STATIC: Lattice Types
 
 

static allows the user to select from a pre-defined set of lattice types, or to define an arbitary lattice. This choice is made in the subroutine setlat.f.

In general, you select a lattice type based on the type of crystal you are studying. Then you enter the information needed to describe this lattice. For example, for a face-centered cubic (fcc) lattice, you enter the cubic lattice constant a, and setlat constructs the primitive vectors:

For many lattices there are two options for entering the lattice parameters. For example, again using the fcc lattice, if you select lattice option +1 you enter the cubic lattice constant a. If, however, you select lattice option -1, you enter the fcc unit cell volume V and the program calculates

a = (4 V)1/3   .

The current primitive lattice types allowed by setlat.f are given below. You may, of course, edit setlat.f to increase the number of available files.

 
Index Description Input Code Defines Primitive Vectors
0 Arbitrary Lattice All lattice parameters Volume
a1 = (a1x,a1y,a1z)
a2 = (a2x,a2y,a2z)
a3 = (a3x,a3y,a3z)
1 face-centered cubic (fcc) lattice Cubic Lattice Constant a V = ¼ a3
a1 = ( 0 , ½ a, ½ a)
a2 = (½ a, 0, ½ a)
a3 = (½ a, ½ a, 0)
-1 Unit Cell Volume V a = (4 V)1/3
2 body-centered cubic (bcc) lattice Cubic Lattice Constant a V = ½ a3
a1 = ( -½ a, ½ a, ½ a)
a2 = (½ a, -½ a, ½ a)
a3 = (½ a, ½ a, -½ a)
-2 Unit Cell Volume V a = (2 V)1/3
3 hexagonal lattice a, c V = ½ 3½ a2c
a1 = ( ½ a, - ½ 3½ a, 0)
a2 = ( ½ a, + ½ 3½ a, 0)
a3 = ( 0 , 0 , c )
-3 Unit Cell Volume V, c/a a = [2V/(c/a)]1/3, c = (c/a) a
4 simple cubic (sc) lattice Cubic Lattice Constant a V = a3
a1 = ( a , 0 , 0 )
a2 = ( 0 , a , 0 )
a3 = ( 0 , 0 , a )
-4 Unit Cell Volume V a = V1/3
5 simple tetragonal lattice a , c V = a2 c
a1 = ( a , 0 , 0 )
a2 = ( 0 , a , 0 )
a3 = ( 0 , 0 , c )
-5 V, (c/a) a=[V/(c/a)]1/3 , c=(c/a) a
6 body-centered tetragonal lattice (bct) a , c V = ½ a2 c
a1 = ( a , 0 , 0 )
a2 = ( 0 , a , 0 )
a3 = ( ½ a , ½ a , ½ c )
-6 V, (c/a) a=[2 V/(c/a)]1/3 , c=(c/a) a
7 simple orthorhombic lattice a, b, c V = a b c
a1 = ( a , 0 , 0 )
a2 = ( 0 , b , 0 )
a3 = ( 0 , 0 , c )
-7 V, (b/a), (c/a) a=[V/(b/a)/(c/a)]1/3, b=(b/a) a, c=(c/a) a
8 base-centered orthorhombic lattice (bco) a, b, c V = ½ a b c
a1 = ( ½ a , - ½ b , 0 )
a2 = ( ½ a , + ½ b , 0 )
a3 = ( 0 , 0 , c )
-8 V, (b/a), (c/a) a=[2 V/(b/a)/(c/a)]1/3, b=(b/a) a, c=(c/a) a
9 rotated simple tetragonal lattice a, c V = ½ a2c
a1 = ( ½ a , - ½ a , 0 )
a2 = ( ½ a , + ½ a , 0 )
a3 = ( 0 , 0 , c )
-9 V, (c/a) a=[2 V/(c/a)]1/3, c=(c/a) a
10 face-centered tetragonal lattice (fct) a, c V = ¼ a2c
a1 = ( ½ a , - ½ a , 0 )
a2 = ( ½ a , + ½ a , 0 )
a3 = ( ½ a , 0 , ½ c )
-10 V, (c/a) a=[4 V/(c/a)]1/3, c=(c/a) a
11 face-centered tetragonal (fct) lattice with fcc-like vectors a, c V = ¼ a2c
a1 = ( 0 , ½ a, ½ c)
a2 = (½ a, 0, ½ c)
a3 = (½ a, ½ a, 0)
-11 V, c/a a = [4 V/(c/a)]1/3, c = (c/a) a
12 rhombohedral lattice a, b (see primitive vectors) V=a3+2b3-3 ab2, theta=arccos[b(2a+b)/( a2+2b2]
a1 = ( a , b , b )
a2 = ( b , a , b )
a3 = ( b , b , a )
-12 V, theta (angle between vectors) a, b
13 body-centered tetragonal lattice (bct) with bcc-like vectors a , c V = ½ a2 c
a1 = ( -½ a , ½ a , ½ c )
a2 = ( ½ a , -½ a , ½ c )
a3 = ( ½ a , ½ a , -½ c )
-13 V, (c/a) a=[2 V/(c/a)]1/3 , c=(c/a) a
14 base-centered orthorhombic lattice (bco) with angle θ specified between the base vectors. Note that "a" is the length of one of the base vectors a , c, θ V = a2 c sin θ
a1 = ( a cos(½ θ) , - a sin(½ θ) , 0 )
a2 = ( a cos(½ θ) , + a sin(½ θ) , 0 )
a3 = ( 0 , 0 , c )
-14 V, (c/a), θ a={V/[(c/a) sinθ]}1/3 , c=(c/a) a

Note that several structures (e.g., the four "different" centered-tetragonal lattices) are merely different representations of the same lattice. Use the representation which is most convenient for your work.

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