Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components epsilon(xx)*. and epsilon(yy)*. For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t = epsilon(yy)*/epsilon(xx)*. We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t = 1) and those with pure shear misfit (t = -1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (-1 < t < 1; t not equal 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0 < t < 1. For systems which allow an invariant line (-1 less than or equal to t < 0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0 < t less than or equal to 1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.

The orientational relaxation of bipolar active regions

In the mean, bipolar active regions are oriented nearly toroidally, according to Hale's polarity law, with a latitude-dependent tilt known as Joy's Law. The tilt angles of individual active regions deviate from this mean behavior and change over time. It has been found that on average the change is toward the mean angle at a rate characteristic of 4.37 days (Howard, 1996). We show that this orientational relaxation is consistent with the standard model of flux tube emergence from a deep dynamo layer. Under this scenario Joy's law results from the Coriolis effect on the rising flux tube (D'Silva and Choudhuri, 1993), and departures from it result from turbulent buffeting of the tubes (Longcope and Fisher, 1996). We show that relaxation toward Joy's angle occurs because the turbulent perturbations relax on shorter time scales than the perturbations from the Coriolis force. The turbulent perturbations relax more rapidly because they are localized to the topmost portion of the convection zone while the Coriolis perturbations are more widely distributed. If a fully-developed active region remains connected to the strong toroidal magnetic field at the base of the convection zone, its tilt will eventually disappear, leaving it aligned perfectly toroidally. On the other hand, if the flux becomes disconnected from the toroidal field the bipole will assume a tilt indicative of the location of disconnection. We compare models which are connected and disconnected from the toroidal field. Only those disconnected at points very deep in the convection zone a-re consistent with observed time scale of orientational relaxation.

An extended Cahn-Hilliard model for interfaces with cubic anisotropy

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

Temperature and density dependent solute vibrational relaxation in supercritical fluoroform

Temperature- and density-dependent vibrational relaxation data for the v6 asymmetric stretch of W(CO)6 in supercritical fluoroform (trifluoromethane, CHF3) are presented and compared to a recent theory of solute vibrational relaxation. The theory, which uses thermodynamic and hydrodynamic conditions of the solvent as input parameters, shows very good agreement in reproducing the temperature- and density-dependent trends of the experimental data with a minimum of adjustable parameters. Once a small number of parameters are fixed by fitting the functional form of the density dependence, there are no adjustable parameters in the calculations of the temperature dependence. © 2001 American Institute of Physics.

Equilibrium and relaxation in turbulent wakes

In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 103 momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.

Structural Relaxation and Crystallization in a Pd40Cu30Ni10P20 Bulk Metallic Glass

The stability of a Pd40Cu30Ni10P20 bulk metallic glass (BMG) against structural relaxation is investigated by isothermal and isochronal annealing heat treatments below and above its glass transition temperature, Tg, for varying periods. Differential scanning calorimetry (DSC) of the annealed samples shows an excess endotherm at Tg, irrespective of the annealing temperature. This recovery peak evolves exponentially with annealing time and is due to the destruction of anneal-induced compositional short range ordering. The alloy exhibits a high resistance to crystallization on annealing below Tg and complex Pd- and Ni-phosphides evolve on annealing above Tg.

Interaction anisotropy and shear instability of aspirin polymorphs established by nanoindentation

Nanoindentation is applied to the two polymorphs of aspirin to examine and differentiate their interaction anisotropy and shear instability. Aspirin provides an excellent test system for the technique because: (i) polymorphs I and II exhibit structural similarity in two dimensions, thereby facilitating clear examination of the differences in mechanical response in relation to well-defined differences between the two crystal structures; (ii) single crystals of the metastable polymorph II have only recently become accessible; (iii) shear instability has been proposed for II. Different elastic moduli and hardness values determined for the two polymorphs are correlated with their crystal structures, and the interpretation is supported by measured thermal expansion coefficients. The stress-induced transformation of the metastable polymorph II to the stable polymorph I can be brought about rapidly by mechanical milling, and proceeds via a slip mechanism. This work establishes that nanoindentation provides ``signature'' responses for the two aspirin polymorphs, despite their very similar crystal structures. It also demonstrates the value of the technique to quantify stability relationships and phase transformations in molecular crystals, enabling a deeper understanding of polymorphism in the context of crystal engineering.

Magnetic and Mechanical Anisotropy in a Manganese 2-Methylsuccinate Framework Structure

Hybrid inorganic-organic framework materials exhibit unique properties that can be advantageously tuned through choice of the inorganic and organic components and by control of the crystal structure. We present a new hydrothermally prepared 3D hybrid framework, [Mn(2-methylsuccinate)](n) (1), comprising alternating 2D manganese oxide sheets and isolated MnO(6) octahedra, pillared via syn, anti-syn carboxylates. Powder magnetic characterization shows that the compound is a homospin Mn(II) ferrimagnet below 2.4 K. The easy-axis is revealed by single-crystal magnetic susceptibility studies and a magnetic structure is proposed. Anisotropic elastic moduli and hardness, observed through nanoindentation on differing crystal facets, were correlated with specific structural features. Such measurements of anisotropy are not commonly undertaken, yet allow for a more comprehensive understanding of structure-property relationships.