Stability of ordered phases

Abstract

621.762 Introduction. It is known that the number of possible and theoretically predicted superlattices of ordered phases is considerably larger than the number of experimentally discovered ones [1]. The main cause why many of the predicted superlattices have so far not been obtained in practice is the problem of stability of ordered phases. The present work deals with an analysis of the conditions of realization of superlattices based on the fcc lattice.During the analysis we imposed limitations, and we examined solely those binary ordered phases for whose description one or two parameters of long-range order are necessary. Such a limitation is very sensible because, firstly, binary ordered phases with three parameters of long-range order have so far not been discovered experimentally, secondly their examination greatly increases the number of possible types of superlattices which is large anyway. The size of the present article also forces us to confine ourselves to face-centered cubic densely packed lattices. The analysis of possible structures is carried out within the framework of the Ising model with rigid lattice, with interatomic pair interaction taken into account. Rigid lattice means that only concentration waves are taken into account, but not waves of atomic displacements. Long-period structures are therefore not dealt with. The analysis of the stability of superlattices was Carried out without regard to entropy, i.e., at zero temperature. These approximations are traditional.

The crystal-geometric factors in Laves phases

“…Все это порождает вопрос, с чем это связано и чем обусловлено их закономерное поведение и боль-шой разброс данных. Вероятно, для первой группы спла-вов при образовании структур выполняется принцип плотной упаковки [6,8] и, в этих соединениях для описа-ния их свойств можно использовать представление ато-мов в виде «твердых сфер». В сплавах второй группы та-кой разброс данных на диаграммах на рис.…”

“…Геометрический подход позволяет наиболее просто и наглядно выявить и описать общие закономерности в строении и стабильности различных кристаллических структур [5][6][7][8]9]. На современном этапе развития кри-сталлохимии и кристаллофизики сплавов применение геометрических факторов не потеряло своей актуаль-ности.…”

Dimensional crystal geometry of binary intermetallic alloys

“…The crystal geometry analysis of intermetallic compound structures allows the superstructure contraction to be investigated. It should be noted that the superstructure contraction characterizes the degree to which the unit cell volume in the concentration dependence deviates from a linear one, that is, it describes the deviation from the Zen law [4,5]. In the Zen law, the atomic volume is the fundamental parameter that describes the crystal lattice.…”

“…The history of studying the formation of various phases depending on the crystal geometry parameters is long [1,2], and this problem remains urgent now [3,4]. Indeed, further development of this approach has allowed a number of radically new principles to be established [5].…”

“…[3,4]. In our work, we concentrate on a search for laws for the AB and А 3 В intermetallic compounds based on an analysis of the crystal geometry parameters, such as the dimensional factor, space filling factor ψ, and superstructure contraction ∆Ω (Table 1).…”