Output-strain
The output of the strain tensor is controlled by this keyword. More
information on strain can be found in the
FAQ
and in the Tutorial "Piezoelectricity and
strain".
!-------------------------------------------------------------------!
$output-strain
optional !
destination-directory
character
required !
strain
character
optional ! yes/no
hydrostatic-strain
character
optional ! yes/no
strain-crystal-system
character
optional ! yes/no
strain-simulation-system
character
optional ! yes/no
displacement-tensor-crystal-system
character
optional ! yes/no
displacement-tensor-simulation-system
character
optional ! yes/no
displacements
character
optional ! yes/no
elastic-energy-density
character
optional ! yes/no
all-tensor-components-in-one-file
character
optional ! yes/no
polarization-vector
character
optional ! yes/no
$end_output-strain
optional !
!-------------------------------------------------------------------!
Syntax:
destination-directory = my-directory/
e.g. = strain/
Name of directory to which the files should be written. Must exist and
directory name has to include the slash (\ for DOS and / for UNIX).
strain = yes / no
! (default: no )
Flag whether to put out the strain tensor. The strain tensor will be
printed out in the
crystal
coordinate system.
Output: e_cr_ij...
The crystal coordinate system is defined for zinc blende in the following
way:
x = [1 0 0]
y = [0 1 0]
z = [0 0 1]
This output gives you information about the strain tensor with respect
to the crystal, i.e. e_cr_xy always refers to x=[1 0 0] ,
y=[0 1 0] .
If you specify a nondefault growth direction/orientation of your
heterostructure under keyword
$domain-coordinates
(e.g. hkl-x-direction-zb = 3 1 1
hkl-y-direction-zb = 0 -1 1
)
then you should also print out the strain tensor in the simulation coordinate
system (see below).
In this case, e_cr_xy refers to x=[1 0 0] ,
y=[0 1 0] as usual but
e_sim_xy refers to x=[3 1 1] , y=[0 -1 1] .
In case, your growth-direction is [0 0 1] along the z axis (hkl-z-direction-zb
= 0 0 1
hkl-y-direction-zb = 0 1 0 ), then
your simulation system is equal to the crystal coordinate system and the
strain output for e_cr_ij... is the same as e_sim_ij...
(i.e. i and j refer to the same x, y and z).
hydrostatic-strain = yes
= no (default)
Flag whether to put out the hydrostatic strain (ehydro = exx
+ eyy + ezz) that is a measure of the volume
change and thus shifts the valence and the conduction band edges. For details
see
FAQ on strain (band shifts and deformation potentials). The hydrostatic
strain is the same in the
crystal
and
simulation coordinate system
because the trace of a matrix is an invariant under rotation transformations.
strain-crystal-system = yes
= no ! (default)
Flag whether to put out the strain tensor in the
crystal coordinate system.
Output: e_cr_ij...
The crystal system is a cartesian system (x, y, z) which is fixed to the
crystal.
This output gives you information about the strain tensor with respect
to the crystal system. (For explanation see above.)
If nothing is specified, the strain in the crystal system will be printed
out by default.
strain-simulation-system = yes !
(default
= no
Flag whether to put out the strain tensor in the
simulation coordinate system.
Output: e_sim_ij...
The simulation system is a cartesian system (x, y, z) in which the simulation
variables are defined.
This output gives you information about the strain tensor with respect
to the simulation system. (For explanation see above.)
displacement-tensor-crystal-system = yes
= no !
(default
Flag whether to put out the displacement tensor in the
crystal coordinate system.
Output: u_cr_ij...
The crystal system is a cartesian system (x, y, z) which is fixed to the
crystal.
This output gives you information about the displacement tensor with respect
to the crystal system. (For explanation see above.)
Note: strain-tensor = 1/2
(displacement-tensor + displacement-tensorT )
epsilonij = 1/2 ( uij
+ uji)
displacement-tensor-simulation-system = yes
= no ! (default
Flag whether to put out the displacement tensor in the
simulation coordinate system.
Output: u_sim_ij...
The simulation system is a cartesian system (x, y, z) in which the simulation
variables are defined.
This output gives you information about the displacement tensor with respect
to the simulation system. (For explanation see above.)
Note: strain-tensor = 1/2
(displacement-tensor + displacement-tensorT )
epsilonij = 1/2 ( uij
+ uji)
displacements = yes
= no ! (default)
Flag whether to put out the displacements of the physical grid nodes.
The displacement vector output is with respect to the
simulation coordinate system (default) and/or optionally with respect
to the
crystal coordinate system
(if either displacement-tensor-crystal-system = yes
or strain-crystal-system = yes ).
In 1D (and in 2D/3D for option homogeneous-strain ) the output for
the displacements u(r) are the displacements from the bulk lattice of a
material at point r to the strained lattice.
In 2D/3D the situation is different: u(r) are the displacements from the
reference lattice to the strained lattice.
elastic-energy-density = yes !
elastic energy density in units of [eV/nm3]
(default)
= yes-GJm3 ! elastic energy density in units
of [GJ/m3]
= no
Flag whether to print out the energy density of the elastic deformation.
By default, the output units are [eV/nm3] .
Alternatively, the units [GJ/m3] can be chosen.
Filename: ElasticEnergyDensity1D_eV.dat (in
units of [eV/nm3] )
ElasticEnergyDensity1D_GJ.dat
(in units of [GJ/m3] )
The total elastic energy is calculated and written to the screen output.
energy of elastic deformation
= 845.50528403E+00 [eV]
energy density of elastic deformation (average) =
4.31380247E+24 [eV/m^3]
= 691.14730718E-06 [GJ/m^3]
all-tensor-components-in-one-file = yes !
= no ! (default)
Flag whether to output all strain tensor and displacement tensor
components into one file (2D/3D simulations).
For 1D simulations, all components are written to one file in any case.
polarization-vector = yes
!
= no ! (default)
Flag whether to write out the piezoelectric, pyroelectric and
the total polarization vector (Ptotal = Ppiezo
+ Ppyro) in units of
[C/m^2] .
IF strain-crystal-system = yes
, the polarization vector will be written out with respect to
the
crystal coordinate system.
IF strain-simulation-system = yes ,
the polarization vector will be written out with respect to the
simulation coordinate system.
The piezoelectric polarization
vector depends on strain and it is zero if no strain is present.
For zinc blende materials where spontaneous polarization is not present,
only the piezoelectric polarization Ppiezo
will be written out.
For wurtzite materials where spontaneous polarization is present, also the
total polarization, i.e. Ptotal = Ppiezo + Ppyro,
will be written out.
The pyroelectric polarization
vector is a material parameter and can also be written out using
$output-material .
Output in 1D
Strain-tensor:
Filename:
strain _cr1D.dat
- strain tensor components with respect to crystal
coordinate system |
All six strain tensor components for each
gridpoint.
Structure:
position[nm] |
e_cr_xx |
e_cr_yy |
e_cr_zz |
e_cr_xy |
e_cr_xz |
e_cr_yz |
e_hydro (optional) |
PoissonRatio (optional) |
Position in space [l0] |
11 component
of strain tensor |
22 component
of strain tensor |
33 component
of strain tensor |
12 component
of strain tensor |
13 component
of strain tensor |
23 component
of strain tensor |
hydrostatic strain
ehy = exx + eyy + ezz |
biaxial Poisson ratio
D = - eps_|_ / eps|| |
Similar for
strain_sim1D.dat - strain tensor
components with respect to simulation coordinate system
and for 2D and 3D.
If hydrostatic-strain = yes
is chosen, then the output for strain_sim1D.dat
contains an additional column with the biaxial Poisson
ratio D.
D = - eps_|_ / eps||
For growth direction along [001], D is given by D100 = 2 c12
/ c11
where c11 and c12 are elastic constants (zinc blende).
More
information on D.
Note: The eij components refer to shear
strain and not to "engineer shear strain".
Shear strain is the average of two strain tensor components, i.e.
eij = 1/2 (dui/dxj + duj/dxi)
whereas engineering shear strain is defined as the total shear strain
eij = dui/dxj + duj/dxi.
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