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>lattice command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>lattice style scale keyword values ...
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</PRE>
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2006-11-14 06:18:34 +08:00
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<UL><LI>style = <I>none</I> or <I>sc</I> or <I>bcc</I> or <I>fcc</I> or <I>diamond</I> or <I>sq</I> or <I>sq2</I> or <I>hex</I> or <I>user</I>
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2006-11-14 06:18:34 +08:00
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<LI>scale = scale factor between lattice and simulation box
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<PRE> for style <I>none</I>:
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scale is not specified (nor any optional args)
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for all other styles:
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2006-11-14 06:18:34 +08:00
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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)
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</PRE>
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>origin</I> or <I>orient</I> or <I>a1</I> or <I>a2</I> or <I>a3</I> or <I>basis</I>
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<PRE> <I>origin</I> 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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<I>orient</I> values = dim i j k
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dim = <I>x</I> or <I>y</I> or <I>z</I>
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i,j,k = integer lattice directions
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<I>a1</I>,<I>a2</I>,<I>a3</I> values = x y z
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x,y,z = primitive vector components that define unit cell
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<I>basis</I> values = x y z
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x,y,z = fractional coords of a basis atom (0 <= x,y,z < 1)
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<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 user 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
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</PRE>
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<P><B>Description:</B>
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</P>
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<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
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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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</P>
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<P>A lattice is used by LAMMPS in two ways. First, the
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<A HREF = "create_atoms.hmtl">create_atoms</A> command creates atoms on the lattice
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points inside the simulation box. Note that the
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<A HREF = "create_atoms.html">create_atoms</A> 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. <A HREF = "region.html">region</A>
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and <A HREF = "velocity.html">velocity</A>), which are often convenient when the
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underlying problem geometry is atoms on a lattice.
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</P>
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<P>The lattice style must be consistent with the dimension of the
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simulation - see the <A HREF = "dimension.html">dimension</A> command. Styles <I>sc</I>
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or <I>bcc</I> or <I>fcc</I> or <I>diamond</I> are for 3d problems. Styles <I>sq</I> or
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<I>sq2</I> or <I>hex</I> are for 2d problems. Style <I>user</I> can be used for
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either 2d or 3d problems.
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</P>
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<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)
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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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</P>
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<HR>
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<P>Lattices of style <I>sc</I>, <I>fcc</I>, <I>bcc</I>, and <I>diamond</I> 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 <I>sc</I> lattice has 1 basis atom at the
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lower-left-bottom corner of the cube. A <I>bcc</I> lattice has 2 basis
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atoms, one at the corner and one at the center of the cube. A <I>fcc</I>
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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 <I>diamond</I> lattice has 8 basis atoms.
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</P>
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<P>Lattices of style <I>sq</I> and <I>sq2</I> 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 <I>sq</I> lattice has 1 basis atom at the lower-left
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corner of the square. A <I>sq2</I> lattice has 2 basis atoms, one at the
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corner and one at the center of the square. A <I>hex</I> 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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</P>
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<P>A lattice of style <I>user</I> 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 <I>basis</I> 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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</P>
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<HR>
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<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 with desired spacings.
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</P>
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<P>The <I>scale</I> 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 <I>scale</I> argument depends on the <A HREF = "unit.html">units</A>
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being used in your simulation.
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</P>
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<P>For unit style <I>real</I> or <I>metal</I>, 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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</P>
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<P>For unit style <I>lj</I>, 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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</P>
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<P>The <I>origin</I> 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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</P>
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<P>The <I>orient</I> option specifies how the unit cell will be rotated when
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mapping it into the simulation box. The <I>dim</I> 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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</P>
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<HR>
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<P>Several LAMMPS commands have the option to use distance units that are
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inferred from "lattice spacings" in the x,y,z directions. E.g. the
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<A HREF = "region.html">region</A> 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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</P>
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<P>These lattice spacings are computed by LAMMPS in the following way. A
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unit cell of the lattice is mapped into the simulation box (scaled,
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shifted, rotated), so that it now has (perhaps) a modified shape and
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orientation. The lattice spacing in X is defined as the difference
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between the min/max extent of the x coordinates of the 8 corner points
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of the modified unit cell. Similarly, the Y and Z lattice spacings
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are defined as the min/max of the y and z coordinates.
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</P>
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<P>Note that if the unit cell has axis-aligned edges (a1,a2,a3) and is
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not rotated (via the <I>orient</I> 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 <I>hex</I> 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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</P>
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<P>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 computed lattice spacings are printed by LAMMPS, so
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their effect in commands that use the spacings should be decipherable.
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</P>
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<HR>
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<P>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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(<A HREF = "create_atoms.html">create_atoms</A>) 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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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>The <I>a1,a2,a3,basis</I> keywords can only be used with style <I>user</I>.
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</P>
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<P>For lattices oriented at an angle or with a non-orthognal unit cell,
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care must be taken when using the <A HREF = "region.html">region</A> and
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<A HREF = "create_atoms.html">create_atoms</A> 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 incorretly at the faces of
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the simulation box.
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2006-09-22 00:22:34 +08:00
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</P>
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<P><B>Related commands:</B>
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</P>
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2006-11-14 06:18:34 +08:00
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<P><A HREF = "dimension.html">dimension</A>, <A HREF = "create_atoms.html">create_atoms</A>,
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2006-09-22 00:22:34 +08:00
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<A HREF = "region.html">region</A>
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</P>
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<P><B>Default:</B>
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</P>
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<PRE>lattice none
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</PRE>
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2006-11-14 06:18:34 +08:00
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<P>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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</P>
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</HTML>
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