Abstract
In order to clarify the physical meaning of the eigenvector of the atomic elastic stiffness matrix, Bija=Δσia/Δεj, static calculations of uniaxial tension are performed on various fcc, bcc, and hcp metals with four different embedded atom method (EAM) potentials. Many fcc metals show instability for the constant volume mode, or the eigenvector of (Δεxx, Δεyy, Δεzz) = (±1, ∓1, 0), under the [001] tension. Bcc also loses resistance against other constant volume mode, (Δεxx, Δεyy, Δεzz) = (±1, ±1, ∓2), in the [001] tension. Hcp shows shear modes Δγyz and Δγzx under the [0001] tension, which correspond to atom migration by dislocation on the slip plane. Similar shear modes appear in the [111] tension of fcc and [110] tension of bcc. Hcp also changes the mode to constant volume and shear in the [1¯010] tension, which imply the deformation in the pyramidal and prismatic planes.
Highlights
We have proposed a deformation mode analysis based on a 6 × 6 matrix of atomic elastic stiffness (AES), Baij = Δσia/Δεj, for each atom to discuss local deformation such as crack propagation and dislocation glide
The isotropic fcc and bcc have the eigenvalues of double root C11 − C12, triple root C44, and C11 + 2C12
Hcp shows the instability of Δγyz and Δγzx shear, which reflects the atom migration on the basal slip plane
Summary
Nishimura et al. evaluated Baij in the buckling simulation of a multi-wall carbon nanotube (MWCNT) and reported that the global buckling of MWCNT is triggered by the emergence of λa(2) < 0 atoms (λa(2) corresponds to ηa(2)), after all the atoms become λa(1) < 0 in MWCNT.. Nishimura et al. evaluated Baij in the buckling simulation of a multi-wall carbon nanotube (MWCNT) and reported that the global buckling of MWCNT is triggered by the emergence of λa(2) < 0 atoms (λa(2) corresponds to ηa(2)), after all the atoms become λa(1) < 0 in MWCNT.6,7 They revealed that the corresponding eigenvectors are {0, 0, 0, 0, γzr, 0}T for λa(1) < 0 (in-plane shear in each CNT surface) and. Four bcc, and four hcp elements were calculated with embedded atom method (EAM) potential by Zhou et al. and compared with different EAM potential for Ni and Al by
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