FM potentials with shifted virial constraint (solid lines). The Al-Ni potentials obtained through force-matching without the virial constraint (dotted) and with the unshifted virial constraint (dashed) are shown for comparison.
Comparison of RDFs from reference ab initio (solid) and FM (dashed) MD simulations.
Diffusion coefficients in liquid Ni100 − x Al x at T = 1795 K (red) and 1525 K (blue) vs. aluminum concentration χAl = x(%). The simulation data are shown in solid lines and experimental data (Ref. 45) are shown in dashed lines. Triangles denote NVT MD results at higher density; circles and left triangles (inset) denote NPT MD results at ambient pressure.
Initial system configuration equilibrated at T = 800 K. The top panel shows the atomic configuration of the system; Al and Ni atoms are represented as red and blue balls, respectively. The bottom panel shows corresponding Al (red) and Ni (blue) particle densities in the z-direction. The thick line outlines a part of the system for which various z-profiles are displayed hereafter (i.e., Figs. 5, 6, and 9).
System temperature T(t) vs. time t from a NPH MD simulation of the system at T ini = 1300 K and P = 0 GPa (top left panel); particle density profiles ρAl(z) (red) and ρNi(z) (blue) along the z-direction at selected time moments labeled on the T(t) plot as t i are shown in remaining frames. On panels t 1 − t 4, the aluminum instant temperature profile T Al(z) is shown in green and in panel t 1 the T Ni(z) is shown in cyan. The T(z) profiles are scaled down by a factor 20 for clarity. In panel t 4 the axis z is shifted left to accommodate the profile.
Pressure P(z) [panel (a)], and fractional coordination number [panel (b)] profiles along the z-direction at times t i from the same simulation as in Fig. 5.
Snapshots of the xz view of the system from the same simulation as in Fig. 5 at times t i (see also Fig. 4).
Temperature T(t) [panel (a)] and compression V(t)/V ini [panel (b)], where V ini is the system initial volume for P = 0 GPa, vs. time from NPH simulations at T ini = 1300 K and P(GPa) = 0 (red), 2 (blue), and 5 (green). Selected ith times labeled as .
Particle density profiles ρ(z) in the z-direction at times from the same simulations as in Fig. 8.
Snapshots of the xz view of the system from the T ini = 1300 K and P = 5 GPa simulation (Figs. 8 and 9) at times .
Coefficients of the least-squares fit of the forces f ij = AlAl, NiNi, AlNi(r) using the expansion in Eq. (11) with n max = 14. Atomic units for force and distance are used. At small separations , the f ij (r) can be extrapolated as with a.u., a.u., a.u. A cut-off of 0.705 nm must be applied to the Al-Al expansion and a cut-off of 0.7938 nm must be applied to the Ni-Ni and Al-Ni expansions. The original numerical forces and potentials are provided in the supplementary material.38
Crystal properties calculated with the new numerical PA FM potentials in comparison with DFT (LDA and GGA), and the experiment. Shown are: a 0 lattice constant; U c cohesive energy and formation energy in parentheses; B bulk modulus; G shear modulus; E Young's modulus (the moduli are isothermal); σ Poisson's ratio; T m melting temperature; α linear thermal expansion coefficient.
Density ρ L (kg/m3) and density temperature coefficient ρ′ (kg/m3/K) for Ni-Al at liquid temperatures T L from the PA model and data from the literature.
Energies (eV) of composition-conserving point-defect complexes in B2-NiAl. Ab initio energies are shown for comparison (the first number is from Ref. 81 and the second one from Ref. 82).
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