Ursula R. Kattner

Development of a diffusion mobility database for Ni-base superalloys

Abstract For the fcc phase of the Ni–Al–Co–Cr–Hf–Mo–Re–Ta–Ti–W system, diffusion data in various constituent binary systems were assessed to establish a multicomponent diffusion mobility database. The diffusion assessment relied on an existing thermodynamic database for the calculation of needed thermodynamic factors. The mobilities determined for the self-diffusion of the components in the fcc phase (a metastable state for some components) were consistent with the correlation of the diffusivity with the melting point. The general agreement of calculated and measured diffusion coefficients in the Ni–Co–Cr–Mo and Ni–Al–Cr–Mo quaternary systems demonstrated the ability of the database to extrapolate to higher order systems. Finally, the mobility database, in conjunction with an available thermodynamic database and a finite-difference diffusion code, was used to simulate a multicomponent diffusion couple between two commercial Ni-base superalloys.

On the Sn-Bi-Ag ternary phase diagram

The selection and evaluation of Pb-free solders requires information that is best determined through a knowledge of ternary and higher order phase diagrams. As part of an ongoing program on Pb-free solder phase diagrams at the National Institute of Standards and Technology, a thermodynamic model is formulated for the Sn-Bi-Ag phase diagram. Thermodynamic functions for the various phases obtained by fitting measured data for the three constituent binary systems are extrapolated to the ternary system using the method of Muggianu. Modeling results are compared to preliminary experimental data for the ternary system and are applied in the calculation of the solidification path.

DTA AND HEAT-FLUX DSC MEASUREMENTS OF ALLOY MELTING AND FREEZING

Publisher Summary This chapter focuses on differential thermal analysis (DTA) and heat-flux differential scanning calorimetry (HF-DSC) of metals and alloys. A thermal analysis guide focused only on metals and alloys is appropriate because metals and alloys behave quite differently from molecular materials such as polymers and organics. Freezing and melting occur rapidly in response to changes in temperature compared to other materials. Melting and freezing transformations, once initiated, take place within, at most, a degree of local thermodynamic equilibrium. Therefore, the chapter also focuses on melting and solidification behavior because special methods can be employed that are not necessarily useful for a broader class of materials and processes. The chapter intends to provide the thermal analysis user with the considerations that are necessary for proper sample preparation and to illustrate how the sample characteristics influence the proper interpretation and analysis of measurements. The chapter describes different types of information usually sought from DTA/HF-DSC during the melting and freezing of alloys. The details of instruments, operation and calibration are described. The goal is to describe the thermal lags between the sample and sample thermocouple that must be understood to enable good analysis of data. The chapter also details the response of the DTA to binary and ternary alloys, respectively.

A thermodynamic description of the TiAl system

Abstract A thermodynamic description of the TiAl system was developed in this study. Nine phases were considered and can be classified as three types — disordered solution phases: liquid, (αTi, hcp), (βTi, bcc), (Al, fcc); ordered intermetallic phases: α 2 -Ti 3 Al (DO 19 ), γ-TiAl (L1 0 ), TiAl 3 (DO 22 ); and stoichiometric phases: TiAl 2 and Ti 2 Al 5 . While the Redlich-Kister equation was used to describe the excess Gibbs energy of the disordered solution phases, a generalized bond-energy model recently developed by us at the University of Wisconsin at Madison was used to describe the Gibbs energy of the ordered intermetallic phases. The model parameters were optimized using the experimental phase equilibrium and thermodynamic data available in the literature. The calculated phase diagram as well as the thermodynamic functions are in good agreement with experimental data. The intrinsic defect concentrations calculated from the model parameters for γ-TiAl were found to be in accord with those obtained from a semiempirical relationship in terms of its enthalpy of formation and the available experimental data. The generalized bond-energy model parameters for the ordered intermetallic phases were converted to those of the compound energy model for the convenience of the users of Thermo-Calc.

The stable and metastable Ti-Nb phase diagrams

The phase transformations which occur in the Ti-Nb binary alloy system have been discussed in two recent papers. The phase relationships were investigated by varying alloy composition and thermal history. In this paper, these results are summarized in complete and thermodynamically consistent calculations of the stable and metastable phase diagrams. The calculations of the metastable equilibria are relevant to the Ti-V and Ti-Mo systems, as well as to several other titanium and zirconium-based transition metal alloy systems.

Phase Diagrams for Lead-Free Solder Alloys

The need for new, improved solder alloys and a better understanding of reactions during the soldering process grows steadily as the need for smaller and more reliable electronic products increases. Information obtained from phase equilibria data and thermodynamic calculations has proven to be an important tool in the design and understanding of new lead-free solder alloys. A wide range of candidate alloys can be rapidly evaluated for proper freezing ranges, susceptibility to contamination effects, and reactions with substrate materials before the expensive process of preparing and testing candidate alloys is initiated.

Thermodynamic Assessment of the Co-Mo System

Experimental thermochemical and phase diagram data for the Co-Mo system were assessed. A consistent thermodynamic description, using a Redlich-Kister model for the solution phases and sublattice and line-compound models for the intermetallics, was obtained, and it agreed well with the critically evaluated experimental data. Several variations of the sublattice model for the σ and μ phases were compared with the traditional models used for these phases in other systems. Measured data indicate an abrupt decrease of the terminal Mo solubility in the fcc (Co) phase with decreasing temperature. This behavior was reproduced well by inclusion of the magnetic contribution to the Gibbs energy of the fcc phase. Addition of the magnetic term also led to the prediction of a fcc (Co) miscibility gap, and a high-temperature stability region of the paramagnetic cph (Co) phase.

A reassessment of the calculated Ni-Nb phase diagram

A revised calculation of the Ni-Nb (nickel-niobium) phase diagram includes realistic enthalpy of formation values for the intermetallic phases that compare with experimental values, a more accurate crystallographic description of the μ phase, and a better fit to the experimentally determined invariant equilibrium temperatures and liquidus-solidus boundaries between liquid and (Ni). The set of parameters describing the Gibbs energy of each phase is given.

Reactive Wetting and Intermetallic Formation

Despite its apparent simplicity, the spreading of molten solder on copper or on solder-coated copper to form a solder joint involves many complex physical processes. Poor solderability of electronic components, while infrequent in absolute numbers, can cause significant manufacturing difficulties when acceptable performance requires less than one failure in 106 joints. An assessment of solderability involves consideration of the entire soldering process including the details of the soldering equipment, the design of the joint geometry, and the wettability of the surfaces to be joined. Wettability involves consideration of the intrinsic rate and extent that solder can spread on a particular surface and is the primary focus of this chapter. Thus we need only consider macroscopically simple geometries of wetting; we will focus on the fundamental physical processes involved in solder wetting and spreading. The ultimate goal is to determine those processes that are most important in order to provide a scientific basis for the analysis of engineering problems in solder technology.

First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305 K), (0.50, 1850 K), and (0.50, 2830 K) without Fvib, and (0.40, 247 K), (0.50, 1620 K), and (0.50, 2600 K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric.