Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters

Thermal and magnetic field-induced martensite-austenite transition in Ni50.3Mn35.3Sn14.4 ribbons

Thermal and field-induced martensite-austenite transition was studied in melt spun Ni50.3Mn35.3Sn14.4 ribbons. Its distinct highly ordered columnarlike microstructure normal to ribbon plane allows the direct observation of critical fields at which field-induced and highly hysteretic reverse transformation starts (H=17kOe at 240K), and easy magnetization direction for austenite and martensite phases with respect to the rolling direction. Single phase L21 bcc austenite with TC of 313K transforms into a 7M orthorhombic martensite with thermal hysteresis of 21K and transformation temperatures of MS=226K, Mf=218K, AS=237K, and Af=244K

Hardy’s inequalities for monotone functions on partly ordered measure spaces

We characterize the weighted Hardy inequalities for monotone functions in Rn +. In dimension n = 1, this recovers the standard theory of Bp weights. For n > 1, the result was previously only known for the case p = 1. In fact, our main theorem is proved in the more general setting of partly ordered measure spaces.

Spreading due to heterogeneity in two-phase flow

Postprint (published version)