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Dedicated to the memory of Z.G.Pinsker. (on the occasion of his 100 th anniversary ) E LECTRON DIFFRACTION STRUCTURE ANALYSIS, PAR T 1. SPECIMENS AND THEIR ELECTRON DIFFRACTION PATTERNS. Vera KLECHKOVSKAYA Institute of Crystallography, Russian Academy of Sciences.
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Dedicated to the memory of Z.G.Pinsker. (on the occasion of his 100th anniversary)ELECTRON DIFFRACTION STRUCTURE ANALYSIS, PART 1.
THEIR ELECTRON DIFFRACTION PATTERNS.
Institute of Crystallography, Russian Academy of Sciences
The basic modern data describing the atomic structure of matter have been obtained by the using of three diffraction methods – X-ray, neutron and electron.
Electron diffraction structure analysis is generally used to study thin films and finely dispersed crystalline materials and allows the complete structure determinations up to establishment of the atomic
coordinates in the crystal lattice and refinement of atomic thermal vibrations and chemical bounding.
analysis of various crystals but also for the analysis of other condensed state of matter – quasi crystals, incommensurate phases, and partly disordered systems, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapor and gases. analysis of various crystals but also for the analysis of other condensed state of matter – quasi crystals, incommensurate phases, and partly disordered systems, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapor and gases.
OF ELECTRON DIFFRACTION STRUCTURE ANALYSIS
Electron Diffraction Camera have been constructed by Z.Pinsker and B.Vainshtein -- gold medal on the International Exhibition in Brussels, 1958.
Z.G.Pinsker (1953) Electron diffraction.London: Butterwords (in Russia, 1949)
B.K.Vainshtein (1964) Structure analysisby
Oxford, Pergamon Press
the obtaining of appropriate diffraction patterns and
their geometrical analysis,
the precision evaluation of diffraction-reflection
the use of the appropriate formulas for recalculation of
the reflection intensities into the structure factors,
Ihkl ~ Kkin |F hkl |2+ K dyn |F hkl |
the solution of the phase problem,
Fourier analysis of the structure.
xyz) = 1/ Fhkl exp[2 i (hx+ky+lz)]
MOSAIC SINGLE CRYSTAL
ONLY THREE TYPE SPECIMENS AND ELECTRON DIFFRACTION PATTERNS MAY BE USED FOR ATOMIC STRUCTURE ANALYSIS UNKNOWN PHASES
k0, k – wave-vectors,
- wave – length,
a*, b* - parameters of reciprocal unit cell
THE RECIPROCAL LATTICE NET IS SAMPLED BY AN EWALD SCHERE ON RADIUS k0 =1/ .
SINCE THE WAVELENGTH OF A 100 kV ELECTRON BEAM IS SOME 40 TIMES AS SMALL AS THAT OF A CuK X-RAY, IT IS OFTEN A SUFFICIENT APPROXIMATION TO SAY THAT THE EWALD SAMPLING SURFACE IS A PLANE IN THE CASE OF ELECTRONS .
A CRYSTAL REPRESENT A THREE DIMENTIONAL PERIODIC DISTRIBUTION OF
THE DISTRIBUTION OF POINTS AT WHICH THE SCATTERING AMPLITUDE DIFFERS
FROM ZERO AND TAKES ON THE VALUE Fhkl IS PERIODIC IN RECIPROCAL SPACE
AND FORMS THE SO-CALLED RECIPROCAL LATTICE
A SPOT PATTERN REPRESENTED A PARTICULAR PLANE OF THE
RECIPROCAL LATTICE PASSING THROUGH OF THE POINT 000
Hhkl = ha* + kb* = lc*
a*, b*, c* are axial vectors,
h,k,l are point indices
A spot pattern is most conveniently characterized by the general
symbol of the reflection located on it.
Iftheplaneisa coordinate one of the indices must be equal to zero since the point 000 always lies in it.
If the plane is non-coordinate, then none of its three indices (hkl) is equal to zero.
The existence of a centre of symmety at a point 000 of the reciprocal lattice of symmetry being recognizable in diffraction phenomena, for only 11 classes of symmetry being recognizable in diffraction phenomena, although 32 classes of crystal symmetry exist. The symmetry of electron diffraction pattern is the symmetry of the plane nets of reciprocal lattice.SYMMETRY OF ELECTRON DIFFRACTION SPOT PATTERNS
Schematic representation of the
structure of the zero layer of the
reciprocal lattice for the six classes
of geometry in spot electron
Triclinic: a b c
Monoclinic: a b c =
Orthorhombic: a b c = = =900
Hexagonal: a = b c = = 900
Tetragonal: a = b c = = = 900
Cubic: a = b = c = = = 900
Having only one plane of reciprocal
lattice for unknown crystal we can`t
determined – this is coordinate oder
non-coordinate plane. And we have
not an information about perpendicular
direction for this plane.
rotation method and
to have three patterns of different zones
Interrelationship between three reciprocal lattice section, i.e. between three electron diffraction patterns of different zones.
of the rotation method
Electron diffraction patterns from samples containing very
large number of small randomly distributed crystals consist
of continuous rings. The radii of the rings are inversely proportional to the interplanar spacings dhkl of a lattice
planes of crystals. The formula
rhkl dhkl = L , (r- radius of the ring)
In reciprocal lattice of a polycrystal is obtained by “spherical rotation” of a reciprocal lattice of a single crystal around a fixed 000 point. It forms a system of sphere placed one inside the other.
A section through such a system of spheres produces a system of rings. Thus geometry of a polycrystalline pattern is a set of lengths Hhkl,i.e. a set of interplanar distances dhkl of a crystal lattice.
The quadratic form for orthorhombic crystals is:
1/d2hkl = h2/a2 + k2/b2 + l2/c2.
Simple division gives all dh00 = a/h, and, analogously, d0k0 and d00l. Further , using the scale, all dhk0 are found from
(dhkl) = (dhk0) + (doko),
then by fixing first l = 1 (one setting of the movable scale) and finding all dhk1, and repeating this operation
a – inverse scuares scale, b – method of finding dhk by using the mouvable scale
Distribution of reciprocal lattice points Distribution of circular scattering of a plate texture along straight lines regions of the reciprocal lattice of a
parallel to the texture axis and texture on coaxial cylinders.
perpendicular to the face lying on the
FORMATION of the circular scattering regions (rings) in the reciprocal lattice of a texture, and relationship between their shape and the structure of the specimen
Transition from a point to a ring (a),
for an ideal texture without disorder (c)
and having distribution function (e)
(d,f) – corresponding diagrams for a real
texture with some disorder.
If there are layer lines on the pattern
(for orthogonal lattice), for a zero layer
line, Rhk = Hhk0. Thus having a set of
R2hk = h2A2 + k2B2 + 2hkAB cos `
R = r (L)-1
We can determined constant A,B, ` of
The two-dimensional lattice.
FIVE PLANE CRYSTALLOGRAPHIC
SYSTEMS OF POINTS
The best formed plate textures are found in crystals with a layer lattice. For the reciprocal lattice of plate texture, the distribution of points along vertical strain lines, parallel to axis z, is characteristic. An important part is played by the modulus of vector Hhkl.
Hhkl = x2 + y2 + z2 =R2 + z2
The doubling of the number of circular scattering regions in the reciprocal lattice of a texture and therefore the number of reflections on the ellipse of a pattern for a non-orthogonal unit cell.
Mosaic single crystal, polycrystal, texture electron diffraction patterns provide valuable material for calculation the parameters of unit cell
and then may be used for complete structural investigations of the crystal with unknown atomic structure.