Computer study of tweed as a precursor to a martensitic transformation of a Bcc lattice
- PDF / 508,121 Bytes
- 5 Pages / 612 x 828 pts Page_size
- 49 Downloads / 220 Views
1.
THEORETICAL M O D E L FOR TWEED M I C R O S T R U C T U R E S
IT is well established experimentally that many cubic alloys exhibit {110} (170) strain modulations ("tweed") in some range of temperature, often followed at lower temperatures by a martensitic transformation, u 4~ The basic question of what causes these strain modulations, whether they occur homogeneously or heterogeneously, and what relation they have to martensitic transformations are all of considerable current interest, and are addressed by the research reported here. The initial approach we have used for constructing a model of a cubic lattice that will have spontaneous strain modulations in some temperature range is to assume that the lattice strain energy E(u) has a double minimum with respect to a homogeneous {ll0}(IT0) strain, u, as diagrammed in Figure 1. Qualitative predictions about the behavior of such a lattice can be made as follows: (a) At temperatures such that kT > e (the energy barrier between minima) thermal fluctuations will give the lattice the time averaged appearance of being cubic as a result of the rapid oscillations between minima. The measured shear elastic constant (C~ - C~2) could be expected to have a very low value corresponding to the curvature of the timeaveraged potential well seen by the fluctuating lattice. Tweed systems typically show anomalously low values of this elastic constant. (b) At temperatures such that kT < e, the shear fluctuations would have relatively long lifetimes and a "condensation" into an increasingly static pattern of localized shear distortions semi-randomly distributed among the 12 equivalent minima (corresponding to the six equivalent shear systems) would occur. (c) At temperatures such that kT ~ e, some configuration of localized shear distortions would be frozen in, unless a new phase transformation to another crystal structure R C. CLAPP, Professor of Metallurgy, J. RIFKIN, Postdoctoral Fellow. and J. KENYON, Graduate Assistant, are with Institute of Materials Science. University of Connecticut, Storrs, CT 06268. L. E. TANNER is Research Scientist, Lawrence Livermore National Laboratory, Livermore, CA 94550. This paper is based on a presentation made in the symposium "Pretransformation Behavior Related to Displacive Transformation in Alloys" presented at the 1986 annual AIME meeting in New Orleans, March 2-6, 1986. under the auspices of the ASM-MSD Structures Committee. METALLURGICALTRANSACTIONS A
E(u)
Fig. l - - L a t t i c e energy at 0 K of a bcc crystal as a function of shear strain u on {110} planes in the (1]'0} direction.
(a martensitic transformation?) had intervened as a result of the large loss in vibrational entropy produced by the condensation. To go beyond these qualitative predictions and to test the model in some detail against experimental observations, we have employed molecular dynamic computer simulations as a practical way to calculate the behavior of such a strongly anharmonic lattice. In order to do this, the first task was to determine what general type of int
Data Loading...
