For a detailed understanding of high-temperature processes in complex solids the identification of the sublattice on which thermal defects are formed is of basic interest. Theoretical studies in intermetallic compounds favor a particular sublattice for thermal vacancy formation. In the present study we detect in ordered MoSi2 thermal vacancies with a low formation enthalpy of H(F)(V)=(1.6+/-0.1...

Whaley’s Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 3 . It is also shown that that every finite modular lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 2 , and every finite distribut...

Rene88 samples were investigated using atom probe tomography and x-ray diffraction using a monochromated synchrotron beam with different energy values to determine the preferred site occupancy of various alloying elements within the ordered γ’ precipitates. Samples were solutionized and cooled at 24 degree C/min with subsequent aging at 760 degrees C. The synchrotron-based x-ray diffraction res...

The electronic structure of an unusual LiSn phase (computed using band structure calculations in the framework of the extended Hückel tight binding theory) is the starting point for a general analysis of the variation of electron-rich multicenter bonding across a period. The LiSn crystal structure of Müller and Schäfer in question contains 2D slabs of Sn atoms arranged as microscopic stairs and...

Let Λ be a lattice in an n-dimensional Euclidean space E and let Λ be a Minkowskian sublattice of Λ, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of Λ. We extend the classification of possible Z/dZ-codes of the quotients Λ/Λ to dimension 9, where dZ is the annihilator of Λ/Λ.

Partial answers are given to two questions. When does a lattice Λ contain a sublattice Λ′ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense that the boundaries of the Voronoi cells for Λ′ do not intersect Λ?

Our aim in this paper is to introduce and study a new sort of fuzzy sublattice (ideal, filter) of a lattice called ) q , ( ∨ ∈ ∈ -fuzzy sublattice (ideal, filter). These fuzzy sublattices (ideals, filters) are characterized by their level sublattices (ideals, filters). Finally, we give a generalization of ) q , ( ∨ ∈ ∈ -fuzzy sublattices (ideals, filters).

In this article, a number of the results relevant to the concept of sublattices of a basic crystallographic lattice are reviewed, emphasizing particularly previously unpublished work on the algebraic aspects. A three-dimensional geometric lattice L can be considered as an infinite Abelian group under addition. A sublattice S of L, which is also three-dimensional, is a subgroup of L such that th...

2014 An extension of the « D.L.P. » theory of Stringfellow taking clustering into account has been applied both to pseudobinary, pseudoternary and pseudoquaternary III V alloys. For alloys with two sites sublattices, this clustering tendency is introduced in each sublattice of the zinc blende through a positive short-range order parameter 03B1i-j depending on temperature and composition. It is ...