lammps/doc/fix_box_relax.txt

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fix box/relax command :h3

[Syntax:]

fix ID group-ID box/relax keyword value ... :pre

ID, group-ID are documented in "fix"_fix.html command :ulb,l
box/relax = style name of this fix command :l
one or more keyword value pairs may be appended
keyword = {iso} or {aniso} or {tri} or {x} or {y} or {z} or {xy} or {yz} or {xz} or {couple} or {nreset} or {vmax} or {dilate}
  {iso} or {aniso} or {tri} value = Ptarget = desired pressure (pressure units)
  {x} or {y} or {z} or {xy} or {yz} or {xz} value = Ptarget = desired pressure (pressure units)
  {couple} = {none} or {xyz} or {xy} or {yz} or {xz}
  {nreset} value = reset reference cell every this many minimizer iterations
  {vmax} value = fraction = max allowed volume change in one iteration
  {dilate} value = {all} or {partial} :pre
:ule

[Examples:]

fix 1 all box/relax iso 0.0 vmax 0.001
fix 2 water box/relax aniso 0.0 dilate partial
fix 2 ice box/relax tri 0.0 couple xy nreset 100 :pre

[Description:]

Apply an external pressure or stress tensor to the simulation box
during an "energy minimization"_minimize.html.  This allows the box
size and shape to vary during the iterations of the minimizer so that
the final configuration will be both an energy minimum for the
potential energy of the atoms, and the system pressure tensor will be
close to the specified external tensor.  Conceptually, specifying a
positive pressure is like squeezing on the simulation box; a negative
pressure typically allows the box to expand.

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The external pressure tensor is specified using one or more of the
{iso}, {aniso}, {tri}, {x}, {y}, {z}, {xy}, {xz}, {yz}, and {couple}
keywords.  These keywords give you the ability to specify all 6
components of an external stress tensor, and to couple various of
these components together so that the dimensions they represent are
varied together during the mimimization.

Orthogonal simulation boxes have 3 adjustable dimensions (x,y,z).
Triclinic (non-orthogonal) simulation boxes have 6 adjustable
dimensions (x,y,z,xy,xz,yz).  The "create_box"_create_box.html, "read
data"_read_data.html, and "read_restart"_read_restart.html commands
specify whether the simulation box is orthogonal or non-orthogonal
(triclinic) and explain the meaning of the xy,xz,yz tilt factors.

The target pressures {Ptarget} for each of the 6 components of the
stress tensor can be specified independently via the {x}, {y}, {z},
{xy}, {xz}, {yz} keywords, which correspond to the 6 simulation box
dimensions.  For example, if the {y} keyword is used, the y-box length
will change during the minimization.  If the {xy} keyword is used, the
xy tilt factor will change.  A box dimension will not change if that
component is not specified.

Note that in order to use the {xy}, {xz}, or {yz} keywords, the
simulation box must be triclinic, even if its initial tilt factors are
0.0.

When the size of the simulation box changes, all atoms are re-scaled
to new positions, unless the keyword {dilate} is specified with a
value of {partial}, in which case only the atoms in the fix group are
re-scaled.  This can be useful for leaving the coordinates of atoms in
a solid substrate unchanged and controlling the pressure of a
surrounding fluid.

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The {couple} keyword allows two or three of the diagonal components of
the pressure tensor to be "coupled" together.  The value specified
with the keyword determines which are coupled.  For example, {xz}
means the {Pxx} and {Pzz} components of the stress tensor are coupled.
{Xyz} means all 3 diagonal components are coupled.  Coupling means two
things: the instantaneous stress will be computed as an average of the
corresponding diagonal components, and the coupled box dimensions will
be changed together in lockstep, meaning coupled dimensions will be
dilated or contracted by the same percentage every timestep.  The
{Ptarget} values for any coupled dimensions must be identical.
{Couple xyz} can be used for a 2d simulation; the {z} dimension is
simply ignored.

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The {iso}, {aniso}, and {tri} keywords are simply shortcuts that are
equivalent to specifying several other keywords together.

The keyword {iso} means couple all 3 diagonal components together when
pressure is computed (hydrostatic pressure), and dilate/contract the
dimensions together.  Using "iso Ptarget" is the same as specifying
these 4 keywords:

x Ptarget
y Ptarget
z Ptarget
couple xyz :pre

The keyword {aniso} means {x}, {y}, and {z} dimensions are controlled
independently using the {Pxx}, {Pyy}, and {Pzz} components of the
stress tensor as the driving forces, and the specified scalar external
pressure.  Using "aniso Ptarget" is the same as specifying these 4
keywords:

x Ptarget
y Ptarget
z Ptarget
couple none :pre

The keyword {tri} means {x}, {y}, {z}, {xy}, {xz}, and {yz} dimensions
are controlled independently using their individual stress components
as the driving forces, and the specified scalar pressure as the
external normal stress.  Using "tri Ptarget" is the same as specifying
these 7 keywords:

x Ptarget
y Ptarget
z Ptarget
xy 0.0 
yz 0.0 
xz 0.0 
couple none :pre

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The {vmax} keyword can be used to limit the fractional change in the
volume of the simulation box that can occur in one iteration of the
minimizer.  If the pressure is not settling down during the
minimization this can be because the volume is fluctuating too much.
The specified fraction must be greater than 0.0 and should be << 1.0.
A value of 0.001 means the volume cannot change by more than 1/10 of a
percent in one iteration when {couple xyz} has been specified.  For
any other case it means no linear dimension of the simulation box can
change by more than 1/10 of a percent.

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With this fix, the potential energy used by the minimizer is augmented
by an additional energy provided by the fix. The overall objective
function then is:

:c,image(Eqs/fix_box_relax1.jpg) 

where {U} is the system potential energy, {P}_t is the desired
hydrostatic pressure, {V} and {V}_0 are the system and reference
volumes, respectively.  {E}_{strain} is the strain energy expression
proposed by Parrinello and Rahman "(Parrinello1981)"_#Parrinello1981.
Taking derivatives of {E} w.r.t. the box dimensions, and setting these
to zero, we find that at the minimum of the objective function, the
global system stress tensor [P] will satisfy the relation:

:c,image(Eqs/fix_box_relax2.jpg) 

where [I] is the identity matrix, [h]_0 is the box dimension tensor of
the reference cell, and [h]_0{d} is the diagonal part of
[h]_0. [S]_{t} is a symmetric stress tensor that is chosen by LAMMPS
so that the upper-triangular components of [P] equal the stress tensor
specified by the user.
 
This equation only applies when the box dimensions are equal to those
of the reference dimensions. If this is not the case, then the
converged stress tensor will not equal that specified by the user.  We
can resolve this problem by periodically resetting the reference
dimensions. The keyword {nreset_ref} controls how often this is done.
If this keyword is not used, or is given a value of zero, then the
reference dimensions are set to those of the initial simulation domain
and are never changed. A value of {nstep} means that every {nstep}
minimization steps, the reference dimensions are set to those of the
current simulation domain. Note that resetting the reference
dimensions changes the objective function and gradients, which
sometimes causes the minimization to fail. This can be resolved by
changing the value of {nreset}, or simply continuing the minimization
from a restart file.

IMPORTANT NOTE: As normally computed, pressure includes a kinetic-
energy or temperature-dependent component; see the "compute
pressure"_compute_pressure.html command.  However, atom velocities are
ignored during a minimization, and the applied pressure(s) specified
with this command are assumed to only be the virial component of the
pressure (the non-kinetic portion).  Thus if atoms have a non-zero
temperature and you print the usual thermodynamic pressure, it may not
appear the system is converging to your specified pressure.  The
solution for this is to either (a) zero the velocities of all atoms
before performing the minimization, or (b) make sure you are
monitoring the pressure without its kinetic component.  The latter can
be done by outputting the pressure from the fix this command creates
(see below) or a pressure fix you define yourself.

IMPORTANT NOTE: Because pressure is often a very sensitive function of
volume, it can be difficult for the minimizer to equilibrate the
system the desired pressure with high precision, particularly for
solids.  Some techniques that seem to help are (a) use the
"min_modify line quadratic" option when minimizing with box
relaxations, and (b) minimize several times in succession if need be,
to drive the pressure closer to the target pressure.  Also note that
some systems (e.g. liquids) will not sustain a non-hydrostatic applied
pressure, which means the minimizer will not converge.

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This fix computes a temperature and pressure each timestep.  The
temperature is used to compute the kinetic contribution to the
pressure, even though this is subsequently ignored by default.  To do
this, the fix creates its own computes of style "temp" and "pressure",
as if these commands had been issued:

compute fix-ID_temp group-ID temp
compute fix-ID_press group-ID pressure fix-ID_temp virial :pre

See the "compute temp"_compute_temp.html and "compute
pressure"_compute_pressure.html commands for details.  Note that the
IDs of the new computes are the fix-ID + underscore + "temp" or fix_ID
+ underscore + "press", and the group for the new computes is the same
as the fix group.  Also note that the pressure compute does not
include a kinetic component.

Note that these are NOT the computes used by thermodynamic output (see
the "thermo_style"_thermo_style.html command) with ID = {thermo_temp}
and {thermo_press}.  This means you can change the attributes of this
fix's temperature or pressure via the
"compute_modify"_compute_modify.html command or print this temperature
or pressure during thermodynamic output via the "thermo_style
custom"_thermo_style.html command using the appropriate compute-ID.
It also means that changing attributes of {thermo_temp} or
{thermo_press} will have no effect on this fix.

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[Restart, fix_modify, output, run start/stop, minimize info:]

No information about this fix is written to "binary restart
files"_restart.html.

The "fix_modify"_fix_modify.html {temp} and {press} options are
supported by this fix.  You can use them to assign a
"compute"_compute.html you have defined to this fix which will be used
in its temperature and pressure calculation, as described above.  Note
that as described above, if you assign a pressure compute to this fix
that includes a kinetic energy component it will affect the
minimization, most likely in an undesirable way.

IMPORTANT NOTE: If both the {temp} and {press} keywords are used in a
single thermo_modify command (or in two separate commands), then the
order in which the keywords are specified is important.  Note that a
"pressure compute"_compute_pressure.html defines its own temperature
compute as an argument when it is specified.  The {temp} keyword will
override this (for the pressure compute being used by fix npt), but
only if the {temp} keyword comes after the {press} keyword.  If the
{temp} keyword comes before the {press} keyword, then the new pressure
compute specified by the {press} keyword will be unaffected by the
{temp} setting.

This fix computes a global scalar which can be accessed by various
"output commands"_Section_howto.html#4_15.  The scalar is the
pressure-volume energy, plus the strain energy, if it exists.

No parameter of this fix can be used with the {start/stop} keywords of
the "run"_run.html command.

This fix is invoked during "energy minimization"_minimize.html, but
not for the purpose of adding a contribution to the energy or forces
being minimized.  Instead it alters the simulation box geometry as
described above.

[Restrictions:]

Only dimensions that are available can be adjusted by this fix.
Non-periodic dimensions are not available.  {z}, {xz}, and {yz}, are
not available for 2D simulations. {xy}, {xz}, and {yz} are only
available if the simulation domain is non-orthogonal.  The
"create_box"_create_box.html, "read data"_read_data.html, and
"read_restart"_read_restart.html commands specify whether the
simulation box is orthogonal or non-orthogonal (triclinic) and explain
the meaning of the xy,xz,yz tilt factors.

[Related commands:]

"fix npt"_fix_nh.html, "minimize"_minimize.html

[Default:]

The keyword defaults are dilate = all, vmax = 0.0001, nreset = 0.

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:link(Parrinello1981)
[(Parrinello1981)] Parrinello and Rahman, J Appl Phys, 52, 7182 (1981).