Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

Ternary rare-earth alumo-silicides—single-crystal growth from Al flux, structural and physical properties

A number of rare-earth alumo-silicides (R-Al-Si) have been synthesized from the corresponding elements by high-temperature reactions, carried out in excess of aluminum to serve as a flux. Under these experimental conditions, large single crystals of all R-Al-Si ternary phases were readily produced. The crystal structures these ternaries adopt were studied by means of powder and single-crystal X-ray diffraction and were classified as follows: (1) the early rare-earths (R=La, Ce, Pr, Nd, Sm, Gd) yield RAl_xSi_2−x, x∼1, non-stoichiometric ternary derivatives of the body-centered α-ThSi₂-type; (2) the late rare-earths (R=Tb, Dy, Ho, Er, Tm) form stoichiometric R₂Al₃Si₂ compounds that crystallize in the C-centered monoclinic Y₂Al₃Si₂-type; (3) the divalent Eu and Yb produce EuAl₂Si₂ and YbAl₂Si₂ with the trigonal CaAl₂Si₂-type, whereas the last lanthanide element, Lu, forms LuAlSi with C-centered orthorhombic YAlGe-type. These structural trends are reviewed, and the evolution of the basic physical properties such as magnetism, heat capacity and electrical resistivity when moving across the series is described in detail.     

Photo-assisted electron injection at a semiconductor—NH3 interface

Illumination of a p-type semiconductor—NH₃ interface (or heterojunction) with photons of energy greater than the semiconductor band gap causes electrons to be injected into the NH₃. There is no hole injection at a n-type electrode. Suggestions are made for the required energy levels in the liquid.     

Isomerisation in the chemistry of platinacyclobutane complexes

The platinacyclobutane complexes PtCl₂L₂(C₃H₅Me)], L  pyridine, CD₃CN, or tetrahydrofuran, exist as mixtures of isomers containing P$\text{tCH}{}_2\text{CHMeC}$H₂ or P$\text{tCHMeCH}{}_2\text{CH}{}_2$ groups in rapid equilibrium. Decomposition occurs in some cases to give [PtCl₂L(CH₃CH₂CHCH₂)]. Stereospecific skeletal isomerisation also occurs in metallocyclobutanes containing the groups P$\text{tCHRCHRC}$H₂  P$\text{tCHRCH}{}_2\text{C}$HR, when R  aryl further decomposition gives ν-allylplatinum complexes.     

Observations on clear solution silicalite-1 growth by nanoslabs

Several research groups have reported the presence of nanometer-sized particles (nanoslabs) in clear solutions, which precipitate the crystalline MFI (ZSM-5) structure. Debate about the growth mechanism for Al-free ZSM-5 (silicalite-1) has revolved around growth by small silicate units (monomers, dimers, etc.) from solution vs growth by nanoslab addition. A model developed for precipitation of uniform sized colloids by addition of sub-colloidal precursor units has been adapted for this zeolite synthesis system. Parameter values were adjusted for the simulation results to match experimental observations from work reported previously, at least to the extent possible. The model involved the simultaneous solution of up to 6000 ordinary differential equations, and required computation times of up to 24 h. The results shed light on the crystal growth mechanism, but pose questions for further investigations of the nucleation mechanism.