ISODISPLACE (isotropy subgroup displacements) is a graphical user interface (GUI) that utilizes the packages within the Isotropy Software Suite. This program finds atomic displacements, atomic ordering, and strains for structural phase transitions induced by order parameters of single or coupled irreducible representations. The output includes (1) a java tool for interactive three-dimensional visualization of the atomic displacements, (2) a java tool for interactive visualization of single-crystal x-ray and neutron diffraction patterns, and (3) a CIF file containing the distorted crystalline structure.
See the EXAMPLE which guides the user through a simple case.
Distorted phase. The crystalline structure with the atomic displacements.
International Tables. International Tables for Crystallography, Vol. A, Edited by Theo Hahn (Kluwer Academic, Dordrecht).
Miller and Love. Tables of irreducible representations found in (1) S. C. Miller and W. F. Love, Tables of Irreducible Representations of Space Groups and Co-Representations of Magnetic Space Groups (Pruett, Boulder, 1967) or (2) A. P. Cracknell, B. L. Davies, S. C. Miller and W. F. Love, Kronecker Product Tables, Vol. 1 (Plenum, New York, 1979).
Kovalev. Tables of irreducible representations found in (1) O. V. Kovalev, Irreducible Representations of the Space Groups (Gordon and Breach, New York, 1965) or (2) O. V. Kovalev, Representations of the Crystallographic Space Groups: Irreducible Representations, Induced Representations and Corepresentations (Gordon and Breach, New York, 1993).
Stokes and Hatch. Tables of isotropy subgroups found in H. T. Stokes and D. M. Hatch, Isotropy Subgroups of the 230 Crystallographic Space Groups (World Scientific, Singapore, 1988). These tables are limited to special k points.
ISO(3+1)D. Tables of isotropy subgroups found at stokes.byu.edu/incommensurate.html. These isotropy subgroups arise from k points with irrational components. Their structures contain one-dimensional incommensurately modulated distortions and have the symmetry of (3+1)-dimensional superspace groups
CIF. Crystallographic Information File containing
information about the structure of a crystal using a standardized
format.
An isotropy subgroup can be conveniently selected within ISODISPLACE by choosing three quantities: (1) a k point in the first Brillouin zone of the parent structure, (2) an irreducible representation (IR) of the parent space-group symmetry, and (3) an order parameter direction in the representation space of the IR. A working knowledge of k points (i.e. reciprocal-space superlattice-peak locations) and their relationship to your supercell basis will help in making effective use of ISODISPLACE. However, even if you don't fully appreciate group theoretical representations, ISODISPLACE provides drop-box menus from which the possibilities can be explored one by one. A server-based Java applet allows you to interactively visualize and manipulate each distortion mode. For a more technical description of the relevant group-theoretical concepts, see H. T. Stokes and D.M. Hatch, Isotropy Subgroups of the 230 Crystallographic Space Groups (World Scientific, Singapore, 1988).
A symmetry motivated basis: The internal degrees of freedom available within a distortion-induced superstructure can be viewed as basis vectors in a generalized distortion space. The set of free atomic x,y,z coordinates constitute one such oft-used basis. In general, ISODISPLACE will generate basis vectors which are linear combinations of the more familiar x,y,z basis vectors. A fundamental advantage of ISODISPLACE is a symmetry-motivated distortion basis dictated by the IR and the order parameter direction of the transition which therefore has special physical and geometric meaning with respect to the energetics of the transition. ISODISPLACE will often generate a basis that includes polyhedral stretches, rotations, shears, buckles, and other familiar displacement patterns, being closely related to the more complicated frozen phonon basis which further depends on masses and interatomic forces. In summary, the principal component of many physical distortions can be captured by a relatively small number of symmetry-motivated degrees of freedom for which ISODISPLACE is an ideal exploratory tool.
Primary and secondary order parameters: In addition to the primary order parameters, ISODISPLACE calculates and displays any secondary order parameters that exist. A primary IR is an IR that can single-handedly generate the final isotropy subgroup symmetry. A primary order parameter is a structural degree of freedom associated with the primary IR. Without going into too much detail, a secondary IR generates secondary order parameters which can coexist within the final superstructure but do not necessarily of themselves generate the final isotropy subgroup (i.e. they don't lower the symmetry enough). For example, any internal degrees of freedom within the parent structure will also exist in the superstructure as secondary order parameters.
Order-parameter types: There are numerous distinct classes of physical order parameters (e.g. displacive, occupancy, strain, magnetic, etc.) that can be associated with isotropy subgroups. ISODISPLACE primarily selects and employs the isotropy subgroups associated with displacive (polar vector) order parameters. However strains (polar 2nd-rank tensor parameters manifested as variations in the unit-cell parameters) are also implemented in ISODISPLACE. In addition, ISODISPLACE includes scalar order parameters in its isotropy-subgroup search routine which are relevant to compositional order-disorder transitions. These transitions cause a single Wyckoff site in the parent cell to split into multiple sites in the supercell with distinct atomic occupancies.
Special k-points: The isotropy subgroups associated with special k points have been pre-calculated and placed in a readily-accessible database so that users can simultaneously search over all special k-points, filtered by user-specified constraints such as crystal system, Bravais lattice type, and/or space group symmetry. Non-special k-points can still be searched one at time, which requires the user to specify a k point, IR, and order parameter direction using drop-down menus.
Incommensurate k-points: These are k points with one or more irrational components. Their isotropy subgroups have also been pre-calculated and placed in a readily-accessible database. However, special searches over this database have not yet implemented.
Structure of parent phase. Usually you start
ISODISPLACE by giving information about the crystalline structure of
the parent (undistorted) phase. This includes the space-group
symmetry, the lattice parameters, and the position of the atoms. ISODISPLACE
requires that you upload this information from a CIF file. If you do
not have a CIF file for the parent structure, you may create one (or
modify an existing one) using ISOCIF. ISODISPLACE also allows you to
automatically start with a cubic perovskite structure.
You can also start ISODISPLACE by (1) uploading a distortion file
previously saved by ISODISPLACE or (2) automatically starting with
a distorted cubic perovskite structure. This takes you directly to the
page showing distortions for a selected IR and order parameter.
CIF file. There are two options
for uploading a CIF file. (1) You may upload the CIF file directly
from a local copy
or (2) you may copy and paste the contents of the CIF file
into a text field.
Sometimes a CIF file cannot be interpreted by ISODISPLACE. This can
happen if, for example, the space-group setting used in the CIF file
is not one of the settings found in International Tables.
In that case, use ISOCIF to read and modify your CIF file.
Space-group preferences. The
International Tables gives more than one setting for some space
groups. You may choose "default" space-group preferences. These
affect the settings used for the space-group symmetries of
all distorted structures throughout the remainder of your session
in ISODISPLACE (unless you return to this page). The setting of the
space-group symmetry of the parent structure is determined by the
CIF file you uploaded independent of your "default" choices.
If you want a different setting for your parent structure, modify
the associated CIF file using ISOCIF.
Monoclinic space groups have settings for six different orientations of the
axes. Choose axes a(b)c, c(-b)a, ab(c), ba(-c),
(a)bc, or (-a)cb. Unique axes are in parentheses. See
Table 4.3.1 in International Tables for more details.
Most monoclinic space groups also have settings for different cell
choices. Choose cell choice 1, 2, or 3.
Orthorhombic space groups have 6 different choices for the
orientation of axes. Choose axes abc, ba-c, cab,
-cba, bca, or a-cb. See Table 4.3.1 in
International Tables for more details.
Trigonal space groups (for example, #146, R3) have settings using
hexagonal axes and rhombohedral axes. Choose one of these.
Some orthorhombic, tetragonal, and cubic space groups (for example,
#227 Fd-3m) have two choices for the position of the origin. Choose
origin choice 1 or 2. For origin choice 2, the origin is always chosen
at a point of inversion.
Search. The "Search" page contains
(1) Information about the parent structure, including nearest-neighbor
distances between different types of atoms, (2) a "View parent" tool,
and (3) four different search methods for finding distorted structures.
View parent. If you click on "View
parent," you will view a three-dimensional rendition of the unit
cell of the parent structure. If no image appears, you may need to
install a new version of Java on your computer. Each type of atom is
represented by a different color. There are two input
parameters. Reasonable default values for these parameters are already
entered and may be used without any adjustment. After viewing the
graphical rendition, you may return to this page and adjust the values
of these parameters if you wish. (1) Radius of the atoms
(Angstroms). This is the radius used in the graphical rendition and
should, for visual clarity, be somewhat smaller than the actual atomic
radii. (2) Maximum bond length (Angstroms). A line will be drawn
between any two atoms with a center-to-center distance less than this
value. This parameter determines which bonds are displayed.
(3) Applet width (pixels). This
parameter allows you to adjust the size of the applet so that it fits
on your computer screen.
Method 1: Search over all special k
points. Instead of choosing a k point, IR, and order
parameter direction, as described below in method 2, you may simply give
information about the symmetry of the distorted phase. You may
specify (1) the crystal system, (2) the space-group symmetry, (3) the
conventional or primitive lattice, and/or (4) whether the space-group
symmetry of the distorted phase is a maximal subgroup of the parent
space group. If you select none of the crystal systems, then all of
them will be considered. Each lattice is specified by three basis
vectors. Each lattice selection also includes lattices which are
rotated by point operators in the parent space group. The choices in
the drop-down lists include only those symmetries of distorted
structures allowed by IRs associated with special k points.
Your selection of the space-group symmetry will generate a drop-down
list of the corresponding isotropy subgroups and their associated
k points, IRs, and order parameter directions as described
below.
Method 2: General method -
search over specific k points.
Choose a
k point in the first Brillouin zone. This choice affects the
possible superlattices which can result from the phase transition.
Each line in the drop-down box contains (1) the label of the k
point using the notation of Miller and Love, (2) the label of the
k point using the notation of Kovalev (only included for
special k points), and (3) the coordinates of the point in
terms of the basis vectors of the reciprocal lattice of the
conventional lattice defined in International Tables. Some
points contain one or more of the parameters
a, b, or c (for example, a,0,0). You must
enter the values of the parameters needed for fully specifying the
position of the point. If no parameters are needed (for example, the
k point 0,0,0), you do not need to enter any values. Points
that contain no parameters are called the
special k points. You must enter all parameters
as rational numbers (for example, 1/2 instead of 0.5).
Incommensurate distortions. If you want to consider
incommensurate distortions, check the box labeled "incommensurate,"
and enter all parameters as decimal numbers (for example, 0.5 instead
of 1/2).
Coupled IRs. If you want to
superimpose distortions from more than one primary order parameter,
you need to couple two or more irreducible representations. Enter the
number of coupled IRs and click on OK. This will take you to a page
where you will choose a k point for each of the coupled IRs.
The data base used by ISODISPLACE does not contain isotropy subgroups
for coupled IRs. If the file containing the isotropy subgroups for
the IRs you select has not been recently generated, you must wait for
its generation, which may take anywhere from a few seconds to
minutes. In rare cases, it may even take hours. Be prepared to wait
while they are being generated. Note that coupled IRs are not yet
implemented at incommensurate k points.
Method 3: Search over arbitrary k points
for specified point group and lattice. Select the point group of the
space-group
symmetry of the distorted phase. Enter information about the lattice
of the distorted phase. You have two choices for entering this
information. (1) Primitive
real-space superlattice. Enter the
vectors that define the primitive lattice of the distorted phase.
These vectors should be given as dimensionless
coordinates of the parent phase. If non-integer values need to be
entered, enter them as rational numbers (for example, 1/2 instead of
0.5). (2) Primitive reciprocal-space superlattice. Enter basis
vectors of the superlattice in reciprocal space. For example, if new
diffraction peaks appear at (1/2,1/2,0), then you may enter
(1/2,1/2,0),(0,1,0),(0,0,1) as basis vectors in reciprocal space.
This would be equivalent to a primitive superlattice defined by
vectors (2,0,0),(-1,1,0),(0,0,1) in real space. When you click on OK,
you will see a drop-down box with various choices of space-group
symmetries, basis vectors and
origins consistent with your selections. If you do not choose a
point group, you will see a drop-down
box with allowed choices of point groups which are
consistent with the basis vectors you entered.
Method 4: Mode decomposition of a distorted
structure. In this
method, you may obtain the distorted phase from a CIF file.
There are two options: (1) You may upload the CIF file
or (2) you may copy and paste the contents of the CIF file
into a text field. In either option, the CIF file is preprocessed
and displayed in a text field where you may edit it if desired.
The setting of the
space-group symmetry of the distorted structure is determined by the
CIF file you uploaded independent of the "default" choices you made earlier.
At this point, you must also enter the basis vectors of the lattice of the
distorted phase in terms of the basis vectors of the parent lattice.
If non-integer values need to be entered, enter them as rational
numbers (for example, 1/2 instead of 0.5). Be careful: the basis
vectors that you use must reflect the shape and the orientation
of your supercell relative to the parent cell.
Also, the types of atoms in the CIF file must match the
types of atoms in the parent phase. At this point, you may also check
the "Nearest-site method" (see description below). When you click on OK,
the program finds the best choice of origin for the distorted structure
relative to the parent structure so that the atomic displacements
required to transform the parent structure to the distorted structure
are as small as possible. The "Distortions" page, as described below,
is displayed with the displacement mode, ordering mode, and strain
amplitudes filled in to match the distorted
phase in the CIF file. Note that the program only tries to minimize
the displacement mode amplitudes, not the ordering mode amplitudes.
If ESDs (estimated standard deviations) are
included in the CIF file for the lattice parameters and/or atomic
positions, then ESDs will also be calculated and shown for the mode and
strain amplitudes. This can be useful in determining which mode
and strain amplitudes are significant. At the top of the page is a
line beginning with "Distorted structure." This gives information about
how the CIF file was interpreted. The unit cell may be rotated and/or
the origin may be shifted.
Nearest-site method: When you check "Nearest-site
method," the program simply tries mapping atoms in the undistorted
structure onto those which are closest in the distorted structure. This
method works well if the distortion is small and the atoms have not
been displaced very far from their original positions. This method is also
must faster. The other method, however, is more thorough and robust, though
it cannot handle very large supercells.
IR. (Method 2 continued)
Choose an irreducible representation
(IR). The list in the drop-down box contains IRs associated with the
k point you selected. The choice of IR affects the symmetry of
the atomic displacements you will obtain. The list contains only IRs
which allow atomic displacements or atomic ordering at one or more of
the unique atomic positions you selected. Each line in the drop-down
box contains the label of the IR using the notation of (1) Miller and
Love and (2) Kovalev (only included for IRs associated with special
k points). Type-2 and type-3 IRs are complex. We want real IRs
since atomic displacements induced by the IR must be real. In these
cases, we obtain the physical IR from the direct sum of the IR
and its complex conjugate. These are indicated in the notation by a
pair of IR symbols (for example, P1P1, where P1 is a type-2 IR which
is equivalent to its own complex conjugate, and A2A3, where A2 and A3
are type-3 IRs which are complex conjugates of each other). Note that
physical IRs are reducible with respect to complex numbers but
irreducible with respect to real numbers.
Order parameter direction. Choose the
direction of the primary order parameter. An order parameter is a
vector in representation space and has the same dimension as the
IR. The isotropy subgroup is defined to be all space group
operators of the parent phase which leave the direction of the order
parameter invariant. The isotropy subgroup for the primary order
parameter defines the symmetry of the distorted phase.
The list in the drop-down box contains all of the possible
directions of the primary order parameter. Each line contains (1) the
symbol (notation of Stokes and Hatch) which denotes the direction of
the order parameter, (2) the order parameter vector components in
representation space, (3) the space group symmetry of the isotropy
subgroup, (4) the basis vectors of the lattice of the isotropy
subgroup in terms of the basis vectors of the lattice of the parent
space group, (5) the origin of the isotropy space group in terms of
the basis vectors of the lattice of the parent space group, (6) the
size s of the primitive unit cell of the isotropy subgroup
relative to the parent space group, and (7) the index i of the
subgroup relative to the parent space group. For incommensurate
structures, the (3+1)-dimensional superspace group symmetry is given,
and the basis vectors of the lattice as well as the origin of the
superspace group is given in (3+1)-dimensional space with four
components.
The data base used by ISODISPLACE contains
isotropy subgroups for single IRs associated with special k
points and for single IRs associated with incommensurate k points.
Files containing the isotropy subgroups for the other IRs or for
coupled IRs must
be generated on demand. If the file for the IR(s) you selected has not
been recently generated, the drop-down list will contain only the
general direction of the order parameter. You can generate the file
containing the other directions and their isotropy subgroups by
clicking on "Generate isotropy subgroups" at the bottom of the
page. The generation of isotropy subgroups make take anywhere from a
few seconds to minutes. In rare cases, it may even take hours. Be
prepared to wait while they are being generated.
Distortions.
This information will appear in a new window. This is for your
convenience, allowing you to have several windows open at the same time,
each containing distortions associated with different order parameters
and different IRs. The new window contains input boxes for the amplitudes
of all of the displacement, occupancy ordering, and strain modes.
All amplitudes are set by default to be zero.
The amplitude of each mode is proportional to one of the free
variables of an order parameter associated with an IR.
Modes are listed for each order parameter. The order
parameter associated with the IR you selected is the primary order
parameter. The other order parameters are secondary. They generate
displacements with symmetry greater than or equal to the symmetry of the
distorted phase. The line describing the mode
contains (1) the space-group symmetry (short
Hermann-Mauguin symbol) of the parent phase, (2) the components of the
k vector (3) the IR associated with the order parameter, (4)
the components of the order parameter vector, (5) the space-group
symmetry (space-group number and the short Hermann-Mauguin symbol) of
the isotropy subgroup associated with the order parameter, (6) the basis
vectors of the lattice of that space group, (7) the origin of that
space group, (8) the
size s of the primitive unit cell of the isotropy subgroup
relative to the parent space group, and (9) the index
i of the subgroup relative to the parent space group.
Displacement modes. Each mode corresponds to a set of
displacements for atoms associated with one of the unique atomic
positions. The amplitude of a mode indicates the magnitude of the
largest displacement (in Angstroms) experienced by any of the atoms
affected by the mode. The total number of displacement modes is equal
to the total number of free parameters for the atomic positions in the
distorted phase. Next to the input boxes we find labels that
distinguish the different displacement modes. Each mode label
contains (1) the identity of the atom and its Wyckoff position, (2)
the IR of the point-group symmetry of the Wyckoff position (the
displacement mode is generated from atomic displacements that belong
to this IR), and (3) one of the free variables in the order parameter
(a,b,c,...).
Ordering modes. Compositional ordering (i.e. occupancy) modes
cause a Wyckoff site in the parent phase to split into two or more
Wyckoff sites in the distorted phase. These modes alter the
occupancies of the atomic sites relative to their corresponding parent
sites. A single occupancy mode represented by scalar s,
associated with a parent atom with occupancy f, results in a
new occupancy of f+s in the distorted
structure. Therefore, s=0 corresponds to an occupation equal to
that in the parent structure, s>0 corresponds to an increased
occupation, s<0 corresponds to a decreased occupation. Next to
each input field, there is a unique mode label containing (1) the
identity of the atom and its Wyckoff position, (2) the word "order" to
distinguish it from displacive modes and (3) one of the free variables
in the order parameter (a,b,c,...).
Strain modes. These modes are distinguished from the
other modes by the word, "strain," contained in the mode label
next to the input box. Each strain mode is some linear combination
of the six strain components, exx, eyy,
ezz, eyz, exz,
exy. The amplitude of a mode indicates the
magnitude of the largest strain component in the mode. Next to the
input boxes we find labels that distinguish the different strain
modes. Each mode label contains (2) the word, "strain," and (2) one
of the free variables in the order parameter (a,b,c,...).
In ferroelectric phase transitions, at least one of the order parameters
will be labeled "ferroelectric." We obtain a proper ferroelectric
if one of the ferroelectric order parameters is primary, otherwise we
obtain an improper ferroelectric. Ferroelectric modes are also infrared
active.
In ferroelastic phase transitions, at least one of the order
parameters allows strain (except for the identity IR, GM1 or GM1+).
This causes the crystal system of the distorted phase to be different
from that of the parent. We obtain a proper ferroelastic if one of
the primary order parameters allows strain, otherwise we obtain an
improper ferroelastic. Order parameters that allow both atomic
displacements and strain are Raman active.
Near the top of the page are six choices:
"View distortion," "View diffraction," "CIF file," "Distortion
file," "Domains," and "Primary order parameters."
For the "View distortion" and "View diffraction" options,
there are additional input parameters which appear near the bottom of
the page. Reasonable default values for these parameters are already
entered and may be used without any adjustment. After viewing the
graphical rendition, you may return to this page and adjust the values
of these parameters if you wish. Parameters for the "View distortion"
option: (1) Atomic radius (Angstroms). This is the radius used in the
graphical rendition and should, for visual clarity, be somewhat
smaller than the actual atomic radii. (2) Maximum bond length
(Angstroms). A line will be drawn between any two atoms with a
center-to-center distance less than this value. This parameter
determines which bonds are displayed. (3) Applet width (pixels). This
parameter allows you to adjust the size of the applet so that it fits
on your computer screen. Parameters for the "View distortion" and
"View diffraction" options: (1) Maximum mode amplitudes allowed by the
slide bars (Angstroms). A large value allows large amplitudes but also
makes the distortions very sensitive to movements of the slide bars.
(2) Maximum strain amplitudes allowed by the slide bars
(dimensionless).
View distortion. This option opens a
new window that runs a Java applet containing a interactive
three-dimensional rendition of the unit cell of the isotropy subgroup.
Slide bars allow you to vary the amplitude of each distortion mode. A
master slide bar at the top allows you to multiply every slide bar by
a factor between 0 and 1. The orientation of the rendition can be
changed by dragging the mouse across the image. The x axis
points to the right, the y axis points up, and the z
axis points out of the screen. Normally, dragging the mouse up or
down rotates the rendition about the x axis, while dragging the
mouse right or left rotates the rendition about the y axis.
You cannot save a distortion from within the applet, but must instead
return to the previous page.
The mouse-dragging feature does not appear to work with the new
Apple JVM Version 1.5.0 that ships with Mac OSX 10.5 (Leopard). We
don't yet know whether this is their problem or ours.
Selecting the older 1.4.2 JVM in the Java Preferences is a temporary
workaround. For all other operating systems and internet browsers that
we have tested, any version of Sun Java equal or higher than 1.4.2 is
sufficient. If the applet does not appear, you should check to
see which version of Java you have installed.
Each distortion mode includes a slide bar, an abbreviated mode label,
and a mode-amplitude indicator. Each unique atom in the supercell
also has an associated checkbox that allows it to be rendered in a
different color (to single it out for closer inspection). Each
checkbox includes an atom label, a total displacement indicator (in
Angstroms), and a total occupancy indicator.
Below the slide bars,
there are several options that affect the rendition:
Atoms: If checked (default), atoms are displayed.
Bonds: If checked (default), bonds between atoms are displayed.
Cells: If checked (default), unit cell boundaries are displayed.
Spin: If checked, dragging the mouse across the image causes the rendition
to continuously spin with a rate that depends on mouse drag velocity.
Animate: If checked, all modes will be animated via the continuous
variation of the master slide bar position.
Color: If checked each chemical element type is represented by a
different color. Otherwise (default) each unique atom of the
parent structure is represented by a different color. In each
case, atom colors are assigned so as to uniformly spread the color
spectrum as widely as possible. Normal: If checked, the mouse-drag
behavior will be as described above. Xrot: If checked, dragging the
mouse up and down across the image results in a pure x-axis rotation.
Yrot: If checked, dragging the mouse right and left across the
image results in a pure y-axis rotation.
Zrot: If checked, dragging the mouse clockwise or counterclockwise about
the center of the image produces a pure z-axis rotation.
Zoom: If checked, dragging the mouse up and down across the image zooms the
rendition in or out.
Note that the Normal, Xrot, Yrot, Zrot and Zoom buttons form a set
of related options, only one of which can be selected. If you want
to view the rendition from a particular crystallographic direction,
check one of the following: SupHKL for a direction perpendicular to
the (hkl) plane of the supercell, SupUVW for a direction [uvw] in the
supercell, ParHKL for a direction perpendicular to the (hkl) plane of
the parent unit cell, ParUVW for a direction [uvw] in the parent unit
cell. Then enter the view coordinates and click on "Apply View" to
orient the rendition in the direction you specified.
Press "r" to reset applet to its initial state.
Press "z" to zero all of the mode amplitudes.
Press "i" to reset the mode amplitudes to their initial values.
Some users will discover that they can (1) use their browser to
save the applet window to an HTML file on your local computer, (2) use
a text editor to eliminate "/iso" from the applet path, (3)
download the applet itself (isodisplace.jar) to the same directory,
and thereby review or present a distortion offline. This can be
useful provided that you understand that we occasionally modify the
content and format of the data sent by ISODISPLACE to the
applet. Thus you may one day find that an older version of the
applet does not work with a newer html file or vice versa, in which
case you should consider updating your offline html and jar
files.
View diffraction. (Please report
any bugs discovered.) This option
produces a new window with a rendition of peak intensities due to
x-ray or neutron diffraction. The righthand side contains the same slide
bars and other information available in the "View distortion" window.
The slide bars allow you to vary the amplitudes
of the modes while viewing their effect on the parent and
superlattice peak intensities within a two-dimensional slice of
reciprocal space.
Each parent or superlattice peak is marked by a small open circle,
even if the peak has zero intensity. Parent peak positions come in
two flavors: RED (systematically absent) and GREEN (normal--not
systematically absent). Superlattice peak positions are indicated by
open BLUE circles.
Each peak intensity is represented on a log scale by the size of a
filled white circle. The central peak at (000) has maximum intensity
Imax and is represented by a filled yellow circle of
maximum radius rmax. Any peak whose intensity
I becomes equal (or nearly equal) to that of the central peak
changes from white to yellow. Any peak with intensity I less
than 10-4Imax has zero radius. All other
peaks are represented by filled white circles with radius
r=rmax[1+log10(I/Imax)/4].
You can determine the 2D slice of reciprocal space to be viewed by
specifying the point at the center of the plot, the direction of the
horizontal axis, and another direction that should be contained in the
upper half of the plot. All three vectors should be specified in
reciprocal lattice (i.e. hkl) units. Note that the horizontal and
upper directions must be defined relative to the center of the plot.
The "Parent" and Super" buttons determine whether these vectors should
are interpreted relative to the parent lattice or the superlattice.
Finally, the "Q Range" field allows you to determine how large of a
slice to view.
The tick marks appear at integer multiples of the user-provided
horizontal and upper hkl direction vectors, and are intended to
help you identify specific peaks within a pattern.
The "Xray" and Neut" buttons allow you to toggle between x-ray and neutron
diffraction patterns. Note that the scattering strength of each
element has been set to the atomic number for x-rays and to the
complex coherent scattering length of the natural isotopic composition
for neutrons. No angle-dependent form factors have been implemented
-- this tool is only intended for detecting qualitative intensity
patterns that arise due to specific distortion modes.
Press "r" to reset applet to its initial state.
Press "z" to zero all of the mode amplitudes.
Press "i" to reset the mode amplitudes to their initial values.
CIF file. This option creates a CIF
file for the distorted phase using the amplitudes entered for each
displacement mode and strain. This allows other software to read the
information about the distorted phase. You may also upload this CIF
file as a new parent phase, allowing you to consider further
distortions. For distortions at commensurate k points, the CIF file
output now includes the details of the linear transformation that relates
free atomic coordinates to displacive mode amplitudes.
Note that atomic occupancy information is not currently
saved to or read from CIF structure files.
Distortion file. This option creates a
file containing all of the information on the current page. If you
save this file, then you can load it at the beginning of ISODISPLACE,
allowing you to immediately return to this point.
Domains. This option creates a
list of all domains of the distorted structure with respect to the
parent structure. Domains are specified by
equivalent directions of the primary order parameter. They are
generated by operators which are contained in the parent space group
but not in the isotropy subgroup. The number of possible domains is
equal to the index of isotropy subgroup relative to the parent space
group. The generating operators may (1) rotate the lattice of the
subgroup (lattice orientation), (2) rotate the contents of the unit
cell relative to the lattice (internal orientation), and/or (3) move
the origin of the subgroup relative to the parent (origin shift).
Each line in the output contains (1) the domain number, (2) the
lattice orientation number, (3) the internal orientation number, (4)
the origin shift number, (5) the components of the order parameter,
(6) the domain generator, (7) the space-group symmetry of the
subgroup, (8) the basis vectors of the lattice of the subgroup, and
(9) the origin of the subgroup relative to the parent. The first
domain contains the original primary order parameter.
Primary order parameters
This option creates a list of all possible sets of primary
order parameters involving any combination of atomic displacements,
strains, or atomic orderings (to save space, only the irrep symbols are
shown). While you typically choose your primary order-parameters before
arriving at the distortion page, you can think of the entries in this
list as alternative sets that would have brought you to the same
distortion symmetry. The true physical primary order parameters, of
course, are those that actually drive the energetics of the transition
-- a topic that ISODISPLACE does not address. The list of
potentially-primary order parameters also indicates for each entry
whether or not the phase transition is allowed to be continuous
according to rules of Landau theory and the rules of renormalization
group theory. This list is not implemented
for incommensurate distortions.
.