forked from lijiext/lammps
229 lines
9.1 KiB
Plaintext
229 lines
9.1 KiB
Plaintext
.. index:: fix orient/fcc
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fix orient/fcc command
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======================
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fix orient/bcc command
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======================
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.. parsed-literal::
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fix ID group-ID orient/fcc nstats dir alat dE cutlo cuthi file0 file1
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fix ID group-ID orient/bcc nstats dir alat dE cutlo cuthi file0 file1
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* ID, group-ID are documented in :doc:`fix <fix>` 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/bcc 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
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Examples
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""""""""
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.. parsed-literal::
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fix gb all orient/fcc 0 1 4.032008 0.001 0.25 0.75 xi.vec chi.vec
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fix gb all orient/bcc 0 1 2.882 0.001 0.25 0.75 ngb.left ngb.right
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Description
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"""""""""""
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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 :ref:`(Janssens) <Janssens>`. The adaptiation to bcc crystals
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is described in :ref:`(Wicaksono1) <Wicaksono1>`. The computed force is only
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applied to 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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.. image:: Eqs/fix_orient_fcc.jpg
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:align: center
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which are fully explained in :ref:`(Janssens) <Janssens>`. For fcc crystals
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this order parameter Xi for atom I in equation (1) is a sum over the
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12 nearest neighbors of atom I. For bcc crystals it is the
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corresponding sum of the 8 nearest neighbors. Rj is the vector from
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atom I to its neighbor J, and RIj is a vector in the reference
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(perfect) crystal. That is, if dir = 0/1, then RIj is a vector to an
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atom coord from file 0/1. Equation (2) gives the expected value of
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the order parameter XiIJ in the other grain. Hi and lo cutoffs are
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defined in equations (3) and (4), using the input parameters *cutlo*
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and *cuthi* as thresholds to avoid adding grain boundary energy when
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the deviation in the order parameter from 0 or 1 is small (e.g. due to
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thermal fluctuations in a perfect crystal). The added potential
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energy Ui for atom I is given in equation (6) where it is interpolated
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between 0 and dE using the two threshold Xi values and the Wi value of
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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 or bcc
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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 or 8 nearest neighbors of each atom
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(which should be valid for an fcc or bcc crystal). A longer/shorter
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cutoff can be imposed by adjusting *alat*\ . If a particular atom has
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less than 12 or 8 neighbors within the cutoff, the order parameter of
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equation (1) is effectively multiplied by 12 or 8 divided by the
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actual number of neighbors 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 shown below. A tutorial that can help for
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writing the orientation files is given in :ref:`(Wicaksono2) <Wicaksono2>`
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Restart, fix_modify, output, run start/stop, minimize info
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""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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No information about this fix is written to :doc:`binary restart files <restart>`.
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The :doc:`fix_modify <fix_modify>` *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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:doc:`thermodynamic output <thermo_style>`.
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The :doc:`fix_modify <fix_modify>` *respa* option is supported by these
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fixes. This allows to set at which level of the :doc:`r-RESPA <run_style>`
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integrator a fix is adding its forces. Default is the outermost level.
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This fix calculates a global scalar which can be accessed by various
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:ref:`output commands <howto_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 :ref:`output commands <howto_15>`. The array
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stores the order parameter Xi and normalized order parameter (0 to 1)
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for 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 :doc:`run <run>` command. This fix is not invoked during :doc:`energy minimization <minimize>`.
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Restrictions
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""""""""""""
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This fix is part of the MISC package. It is only enabled if LAMMPS
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was built with that package. See the :ref:`Making LAMMPS <start_3>` section for more info.
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This fix should only be used with fcc or bcc lattices.
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Related commands
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""""""""""""""""
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:doc:`fix_modify <fix_modify>`
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**Default:** none
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----------
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.. _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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.. _Wicaksono1:
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**(Wicaksono1)** Wicaksono, Sinclair, Militzer, Computational Materials
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Science, 117, 397-405 (2016).
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.. _Wicaksono2:
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**(Wicaksono2)** Wicaksono, figshare,
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https://dx.doi.org/10.6084/m9.figshare.1488628.v1 (2015).
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----------
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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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.. parsed-literal::
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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
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file1:
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.. parsed-literal::
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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
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Section_commands.html#comm
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