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268 lines
13 KiB
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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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<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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<UL><LI>style = <I>none</I> or <I>sc</I> or <I>bcc</I> or <I>fcc</I> or <I>hcp</I> or <I>diamond</I> or <I>sq</I> or <I>sq2</I> or <I>hex</I> or <I>custom</I>
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<LI>scale = scale factor between lattice and simulation box
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<PRE> scale = reduced density rho* (for LJ units)
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scale = lattice constant in distance units (for all other 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>spacing</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>spacing</I> values = dx dy dz
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dx,dy,dz = lattice spacings in the x,y,z box 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 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
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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.html">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
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(e.g. <A HREF = "create_box.html">create_box</A>, <A HREF = "region.html">region</A> and
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<A HREF = "velocity.html">velocity</A>), which are often convenient to use 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>hcp</I> or <I>diamond</I> are for 3d problems. Styles
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<I>sq</I> or <I>sq2</I> or <I>hex</I> are for 2d problems. Style <I>custom</I> can be
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used for 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 crystallography, 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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<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
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re-defined and are used for all subsequent commands (that use lattice
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attributes). For example, a sequence of lattice,
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<A HREF = "region.html">region</A>, and <A HREF = "create_atoms.html">create_atoms</A> commands
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can be repeated multiple times to build a poly-crystalline model with
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different geometric regions populated with atoms in different lattice
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orientations.
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</P>
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<HR>
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<P>A lattice of style <I>none</I> does not define a unit cell and basis set,
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so it cannot be used with the <A HREF = "create_atoms.html">create_atoms</A>
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command. However it does define a lattice spacing via the specified
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scale parameter. As explained above the lattice spacings in x,y,z can
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be used by other commands as distance units. No additional
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keyword/value pairs can be specified for the <I>none</I> style. By
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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 HREF = "units.html">units</A> command.
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</P>
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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, a2 = 0 1 0, and a3 = 0 0 1. Style <I>hcp</I> 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
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within the unit cell are described in any solid-state physics text. A
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<I>sc</I> lattice has 1 basis atom at the lower-left-bottom corner of the
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cube. A <I>bcc</I> lattice has 2 basis atoms, one at the corner and one at
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the center of the cube. A <I>fcc</I> lattice has 4 basis atoms, one at the
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corner and 3 at the cube face centers. A <I>hcp</I> lattice has 4 basis
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atoms, two in the z = 0 plane and 2 in the z = 0.5 plane. A <I>diamond</I>
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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 and a2 = 0 1
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0. A <I>sq</I> lattice has 1 basis atom at the lower-left corner of the
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square. A <I>sq2</I> lattice has 2 basis atoms, one at the corner and one
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at the center of the square. A <I>hex</I> 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.
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It has 2 basis atoms, one at the corner and one at the center of the
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rectangle.
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</P>
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<P>A lattice of style <I>custom</I> 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
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and a3 are 3 orthogonal unit vectors (edges of a unit cube). But you
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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 <I>basis</I>
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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,
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where bx,by,bz are the 3 values specified for the <I>basis</I> keyword.
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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.
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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 = "units.html">units</A>
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being used in your simulation.
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</P>
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<P>For all unit styles except <I>lj</I>, the scale argument is specified in
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the distance units defined by the unit style. For example, in <I>real</I>
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or <I>metal</I> 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 <I>cgs</I> units, the spacing would be 3.52
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cm.
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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, and similarly for y and z. The 3 lattice directions you
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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.
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</P>
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<P>IMPORTANT NOTE: 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 <I>hcp</I> or <I>hex</I> lattice or the more general lattice
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style <I>custom</I> with non-orthogonal a1,a2,a3 vectors, then you should
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think of the 3 <I>orient</I> 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.
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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 box directions.
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E.g. the <A HREF = "region.html">region</A> command can create a block of size
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10x20x20, where 10 means 10 lattice spacings in the x direction.
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</P>
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<P>IMPORTANT NOTE: Though they are called lattice spacings, all the
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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 HREF = "units.html">units</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
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cell), you can define the 3 values to be whatever you wish, via the
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<I>spacing</I> option.
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</P>
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<P>If the <I>spacing</I> 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
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has (perhaps) a modified size and orientation. The lattice spacing in
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X is defined as the difference between the min/max extent of the x
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coordinates of the 8 corner points of the modified unit cell (4 in
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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.
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</P>
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<P>Note that if the unit cell is orthogonal with axis-aligned edges (no
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rotation via the <I>orient</I> 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 <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>IMPORTANT NOTE: For non-orthogonal unit cells and/or when a rotation
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is applied via the <I>orient</I> keyword, then the lattice spacings
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computed by LAMMPS are typically less intuitive. In particular, in
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these cases, there is no guarantee that a particular lattice spacing
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is an integer multiple of the periodicity of the lattice in that
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direction. Thus, if you create an orthogonal periodic simulation box
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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 HREF = "create_atoms.html">create_atoms</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.
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</P>
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<P>The <I>spacing</I> 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 edge length independent of the scale factor. As mentioned
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above, this option can be useful if the spacings LAMMPS computes are
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inconvenient to use in subsequent commands, which can be the case for
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non-orthogonal or rotated lattices.
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</P>
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<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.
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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>custom</I>.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "dimension.html">dimension</A>, <A HREF = "create_atoms.html">create_atoms</A>,
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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 1.0
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</PRE>
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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 0,
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a2 = 0 1 0, and a3 = 0 0 1.
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</P>
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</HTML>
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