## Elements of X-ray Diffraction1 Properties of X-rays 2 Geometry of Crystals 3 Diffraction I: Directions of Diffracted Beams 4 Diffraction II: Intensities of Diffracted Beams 5 Diffraction III: Non-Ideal Samples 6 Laure Photographs 7 Powder Photographs 8 Diffractometer and Spectrometer 9 Orientation and Quality of Single Crystals 10 Structure of Polycrystalline Aggregates 11 Determination of Crystal Structure 12 Precise Parameter Measurements 13 Phase-Diagram Determination 14 Order-Disorder Transformation 15 Chemical Analysis of X-ray Diffraction 16 Chemical Analysis by X-ray Spectrometry 17 Measurements of Residual Stress 18 Polymers 19 Small Angle Scatters 20 Transmission Electron Microscope |

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Page 99

(3-10) In order for diffraction to occur, d must be an integral multiple of 27; in

order for this to be true simultaneously for many p, q, r (i.e., for many different

scattering sites) h", k' and l' must be integers which will now be written h, k and l.

Thus, / or (S - So/A) must start and end on points of the reciprocal lattice. The

conditions for diffraction can be represented graphically in reciprocal space using

the

dimensional crystal ...

(3-10) In order for diffraction to occur, d must be an integral multiple of 27; in

order for this to be true simultaneously for many p, q, r (i.e., for many different

scattering sites) h", k' and l' must be integers which will now be written h, k and l.

Thus, / or (S - So/A) must start and end on points of the reciprocal lattice. The

conditions for diffraction can be represented graphically in reciprocal space using

the

**Ewald sphere**construction [2.3]. While the reciprocal lattice of a threedimensional crystal ...

Page 100

An example of the

orthorhombic crystal with lattice parameters a, + 2.0 Å, a, - 1.0 Å and as = 3.0 A.

The corresponding magnitudes of the reciprocal lattice vectors are bi = 0.5 Å", b.

= 1.0 A" and b, = 0.33 A', and Fig. 3-6 shows the reciprocal lattice adjacent to the

direct space lattice. If the orthorhombic crystal is oriented for 100 diffraction with

Cu Ka radiation (A = 1.54 A), S, must make an angle of 22.6° with (100). This is

shown ...

An example of the

**Ewald sphere**construction is shown in Fig. 3-6 for a simpleorthorhombic crystal with lattice parameters a, + 2.0 Å, a, - 1.0 Å and as = 3.0 A.

The corresponding magnitudes of the reciprocal lattice vectors are bi = 0.5 Å", b.

= 1.0 A" and b, = 0.33 A', and Fig. 3-6 shows the reciprocal lattice adjacent to the

direct space lattice. If the orthorhombic crystal is oriented for 100 diffraction with

Cu Ka radiation (A = 1.54 A), S, must make an angle of 22.6° with (100). This is

shown ...

Page 118

The very small wavelength of the electrons means that the radius of the

corresponding

reciprocal lattice points or compared to the

0.037 A radiation, the

and to ~0.5 Å" for the reciprocal lattice spacing. This means that the curvature of

the

in the vicinity ...

The very small wavelength of the electrons means that the radius of the

corresponding

**Ewald sphere**is very large compared to the spacing betweenreciprocal lattice points or compared to the

**Ewald sphere**diameter for x-rays. For0.037 A radiation, the

**Ewald sphere**radius is 25 Á" compared to ~1 Å" for x-raysand to ~0.5 Å" for the reciprocal lattice spacing. This means that the curvature of

the

**Ewald sphere**is gradual compared to the reciprocal lattice spacings, and that,in the vicinity ...

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#### LibraryThing Review

User Review - ron_benson - LibraryThingExcellent reference book. Needs some updating in terms of advances in detector technology. Read full review

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### Common terms and phrases

alloy AuCu austenite axes axis back-reflection Bragg angle Bragg's law Bravais lattice calculated camera composition constant copper crystallite cubic curve decreases density detector determined diffracted beam diffracted intensity diffraction lines diffraction pattern diffractometer direction effect electrons energy equation error Ewald sphere example extrapolation face-centered face-centered cubic factor film fraction given grain hexagonal Hull/Debye–Scherrer incident beam indices integrated intensity lattice parameter lattice points Laue pattern Laue spots layer martensite measured metal normal observed obtained orthorhombic parallel peak percent phase photographic pinhole plane plot pole figure position powder pattern preferred orientation produce projection pulses radiation rays reciprocal lattice reciprocal space reflection relative rotation sample scattering shown in Fig shows slit solid solution space specimen stress substance superlattice surface symmetry temperature tetragonal texture tion transmission unit cell vector voltage wave wavelength x-ray diffraction x-ray tube