lattice hex 0.85
lattice sq 0.8 origin 0.0 0.5 0.0 orient x 1 1 0 orient y -1 1 0
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 & basis 0.0 0.0 0.0 basis 0.5 0.5 0.5 lattice none 2.0 Description:
Define a lattice for use by other commands. In LAMMPS, a lattice is 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 crystallographic lattices.
A lattice is used by LAMMPS in two ways. First, the create_atoms command creates atoms on the lattice points inside the simulation box. Note that the create_atoms command allows different atom types 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 used by other commands as distance units (e.g. create_box, region and velocity), which are often convenient to use when the underlying problem geometry is atoms on a lattice.
The lattice style must be consistent with the dimension of the simulation - see the dimension command. Styles sc or bcc or fcc or hcp or diamond are for 3d problems. Styles sq or sq2 or hex are for 2d problems. Style custom can be used for either 2d or 3d problems.
A lattice consists of a unit cell, a set of basis atoms within that 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 \have to be a \
A lattice of style none does not define a unit cell and basis set, so it cannot be used with the create_atoms 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 keyword/value pairs can be specified for the none style. By default, a \the units command.
Lattices of style sc, fcc, bcc, and diamond are 3d lattices that define a cubic unit cell with edge length = 1.0. This means a1 = 1 0 0, a2 = 0 1 0, and a3 = 0 0 1. Style hcp has a1 = 1 0 0, a2 = 0 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 sc lattice has 1 basis atom at the lower-left-bottom corner of the cube. A bcc lattice has 2 basis atoms, one at the corner and one at the center of the cube. A fcc
lattice has 4 basis atoms, one at the corner and 3 at the cube face centers. A hcp lattice has 4 basis atoms, two in the z = 0 plane and 2 in the z = 0.5 plane. A diamond lattice has 8 basis atoms.
Lattices of style sq and sq2 are 2d lattices that define a square unit cell with edge length = 1.0. This means a1 = 1 0 0 and a2 = 0 1 0. A sq lattice has 1 basis atom at the lower-left corner of the square. A sq2 lattice has 2 basis atoms, one at the corner and one at the center of the square. A hex style is also a 2d lattice, but 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 rectangle.
A lattice of style custom allows you to specify a1, a2, a3, and a 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, so that they describe a tilted parallelepiped. Via the basis keyword you add atoms, one at a time, to the unit cell. Its arguments are fractional coordinates (0.0 <= x,y,z < 1.0). The position vector x of a basis atom within the unit cell is thus a linear combination of 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 basis keyword.
This sub-section discusses the arguments that determine how the idealized unit cell is transformed into a lattice of points within the simulation box.
The scale argument determines how the size of the unit cell will be 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. The meaning of the scale argument depends on the units being used in your simulation. For all unit styles except lj, the scale argument is specified in the distance units defined by the unit style. For example, in real or metal units, if the unit cell is a unit cube with edge length 1.0, specifying scale = 3.52 would create a cubic lattice with a spacing of 3.52 Angstroms. In cgs units, the spacing would be 3.52 cm.
For unit style lj, the scale argument is the Lennard-Jones reduced density, typically written as rho*. LAMMPS converts this value into the multiplicative factor via the formula \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 density.
The origin option specifies how the unit cell will be shifted or translated when mapping it into the simulation box. The x,y,z values are fractional values (0.0 <= x,y,z < 1.0) meaning shift the lattice by a fraction of the lattice spacing in each dimension. The meaning of \
The orient option specifies how the unit cell will be rotated when mapping it into the simulation box. The dim argument is one of the 3 coordinate axes in the simulation box. The other 3 arguments are the crystallographic direction in the
lattice that you want to orient along that axis, specified as integers. E.g. \box will be the [210] lattice direction. The 3 lattice directions you specify 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 custom with non-orthogonal a1,a2,a3 vectors, then think of the 3 orient 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.
Several LAMMPS commands have the option to use distance units that are inferred from \directions. E.g. the region command can create a block of size 10x20x20, where 10 means 10 lattice spacings in the x direction.
The spacing 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. If the spacing 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.
Note that if the unit cell is orthogonal with axis-aligned edges (not rotated via the orient 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 hex 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. IMPORTANT NOTE: For non-orthogonal unit cells and/or when a rotation is applied via the orient 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 create_atoms command, you will NOT necessarily create a periodic system. I.e. atoms may overlap incorrectly at the faces of the simulation box.
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.
Restrictions:
The a1,a2,a3,basis keywords can only be used with style custom. Related commands:
dimension, create_atoms, region Default: lattice none 1.0
For other lattice styles, the option defaults are origin = 0.0 0.0 0.0, orient = x 1 0 0, orient = y 0 1 0, orient = z 0 0 1, a1 = 1 0 0, a2 = 0 1 0, and a3 = 0 0 1.
LAMMPS WWW Site - LAMMPS Documentation - LAMMPS Commands
region command Syntax:
region ID style args keyword arg ...
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
ID = user-assigned name for the region
style = delete or block or cone or cylinder or plane or prism or sphere or union or intersect delete = no args
block args = xlo xhi ylo yhi zlo zhi
xlo,xhi,ylo,yhi,zlo,zhi = bounds of block in all dimensions (distance units) cone args = dim c1 c2 radlo radhi lo hi dim = x or y or z = axis of cone
c1,c2 = coords of cone axis in other 2 dimensions (distance units) radlo,radhi = cone radii at lo and hi end (distance units) lo,hi = bounds of cone in dim (distance units) cylinder args = dim c1 c2 radius lo hi dim = x or y or z = axis of cylinder
c1,c2 = coords of cylinder axis in other 2 dimensions (distance units) radius = cylinder radius (distance units) radius can be a variable (see below)
lo,hi = bounds of cylinder in dim (distance units) plane args = px py pz nx ny nz
px,py,pz = point on the plane (distance units)
nx,ny,nz = direction normal to plane (distance units) prism args = xlo xhi ylo yhi zlo zhi xy xz yz
xlo,xhi,ylo,yhi,zlo,zhi = bounds of untilted prism (distance units) xy = distance to tilt y in x direction (distance units) xz = distance to tilt z in x direction (distance units) yz = distance to tilt z in y direction (distance units) sphere args = x y z radius
x,y,z = center of sphere (distance units) radius = radius of sphere (distance units) radius can be a variable (see below) union args = N reg-ID1 reg-ID2 ...
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? N = # of regions to follow, must be 2 or greater reg-ID1,reg-ID2, ... = IDs of regions to join together intersect args = N reg-ID1 reg-ID2 ...
N = # of regions to follow, must be 2 or greater reg-ID1,reg-ID2, ... = IDs of regions to intersect zero or more keyword/arg pairs may be appended keyword = side or units or move or rotate side value = in or out
in = the region is inside the specified geometry out = the region is outside the specified geometry units value = lattice or box
lattice = the geometry is defined in lattice units
box = the geometry is defined in simulation box units move args = v_x v_y v_z
v_x,v_y,v_z = equal-style variables for x,y,z displacement of region over time rotate args = v_theta Px Py Pz Rx Ry Rz
v_theta = equal-style variable for rotaton of region over time (in radians) Px,Py,Pz = origin for axis of rotation (distance units) Rx,Ry,Rz = axis of rotation vector
Examples:
region 1 block -3.0 5.0 INF 10.0 INF INF region 2 sphere 0.0 0.0 0.0 5 side out
region void cylinder y 2 3 5 -5.0 EDGE units box region 1 prism 0 10 0 10 0 10 2 0 0
region outside union 4 side1 side2 side3 side4
region 2 sphere 0.0 0.0 0.0 5 side out move v_left v_up NULL Description:
This command defines a geometric region of space. Various other commands use regions. For example, the region can be filled with atoms via the create_atoms command. Or a bounding box around the region, can be used to define the simulation box via the create_box command. Or the atoms in the region can be identified as a group via
the group command, or deleted via the delete_atoms command. Or the surface of the region can be used as a boundary wall via the fix wall/region command.
Commands which use regions typically test whether an atom's position is contained in the region or not. For this purpose, coordinates exactly on the region boundary are considered to be interior to the region. This means, for example, for a spherical region, an atom on the sphere surface would be part of the region if the sphere were defined with the side in keyword, but would not be part of the region if it were defined using the side out keyword. See more details on the side keyword below.
Normally, regions in LAMMPS are \
the move or rotate keyword is used, as described below, the region becomes \orientation changes with time. This may be useful, for example, when thermostatting a region, via the compute temp/region command, or when the fix wall/region command uses a region surface as a bounding wall on particle motion, i.e. a rotating container.
The delete style removes the named region. Since there is little overhead to defining extra regions, there is normally no need to do this, unless you are defining and discarding large numbers of regions in your input script.
The lo/hi values for block or cone or cylinder or prism styles can be specified as EDGE or INF. EDGE means they extend all the way to the global simulation box boundary. Note that this is the current box boundary; if the box changes size during a simulation, the region does not. INF means a large negative or positive number (1.0e20), so it should encompass the simulation box even if it changes size. If a region is defined before the simulation box has been created
(via create_box or read_data or read_restart commands), then an EDGE or INF parameter cannot be used. For
a prismregion, a non-zero tilt factor in any pair of dimensions cannot be used if both the lo/hi values in either of those dimensions are INF. E.g. if the xy tilt is non-zero, then xlo and xhi cannot both be INF, nor can ylo and yhi.
IMPORTANT NOTE: Regions in LAMMPS do not get wrapped across periodic boundaries, as specified by
the boundary command. For example, a spherical region that is defined so that it overlaps a periodic boundary is not treated as 2 half-spheres, one on either side of the simulation box.
IMPORTANT NOTE: Regions in LAMMPS are always 3d geometric objects, regardless of whether the dimension of a simulation is 2d or 3d. Thus when using regions in a 2d simulation, you should be careful to define the region so that its intersection with the 2d x-y plane of the simulation has the 2d geometric extent you want.
For style cone, an axis-aligned cone is defined which is like a cylinder except that two different radii (one at each end) can be defined. Either of the radii (but not both) can be 0.0.
For style cone and cylinder, the c1,c2 params are coordinates in the 2 other dimensions besides the cylinder axis dimension. For dim = x, c1/c2 = y/z; for dim = y, c1/c2 = x/z; for dim = z, c1/c2 = x/y. Thus the third example above
specifies a cylinder with its axis in the y-direction located at x = 2.0 and z = 3.0, with a radius of 5.0, and extending in the y-direction from -5.0 to the upper box boundary.
For style plane, a plane is defined which contain the point (px,py,pz) and has a normal vector (nx,ny,nz). The normal
vector does not have to be of unit length. The \see the discussion of the side option below.
For style prism, a parallelepiped is defined (it's too hard to spell parallelepiped in an input script!). The parallelepiped has its \ylo,0); C = (xz,yz,zhi-zlo). Xy,xz,yz can be 0.0 or positive or negative values and are called \the amount of displacement applied to faces of an originally orthogonal box to transform it into the parallelepiped. A prism region that will be used with the create_box command to define a triclinic simulation box must have tilt factors (xy,xz,yz) that do not skew the box more than half the distance of corresponding the parallel box length. For example, if xlo = 2 and xhi = 12, then the x box length is 10 and the xy tilt factor must be between -5 and 5. Similarly, both xz and yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2. Note that this is not a limitation, since if the maximum tilt factor is 5 (as in this example), then configurations with tilt = ..., -15, -5, 5, 15, 25, ... are all geometrically equivalent.
The radius value for style sphere and cylinder can be specified as an equal-style variable. If the value is a variable, it should be specified as v_name, where name is the variable name. In this case, the variable will be evaluated each timestep, and its value used to determine the radius of the region.
Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent radius.
See Section_howto 12 of the doc pages for a geometric description of triclinic boxes, as defined by LAMMPS, and how to transform these parameters to and from other commonly used triclinic representations.
The union style creates a region consisting of the volume of all the listed regions combined. The intersect style creates a region consisting of the volume that is common to all the listed regions.
IMPORTANT NOTE: The union and intersect regions operate by invoking methods from their list of sub-regions. Thus you cannot delete the sub-regions after defining the union or intersection region.
The side keyword determines whether the region is considered to be inside or outside of the specified geometry. Using this keyword in conjunction with union and intersect regions, complex geometries can be built up. For example, if the interior of two spheres were each defined as regions, and a union style with side = out was constructed listing the region-IDs of the 2 spheres, the resulting region would be all the volume in the simulation box that was outside both of the spheres.