Solid state structure is characterized by simmetrical display of atoms in the form of crystals. A crystal is described as a lattice of points named nodes, simmetrical distributed in space, and an atom/group of atoms/molecule placed in each node.

Brown sugar crystals

# The sclattice function generates a data frame containing the
# coordinates of  the nodes.
# The number of nodes in a line is n+1. The total number of nodes
# is (n+1)^3.

sclattice <- function(n){nr <- 0
                        x <- 0
                        y <- 0
                        z <- 0
        for (i in 0:n){for (j in 0:n) {for (k in 0:n){
                nr <- nr+1
                x[nr]<-i
                y[nr]<-j
                z[nr]<-k
        }}}
sclattice <- as.data.frame(cbind(x,y,z))
}

• 1D lattice is a string of atoms displayed in line at evan distances

• 2D lattice is obtained by translating repeatedly the 1D lattice in a plain

• 3D lattice is obtained by translating the 2D lattice

The unit cell is the smallest part of the crystal. The crystal is generated by repeting the unit cell. Three cubic unit cells are presented next: