Vibrational and thermodynamic properties of metals from a model embedded-atom potential

Closing the Gap Between Nano- and Macroscale: Atomic Interactions vs. Macroscopic Materials Behavior

“…(55) at T = 300 K yields the thermal expansion coefficient of α th = 9.1 · 10 −6 K −1 . This value is smaller than the corresponding literature value α th Cu ≈ 15 · 10 −6 K −1 (Bian et al, 2008), whereas the temperature dependence R 01 = R 01 (T) ⇔ a (e) = a (e) (T) qualitatively agrees with experimental observations. The reasons for the deviations are different.…”

“…(Johnson, 1989). Squared, red points identify experimental data at room temperature according to the literature, (Bian et al, 2008;Svensson et al, 1967). At finite temperature real crystal vibrations show a wide range of wave vectors and frequencies.…”

“…Here we considered the three elemental symmetry directions of the FCC-structure, namely ξ[100], ξ [011],a n dξ [111] with ξ ∈ [0, 2π/a (e) ] or ξ ∈ [0, π/a (e) ], respectively (1st BRILLOUIN zone 9 ). The squared, discrete points are added for comparative purposes and identify experimental data obtained from (Bian et al, 2008;Svensson et al, 1967). By means of quantum-mechanics and statistical physics the kinetic energy, resulting from lattice vibrations, can be written as, cf.…”

“…In (Bian et al, 2008) the authors, for example, uniformly discretized the BRILLOUIN zone by 20 3 grid points and used a weighted sum of 256 different wave vectors. However, such procedure requires considerable computational capacities since the eigenvalue-problem of Eq.…”

“…Consequently, α th is insufficiently reproduced. Indeed, incorporating more wave vectors leads to more accurate results (Bian et al, 2008;Kagaya et al, 1988), but the computational costs drastically increase. In case of cubic lattice symmetry the heat capacity at constant pressure, c p , can be easily calculated via the relation c p (T)=c v (T)+3T(C 1111 + 2C 1122 )α 2 th (T).…”