The effect of composition on the time-dependent nucleation rates in Zr65Al7.5Ni10CU17.5 glasses is investigated to better understand nucleation processes in partitioning systems. Asquenched glasses were annealed to produce a homogeneous dispersion of nanocrystals within the amorphous matrix. The nucleation rates were estimated from the number of crystallites produced as function of annealing time, using scanning and transmission electron microscopy. Experimental results for single and multiple-step annealing treatments are presented. The nucleation results are discussed briefly within the time-dependent model of the classical theory of nucleation.

Most of the physical properties of systems underlying first order phase transitions, I. e. the scattering properties, can be obtained from the spatial correlation functions. For the case of nucleation and growth kinetics it is possible to obtain all the correlation functions from the particle size distribution. In this paper we obtain the spatial correlation functions corresponding to several kinetics; in particular the correlation functions corresponding to the microstructure developed in partitioning transformations are obtained.

In principle, Kinetic Lattice Monte Carlo (KLMC) methods can accurately simulate the precipitation of coherent phases by tracking the motion of a vacancy and the corresponding diffusion and clustering of solutes. The fidelity of the KLMC simulations depends primarily on the validity of the assumed interatomic potentials. These potentials must provide accurate solute-solute-solvent-vacancy energetics over the length scales relevant to the physical decomposition paths. Of course, simulating long range strain energy interactions is the biggest challenge, but the significance of this contribution is less in systems manifesting primarily dilational strains. Simple nearest neighbor (NN) potentials, used in previous KLMC of decomposition kinetics of dilute Fe-Cu alloys are generally not able to reproduce alloy property combinations like vacancy formation energies, dilute heats of solution and the coherent interface energies. Further, solute diffusion in bcc alloys requires jumps between first and second nearest neighbors, and is governed by, at minimum, at least three independent jump frequencies. The jump frequencies are controlled by the binding energies of atoms out to at least second nearest neighbor positions (which are only about 15% further away from the solute than the first nearest neighbor) and are also influenced by solute-modified saddle point activation energies. Thus longer range multiatom embedded-atom-method (EAM) type potentials can, in principle, provide a more realistic simulation of diffusion and solute clustering compared to NN based models. However, this refinement comes at a much higher computational cost. While they cannot be directly compared, this study presents KLMC results for both a simplified EAM versus a NN potential, and describes important new mechanistic insight provided by these atomistic simulations.

The diffusion process at a temperature just below the glass-transition temperature is studied in a computer model of amorphous Ni81B19. The observed diffusion events cause structural changes that are highly localized and are correlated with low-frequency localized vibrational modes. The excitation of such a mode can result in a “jump”, which is identical to the diffusion event. The jump has a cooperative character involving some tens of atoms and can be of a reversible or of an irreversible nature.

The mechanism of formation of a chessboard-like structure observed during coherent decomposition in alloys with several orientation variants of the precipitate phase is considered. It is based on the accommodation of coherency strain achieved by spatial rearrangement of orientation variants of the precipitate phase in an optimal pattern. The computational model of precipitation of the ordered tetragonal phase, based on the continuum stochastic field kinetic equations for the composition and lro parameters profiles, is formulated. Its numerical solution describes the spatial and temporal evolution of the microstructure, from nucleation to coarsening. It is shown that the chessboard-like microstructure is produced by strain-driven, self-assembling of orientation variants of the precipitate phase, faceted by the planes normal to the elastically soft directions. Coarsening of such microstructures occurs by consequent disappearance of entire rows of “tiles” in the pattern.

The influence of an applied uniaxial compressive stress on the coarsening of γ′ (Ni3A1) precipitates at 640°C in a Ni-13.36 at. % Al alloy was studied experimentally. The investigation was done using cylindrical doubly-tapered monocrystalline specimens with axes of revolution parallel to [100]. At an applied load of 940 N the compressive stress varied from ∼30 to ∼130 MPa in any given specimen. Over this range of stresses the strain was primarily elastic. Dark-field transmission electron microscopy, coupled with image-analysis software, was used to characterize evolution of the γ′ precipitate morphology, and the kinetics of coarsening in (100) were investigated for aging times up to 504 h. We find, quite unexpectedly, that the relationship between the kinetics of coarsening and the applied stress is not monotonic. Instead, a maximum in the coarsening rate obtains at an intermediate stress, in the neighborhood of 55 ± 10 MPa. Theoretical work by Johnson predicts that for certain combinations of lattice and elastic-constant mismatch, an extremum of the solubility limit exists in elastically isotropic specimens aged under uniaxial stress. The theory is not sophisticated enough to enable a quantitative comparison with experimental results, but provides some rationale for our unexpected finding.

Recent work has suggested that vibrational effects can play a significant role in determining alloy phase equilibria. In order to better understand these effects and the methods used in their calculation, we investigate the vibrational properties of disordered Ni3A1 using the Embedded-Atom Method. We examine the effectiveness of the Special Quasirandom Structure (SQS) approximation, and find that an SQS-8 can accurately represent the vibrational thermodynamics of the disordered state. By the use of Monte Carlo (MC) techniques, we also find that the quasiharmonic approximation becomes less accurate as we approach the melting temperature, but that the accuracy may be extended to higher temperatures by resorting to the MC equation of state giving the specific volume as a function of temperature.

Iron oxides and oxyhydroxides are widespread in nature. Understanding the thermodynamic properties of the transformation in the iron oxide/hydroxide system permits the characterization of numerous geochemical processes including weathering, soil chemistry, and diagenesis in continental and oceanic environments. The aim of this study is to measure the energetics of a series of metastable oxides and oxyhydroxides in order to determine the effects of polymorphism, of oxidation state and of hydration. High temperature solution calorimetry using sodium molybdate as a solvent and transposed temperature drop calorimetry at 979 K were used.

Enthalpies of formation from the elements of the metastable iron oxides and oxyhydroxides were calculated from the measured values of the enthalpies of drop solution. The experiments allow an estimate of the enthalpy of formation from the elements of γFe2O3 (−817.4 ± 1.2 kJ/mol for sample with tetragonal symmetry and −816.9 ± 1.2 kJ/mol for sample with cubic symmetry) and β-FeOOH (−561.3 ± 3.1 kJ/mol) which are currently unavailable in the literature.

The stability of the structure depends mostly on the degree of hydration and on the average oxidation state of iron. It depends less strongly on the topology of the structure itself and of the tunnel anion.

The self-diffusion constants for the monovacancy mechanism in the 5d transition-metals with bcc structure (β-Hf, Ta and W) are investigated by first-principles pseudopotential calculations within the framework of the Local Density Functional Theory. The formation and migration energies, calculated for relaxed configurations using supercells containing 27 and 54 atomic sites, are in quite good agreement with experimental data in Ta and W, with a discrepancy lower than 10 %. Preliminary results in β-Hf using smaller supercells suggest very large relaxation energies. The effect of finite electron-temperature is shown to be quite important, and very different from one element to the other: the electron contribution to the activation entropy is negative in Ta and positive in W, reaching respectively −2 kB and 2 kB at the melting temperature. Using simple estimates for the attempt frequencies and the vibrational formation entropies, the calculated self-diffusion coefficient is in exceptional agreement with experiments in W, and clearly reproduces an accelerated diffusivity in Ta.

The strength of nickel-base superalloys hardened through precipitation is related to the volume fraction, particle size and distribution of the precipitate phase γ′: Ni3(Al,Ti). Such particles grow during the initial heat treatment and for long aging times, and it is very important to predict the kinetics growth owing to its technological application at high temperatures. In this work, we performed the analysis of the particle coarsening in IN-713C during long aging times at constant temperature (T=1223K), given an initial size, the volume fraction distribution of the γ′ precipitate phase, the evaluation of two different heat treatments through the microstructure analysis and γ′ morphology and tensile properties between 873–1123K. We found that for short aging times, t < 9×106s, the coarsening can be approximated by a linear volumetric growth as predicted by LSW theory. For a time greater than 9×106s the growth rate of γ′ precipitate shows an asymptotic behavior in both heat treatments.

On the basis of the discrete phase field method where the difference expression of non-linear kinetic equation, the composition dependencies of the atomic interchange energy and the inhomogeneous elasticity are taken into consideration so as to be applicable for the real alloy system. The phase decomposition and the microstructure formation are computer simulated for the Fe-Al- Co ternary ordering alloy by utilizing the thermodynamic data.

Ordering in CuAu3 was investigated by residual resistivity and X-ray scattering. L12 longrange ordering (LRO) in this alloy is quite sluggish, therefore for low quenching temperatures and sufficiently short annealing times only effects of short-range order (SRO) are observed. With increasing quenching temperature and/or increasing annealing time evolution of LRO was observed by both residual resistometry and X-ray scattering. From the resistivity measurements information can be gained on the boundaries of the order-disorder two-phase field. An analysis of SRO-relaxation yields an ordering activation energy of 2.1±0.1 eV.

The microstructure developed in primary crystallizations is studied under realistic conditions. The primary crystallization of an amorphous alloy is modeled by considering the thermodynamics of a metastable phase transition and the kinetics of nucleation and crystal growth under isothermal annealing. A realistic growth rate, including an interface controlled growth at the beginning of the growth of each single grain and diffusion controlled growth process with soft impingement afterwards is considered. The reduction in the nucleation rate due to the compositional change in the remaining amorphous matrix is also taken into account. The microstructures developed during the transformation are obtained by using the Populational KJMA method, from the above thermodynamic and kinetic factors. Experimental data of transformed fraction, grain density, average grain size, grain size distribution and other related parameters obtained from annealed metallic glasses are modeled.

We present results concerning the study of growth and coarsening kinetics of ordered domains in a binary alloy exhibiting a B2 ordering at the stoichiometric composition. This study has been performed within the framework of an atomistic kinetic model based on vacancy migration using Monte Carlo simulations techniques. Contrary to the standard Lifshitz-Allen-Cahn law, it is observed that the coarsening exponent is a function of the annealing temperature, and also of parameters controlling the migration of the vacancy.

A large kinetics hysteresis is found to exist between the forward and backward reactions of the L12 ↔ DO19 transformation in Fe3Ge. The slow DO19 to L12 transformation leaves behind very stable twins and stacking fault debris. In-situ annealing experiments in the transmission electron microscope revealed that nucleation for the reverse L12 to DO19 reaction takes place efficiently at these defects.

Pronounced nonlinear enhancements in dielectric responses and decreases in phase transformation temperatures were induced under moderate ac fields and high field cycling for La modified lead zirconate titanate (PZT) ceramics. Polarization disordering could be inhibited by introducing acceptor dopants into La modified PZT compositions and by DC bias field. Analysis of the frequency dispersion revealed that the field driven transformation in lower La content PZT is a field assisted activation process, while the transformation in higher La content PZT relaxors is intrinsically a thermal activated process.

The effect of thermal cycling under a constant tensile load on the transformation temperatures (TTs) of NiTi-based shape memory alloys (SMAs) is investigated. Three SMAs are examined in this study: a near equiatomic binary Ni49Ti51 alloy and two ternary Ni49Ti51-xHfx alloys with 1 at% and 3 at% Hf. The SMAs are in the form of wires with 40% cold work (reduction in area) and heat treated between 300°C and 600°C. These SMA wires are thermally cycled between their martensite (M) and austenite (A) phases for 100 cycles under an axial tensile stress of 206.8MPa (30Ksi) in air. Results show that the effect of thermal cycling on the M and A TTs depends on heat treatment (HT) temperature and composition in a complex manner. For example, the M TT, of the binary NiTi SMA heat treated between 300°C and 450°C, increases during thermal cycling. However, with HT temperatures between 500°C and 600°C, the M TIT decreases slightly during thermal cycling. For the NiTi-based SMAs that contain 1 at% and 3 at% Hf, the M TT increases during thermal cycling for HT temperatures up to 500°C, and the M TT decreases during thermal cycling when heat treated at 600°C. These results are due to changes in internal stress and structure, such as dislocation density and arrangement, which are affected by HT temperature and thermal cycling. The influence of Hf content on the changes in the M and A TTs during thermal cycling is also shown.

The morphology and its evolution of a single coherent precipitate was investigated using the Cahn-Hilliard equation and Khachaturyan's continuum elasticity theory for solid solutions. A cubic solid solution with negative elastic anisotropy and isotropic interfacial energy was considered. The lattice mismatch between the precipitate and the matrix was assumed to be purely dilatational and its compositional dependence obeys the Vegard's law. Both two- and three-dimensional systems were studied. The Cahn-Hilliard equation was numerically solved using a semi-implicit Fourier-spectral method. It was demonstrated that, with increasing elastic energy contribution, the equilibrium shape of a coherent particle gradually changes from a circle to a square in two dimensions, and from a sphere to a cube in three dimensions, and the composition profile becomes increasingly inhomogeneous within the precipitate with the minimum at the center of the particle, consistent with previous theoretical studies and experimental observations. It was also shown that, with sufficiently large elastic strain energy contribution, a coherent particle may split to four particles from a square, or eight particles from a sphere, during its evolution to equilibrium. For both two and three dimensions, the splitting starts by nucleating the matrix phase at the center of the particle.

Models that describe hardness of materials do not account for stress-induced phase transformations that occur under sharp indenters. However, experimental work shows that some materials can be transformed under the indenter into new, high-pressure phases with properties that differ significantly from those of the pristine material. In particular, semiconductors (Si, Ge and other) experience Herzfeld-Mott transition (metallization). Significant volume changes can accompany these transformations. In the present paper, Tanaka's model [1] has been modified to account for reversible phase transformations under contact loading.

We report on large-scale three-dimensional simulations of phase separation in model binary alloy systems in the presence of elastic fields. The elastic field has several important effects on the morphology of the system: the ordered domains are subject to shape transformations, and spatial ordering. In contrast to two-dimensional system, no significant slowing down in the growth is observed. There is also no evidence of any “reverse coarsening” of the domains.