This presentation contains the technique of X-ray Crystallography in simplified form.

1. X-RAY DIFFRACTION
Femina Anjum
PhD Scholar (Animal Biotech.)
Deptt. Of Veterinary microbio. &Biotech.
Rajasthan university of Veterinary and Animal
Sciences
1

2. overview
 Introduction
 Method
 Overview of single-crystal x-ray diffraction
 Crystallization
 Data collection
 Mounting the crystal
 X-ray sources
 Recording the reflections
 Data analysis
 Deposition of the structure
 Diffraction theory
 Applications
 Summary 2

3. Introduction
3

4.  X-ray crystallography is a technique used for
determining the atomic and molecular structure of
a crystal.
 Measuring the angles and intensities of these
diffracted beams.
 From the electron density, the mean positions of the
atoms in the crystal can be determined.
4

5. • For electromagnetic radiation to be diffracted the
spacing
in the grating should be of the same order as the
wavelength
• In crystals the typical interatomic spacing ~ 2-3 Å so the
suitable radiation is X-rays
Beam of electrons Target
X-rays
A accelerating charge radiates electromagnetic radiation 5

6. Information in a Diffraction Pattern
 Phase Identification
 Crystal Size
 Crystal Quality
 Texture (to some extent)
 Crystal Structure
6

7. Crystal Systems and Bravais Lattices
7

8. Structure of Common Materials
 Metals
 Copper: FCC
 -Iron: BCC
 Silver: FCC
 Aluminium: FCC
 Ceramics
 SiC: Diamond Cubic
 MgO:SC
8

9. Heat
Incident X-rays
SPECIMEN
Transmitted beam
Fluorescent X-rays
Electrons
Compton recoil Photoelectrons
Scattered X-rays
Coherent
From bound charges
Incoherent (Compton modified)
From loosely bound charges
X-rays can also be refracted (refractive index slightly less than 1) and reflected (at very small a
9

10. Method
10

11. Single Crystal Diffraction (SCD)
 Used to determine:
 crystal structure
 orientation
 degree of crystalline perfection/imperfections
 Sample is illuminated with monochromatic
radiation
 The sample axis, phi, and the goniometer axes
omega and 2theta are rotated to capture diffraction
spots from at least one hemisphere
 Easier to index and solve the crystal structure
because it’s diffraction peak is uniquely resolved
11

12. Procedure
 It includes 3 steps:-
 First step is to obtain an adequate crystal of the
material under study.
 Second step- the crystal is placed in an intense
beam of X-rays.
 Third step- these data are combined
computationally with complementary chemical
information.
12

13. Crystallization
 Small molecules- crystallized by methods, such
as chemical vapor deposition and
recrystallization.
 Macromolecule- crystallization must be carried
out so as to maintain a stable structure.
 Protein-
Crystallization in solution by precipitation
Crystallization of protein under oil
 It is extremely difficult to predict good conditions
for nucleation or growth of well-ordered crystals.
 Having failed to crystallize a target molecule, a
crystallographer may try again with a slightly
modified version of the molecule; even small
changes in molecular properties can lead to large
differences in crystallization behavior. 13

14. Data collection
14

15. Mounting the crystal
 In the past, crystals were loaded into glass
capillaries with the crystallization solution.
 Nowadays, crystals of small molecules are typically
attached with oil or glue to a glass fiber or a loop,
which is made of nylon or plastic and attached to a
solid rod.
 Protein crystals are scooped up by a loop, then
flash-frozen with liquid nitrogen.
 The capillary or loop is mounted on a goniometer. 15

16. Two Circle Diffractometer
 For polycrystalline Materials
16

17. Four Circle Diffractometer
For single crystals
17

18. X-ray generation
• X-ray tube (λ = 0.8-2.3 Ǻ)
• Rotating anode (λ = 0.8-2.3 Ǻ)
• Synchrotron (λ ranging from infrared to X-ray)
18

19. Electrons
X-rays
Be window
Metal anodeW cathode
X-ray tube
Rotating anode
19

20.  X-ray bulb emitting all radiations from IR to X-rays
Synchrotron
20

21. Recording the reflections
 The intensity of reflections recorded provide the
information to determine the arrangement of
molecules within the crystal in atomic detail.
 The intensities of these reflections may be
recorded with photographic film, an area detector
or with a charge-coupled device (CCD) image
sensor.
 Measures of deffraction quality-mosaicity,
disorder and pathologies.
 One image of spots is insufficient to reconstruct
the whole crystal so the crystal must be rotated
step-by-step through 180°, with an image
recorded at every step.
21

22. Diffraction Methods
Method Wavelength Angle Specimen
Laue Variable Fixed Single
Crystal
Rotating
Crystal
Fixed Variable Single
Crystal
Powder Fixed Variable Powder

23. Laue Method
• Uses Single crystal
• Uses White Radiation
• Used for determining crystal orientation and quality
Transmission Zone axis
crystal
Incident beam
Film
Reflection
Zone axis
crystal
Incident beam Film
23

24. Rotating Crystal Method
 Determination of unknown crystal structures
24

25. Powder Method
• Useful for determining lattice parameters with high precision and for
identification of phases
Incident Beam Sample
Film
25

26. Data analysis
26

27. Crystal symmetry, unit cell, and
image scaling
 The two-dimensional diffraction patterns is
converted into a three-dimensional model of the
electron density; the conversion uses the
mathematical technique of Fourier transforms.
 The crystallographer must
determine which variation corresponds
to which spot (indexing), the relative strengths of
the spots in different images (merging and
scaling) and how the variations should be
combined to yield the total electron density
(phasing).
27

28. Initial phasing
 The data collected from a diffraction experiment is
a reciprocal space representation of the crystal
lattice.
 An electron density map allows a crystallographer
to build a starting model of the molecule.
 The phase cannot be directly recorded during a
diffraction experiment: this is known as the phase
problem.
 Initial phase estimates can be obtained in a
variety of ways:
Ab initio phasing or direct methods
Molecular replacement
Anomalous X-ray scattering
28

29. Model building and phase
refinement
 Having obtained initial phases, an initial model can be
built.
 Given a model of some atomic positions, these
positions and their respective Debye-Waller
factors (or B-factors, accounting for the thermal
motion of the atom) can be refined to fit the observed
diffraction data, ideally yielding a better set of phases.
 A new model can then be fit to the new electron
density map and a further round of refinement is
carried out. This continues until the correlation
between the diffraction data and the model is
maximized.
 The agreement is measured by an R-factor defined
as
R=
∑all reflections |F0-Fc|
————————
∑all reflections|F0|
Here, F= structure factor
electronanbyscatteredwaveofAmplitude
ucinatomsallbyscatteredwaveofAmplitude
FactorStructureF  29

30. Structure Factor
2 ( )
1
n n n
N
i hu kv lw
hkl nF f e   
 
− h,k,l : indices of the diffraction plane under
consideration
− u,v,w : co-ordinates of the atoms in the lattice
− N : number of atoms
− fn : scattering factor of a particular type of atom
Intensity of the diffracted beam  |F|2
30

31. Disorder
 Disorder can take many forms but in general
involves the coexistence of two or more species
or conformations.
 Failure to recognize disorder results in flawed
interpretation.
 Pitfalls from improper modeling of disorder are
illustrated by the discounted hypothesis of bond
stretch isomerism.
 Disorder is modeled with respect to the relative
population of the components, often only two, and
their identity.
 In structures of large molecules and ions, solvent31

32. Deposition of the
structure
32

33.  Once the model of a molecule's structure has
been finalized, it is often deposited in
a crystallographic database such as
the Cambridge Structural Database, the Inorganic
Crystal Structure Database (ICSD) or the Protein
Data Bank.
 Many structures obtained in private commercial
ventures to crystallize medicinally relevant
proteins are not deposited in public
crystallographic databases.
33

34. Diffraction theory
34

35.  The main goal of X-ray crystallography is to determine
the density of electrons f(r) throughout the crystal
using the formula
 Here,
r= the three-dimensional position vector within the
crystal
F(q)= Fourier transform
q=three dimensional real vector represents a point in
reciprocal space
 The length of q corresponds to 2π divided by the
wavelength of the oscillation. The corresponding
formula for a Fourier transform will be used below
 where the integral is summed over all possible values
of the position vector r within the crystal. 35

36.  The Fourier transform F(q) is generally a complex
number, and therefore has a magnitude |F(q)|
and a phase φ(q) related by the equation
 The intensities of the reflections observed in X-
ray diffraction give us the magnitudes |F(q)| but
not the phases φ(q).
 Combining the magnitudes and phases yields the
full Fourier transform F(q), which may be inverted
to obtain the electron density f(r).
36

37. Bragg’s Law
n=2d.sin
n: Order of reflection
d: Plane spacing
: Bragg Angle
λ should be less than
twice the d spacing we
want to study
Path difference must be integral multiples of the wavelength
in=out

38. The Ewald Sphere
• The reciprocal lattice points are the values of
momentum transfer for which the Bragg’s
equation is satisfied
• For diffraction to occur the scattering vector
must be equal to a reciprocal lattice vector
• Geometrically  if the origin of reciprocal
space is placed at the tip of ki then diffraction
will occur only for those reciprocal lattice
points that lie on the surface of the Ewald
sphere 38

39. 01
10
02
00 20
2
(41)
Ki
KD
DK
Reciprocal Space
DK = K = Diffraction Vector
Ewald Sphere
The Ewald Sphere touches the
reciprocal lattice (for point
41)
 Bragg’s equation is satisfied
for 41
39

40. Real space Reciprocal space
Crystal Lattice Reciprocal Lattice
Crystal structure Diffraction pattern
Unit cell content Structure factor
x
y
y’
x’
y’
x’
40

41. Application
41

42.  X-ray method for investigation of drugs
X-ray diffraction was used for the identification of
antibiotic drugs such as: eight β-lactam,
three tetracycline (doxycycline
hydrochloride, oxytetracycline dehydrate, tetracycline
hydrochloride) and
two macrolide (azithromycin, erythromycin estolate)
antibiotic drugs.
 X-ray method for investigation of textile fibers and
polymers
Forensic examination of any trace evidence is based
upon Locard's exchange principle.
Textile fibers are a mixture of crystalline and
amorphous substances.
The measurement of the degree of crystalline gives
useful data in the characterization of fibers using X-
ray diffractometry. 42

43.  X-ray method for investigation of bone
Hiller investigated the effects of heating and
burning on bone mineral using X-ray diffraction
(XRD) techniques.
 The bone samples were heated in temperature of
500, 700, and 900 for 15 and 45 min.
The results show bone crystals began to change
during the first 15 min of heating at 500 and
above. At higher temperatures, thickness and
shape of crystals of bones appear stabilized, but
when the samples were heated at lower
temperature or for shorter period, XRD traces
showed extreme changes in crystal parameters.
 Integrated circuits
X-ray diffraction has been demonstrated as a
method for investigating the complex structure
of integrated circuits.
43

44. Summary
44

45.  X-ray Diffraction is a very useful technique to
characterize materials for following
information
 Phase analysis
 Lattice parameter determination
 Strain determination
 Texture and orientation analysis
 Order-disorder transformation
 and many more things
 Choice of correct type of method is critical for
the kind of work one intends to do. 45

46. References
46
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crystals". Nature. 29 (738):186.
 Bragg WH (1908). "The nature of γ- and X-rays". Nature. 77 (1995): 270.
 Pauling L (1923). "The Crystal Structure of Magnesium Stannide". J. Am. Chem.
Soc. 45(12): 2777.
 Müller A (1923). "The X-ray Investigation of Fatty Acids". Journal of the Chemical
Society (London). 123: 2043.
 Kendrew J. C., et al. (1958-03-08). "A Three-Dimensional Model of the
Myoglobin Molecule Obtained by X-Ray Analysis". Nature. 181 (4610): 662–6.
 Scapin G (2006). "Structural biology and drug discovery". Curr. Pharm.
Des. 12 (17): 2087–97.
 Suryanarayana, C.; Norton, M. Grant (2013-06-29). X-Ray Diffraction: A
Practical Approach. Springer Science & Business Media.
 Rupp B; Wang J (2004). "Predictive models for protein
crystallization". Methods. 34 (3): 390–407.
 Jeruzalmi D (2006). "First analysis of macromolecular crystals: biochemistry and
x-ray diffraction". Methods Mol. Biol. 364: 43–62.
 Garman, E. F.; Schneider, T. R. (1997). "Macromolecular
Cryocrystallography". Journal of Applied Crystallography. 30 (3): 211.
 Ravelli RB; Garman EF (2006). "Radiation damage in macromolecular
cryocrystallography". Curr. Opin. Struct. Biol. 16 (5): 624–9.
 Hiller, JC; Thompson, TJ; Evison, MP; Chamberlain, AT; Wess, TJ (December
2003). "Bone mineral change during experimental heating: an X-ray scattering
investigation". Biomaterials. 24 (28): 5091–7.
 Courtland, Rachel (17 March 2017). "X-rays Map the 3D Interior of Integrated

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