Constitutional and Thermal Defects in Nickel Aluminides
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The formation energies of intrinsic point defects and the interaction energies of possible defect pairs in NiA1 are calculated from first principles within an order-N, locally self-consistent Green's function method in conjunction with the multipole electrostatic corrections to the atomic sphere approximation. The theory correctly reproduces the ground-state properties of the off-stoichiometric NiAl alloys. The constitutional defects (antisite Ni atoms in Ni-rich and Ni vacancies in Al-rich NiAl) are shown to form ordered structures in the ground state, in which the defects of the same kind tend to avoid each other at the shortest separation distance on their sublattice. A mean-field theory is applied to calculate the equilibrium concentrations of thermal defects. The statistics of thermal defects is interpreted in terms of dominant composition-conserving complex defects which are shown to be triple defects in Ni-rich and nearly stoichiometric NiAl. In the Al-rich region a novel thermal excitation dominates where two constitutional Ni vacancies are replaced by one antisite Al atom. The number of vacancies, as well as the total number of point defects decrease with temperature in Al-rich NiAl. The boundary between the two regions is treated analytically. The vacancy concentration exhibits a minimum in its temperature dependence at the boundary. Similar analysis is applied to study constitutional and thermal defects in Ni3Al. The calculated effective vacancy formation energy in Ni 3AAas a function of concentration is in excellent agreement with recent experimental data. METHODOLOGY Defect concentrations
Let us consider a single-phase, off-stoichiometric alloy having a fixed atomic composition, AI-xBx. We assume two inequivalent sublattices A and B with the multiplicity factors mA and mB, respectively, so the ideal stoichiometric composition is AmAmB. The alloy components (A atoms, B atoms, and vacancies, i={A,B,V}) may occupy N lattice sites on the two sublattices a ={A,B 1. The sublattices have balanced number of lattice sites, N a=(m ,/m)N, where m=mA+mB. Let us denote the number of lattice sites on sublattice x occupied by component i as nia. The number of A atoms, nA=nAA+nAB, the number of B atoms, nB=nBA+nBB, and the total number of atoms, Nat=nA+ nB. are
fixed. At the same time, the number of vacancies in the alloy nv=nvA+nvB, as well as the total number of lattice sites, N, are allowed to vary. To describe the distribution of alloy components between the sublattices, we use atomic concentrations defined with respect to the total number of atoms: xia = ni /Nat. One can easily transform between atomic and site concentrations, cia = nia/N a, using the following relationship: cia= (m/m a) xia/(l+xv), where xv = xVA + XVB is the net concentration of vacancies. Among the four total defect concentrations, xd where d= {BA,VA,ABVB }, only three are linearly independent: XBA - XAB + (mB/m)XVA - (mA/m)xVB =
6
(1)
Here 8 = x - (mB/m) is the deviation from stoichiometry. Those defects which are present in the ground s
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