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< title > lattice command — LAMMPS 15 May 2015 version documentation< / title >
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< li class = "toctree-l1" > < a class = "reference internal" href = "Section_intro.html" > 1. Introduction< / a > < / li >
< li class = "toctree-l1" > < a class = "reference internal" href = "Section_start.html" > 2. Getting Started< / a > < / li >
< li class = "toctree-l1" > < a class = "reference internal" href = "Section_commands.html" > 3. Commands< / a > < / li >
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< li class = "toctree-l1" > < a class = "reference internal" href = "Section_accelerate.html" > 5. Accelerating LAMMPS performance< / a > < / li >
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< li class = "toctree-l1" > < a class = "reference internal" href = "Section_tools.html" > 9. Additional tools< / a > < / li >
< li class = "toctree-l1" > < a class = "reference internal" href = "Section_modify.html" > 10. Modifying & extending LAMMPS< / a > < / li >
< li class = "toctree-l1" > < a class = "reference internal" href = "Section_python.html" > 11. Python interface to LAMMPS< / a > < / li >
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< div class = "section" id = "lattice-command" >
< span id = "index-0" > < / span > < h1 > lattice command< a class = "headerlink" href = "#lattice-command" title = "Permalink to this headline" > ¶< / a > < / h1 >
< div class = "section" id = "syntax" >
< h2 > Syntax< a class = "headerlink" href = "#syntax" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < pre > lattice style scale keyword values ...
< / pre > < / div >
< / div >
< ul class = "simple" >
< li > style = < em > none< / em > or < em > sc< / em > or < em > bcc< / em > or < em > fcc< / em > or < em > hcp< / em > or < em > diamond< / em > or < em > sq< / em > or < em > sq2< / em > or < em > hex< / em > or < em > custom< / em > < / li >
< li > scale = scale factor between lattice and simulation box< / li >
< / ul >
< div class = "highlight-python" > < div class = "highlight" > < pre > scale = reduced density rho* (for LJ units)
scale = lattice constant in distance units (for all other units)
< / pre > < / div >
< / div >
< ul class = "simple" >
< li > zero or more keyword/value pairs may be appended< / li >
< li > keyword = < em > origin< / em > or < em > orient< / em > or < em > spacing< / em > or < em > a1< / em > or < em > a2< / em > or < em > a3< / em > or < em > basis< / em > < / li >
< / ul >
< pre class = "literal-block" >
< em > origin< / em > values = x y z
x,y,z = fractions of a unit cell (0 < = x,y,z < 1)
< em > orient< / em > values = dim i j k
dim = < em > x< / em > or < em > y< / em > or < em > z< / em >
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i,j,k = integer lattice directions
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< em > spacing< / em > values = dx dy dz
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dx,dy,dz = lattice spacings in the x,y,z box directions
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< em > a1< / em > ,*a2*,*a3* values = x y z
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x,y,z = primitive vector components that define unit cell
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< em > basis< / em > values = x y z
x,y,z = fractional coords of a basis atom (0 < = x,y,z < 1)
< / pre >
< / div >
< div class = "section" id = "examples" >
< h2 > Examples< a class = "headerlink" href = "#examples" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < pre > lattice fcc 3.52
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lattice hex 0.85
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lattice sq 0.8 origin 0.0 0.5 0.0 orient x 1 1 0 orient y -1 1 0
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lattice custom 3.52 a1 1.0 0.0 0.0 a2 0.5 1.0 0.0 a3 0.0 0.0 0.5 &
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basis 0.0 0.0 0.0 basis 0.5 0.5 0.5
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lattice none 2.0
< / pre > < / div >
< / div >
< / div >
< div class = "section" id = "description" >
< h2 > Description< a class = "headerlink" href = "#description" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > Define a lattice for use by other commands. In LAMMPS, a lattice is
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simply a set of points in space, determined by a unit cell with basis
atoms, that is replicated infinitely in all dimensions. The arguments
of the lattice command can be used to define a wide variety of
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crystallographic lattices.< / p >
< p > A lattice is used by LAMMPS in two ways. First, the
< a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a > command creates atoms on the lattice
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points inside the simulation box. Note that the
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< a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a > command allows different atom types
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to be assigned to different basis atoms of the lattice. Second, the
lattice spacing in the x,y,z dimensions implied by the lattice, can be
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used by other commands as distance units
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(e.g. < a class = "reference internal" href = "create_box.html" > < em > create_box< / em > < / a > , < a class = "reference internal" href = "region.html" > < em > region< / em > < / a > and
< a class = "reference internal" href = "velocity.html" > < em > velocity< / em > < / a > ), which are often convenient to use when the
underlying problem geometry is atoms on a lattice.< / p >
< p > The lattice style must be consistent with the dimension of the
simulation - see the < a class = "reference internal" href = "dimension.html" > < em > dimension< / em > < / a > command. Styles < em > sc< / em >
or < em > bcc< / em > or < em > fcc< / em > or < em > hcp< / em > or < em > diamond< / em > are for 3d problems. Styles
< em > sq< / em > or < em > sq2< / em > or < em > hex< / em > are for 2d problems. Style < em > custom< / em > can be
used for either 2d or 3d problems.< / p >
< p > A lattice consists of a unit cell, a set of basis atoms within that
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cell, and a set of transformation parameters (scale, origin, orient)
that map the unit cell into the simulation box. The vectors a1,a2,a3
are the edge vectors of the unit cell. This is the nomenclature for
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“ primitive” vectors in solid-state crystallography, but in LAMMPS the
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
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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,
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< a class = "reference internal" href = "region.html" > < em > region< / em > < / a > , and < a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a > commands
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can be repeated multiple times to build a poly-crystalline model with
different geometric regions populated with atoms in different lattice
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orientations.< / p >
< hr class = "docutils" / >
< p > A lattice of style < em > none< / em > does not define a unit cell and basis set,
so it cannot be used with the < a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a >
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command. However it does define a lattice spacing via the specified
scale parameter. As explained above the lattice spacings in x,y,z can
be used by other commands as distance units. No additional
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keyword/value pairs can be specified for the < em > none< / em > style. By
default, a “ lattice none 1.0” is defined, which means the lattice
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spacing is the same as one distance unit, as defined by the
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< a class = "reference internal" href = "units.html" > < em > units< / em > < / a > command.< / p >
< p > Lattices of style < em > sc< / em > , < em > fcc< / em > , < em > bcc< / em > , and < em > diamond< / em > are 3d lattices
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that define a cubic unit cell with edge length = 1.0. This means a1 =
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1 0 0, a2 = 0 1 0, and a3 = 0 0 1. Style < em > hcp< / em > has a1 = 1 0 0, a2 = 0
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sqrt(3) 0, and a3 = 0 0 sqrt(8/3). The placement of the basis atoms
within the unit cell are described in any solid-state physics text. A
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< em > sc< / em > lattice has 1 basis atom at the lower-left-bottom corner of the
cube. A < em > bcc< / em > lattice has 2 basis atoms, one at the corner and one at
the center of the cube. A < em > fcc< / em > lattice has 4 basis atoms, one at the
corner and 3 at the cube face centers. A < em > hcp< / em > lattice has 4 basis
atoms, two in the z = 0 plane and 2 in the z = 0.5 plane. A < em > diamond< / em >
lattice has 8 basis atoms.< / p >
< p > Lattices of style < em > sq< / em > and < em > sq2< / em > are 2d lattices that define a square
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unit cell with edge length = 1.0. This means a1 = 1 0 0 and a2 = 0 1
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0. A < em > sq< / em > lattice has 1 basis atom at the lower-left corner of the
square. A < em > sq2< / em > lattice has 2 basis atoms, one at the corner and one
at the center of the square. A < em > hex< / em > style is also a 2d lattice, but
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the unit cell is rectangular, with a1 = 1 0 0 and a2 = 0 sqrt(3) 0.
It has 2 basis atoms, one at the corner and one at the center of the
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rectangle.< / p >
< p > A lattice of style < em > custom< / em > allows you to specify a1, a2, a3, and a
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list of basis atoms to put in the unit cell. By default, a1 and a2
and a3 are 3 orthogonal unit vectors (edges of a unit cube). But you
can specify them to be of any length and non-orthogonal to each other,
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so that they describe a tilted parallelepiped. Via the < em > basis< / em >
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keyword you add atoms, one at a time, to the unit cell. Its arguments
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are fractional coordinates (0.0 < = x,y,z < 1.0). The position vector
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x of a basis atom within the unit cell is thus a linear combination of
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the the unit cell’ s 3 edge vectors, i.e. x = bx a1 + by a2 + bz a3,
where bx,by,bz are the 3 values specified for the < em > basis< / em > keyword.< / p >
< hr class = "docutils" / >
< p > This sub-section discusses the arguments that determine how the
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idealized unit cell is transformed into a lattice of points within the
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simulation box.< / p >
< p > The < em > scale< / em > argument determines how the size of the unit cell will be
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scaled when mapping it into the simulation box. I.e. it determines a
multiplicative factor to apply to the unit cell, to convert it to a
lattice of the desired size and distance units in the simulation box.
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The meaning of the < em > scale< / em > argument depends on the < a class = "reference internal" href = "units.html" > < em > units< / em > < / a >
being used in your simulation.< / p >
< p > For all unit styles except < em > lj< / em > , the scale argument is specified in
the distance units defined by the unit style. For example, in < em > real< / em >
or < em > metal< / em > units, if the unit cell is a unit cube with edge length
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1.0, specifying scale = 3.52 would create a cubic lattice with a
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spacing of 3.52 Angstroms. In < em > cgs< / em > units, the spacing would be 3.52
cm.< / p >
< p > For unit style < em > lj< / em > , the scale argument is the Lennard-Jones reduced
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density, typically written as rho*. LAMMPS converts this value into
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the multiplicative factor via the formula “ factor^dim = rho/rho*” ,
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where rho = N/V with V = the volume of the lattice unit cell and N =
the number of basis atoms in the unit cell (described below), and dim
= 2 or 3 for the dimensionality of the simulation. Effectively, this
means that if LJ particles of size sigma = 1.0 are used in the
simulation, the lattice of particles will be at the desired reduced
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density.< / p >
< p > The < em > origin< / em > option specifies how the unit cell will be shifted or
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translated when mapping it into the simulation box. The x,y,z values
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are fractional values (0.0 < = x,y,z < 1.0) meaning shift the lattice
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by a fraction of the lattice spacing in each dimension. The meaning
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of “ lattice spacing” is discussed below.< / p >
< p > The < em > orient< / em > option specifies how the unit cell will be rotated when
mapping it into the simulation box. The < em > dim< / em > argument is one of the
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3 coordinate axes in the simulation box. The other 3 arguments are
the crystallographic direction in the lattice that you want to orient
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along that axis, specified as integers. E.g. “ orient x 2 1 0” means
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the x-axis in the simulation box will be the [210] lattice
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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
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orthogonal and obey the right-hand rule, i.e. (X cross Y) points in
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the Z direction.< / p >
< div class = "admonition warning" >
< p class = "first admonition-title" > Warning< / p >
< p class = "last" > The preceding paragraph describing lattice directions
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is only valid for orthogonal cubic unit cells (or square in 2d). If
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you are using a < em > hcp< / em > or < em > hex< / em > lattice or the more general lattice
style < em > custom< / em > with non-orthogonal a1,a2,a3 vectors, then you should
think of the 3 < em > orient< / em > vectors as creating a 3x3 rotation matrix
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which is applied to a1,a2,a3 to rotate the original unit cell to a new
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orientation in the simulation box.< / p >
< / div >
< hr class = "docutils" / >
< p > Several LAMMPS commands have the option to use distance units that are
inferred from “ lattice spacings” in the x,y,z box directions.
E.g. the < a class = "reference internal" href = "region.html" > < em > region< / em > < / a > command can create a block of size
10x20x20, where 10 means 10 lattice spacings in the x direction.< / p >
< div class = "admonition warning" >
< p class = "first admonition-title" > Warning< / p >
< p class = "last" > Though they are called lattice spacings, all the
commands that have a “ units lattice” option, simply use the 3 values
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as scale factors on the distance units defined by the
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< a class = "reference internal" href = "units.html" > < em > units< / em > < / a > command. Thus if you do not like the lattice
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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
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< em > spacing< / em > option.< / p >
< / div >
< p > If the < em > spacing< / em > option is not specified, the lattice spacings are
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computed by LAMMPS in the following way. A unit cell of the lattice
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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
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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 (no
rotation via the < em > orient< / em > keyword), then the lattice spacings in each
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dimension are simply the scale factor (described above) multiplied by
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the length of a1,a2,a3. Thus a < em > hex< / em > style lattice with a scale
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factor of 3.0 Angstroms, would have a lattice spacing of 3.0 in x and
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3*sqrt(3.0) in y.< / p >
< div class = "admonition warning" >
< p class = "first admonition-title" > Warning< / p >
< p class = "last" > For non-orthogonal unit cells and/or when a rotation
is applied via the < em > orient< / em > keyword, then the lattice spacings
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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
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then fill it with atoms via the < a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a >
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command, you will NOT necessarily create a periodic system.
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I.e. atoms may overlap incorrectly at the faces of the simulation box.< / p >
< / div >
< p > The < em > spacing< / em > option sets the 3 lattice spacings directly. All must
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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
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non-orthogonal or rotated lattices.< / p >
< p > Note that whenever the lattice command is used, the values of the
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lattice spacings LAMMPS calculates are printed out. Thus their effect
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in commands that use the spacings should be decipherable.< / p >
< / div >
< hr class = "docutils" / >
< div class = "section" id = "restrictions" >
< h2 > Restrictions< a class = "headerlink" href = "#restrictions" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > The < em > a1,a2,a3,basis< / em > keywords can only be used with style < em > custom< / em > .< / p >
< / div >
< div class = "section" id = "related-commands" >
< h2 > Related commands< a class = "headerlink" href = "#related-commands" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > < a class = "reference internal" href = "dimension.html" > < em > dimension< / em > < / a > , < a class = "reference internal" href = "create_atoms.html" > < em > create_atoms< / em > < / a > ,
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< h2 > Default< a class = "headerlink" href = "#default" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < pre > lattice none 1.0
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< p > For other lattice styles, the option defaults are origin = 0.0 0.0
2008-04-15 05:37:10 +08:00
0.0, orient = x 1 0 0, orient = y 0 1 0, orient = z 0 0 1, a1 = 1 0 0,
2015-07-30 22:53:28 +08:00
a2 = 0 1 0, and a3 = 0 0 1.< / p >
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