2006-09-22 00:22:34 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>fix orient/fcc command
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</H3>
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<PRE>fix ID group-ID orient/fcc nstats dir alat dE cutlo cuthi file0 file1
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>nstats = print stats every this many steps, 0 = never
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<LI>dir = 0/1 for which crystal is used as reference
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<LI>alat = fcc cubic lattice constant (distance units)
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<LI>dE = energy added to each atom (energy units)
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<LI>cutlo,cuthi = values between 0.0 and 1.0, cutlo < cuthi
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<LI>file0,file1 = files that specify orientation of each grain
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>fix gb all orient/fcc 0 1 4.032008 0.001 0.25 0.75 xi.vec chi.vec
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>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 <A HREF = "#Janssens">(Janssens)</A>. The force is only applied to
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atoms in the fix group.
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</P>
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<P>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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</P>
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<P>The potential energy added to atom I is given by these formulas
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</P>
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<CENTER><IMG SRC = "Eqs/fix_orient_fcc.jpg">
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</CENTER>
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<P>which are fully explained in <A HREF = "#Janssens">(Janssens)</A>. 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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2008-03-01 09:13:20 +08:00
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(4), using the input parameters <I>cutlo</I> and <I>cuthi</I> as thresholds to
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2006-09-22 00:22:34 +08:00
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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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2008-03-01 09:13:20 +08:00
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two threshold Xi values and the Wi value of equation (5).
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2006-09-22 00:22:34 +08:00
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</P>
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<P>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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</P>
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2008-03-01 09:13:20 +08:00
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<P>In equation (1), the reference vector used for each neighbor is the
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2006-09-22 00:22:34 +08:00
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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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</P>
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<P>The <I>dir</I> 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 <I>dE</I> is positive.
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The reverse will be true if <I>dE</I> is negative.
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</P>
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<P>The <I>alat</I> 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 <I>alat</I>. 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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</P>
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<P>The <I>dE</I> 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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</P>
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<P>The <I>cutlo</I> and <I>cuthi</I> 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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</P>
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<P><I>File0</I> and <I>file1</I> 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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</P>
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2007-10-11 06:28:11 +08:00
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<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
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2007-06-26 08:03:39 +08:00
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</P>
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<P>No information about this fix is written to <A HREF = "restart.html">binary restart
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files</A>.
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</P>
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<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> 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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<A HREF = "thermo_style.html">thermodynamic output</A>.
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</P>
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2007-10-10 02:24:42 +08:00
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<P>The potential energy change due to this fix is stored as a scalar
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quantity, which can be accessed by various <A HREF = "Section_howto.html#4_15">output
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2008-01-03 03:25:15 +08:00
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commands</A>. The scalar value calculated by
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this fix is "extensive", meaning it scales with the number of atoms in
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the simulation.
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2007-06-26 08:03:39 +08:00
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</P>
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<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
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the <A HREF = "run.html">run</A> command. This fix is not invoked during <A HREF = "minimize.html">energy
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minimization</A>.
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2006-09-22 00:22:34 +08:00
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</P>
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<P><B>Restrictions:</B>
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</P>
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<P>This fix should only be used with fcc lattices.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_modify.html">fix_modify</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<A NAME = "Janssens"></A>
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<P><B>(Janssens)</B> Janssens, Olmsted, Holm, Foiles, Plimpton, Derlet, Nature
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Materials, 5, 124-127 (2006).
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</P>
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<HR>
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<P>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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</P>
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<P>file0:
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</P>
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<PRE> 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
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</PRE>
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<P>file1:
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</P>
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<PRE> -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
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</PRE>
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</HTML>
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