Short range order diffuse intensity calculations in the cluster variation method

Recently, measurements of short-range order (SRO) diffuse neutron scattering intensity have been performed on quenched Cu-Zn alloys with 22.4 to 31.1 atomic percent (a/o) Zn, and pair interactions were obtained by Inverse Monte Carlo simulation [1]. These results are compared to SRO intensities and effective pair interactions obtained from first-principles electronic structure calculations. The theoretical SRO intensities were calculated with the Cluster Variation Method (CVM) in the tetrahedron-octahedron approximation with first-principles pair interactions as input. More generally, phase stability in the Cu-Zn alloy system is discussed, using ab-initio energetic properties.

Download Full-text

SHORT RANGE ORDERING AND LOCAL DISPLACEMENT OF ALLOYS STUDIED BY CVM

International Journal of Computational Materials Science and Engineering ◽

10.1142/s2047684112500182 ◽

2012 ◽

Vol 01 (02) ◽

pp. 1250018 ◽

Cited By ~ 4

Author(s):

TETSUO MOHRI

Keyword(s):

Short Range ◽

Lattice Distortion ◽

Cluster Variation Method ◽

Real Space ◽

Variation Method ◽

Diffuse Intensity ◽

Local Lattice Distortion ◽

Wide Range ◽

Local Lattice ◽

Cluster Variation

Cluster Variation Method (CVM) is a powerful statistical mechanics means to investigate phase equilibria of an alloy. The advantageous feature of the CVM stems from the fact that wide range of atomic correlations which play an important role at the phase transition is efficiently incorporated into the free energy formula. Hence, configurational fluctuation can be systematically studied through the calculations of correlation functions in the real space and short range order diffuse intensity spectrum in the k-space. However, one of the deficiencies of the conventional CVM is the fact that local lattice distortion (local atomic displacement) is not correctly dealt with. In order to improve such shortcomings, Continuous Displacement Cluster Variation Method (CDCVM) has been developed. In the CDCVM, local lattice distortion is mapped onto the configurational freedom of a multi-component alloy on a rigid (uniformly deformable) lattice. With CDCVM, the applicability of CVM is enlarged and the calculations of diffuse intensity spectrum originating from local lattice distortion can be performed.

Download Full-text

High Temperature Measurements of Neutron Diffuse Scattering in a FeAll9.Sat% Single Crystal. Influence of Magnetism on Chemical Order.

MRS Proceedings ◽

10.1557/proc-213-69 ◽

1990 ◽

Vol 213 ◽

Cited By ~ 1

Author(s):

V. Pierron-Bohnes ◽

M.C. Cadeville ◽

O. Schaerpf ◽

A. Finel

Keyword(s):

Diffuse Scattering ◽

Short Range ◽

Short Range Order ◽

Magnetic Coupling ◽

Pair Interaction ◽

Cluster Variation Method ◽

Range Order ◽

Variation Method ◽

Ferromagnetic Phase ◽

Effective Pair

ABSTRACTThe influence of magnetism on atomic short range order is shown in a single crystalline FeAl19.sat% alloy in the disordered phase. The short range order has been measured in the paramagnetic state between 973 and 1573 K on D7 at ILL through neutron diffuse scattering in the [110] plane. The effective pair interaction potentials V1 , V2, V3 and V5 are calculated through an inverse cluster variation method. The results are compared to those obtained through X-ray diffuse scattering on the same alloy frozen in the ferromagnetic order state at 772 K. The effect of magnetic coupling on the atomic order is the most important on the 1st effective potential, which is smaller by about a factor 2 in the ferromagnetic phase than in the paramagnetic one.

Download Full-text

Theoretical Investigation of Alloy Phase Equilibria by Continuous Displacement Cluster Variation Method

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.172-174.1119 ◽

2011 ◽

Vol 172-174 ◽

pp. 1119-1127

Author(s):

Tetsuo Mohri

Keyword(s):

Phase Equilibria ◽

Lattice Point ◽

Cluster Variation Method ◽

Lattice Points ◽

Variation Method ◽

Bravais Lattice ◽

Diffuse Intensity ◽

Wide Range ◽

Cluster Variation ◽

Continuous Displacement

Continuous Displacement Cluster Variation Method is employed to study binary phase equilibria on the two dimensional square lattice with Lennard-Jones type pair potentials. It is confirmed that the transition temperature decreases significantly as compared with the one obtained by conventional Cluster Variation Method. This is ascribed to the distribution of atomic pairs in a wide range of atomic distance, which enables the system to attain the lower free energy. The spatial distribution of atomic species around a Bravais lattice point is visualized. Although the average position of an atom is centred at the Bravais lattice point, the maximum pair probability is not necessarily attained for the pairs located at the neighboring Bravais lattice points. In addition to the real space information, k-space information are calculated in the present study. Among them, the diffuse intensity spectra due to short range ordering and atomic displacement are discussed.

Download Full-text

Short-range ordering of Cu3Au above Tc in the topmost 80 A of a (001) face

Journal of Materials Research ◽

10.1557/jmr.1997.0013 ◽

1997 ◽

Vol 12 (1) ◽

pp. 75-82 ◽

Cited By ~ 8

Author(s):

M. Kimura ◽

J. B. Cohen ◽

S. Chandavarkar ◽

K. Liang

Keyword(s):

Short Range ◽

Short Range Order ◽

Surface Region ◽

Antiphase Domain ◽

Range Order ◽

Two Dimensional ◽

X Ray Diffraction ◽

Diffuse Intensity ◽

Near Surface ◽

Atomic Displacements

The short-range order in the near surface region of the Cu3Au(001) face was investigated above the critical temperature by glancing-incidence x-ray diffraction, measuring the diffuse intensity throughout a two-dimensional region of reciprocal space. This intensity was analyzed quantitatively to obtain the two-dimensional Cowley–Warren short-range-order parameters and atomic displacements. Monte-Carlo simulation based on these values has revealed that the atomic configurations in the surface consist of ordered domains and clusters in a disordered matrix. There is a large number of {10} antiphase domain boundaries (APDB).

Download Full-text

Short-range order in ND4Br studied by diffuse neutron scattering

Acta Crystallographica Section A ◽

10.1107/s0567739471000792 ◽

1971 ◽

Vol 27 (4) ◽

pp. 348-353 ◽

Cited By ~ 33

Author(s):

R. S. Seymour

Keyword(s):

Ising Model ◽

Short Range ◽

Short Range Order ◽

Field Approximation ◽

Range Order ◽

Mean Field Approximation ◽

Ammonium Ion ◽

Ammonium Bromide ◽

Hydrogen Atoms ◽

Diffuse Intensity

Diffuse elastic scattering of neutrons has been observed from a single crystal of deuterated ammonium bromide and is interpreted as being due to short-range order among ammonium ion orientations. Both the temperature dependence of the diffuse intensity and its distribution in reciprocal space can be described in terms of a simple Ising model of the order-disorder transition. An expression for the diffuse intensity obtained from the mean-field approximation to the Ising model is least-squares fitted to the data. Interactions between first, second and third nearest neighbour ammonium ions have to be included in the model to give an adequate fit. The interaction energies so obtained are compared with calculations based on a simple electrostatic theory, For agreement, a charge of 0.358e on hydrogen atoms and a polarizability of 1.40 Å3 for Br− ions have to be assumed in the calculations and the significance of these unlikely values is discussed.

Download Full-text

A modulation wave approach to the order hidden in disorder

IUCrJ ◽

10.1107/s2052252514022556 ◽

2015 ◽

Vol 2 (1) ◽

pp. 74-84 ◽

Cited By ~ 8

Author(s):

Ray Withers

Keyword(s):

Long Range ◽

Short Range ◽

Short Range Order ◽

Large Family ◽

Range Order ◽

Crystal Chemical ◽

Diffuse Intensity ◽

Flexible Materials ◽

Modulation Wave ◽

Wave Approach

The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered `disorder' is pointed out. It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions. The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions.

Download Full-text