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@ -82,6 +82,15 @@ are the edge vectors of the unit cell. This is the nomenclature for
unit cell they determine does not have to be a "primitive cell" of
minimum volume.
</P>
<P>Note that the lattice command can be used multiple times in an input
script. Each time it is invoked, the lattice attributes are
re-defined and are used for all subsequent commands (that use lattice
attributes). For example, a sequence of lattice,
<A HREF = "region.html">region</A>, and <A HREF = "create_atoms.html">create_atoms</A> commands
can be repeated multiple times to build a poly-crystalline model with
different geometric regions populated with atoms in different lattice
orientations.
</P>
<HR>
<P>A lattice of style <I>none</I> does not define a unit cell and basis set,
@ -168,61 +177,73 @@ mapping it into the simulation box. The <I>dim</I> argument is one of the
the crystallographic direction in the lattice that you want to orient
along that axis, specified as integers. E.g. "orient x 2 1 0" means
the x-axis in the simulation box will be the [210] lattice
direction. The 3 lattice directions you specify must be mutually
direction, and similarly for y and z. The 3 lattice directions you
specify do not have to be unit vectors, but they must be mutually
orthogonal and obey the right-hand rule, i.e. (X cross Y) points in
the Z direction. Note that this description is really only valid for
orthogonal lattices. If you are using the more general lattice style
<I>custom</I> with non-orthogonal a1,a2,a3 vectors, then think of the 3
<I>orient</I> options as creating a 3x3 rotation matrix which is applied to
a1,a2,a3 to rotate the original unit cell to a new orientation in the
simulation box.
the Z direction.
</P>
<P>IMPORTANT NOTE: The preceding paragraph describing lattice directions
is only valid for orthogonal cubic unit cells (or square in 2d). If
you are using a <I>hcp</I> or <I>hex</I> lattice or the more general lattice
style <I>custom</I> with non-orthogonal a1,a2,a3 vectors, then you should
think of the 3 <I>orient</I> vectors as creating a 3x3 rotation matrix
which is applied to a1,a2,a3 to rotate the original unit cell to a new
orientation in the simulation box.
</P>
<HR>
<P>Several LAMMPS commands have the option to use distance units that are
inferred from "lattice spacing" in the x,y,z box directions. E.g. the
<A HREF = "region.html">region</A> command can create a block of size 10x20x20,
where 10 means 10 lattice spacings in the x direction.
inferred from "lattice spacings" in the x,y,z box directions.
E.g. the <A HREF = "region.html">region</A> command can create a block of size
10x20x20, where 10 means 10 lattice spacings in the x direction.
</P>
<P>The <I>spacing</I> option sets the 3 lattice spacings directly. All must
be non-zero (use 1.0 for dz in a 2d simulation). The specified values
are multiplied by the multiplicative factor described above that is
associated with the scale factor. Thus a spacing of 1.0 means one
unit cell independent of the scale factor. This option can be useful
if the spacings LAMMPS computes are inconvenient to use in subsequent
commands, which can be the case for non-orthogonal or rotated
lattices.
<P>IMPORTANT NOTE: Though they are called lattice spacings, all the
commands that have a "units lattice" option, simply use the 3 values
as scale factors on the distance units defined by the
<A HREF = "units.html">units</A> command. Thus if you do not like the lattice
spacings computed by LAMMPS (e.g. for a non-orthogonal or rotated unit
cell), you can define the 3 values to be whatever you wish, via the
<I>spacing</I> option.
</P>
<P>If the <I>spacing</I> option is not specified, the lattice spacings are
computed by LAMMPS in the following way. A unit cell of the lattice
is mapped into the simulation box (scaled, shifted, rotated), so that
it now has (perhaps) a modified size and orientation. The lattice
spacing in X is defined as the difference between the min/max extent
of the x coordinates of the 8 corner points of the modified unit cell.
Similarly, the Y and Z lattice spacings are defined as the difference
in the min/max of the y and z coordinates.
is mapped into the simulation box (scaled and rotated), so that it now
has (perhaps) a modified size and orientation. The lattice spacing in
X is defined as the difference between the min/max extent of the x
coordinates of the 8 corner points of the modified unit cell (4 in
2d). Similarly, the Y and Z lattice spacings are defined as the
difference in the min/max of the y and z coordinates.
</P>
<P>Note that if the unit cell is orthogonal with axis-aligned edges (not
rotated via the <I>orient</I> keyword), then the lattice spacings in each
<P>Note that if the unit cell is orthogonal with axis-aligned edges (no
rotation via the <I>orient</I> keyword), then the lattice spacings in each
dimension are simply the scale factor (described above) multiplied by
the length of a1,a2,a3. Thus a <I>hex</I> style lattice with a scale
factor of 3.0 Angstroms, would have a lattice spacing of 3.0 in x and
3*sqrt(3.0) in y.
</P>
<P>IMPORTANT NOTE: For non-orthogonal unit cells and/or when a rotation
is applied via the <I>orient</I> keyword, then the lattice spacings may be
less intuitive. In particular, in these cases, there is no guarantee
that the lattice spacing is an integer multiple of the periodicity of
the lattice in that direction. Thus, if you create an orthogonal
periodic simulation box whose size in a dimension is a multiple of the
lattice spacing, and then fill it with atoms via the
<A HREF = "create_atoms.html">create_atoms</A> command, you will NOT necessarily
create a periodic system. I.e. atoms may overlap incorrectly at the
faces of the simulation box.
is applied via the <I>orient</I> keyword, then the lattice spacings
computed by LAMMPS are typically less intuitive. In particular, in
these cases, there is no guarantee that a particular lattice spacing
is an integer multiple of the periodicity of the lattice in that
direction. Thus, if you create an orthogonal periodic simulation box
whose size in a dimension is a multiple of the lattice spacing, and
then fill it with atoms via the <A HREF = "create_atoms.html">create_atoms</A>
command, you will NOT necessarily create a periodic system.
I.e. atoms may overlap incorrectly at the faces of the simulation box.
</P>
<P>Regardless of these issues, the values of the lattice spacings LAMMPS
calculates are printed out, so their effect in commands that use the
spacings should be decipherable.
<P>The <I>spacing</I> option sets the 3 lattice spacings directly. All must
be non-zero (use 1.0 for dz in a 2d simulation). The specified values
are multiplied by the multiplicative factor described above that is
associated with the scale factor. Thus a spacing of 1.0 means one
unit cell edge length independent of the scale factor. As mentioned
above, this option can be useful if the spacings LAMMPS computes are
inconvenient to use in subsequent commands, which can be the case for
non-orthogonal or rotated lattices.
</P>
<P>Note that whenever the lattice command is used, the values of the
lattice spacings LAMMPS calculates are printed out. Thus their effect
in commands that use the spacings should be decipherable.
</P>
<HR>