极端非平衡条件下过冷熔体枝晶生长模型

考虑界面非平衡、弯曲界面对驱动力的影响,并且摒弃液固相线线性假设,得到了界面移动热力学驱动力;从液固相线非线性条件下的动力学边界条件出发,对稳定性判据进行了修正;在溶质截留模型中,综合考虑弛豫效应和非线性液固相线的影响,对Aziz模型进行了修正;基于相图分析,得到过冷度分配.综合以上分析,在非线性液固相线基础上,得到了新的二元过冷熔体自由枝晶生长模型.将该模型应用到Ni-0.7%B合金中,结果表明无论从定性上还是定量上都与实验结果吻合得很好.     

Dendritic growth of undercooled nickel-tin: Part II

High-speed optical temperature measurements were made of the solidification behavior of levitated metal samples within a transparent glass medium. Two undercooled Ni-Sn alloys were examined, one a hypoeutectic alloy and the other of eutectic composition. Recalescence times for the 9 mm diameter samples studied decreased with increasing undercooling from the order of 1.0 second at 50 K under-cooling to less than 10⁻³ second for undercoolings greater than 200 K. Both alloys recalesced smoothly to a maximum recalescence temperature at which the solid was at or near its equilibrium composition and equilibrium weight fraction. For the samples of hypoeutectic alloy that recalesced above the eutectic temperature, a second nucleation event occurred on cooling to the eutectic temperature. For samples which recalesced only to the eutectic temperature, no subsequent nucleation event was observed on cooling. It is inferred in this latter case that both the α and β phases were present at the end of recalescence. The thermal data obtained suggest a solidification model involving (1) dendrites of very fine structure growing into the melt at temperatures near the bulk undercooling temperature, (2) thickening of dendrite arms with rapid recalescence, and (3) continued, much slower recalescence accompanying dendrite ripening.     

Dendritic growth of undercooled nickel-tin: Part I

Solidification of undercooled Ni-25 wt pct Sn alloy was observed by high-speed cinematography and results compared with optical temperature measurements. Samples studied were rectangular in cross-section, and were encased in glass. Cinematographic measurements were carried out on samples undercooled from 68 to 146 K. These undercoolings compare with a temperature range of 199 K from the equilibrium liquidus to the extrapolated equilibrium solidus. At all undercoolings studied, the high-speed photography revealed that solidification during the period of recalescence took place with a dendrite-like front moving across the sample surface. Spacings of the apparent “dendrite” were on the order of millimeters. The growth front moved at measured velocities ranging from 0.07 meters per second at 68 K undercooling to 0.74 meters per second at 146 K undercooling. These velocities agree well with results of calculations according to the model for dendrite growth of Lipton, Kurz, and Trivedi. It is concluded that the coarse structure observed comprises an array of very much finer, solute-controlled dendrites.     

Dendritic solidification of Cu-Ni alloys: Part I. Initial growth of dendrite structure

Small Cu-Ni melts were furnace cooled at different rates and with different "nucleation" temperatures. Thermal analysis showed that the thermal arrests associated with the formation of the dendrite skeletons showed a significant supercooling below the liquidus temperatures. This supercooling increased with increased rates of heat extraction,i.e. higher cooling rates and lower "nucleation" temperatures; and was associated with higher dendrite growth velocities. The solute content of the dendrites measured on samples quenched during the thermal arrest quantitatively supported these observations. The magnitude of the supercooling for a given rate of heat extraction varied directly with the freezing range of the alloy but remained finite (although small) for unalloyed copper. The approximate measurements of dendrite growth velocities for one alloy (40 wt pet Ni) at different supercoolings agreed well with the predictions of Trivedi’s theory of dendrite growth. E. A. FEEST, formerly Graduate Student, University of Sussex K. HOLM, formerly Visiting Research Student, University of Susses     

Advanced Solute Conservation Equations for Dendritic Solidification Processes Part I: Experiments and Theory

The macrosegregation formed in dendritic equiaxed structure during early stages of solidification of Al‐4.5%Cu alloy has been studied by experimental work and by metallurgical study of cast samples taken from the experimental work. An experimental work was conducted to study the coupled effect of natural convection streams, interdendritic strain and mushy permeability of Al‐4.5%Cu aluminum alloy solidified in horizontal rectangular parallelepiped cavity at different superheats. The metallurgical study includes macro‐microstructure evaluation, measurements of grain size of equiaxed crystals and macrosegregation analysis. This study shows that the level of surface segregation exhibiting as positive segregation varies with superheat whereas the rest of inner ingot areas show the light fluctuation in segregation values. In addition to experimental work, there is a mathematical study which contains a complete derivation of local solute redistribution equations based on Fleming's approach under different solute diffusion mechanisms in the dendritic solid. This derivation includes also the effects of interdendritic strain and mushy permeability on the local solute redistribution distribution. Owing to the length of the study, it is presented in two parts. The first part describes the experimental work and its results as well as a detail derivation of solute conservation equations. This part also involves comparison and discussion between existing and proposed solute conservation equations. The second part contains the mathematical analyses of a two dimensional mathematical model of fluid flow, heat flow, solidification, interdendritic strain and macrosegregation. Also, this part also contains the numerical simulations by using finite difference technique “FDT” to create convection patterns, heat transfer, interdendritic strain, and macrosegregation distributions. This part also includes comparisons between the available measurements and model predications as well as full discussion of different model simulations. The mechanism of interdendritic strain generation and macrosegregation formation during solidification of dendritic equiaxed structure under different diffusion mechanisms in dendritic solid has also been explained and discussed.     

Growth Simulations and Experiments on Needle-Electrode Electrodeposited Dendritic Crystals

Numerical simulations of crystal growth using an improved diffusion-limited aggregation (DLA) model were performed and their validity verified by comparison with experimentally grown electrodeposited crystals. The shape and growth of the needle-electrode electrodeposited nickel dendrites were studied. The results show that the electrodeposited materials obtained in the experiment are similar to the particle clusters resulting from the simulation; their fractal dimensions are close to one another and the DLA model effectively explains the rules determining growth of the dendritic crystals. Apart from the velocity and concentration of the particles, the combination probability in the DLA model, applied voltage, deposition time and the electrolyte temperature used for electrodeposition are all important. The deposition layers of the simulated particles have significant fractal structure.     

Dendritic Growth tip velocities and radii of curvature in microgravity

Dendritic growth is the common mode of solidification encountered when metals and alloys freeze under low thermal gradients. The growth of dendrites in pure melts depends on the transport of latent heat from the moving crystal-melt interface and the influence of weaker effects like the interfacial energy. Experimental data for critical tests of dendritic growth theories remained limited because dendritic growth can be complicated by convection. The Isothermal Dendritic Growth Experiment (IDGE) was developed specifically to test dendritic growth theories by performing measurements with succinonitrile (SCN) in microgravity, thus eliminating buoyancy-induced convection. The first flight of the IDGE in 1994 operated for 9 days at a mean quasi-static acceleration of 0.7 × 10⁻⁶ g ₀. The velocity and radius data show that at supercoolings above approximately 0.4 K, dendritic growth in SCN under microgravity conditions is diffusion limited. By contrast, under terrestrial conditions, dendritic growth of SCN is dominated by convection for supercoolings below 1.7 K. The theoretical and experimental Peclet numbers exhibit modest disagreement, indicating that transport theories of dendritic solidification required some modification. Finally, the kinetic selection role for dendritic growth, VR ²=constant, where V is the velocity of the tip and R is the radius of curvature at the tip, appears to be independent of the gravity environment, with a slight dependence on the supercooling.     

The modified quasi-chemical model: Part III. Two sublattices

The modified quasi-chemical model in the pair approximation for short-range ordering (SRO) in liquids is extended to solutions with two sublattices. Short-range ordering of nearest-neighbor pairs is treated, and the effect of second-nearest-neighbor (SNN) interactions upon this ordering is taken into account. The model also applies to solid solutions, if the number of lattice sites and coordination numbers are held constant. It may be combined with the compound-energy formalism to treat a wide variety of solution types. A significant computational simplification is achieved by formally treating the nearest-neighbor pairs as the “components” of the solution. The model is applied to an evaluation/optimization of the phase diagram of the Li,Na,K/F,Cl,SO₄ system.     

Niti and NiTi-TiC composites: Part III. shape-memory recovery

The transformation behavior of near-equiatomic NiTi containing 0, 10, and 20 vol pct TiC particulates is investigated by dilatometry. Undeformed composites exhibit a macroscopic transformation strain larger than predicted when assuming that the elastic transformation mismatch between the matrix and the particulates is unrelaxed, indicating that the mismatch is partially accommodated by matrix twinning during transformation. The thermal recovery behavior of unreinforced NiTi which was deformed primarily by twinning in the martensite phase shows that plastic deformation by slip increases with increasing prestrain, leading to (1) a decrease of the shape-memory strain on heating, (2) an increase of the two-way shape-memory strain on cooling, (3) a widening of the temperature interval over which the strain recovery occurs on heating, and (4) an increase of the transformation temperature hysteresis. For NiTi composites, the recovery behavior indicates that most of the mis-match during mechanical deformation between the TiC particulates and the NiTi matrix is relaxed by matrix twinning. However, some relaxation takes place by matrix slip, resulting in the following trends with increasing TiC content at constant prestrain: (1) decrease of the shape-memory strain on heating, (2) enhancement of the two-way shape-memory strain on cooling, and (3) broadening of the transformation interval on heating. K.L. FUKAMI-USHIRO, formerly Graduate Student, Department of Materials Science and Engineering, Massachusetts Institute of Technology     

Nuclear cardiology, Part III: Scintigraphic evaluation of cardiac perfusion

OBJECTIVE: After reading Part III of this series of nuclear cardiology articles, the technologist should be able to: (a) compare and contrast radiopharmaceuticals used for myocardial perfusion imaging; (b) describe imaging protocols used for detecting coronary artery disease; and (c) describe imaging patterns seen following reconstruction of myocardial images.     

Characteristics of lath martensite: Part III. Some theoretical considerations

Using newly available experimental information, the phenomenological crystallographic theory of martensite transformations has been applied to lath martensite. Experimental observations on the habit plane, orientation relationship, and the interface dislocations are in agreement with the theory using the Bain strain and two lattice invariant shears, one on (lll)[?101]_f and the other on (100)[0?11]_f. The theoretical approach is based on the maintenance of a glissile interface when experimentally observed misfit dislocations are incorporated in the experimental habit plane. The predicted shape deformation magnitude is 0.96, which is comparatively quite large, but because of extensive accommodation deformation in the martensite, the experimentally observed shape strain magnitude may be considerably smaller than the true value. The large martensite shape deformation appears to be responsible for the intrinsic lath morphology and the restricted growth of the martensite in a direction parallel to the shape deformation. The high density of dislocations in the laths probably arises because of accommodation distortion. Theory predicts a highly coherent martensite/austenite interface consisting of one set of steps on (lll)_f with associated dislocations and one set of screw dislocations in the direction [0?11]_f.     

Advanced Solute Conservation Equations for Dendritic Solidification Processes Part II: Numerical Simulations and Comparisons

The mathematical model of derived solute equations in part I for equiaxed dendritic solidification with melt convection streams and interdendritic thermo‐metallurgical strain is applied numerically to predict macrosegregation distributions with different diffusing mechanisms in dendritic solid. Numerical and experimental results are present for solidification of a Al–4.5% Cu alloy inside horizontal rectangular cavity at different superheats. The numerical simulations were performed by using simpler method developed by Patanker. The experiments were conducted to measure the cooling curves via thermocouples and the metallurgical examinations to measure the grain size and macrosegregation distributions in Part I. Preliminary validity of the model is demonstrated by the qualitative and quantitative agreements between the measurements and predications of cooling curves and predicted macrosegregation distributions including mushy permeability and interdendritic strain. In addition, several important features of macrosegregation in equiaxed dendritic solidification are identified through this combined experimental and numerical study. Also, quantitative agreements between the numerical simulations and experiments reveal several areas for future research work. The differences and errors between predicted macrosegregation results under different diffusing mechanisms have been discussed.     

Growth of ternary composites from the melt: Part I

A simple constitutional supercooling analysis is given for predicting interface stability in plane front solidification of ternary alloys containing one, two, or three phases. It is concluded that polyphase composites can be grown from ternary alloys by plane front solidification provided thermal gradient is sufficiently high, growth rate is low, convection is low and kinetic undercooling is small. Calculated examples of conditions required for stability are given for three-phase alloys from the aluminum-rich corner of the Al-Cu-Ni system. It is seen that the most stable compositions (with respect to interface breakdown) lie nearly, but not exactly, on lines of two-fold saturation. Formerly Research Assistant, Massachusetts Institute of Technology, Cambridge, Mass.     

Growth of ternary composites from the melt: Part II

Ternary alloys from the aluminum-rich corner of the Al-Cu-Ni system were unidirectionally solidified under a wide variety of growth conditions. Plane front solidification was achieved at sufficiently high thermal gradients and slow growth rates. Conditions necessary to cause planar interface breakdown in both two and three phase alloys compare well to those predicted by a simple constitutional supercooling criterion. Nonplanar microstructures obtained were cellular or dendritic and both single phase and two phase dendrites were observed. Microstructures of specimens solidified with planar and nonplanar fronts are discussed in terms of the ternary phase diagram and the solute “diffusion paths.” Formerly Research Assistant, Massachusetts Institute of Technology, Cambridge, Mass. 02139     

Modeling of mechanical alloying: Part III. Applications of computational programs

The computational modeling programs described in part II of this series are used in two ways. One is to compare program predictions to previous experimental data, thereby testing to some extent the utility of the programs. At this stage of their development, program “predictions” with respect to processing time, microstructural scale, and similar parameters are accurate to within a factor of 2 or so. Even so, the predictions offer support of the model developed in part I of this series and provide a vehicle for both model and process refinements. In addition to “testing” the model and the program in these manners, the effect of uncertainty in input material properties on program predictions is explored. Formerly Graduate Student, Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903 Formerly Professor, Department of Materials Science and Engineering, University of Virginia