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### fix deform command

Syntax:

    fix ID group-ID deform N parameter args ... keyword value ...

- ID, group-ID are documented in fix command
- deform = style name of this fix command
- N = perform box deformation every this many timesteps
- one or more parameter/arg pairs may be appended

      parameter = x or y or z or xy or xz or yz
        x, y, z args = style value(s)
          style = final or delta or scale or vel or erate or trate or volume or wiggle or variable
            final values = lo hi
              lo hi = box boundaries at end of run (distance units)
            delta values = dlo dhi
              dlo dhi = change in box boundaries at end of run (distance units)
            scale values = factor
              factor = multiplicative factor for change in box length at end of run
            vel value = V
              V = change box length at this velocity (distance/time units),
      	    effectively an engineering strain rate
            erate value = R
              R = engineering strain rate (1/time units)
            trate value = R
              R = true strain rate (1/time units)
            volume value = none = adjust this dim to preserve volume of system
            wiggle values = A Tp
              A = amplitude of oscillation (distance units)
      	Tp = period of oscillation (time units)
            variable values = v_name1 v_name2
              v_name1 = variable with name1 for box length change as function of time
      	v_name2 = variable with name2 for change rate as function of time
        xy, xz, yz args = style value
          style = final or delta or vel or erate or trate or wiggle
            final value = tilt
              tilt = tilt factor at end of run (distance units)
            delta value = dtilt
              dtilt = change in tilt factor at end of run (distance units)
            vel value = V
              V = change tilt factor at this velocity (distance/time units),
      	    effectively an engineering shear strain rate
            erate value = R
              R = engineering shear strain rate (1/time units)
            trate value = R
              R = true shear strain rate (1/time units)
            wiggle values = A Tp
              A = amplitude of oscillation (distance units)
      	Tp = period of oscillation (time units)
            variable values = v_name1 v_name2
              v_name1 = variable with name1 for tilt change as function of time
      	v_name2 = variable with name2 for change rate as function of time

- zero or more keyword/value pairs may be appended
- keyword = remap or flip or units

        remap value = x or v or none
          x = remap coords of atoms in group into deforming box
          v = remap velocities of all atoms when they cross periodic boundaries
          none = no remapping of x or v
        flip value = yes or no
          allow or disallow box flips when it becomes highly skewed
        units value = lattice or box
          lattice = distances are defined in lattice units
          box = distances are defined in simulation box units

Examples:

    fix 1 all deform 1 x final 0.0 9.0 z final 0.0 5.0 units box
    fix 1 all deform 1 x trate 0.1 y volume z volume
    fix 1 all deform 1 xy erate 0.001 remap v
    fix 1 all deform 10 y delta -0.5 0.5 xz vel 1.0

Description:

Change the volume and/or shape of the simulation box during a dynamics run. Orthogonal simulation boxes have 3 adjustable parameters (x,y,z). Triclinic (non-orthogonal) simulation boxes have 6 adjustable parameters (x,y,z,xy,xz,yz). Any or all of them can be adjusted independently and simultaneously by this command. This fix can be used to perform non-equilibrium MD (NEMD) simulations of a continuously strained system. See the fix nvt/sllod and compute temp/deform commands for more details.

For the x, y, z parameters, the associated dimension cannot be shrink-wrapped. For the xy, yz, xz parameters, the associated 2nd dimension cannot be shrink-wrapped. Dimensions not varied by this command can be periodic or non-periodic. Dimensions corresponding to unspecified parameters can also be controlled by a fix npt or fix nph command.

The size and shape of the simulation box at the beginning of the simulation run were either specified by the create_box or read_data or read_restart command used to setup the simulation initially if it is the first run, or they are the values from the end of the previous run. The create_box, read data, and read_restart commands specify whether the simulation box is orthogonal or non-orthogonal (triclinic) and explain the meaning of the xy,xz,yz tilt factors. If fix deform changes the xy,xz,yz tilt factors, then the simulation box must be triclinic, even if its initial tilt factors are 0.0.

As described below, the desired simulation box size and shape at the end of the run are determined by the parameters of the fix deform command. Every Nth timestep during the run, the simulation box is expanded, contracted, or tilted to ramped values between the initial and final values.

For the x, y, and z parameters, this is the meaning of their styles and values.

The final, delta, scale, vel, and erate styles all change the specified dimension of the box via "constant displacement" which is effectively a "constant engineering strain rate". This means the box dimension changes linearly with time from its initial to final value.

For style final, the final lo and hi box boundaries of a dimension are specified. The values can be in lattice or box distance units. See the discussion of the units keyword below.

For style delta, plus or minus changes in the lo/hi box boundaries of a dimension are specified. The values can be in lattice or box distance units. See the discussion of the units keyword below.

For style scale, a multiplicative factor to apply to the box length of a dimension is specified. For example, if the initial box length is 10, and the factor is 1.1, then the final box length will be 11. A factor less than 1.0 means compression.

For style vel, a velocity at which the box length changes is specified in units of distance/time. This is effectively a "constant engineering strain rate", where rate = V/L0 and L0 is the initial box length. The distance can be in lattice or box distance units. See the discussion of the units keyword below. For example, if the initial box length is 100 Angstroms, and V is 10 Angstroms/psec, then after 10 psec, the box length will have doubled. After 20 psec, it will have tripled.

The erate style changes a dimension of the the box at a "constant engineering strain rate". The units of the specified strain rate are 1/time. See the units command for the time units associated with different choices of simulation units, e.g. picoseconds for "metal" units). Tensile strain is unitless and is defined as delta/L0, where L0 is the original box length and delta is the change relative to the original length. The box length L as a function of time will change as

    L(t) = L0 (1 + erate*dt)

where dt is the elapsed time (in time units). Thus if erate R is specified as 0.1 and time units are picoseconds, this means the box length will increase by 10% of its original length every picosecond. I.e. strain after 1 psec = 0.1, strain after 2 psec = 0.2, etc. R = -0.01 means the box length will shrink by 1% of its original length every picosecond. Note that for an "engineering" rate the change is based on the original box length, so running with R = 1 for 10 picoseconds expands the box length by a factor of 11 (strain of 10), which is different that what the trate style would induce.

The trate style changes a dimension of the box at a "constant true strain rate". Note that this is not an "engineering strain rate", as the other styles are. Rather, for a "true" rate, the rate of change is constant, which means the box dimension changes non-linearly with time from its initial to final value. The units of the specified strain rate are 1/time. See the units command for the time units associated with different choices of simulation units, e.g. picoseconds for "metal" units). Tensile strain is unitless and is defined as delta/L0, where L0 is the original box length and delta is the change relative to the original length.

The box length L as a function of time will change as

    L(t) = L0 exp(trate*dt)

where dt is the elapsed time (in time units). Thus if trate R is specified as ln(1.1) and time units are picoseconds, this means the box length will increase by 10% of its current (not original) length every picosecond. I.e. strain after 1 psec = 0.1, strain after 2 psec = 0.21, etc. R = ln(2) or ln(3) means the box length will double or triple every picosecond. R = ln(0.99) means the box length will shrink by 1% of its current length every picosecond. Note that for a "true" rate the change is continuous and based on the current length, so running with R = ln(2) for 10 picoseconds does not expand the box length by a factor of 11 as it would with erate, but by a factor of 1024 since the box length will double every picosecond.

Note that to change the volume (or cross-sectional area) of the simulation box at a constant rate, you can change multiple dimensions via erate or trate. E.g. to double the box volume in a picosecond picosecond, you could set "x erate M", "y erate M", "z erate M", with M = pow(2,1/3) - 1 = 0.26, since if each box dimension grows by 26%, the box volume doubles. Or you could set "x trate M", "y trate M", "z trate M", with M = ln(1.26) = 0.231, and the box volume would double every picosecond.

The volume style changes the specified dimension in such a way that the box volume remains constant while other box dimensions are changed explicitly via the styles discussed above. For example, "x scale 1.1 y scale 1.1 z volume" will shrink the z box length as the x,y box lengths increase, to keep the volume constant (product of x,y,z lengths). If "x scale 1.1 z volume" is specified and parameter y is unspecified, then the z box length will shrink as x increases to keep the product of x,z lengths constant. If "x scale 1.1 y volume z volume" is specified, then both the y,z box lengths will shrink as x increases to keep the volume constant (product of x,y,z lengths). In this case, the y,z box lengths shrink so as to keep their relative aspect ratio constant.

For solids or liquids, note that when one dimension of the box is expanded via fix deform (i.e. tensile strain), it may be physically undesirable to hold the other 2 box lengths constant (unspecified by fix deform) since that implies a density change. Using the volume style for those 2 dimensions to keep the box volume constant may make more physical sense, but may also not be correct for materials and potentials whose Poisson ratio is not 0.5. An alternative is to use fix npt aniso with zero applied pressure on those 2 dimensions, so that they respond to the tensile strain dynamically.

The wiggle style oscillates the specified box length dimension sinusoidally with the specified amplitude and period. I.e. the box length L as a function of time is given by

    L(t) = L0 + A sin(2*pi t/Tp)

where L0 is its initial length. If the amplitude A is a positive number the box initially expands, then contracts, etc. If A is negative then the box initially contracts, then expands, etc. The amplitude can be in lattice or box distance units. See the discussion of the units keyword below.

The variable style changes the specified box length dimension by evaluating a variable, which presumably is a function of time. The variable with name1 must be an equal-style variable and should calculate a change in box length in units of distance. Note that this distance is in box units, not lattice units; see the discussion of the units keyword below. The formula associated with variable name1 can reference the current timestep. Note that it should return the "change" in box length, not the absolute box length. This means it should evaluate to 0.0 when invoked on the initial timestep of the run following the definition of fix deform. It should evaluate to a value > 0.0 to dilate the box at future times, or a value < 0.0 to compress the box.

The variable name2 must also be an equal-style variable and should calculate the rate of box length change, in units of distance/time, i.e. the time-derivative of the name1 variable. This quantity is used internally by LAMMPS to reset atom velocities when they cross periodic boundaries. It is computed internally for the other styles, but you must provide it when using an arbitrary variable.

Here is an example of using the variable style to perform the same box deformation as the wiggle style formula listed above, where we assume that the current timestep = 0.

    variable A equal 5.0
    variable Tp equal 10.0
    variable displace equal "v_A * sin(2*PI * step*dt/v_Tp)"
    variable rate equal "2*PI*v_A/v_Tp * cos(2*PI * step*dt/v_Tp)"
    fix 2 all deform 1 x variable v_displace v_rate remap v

For the scale, vel, erate, trate, volume, wiggle, and variable styles, the box length is expanded or compressed around its mid point.

For the xy, xz, and yz parameters, this is the meaning of their styles and values. Note that changing the tilt factors of a triclinic box does not change its volume.

The final, delta, vel, and erate styles all change the shear strain at a "constant engineering shear strain rate". This means the tilt factor changes linearly with time from its initial to final value.

For style final, the final tilt factor is specified. The value can be in lattice or box distance units. See the discussion of the units keyword below.

For style delta, a plus or minus change in the tilt factor is specified. The value can be in lattice or box distance units. See the discussion of the units keyword below.

For style vel, a velocity at which the tilt factor changes is specified in units of distance/time. This is effectively an "engineering shear strain rate", where rate = V/L0 and L0 is the initial box length perpendicular to the direction of shear. The distance can be in lattice or box distance units. See the discussion of the units keyword below. For example, if the initial tilt factor is 5 Angstroms, and the V is 10 Angstroms/psec, then after 1 psec, the tilt factor will be 15 Angstroms. After 2 psec, it will be 25 Angstroms.

The erate style changes a tilt factor at a "constant engineering shear strain rate". The units of the specified shear strain rate are 1/time. See the units command for the time units associated with different choices of simulation units, e.g. picoseconds for "metal" units). Shear strain is unitless and is defined as offset/length, where length is the box length perpendicular to the shear direction (e.g. y box length for xy deformation) and offset is the displacement distance in the shear direction (e.g. x direction for xy deformation) from the unstrained orientation.

The tilt factor T as a function of time will change as

    T(t) = T0 + L0*erate*dt

where T0 is the initial tilt factor, L0 is the original length of the box perpendicular to the shear direction (e.g. y box length for xy deformation), and dt is the elapsed time (in time units). Thus if erate R is specified as 0.1 and time units are picoseconds, this means the shear strain will increase by 0.1 every picosecond. I.e. if the xy shear strain was initially 0.0, then strain after 1 psec = 0.1, strain after 2 psec = 0.2, etc. Thus the tilt factor would be 0.0 at time 0, 0.1*ybox at 1 psec, 0.2*ybox at 2 psec, etc, where ybox is the original y box length. R = 1 or 2 means the tilt factor will increase by 1 or 2 every picosecond. R = -0.01 means a decrease in shear strain by 0.01 every picosecond.

The trate style changes a tilt factor at a "constant true shear strain rate". Note that this is not an "engineering shear strain rate", as the other styles are. Rather, for a "true" rate, the rate of change is constant, which means the tilt factor changes non-linearly with time from its initial to final value. The units of the specified shear strain rate are 1/time. See the units command for the time units associated with different choices of simulation units, e.g. picoseconds for "metal" units). Shear strain is unitless and is defined as offset/length, where length is the box length perpendicular to the shear direction (e.g. y box length for xy deformation) and offset is the displacement distance in the shear direction (e.g. x direction for xy deformation) from the unstrained orientation.

The tilt factor T as a function of time will change as

    T(t) = T0 exp(trate*dt)

where T0 is the initial tilt factor and dt is the elapsed time (in time units). Thus if trate R is specified as ln(1.1) and time units are picoseconds, this means the shear strain or tilt factor will increase by 10% every picosecond. I.e. if the xy shear strain was initially 0.1, then strain after 1 psec = 0.11, strain after 2 psec = 0.121, etc. R = ln(2) or ln(3) means the tilt factor will double or triple every picosecond. R = ln(0.99) means the tilt factor will shrink by 1% every picosecond. Note that the change is continuous, so running with R = ln(2) for 10 picoseconds does not change the tilt factor by a factor of 10, but by a factor of 1024 since it doubles every picosecond. Note that the initial tilt factor must be non-zero to use the trate option.

Note that shear strain is defined as the tilt factor divided by the perpendicular box length. The erate and trate styles control the tilt factor, but assume the perpendicular box length remains constant. If this is not the case (e.g. it changes due to another fix deform parameter), then this effect on the shear strain is ignored.

The wiggle style oscillates the specified tilt factor sinusoidally with the specified amplitude and period. I.e. the tilt factor T as a function of time is given by

    T(t) = T0 + A sin(2*pi t/Tp)

where T0 is its initial value. If the amplitude A is a positive number the tilt factor initially becomes more positive, then more negative, etc. If A is negative then the tilt factor initially becomes more negative, then more positive, etc. The amplitude can be in lattice or box distance units. See the discussion of the units keyword below.

The variable style changes the specified tilt factor by evaluating a variable, which presumably is a function of time. The variable with name1 must be an equal-style variable and should calculate a change in tilt in units of distance. Note that this distance is in box units, not lattice units; see the discussion of the units keyword below. The formula associated with variable name1 can reference the current timestep. Note that it should return the "change" in tilt factor, not the absolute tilt factor. This means it should evaluate to 0.0 when invoked on the initial timestep of the run following the definition of fix deform.

The variable name2 must also be an equal-style variable and should calculate the rate of tilt change, in units of distance/time, i.e. the time-derivative of the name1 variable. This quantity is used internally by LAMMPS to reset atom velocities when they cross periodic boundaries. It is computed internally for the other styles, but you must provide it when using an arbitrary variable.

Here is an example of using the variable style to perform the same box deformation as the wiggle style formula listed above, where we assume that the current timestep = 0.

    variable A equal 5.0
    variable Tp equal 10.0
    variable displace equal "v_A * sin(2*PI * step*dt/v_Tp)"
    variable rate equal "2*PI*v_A/v_Tp * cos(2*PI * step*dt/v_Tp)"
    fix 2 all deform 1 xy variable v_displace v_rate remap v

All of the tilt styles change the xy, xz, yz tilt factors during a simulation. In LAMMPS, tilt factors (xy,xz,yz) for triclinic boxes are normally bounded by half the distance of the parallel box length. See the discussion of the flip keyword below, to allow this bound to be exceeded, if desired.

For example, if xlo = 2 and xhi = 12, then the x box length is 10 and the xy tilt factor must be between -5 and 5. Similarly, both xz and yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2. Note that this is not a limitation, since if the maximum tilt factor is 5 (as in this example), then configurations with tilt = ..., -15, -5, 5, 15, 25, ... are all equivalent.

To obey this constraint and allow for large shear deformations to be applied via the xy, xz, or yz parameters, the following algorithm is used. If prd is the associated parallel box length (10 in the example above), then if the tilt factor exceeds the accepted range of -5 to 5 during the simulation, then the box is flipped to the other limit (an equivalent box) and the simulation continues. Thus for this example, if the initial xy tilt factor was 0.0 and "xy final 100.0" was specified, then during the simulation the xy tilt factor would increase from 0.0 to 5.0, the box would be flipped so that the tilt factor becomes -5.0, the tilt factor would increase from -5.0 to 5.0, the box would be flipped again, etc. The flip occurs 10 times and the final tilt factor at the end of the simulation would be 0.0. During each flip event, atoms are remapped into the new box in the appropriate manner.

The one exception to this rule is if the 1st dimension in the tilt factor (x for xy) is non-periodic. In that case, the limits on the tilt factor are not enforced, since flipping the box in that dimension does not change the atom positions due to non-periodicity. In this mode, if you tilt the system to extreme angles, the simulation will simply become inefficient due to the highly skewed simulation box.

Each time the box size or shape is changed, the remap keyword determines whether atom positions are remapped to the new box. If remap is set to x (the default), atoms in the fix group are remapped; otherwise they are not. Note that their velocities are not changed, just their positions are altered. If remap is set to v, then any atom in the fix group that crosses a periodic boundary will have a delta added to its velocity equal to the difference in velocities between the lo and hi boundaries. Note that this velocity difference can include tilt components, e.g. a delta in the x velocity when an atom crosses the y periodic boundary. If remap is set to none, then neither of these remappings take place.

Conceptually, setting remap to x forces the atoms to deform via an affine transformation that exactly matches the box deformation. This setting is typically appropriate for solids. Note that though the atoms are effectively "moving" with the box over time, it is not due to their having a velocity that tracks the box change, but only due to the remapping. By contrast, setting remap to v is typically appropriate for fluids, where you want the atoms to respond to the change in box size/shape on their own and acquire a velocity that matches the box change, so that their motion will naturally track the box without explicit remapping of their coordinates.

IMPORTANT NOTE: When non-equilibrium MD (NEMD) simulations are performed using this fix, the option "remap v" should normally be used. This is because fix nvt/sllod adjusts the atom positions and velocities to induce a velocity profile that matches the changing box size/shape. Thus atom coordinates should NOT be remapped by fix deform, but velocities SHOULD be when atoms cross periodic boundaries, since that is consistent with maintaining the velocity profile already created by fix nvt/sllod. LAMMPS will warn you if the remap setting is not consistent with fix nvt/sllod.

IMPORTANT NOTE: For non-equilibrium MD (NEMD) simulations using "remap v" it is usually desirable that the fluid (or flowing material, e.g. granular particles) stream with a velocity profile consistent with the deforming box. As mentioned above, using a thermostat such as fix nvt/sllod or fix lavgevin (with a bias provided by compute temp/deform), will typically accomplish that. If you do not use a thermostat, then there is no driving force pushing the atoms to flow in a manner consistent with the deforming box. E.g. for a shearing system the box deformation velocity may vary from 0 at the bottom to 10 at the top of the box. But the stream velocity profile of the atoms may vary from -5 at the bottom to +5 at the top. You can monitor these effects using the fix ave/spatial, compute temp/deform, and compute temp/profile commands. One way to induce atoms to stream consistent with the box deformation is to give them an initial velocity profile, via the velocity ramp command, that matches the box deformation rate. This also typically helps the system come to equilibrium more quickly, even if a thermostat is used.

IMPORTANT NOTE: If a fix rigid is defined for rigid bodies, and remap is set to x, then the center-of-mass coordinates of rigid bodies will be remapped to the changing simulation box. This will be done regardless of whether atoms in the rigid bodies are in the fix deform group or not. The velocity of the centers of mass are not remapped even if remap is set to v, since fix nvt/sllod does not currently do anything special for rigid particles. If you wish to perform a NEMD simulation of rigid particles, you can either thermostat them independently or include a background fluid and thermostat the fluid via fix nvt/sllod.

The flip keyword allows the tilt factors for a triclinic box to exceed half the distance of the parallel box length, as discussed above. If the flip value is set to yes, the bound is enforced by flipping the box when it is exceeded. If the flip value is set to no, the tilt will continue to change without flipping. Note that if you apply large deformations, this means the box shape can tilt dramatically LAMMPS will run less efficiently, due to the large volume of communication needed to acquire ghost atoms around a processor's irregular-shaped sub-domain. For extreme values of tilt, LAMMPS may also lose atoms and generate an error.

The units keyword determines the meaning of the distance units used to define various arguments. A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacing. Note that the units choice also affects the vel style parameters since it is defined in terms of distance/time. Also note that the units keyword does not affect the variable style. You should use the xlat, ylat, zlat keywords of the thermo_style command if you want to include lattice spacings in a variable formula.

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

No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix. No global or per-atom quantities are stored by this fix for access by various output commands.

This fix can perform deformation over multiple runs, using the start and stop keywords of the run command. See the run command for details of how to do this.

This fix is not invoked during energy minimization.

Restrictions:

You cannot apply x, y, or z deformations to a dimension that is shrink-wrapped via the boundary comamnd.

You cannot apply xy, yz, or xz deformations to a 2nd dimension (y in xy) that is shrink-wrapped via the boundary comamnd.

Related commands:

change_box

Default:

The option defaults are remap = x, flip = yes, and units = lattice.