X-ray Diffraction Laboratory
Frequently asked questions
Basic Questions
What
is X-ray Diffraction?
Why do you
use X-rays?
Why do
you use crystals?
How do
you determine molecular structure from X-rays and Crystals?
What
are crystal lattices and the unit cell?
What
are the Bravais Lattices?
What is a Space Group?
Local
Question (for Laboratory users)
How and
where to submit samples
To
reserve instrument time you must...
How much will
it cost?
Do I you
need general X-ray safety training YES IF ..
What free
crystallographic programs do I need to get started ...
If the X-ray
lab collects my data and I want to solve and refine my structure ...
How do I
access the Cambridge Data Base?
I need help on solving and/or refining my structure
General
Questions
How
do I grow good crystals?
How
do I mount my sample?
Odds and Ends
Historical
Must
Read Book List for Crystallographers
Basic Information
X-rays scatter off of electrons, in a process of absorption and re-admission. Diffraction is the accumulative result of the x-ray scattering of a group of electrons. For an incident X-ray photon of monochromatic wavelength ?, coherent waves are produced at an angle of theta (2-theta with respect to the incident x-ray) if the electron groups interact with the x-ray and are spaced at a distance d. The interaction is described by Bragg's law : nlamda =2dsin(theta). The intensity of the scattered x-ray is proportional to the number of electrons that the x-ray is scattered from.
Normally one would use a microscope to view small objects. For a microscope, light is scattered by an object and collected using lenses, which in turn magnifies the image of the object. The limit of the microscope is intrinsic to the nature of the electromagnetic radiation that is used to probe the object. If we use light we cannot look at objects smaller than the wavelength of light which is about 10 -6 m. Since the atom has dimensions of about 10-10 m we cannot image an atom with a photon of light. X-rays, on the other hand, have a wavelength of about 10 -10 m and are suitable for imaging objects at the atomic scale.
To observe a single object, we normally fix the object to a microscope slide. To view an atom we would need some method to handle a small atom and align it in the microscope. This would be quite difficult and the x-rays scattered by a single atom is extremely week. A better method is to use 1020atoms (the number found in a small -crystal) and to sum the scattered x-rays from each atom. The trick is to align the atoms in neat orderly rows and columns so that the scattered x-rays would form predictable patterns that are based on the original arrangement of the atoms. All of the atoms of a single-crystal are oriented the same way and the scattered x-rays are superimposed and can be measured. Each scattering event that is measures is called a "reflection". There is typically 2000 to 100000 independent reflections for each single-crystal.
We can determine Molecular Structure ....
The scattered x-rays contain both angular and intensity information. The information concerning the position of the electrons (and atoms) involves both the amplitude and phase of the scattered intensities. For standard data collection techniques the amplitudes for the diffracted intensities are measured, however the phases are lost due to the nature of the experiment. Direct methods is employed to re-determine the phases.
Structure determination is the process of model building, structural factor (intensity) prediction and comparison to the observed structure factors. The model is constructed by introduction of atomic positions at electron density maxima. The model is then employed to predict structural factors which are refined (non-linear least squares) against the observed structural factors. The comparison between the predicted and observed structure factors is known as the residual and attests for the validity of the model.
Crystal Lattice and the unit cell are ...
A single-crystal is described as an order set of atoms (electrons) in a fixed orientation. Typically a single crystal suitable of analysis is at least 50 µm in its smallest dimension and not more than 500 µm in its largest. The smallest non-reproducible volume of the crystal is called the unit cell. The size of the unit cell ranges from a few hundred cubic angstroms (10-10 m) to 10's of thousands. By application of symmetry the unit cell can be repeated, in three dimensions, to describe the entire crystal. The unit cell in turn can be described by three non-coplanar axis a, b and c and the inter axis angles alpha ,beta and gamma which are called the Lattice Parameters. Seven crystal systems are described in terms of the lattice parameters
| SYSTEM | UNIT CELL LENGTH | UNIT CELL ANGLES |
| 1) Cubic | a = b = c | alpha=beta=gamma=90deg |
| 2) Tetragonal | a = b | alpha=beta=gamma=90deg |
| 3) Orthorhombic | no conditions | alpha=beta=gamma=90deg |
| 4) Rhombohedral | a = b = c | alpha=beta=gamma does not equal 90deg |
| 5) Hexagonal | a = b | alpha=beta=90deg gamma=120deg |
| 6) Monoclinic | no conditions | alpha=beta=90 deg |
| 7) Triclinic | no conditions | no conditions |
| Lattice | Symbol |
| 1) Primitive | P |
| 2) (single face centered cells) | |
| A face (bc plane) - centered | A |
| B face (ac plane) - centered | B |
| C face (ab plane) - centered | C |
| 3) Face - centered | F |
| 4) Body - centered | I |
Space groups are a way of describing how objects are arranged in three-dimensional space. There are four symmetry operations allowed in three dimensional "space".
| Operation | Symbol (Hermann) | Symbol (Schoenflies) |
| Rotation | 1,2,3,4,6 | E, C2, C3, C4, C6 |
| Reflection | m | Cm |
| Inversion | -1, 2/m | i |
| Rotation/Inversion | -1,-3,-4,-6 | n/a |
A symmetry operation followed by translation is also allowed
Screw axis 21, 31, 32, 41, 43, 61, 65
Glide planes a,b,c,n,d
A space group is described as a closed set of symmetry operations that describe the total symmetry of a given volume of space (unit cell). The first letter of the space group describes the centered cell (P, A, B, C, F or I). The following symbols represent the smallest set of non-reducible symmetry operations.
e.g. Pmmm Primitive cell with three perpendicular mirror planes
Local Questions
How and where to submit samples
Submit your samples to the X-ray staff for approval. Bring your sample to rm 2409 between 9:00am-5:00pm weekdays
There are two ways to submit your sample and determine your structure.
1st ) You can request that
the x-ray diffraction laboratory staff undertake the investigation.
This way
is suggested if ...
a) you
undertake only a few structural determinations a year
b) your
advisor does not want you to undertake the time and expense of
learning a new skill.
2nd ) You can be trained and
you can do your own work. This method is suggested if ...
a) your
structures are major part of your research
b) you
must defend your structures before skeptical investigators
To reserve instrument time ...
If you choose for the x-ray
diffraction laboratory staff to do your structure or powder diffraction
experiment then we will
reserve time for you.
If not you should reserve
time on one of the three CCD diffractometers, the GADDS diffractometer, the
D8 discover, the D8 vario or the SAXS instrument
To reserve time please come
to room 2409 and select a date on one of the four single crystal diffractometers
and to room 2407 to reserve time for the X-ray powder instruments.
See the x-ray diffraction facility manager for the SAXS reservation.
The price for single-crystal services rendered is $60/day for Chemistry and other qualified TAMU users. For outside users the cost is $300/day (See note). For Industrial users please call 979-845-9125 or e-mail.
For Powder Data Collection the price is $5/hour for Chemistry, $10/hour for qualified TAMU users and $60/hour for all outside users.
For Industrial users please call 979-845-9125 or e-mail.
Yes you need safety training IF ...
Yes !! : If you intend to do your own structures
No : If you wish for the staff to do your structures
X-ray Safety Training
Before you begin the x-ray staff will train you on the site specific safety issues.
Goto NEW USERS page for further details.
For more general x-ray safety training you will be expected to attend one of the classes presented by the Environmental Health and Safety Department (EHSD). Their training schedule can be found here : General X-ray Training
Free crystallographic programs to get started ....
You should download some of the free crystallographic software on the net
a)WinGX - A GUI (windows) for some of the most popular (and free) software. First download the software and then e-mail the author for a free license. SHELXS, SHELXL, PLATON, SIR92 and several other valuable programs come with the package.
b)GTREP - A structure graphics and plotting program. Will plot thermal ellipsoids.
C)Mercury from the CSD
See Crystallographic Program Guide
If the X-ray lab collects the data we will provide ..
You will be given (at least) two files project_name.HKL and project_name.INS with these files and WinGX you can solve refine and display your structure. The X-ray Staff will assist you the first few times.
The Cambridge Crystallographic Data Base can be ..
The Cambridge
Crystallographic Data Base is located on a PC computer RedHat Linux
9.0 (xray.chem.tamu.edu) and can be accessed by
a) Windows
You will need the program X-WIN
How do I get XWIN and set it up on my Windows PC
or
LiveCD see : CSD for Windows
b) Linux
You must set xhost to + and telnet to xray.chem.tamu.edu
(note you should have the MESA
OpenGL library)
a more secure method is to use the ssh command
you must set the DISPLAY command
in the .cshrc : setenv DISPLAY = `echo $SSH_CLIENT | awk
'{print $1};'`:0.0
or
in the .bashrc : DISPLAY=`echo $SSH_CLIENT | awk '{print $1};'`:0.0
c) A Silicon Graphics Computer, access the same as Linux
d) Macintosh under xdarwin (or x11), access the same as Linux.
You can get help with your structure. Goto the Helk Desk on this site
General Questions
Crystals : See Growing Crystals
Recommended reading
P.G. Jones:
Crystal growing, Chemistry in Britain (1981) 17, 222-225.
J. Hulliger:
Chemistry and Crystal Growth, Angew. Chem. Int. Ed. Engl. (1994) 33,
143-162. Angew. Chem. (1994) 106, 151-171.
A. Holden, P.
Morrison: Crystals and Crystal Growing, MIT Press, Cambridge,
Massachusetts (1982) ISBN 0-262-58050-0
J.W. Mullin:
Crystallization, Butterworth-Heinemann, Oxford, Great Britain (1993)
ISBN 0-7506-1129-4
How do
I mount my sample?
Two methods are commonly employed.
a)Thin
glass fiber
A thin glass fiber is pulled
and attached to a copper pin (magnetic base, Hampton) with clay and
finger nail polish. The fiber can be pulled by heating a
Klimax® melting point tube in a hot flame. The fiber is
typically 50 to 100 mm in diameter. The crystal is glued to the
fiber with an adhesive.
b)Nylon loop
A thin (thickness =
20mm) 0.7 mm diameter nylon loop (Hampton) that is attached to
a magnetic base is coated with Paratone® or Apieazon®
grease is used to "lasso" (Texas style) a crystal and
pulled it off the microscope plate.
Hints
-Crystals can be covered with
a thin layer of oil to prevent decomposition in air.
Mineral oil.
Paratone® (a
poly-isobutylene: additive free STP)
Poly-isobutylene (is
available in several viscosities)
Perfluorinated oils
(Krytox® oil)
Epoxy resin (less hardener)
Apieazon® grease
-If your crystals lose
solvent, try adding a few drops of the solvent (mother liquor) to
mineral oil or paratone and then cover the crystals with this
mixture. Some experimentation on solvent concentrations in the
oil may be needed.
-Adhesives for specimen pins
super
glue
holds up to 373K dries fast
dental
cemen
to 573K dheres to glass well
Epoxy
resins
to 373K slow drying
Apiezon®
Grease(T)
to 103K slow scatter
Silicon Grease (not
4)
to 133K Si scatter (cheap)
Vaseline
to 200K
sticky
Balsam
to RT dilute with
xylene)
Wax
to RT
permanent
Crystallographic Papers
Birth of Crystallography :
1669 Nicolaus Skno : Determined that angles between crystal faces remained constant between crystals of the same compound.
1895 Rontgen :
Discovers X-rays : Science (1896) 53, 274. (in English)
First X-ray Diffraction
Experiment : Friedrick, W. Knipping, P. & Laue,
M. Bravarian Acad. Sci. (1912) 303.
First Structure Determination
: Bragg, W.H & Bragg W.L. Proc. Royal. Soc. (1913) A88, 428.
First X-ray Camera (Powder):
Debye, P. & Scherrer, P. Phys Z. (1916) 17, 277-283.
Hull, A. W. Phys. Rev. (1917) 10, 661-696.
First X-ray Diffraction
Instrument: Weissenberg, K. Z.Phys. (1924) 23, 229.
First Geiger Counter:
Locher, G.L. & LeGalley, D.P. Phys. Rev. (1933) 46, 1047.
First X-ray Precession
Instrument : Buerger, M.J. "X-ray Crystallography"
(1942) Wiley, New York
First Scintillation Counter:
West, H.I., Mayerhot, W.E., Hotstadter, R. Phys. Rev. (1951) 81, 141.
Top Ten Must Read Crystallographic Books.
1. Crystal structure determination by: Werner
Massa
"My favorite introduction to Crystallography"
"It's the one book I would force into a
student hands!"
2. Crystal Structure Analysis by: Glusker and Trueblood
"A good starter for the common scientist"
3. Crystal Structure Determination and Crystal Structure
Analysis by: Bill Clegg
"One of my favourite and informative
book(s). First time crystallographers should read these books first."
4. Cystallography Made Crystal Clear by: Gale Rhodes
"For the Novice/macromolecular user"
5. Fundamentals of Powder Diffraction and Structural
Characterization of Materials by: Pecharsky and Zavalij
"Only book that I know of that explains
indexing and indexing programs"
"A must own book for the powder and
single-crystal diffractionist!"
"A gota-have book for people interested in
the bigger picture"
6. Structure Determination by X-ray Crystallography by: Ladd and Palmer
"I have given Ladd
and Palmer to non-crystallographers who needed to gain
a basic
understanding of the process."
7. X-ray Structure Determination by: Stout and Jensen
"a good, practical book for
the student after they are into the subject"
8. X-ray Analysis and the Structure of Organic Molecules by: Dunitz
"a
great book (even for an inorganic chemist) and it is filled Jack's
usual wit"
"The
section on weighting schemes in least squares is a must read"
9. The Determination of Crystals Structures by: Lipson & Cochran
"It
is still an amazing book!"
10. Fundamentals of Crystallography edited by C. Giacovazzo
"A MUST HAVE for a lab"
"For
more advanced students Giacovazzo is a must."
Absolute Configuration
Absolute Configuration
Jones, P.G.
(1986) Acta Cryst.A42, 57-57.
Flack
absolute structure
H.D. Flack
(1983) Acta Cryst.A39, 876-881
G.
Bernardinelli and H.D. Flack (1985) Acta Cryst.A41, 500-511.
H.D. Flack and
G. Bernardinelli (2000) J. Appl. Cryst. 33, 1143-1148.
Rogers
absolute structure
Rogers D.
(1981) Acta Cryst.A37 734-741.
Jones P.G.
(1984) Acta Cryst.A40, 660-662.
Hamiltons' R-test
Hamilton, W.C.
(1965) Acta Cryst.18, 502-510.
Alternative
to Hamitons' R-test
Rothstein,
S.M. ; Richardson, M.F. and Bell, W.D. (1978) Acta Cryst.A34, 969-974
Absorption
Absorption Coefficients
International Tables for
Crystallography, Volume C (1992), Ed. A.J.C. Wilson, Kluwer Academic
Publishers, Dordrecht: 4.2.4.2 (pp. 193-199).
Absorption Correction
Blessing, R.H. (1995) Acta
Cryst. A51, 33-38.
Azimuthal only (no theta dependence)
North A.C., Philips, D.C. and
Mathews, F. (1968) Acta Cryst .A24, 350-359.
Azimuthal + theta correction
Flack, H.D. (1974) Acta
Cryst. A30, 569-573.
Analytical
DeMeulenaer, J. and Tompa, H.
(1965) Acta Cryst. 19, 1014-1018.
Katayama, C. (1986) Acta
Cryst. A42, 19-23.
Numerical
Busing, W.R. and Levy, H.A.
(1957) Acta Cryst. 10, 180-182.
Coppens, P., Leiserowitz, L.
and Rabinovich, D. (1965) Acta Cryst. 18, 1035-1038.
Statistical
Katayama, C. (1972) Acta
Cryst. A28, 293-295.
Difabs
Walker, N. and Straurt, D.
(1983) Acta Cryst. A39 158-166.
XABS2
Parkin, S.; Moezzi,B. and
Hope, H. (1995) J.Appl.Cryst. 28, 53-56.
Sperical
International Tables for
X-ray Crystallography, Vol II. Birmingham; Kynoch Press., Tables
5.3.6B pages 302-305.
Back
to Top
Tests for Center of Symmetry
Wilson, A.J.C. (1949) Acta
Cryst., 2, 318-321.
Howells, E.R.; Phillips, D.C.
& Rogers D. (1950) Acta Cryst., 3, 210-214.
Marsh, R.E. (1986) Acta
Cryst., B42, 193-198.
Crystallographic Information File
CIF format :: I.U.Cr.
Commission on Crystallographic Data:
S.R. Hall, F.H. Allen and
I.D. Brown (1991) Acta Cryst., A47, 655-685.
Chemical
Group Modeling
Ipso-angles of phenyl
rings differ systematically from 120 degrees
P.G. Jones (1988) J.
Organomet. Chem., 345, 405
T. Maetzke and D. Seebach
(1989) Helv. Chim. Acta, 72, 624-630
A. Domenicano, "Accurate
Molecular Structures", eds. Domenicano and Hargittai, Chapter
18, OUP (1992)
Standard (restraint) bond
lengths based on the CSD
F.H.Allen, O. Kennard, D.G.
Watson, L. Brammer, A.G. Orpen and R. Taylor in Sections 9.5 and 9.6
of Volume C of "International Tables for Crystallography"
(1992), Ed. A.J.C. Wilson, Kluwer Academic Publishers, Dordrecht, pp.
685- 791.
Standard (retraint) bond
lengths for protiens
R.A. Engh and R. Huber (1991)
Acta Cryst., A47, 392-400.
Standard (restraint) bond
lengths For nucleic acids
R. Taylor and O. Kennard
(1982) J. Mol. Struct., 78, 1-28 (bases and phosphates)
S. Arnott and D.W.L. Hukins
(1972) Biochem. J., 130, 453-465 (furanose rings).
Plainarity of nucleic acid bases
R. Taylor and O. Kennard
(1982) J. Am. Chem. Soc., 104, 3209-3212
Diffuse solvent modeling
by Babinet's principle
R. Langridge, D.A. Marvin,
W.E. Seeds, H.R. Wilson, C.W. Hooper, M.H.F. Wilkins and L.D.
Hamilton (1960) J. Mol. Biol., 2, 38-64
H. Driessen, M.I.J. Haneef,
G.W. Harris, B. Howlin, G. Khan and D.S. Moss, J. (1989) J. Appl.
Cryst., 22, 510-516
Rigid body analysis
Schomaker, V. and Trueblood,
K.N. (1968) Acta Cryst., B24, 63-76.
Data Collection and Reduction
Area Detection -CCD
strategies
S. Ruhl and M. Bolte (2000)
215, 499-509
Area Detection -peak bases
Bolotovsky, R.; White, M.A.;
Darovsky, A. and Coppens, P. (1995), J. Appl. Cryst. 28, 86-95.
Diffractometer
Alexander, L & Gordon
S.S. (1962) Acta Cryst., 15, 983-1004.
Diffractometer Alignment
Samson, S. and Schuelke, W.W.
(1967) Rev. Sci. Instr., 38, 1273-1283.
Cell reduction and Lattice Symmetry
Glegg, W. (1981) Acta Cryst.,
A37, 913-915.
Gruber, B. (1973) Acta
Cryst., A29, 433-440.
Scan type Wyckoff
Wyckoff, H.W.; Doscher, M.;
Tsernoglou, D.; Inagami, T.; Johnson, L.; Hardman, K.D.; Allewell,
N.M.; Kelly,M. & Richards, F. (1967) J. Mol. Biol., 27, 563-578.
Data Reduction
Blessing, R.H. (1987) Cryst.
Rev., 1, 3-58.
Blessing, R.H. & Langs,
D.A. (1987) J.Appl. Cryst., 20, 427-428.
X-ray beam and Detection
Harkema, S.; Dam, J.; Van
Hummel, G.J. and Reuvers, A.J. (1980) Acta Cryst., A36, 433-435.
Katrusiak, A. & Ryan,
T.W. (1988) Acta Cryst., A44, 623-627.
Nelson, J.T. & Ellickson,
R.T. (1955) J. Am. Opt. Soc., 45, 984-986.
Intensities
Slaughter, M. (1968)
Kristallogr., 129, 24-35.
McCanlish, L.E.; Stour. G.H.
and Andrews, L.C. (1975) Acta Cryst., A31, 245-249.
French, S. & Wilson, K.
(1978) Acta Cryst., A34, 517-525.
Learnt Profile Analysis
Diamond, R. (1969) Acta
Cryst., A25, 43-55.
Clegg, W. (1981) Acta Cryst.,
A37, 22-28.
Lehmann/Larsen method
Lehmann, M.S. & Larsen,
F.K. (1974) Acta Cryst., A30, 580-584.
Floating Baseline
Reibenspies, J.H. (1994)
J.Appl.Cryst. 26,426-430.
Normal Back/Peak/Back
Tickle, I.J. (1975) Acta
Cryst. B31, 329-331.
Slope Detection method
Grant, D.F. & Gabe, E.J.
(1978) J.Appl. Cryst. 11, 114-120.
Misc. procedures and investigations
Spencer S.A. and Kossiakoff
(1980) J. Appl. Cryst., 13, 563-571.
Dudka, A.P. and Loshmanov,
A.A. (1992) Sov. Phys. Crystallogr., 36, 625-626.
Langford, J.L. (1978) J.
Appl. Cryst., 11, 10-14.
Lehmann, M.S. (1975) J. Appl.
Cryst., 8, 619-622.
Chulichkov, A.I.;
Chulichkova, M.; Fetisov, G.; Pyt'ev,Y.P.; Lupyan, Y.V.;Laltionov,
A.V.; Nesterenko, A.P. and Aslanov, L.A. (1987) Sov. Phys.
Crystallogr., 32, 649-653.
van der Wal, H.R.; de Boer,
J.L. and Vos, A. (1979) Acta Cryst., A35, 685-688.
Strel'tsov, V.A. and
Zavodnik, V.E. (1989) Sov. Phys. Crystallogr., 34, 824-828.
Norrestam, R. (1972) Acta
Chem. Scand., 26, 13-21.
Rigoult, P. J. (1979)
J.Appl.Cryst., 12, 116-118.
Blessing, R.H.; Coppens, P.
& Beker, P. (1972) J. Appl. Cryst., 7, 488-492.
Rossman, M.G. (1979) J. Appl.
Cryst., 12, 255-238.
Reflection Intensity Photography
Xuong, N. & Freer S. Acta
Cryst., B27, 2380-2387.
Laue Film Integration &
Deconvolution
Shrive, A.K.; Clifton,I.J.;
Hajdu, J. and Greenhough T.J. (1990) J. Appl. Cryst., 23, 169-174.
Decay Correction
Abrahams, S.C. and Marsh, P.
(1987) Acta Cryst., A43, 265-269.
Ibers, J.A. (1969) Acta
Cryst., B25, 1667-1668.
Back
to Top
Extinction Correction
A.C. Larson in
"Crystallographic Computing" (1970), Ed. F.R. Ahmed,
Munksgaard, Copenhagen, pp. 291-294.
Larson, A.C. (1967) Acta
Cryst., 23, 664-665.
Zachariasen, W.H. (1963) Acta
Cryst., 16, 1139-1144.
Least Squares Refinement
Floating origin restraints:
H.D. Flack and D.
Schwarzenbach (1988) Acta Cryst., A44 499-506.
Use of all data in refinement.
F. L. Hirshfeld and D.
Rabinovich (1973) Acta Cryst., A29, 510-513
L. Arnberg, S. Hovmoller and
S. Westman (1979) Acta Cryst., A35, 497-499
Refinement of racemic twins
Pratt, Coyle and Ibers (1971)
J. Chem. Soc., 2146-2151
Jameson (1982) Acta Cryst.,
A38, 817-820.
Conjugated Gradient L. S. algorithm
W.A. Hendrickson and J.H.
Konnert "Computing in Crystallography", Ed. R. Diamond, S.
Ramaseshan and K. Venkatesan, I.U.Cr. and Indian Academy of Sciences,
Bangalore 1980, pp. 13.01-13.25.
D.E. Tronrud (1992) Acta
Cryst., A48, 912-916.
Least-Squares Restraints :
J.S. Rollett in
"Crystallographic Computing", Ed. F.R. Ahmed, S.R. Hall and
C.P. Huber, Munksgaard, Copenhagen, (1970) pp. 167-181.
F.L. Hirshfeld (1976) Acta
Cryst., A32, 239-244
K.N. Trueblood and J.D.
Dunitz (1983) Acta Cryst., B39,120-133.
.J. Didisheim and D.
Schwarzenbach (1987) Acta Cryst., A43, 226-232
Shift limiting
least-squares restraints (damping) Marquardt algorithm ::
Marquardt (1963) J. Soc. Ind.
Appl. Math., 11, 431-441.
Back
to Top
Program References
SHELXTL-PLUS
Sheldrick, G. (1990) SHELXTL-PLUS revision 4.11V, SHELXTL-PLUS users manual,Siemens Analytical X-ray Inst. Inc., Madison WI, U.S.A.
SHELXS-86
Sheldrick, G. (1986)
SHELXS-86 Program for Crystal Structure Solution, Institüt
für Anorganische Chemie der Universität, Tammanstrasse 4,
D-3400 Gottingen, Germany.
SHELXL-97
Sheldrick, G. (1997)
SHELXL-97 Program for Crystal Structure Refinement, Institüt
für Anorganische Chemie der Universität, Tammanstrasse 4,
D-3400 Gottingen, Germany.
TEXSAN
teXsan : Single Crystal
Structure Analysis Software, Version 1.6 (1993). Molecular Structure
Corporation, The Woodlands, Texas 77381.
DIRDIF-99
Beurskens, P., Admiraal, G.,
Beurskens G., Bosman, S., Garicia-Granda, R., Gould, J., Smykalla, A.
and Smykalla, C. (1992). DIRDIF-99 program system, Technical Report
of the Crystallography Laboratory, University of Nijmegen, The Netherlands
SIR-97
Giacovazzo C. (1997) SIR-97
Program for Crystal Structure Solution, Inst. di Ric. per lo Sviluppo
di Metodologie Cristallograpfiche, CNR, Univ. of Bari, Italy.
SIR-88
SIR88 : Burla, M.C.; Camalli,
M.; Ccascarano, G.; Giacovazzo, C.; Polidori, G. and Viterbo, D.
(1989) J. Appl. Cryst. 22, 389-393.
PATSEE
Egert, E. (1985) PATSEE
Program for Crystal Structure Solution by Integrated Patterson and
Direct Methods, Institüt für Anorganische Chemie der
Universität, Tammanstrasse 4, D-3400 Gottingen, Germany. Egert,
E. and Sheldrick, G. (1985) Acta Cryst A41, 262-268.
SHAKAL
SCHAKAL88 : Keller, E. (1989)
J. Appl. Cryst. 22, 12-22.
PLUTON
Spek, A.L.. (2002) PLUTON.
Program for Molecular and Crystal Graphics. Vakgroep Algemene Chemie,
University of Utrecht, Afdeling Kristal-En Structuurchemie, Padualaan
8, 3584 Ch Utrecht, The Netherlands.
PLATON
Spek, A.L.. (2002) PLATON.
Program for Crystal Structure Results Analysis. Vakgroep Algemene
Chemie, University of Utrecht, Afdeling Kristal-En Structuurchemie,
Padualaan 8, 3584 Ch Utrecht, The Netherlands.
ORTEP-76
Johnson, C.K. (1976)
ORTEP-II. A Fortran Thermal-Ellipsoid Program, Report ORNL-5138. Oak
Ridge National Laboratory, Oak Ridge Tennessee.
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Space
groups/ Laue symmetry / Unit cell
polar space groups
H.D. Flack and D.
Schwarzenbach (1988) Acta Cryst., A44 499-506
MISSYM
LePage, Y. (1987) J Appl.
Cryst., 20, 264-269
Lattice symmetry determination
Mighell, A.D. and Rodgers,
J.R. (1980) Acta Cryst., A36, 321-326.
Baur, W.H. and Tilmanns, E.
(1986) Acta Cryst., B42, 95-111.
Structure inversion for
special space groups
E. Parthe and L.M. Gelato
(1984) Acta Cryst., A40, 169-183
G. Bernardinelli and H.D.
Flack (1985) Acta Cryst., A41, 500-511
Statistical Descriptors in Crystallography
D. Schwarzenbach; Abrahams, S.C.; Flack, H.D.; Gonschorek, W.; Hahn, T;Huml, K.; Marsh, R.E.; Prince, E.; Robertson, B.E.; Rollet, J.S. and Wilson, A.J.C. (1989) Acta Cryst., A45, 63-75.
Twinning
Racemic twinning
H.D. Flack (1983) Acta Cryst., A39, 876-881.
Twinning structural reasons.
W. Hoenle and H.G. von Schnering (1988) Z. Krist., 184, 301-305.
Buerger, M.J. (1945) J. Am. Miner., 30, 469-482.
SHELXL-97
R. Herbst-Irmer, G. Sheldrick
(1998) Acta Cryst, B54, 443-449.
Weighting Scheme
Statistical bias
A.J.C. Wilson (1976) Acta Cryst., A32, 994-996.
Exponential weights
J.D. Dunitz and P. Seiler (1973) Acta Cryst., B29, 589-595.
X-ray flux
Honkimaki, V.; Sleight, J. and Suorott, P. (1990) J. Appl. Cryst., 23, 412-417.