forked from lijiext/lammps
179 lines
7.8 KiB
Plaintext
179 lines
7.8 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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fix orient/fcc command :h3
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fix ID group-ID orient/fcc nstats dir alat dE cutlo cuthi file0 file1 :pre
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ID, group-ID are documented in "fix"_fix.html command
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nstats = print stats every this many steps, 0 = never
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dir = 0/1 for which crystal is used as reference
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alat = fcc cubic lattice constant (distance units)
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dE = energy added to each atom (energy units)
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cutlo,cuthi = values between 0.0 and 1.0, cutlo < cuthi
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file0,file1 = files that specify orientation of each grain :ul
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[Examples:]
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fix gb all orient/fcc 0 1 4.032008 0.001 0.25 0.75 xi.vec chi.vec :pre
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[Description:]
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The fix applies an orientation-dependent force to atoms near a planar
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grain boundary which can be used to induce grain boundary migration
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(in the direction perpendicular to the grain boundary plane). The
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motivation and explanation of this force and its application are
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described in "(Janssens)"_#Janssens. The force is only applied to
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atoms in the fix group.
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The basic idea is that atoms in one grain (on one side of the
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boundary) have a potential energy dE added to them. Atoms in the
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other grain have 0.0 potential energy added. Atoms near the boundary
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(whose neighbor environment is intermediate between the two grain
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orientations) have an energy between 0.0 and dE added. This creates
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an effective driving force to reduce the potential energy of atoms
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near the boundary by pushing them towards one of the grain
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orientations. For dir = 1 and dE > 0, the boundary will thus move so
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that the grain described by file0 grows and the grain described by
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file1 shrinks. Thus this fix is designed for simulations of two-grain
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systems, either with one grain boundary and free surfaces parallel to
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the boundary, or a system with periodic boundary conditions and two
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equal and opposite grain boundaries. In either case, the entire
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system can displace during the simulation, and such motion should be
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accounted for in measuring the grain boundary velocity.
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The potential energy added to atom I is given by these formulas
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:c,image(Eqs/fix_orient_fcc.jpg)
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which are fully explained in "(Janssens)"_#Janssens. The order
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parameter Xi for atom I in equation (1) is a sum over the 12 nearest
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neighbors of atom I. Rj is the vector from atom I to its neighbor J,
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and RIj is a vector in the reference (perfect) crystal. That is, if
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dir = 0/1, then RIj is a vector to an atom coord from file 0/1.
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Equation (2) gives the expected value of the order parameter XiIJ in
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the other grain. Hi and lo cutoffs are defined in equations (3) and
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(4), using the input parameters {cutlo} and {cuthi} as thresholds to
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avoid adding grain boundary energy when the deviation in the order
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parameter from 0 or 1 is small (e.g. due to thermal fluctuations in a
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perfect crystal). The added potential energy Ui for atom I is given
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in equation (6) where it is interpolated between 0 and dE using the
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two threshold Xi values and the Wi value of equation (5).
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The derivative of this energy expression gives the force on each atom
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which thus depends on the orientation of its neighbors relative to the
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2 grain orientations. Only atoms near the grain boundary feel a net
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force which tends to drive them to one of the two grain orientations.
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In equation (1), the reference vector used for each neighbor is the
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reference vector closest to the actual neighbor position. This means
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it is possible two different neighbors will use the same reference
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vector. In such cases, the atom in question is far from a perfect
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orientation and will likely receive the full dE addition, so the
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effect of duplicate reference vector usage is small.
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The {dir} parameter determines which grain wants to grow at the
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expense of the other. A value of 0 means the first grain will shrink;
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a value of 1 means it will grow. This assumes that {dE} is positive.
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The reverse will be true if {dE} is negative.
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The {alat} parameter is the cubic lattice constant for the fcc
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material and is only used to compute a cutoff distance of 1.57 * alat
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/ sqrt(2) for finding the 12 nearest neighbors of each atom (which
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should be valid for an fcc crystal). A longer/shorter cutoff can be
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imposed by adjusting {alat}. If a particular atom has less than 12
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neighbors within the cutoff, the order parameter of equation (1) is
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effectively multiplied by 12 divided by the actual number of neighbors
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within the cutoff.
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The {dE} parameter is the maximum amount of additional energy added to
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each atom in the grain which wants to shrink.
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The {cutlo} and {cuthi} parameters are used to reduce the force added
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to bulk atoms in each grain far away from the boundary. An atom in
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the bulk surrounded by neighbors at the ideal grain orientation would
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compute an order parameter of 0 or 1 and have no force added.
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However, thermal vibrations in the solid will cause the order
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parameters to be greater than 0 or less than 1. The cutoff parameters
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mask this effect, allowing forces to only be added to atoms with
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order-parameters between the cutoff values.
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{File0} and {file1} are filenames for the two grains which each
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contain 6 vectors (6 lines with 3 values per line) which specify the
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grain orientations. Each vector is a displacement from a central atom
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(0,0,0) to a nearest neighbor atom in an fcc lattice at the proper
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orientation. The vector lengths should all be identical since an fcc
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lattice has a coordination number of 12. Only 6 are listed due to
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symmetry, so the list must include one from each pair of
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equal-and-opposite neighbors. A pair of orientation files for a
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Sigma=5 tilt boundary are show below.
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[Restart, fix_modify, output, run start/stop, minimize info:]
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No information about this fix is written to "binary restart
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files"_restart.html.
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The "fix_modify"_fix_modify.html {energy} option is supported by this
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fix to add the potential energy of atom interactions with the grain
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boundary driving force to the system's potential energy as part of
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"thermodynamic output"_thermo_style.html.
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This fix calculates a global scalar which can be accessed by various
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"output commands"_Section_howto.html#4_15. The scalar is the
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potential energy change due to this fix. The scalar value calculated
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by this fix is "extensive".
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This fix also calculates a per-atom array which can be accessed by
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various "output commands"_Section_howto.html#4_15. The array stores
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the order parameter Xi and normalized order parameter (0 to 1) for
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each atom. The per-atom values can be accessed on any timestep.
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No parameter of this fix can be used with the {start/stop} keywords of
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the "run"_run.html command. This fix is not invoked during "energy
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minimization"_minimize.html.
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[Restrictions:]
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This fix should only be used with fcc lattices.
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[Related commands:]
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"fix_modify"_fix_modify.html
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[Default:] none
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:line
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:link(Janssens)
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[(Janssens)] Janssens, Olmsted, Holm, Foiles, Plimpton, Derlet, Nature
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Materials, 5, 124-127 (2006).
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:line
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For illustration purposes, here are example files that specify a
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Sigma=5 <100> tilt boundary. This is for a lattice constant of 3.5706
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Angs.
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file0:
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0.798410432046075 1.785300000000000 1.596820864092150
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-0.798410432046075 1.785300000000000 -1.596820864092150
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2.395231296138225 0.000000000000000 0.798410432046075
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0.798410432046075 0.000000000000000 -2.395231296138225
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1.596820864092150 1.785300000000000 -0.798410432046075
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1.596820864092150 -1.785300000000000 -0.798410432046075 :pre
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file1:
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-0.798410432046075 1.785300000000000 1.596820864092150
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0.798410432046075 1.785300000000000 -1.596820864092150
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0.798410432046075 0.000000000000000 2.395231296138225
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2.395231296138225 0.000000000000000 -0.798410432046075
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1.596820864092150 1.785300000000000 0.798410432046075
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1.596820864092150 -1.785300000000000 0.798410432046075 :pre
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