On the coefficients of distribution of components and some regularities of the crystallization of alloys in three-component systems

The computation-graphical technique was used to study the equilibrium and nonequilibrium crystallization of the three-component solid solution alloys. Complex regularities of the component redistribution in the solid and liquid phases at the crystallization have been revealed. It is shown that during the crystallization of a number of alloys the distribution coefficient values of some components may vary from k < 1 to k = 1 and then k > 1. A new graphical analysis method of the three-component alloy crystallization has been proposed. Compound diffusion processes going on at the crystallization of such alloys have been revealed and the peculiarities of the component redistribution at the directional solidification of samples of such alloys, being important for the crystallization refining, have been defined.     

Sediment Control of Facilitated Transport and Enhanced Desorption

Laboratory column experiments examined the facilitated transport and enhanced desorption of benz(a)anthracene [B(a)A] by dissolved natural organic matter (OM) in sediments of low organic carbon content. The two-component experiments examining OM-sediment interaction and B(a)A-sediment interaction were modeled to determine the value of the linear rate constants describing transfer of B(a)A and OM between water and sediment. It was found that a two-rate approach better simulated B(a)A breakthrough and elution in the sediment relative to a one-rate approach. In contrast, OM-sediment interaction was well-simulated with a one-rate approach due to low OM sorption by sediment. The three-component experiments examining facilitated transport and enhanced desorption of B(a)A by dissolved OM, showed rapid linear reversible B(a)A-OM interaction. The value, within a factor of 2, of the equilibrium distribution constant for benz(a)anthracene distribution between water and OM was ～1E6 for soil humic acid and ～1E5 for Suwannee River humic acid. Simulations of the three-component experiments based on the equilibrium distribution constants for B(a)A-OM interaction and the rate constants determined from the two-component experiments were performed to determine whether rate constants differed in the two-component versus three-component systems. The simulations captured the major features of the facilitated transport and enhanced desorption data; however, discrepancies indicated that either the two-rate model for solute-sediment interaction was inappropriate, or that B(a)A transfer from sediment to dissolved OM was altered in the three-component system relative to the two-component system.     

Liquid decomposition, droplet coagulation and droplet-interface interactions in hypermonotectic Al-Bi alloys

Liquid decomposition in slightly hypermonotectic Al-Bi alloys has been investigated by synchrotron radiography during directional solidification. The L→L ₁+L ₂ reaction was found to be almost completely suppressed, appearing in close proximity to or simultaneous with the monotectic reaction, corresponding to a L(Bi)-supersaturation of 0.3. The liquid supersaturation also undercooled the monotectic reaction, where gravity, thermo-solutal Marangoni and Stokes drag set up a force-balance that control a strongly size dependent L ₂ droplet motion. The size dependant droplet motion gives rise to complex meso- and micro scale hydrodynamics that together with short-range non-hydrodynamic and hydrodynamic L ₂-L ₂ interactions have been identified as the main mechanisms behind droplet coagulation. The relatively substantial coagulation dynamics result in a bimodal droplet size distribution at the advancing solidification front. By varying the experimental parameters it was possible to study the droplet-α-Al-liquid interface interactions with both planar and curved interface morphologies. These interactions will be decisive for the final Bi particle distribution in the α-Al matrix. In contrast to what is most commonly assumed for pushing/engulfment of solid particles it was found that the larger droplets tended to be pushed by the front while smaller droplets are more frequently engulfed or entrapped. This result could be ascribed to effects on the droplets caused by the presence of solutal gradients ahead of the solidification front as well as dropletdroplet interactions.     

Relation between the solidification rate of a binary alloy and the alloying-element distribution coefficient

The change in the rate of equilibrium and nonequilibrium (according to Petrov–Scheil) solidification in binary model and some real solid-solution alloys with a distribution coefficient 0.2–2.5 is comprehensively analyzed. A relation between the solidification rate, on the one hand, and growth restriction factor Q and supercooling parameter P, which are used to determine the grain sizes in as-cast alloys, is revealed.     

Solute interaction and internal friction spectra in solid solutions

On purpose to verify the applicability of models of solute atoms interaction in b.c.c. metals internal friction due to “diffusion under stress” of interstitials was calculated. For interstitial-interstitial (i-i) and interstitial-substitutional (i-s) interaction a strain-induced interaction model with additional Coulomb repulsion in (i-i) case and additional “chemical” interaction in (i-s) case was used. Calculations were made with concrete values of interaction energies. It was shown that the Snoek peak's shape in Ta-O was very sensitive to the (i-i) potential details. Computer simulation showed that the broadening of the maximum in experiments is caused by appearance of short-range order due to long-range (i-i) interaction and the Coulomb repulsion is important up to the third coordination shell. The used (i-i) interaction model is applicable to Ta-O solid solution. In the (i-s) case the influence of s-atoms on the Snoek relaxation due to O and N in V, Nb and Ta and N and C in α-Fe was calculated by using Koiwa's theory. On the whole there is a good agreement between experimental and calculated spectra for Nb, V, Ta and no agreement for α-Fe. Thus the used (i-s) interaction model is only applicable to V, Nb and Ta solutions.     

Solidification of Highly Undercooled Hypereutectic Ni-Ni3B Alloy Melt

The solidification of undercooled Ni-4.5 wt pct B alloy melt was investigated by using the glass fluxing technique. The alloy melt was undercooled up to ΔT _p ~ 245 K (245 °C), where a mixture of α-Ni dendrite, Ni₃B dendrite, rod eutectic, and precipitates was obtained. If ΔT _p < 175 K ± 10 K (175 °C ± 10 °C), the solidification pathway was found as primary transformation and eutectic transformation (L → Ni₃B and L → Ni/Ni₃B); if ΔT _p ≥ 175 K ± 10 K (175 °C ± 10 °C), the pathway was found as metastable eutectic transformation, metastable phase decomposition, and residual liquid solidification (L → Ni/Ni₂₃B₆, Ni₂₃B₆ → Ni/Ni₃B, and L_r → Ni/Ni₃B). A high-speed video system was adopted to observe the solidification front of each transformation. It showed that for residual liquid solidification, the solidification front velocity is the same magnitude as that for eutectic transformation, but is an order of magnitude larger than for metastable eutectic transformation, which confirms the reaction as L_r → Ni/Ni₃B; it also showed that this velocity decreases with increasing ΔT _r, which can be explained by reduction of the residual liquid fraction and decrease of Ni₂₃B₆ decomposition rate.     

Solidification of Al-4.5 wt pct Cu-Replicated Foams

Microcellular Al-4.5 wt pct Cu of 400- or 75-μm average pore diameter is solidified at cooling rates ranging from ?30 K/min to ?0.45 K/min (?30 °C/min to ?0.45 °C/min). In the 400-μm pore size samples, the dendritic character is lost, and the level of microsegregation, which is quantified by the minimum copper content of the matrix, is reduced when the cooling rate is lowered. The 75-μm pore size samples show no dendritic microstructural features and low levels of microsegregation, even at the higher cooling rates explored. Microstructural maps, based on solidification theory developed for metal matrix composites, satisfactorily describe the microstructure of the Al-4.5 wt pct Cu foams. A finite difference model giving the minimum copper content as a function of the reinforcement size and cooling rate, developed for fiber-reinforced metals, is also valid for replicated Al-4.5 wt pct Cu foam. This work thus extends to particulate composites and, by extension, to replicated microcellular alloys, results originally derived from the study of fiber-reinforced metal solidification.     

Kinetics of mixed rare earths minerals decomposed by CaO with NaCl-CaCl2 melting salt

For increasing reaction rate and reducing decomposing temperature, TG-DTA, XRD, SEM and Chemical analysis were used to study the kinetics of mixed rare earths minerals decomposed by CaO with NaCl-CaCl₂. The results showed that the reaction rate increased with increasing of NaC-CaCl₂ addition, CaO addition, and decomposition temperature. The kinetics of mixed rare earths minerals decomposed by CaO conformed to 1-2/3X-(1-X)^2/3=k_dt mode. The decomposition reaction rate was controlled by two steps, and the activation energy was decreased with adding of NaCl-CaCl₂ melting salt. The micro-pattern of products was loosening and porous with NaCl-CaCl₂ in decomposition system.     

Thermodynamic activity of the liquid-phase components in the CaO · SiO2-CaO · Al2O3 · 2SiO2-CaO · TiO2 · SiO2 system with four-phase invariant equilibrium

The CaO · SiO₂-CaO · Al₂O₃ · 2SiO₂-CaO · TiO₂ · SiO₂ system is analyzed. Thermodynamic analysis of monovariant and invariant solidification shows that, for invariant equilibrium and for solidification along the boundary curve between the solidification fields of anorthite and sphene, peritectic processes are observed. The invariant-state parameters of the system are determined: t = 1513 K; a _CaO = 0.0407; $a_{SiO_2 } = 0.5268$ ; $a_{Al_2 O_3 } = 0.00003$ , $a_{TiO_2 } = 0.005$ ). A corrected phase diagram is presented.     

Solidification of highly undercooled Fe-P alloys

Rapid solidification behavior of highly undercooled iron-phosphorus alloys was investigated by using a high-speed optical temperature measurement system. The experimental results on solidification rate as a function of bulk undercooling agree well with a model which includes a treatment of nonequilibrium effects during the solidification process. The model is based on an earlier analysis by Boettinger, Coriell, and Trivedi_[81] (BCT) and employs temperature-dependent values of equilibrium liquidus slope, equilibrium solute distribution coefficient, and solute interdiffusion coefficient. Values of the kinetic parameters,a ₀ andV ₀ , in the analysis which best fit the experimental results are 5 x 10_-10 m and 600 m/s, respectively. Comparison of experimental results and theory suggests that a transition from local equilibrium to nonequilibrium solidification takes place with increasing undercooling and that interface kinetic effects become predominant at higher undercooling (or growth velocity).     

Microstructure development during rapid solidification of highly supersaturated Cu-Co alloys

We report a detailed microstructure analysis of rapidly quenched Cu_1−xCo_x (0.1 ⩽ × ⩽ 0.5) alloys. The chemical homogeneity of the alloys was investigated on nanometer scale using a combination of AP/FIM- and TEM-studies. Cu-Co alloys with a Co concentration up to 10 at.% Co can be prepared homogeneously by rapid quenching. For larger Co contents, the microstructure is determined by a competition between polymorphic solidification, nucleation of the Co-rich solid solution from the melt, and spinodal decomposition of the unstable supersaturated solid solution. The microstructures are discussed in terms of the kinetics of the Cu-Co system, provided quantitatively by recent thermodynamic calculations.     

Equilibrium crystallization of alloys of ternary solid solutions

Equilibrium crystallization of continuous solid solutions in ternary systems is considered. It is shown that in each ternary and multicomponent alloy with unlimited solubility of components in the liquid and solid states, equilibrium crystallization is realized similarly to a binary alloy due to diffusion decomposition of liquid and its diffusion interaction with the previously precipitated solid phase. The distinction is the formation, at a decreased temperature, of nonequilibrium compositions of the liquid and solid phases, with conservation of the composition of the solid phase, which had been at equilibrium for the temperature before the decrease; this takes place owing to the decomposition diffusion of the liquid. The diffusion interaction of all phase components leads to the formation of equilibrium of liquid and solid phases for a new temperature. By plotting and calculation, it is shown that in ternary systems, for certain alloy compositions at definite stages of crystallization, the fraction of the solid phase can decrease due to the diffusion interaction, which is excluded for solid solutions of binary alloys.     

Rapid melting and solidification of a surface due to a moving heat flux

Rapid melting and solidification of a semi-infinite substrate subjected to a high intensity heat flux over a circular region on its bounding surface moving with a constant velocity is considered. General expressions are developed for the coefficients in the finite difference equation governing the heat transfer in moving orthogonal curvilinear coordinate systems. These expressions are reduced to their specific forms in terms of dimensionless nodal temperature and enthalpy for a moving oblate spheroidal coordinate system. Quasisteady state conditions are assumed and the thermal properties of the substrate in the liquid and solid phase are considered constant and equal. It is also assumed that the substrate melts and solidifies at a single temperature. Temperature distributions in the molten region and the adjacent heat affected zone are computed along with the liquid-solid interface shape, its velocity and other important solidification variables. Both uniform and Gaussian heat flux distributions within the circular region are considered. The results are presented in their most general form—in terms of dimensionless numbers when possible. Specific criteria for the melting of the substrate are established. It is shown that the three variables, absorbed heat fluxq, the radius of the circular regiona and the velocity of the moving fluxU, could be combined into two independent variables. That is, the dimensionless temperature distribution in the metal pool and the solid substrate remain the same as long as the productsqa andUa orU/q are kept constant. The effect of these variables on cooling rate in the liquid and the ratio of temperature gradient to growth rate at the solid-liquid interface are discussed using an aluminum substrate as an example.     

Microstructure and Hydrogen-Induced Failure Mechanisms in Fe and Ni Alloy Weldments

The microstructure and fracture morphology of AISI 8630-IN625 and ASTM A182-F22-IN625 dissimilar metal weld interfaces were compared and contrasted as a function of postweld heat treatment (PWHT) duration. For both systems, the microstructure along the weld interface consisted of a coarse grain heat-affected zone in the Fe-base metal followed by discontinuous martensitic partially mixed zones and a continuous partially mixed zone on the Ni side of the fusion line. Within the partially mixed zone on the Ni side, there exists a 200-nm-wide transition zone within a 20-??m-wide planar solidification region followed by a cellular dendritic region with Nb-Mo?Crich carbides decorating the dendrite boundaries. Although there were differences in the volume of the partially mixed zones, the major difference in the metal weld interfaces was the presence of M₇C₃ precipitates in the planar solidification region, which had formed in AISI 8630-IN625 but not in ASTM A182-F22-IN625. These precipitates make the weldment more susceptible to hydrogen embrittlement and provide a low energy fracture path between the discontinuous partially mixed zones.     

The directional solidification of Pb-Sn-Cd alloys

The growing interest in composite structures for new material applications makes it necessary to determine just how generally we can apply existing solidification theory to controlled three-phase ternary solidification. The Pb-Sn-Cd ternary eutectic system was used as a suitable model system to completely map the phase morphology as a function of G/R and compositions. By carefully controlling the freezing rate and the thermal gradient in the liquid ahead of the solid-liquid interface (in the range 400 to 500 C/cm) the following areas of interest were investigated: 1) the effect of growth velocity and composition on coupled structures, 2) ternary impurities and their effect on the minimum G/R for coupled growth in a binary system, 3) the effect of growth velocity and composition on the nonplanar interface structures, and 4) the adaptability of present theories (the constitutional supercooling criterion and Cline’s binary analysis) in predicting the region of coupled growth in a three-component eutectic system growing at steady-state. It was found that much of the one and two-phase directional solidification theory and terminology can be directly extended to a ternary eutectic system. This suggests a further extension to n-phase, m-component systems (m ≥ n) with at least a qualitative understanding of the solidification process. The Authors wish to acknowledge the support of the National Science Foundation which made this study possible.     

Magnetostriction, composition and microstructure of Tb0.29（Dy1–xPrx）0.71Fe1.97 alloys with heat treatment

Tb_0.29(Dy_1-xPr_x)_0.71Fe_1.97 (x=0, 0.1, 0.2 and 0.3) alloys prepared by the directional solidification method were treated at 1073, 1123, 1173, 1223 and 1273 K for 4 h for homogenization, respectively. The magnetostriction, micro-morphology and composition distribution were studied by the standard resistance strain gauge technique, optical microscopy and scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS). The results indicated that heat treatment could make the microstructure of alloys homogeneous effectively and improve the magnetostriction significantly. The optimum temperature was 1223 K. Compared to the as-cast ones, the increase amplitudes of magnetostriction of the corresponding samples were 39.5%, 64.9%, 95.3% and 50.8% when x=0, 0.1, 0.2 and 0.3, respectively at the compressive stress of 2 MPa and a magnetic field of 80 kA/m. The compressive stress could also improve the magnetostriction. However, further Pr element addition and over high heat treatment temperature would lead to the excessive decomposition of PrFe₂ and destroy the homogeneity, resulting in the decline of magnetostriction of alloys.     

On the geometrical representation of phase equilibria

In order to achieve a rational and optimal representation of thermodynamic information in a two-dimensional plot for multicomponent systems, three types of equilibrium phase dia-grams are investigated with regard to their topology. These three types are 1) diagrams in which the coordinates are given by two generalized thermodynamic potential functions ; 2) diagrams in which one generalized thermodynamic potential function is replaced by a ratio of conjugate extensive variables; 3) diagrams in which both generalized thermody-namic potential functions are replaced by ratios of conjugate extensive variables. In the second part of this investigation, the general considerations are used to calculate and construct phase diagrams of ternary systems of the kindA-B-X. It is shown that the pro-posed representations, especially the ones using logp X ₂-n _A/(n _A +n _B ) as generalized thermodynamic potential and conjugate extensive variable coordinates (which are topo-logically analogous to the well knownT- x _i -diagrams of binary systems) allow conclusions of practical importance to be drawn. The ternary systems discussed in detail are Co-Ni-O, Ag-Cu-Cl, Cu-Ni-S, Pb-Sn-Cl, Ag-Sb-S, Mg-Ni-O, Fe-Cr-O, and Fe-Ni-O.     

Effect of Magnetic Interaction on Thermally Activated Reversal in a Magnet With a Distribution of Energy Barriers

The time dependence of magnetization is usually expressed as M(t)=M₀-SInt [see Proc. Phys. Soc. 62, 562 (1949)] for magnetic viscosity experiments. Considering magnetic interaction during the thermal activation process, a form as M(t)=M₀-SIn(t+t₀) is deduced. The dipolar interaction and exchange coupling in a magnet can lead to positive and nonpositive t₀, respectively. In the experiments of the magnetic viscosity for nanocrystalline Pr₂Fe₁₄B ribbons, the existence of positive t₀ is confirmed.     

Solidification paths of TiTaAl alloys

Microstructure evolution during solidification and high temperature phase equilibria were investigated for TiTaAl alloys in the vicinity of the 50 at.%Al isoconcentrate. Examination of dendrite morphologies and segregation profiles were used to deduce the phase sequencing during solidification and the boundaries of the relevant liquidi surfaces. In situ high-temperature X-ray diffraction and isothermal annealing experiments were conducted to determine the phases present at elevated temperatures and coupled with extensive characterization by transmission electron microscopy to elucidate the solid state transformations during cooling of the solidification microstructure. For approximately equiatomic TiAl, the primary phase selected from the liquid was α for the leaner Ta concentrations (< 7% Ta), as in the binary alloys of equivalent Al content, but changed to β with increasing Ta levels (> 10 %). With increasing Al and Ta the α liquidus penetrates deeply into the ternary. The interdendritic segregate was always γ. Dendrites of the β-forming alloys were heavily segregated leading to different microconstituents in the core and bulk dendrite regions during post-solidification cooling. In alloys with < 15 % Ta, (α₂ + γ_t) lath formed in the dendrite bulk due to the decomposition of α, with σ precipitating in the core (> 10% Ta). With increasing Ta levels the lath is gradually replaced by polycrystalline γ which grows into the dendrite bulk, and the core decomposes into a lamellar (γ + σ) microstructure from the decomposition of σ. The γ segregate does not transform further.     

Dendritic solidification—III. Some further refinements to the model for dendritic growth under an imposed thermal gradient

Some further refinements to a simple model for dendritic solidification (presented earlier by the author) in a binary alloy melt under an imposed positive thermal gradient are presented. Two new expressions for the dendrite tip undercooling have been obtained and shown to yield a limiting value of ΔT₀ and very small growth rates. Here ΔT₀ is the equilibrium solidification range of the alloy. At very large growth rates, all three tip undercooling expressions reach the same limiting value depending on the value of a dimensionless parameter λ which is related to the effective diffusion distance ahead of the dendrite tip. The predicted tip undercoolings are, however, somewhat lower at intermediate growth rates. An improved calculation for the solute buildup at the dendrite tip due to curvature effects is also included.