**Atomic elastic stiffness analysis to predict twinning in Fe single
crystal under shear**

K Yashiro and S Tsuchiya and K Naito, COMPUTATIONAL MATERIALS SCIENCE, 183, 109804 (2020).

DOI: 10.1016/j.commatsci.2020.109804

As a series study that discusses local instability by atomic elastic
stiffness, B-ij(a) = Delta sigma(a)(i)/Delta epsilon(j), molecular
dynamics simulations of simple shear on Fe perfect lattice are performed
to discuss twin deformation. In the simulation of extremely low
temperature of 0.1 K, many twin boundaries are nucleated in a periodic
slab cell of stacked ((1) over bar(1) over bar2) planes just after the
stress drop or elastic limit under shear. The 1st eigenvalue eta(a(1))
of the 6 x 6 matrix B-ij(a) shows fluctuation in each ((1) over bar(1)
over bar2) planes just before the elastic limit. At the stress-strain
peak, eta(a(1)) < 0 or unstable layers emerge and twin deformation
occurs at these unstable "band" in the simulation cell. The period of
the eta(a(1)) fluctuation is almost constant even if the cell size is
expanded in the **<(1)over bar>(1) over bar2** and **1 (1) over bar0**
direction, while the unstable band arrays tilt normal to the diagonal
line of the simulation cell, under the cell expansion in the **1 1 1**
direction. At the elevated temperature of 300 K, the simultaneous
periodic band never appears but a few unstable bands appear locally in
time sequence and bring twinning there.

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