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Particle-based multiscale coarse graining with density-dependent potentials: Application to molecular crystals (hexahydro-1,3,5-trinitro-s-triazine)
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Image of FIG. 1.
FIG. 1.

Coarse graining of the RDX molecule into one-site and four-site representations.

Image of FIG. 2.
FIG. 2.

Panel (a): One-site MS-CG force profiles as obtained from force-matching to 550 K (thin solid) and 350/550 K (thick solid) samplings. For 350/550 K force (MS-CG/0 model), possible choices of core interactions corresponding to core distances outlined in panel (b) in vertical lines are shown in dash-dash-dotted (hard-wall core) and dashed (exponential core). Panel (b): One-site MS-CG potentials at different pressures and T = 300 K. Vertical dashed lines mark possible selections of the core distance. Shown are potentials at P (GPa): 0 (filled circles), 0.5 (filled squares), 1 (filled triangles), 2 (empty circles), 3 (empty squares), 5 (empty triangles), 10 (stars). The P = 0 GPa potential corresponds to 350 K/550 K force in panel (a). Dotted line shows the potential corresponding to 550 K force in panel (a). On both panels dot-dashed line outlines the atomistic c.m.-c.m. RDF in arbitrary units.

Image of FIG. 3.
FIG. 3.

Comparison of RDX unit cells calculated at T = 4.5 K using atomistic and MS-CG-D models. For the atomistic model unit cell, red balls denote the molecular c.m. locations superimposed upon the ball-and-stick representations of the molecules, whereas green balls denote the CG interaction sites.

Image of FIG. 4.
FIG. 4.

Comparison of the α-RDX crystal lattice structure from simulations using the atomistic (red balls denote molecular c.m.) and MS-CG-D (green balls) models. Panel (a): [001]-view of lattice from the MS-CG-D simulation; Panel (b): Same view as in panel (a) for the atomistic model; Panel (c): [100]-view of superimposed lattices; Panel (d): [010]-view. In panels (a), (b), and (c) dotted and dashed lines outline location of planes in the atomistic lattice, which correspond to planes shown in dotted and solid lines for MS-CG-D lattice. In panel (b), atomistic planes (dashed) move to new locations in MS-CG-D lattice (solid) in panel (a). In panel (c), the two distinct planes in the atomistic representation (dashed) collapse into a single plane in the MS-CG representation (solid line).

Image of FIG. 5.
FIG. 5.

Panel (a): c.m. RDFs from atomistic (solid), MS-CG 350/550 K (dotted), and 550 K (dashed) simulations of liquid RDX at T = 550 K using one-site (black) and four-site (color) MS-CG models. Panel (b): c.m. RDFs from atomistic (solid) and one-site MS-CG-D (dashed) simulations at different P. Shown are P (GPa): 0 (cyan), 0.5 (black), 1 (blue), 2 (green), and 5 (red). Panel (c): c.m. RDFs from atomistic (thick solid) and MS-CG-D (thin solid) simulations of crystalline RDX at T = 300 K. The corresponding running coordination number N c shown in dashed lines.

Image of FIG. 6.
FIG. 6.

Distributions of the order parameter Eqs. (38) and (39) with different coordination number N c for atomistic (thick) and MS-CG-D (thin) models. The MS-CG-D results shown for reference crystal structure {R IK } from atomistic (solid) and MS-CG-D (dashed) models.

Image of FIG. 7.
FIG. 7.

Panel (a): Snapshots of the liquid-solid interface from simulation of slab melting at T = 490 K, at which close-packed structure formed at the interface (upper), and more common configuration (bottom). In the upper snapshot, the closed-packed domains of different from hP2 structure are contoured by dotted line. Such domains are artifact of the model reflecting limited transferability of the model to heterogeneous structures such as interfaces. These domains are similar to those shown in inset to Fig. 4(a) and discussed in the text. Panel (b): Equilibrium global order parameter, Eq. (39) with N c = 12 as a function of T for crystal. Insert shows for crystal at T = 450 and 550 K.

Image of FIG. 8.
FIG. 8.

Comparison of isotherms for crystalline RDX at T = 300 K (crosses) and molten RDX at T = 550 K (circles) from atomistic (solid) and MS-CG-D (dashed) models. Panel (a): V/V 0P isotherm, where V 0 is ambient volume; Panel (b) ΔU conf P isotherm, where is the change in the total internal potential energy with respect to the ambient value .

Image of FIG. 9.
FIG. 9.

Panel (a): All-atom VDOS (dashed), atomistic VDOS of c.m. (thin solid), and MS-CG-D (thick solid) in arbitrary units. The vertical dashed lines mark the parts of spectrum: (I) Only lattice modes associated with movements and rotations of molecular c.m.; (II) Mix of c.m. lattice modes with wagging and torsional modes of nitro groups. Panel (b): All-atom VDOS with portion of spectrum shown in panel (a) marked with a vertical solid line. The vertical dashed line (150 cm−1) marks the low frequency region in which lattice modes are present.

Image of FIG. 10.
FIG. 10.

Panel (a): Hugoniot curves of RDX from the atomistic model (circles), the MG-CG-D model (triangles), and experiment (solid line). Panel (b): Pressure vs. temperature for the calculated shock Hugoniot of RDX from atomistic (circles) and MS-CG-D (squares) models. Dashed line depicts the MS-CG-D melting curve using the Kraut-Kennedy relation as discussed in the text. Right T-axis is for the atomistic model and left T-axis is for the MS-CG-D model.

Image of FIG. 11.
FIG. 11.

The profiles of (top frame) molecular density ρ mol , (middle frame) effective translational temperature T eff , atomistic temperature T atm (filled circles), and (bottom frame) global order parameter [Eq. (39)] in shocked RDX from atomistic (thick) and MS-CG-D (thin) simulations. Panel (a): V p = 1 km/s; Panel (b): V p = 3 km/s. The MS-CG-D ρ mol curve is shifted up by difference Δρ0 = 0.215 in the values of atomistic and MS-CG-D molecular density of crystal at T = 4.5 K for a better comparison.


Generic image for table
Table I.

Coefficients A n of the least-squares fit of the one-site MS-CG force at P = 0 GPa using the polynomial equation (35) (second column) and Chebyshev series equations (36) and (37) (third column), with power of the term n shown in the first column. Atomic units for force and distance were used. For the Chebyshev series, the following radii were used in Eq. (37): R core = 8.5 a.u., R cut = 29.011 a.u. The expansions were switched to zero using the linear switching function as in Eq. (33) with δ R = 4.0 a.u. for a polynomial expansion and with δ R = 2.0 a.u. for a Chebyshev expansion. The fourth column shows the values of parameters for the density dependent contribution Eq. (33). At R < R core = 8.5 a.u., the force extrapolated as discussed in Sec. III B. A cutoff of 1.535 nm must be applied to the expansions.

Generic image for table
Table II.

Lattice parameters a, b, c and density ρ of the RDX crystal at different T and P = 0 GPa from atomistic and MS-CG-D models.

Generic image for table
Table III.

Young's (E) and shear (G) moduli at different T (K) and P (GPa). Units are GPa.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Particle-based multiscale coarse graining with density-dependent potentials: Application to molecular crystals (hexahydro-1,3,5-trinitro-s-triazine)