scholarly journals Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

2021 ◽  
Author(s):  
Puwadet Sutipanya ◽  
Takashi Arai
Keyword(s):  
Phase Separation ◽  
Structure Factor ◽  
Lattice Point ◽  
Local Density ◽  
Lattice Points ◽  
Concentration Fluctuations ◽  
Coarse Grained ◽  
Partial Structure ◽  
Disordered Lattice ◽  
Structure Factors

Abstract The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

X-ray Diffraction Study of Molten Te and Tl-Te Alloys

1975 ◽  
Vol 30 (12) ◽  
pp. 1655-1660 ◽  
Author(s):  
Y. Waseda ◽  
S. Tamaki
Keyword(s):  
Structure Factor ◽  
Molten Metals ◽  
X Ray Diffraction ◽  
Partial Structure ◽  
X Ray ◽  
Partial Structures ◽  
Structure Factors ◽  
Diffraction Patterns ◽  
Total Structure ◽  
Constituent Elements

Abstract X-ray diffraction patterns have been obtained from molten Te at 470, 520 and 570 °C. The heights of the peak maxima in the structure factor were much the same in contrast with those of typical molten metals such as sodium.Molten Tl-Te alloys have been studied by X-ray diffraction for the alloy compositions 25, 33.3, 50, 60 and 75 at% Te at 500 °C and at about 20 °C above the liquidus. The total structure factors for the 25 and 33.3 at% Te alloys were almost the same as that of pure Tl. This implies that the atomic arrangement of these molten alloys is very close to that of pure Tl. Although a drastic change is not found in the general form of the structure factor, the parameter of the range of local atomic order abruptly increases on passing from Tl2Te to more Te-rich alloys. The three partial structures were also evaluated from the observed X-ray intensities assuming that each partial structure is independent of the relative abundance of the constituent elements in the alloys.

A Combined IKL-ALCHEMI Technique for atom Configurations in Multinary Ordering Alloys and its Application to Cu-Au-Pd

1990 ◽  
Vol 48 (2) ◽  
pp. 488-489
Author(s):  
Syo Matsumura ◽  
Takao Moriraura ◽  
Kensuke Oki
Keyword(s):  
Binary Alloy ◽  
Structure Factor ◽  
Superlattice Reflection ◽  
Lattice Points ◽  
Atomic Configuration ◽  
Experimental Procedure ◽  
Pair Correlations ◽  
X Ray ◽  
Structure Factors ◽  
Independent Parameters

Diffraction technique of x ray, electron or neutron has been extensively utilized to determine atomic configuration in ordering alloys. The method of analysis has been well established for the binary alloy case. From the diffracted intensities or the values of structure factors, we can straightforwardly determine site-occupancies or pair-correlations of atoms on the fundamental lattice points in a binary alloy. For ternary or multinary alloys, however, it turns impossible to obtain the quantities concerning atomic configuration by the conventinal diffraction technique. This impossibility in the multinary case is due to the fact that the structure factor of a superlattice reflection is a function of two or more independent parameters describing the atomic configuration. In this paper we propose an experimental procedure to break through this impossibility; simultaneous employment of the Intersecting Kikuch-line (IKL) method and ALCKEMI (Atom Location by Channeling Enhanced Microanalysis) enables us to determine the occupation probabilities of constituent atoms on lattice sites in ternary or multinary ordering alloys.

The structure of molten and glassy 2:1 binary systems: an approach using the Bhatia—Thornton formalism

1992 ◽  
Vol 437 (1901) ◽  
pp. 591-606 ◽  
Keyword(s):  
Structure Factor ◽  
Binary Systems ◽  
Range Order ◽  
Partial Structure ◽  
Systematic Analysis ◽  
Glass Forming ◽  
Structure Factors ◽  
Total Structure Factor ◽  
Diffraction Patterns ◽  
Total Structure

A systematic analysis of those liquid binary 2:1 systems (denoted MX 2 ), for which experimental partial structure factors are available from the isotopic substitution method in neutron diffraction, is made using the Bhatia-Thornton (BT) formalism.Particular attention is paid to the origin of the first sharp diffraction peak (FSDP ), which occurs in the measured diffraction patterns for some of the MX 2 systems, since it appears, from recent studies, that this feature is a signature of directional bonding. It is found that FSDPS can occur in all three BT partial structure factors S xB (k). A FSDP feature in the concentration-concentration partial structure factor S cc (k) is not, however, pronounced except in the case of MgCl 2 and the glass forming network melts ZnCl 2 and GeSe 2 . To the extent that these systems can be regarded as ionic melts a FSDP in S cc (k) implies a non-uniformity in the charge distribution on the scale of the intermediate-range order (IRO). The structure of molten GeSe 2 is compared with the structures of molten ZnCl 2 , glassy GeS 2 and glassy Si0 2 . Although the GeSe 2 and ZnCl 2 melts have different short-range order, there are similarities in the observed IRO which can be attributed to the arrangement of the electropositive species M. The essential features of the measured total structure factor for glassy GeS 2 can be reproduced by using the molten GeSe 2 S zB (k). This result lends support to the notion that the S zB (k) for liquid GeSe 2 (and ZnCl 2 ) are characteristic of both the liquid and glassy states of other network glass forming systems. The structures of molten GeSe 2 (or ZnCl 2 ) and glassy Si0 2 are, however, found to be different. The observed discrepancies are largest in the region of the FSDP which signifies pronounced differences in the nature of the IRO for these systems.

Neutron Diffraction with the Metallic Glass Ni31Dy69 ( + 10 a/o D) Using Isotopic Substitution

1985 ◽  
Vol 40 (2) ◽  
pp. 191-192
Author(s):  
A. Wildermuth ◽  
P. Lamparter ◽  
S. Steeb
Keyword(s):  
Amorphous Alloy ◽  
Neutron Diffraction ◽  
Metallic Glass ◽  
Structure Factor ◽  
Isotopic Substitution ◽  
Diffraction Experiment ◽  
Partial Structure ◽  
Neutron Diffraction Experiment ◽  
Partial Structure Factor ◽  
Structure Factors

By neutron diffraction using the method of isotopic substitution with the amorphous alloy Ni31Dy69 the partial structure factors SNiNi, SDyDy and SNiDy were obtained, furthermore with the same specimen containing 10 a/o deuterium a partial structure factor SDD resulted. For the evaluation of SDD it was necessary to perform the neutron diffraction experiment with an alloy whose both components were zero scattering isotopic mixtures of Ni or Dy, respectively.

CALCULATION OF THE PARTIAL STRUCTURE FACTORS IN BINARY LIQUID ALLOYS BY A THERMODYNAMICAL APPROACH

1980 ◽  
Vol 41 (C8) ◽  
pp. C8-586-C8-589
Author(s):  
M. Favre-Bonte ◽  
J. C. Joud ◽  
P. Hicter ◽  
P. Desre
Keyword(s):  
Liquid Alloys ◽  
Partial Structure ◽  
Binary Liquid ◽  
Structure Factors

DETERMINATION BY POLARIZED NEUTRON DIFFRACTION OF THE THREE PARTIAL STRUCTURE FACTORS OF A Co81.511B18.5 GLASS

1982 ◽  
Vol 43 (C9) ◽  
pp. C9-23-C9-29
Author(s):  
J. M. Dubois ◽  
P. Chieux ◽  
G. Le Caer ◽  
J. Schweitzer ◽  
J. Bletry
Keyword(s):  
Neutron Diffraction ◽  
Partial Structure ◽  
Structure Factors ◽  
Polarized Neutron

scholarly journals Bounds on the Lattice Point Enumerator via Slices and Projections

2021 ◽  
Author(s):  
Ansgar Freyer ◽  
Martin Henk
Keyword(s):  
Convex Body ◽  
Lattice Point ◽  
Geometric Mean ◽  
Discrete Analogue ◽  
Lattice Points ◽  
General Context ◽  
General Bound

AbstractGardner et al. posed the problem to find a discrete analogue of Meyer’s inequality bounding from below the volume of a convex body by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question of bounding the number of lattice points of a convex body in terms of slices, as well as projections.

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