# Length Scale in LJ Units

In one of the worked examples in Lammps documentation for calculating thermal conductivity using NEMD simulation, the length scale in the x and y directions were 18.82 in the calculation of thermal conductivity, while the input for both was 10. How did we come up with 18.82?

# settings

variable x equal 10
variable y equal 10
variable z equal 20

variable rho equal 0.85
variable t equal 0.7
variable rc equal 3.0
variable tlo equal 0.3
variable thi equal 1.0

# setup problem

units lj
atom_style atomic

lattice fcc \${rho}
region box block 0 \$x 0 \$y 0 \$z
create_box 1 box
create_atoms 1 box
mass 1 1.0

velocity all create \$t 87287

pair_style lj/cut \${rc}
pair_coeff 1 1 1.0 1.0

neighbor 0.3 bin
neigh_modify delay 0 every 1

# heat layers

region hot block INF INF INF INF 0 1
region cold block INF INF INF INF 10 11
compute Thot all temp/region hot
compute Tcold all temp/region cold

# 1st equilibration run

fix 1 all nvt temp \$t \$t 0.5
thermo 100
run 1000

velocity all scale \$t

unfix 1

# 2nd equilibration run

fix 1 all nve
fix hot all langevin {thi} {thi} 1.0 59804 tally yes
fix cold all langevin {tlo} {tlo} 1.0 287859 tally yes
fix_modify hot temp Thot
fix_modify cold temp Tcold

variable tdiff equal c_Thot-c_Tcold
thermo_style custom step temp c_Thot c_Tcold f_hot f_cold v_tdiff
thermo 1000
run 10000

# reset langevin thermostats to zero energy accumulation

compute ke all ke/atom
variable temp atom c_ke/1.5

fix hot all langevin {thi} {thi} 1.0 59804 tally yes
fix cold all langevin {tlo} {tlo} 1.0 287859 tally yes
fix_modify hot temp Thot
fix_modify cold temp Tcold

fix ave all ave/time 10 100 1000 v_tdiff ave running
thermo_style custom step temp c_Thot c_Tcold f_hot f_cold v_tdiff f_ave

fix 2 all ave/spatial 10 100 1000 z lower 0.05 v_temp &
file profile.langevin units reduced

run 20000

The lattice command — LAMMPS documentation determines the lattice spacing and the region command — LAMMPS documentation then uses these to create a rectangular region which is then converted into the simulation box with the create_box command — LAMMPS documentation

The screen and logfile will then show the box dimensions and thus the length scales for the system (they can also be output via a custom thermo style or print commands).