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We study the dynamics and morphology of grain growth with anisotropic energy and mobility of grain boundaries using a generalized phase field model. In contrast to previous studies, both inclination and misorientation of the boundaries are considered. The model is first validated against exact analytical solutions for the classical problem of an island grain embedded in an infinite matrix. It is found that grain boundary energy anisotropy has a much stronger effect on grain shape than that of mobility anisotropy. In a polycrystalline system with mobility anisotropy, we find that the system evolves in a non-self-similar manner and grain shape anisotropy develops. However, the average area of the grains grows linearly with time, as in an isotropic system. The effect of anisotropy in energy and mobility of grain boundaries on the kinetics of grain growth and morphological evolution is a relatively unexplored problem. Studies have shown that energy and mobility of a grain boundary depend on the misorientation between the two crystals and the inclination of the grain boundary [1]. In addition, phenomena as segregation of impurities [2] or presence of a liquid phase [3] at the grain boundaries may also result in anisotropy of both energy and mobility.Although most computer simulations of grain growth have been performed for isotropic cases [4][5][6][7][8], anisotropy in grain boundary properties has been introduced in a number of simulations, mainly by the Monte Carlo method [9][10][11][12][13][14][15]. For example in the study of texture development during grain growth [9][10][11], grains are divided into two types and the contacts between them form three kinds of grain boundaries of either small or large misorientations. To take into account the full range of grain orientations, more general approaches have been proposed [12][13][14][15]. However, all these models consider either misorientation or inclination dependence of grain boundary properties. A simple dislocation model of the grain boundary shows that both energy and mobility of the boundary could depend strongly on both misorientation and inclination [16]. Furthermore, in the models that deal with inclination dependence [14,15] only a few inclinations are considered and the use of only first neighbors for the calculation of boundary inclination results in an intrinsic energy and mobility anisotropy associated with the discrete lattice used in the simulations [17].In this paper, to study the kinetics and morphology of grain growth in anisotropic systems, we extend the phase field approach to take into account both inclination and misorientation dependence of grain boundary energy and mobility. The phase field method has been successfully applied for computer simulation of isotropic grain growth [7,8], phase transformations [18], and solidification [19]. In this model, the polycrystalline microstructure is described by a set of non-conserved order parameter fields (η 1 , η 2 , . . . , η p ), each representing grains of a given crystallographic orientation. Mic...

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In a study of the influence of ZrB 2 additions on the irreversibility field, µ ο H irr and the upper critical field B c2 , bulk samples with 7.5 at. % ZrB 2 additions were made by a powder milling and compaction technique. These samples were then heated to 700-900 o C for 0.5 hours. Resistive transitions were measured at 4.2 K and µ ο H irr and B c2 values were determined. An increase in B c2 from 20.5 T to 28.6 T and enhancement of µ ο H irr from 16 T to 24 T were observed in the ZrB 2 doped sample as compared to the binary sample at 4.2 K. Critical field increases similar to those found with SiC doping were seen at 4.2 K.At higher temperatures, increases in µ ο H irr were also determined by M-H loop extrapolation and closure. Values of µ ο H irr which were enhanced with ZrB 2 doping (as compared to the binary) were seen at temperatures up to 34 K, with µ ο H irr values larger than those for SiC doped samples at higher temperatures. The transition temperature, T c , was then measured using DC susceptibility and a 2.5 K drop of the midpoint of T c was observed. The critical current density was determined using magnetic measurements and was found to increase at all temperatures between 4.2 K and 35 K with ZrB 2 doping. by an in-situ reaction of a stoichiometric mixture of 99.9 % pure Mg and amorphous B powders with a typical size of 1-2 µm. Powders were mixed in SPEX mill for 48 mins. KeywordsDoping was achieved by adding 7.5 mol% of ZrB 2 (from Alfa Aesar) prior to the mixing.Powders with SiC were doping were also fabricated for comparison. The milled powder was then compacted in the form of a cylindrical pellet in a steel die. These pellets were heat-treated in a steel holder, encapsulated in a quartz tube under 200 torr of Ar. Details of the sample composition, and heat-treatment are given in Table I. After sintering at temperatures of from 700-900 deg C for 0.5 hours, the cylindrical pellets were reshaped into cuboids for property measurements.Magnetization measurements were performed from 4.2 K to 40 K on these samples using a vibrating sample magnetometer (VSM) with field sweep amplitude of 1.7 T and a sweep rate of 0.07 T/s. Susceptibility, χ dc, vs. temperature, T measurements were performed using a 50 mT field sweep amplitude after initial zero field cooling.Magnetically determined critical current density, J c, at various temperatures was extracted from the magnetization loop using the Bean model 15 .At 4.2 K, µ o H irr , and B c2 were determined by resistive transitions with applied field, with the measurements being performed at the National High Magnetic Field Laboratory (NHMFL) Tallahassee. A four point resistance measurement was performed, using silver paste to connect the leads, and the distance between the voltage taps was 5mm. The applied current was 10 mA, and current reversal was used. All measurements were made at 4.2 K in applied fields ranging from 0 to 33 T. The samples were placed perpendicular to the applied field, values of µ 0 H irr and B c2 being obtained taking the 10%and 90%...

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The symmetry of a crystal has profound effects on its physical properties and so does symmetry-breaking on the characteristics of a phase transition from one crystal structure to another. For an important class of smart materials, the ferroics, their functionality and performance are associated with cycles of transitions from multiple structural states of one phase to those of the other. Using group and graph theories we construct phase transition graph (PTG) and show that both the functionality and performance of ferroics are dictated by the topology of their PTGs. In particular, we demonstrate how the giant piezoelectricity in ferroelectrics and the functional fatigue in shape memory alloys (SMAs) are related to their unique PTG topological features. Using PTG topology as a guide, we evaluate systematically new systems potentially having giant piezoelectricities and giant electro-and magneto-strictions and discuss the design strategies for high performance SMAs with much improved functional fatigue resistance.

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