Changes to the NH fix enabling Cauchy stress control (Cauhchystat) due to ...

  {scaleyz} value = {yes} or {no} = scale yz with lz

  {scalexz} value = {yes} or {no} = scale xz with lz

  {flip} value = {yes} or {no} = allow or disallow box flips when it becomes highly skewed

  {cauchystat} cauchystat values = alpha continue

    alpha = strength of Cauchystat control parameter

    continue = {yes} or {no} = whether of not to continue from a previous run

  {fixedpoint} values = x y z

    x,y,z = perform barostat dilation/contraction around this point (distance units)

  {update} value = {dipole} or {dipole/dlm}

and if the tilt factor is not coupled to the barostat via keywords

{tri}, {yz}, {xz}, and {xy}.

Without the {cauchystat} keyword, the barostat algorithm

controls the Second-Piola Kirchhoff stress, which is a stress measure

referred to the undeformed (initial) simulation box.  If the box

deforms substantially during the equilibration, the difference between

the set values and the final true (Cauchy) stresses can be

considerable.

The {cauchystat} keyword modifies the barostat as per Miller et

al. (Miller)_"#nh-Miller" so that the Cauchy stress is controlled.

{alpha} is the non-dimensional parameter, typically set to 0.001 or

0.01 that determines how aggresively the algorithm drives the system

towards the set Cauchy stresses.  Larger values of {alpha} will modify

the system more quickly, but can lead to instabilities.  Smaller

values will lead to longer convergence time.  Since {alpha} also

influences how much the stress fluctuations deviate from the

equilibrium fluctuations, it should be set as small as possible.

A {continue} value of {yes} indicates that the fix is subsequent to a

previous run with the Cauchystat fix, and the intention is to continue

from the converged stress state at the end of the previous run.  This

may be required, for example, when implementing a multi-step loading/unloading

sequence over several fixes.

Setting {alpha} to zero is not permitted.  To "turn off" the

Cauchystat control and thus restore the equilibrium stress

fluctuations, two subsequent fixes should be used.  In the first, the

Cauchystat is used and the simulation box equilibrates to the correct

shape for the desired stresses.  In the second, the {fix} statement is

identical except that the {cauchystat} keyword is removed (along with

related {alpha} and {continue} values). This restores the original

Parrinello-Rahman algorithm, but now with the correct simulation box

shape from the first fix.

These fixes can be used with dynamic groups as defined by the

"group"_group.html command.  Likewise they can be used with groups to

which atoms are added or deleted over time, e.g. a deposition

The keyword defaults are tchain = 3, pchain = 3, mtk = yes, tloop =

ploop = 1, nreset = 0, drag = 0.0, dilate = all, couple = none,

cauchystat = no,

scaleyz = scalexz = scalexy = yes if periodic in 2nd dimension and

not coupled to barostat, otherwise no.

:link(nh-Dullweber)

[(Dullweber)] Dullweber, Leimkuhler and McLachlan, J Chem Phys, 107,

5840 (1997).

:link(nh-Miller)

[(Miller)] Miller, Tadmor, Gibson, Bernstein and Pavia, J Chem Phys,

144, 184107 (2016).

units		metal

atom_style	atomic

atom_modify	map array

processors      1 1 1

# Box and atom positions:

boundary p p p

# Defining lattice and creating simulation

# box with atoms inside

lattice          fcc 4.05

region           simbox prism 0 5 0 5 0 5 0 0 0 units lattice

create_box       2 simbox

create_atoms     2 box

# Atomic mass:

mass 1 58.69

mass 2 26.98154

# Potential, Al fcc crystal

pair_style eam/alloy

pair_coeff * * ../Mishin-Ni-Al-2009.eam.alloy Ni Al

thermo 100

thermo_style custom step temp pxx pyy pzz pxy pxz pyz

compute cna all cna/atom 2.8

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1 couple none cauchystat 0.001 no

dump 1 all cfg 1000 test*.cfg mass type xs ys zs type c_cna

timestep 0.002

variable px equal pxx

variable py equal pyy

variable pz equal pzz

variable sxy equal pxy

variable sxz equal pxz

variable syz equal pyz

variable t equal temp

fix avg all ave/time 1 100 100 v_t v_px v_py v_pz v_sxy v_sxz v_syz file avg.txt

variable lx equal lx

variable ly equal ly

variable lz equal ly

variable xy equal xy

variable xz equal xz

variable yz equal yz

fix box all ave/time 1 100 100 v_lx v_ly v_lz v_xy v_xz v_yz file box.txt

velocity all create 1200 4928459 rot yes dist gaussian

run 10000

unfix 1

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1 xy -10000.0 -10000.0 0.1 couple none cauchystat 0.001 yes

run 10000

unfix 1

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1  xy -10000.0 -10000.0 0.1 couple none

run 10000

units		metal

atom_style	atomic

atom_modify	map array

processors      1 1 1

# Box and atom positions:

boundary p p p

# Defining lattice and creating simulation

# box with atoms inside

lattice          fcc 4.05

region           simbox prism 0 5 0 5 0 5 0 0 0 units lattice

create_box       2 simbox

create_atoms     2 box

# Atomic mass:

mass 1 58.69

mass 2 26.98154

# Potential, Al fcc crystal

pair_style eam/alloy

pair_coeff * * ../Mishin-Ni-Al-2009.eam.alloy Ni Al

thermo 100

thermo_style custom step temp pxx pyy pzz pxy pxz pyz

compute cna all cna/atom 2.8

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1 couple none

dump 1 all cfg 1000 test*.cfg mass type xs ys zs type c_cna

timestep 0.002

variable px equal pxx

variable py equal pyy

variable pz equal pzz

variable sxy equal pxy

variable sxz equal pxz

variable syz equal pyz

variable t equal temp

fix avg all ave/time 1 100 100 v_t v_px v_py v_pz v_sxy v_sxz v_syz file avg.txt

variable lx equal lx

variable ly equal ly

variable lz equal ly

variable xy equal xy

variable xz equal xz

variable yz equal yz

fix box all ave/time 1 100 100 v_lx v_ly v_lz v_xy v_xz v_yz file box.txt

velocity all create 1200 4928459 rot yes dist gaussian

run 10000

unfix 1

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1 xy -10000.0 -10000.0 0.1 couple none

run 10000

unfix 1

fix 1 all npt temp 600.0 600.0 1.0 x 0.0 0.0 0.1 y 0.0 0.0 0.1 z 0.0 0.0 0.1  xy -10000.0 -10000.0 0.1 couple none

run 10000