Full Potential LMTO Study of TiAl Alloy
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FULL POTENTIAL LMTO STUDY OF TiAl ALLOY
Pradeep K. Khowash, David L. Price*, Bernard R. Cooper Department of Physics, West Virginia University, Morgantown, WV, 26506 *Department of Physics, Memphis State University, TN, 38152
ABSTRACT We have used a full potential all electron LMTO total energy calculation with a true interstitial to establish a baseline understanding of pure -t-TiAl. The c and a lattice parameters, Bulk modulus and the Young's modulus are calculated and found to be in excellent agreement with reported experimental values.
I. INTRODUCTION In recent years, TiAI has gained considerable importance due to its high temperature applications as a reenforced material in turbine blades. Ti, All- , has different phases with varying x. From xý--0.62 to 0.75 gives the ci-2 phase with composition AITi2 . From x•0.37 to 0.50 gives the -y phase, the phase of our interest because of high melting point (1200C) of the material in this concentration range. We use an all electron full potential fully self-consistent calculation to study pure stoichiometric TiAl material. Highly accurate total energies are calculated for different lattice distances to find the theoretical lattice constants. The density of states is plotted in order to understand the nature of bonding. Discussion regarding the ratio c/a is made based on our calculations and experimental findings. The elastic constants are calculated and compared with experiment and other calculations wherever available. II. METHOD OF CALCULATION We use a full potential linear combination of muffin tin orbital (LMTO) method to study the electronic structure and total energies of the material in question. The space within a unit cell is divided into atomic or muffin-tin sphere regions and the interatomic (interstitial) region [1-3]. The potential in any muffin-tin sphere (atomic region) is expressed as a sum of lattice harmonics, V.j= EZV.. h(r)fl.,h((1
Mat. Res. Soc. Symp. Proc. Vol. 186. ©1991 Materials Research Society
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where a indicates the atomic type in the unit cell, and the functions rla,h (f) are the lattice harmonics invariant under the local point group operations. In the present fullpotential, the potential in the interatomic region is given by a Fourier series,
V,(rl = Ze'V (v&d)
(2)
where G are the reciprocal lattice vectors; and we use optimized [2]energy parameters (self-consistently determined) and structural constants. The true full potential is used to generate muffin-tin potentials required for constructing the basis states at each iteration (successive solution of Poisson and Schrodinger equations). These states are defined as the Bloch sum
M..
a,
-
-
(3)
Ia
where 1 and m represent quantum numbers and & is the position of the a"h atomic sphere in the unit cell, and
2
K
4D,are written as
is the interstitial kinetic energy. The muffin tin orbitals, [5g.a...(ra)+B•.a...(ra)]Yim(9),
.,~,c,,I•
(' --
-+'1'n, (r)]Yi,m (f),
(4)
CE[C.,,1,,(rg) + D ,,,,Crp)]v,, The functions O(r) are solutions of the semi-relativistic Dirac equation
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