# Heating upon sudden elastic compression

Hello,

I would expect the heating of an elastic material upon sudden elastic compression using such commands as change_box, fix box/relax or fix deform to be given simply by the first law of thermodynamics, i.e. Delta Q=Delta U + P Delta V where P is constant since the compression is applied suddenly as in a square-wave pressure pulse (this is equivalent to the change in enthalpy). This heat released by the material upon elastic compression should then be re-absorbed entirely by the material assuming periodic boundary conditions, and this is what gives rise to the rise in temperature of the material after the compression. If I'm not wrong then this heat released is basically converted entirely into thermal vibrational energy upon re-absorption (3NkbT in the classical limit). I tried calculating the thermal energy of iron for example from static zero-temperature energy surface calculations and phonon vibrational calculations, however my predictions for the rise in temperature upon elastic compression from these static calculations according to the above reasoning is much higher than the one I observe in the actual dynamic simulations. Can you see anything wrong with my reasoning? I've attached an example of input file showing the various compression commands that I've tried ( change_box, fix box/relax or fix deform).

Many thanks,

Gabriele Mogni

log log.deform
units metal
boundary p p p
atom_style atomic
pair_style eam/alloy

atom_modify map array

lattice bcc 2.8665

region box block 0 20 0 20 0 20

create_box 1 box

create_atoms 1 box

mass * 55.847
pair_coeff * * Fe_Ack.eam Fe

compute red_temp all temp/partial 1 1 0

velocity all create 0 5812775

thermo 1000
thermo_style custom step temp vol lx ly lz press pxx pyy pzz etotal pe

thermo_modify norm yes lost warn flush yes

fix 1 all nve

timestep 0.001

run 0

#fix 2 all box/relax iso 339000
#minimize 1.0e-15 1.0e-15 100000 1000000

#fix 2 all deform 1 x final 0.0 55.345386 y final 0.0 55.345386 z final 0.0 55.345386 units box

change_box all x final 0.0 55.345386 y final 0.0 55.345386 z final 0.0 55.345386 remap units box

#run 1

#fix 2 all npt temp 300 300 0.10 iso 339000.0 339000.0 1.0

run 100000

Hello,

I would expect the heating of an elastic material upon sudden elastic
compression using such commands as change_box, fix box/relax or fix
deform to be given simply by the first law of thermodynamics, i.e. Delta
Q=Delta U + P Delta V where P is constant since the compression is
applied suddenly as in a square-wave pressure pulse (this is equivalent
to the change in enthalpy). This heat released by the material upon
elastic compression should then be re-absorbed entirely by the material
assuming periodic boundary conditions, and this is what gives rise to
the rise in temperature of the material after the compression. If I'm
not wrong then this heat released is basically converted entirely into
thermal vibrational energy upon re-absorption (3NkbT in the classical
limit). I tried calculating the thermal energy of iron for example from
static zero-temperature energy surface calculations and phonon
vibrational calculations, however my predictions for the rise in
temperature upon elastic compression from these static calculations
according to the above reasoning is much higher than the one I observe
in the actual dynamic simulations. Can you see anything wrong with my
reasoning?

when you add potential energy to a system, only about _half_ of it should
be converted to kinetic energy during the subsequent equilibration
(assuming harmonic and pairwise additive interactions).

axel.