I
have
made
available
several
computer
programs
that
I
have
written
over
the
last
few
years, which I hope you will find useful. These are the following:
Mike Glazer’s Website
VIBRATE!
Program
to compute irreducible representations
CHAINPLOT
Demonstrate the motion of atoms on a chain
FOURIER
Demonstrate Fourier synthesis as used
in crystallography
MEGAW
Compute effect of octahedral tilting in perovskites
WINDICVOL
GUI interface to the DICVOL91 powder autoindexing
program
WINOPTACT
Calculation of optical rotation and birefringence from
a crystal structure
SUMO
Simple user-defined mathematical operations
REFINE
General non-linear least-squares refinement with user-
defined functions
I
have
made
available
several
computer
programs
that
I
have
written
over
the
last
few
years,
which
I
hope
you
will
find
useful.
These
are the following:
Mike Glazer’s Website
VIBRATE!
Program
to compute irreducible representations
CHAINPLOT
Demonstrate the motion of atoms on a chain
FOURIER
Demonstrate Fourier synthesis as used
in crystallography
MEGAW
Compute effect of octahedral tilting in perovskites
WINDICVOL
GUI interface to the DICVOL91 powder autoindexing
program
WINOPTACT
Calculation of optical rotation and birefringence from
a crystal structure
SUMO
Simple user-defined mathematical operations
REFINE
General non-linear least-squares refinement with user-
defined functions
Mike Glazer’s Website
NOTE: Users prior to April 11 2013 should download Version 2.7,
as several bug fixes have been made.
VIBRATE!
is
a
program,
written
by
Professor
Mike
Glazer
(Oxford
University)
to
run
on
Microsoft
Windows,
in
order
to
compute
the
irreducible
representations
for
normal
modes
of
vibration
and
magnetic
modes
directly
from
a
crystal
structure
using
Factor
Group
Analysis.
The
default
is
to
carry
out
the
analysis
for
modes
at
the
centre
of
the
Brillouin
Zone
(k
=
0)
and
as
such
is
ideal
for
spectroscopy
applications
such
as
Raman
or
Infra-Red
Spectroscopy.
Operation
of
the
program
is
very
simple.
It
is
first
necessary
to
input
the
crystal
structure
and
once
this
is
done
the program automatically computes the rest.
Input
of
the
crystal
structure
is
done
by
specifying
a
space
group
and
the
positions
of
the
atoms.
Alternatively
input
is
immediate
using
a
Crystallographic
Information
File
(CIF),
the
usual
way
that
crystal
structure
information
is
available
these
days.Note
that
in
Windows
7
you
should
use
Compatibility
Mode
for
XP.
The
latest
Version2.5
now
has VRML structure plotting installed. Read Help File for details to enable this to work.
Below
is
shown
a
typical
screen
view
for
the
tetragonal
form
of
BaTiO
3
showing
that
the
irreducible
representations
are 4A1+B1+5E in point group 4mm(C
4v
)
The
direct
output
also
lists
the
invariances
for
IR
and
Raman
selection
rules
for
the
relevant
irreducible representations.
In order to enter atoms manually, this
is done through a simple dialog box (left).
In addition, character projection
operators can be listed enabling the
symmetry-adapted vectors to be drawn
on a crystal structure diagram.
For example, in the case of BaTiO
3
, the T
2u
(
G
5
-
)
irreducible representation leads to the following
symmetry-adapted vectors:
We see from this that only the oxygen atoms are involved in motion
corresponding to this irreducible representation. For example, the y
movement of O1 is opposite to the y movement of O3 (first line), the
z movement of O1 is opposite to the z movement of O2 (second line),
and the x movement of O2 is opposite to the x motion of O3 (third line).
Another selectable feature repeats the calculations atom by atom
so you can then see which atomic movements contribute to which
irreducible representations. In addition, a button is available to
enable the computation to switch to magnetic modes.
For solid-state specialists, there is also a facility to derive the
irreducible representations for normal modes at k ≠ 0.
A short paper describing the program has recently been published
in J. Appl. Cryst.(
doi:10.1107/S0021889809040424
). If you would
like to obtain a copy of VIBRATE!
click here
.
In addition, you can
download a PDF
of the Help File which contains more details about
the program and how to use it. Any problems then please email
Mike Glazer
Mike Glazer’s Website
NOTE:
Users
prior
to
April
11
2013
should
download
Version 2.7,
as several bug fixes have been made.
VIBRATE!
is
a
program,
written
by
Professor
Mike
Glazer
(Oxford
University)
to
run
on
Microsoft
Windows,
in
order
to
compute
the
irreducible
representations
for
normal
modes
of
vibration
and
magnetic
modes
directly
from
a
crystal
structure
using
Factor
Group
Analysis.
The
default
is
to
carry
out
the
analysis
for
modes
at
the
centre
of
the
Brillouin
Zone
(k
=
0)
and
as
such
is
ideal
for
spectroscopy
applications
such
as
Raman
or
Infra-Red
Spectroscopy.
Operation
of
the
program
is
very
simple.
It
is
first
necessary
to
input
the
crystal
structure
and
once
this
is
done
the
program
automatically computes the rest.
Input
of
the
crystal
structure
is
done
by
specifying
a
space
group
and
the
positions
of
the
atoms.
Alternatively
input
is
immediate
using
a
Crystallographic
Information
File
(CIF),
the
usual
way
that
crystal
structure
information
is
available
these
days.Note
that
in
Windows
7
you
should
use
Compatibility
Mode
for
XP.
The
latest
Version2.5
now
has
VRML
structure
plotting
installed.
Read
Help
File
for
details to enable this to work.
Below
is
shown
a
typical
screen
view
for
the
tetragonal
form
of
BaTiO
3
showing
that
the
irreducible
representations are 4A1+B1+5E in point group 4mm(C
4v
)
The
direct
output
also
lists
the
invariances
for
IR
and
Raman
selection
rules
for
the
relevant
irreducible representations.
In order to enter atoms manually, this
is done through a simple dialog box (left).
In addition, character projection
operators can be listed enabling the
symmetry-adapted vectors to be drawn
on a crystal structure diagram.
For example, in the case of BaTiO
3
, the T
2u
(
G
5
-
)
irreducible representation leads to the following
symmetry-adapted vectors:
We see from this that only the oxygen atoms are involved in motion
corresponding to this irreducible representation. For example, the y
movement of O1 is opposite to the y movement of O3 (first line), the
z movement of O1 is opposite to the z movement of O2 (second line),
and the x movement of O2 is opposite to the x motion of O3 (third line).
Another selectable feature repeats the calculations atom by atom
so you can then see which atomic movements contribute to which
irreducible representations. In addition, a button is available to
enable the computation to switch to magnetic modes.
For solid-state specialists, there is also a facility to derive the
irreducible representations for normal modes at k ≠ 0.
A short paper describing the program has recently been published
in J. Appl. Cryst.(
doi:10.1107/S0021889809040424
). If you would
like to obtain a copy of VIBRATE!
click here
.
In addition, you can
download a PDF
of the Help File which contains more details about
the program and how to use it. Any problems then please email
Mike Glazer
Mike Glazer’s Website
1-dimensional example 2-dimensional example
Be
aware
of
an
error
in
the
literature
and
on
the
web
with
respect
to
the
diatomic
chain.
On
the
left
is
a
typical
drawing
of
the
atomic
displacement
for
transverse
acoustic
and
optic
modes.
You
see
this
diagram
everywhere,
but
actually
it
is
not
quite
correct.
What
has
been
forgotten
is
that
for
wave-vectors
less
than
the
Brillouin
Zone,
the
waves
are
running
waves.
If
this
diagram
were
correct,
as
the
crest
of
the
wave
moves
from
say
left
to
right,
the
amplitudes
of
the
heavy
and
light
atoms
seem
to
have
the
same
magnitude.
But
this
is
not
possible.
In
the
acoustic
mode,
the
heavy
atoms
have
larger
displacements
than
the
light
ones,
and
vice-versa
for
the
optic
mode.
Therefore,
in
the
acoustic
mode
there
must
be
two
waves:
one
for
the
heavy
atoms
and
one
for
the
light
atoms
(same
frequency
and
wavelength
but
different
amplitudes)!
The
diagram
is
therefore
at
best
misleading.
It
is
correct
in
Brilliouin’s
1946
book
and
in
Wannier’s
1958
book,
but
it
seems
to
be
wrong
everywhere
since.
So
someone
in
the
1950’s
I
guess
drew
the
wrong
diagram
and
this
has
been
propagated
for the last 50 years or so. The simulation below gets it right.
Monatomic and Diatomic
Chains
Note:BUGFIX 20 Jan 2012: I have corrected a bug in the alternating force constants
routine
.
Monatomic and Diatomic Chains
I have made available for downloading two programs designed to demonstrate
vibrations of a linear 1-dimensional chain and a 2-dimensional array. These
programs are useful for teaching undergraduates typically in a Condensed Matter
Physics lecture course.
Mike Glazer’s Website
1-dimensional example 2-dimensional example
Note:BUGFIX 20 Jan 2012: I have corrected a bug in the alternating force constants
routine
.
Monatomic and Diatomic Chains
I have made available for downloading two programs designed to demonstrate
vibrations of a linear 1-dimensional chain and a 2-dimensional array. These
programs are useful for teaching undergraduates typically in a Condensed Matter
Physics lecture course.
Mike Glazer’s Website
Fourier2D & Fourier3D
This is an educational computer program written to demonstrate the process of Fourier Synthesis. This is a mathematical technique used in the solution of crystal structures by adding together plane waves in different orientations with different amplitudes (structure factors) and phases. The program allows waves to be added one after another or to read in a file containing a list of indices h k l and structure factors and phases in order to generate a Fourier projection. The resulting Fourier2D projection is plotted in a variety of different ways. Some examples are shown below demonstrating a projection of the potassium benzoyl penicillin structure as determined by Dorothy Hodgkin in the early 1940s. I also show a nice film of high- temperature quartz. I have also added a 3-dimensional Fourier program Fourier3D which plots Fourier sections rather than just projections. Go to Get Programs to download.
Click on above icon to view help file
Mike Glazer’s Website
Fourier2D & Fourier3D
This is an educational computer program written to demonstrate the process of Fourier Synthesis. This is a mathematical technique used in the solution of crystal structures by adding together plane waves in different orientations with different amplitudes (structure factors) and phases. The program allows waves to be added one after another or to read in a file containing a list of indices h k l and structure factors and phases in order to generate a Fourier projection. The resulting Fourier2D projection is plotted in a variety of different ways. Some examples are shown below demonstrating a projection of the potassium benzoyl penicillin structure as determined by Dorothy Hodgkin in the early 1940s. I also show a nice film of high- temperature quartz. I have also added a 3-dimensional Fourier program Fourier3D which plots Fourier sections rather than just projections. Go to Get Programs to download.
Click on above icon to view help file
Mike Glazer’s Website
Megaw
is
a
program
written
in
honour
of
Dr.
Helen
D.
Megaw,
renowned
particularly
for
her
work
in
Cambridge
on
the
crystal
structures
of
perovskites.
As
part
of
that
study,
she
became
interested
in
how
to
describe
the
structures
in
terms
of
tilted
oxygen
octahedra,
a
problem
that
I
tackled
and
for
which I derived a way to classify tilt systems in perovskites
doi.org/10.1107/S0567740872007976
doi.org/10.1107/S0567739475001635
This
seems
to
have
been
widely
accepted.
This
computer
program
runs
under
WINDOWS.
Below
is
shown
a
view
of
the
screen.
Positive
and
negative
octahedral
tilts
can
be
dialled
in
and
any
of
the
tilt
systems
constructed.
At
the
bottom,the
powder
pattern
(X-rays
or
neutrons)
is
drawn,
together
with
indicationswhere
extra
peaks
due
to
the
tilting
appear.
At
bottom
right
is
a
pull-down
box
that
lists
the
calculated
values of the square of the structure factors.
See
also
the
program
SPUDS
which
enables
the
tilt
systems
to
be calculated.
Change
of
octahedral
tilt
in
LiNbO3
showing
its
relationship
to
perosvkite.
Megaw
showed
that
this
structure
could
be
treated
as
an
extreme
example
of
a
tilted
perovskite
by
rotating
the
octahedra
about
the trigonal axis through a very large angle.
doi.org/10.1107/S0567739468001282
Mike Glazer’s Website
Megaw
is
a
program
written
in
honour
of
Dr.
Helen
D.
Megaw,
renowned
particularly
for
her
work
in
Cambridge
on
the
crystal
structures
of
perovskites.
As
part
of
that
study,
she
became
interested
in
how
to
describe
the
structures
in
terms
of
tilted
oxygen
octahedra,
a
problem
that
I
tackled
and
for
which
I
derived
a
way
to
classify
tilt
systems in perovskites
doi.org/10.1107/S0567740872007976
doi.org/10.1107/S0567739475001635
This
seems
to
have
been
widely
accepted.
This
computer
program
runs
under
WINDOWS.
Below
is
shown
a
view
of
the
screen.
Positive
and
negative
octahedral
tilts
can
be
dialled
in
and
any
of
the
tilt
systems
constructed.
At
the
bottom,the
powder
pattern
(X-rays
or
neutrons)
is
drawn,
together
with
indicationswhere
extra
peaks
due
to
the
tilting
appear.
At
bottom
right
is
a
pull-down
box
that
lists
the
calculated
values
of the square of the structure factors.
See
also
the
program
SPUDS
which
enables
the tilt systems to be calculated.
Change
of
octahedral
tilt
in
LiNbO3
showing
its
relationship
to
perosvkite.
Megaw
showed
that
this
structure
could
be
treated
as
an
extreme
example
of
a
tilted
perovskite
by
rotating
the
octahedra
about
the
trigonal
axis
through a very large angle.
doi.org/10.1107/S0567739468001282
Mike Glazer’s Website
WinDicVol
A Windows version of the well known powder autoindexing program DICVOL. This version of DicVol91 was written originally by Daniel Louer, and I have adapted it to work within a Windows environment. The usual way in which you are likely to works is 1 . Create a file of data using F ile/Control Data 2 . IMPORTANT! Save file with File/Save 3 . Run/Run will run the DICVOL91 program 4 . Run/Output allows you to inspect the output file 5 . Run/Cell Results give a list of the latest cell paramaters 6 . At any time, you can use File/Open to open an existing data file and then File/Control Data. Do not forget to save the file befoire running DicVol9 on it.
Mike Glazer’s Website
WinDicVol
A Windows version of the well known powder autoindexing program DICVOL. This version of DicVol91 was written originally by Daniel Louer, and I have adapted it to work within a Windows environment. The usual way in which you are likely to works is 1 . Create a file of data using F ile/Control Data 2 . IMPORTANT! Save file with File/Save 3 . Run/Run will run the DICVOL91 program 4 . Run/Output allows you to inspect the output file 5 . Run/Cell Results give a list of the latest cell paramaters 6 . At any time, you can use File/Open to open an existing data file and then File/Control Data. Do not forget to save the file befoire running DicVol9 on it.
Mike Glazer’s Website
This
program
reads
a
crystal
structure
via
a
Crystallographic
Information
File
(CIF),
and
computes
optical
birefringence
as
well
as
the
sign
and
magnitude
of
the
specific
optical
rotation.
As
well
as
structural
information
it
is
necessary
to
include
estimated
electronic
polarizabilities
for
each
atom.
To
understand the process, I advise reading of two papers
1
.
Glazer
and
Stadnicka
(1986)
.
On
the
origin
of
optical
activity
in
crystal
structures.
This
provides
a
simple
explanation
of
how
the
sign
of
optical
rotation
is
related
to
inorganic crystal structure.
2
.
Devarajan
and
Glazer
(1986)
and
Erratum.
Theory
and
computation
of
optical
rotatory
power
in
inorganic
crystals.
This
paper
gives
the
full
theory
used
in
the
program
WinOptact.
Mike Glazer’s Website
This
program
reads
a
crystal
structure
via
a
Crystallographic
Information
File
(CIF),
and
computes
optical
birefringence
as
well
as
the
sign
and
magnitude
of
the
specific
optical
rotation.
As
well
as
structural
information
it
is
necessary
to
include
estimated
electronic
polarizabilities
for
each
atom.
To
understand
the
process,
I
advise
reading
of
two
papers
1
.
Glazer
and
Stadnicka
(1986)
.
On
the
origin
of
optical
activity
in
crystal
structures.
This
provides
a
simple
explanation
of
how
the
sign
of
optical
rotation
is
related
to
inorganic
crystal
structure.
2
.
Devarajan
and
Glazer
(1986)
and
Erratum.
Theory
and
computation
of
optical
rotatory
power
in
inorganic
crystals.
This
paper
gives
the
full
theory used in the program WinOptact.
Mike Glazer’s Website
Click on the Sumo wrestler to read the Help File
SUMO- Simple user-defined mathematical
operations
Don’t wrestle with mathematics: use SUMO!
A
useful
program
that
enables
you
to
enter
your
own
mathematical
functions,
then
evaluate
them.
You
can
define
your
won
functions,
constants
and
variables
and
can
also
carry
our
1
and
2-dimensional
continuous
plots.
Read
the
Help
file
first
in
order
to
understand how to use the program.
Mike Glazer’s Website
Click on the Sumo wrestler to read the Help File
SUMO- Simple user-defined mathematical operations
Don’t wrestle with mathematics: use SUMO!
A
useful
program
that
enables
you
to
enter
your
own
mathematical
functions,
then
evaluate
them.
You
can
define
your
won
functions,
constants
and
variables
and
can
also
carry
our
1
and
2-dimensional
continuous
plots.
Read
the
Help
file
first
in
order
to
understand
how
to
use
the
program.
Mike Glazer’s Website
Refine
This program allows the user to carry out a non- linear least-squares refinement of imported data with respect to a user-defined mathematical function. As this involves cycles of refinement, it is necessary to supply starting values of the refineable parameters a[1] a[2] a[3]……. The Help file explains how to do this, and there are three example files to try out.
Mike Glazer’s Website
Refine
This program allows the user to carry out a non-linear least-squares refinement of imported data with respect to a user-defined mathematical function. As this involves cycles of refinement, it is necessary to supply starting values of the refineable parameters a[1] a[2] a[3]……. The Help file explains how to do this, and there are three example files to try out.
Mike Glazer’s Website
Mike Glazer’s Website
This
video
was
made
for
the
Cheltenham
Science
Festival
to
be
shown
in
the
Warwick University tent as a celebration of the beauty of crystal structures.
Mike Glazer’s Website
This
video
was
made
for
the
Cheltenham
Science
Festival
to
be
shown
in
the
Warwick
University
tent
as
a
celebration of the beauty of crystal structures.
Mike Glazer’s Website
My Bragg Lecture at the Royal Institution