Crystal Structure Determination and
Refinement Using the
Bruker AXS SMART APEX System
Charles Campana
Bruker Nonius
Flowchart for Method
Select, mount, and opti call y ali gn a sui tabl e crystal
Eval uate crystal quali ty; obtain uni t cel l geometry
and prel iminary symmetry informati on
Measure intensity data
Data reducti on
Sol ve the structure
Adapted from William Clegg
“Crystal Structure Determination”
Oxford 1998.
Complete and refi ne the structure
Interpret the resul ts
Crystal Growing Techniques
 Slow
evaporation
 Slow
cooling
 Vapor
diffusion
 Solvent
diffusion
 Sublimation
http://laue.chem.ncsu.edu/web/GrowXtal.html
http://www.as.ysu.edu/~adhunter/YSUSC/Manual
/ChapterXIV.pdf
Examples of Crystals
Growing Crystals
Kirsten Böttcher and Thomas Pape
Select and Mount the Crystal

Use microscope

Size: ~0.4 (±0.2) mm

Transparent, faces, looks single

Epoxy, caulk, oil, grease to affix

Glass fiber, nylon loop, capillary
What are crystals ?
Crystallographic Unit Cell
Unit Cell Packing Diagram - YLID
7 Crystal Systems - Metric
Constraints
Triclinic - none
 Monoclinic -  =  = 90,   90
 Orthorhombic -  =  =  = 90
 Tetragonal -  =  =  = 90, a = b
 Cubic -  =  =  = 90, a = b = c
 Trigonal -  =  = 90,  = 120, a = b
(hexagonal setting) or  =  =  , a = b = c
(rhombohedral setting)
 Hexagonal -  =  = 90,  = 120, a = b

X-Ray Diffraction Pattern from
Single Crystal
Rotation Photograph
X-Ray Diffraction
X-ray beam
  1Å
(0.1 nm)
~ (0.2mm)3 crystal
~1013 unit cells, each ~
(100Å)3
Diffraction pattern on
CCD or image plate
Bragg’s law
n = 2d sin()


d
We can think of diffraction as reflection at sets of planes
running through the crystal. Only at certain angles 2 are
the waves diffracted from different planes a whole
number of wavelengths apart, i.e., in phase. At other
angles, the waves reflected from different planes are out
of phase and cancel one another out.
Reflection Indices
z
These planes must intersect
the cell edges rationally,
otherwise the diffraction from
the different unit cells would
interfere destructively.
y
x
We can index them by the
number of times h, k and l that
they cut each edge.
The same h, k and l values are
used to index the X-ray
reflections from the planes.
Planes 3 -1 2 (or -3 1 -2)
Diffraction Patterns
Two successive CCD detector images with a crystal
rotation of one degree per image
For each X-ray reflection (black dot), indices h,k,l can be
assigned and an intensity I = F 2 measured
Reciprocal space
 The
immediate result of the X-ray diffraction
experiment is a list of X-ray reflections hkl
and their intensities I.

We can arrange the reflections on a 3D-grid
based on their h, k and l values. The smallest
repeat unit of this reciprocal lattice is known
as the reciprocal unit cell; the lengths of the
edges of this cell are inversely related to the
dimensions of the real-space unit cell.

This concept is known as reciprocal space; it
emphasizes the inverse relationship between
the diffracted intensities and real space.
The structure factor F and
electron density 
Fhkl =
V xyz exp[+2i(hx+ky+lz)] dV
xyz = (1/V) hkl Fhkl exp[-2i(hx+ky+lz)]
F and  are inversely related by these Fourier transformations.
Note that  is real and positive, but F is a complex number: in
order to calculate the electron density from the diffracted intensities,
I = F2, we need the PHASE ( ) of F. Unfortunately it is almost
impossible to measure  directly! F(h,k,l) = A + iB
The Crystallographic Phase
Problem
The Crystallographic Phase Problem

In order to calculate an electron density map, we
require both the intensities I = F 2 and the phases  of
the reflections hkl.

The information content of the phases is appreciably
greater than that of the intensities.

Unfortunately, it is almost impossible to measure the
phases experimentally !
This is known as the crystallographic phase problem and
would appear to be insoluble
Real Space and Reciprocal Space
Real Space
 Unit Cell (a, b, c, , , )
 Electron Density, (x,
y, z)
 Atomic Coordinates –
x, y, z
 Thermal Parameters –
Bij or Uij
 Bond Lengths (A)
 Bond Angles (º)
 Crystal Faces
Reciprocal Space
 Unit Cell (a*, b*, c*, *,
*, *)
 Diffraction Pattern
 Reflections – h,h,l
 Integrated Intensities –
I(h,k,l)
 Structure Factors –
F(h,k,l)
 Phase – (h,k,l)
Goniometer Head
3-Axis Rotation (SMART)
3-Axis Goniometer
SMART 6000 System
SMART APEX System
SMART APEX System
Kappa axes (X8)
Kappa Rotation
Kappa in X8APEX
Short X-ray beam path
Kappa Goniometer
Bruker X8APEX
APEX detector
CCD Chip Sizes
X8 APEX, SMART APEX,
6000, 6500
4K CCD 62x62 mm
Kodak 1K CCD 25x25 mm
SMART 1000, 1500
& MSC Mercury
SITe 2K CCD 49x49 mm
SMART 2000
APEX detector
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transmission of fiber-optic
taper depends on 1/M2
APEX with direct 1:1 imaging
1:1 is 6x more efficient than
2.5:1
improved optical transmission
by almost an order of
magnitude
allowing data on yet smaller
micro-crystals or very weak
diffractors.
original SMART: 17 e/Mo
photon; APEX: 170 e/Mo
photon
project database
default settings
detector calibration
SMART
ASTRO
setup
sample screening
data collection strategy
data collection
SAINTPLUS
new project
change parameters
SAINT: integrate
SADABS: scale & empirical absorption correction
SHELXTL
new project
XPREP: space group determination
XS: structure solution
XL: least squares refinement
XCIF: tables, reports
George M. Sheldrick
Professor, Director of Institute and part-time programming technician
1960-1966: student at Jesus College and Cambridge University, PhD
(1966)
with Prof. E.A.V. Ebsworth entitled "NMR Studies of Inorganic
Hydrides"
1966-1978: University Demonstrator and then Lecturer at Cambridge
University; Fellow of Jesus College, Cambridge
Meldola Medal (1970), Corday-Morgan Medal (1978)
1978-now: Professor of Structural Chemistry at the University of
Goettingen
Royal Society of Chemistry Award for Structural Chemistry (1981)
Leibniz Prize of the Deutsche Forschungsgemeinschaft (1989)
Member of the Akademie der Wissenschaften zu Goettingen (1989)
Patterson Prize of the American Crystallographic Association (1993)
Author of more than 700 scientific papers and of a program called
SHELX
Interested in methods of solving and refining crystal structures (both
small
molecules and proteins) and in structural chemistry
email: gsheldr@shelx.uni-ac.gwdg.de
fax: +49-551-392582
SHELXTL vs. SHELX*
http://shelx.uni-ac.gwdg.de/SHELX/index.html

SHELXTL (Bruker Nonius)
 XPREP (space group det’m)
 XS (structure solution)
 XM
 XE
 XL (least-squares
refinement)
 XPRO
 XWAT
 XP (plotting)
 XSHELL (GUI interface)
 XCIF (tables, reports)
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SHELX (Public Domain)*
None
SHELXS
SHELXD
SHELXE
SHELXL
SHELXPRO
SHELXWAT
None
None
CIFTAB