J. E. Morral

Particle coarsening in binary and multicomponent alloys

The theory of particle coarsening (Ostwald ripening) for multicomponent alloys was reviewed recently by Umantsev and Olson. In addition, they presented their own formulation for systems with a diagonal diffusivity matrix and they discussed how coarsening is affected by non-ideal behavior of the solid solution surrounding the precipitate particles. The present communication extends their work to include off diagonal terms in the diffusivity and shows that coarsening is independent of the solid solution thermodynamics followed by the continuous phase. This independence was recognized before, because changes in the diffusivity due to non-ideal behavior are balanced by changes in the concentration differences, due to surface curvature, that drive diffusion.

A PHASE FIELD STUDY OF MICROSTRUCTURAL CHANGES DUE TO THE KIRKENDALL EFFECT IN TWO-PHASE DIFFUSION COUPLES

The phase field method was used to simulate the interdiffusion in ternary, two-phase diffusion couples. Model γ+γ′ alloys were designed so that changes in the microstructure could be attributed to either coarsening or the Kirkendall effect. For the model parameters adopted in the study, particle coarsening increased the average precipitate size, but it had little influence on the diffusion path. However, the Kirkendall effect, which was introduced by setting atomic mobilities to different values, changed the diffusion path slope and led to the formation of “horns” on the two-phase diffusion path. Although the results obtained were somewhat dependent on the model parameters, they demonstrate the value of the phase field method when studying complex interdiffusion problems.

A local equilibrium model for internal oxidation

Alloys that are internally oxidized under conditions of local equilibrium have concentration profiles that must satisfy certain conditions. These conditions are outlined in general and then illustrated with an error function model that assumes a constant effective diffusivity in the oxidized region and a linear variation of oxide solubility with concentration. The error function model is different from previous error function models in that it satisfies all of the local equilibrium conditions. A numerical example is given to illustrate predictions of the model. The model predictions include that the average concentration of the solute (oxidized solute) in the internal oxidation region will always be less than the initial concentration of solute in the alloy, that the average concentration of solute decreases with increasing solute diffusivity, and that the concentration of solute at the moving boundary between the internal oxidation region and unoxidized region approaches the initial alloy concentration as the solubility product and solute diffusivity approach zero.

Application of commercial computer codes to modeling the carburizing kinetics of alloy steels

When steels remain single phase during carburizing, it is well known how to model their carburizing kinetics with finite difference and finite element computer codes . [1-41 In addition to writing original computer codes, investigators can apply commercial codes for heat-transfer analysis by making the following substitutions: tSl carbon concentration for temperature, diffusivity of carbon for thermal conductivity, and the integer one for the product of density and specific heat. In this case, the only property data needed are the carbon diffusivity vs carbon concentration and information about the boundary conditions (e.g. , constant concentration at the surface). When alloy steels form carbides in the carburized zone, for example, as occurs in M50NiL, t61 the same computer codes can be applied except that additional physical property data are needed. The following work describes the data that are needed, indicates how the data are entered in heat-transfer programs, and suggests a method for obtaining the data from a single carburizing experiment. The basis for modeling multicomponent, multiphase carburizing is the following mass balance equation which states that the total carbon (carbide plus matrix carbon) in a differential volume element, ct~ ~ changes with time, t, according to the divergence of the carbon flux:

Application of the square root diffusivity to diffusion in Ni-Cr-Al-Mo alloys

The square root diffusivity matrix [r] and diffusivity matrix [D] have been measured for a Ni-4.0 at. pct Cr-6.3 at. pct Al-3.5 at. pct Mo quaternary alloy at 1100 °C. Using a constant diffusivity analysis, the diffusivities were obtained from three diffusion couples having small initial concentration differences of 5 at. pct or less. When elements of [r] were substituted into the error function solution of the diffusion equation, it was found that the predicted concentration profiles were accurate to within ±0.1 at. pct of measured values. Also, it was found that Mo tends to reduce the diffusion kinetics of Cr and Al in Ni-base alloys. These results suggest that these methods of analyzing diffusion data and predicting interdiffusion data can be applied to alloys containing more than four components.

Application of the square root

The square root diffusivity matrix [r] and diffusivity matrix [D] have been measured for a Ni-4.0 at. pct Cr-6.3 at. pct Al-3.5 at. pct Mo quaternary alloy at 1100 °C. Using a constant diffusivity analysis, the diffusivities were obtained from three diffusion couples having small initial concentration differences of 5 at. pct or less. When elements of [r] were substituted into the error function solution of the diffusion equation, it was found that the predicted concentration profiles were accurate to within ±0.1 at. pct of measured values. Also, it was found that Mo tends to reduce the diffusion kinetics of Cr and Al in Ni-base alloys. These results suggest that these methods of analyzing diffusion data and predicting interdiffusion data can be applied to alloys containing more than four components.

The effect of composition on marker movement and kirkendall porosity in ternary alloys

A linear model which predicts Kirkendall marker movement in multicomponent diffusion couples has been tested with a series of Ni-Cr-Al γ-phase alloys. The test results followed the model to within experimental scatter, even though the model assumes constant diffusivity in the reaction zone. Comparing the model predictions with previous work suggests that the model can be used in alloy design to eliminate Kirkendall porosity. In addition, preliminary results suggest that the coefficients of the model can be predicted with useful accuracy from fundamental diffusion data.

A model for the Kirkendall effect

Abstract A model is proposed which predicts that Kirkendall marker movement is a linear function of alloy composition. The model assumes that concentration gradients and intrinsic diffusivities at the Kirkendall plane are similar to those at the Matano plane; and that concentration gradients can be approximated by referring to a constant diffusivity system. The physical constants in the model are functions of intrinsic diffusivities and square root diffusivities. The model suggests how Kirkendall porosity can be reduced or eliminated in ternary and higher order alloys by proper alloy selection.

Effect of Hot-Dip Silicon-Aluminizing on the Anti-Carburization Behavior of High-Temperature-Resistant Steel HK40

High-temperature-resistant (HTR) austenitic steel HK40 is employed for being silicon-aluminized by being hot-dipped in molten aluminum and silicon alloys and diffused subsequently at 1200°C. The phases, microstructures and concentration for elements of interest in the treated case are investigated by x-ray diffraction (XRD), optical microscopy (OM), scanning electron microscopy (SEM) and energy dispersive spectrum of x-ray (EDS). The case composes of three main zones: the former hot-dipped coating zone, inter-diffusion zone, and diffusion zone of Al and Si, all of which contain quite higher contents of aluminum and silicon than substrate. Pack-carburization is used for assessing the anti-carburization behavior of the treated case. The treated case shows excellent property in hindering the inward-diffusion of carbon, even if the former hot-dipped coating zone spalls off with only diffusion zone left. High contents of aluminum, silicon and oxygen are still detected on surface of the silicon-aluminized specimen after carburization. Good anti-carburization ability of the silicon-aluminized specimen is believed mainly to be the result of the dense and stable Al2O3 and SiO2 films formed on the surface.

Databases for Computational Thermodynamics and Diffusion Modeling

Databases for computational thermodynamics and diffusion modeling can be applied to the prediction of phase diagrams and microstructural evolution. These predictions can be used for alloy and process design, as well as to improve modeling capabilities that would decrease the time for new alloy and process development. Databases that are currently available to scientists, engineers, and students need to be expanded and improved. Accordingly, a workshop was held March 21–22, 2002, to identify the database and information delivery tool needs of industry and education. As a result of the workshop a roadmap was developed to show how these needs can be met during the next decade in a cost-effective way through expanded collaborative efforts in education, basic research, and database development. The workshop consisted of a series of invited talks given to the group as a whole followed by general discussions of needs and benefits, and the construction of a roadmap of future activities. A brief report of a follow-up meeting held on May 27, 2003, is given in the Appendix.