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Graphs of Radial Distribution Function (RDF) for BCC and
FCC configurations
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Abstract
Shape memory alloys exhibit the remarkable properties of
pseudoelasticity and the shape memory effect due to a
diffusionless solid-to-solid, martensitic, phase transformation. This
behavior arises in NiTi from the interplay of high symmetry phases
(Austenite, high temperature) with low symmetry phases (Martensite and
R-phase, low temperature). To understand these martensitic phase
transformations a series of Molecular Dynamics (MD) simulations are conducted
to determine the relative stability of two Lennard-Jones, biatomic, cubic
lattice configurations as temperature is varied. It is found that the BCC
cubic configuration is stable for a range of temperatures but, that the FCC
configuration is unstable and degenerates to an unordered arrangement for all
temperatures investigated.
Introduction
Shape memory alloys, such as equi-atomic NiTi, exhibit two remarkable
properties: the shape memory effect and pseudoelasticity. The
shape memory effect is the ability of the material to erase relatively large
mechanically induced strains (up to 8%) by moderate increases in temperature
(approx. 10-20 Degrees C). Pseudoelasticity refers to the ability in a somewhat
higher temperature regime to accommodate these strains during loading and
recovery upon unloading (via a hysteresis loop). The underlying mechanism is a
reversible martensitic transformation between solid-state phases, often
occurring near room temperature. The transformation can be induced by changes
in stress due to the strong thermo-mechanical coupling.
It is well known that the underlying mechanism for NiTi's remarkable behavior
is a diffusionless solid-to-solid, or martensitic, phase transformation. The
behavior arises from the interplay of solid-state phases, a high temperature
phase (Austenite), having a crystal structure with a high degree of symmetry
(cubic), and low temperature phases (Martensite and R-phase), having crystal
structures with a low degree of symmetry (monoclinic and rhombohedral,
respectively).
Efforts to theoretically model this problem have focused on assuming an energy
density with the transformation properties noted above and determining
properties of the resulting equilibrium configurations. Here a different
approach is taken, in which, atomistic lattice interactions are considered and
the interaction physics is allowed to determine the phases which are observed.
Simulation
A Lennard-Jones interaction potential is used for the two species MD
simulations. The bond parameters for the three interactions were determined by
a fit to potentials used in the previous research (Elliott et. al.), such that
at zero temperature the FCC configuration is predicted to be stable.
The perfect BCC and FCC configurations are used as initial conditions. The
initial lattice spacing is chosen, through trial-and-error, such that the
system is at nearly zero pressure. Each configurations is then run for 50 time
steps (5000 iterations) at constant temperature and volume, with the temperature
set at each of the following values 0.01, 0.05, 0.10, and 0.20.
Data Analysis
The Radial Distribution Function (RDF) is used to analyze the results of the
simulations. The RDF of the final step of each simulation is compared to that
of the corresponding perfect configuration. Thus, it is possible to determine
if the structure of the crystal has been retained or if the crystal is
unstable and became unordered.
It is found that in all temperature cases the BCC crystal retains the character
of the original configuration and is thus "stable". For the FCC crystal
though, the RDF shows that the crystal structure is lost, indicating that the
FCC configuration is "unstable". In calculating the RDF all atoms were
considered, that is, the RDF results shown include both atomic species in the
simulation.
References
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Journal of the Mechanics and Physics of Solids, 43(8):1243-1281, August 1995
John A. Shaw, "Material Instabilities in a Nickel-Titanium Shape Memory Alloy,"
PhD thesis, The University of Texas at Austin, Austin, TX 78712, January 1997
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