Computer simulation of the fine structures in A-B alloy

Computer simulation was used to study the fine structures of 2Dsquare lattice. The temperatures used in the experiment was below the TC = 770k. Within this range of temperatures, the 2Dsquare lattice through a chain of successive nonequilibrium configurations which is achieved through the diffusion of atoms into vacant places of lattice .The equilibrium state has been obtained by averaging a number of runs (15-16) million time steps. In equilibrium state of lattice the results showed the existence of different kinds of the fine structures (microdomains, clusters, segregations and antiphase domain boundaries). At a temperatures above TC, clusters and segregations appear and the concentration of atoms in clusters was 0.5 and in segregation 0.1. Also we noticed the changes in microdomains sizes with temperatures.

. The Bragg-Williams used approximation method, they found a relationship between the atoms interaction energies and configuration energy [9].
All previous investigations focused on the final results without passing through the stages of crystallographic structure formation.The computer simulation experiment allowed us to observe these structures and create many facts from successive images of atoms distribution.

Computer simulation experiment
We have used the 2D square lattice (rigid lattice) of BCC and FCC crystals, corresponding to the Ising model [10].The lattice belong to the planes (100) and ( 111) (in two-dimensional lattice the planes representation in ( 10) and ( 11)).The block contains 10000 atoms with periodic boundary condition.We include a single vacancy.In first and second coordination spheres, the interaction between atom-atom and atom-vacancy are equal to zero.

Results and discussion
The fine structures are generated in the lattice when the lattice undergoes a phase transformations brought about by changing temperature from 0.1TC to 1.3TC.
In figure (1a) show the ideal lattice for the used model at T= 0k, which is a big monodomain.
In fig.
(1b) the lattice exposure to a temperature of less than 0.1TC, a substitution point defect appear inside the momnodomain, so that the long -range order parameter reduced to 0.95.
In fig.(1c) the lattice exposure to a temperature above 0.1TC, another structure start to appear with increment of substitution point defect and these structures are microdomains, clusters (groups of a like atoms) and segregations (groups of unlike atoms).
Microdomain usually contains 100 atoms or less.The behavior of the microdomains changed with the time in equilibrium state, therefore, they unstable structures.
The structure of microdomain inside the domain represent antiphase microdomain (APM).
Also, the boundaries between domains are represented antiphase domain boundaries (APDB).The segregation structure has a role in the disorder process through its fluctuation in the lattice which increase atomic distribution in addition to the vacancy mechanism, as in figure (5).There are many theories that describe the segregation mechanisms in complex system as mentioned in the reference [ 16]. and Cohen [17], they found the probabilities to form clusters, segregations and short-range order of a binary AB alloy with N atoms.Fenske and Lott [18], used neutron diffraction to study the phase transitions in Fe50 Pt50 alloy as a function of annealing temperature at T≪TC and T~ TC.And the current study results goes parallel with calculations of diffusion in FCC.binary alloys using the fly Kinetic Monte Carlo [19].

Conclusion
The appearance of fine structures in the lattice leads to a reduction in the long-range order parameters and the same time leads to a growth the short-range order parameters.The number and size of fine structures increases with the rise in temperature under TC and at temperature near TC the microdomain size of the short-range order start decrease.At temperature above TC appear only clusters and segregations.

Vol: 13
No:3 , July 2017 DOI : http://dx.doi.org/10.24237/djps.1303.188BP-ISSN: 2222-8373 E-ISSN: 2518-9255 We will focus on fine structures growth in lattice which undergo an order-disorder phase transition and discusses the relation of the fine structures sizes with the temperature.In this work two sorts of atoms (A& B) used occupying the square lattice periodically.The number of atoms (A & B) is kept constant in computer experiment.This study use stoichiometric composition ( A3B or AB3) of AB alloy in computer simulation.We used temperatures below the critical temperature (TC = 770k), where TC is the temperature of long-range order disappearing in atomic system of 2D-square lattice.
The diffusion process is started after the temperatures change about 0 k.The state of system is changed in fixed time tn.In this work the number of vacancy jump were the measure of process duration tn= n,.Where Q= Probability.K = Boltzman , s constant .EV= activation energy.T= absolute temperature.On the other hand, Q may be expressed by the following form: Vol: 13 No:3 , July 2017 DOI : http://dx.doi.org/10.24237/djps.1303.188BP-ISSN: 2222-8373 E-ISSN: 2518-9255 where pkl = Probability of jump of k-th atom on l-th coordinational sphere in a vaacnt place.The interaction energy between k-th atom and l-th coordinational sphere Ekl .The fraction of atoms in a system having maximal energy than Ekl, therefor the average energy of any atom can be exppressed in the following terms: k=1,.., 4, l=1,..,2, where b= parameter describes the temperature effect on ordering process.Parameter b can be change from zero to unit.Where ᵡ = the empirical model constant.Now the probability pkl defined as: Where A = normalization constant.The equations (1-5) are important in this model and belong to [11-15].The process of ordering was included three stage: I-initial diffusion (vacancy mechanism).II-Formation and growth of ordered regions-were named domains.III-Fine structures growth in lattice.The equilibrium state of lattice obtained after 15-16 million time steps.Vol: 13 No:3 , July 2017 DOI : http://dx.doi.org/10.24237/djps.1303.188BP-ISSN: 2222-8373 E-ISSN: 2518-9255 In fig.(2a) the lattice exposure to a temperature above 0.2TC antiphase microdomain(APM) and antiphase domain boundaries (APDB) appear.In fig.(2b) and fig.(2c) on lattice exposure to a temperature above 0.3TC, antiphase domain boundary(APDB) become more extended because of microdomains, clusters and segregations localization on it and this limit the diffusion of the atoms in the vacancies in the lattice, so we need to increase the temperature of the lattice to more than 0.3TC.In fig.(3a) and fig.(3b) lattice exposure to a temperature above 0.6TC domain fluctuation starts inside the antiphase domain boundary( APDB).Where these fluctuations destroy the Vol: 13 No:3 , July 2017 DOI : http://dx.doi.org/10.24237/djps.1303.188BP-ISSN: 2222-8373 E-ISSN: 2518-9255 large domains and small new domains appear.The long-range order parameter decrease to 0.59.This stage represent the beginning of the growth of the short-range order parameter.At a temperature above 0.72TC ,the domains destruction increase the number of microdomains, clusters and segregations.For this reason the long-range order decrease to 0.48, as in figure (3c).At the end of each stage during the simulation , we calculated the concentration of atoms ( in relative unit) inside domains, microdomains, clusters and segregations .These calculations are plotted vs temperature, as in fig.(4).At temperature above TC, microdomains disappear and clustres are formed.The concentration of atoms in the clusters and segregations reach to 0.6.The concentration of atoms in the segregations is 0.1 and that in the clusters is 0.5, so that the clusters are the main contributor to the disordering, For this reason the long-range order decrease son the long-range order decrease to less 0.30.

Figure ( 6 )
Figure (6), shows the variation of the microdomains size ( in relative unit) with temperatures in equilibrium state.The structure of a microdomain situated inside an ordered domain represents antiphase order and the maximum microdomain size is obtained at a temperature