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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.

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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.

SPECIMENS AND

THEIR ELECTRON DIFFRACTION PATTERNS.

Vera KLECHKOVSKAYA

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.

All three radiations are used not only for the structure

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.

SCHEMATIC ILLUSTRATING BRANCHES OF MODERN CRYSTALLOGRAPHY, THEIR APPLICATIONS, AND THE RELATION OF CRYSTALLOGRAPHY TO THE NATURAL SCIENCES

“Heart”of this

scheme

ZINOVII PINSKER BORIS VAINSHTEIN 1904 – 1986 1921 - 1996

“The PARENTS”

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.

the classical monographs:

Z.G.Pinsker (1953) Electron diffraction.London: Butterwords (in Russia, 1949)

B.K.Vainshtein (1964) Structure analysisby

electron diffraction.

Oxford, Pergamon Press

(in Russia,1956)

MAIN STAGES OF ATOMIC STRUCTURE ANALYSIS

the obtaining of appropriate diffraction patterns and

their geometrical analysis,

the precision evaluation of diffraction-reflection

intensities,

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)]

hkl

ELECTRON DIFFRACTION PATTERNS FOR STRUCTURE ANALYSIS

MOSAIC SINGLE CRYSTAL

PLATELIKE TEXTURE

POLYCRYSTAL

ONLY THREE TYPE SPECIMENS AND ELECTRON DIFFRACTION PATTERNS MAY BE USED FOR ATOMIC STRUCTURE ANALYSIS UNKNOWN PHASES

GEOMETRICAL ASPECTS OF ELECTRON DIFFRACTION

EWALD CONSTRUCTION FOR X-RAY END ELECTRONk0, 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 .

SPOT-TYPE ELECTRON DIFFRACTION PATTERNS

A CRYSTAL REPRESENT A THREE DIMENTIONAL PERIODIC DISTRIBUTION OF

SCATTERING MATERIAL.

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

INDEXING OF AN ELECTRON DIFFRACTION PATTERN OF MOSAIC SINGLE CRYSTAL

Coordinate plane

Non-coordinate plane

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 PATTERNSSchematic representation of the

structure of the zero layer of the

reciprocal lattice for the six classes

of geometry in spot electron

diffraction patterns

The relationships between the axis and anglesin unit cells:

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.

Schematicrepresentation

of the rotation method

POLYCRYSTAL-TYPE ELECTRON DIFFRACTION PATTERN

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)

is used.

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 calculation for orthogonal lattices

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

OBLIQUE TEXTURE ELECTRON DIFFRACTION PATTERNS

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

support.

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.

PROJECTION NET AND THE CORRESPONDING SET OF Rhk VALUES

If there are layer lines on the pattern

(for orthogonal lattice), for a zero layer

line, Rhk = Hhk0. Thus having a set of

values :

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

DETERMINATION OF PERIOD c* and ANGLES

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.

CONCLUSION

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.

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