Analytical solutions for non-linear conversion of a porous solid particle in a gas–I. Isothermal conversion

Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with solid conversion and external film transport. Results include expressions for the concentration distributions of the solid and gaseous reactant, the propagation velocity of the conversion zone inside the particle, the conversion time and the conversion rate. The complete analytical description of the non-linear conversion process is based on a combination of two asymptotic solutions. The asymptotic solutions are derived in closed form from the governing non-linear coupled partial differential equations pertaining to conservation of mass of solid and gaseous reactant, considering the limiting cases of a small and large Thiele modulus, respectively. For a small Thiele modulus, the solutions correspond to conversion dominated by reaction kinetics. For a large Thiele modulus, conversion is strongly influenced by internal and external transport processes and takes place in a narrow zone near the outer surface of the particle: solutions are derived by employing boundary layer theory. In Part II of this paper the analytical solutions are extended to non-isothermal conversion and are compared with results of numerical simulations

Theory of the ferromagnetism in TiCrN solid solutions

First-principles calculations are used to investigate the magnetic properties of Ti$_{1-x}$Cr$_{x}$N solid solutions. We show that the magnetic interactions between Cr spins that favour antiferromagnetism in CrN is changed upon alloying with TiN leading to the appearance of ferromagnetism in the system at approximately $x \leq 0.50$ in agreement with experimental reports. Furthermore we suggest that this effect originates in an electron density redistribution from Ti to Cr that decreases the polarization of Cr d-states with t$_{2g}$ symmetry while it increases the polarization of Cr d-states with e$_g$ symmetry, both changes working in favour of ferromagnetism.Comment: 21 pages, 7 figure

Alloy softening in binary iron solid solutions

An investigation was conducted to determine softening and hardening behavior in 19 binary iron-alloy systems. Microhardness tests were conducted at four temperatures in the range 77 to 411 K. Alloy softening was exhibited by 17 of the 19 alloy systems. Alloy softening observed in 15 of the alloy systems was attributed to an intrinsic mechanism, believed to be lowering of the Peierls (lattice friction) stress. Softening and hardening rates could be correlated with the atomic radius ratio of solute to iron. Softening observed in two other systems was attributed to an extrinsic mechanism, believed to be associated with scavenging of interstitial impurities

Vacancy-Impurity Nanoclusters in Solid Solutions 3He−4He^3He - ^4He

The existence of vacancy--impurity clusters due to quantum properties of vacancies in phase separated solid solutions of 4He in 3He is analyzed and discussed. Additional mechanism called vacancy assisted nucleation is proposed. According to this assumption the vacancy-impurity clusters should have b.c.c. structure.Comment: 5 pages, 1 figure, Late