Effect of vacancy creation and annihilation on grain boundary motion.

Interaction of vacancies with grain boundaries (GBs) is involved in many processes occurring in materials, including radiation damage healing, diffusional creep, and solid-state sintering. We analyze a model describing a set of processes occurring at a GB in the presence of a non-equilibrium, non-homogeneous vacancy concentration. Such processes include vacancy diffusion toward, away from, and across the GB, vacancy generation and absorption at the GB, and GB migration. Numerical calculations within this model reveal that the coupling among the different processes gives rise to interesting phenomena, such as vacancy-driven GB motion and accelerated vacancy generation/absorption due to GB motion. The key combinations of the model parameters that control the kinetic regimes of the vacancy-GB interactions are identified via a linear stability analysis. Possible applications and extensions of the model are discussed.

Solidification of Ni-Re Peritectic Alloys.

Differential thermal analysis (DTA) and microstructural and microprobe measurements of DTA and as-cast Ni-Re alloys with compositions between 0.20 and 0.44 mass fraction Re provide information to resolve differences in previously published Ni-Re phase diagrams. This investigation determines that the peritectic invariant between liquid, Re-rich hexagonal close packed and Ni-rich face center cubic phases, L + HCP → FCC, occurs at 1561.1 °C ± 3.4 °C (1σ) with compositions of liquid, FCC and HCP phases of 0.283 ± 0.036, 0.436 ± 0.026, and 0.828 ± 0.037 mass fraction Re, respectively. Analysis of the microsegregation in FCC alloys yields a partition coefficient for solidification, k = 1.54 ± 0.09 (mass frac./mass frac.). A small deviation from Scheil behavior due to dendrite tip kinetics is documented in as-cast samples. No evidence of an intermetallic phase is observed.

Phase field modeling of electrochemistry. I. Equilibrium.

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-Hückel theories. We calculate the surface free energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.

Phase field modeling of electrochemistry. II. Kinetics.

The kinetic behavior of a phase field model of electrochemistry is explored for advancing (electrodeposition) and receding (electrodissolution) conditions in one dimension. We previously described the equilibrium behavior of this model [J. E. Guyer, W. J. Boettinger, J. A. Warren, and G. B. McFadden, Phys. Rev. E 69, 021603 (2004)]. We examine the relationship between the parameters of the phase field method and the more typical parameters of electrochemistry. We demonstrate ohmic conduction in the electrode and ionic conduction in the electrolyte. We find that, despite making simple, linear dynamic postulates, we obtain the nonlinear relationship between current and overpotential predicted by the classical "Butler-Volmer" equation and observed in electrochemical experiments. The charge distribution in the interfacial double layer changes with the passage of current and, at sufficiently high currents, we find that the diffusion limited deposition of a more noble cation leads to alloy deposition with less noble species.

Transformation of BCC and B2 High Temperature Phases to HCP and Orthorhombic Structures in the Ti-Al-Nb System. Part II: Experimental TEM Study of Microstructures.

Possible transformation paths that involve no long range diffusion and their corresponding microstructural details were predicted by Bendersky, Roytburd, and Boettinger [J. Res. Natl. Inst. Stand. Technol. 98, 561 (1993)] for Ti-Al-Nb alloys cooled from the high temperature BCC/B2 phase field into close-packed orthorhombic or hexagonal phase fields. These predictions were based on structural and symmetry relations between the known phases. In the present paper experimental TEM results show that two of the predicted transformation paths are indeed followed for different alloy compositions. For Ti-25Al-12.5Nb (at%), the path includes the formation of intermediate hexagonal phases, A3 and DO19, and subsequent formation of a metastable domain structure of the low-temperature O phase. For alloys close to Ti-25Al-25Nb (at%), the path involves an intermediate B19 structure and subsequent formation of a translational domain structure of the O phase. The path selection depends on whether B2 order forms in the high temperature cubic phase prior to transformation to the close-packed structure. The paper also analyzes the formation of a two-phase modulated microstructure during long term annealing at 700 °C. The structure forms by congruent ordering of the DO19 phase to the O phase, and then reprecipitation of the DO19 phase, possibly by a spinodal mechanism. The thermodynamics underlying the path selection and the two-phase formation are also discussed.

Transformation of BCC and B2 High Temperature Phases to HCP and Orthorhombic Structures in the Ti-Al-Nb System. Part I: Microstructural Predictions Based on a Subgroup Relation Between Phases.

Possible paths for the constant composition coherent transformation of BCC or B2 high temperature phases to low temperature HCP or Orthorhombic phases in the Ti-Al-Nb system are analyzed using a sequence of ciystallographic structural relationships developed from subgroup symmetry relations. Symmetry elements lost in each step of the sequence determine the possibilities for variants of the low symmetry phase and domains that can be present in the microstructure. The orientation of interdomain interfaces is determined by requiring the existence of a strain-free interface between the domains. Polydomain structures are also determined that minimize elastic energy. Microstructural predictions are made for comparison to experimental results given by Benderslcy and Boettinger [J. Res. Natl. Inst. Stand. Technol. 98, 585 (1993)].

X-ray magnifier.

A method for the magnification of x-ray radiographic images is described and demonstrated. This magnifier employs two successive asymmetric diffractions of an x-ray beam from highly perfect silicon crystals. The two diffractions magnify the beam in two perpendicular directions. A device with a magnification of 25x is demonstrated for Cu K(alpha) radiation. This device preserves and sometimes improves the resolution inherent in the radiographic technique. The x-ray magnifier is particularly useful in circumventing the relatively poor spatial resolution of electro-optical imaging systems needed for real-time observations. Basic limits on magnification and resolution using this method are described.