Reciprocal-space analysis of short-range-order intensities by 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

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

Thermodynamics of mixing and ordering in the diopside–jadeite system: I. A CVM model

Mineralogical Magazine ◽

10.1180/0026461026640046 ◽

2002 ◽

Vol 66 (4) ◽

pp. 513-536 ◽

Cited By ~ 10

Author(s):

V. L. Vinograd

Keyword(s):

Free Energy ◽

Cluster Variation Method ◽

Solution Calorimetry ◽

Range Order ◽

Variation Method ◽

Energy Of Mixing ◽

Equilibrium Data ◽

Thermodynamics Of Mixing ◽

Cluster Variation ◽

Free Energy Of Mixing

AbstractSolution calorimetry and phase equilibrium data for the diopside–jadeite system are assessed using a combination of the cluster variation method (CVM) and Redlich-Kister (RK) polynomial expansion. The CVM is used to model part of the free energy of mixing which depends on short-range order (SRO) and long-range order (LRO) effects. The SRO/LRO independent part of the free energy is modelled using an RK polynomial. The parameters of the RK and CVM models are obtained through the fit to the experimental data. The best-fit parameters are used to calculate activity-composition relations and a temperature-composition phase diagram of the diopside–jadeite system.

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

A data-driven approach to approximate the correlation functions in cluster variation method

Modelling and Simulation in Materials Science and Engineering ◽

10.1088/1361-651x/ac3a16 ◽

2021 ◽

Author(s):

Abhishek Kumar Thakur ◽

Rajendra Prasad Gorrey ◽

Vikas Jindal ◽

Krishna Muralidharan

Keyword(s):

Correlation Functions ◽

Short Range ◽

Cluster Variation Method ◽

Data Driven ◽

Variation Method ◽

Internal Variables ◽

Data Driven Approach ◽

Cluster Variation ◽

Bcc Phase

Abstract The cluster variation method (CVM) is one of the thermodynamic models used to calculate phase diagrams considering short range order (SRO). This method predicts the SRO values through internal variables referred to as correlation functions (CFs), accurately up to the cluster chosen in modeling the system. Determination of these CFs at each thermodynamic state of the system requires solving a set of nonlinear equations using numerical methods. In this communication, a neural network model is proposed to predict the values of the CFs. This network is trained for the BCC phase under tetrahedron approximation for both ordering and phase separating systems. The results show that the network can predict the values of the CFs accurately and thereby Helmholtz energy and the phase diagram with significantly less computational burden than that of conventional methods used.

Download Full-text

ANALYTICAL DESCRIPTION OF TEMPERATURE DEPENDENCE OF A POSITION IN RECIPROCAL SPACE OF THE SHORT-RANGE ORDER FOURIER TRANSFORM'S MAXIMUM IN ALLOYS

Journal of Physics and Chemistry of Solids ◽

10.1016/s0022-3697(98)00233-9 ◽

1998 ◽

Vol 59 (9) ◽

pp. 1469-1472 ◽

Cited By ~ 9

Author(s):

R.V. Chepulskii ◽

V.N. Bugaev

Keyword(s):

Temperature Dependence ◽

Short Range ◽

Short Range Order ◽

Analytical Description ◽

Reciprocal Space ◽

Range Order

Download Full-text

BILINEAR ANALYSIS OF SHORT-RANGE ORDER IN METALLIC SOLID SOLUTIONS

International Journal of Modern Physics B ◽

10.1142/s0217979292001201 ◽

1992 ◽

Vol 06 (13) ◽

pp. 2393-2407

Author(s):

AKHTAR MAHMOOD ◽

FARID A. KHWAJA

Keyword(s):

Numerical Calculation ◽

Critical Temperature ◽

Solid Solutions ◽

Short Range ◽

Short Range Order ◽

Order Parameters ◽

Reciprocal Space ◽

Range Order ◽

Intensity Data ◽

Volume Analysis

Short-range order parameters and short-range order dependent diffuse intensities are calculated using bilinear analysis in Cu 72 Au 28, Ni-Al and Ni 3 Fe systems. The appearance of short-range order in alloys, quenched from below and above the critical temperature, is also studied using this method. The short-range order parameters calculated in this approach are found to be in agreement with the values determined from volume analysis. Nevertheless, the results of numerical calculation indicate that these parameters can be accurately determined only up to eight coordination shells using the intensity data measured along two lines in the reciprocal space.

Download Full-text