forked from lijiext/lammps
223 lines
9.7 KiB
Plaintext
223 lines
9.7 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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lattice command :h3
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[Syntax:]
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lattice style scale keyword values ... :pre
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style = {none} or {sc} or {bcc} or {fcc} or {diamond} or \
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{sq} or {sq2} or {hex} or {custom} :ulb,l
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scale = scale factor between lattice and simulation box :l
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for style {none}:
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scale is not specified (nor any optional args)
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for all other styles:
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scale = reduced density rho* (for LJ units)
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scale = lattice constant in Angstroms (for real or metal units) :pre
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zero or more keyword/value pairs may be appended :l
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keyword = {origin} or {orient} or {spacing} or {a1} or {a2} or {a3} or {basis} :l
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{origin} values = x y z
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x,y,z = fractions of a unit cell (0 <= x,y,z < 1)
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{orient} values = dim i j k
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dim = {x} or {y} or {z}
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i,j,k = integer lattice directions
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{spacing} values = dx dy dz
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dx,dy,dz = lattice spacings in the x,y,z box directions
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{a1},{a2},{a3} values = x y z
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x,y,z = primitive vector components that define unit cell
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{basis} values = x y z
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x,y,z = fractional coords of a basis atom (0 <= x,y,z < 1) :pre
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:ule
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[Examples:]
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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 :pre
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[Description:]
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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
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atoms, that is replicated infinitely in all dimensions. The arguments
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of the lattice command can be used to define a wide variety of
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crystallographic lattices.
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A lattice is used by LAMMPS in two ways. First, the
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"create_atoms"_create_atoms.hmtl command creates atoms on the lattice
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points inside the simulation box. Note that the
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"create_atoms"_create_atoms.html command allows different atom types
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to be assigned to different basis atoms of the lattice. Second, the
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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 (e.g. "region"_region.html
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and "velocity"_velocity.html), which are often convenient when the
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underlying problem geometry is atoms on a lattice.
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The lattice style must be consistent with the dimension of the
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simulation - see the "dimension"_dimension.html command. Styles {sc}
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or {bcc} or {fcc} or {diamond} are for 3d problems. Styles {sq} or
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{sq2} or {hex} are for 2d problems. Style {custom} can be used for
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either 2d or 3d problems.
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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)
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that map the unit cell into the simulation box. The vectors a1,a2,a3
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are the edge vectors of the unit cell. This is the nomenclature for
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"primitive" vectors in solid-state crytallography, but in LAMMPS the
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unit cell they determine does not have to be a "primitive cell" of
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minimum volume.
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:line
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Lattices of style {sc}, {fcc}, {bcc}, and {diamond} 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 0.0 0.0, a2 = 0.0 1.0 0.0, and a3 = 0.0 0.0 1.0. The placement of
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the basis atoms within the unit cell are described in any solid-state
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physics text. A {sc} lattice has 1 basis atom at the
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lower-left-bottom corner of the cube. A {bcc} lattice has 2 basis
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atoms, one at the corner and one at the center of the cube. A {fcc}
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lattice has 4 basis atoms, one at the corner and 3 at the cube face
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centers. A {diamond} lattice has 8 basis atoms.
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Lattices of style {sq} and {sq2} are 2d lattices that define a square
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unit cell with edge length = 1.0. This means a1 = 1.0 0.0 0.0 and a2
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= 0.0 1.0 0.0. A {sq} lattice has 1 basis atom at the lower-left
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corner of the square. A {sq2} lattice has 2 basis atoms, one at the
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corner and one at the center of the square. A {hex} style is also a
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2d lattice, but the unit cell is rectangular, with a1 = 1.0 0.0 0.0
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and a2 = 0.0 sqrt(3.0) 0.0. It has 2 basis atoms, one at the corner
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and one at the center of the rectangle.
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A lattice of style {custom} allows you to specify a1, a2, a3, and a list
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of basis atoms to put in the unit cell. By default, a1,a2,a3 are 3
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orthogonal unit vectors (edges of a unit cube). But you can specify
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them to be of any length and non-orthogonal to each other, so that
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they describe a tilted parallelepiped. Via the {basis} keyword you
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add atoms, one at a time, to the unit cell. Its arguments are
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fractional coordinates (0.0 <= x,y,z < 1.0), so that a value of 0.5
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means a position half-way across the unit cell in that dimension.
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:line
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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.
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The {scale} 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
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multiplicative factor to apply to the unit cell, to convert it to a
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lattice of the desired size and distance units in the simulation box.
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The meaning of the {scale} argument depends on the "units"_unit.html
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being used in your simulation.
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For unit style {real} or {metal}, the scale argument is in Angstroms.
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For example, if the unit cell is a unit cube with edge length 1.0,
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setting scale = 3.52 would create a cubic lattice with a spacing of
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3.52 Angstroms.
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For unit style {lj}, 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 =
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the number of basis atoms in the unit cell (described below), and dim
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= 2 or 3 for the dimensionality of the simulation. Effectively, this
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means that if LJ particles of size sigma = 1.0 are used in the
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simulation, the lattice of particles will be at the desired reduced
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density.
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The {origin} 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.
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The {orient} option specifies how the unit cell will be rotated when
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mapping it into the simulation box. The {dim} argument is one of the
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3 coordinate axes in the simulation box. The other 3 arguments are
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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. The 3 lattice directions you specify 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.
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:line
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Several LAMMPS commands have the option to use distance units that are
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inferred from "lattice spacing" in the x,y,z box directions. E.g. the
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"region"_region.html command can create a block of size 10x20x20,
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where 10 means 10 lattice spacings in the x direction.
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The {spacing} 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
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are multiplied by the multiplicative factor described above that is
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associated with the scale factor. Thus a spacing of 1.0 means one
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unit cell independent of the scale factor. This option can be useful
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if the spacings LAMMPS computes are inconvenient to use in subsequent
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commands, which can be the case for non-orthogonal or rotated/scaled
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lattices.
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If the {spacing} 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, shifted, rotated), so that
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it now has (perhaps) a modified shape and orientation. The lattice
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spacing in X is defined as the difference between the min/max extent
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of the x coordinates of the 8 corner points of the modified unit cell.
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Similarly, the Y and Z lattice spacings are defined as the min/max of
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the y and z coordinates.
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Note that if the unit cell has axis-aligned edges (a1,a2,a3) and is
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not rotated (via the {orient} keyword), then the lattice spacings in
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each dimension are simply the scale factor (descibed above) multiplied
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by the length of a1,a2,a3. Thus a {hex} 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.
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For unit cells with a more general shape or when a rotation is
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applied, the lattice spacing is less intuitive. But regardless, the
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values of the lattice spacings LAMMPS will use are printed out, so
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their effect in commands that use the spacings should be decipherable.
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:line
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The command "lattice none" can be used to turn off a previous lattice
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definition. Any command that attempts to use the lattice directly
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("create_atoms"_create_atoms.html) or associated lattice spacings will
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then generate an error. No additional arguments need be used with
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"lattice none".
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:line
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[Restrictions:]
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The {a1,a2,a3,basis} keywords can only be used with style {custom}.
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For lattices oriented at an angle or with a non-orthognal unit cell,
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care must be taken when using the "region"_region.html and
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"create_atoms"_create_atoms.html commands to create a periodic system.
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If the box size is not chosen appropriately, the system may not
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actually be periodic, and atoms may overlap incorrectly at the faces
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of the simulation box.
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[Related commands:]
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"dimension"_dimension.html, "create_atoms"_create_atoms.html,
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"region"_region.html
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[Default:]
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lattice none :pre
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For other lattice styles, the option defaults are origin = 0.0 0.0
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0.0, orient = x 1 0 0, orient = y 0 1 0, orient = z 0 0 1, a1 = 1.0
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0.0 0.0, a2 = 0.0 1.0 0.0, and a3 = 0.0 0.0 1.0.
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