 °C.     

The Dy-Zn phase diagram

The dysprosium-zinc phase diagram has been investigated over its entire composition range by using differential thermal analysis, (DTA) metallographic analysis, X-ray powder diffraction, and electron probe microanalysis (EPMA). Seven intermetallic phases have been found and their structures confirmed. DyZn, DyZn₂, Dy₁₃Zn₅₈, and Dy₂Zn₁₇ melt congruently at 1095 °C, 1050 °C, 930 °C, and 930 °C, respectively. DyZn₃, Dy₃Zn₁₁, and DyZn₁₂ form through peritectic reactions at 895 °C, about 900 °C and 685 °C, respectively. Four eutectic reactions occur at 850 °C and 30.0 at pct Zn (between (Dy) and DyZn), 990 °C and 60.0 at pct Zn (between DyZn and DyZn₂), 885 °C and 76.0 at pct Zn (between DyZn₃ and Dy₃Zn₁₁), and 875 °C and 85.0 at pct Zn (involving Dy₁₃Zn₅₈ and Dy₂Zn₁₇). The Dy-rich end presents a catatectic equilibrium; a degenerate invariant effect has been found in the Zn-rich region. The phase equilibria of the Dy-Zn alloys are discussed and compared with those of the other known RE-Zn systems (RE=rare earth metal) in view of the regular change in the relative stabilities of the phases across the lanthanide series     

The Nd-Zn phase diagram

Metallographie, thermal, and X-ray techniques were used to determine the phase relations in the Nd-Zn system. Eight compounds, three eutectics and a eutectoid were found. The compounds NdZn, NdZn₂, and Nd₂Znn melt congruently at 923°, 925°, and 981°C respectively. The compounds Nd₃Zn₁₁, NdZn_4.46, and Nd₃Zn₂₂ undergo peritectic decomposition at 870°, 902°, and 950°C respectively, while NdZn₃ undergoes peritectoid decomposition at 849°C. The eutectics occur at 12 wt pct Zn and 630°C, 38 wt pct Zn and 868°C, and 56 wt pct Zn and 854°C. The eutectoid occurs at 4 wt pct Zn and 622°C. The existence of a NdZn₁₂ phase of the SmZn₁₂ type structure has been confirmed. An allotropie transformation between the tetragonal NdZn₁₁ structure and the hexagonal NdZn₁₂ defect structure is proposed.     

The neodymium-gold phase diagram

The Nd-Au phase diagram was studied in the 0 to 100 at. pct Au composition range by differential thermal analysis (DTA), X-ray diffraction (XRD), optical microscopy (LOM), scanning electron microscopy (SEM), and electron probe microanalysis (EPMA). Six intermetallic phases were identified, the crystallographic structures were determined or confirmed, and the melting behavior was determined, as follows: Nd₂Au, orthorhombic oP12-Co₂Si type, peritectic decomposition at 810 °C; NdAu, R.T. form, orthorhombic oP8-FeB type, H.T. forms, orthorhombic oC8-CrB type and, at a higher temperature, cubic cP2-CsCl type, melting point 1470 °C; Nd₃Au₄, trigonal hR42-Pu₃Pd₄ type, peritectic decomposition at 1250 °C; Nd₁₇Au₃₆, tetragonal tP106-Nd₁₇Au₃₆ type, melting point 1170 °C; Nd₁₄Au₅₁, hexagonal hP65-Gd₁₄Ag₅₁ type, melting point 1210 °C; and NdAu₆, monoclinic mC28-PrAu₆ type, peritectic decomposition at 875 °C. Four eutectic reactions were found, respectively, at 19.0 at. pct Au and 655 °C, at 63.0 at. pct Au and 1080 °C, at 72.0 at. pct Au and 1050 °C, and, finally, at 91.0 at. pct Au and 795 °C. A catatectic decomposition of the (βNd) phase, at 825 °C and ≈1 at. pct Au, was also found. The results are briefly discussed and compared to those for the other rare earth-gold (R-Au) systems. A short discussion of the general alloying behavior of the “coinage metals” (Cu, Ag, and Au) with the rare-earth metals is finally presented.     

Liquidus surface of the Mg-Sm-Tb phase diagram

Differential thermal, electron microprobe, and X-ray diffraction analyses and metallography are used to study Mg-Sm-Tb alloys containing up to 30% Sm or Tb. Polythermal sections and the solidification surface of the Mg-Sm-Tb phase diagram are constructed for the Mg-rich region. In the composition range under study, nonvariant transition-type equilibrium L + Mg₂₄Tb₅ = (Mg) + Mg₄₁Sm₅ is found to exist at a temperature of 539°C.     

Al-rich portion of the Al-Hf phase diagram

Electrical resistivity measurements, differential thermal analysis, optical microscopy, and the deposition of hafnium compound particles from a melt are used to study the Al-rich portion of the Al-Hf phase diagram. Prominence is given to the hafnium solubility in solid and liquid aluminum. The studies show a peritectic character of the invariant reaction during the solidification of alloys with sufficiently high hafnium contents and a slight difference between the peritectic and melting temperatures of pure aluminum. The hafnium solubility in solid and liquid aluminum is shown to increase with the temperature. The hafnium solubility in solid aluminum at the peritectic temperature (maximum solubility) is 1.00 wt % (0.153 at %); the hafnium solubility in liquid aluminum at this temperature is 0.43 wt % (0.065 at %).     

The phase diagram of the Ni-VC-NbC system

Conclusions The Ni-VC_0.87-NbC_0.9 system has a ternary eutectic in the solidification of which the equilibrium phases are an Ni-base solid solution, (V, Nb)C carbide containing 10% NbC_0.9 and 90% VC_0.87, and (V, Nb)C carbide containing 20% VC_0.87 and 80% NbC_0.9. The point of the four-phase nonvariant equilibrium is in the region of the alloy containing 3% NbC_0.9 and 6% VC_0.87 and the temperature of the equilibrium is 1300±15°C. The diagram of the phase equilibria (Fig. 3) of this system has the same form as for the Ni-TiC-ZrC and Ni-TiC-HfC systems [9, 10].Translated from Poroshkovaya Metallurgiya, No. 8(296), pp. 67–79, August, 1987.     

Nickel-rich portion of the Ni-Al-Nb phase diagram

The solubility of Nb + Al in the γ solid solution decreases markedly with decreasing temperature; thus alloys can be prepared that are γ at 1200°C and yet contain 50 pct γ’ precipitate after aging at 800°C. Thermal stability of the γ’ precipitate is related to the lattice mismatch between the γ and γ’ phases; the smaller the mismatch the lower is the interfacial elastic energy and the more stable is the γ’. Upon aging certain alloys at 800°C a γ’ growth interface other than the normal (100)_γll(100)_γ’ is observed. The maximum solubility of the niobium in γ’ is ∼7 at. pct; the width of the γ’ field increases with increasing niobium content but it is essentially independent of temperature. Replacing aluminum by niobium in γ’ gives hardnesses of up to 400 Dpn.