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The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
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10.1063/1.3454907
/content/aip/journal/jcp/132/23/10.1063/1.3454907
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/23/10.1063/1.3454907

Figures

Image of FIG. 1.
FIG. 1.

Orientationally ordered crystal structures for tetrahedral patchy particles: (a) diamond, (b) bcc, and (c) fcc-o. Two views are shown in each case, with the picture on the right corresponding to a rotation of the structure by [(a) and (b)] and (c) about the axis.

Image of FIG. 2.
FIG. 2.

Chemical potential as a function of pressure for the fluid phase and the diamond and bcc solids for the 12-6 LJ model along the isotherm.

Image of FIG. 3.
FIG. 3.

Fluid-bcc and diamond-bcc coexistence lines for the 12-6 LJ model obtained from Gibbs–Duhem simulations. Above , the diamond solid is not mechanically stable.

Image of FIG. 4.
FIG. 4.

Phase diagram of model patchy particles with tetrahedral symmetry for the 12-6 model and a patch width of as a function of (a) pressure and temperature, and (b) temperature and density. The dot in (a) indicates the thermodynamic state point at which direct coexistence simulations of the fluid-diamond and fluid-bcc interface were performed to study the growth behavior of these solids.

Image of FIG. 5.
FIG. 5.

Phase diagram of model patchy particles with tetrahedral symmetry for the 20-10 model and a patch width of as a function of (a) pressure and temperature, and (b) temperature and density.

Image of FIG. 6.
FIG. 6.

Enlarged view of the low temperature and low pressure region of the phase diagram for the 20-10 model.

Image of FIG. 7.
FIG. 7.

(a) Densities and (b) energies of the bcc solid (squares and solid line) and of the diamond solid (circles and dashed line) along the isobar for the 20-10 model.

Image of FIG. 8.
FIG. 8.

Chemical potential difference between the bcc and diamond solids along the isobar for (a) the 12-6 model and (b) the 20-10 model. The contributions of potential energy, , and entropy to the chemical potential are also given.

Image of FIG. 9.
FIG. 9.

Final configuration of the direct coexistence simulations of a fluid-diamond interface at and for the 12-6 model. Initially the simulation box contained 512 molecules in a diamond solid (i.e., unit cells) plus another 512 molecules in the fluid phase. Two different representations are shown. In (a) molecules that were in the diamond crystal in the initial configuration are colored in blue, whereas those that were fluid molecules in the initial configuration are shown in red. In (b) molecules that belong to the same diamond sublattice are colored in red, whereas those molecules not connected to the sublattice (i.e., defects) are colored in blue. As can be seen, the diamond crystal grows with a small number of defects.

Image of FIG. 10.
FIG. 10.

Final configuration of the direct coexistence simulations of a fluid-bcc interface at and for a simulation box containing 1296 molecules for the 12-6 model. Initially the simulation box contained 432 molecules in a bcc solid (i.e., unit cells) and 864 molecules of fluid. (a) and (b) show two different representations of the final configuration of the simulation, in which all the fluid has crystallized. (a) The molecules that were in the bcc solid structure in the initial configuration are colored in blue, whereas those that were fluid molecules in the starting configuration are colored in red. It can be seen that almost all the fluid has solidified into a diamond crystal. Only one or two incomplete bcc layers form at the two bcc-fluid interfaces. Most likely the defects in these first layers make less and less probable the growth of the bcc solid. (b) As mentioned in the manuscript a bcc solid is formed by two interpenetrating diamond solids. The two sublattices are highlighted by coloring the particles belonging to each sublattice in a different color, red for one sublattice and blue for the other. It can be seen that in this particular example, the same sublattice grew from each of the two interfaces. However, when the two diamond crystals growing from the two interfaces meet, some defects appear because as some particles were used to form one or two incomplete bcc layers at the bcc-fluid interfaces, the number of available particles is incommensurate with the dimensions of the simulation box (even though we chose it to be commensurate).

Tables

Generic image for table
Table I.

Coexistence points for the 12-6 model obtained using thermodynamic integration together with the Helmholtz free energies given as supplementary material (Ref. 60). Uncertainties in the potential energy per particle are smaller than 0.01.

Generic image for table
Table II.

Coexistence points for the 12-6 model obtained using the direct coexistence method. For comparison, the results from free energy calculations are also given.

Generic image for table
Table III.

Coexistence points for the 20-10 model obtained using thermodynamic integration together with the Helmholtz free energies given in the supplementary material (Ref. 60). Uncertainties in the densities are of the order of 0.001 and in the potential energy per particle are smaller than 0.01.

Generic image for table
Table IV.

Coexistence points for the 20-10 model obtained using the direct coexistence method. For comparison, the results from free energy calculations are also given.

Generic image for table
Table V.

Thermodynamic properties of the triple points found for the 20-10 model.

Generic image for table
Table VI.

Density and potential energy at zero temperature and pressure for the diamond and bcc solids for the two studied model potentials.

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/content/aip/journal/jcp/132/23/10.1063/1.3454907
2010-06-21
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The stability of a crystal with diamond structure for patchy particles with tetrahedral symmetry
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/23/10.1063/1.3454907
10.1063/1.3454907
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