LAMMPS from scratch · 20 min

Building the system

Four lines turn a number into a crystal: lattice, region, create_box and create_atoms. You derive the lattice spacing, box size and atom count by hand for any lattice, then let LAMMPS build it and compare its log line by line, including a box size that does not fit the crystal.

What lattice, region, create_box and create_atoms each do, and in which units
Predict the lattice spacing, box size and number of atoms for sc, bcc, fcc, diamond and 2D lattices
See what happens when the box is not a whole number of lattice cells

1 · Understand: four lines, one crystal

Line	What it does	In melt
`lattice fcc 0.8442`	describes a pattern of points: the FCC cube with 4 atoms; in LJ units the number is the density, so the cube edge is a = (4/0.8442)^1/3	a = 1.6795962
`region box block 0 10 0 10 0 10`	a named shape; numbers are counted in lattice spacings	a cube 16.795962 on each side
`create_box 1 box`	makes the simulation box with that shape and 1 atom type	box (0,0,0) to (16.795962, …)
`create_atoms 1 box`	puts an atom of type 1 on every lattice point inside the region	4 × 10³ = 4000 atoms

In LJ units the lattice number is a density; in every other unit style it is the lattice constant itself (for copper in metal units, lattice fcc 3.615 means a = 3.615 Å). LAMMPS confirms what it built in three log lines:

Lattice spacing in x,y,z = 1.6795962 1.6795962 1.6795962 Created orthogonal box = (0 0 0) to (16.795962 16.795962 16.795962) Created 4000 atoms

2 · The rules by hand

Lattice	atoms per cell n	spacing a (LJ units, density ρ)	nearest neighbour
sc (simple cubic)	1	(1/ρ)^1/3	a
bcc	2	(2/ρ)^1/3	a√3/2
fcc	4	(4/ρ)^1/3	a/√2
diamond	8	(8/ρ)^1/3	a√3/4
sq (2D square)	1	(1/ρ)^1/2	a
hex (2D)	2 in an a × √3a cell	(2/(ρ√3))^1/2	a

box length = number of cells × spacing atoms = n × cells_x × cells_y × cells_z (whole numbers of cells) fcc, ρ = 0.8442, 3 cells: a = (4/0.8442)^(1/3) = 1.6795962, L = 5.0387886, N = 4 × 27 = 108

3 · Modify, predict, observe: the lattice builder

Pick a lattice, a density and the number of cells. The page predicts the three log lines; LAMMPS then builds the system and the numbers are compared.

lattice density cells

Try:

Predict by hand

What the builder shows

For whole numbers of cells, three lines of arithmetic predict exactly what LAMMPS builds.
With 2.5 cells LAMMPS still makes a box, and fills it with only the 63 lattice points that fit inside. Nothing warns you: across the periodic boundary the next copy starts half a cell too early, so atoms meet at the wrong distance and the crystal is broken. Choose whole numbers of cells for crystals.
In 2D the hex lattice has a rectangular cell, √3 times longer in y: its spacing line shows two different numbers.

Your turn

1. How many atoms does lattice bcc 0.8442 with region box block 0 5 0 5 0 5 give, and what is the box length?

2. Count the 63 atoms of the 2.5-cell fcc box by hand.

3. In metal units you write lattice fcc 0.8442. What goes wrong?