## Elements of X-ray DiffractionIntended to acquaint the reader with the theory of x-ray diffraction, the experimental methods involved, and the main applications. The book is a collection of principles and methods stressing X-ray diffraction rather than metallurgy. The book is written entirely in terms of the Bragg law and can be read without any knowledge of the reciprocal lattice. It is divided into three main parts— Fundamentals; experimental methods; and applications. Designed for beginners, not as a reference tool for the advanced reader. |

### From inside the book

Results 1-3 of 83

Page 110

The total scattered intensity at P is obtained by summing the intensities of these

two scattered components: IP = IPy + Ifl = 4 Co» + t0, cos2 20) r ,4-2, This is the

Thomson

intensity of the scattered beam is only a minute fraction of the intensity of the

incident beam; the value of K is 7.94 x l0" 30 m2, so that IP/I0 is only 7.94 x l0" 26

in the forward direction at I cm from the electron. The

the ...

The total scattered intensity at P is obtained by summing the intensities of these

two scattered components: IP = IPy + Ifl = 4 Co» + t0, cos2 20) r ,4-2, This is the

Thomson

**equation**for the scattering of an x-ray beam by a single electron. Theintensity of the scattered beam is only a minute fraction of the intensity of the

incident beam; the value of K is 7.94 x l0" 30 m2, so that IP/I0 is only 7.94 x l0" 26

in the forward direction at I cm from the electron. The

**equation**also shows thatthe ...

Page 139

4-12 INTENSITIES OF POWDER PATTERN LINES We are now in a position to

gather together the factors discussed in preceding sections into an

the relative intensity of powder pattern lines. Debye-Scherrer Camera (

Approximate) = \F\2p l + cos2 20\ sin2 0 cos 0 J (4-l9) where / = relative

integrated intensity (arbitrary units), F = structure factor, p = multiplicity factor, and

0 = Bragg angle. The trigonometric terms in parentheses are the Lorentz-

polarization factor. In arriving ...

4-12 INTENSITIES OF POWDER PATTERN LINES We are now in a position to

gather together the factors discussed in preceding sections into an

**equation**forthe relative intensity of powder pattern lines. Debye-Scherrer Camera (

Approximate) = \F\2p l + cos2 20\ sin2 0 cos 0 J (4-l9) where / = relative

integrated intensity (arbitrary units), F = structure factor, p = multiplicity factor, and

0 = Bragg angle. The trigonometric terms in parentheses are the Lorentz-

polarization factor. In arriving ...

Page 361

... da or = 2(a + bxt - y,) + 2(a + bx2 - y2) + • • • = 0, £a + ft£jr-£>' = 0. (ll-l6) The

best value of b is found in a similar way: ^£(g } = 2*,(a + bXl - yt) + 2x2(a + bx2 -

y2) + • • • = 0, CD or a £ x + b £ x2 - £ xy = 0. (ll-l7)

the normal

best values of a and b, which can then be substituted into Eq. (ll-l4) to give the

as follows: ...

... da or = 2(a + bxt - y,) + 2(a + bx2 - y2) + • • • = 0, £a + ft£jr-£>' = 0. (ll-l6) The

best value of b is found in a similar way: ^£(g } = 2*,(a + bXl - yt) + 2x2(a + bx2 -

y2) + • • • = 0, CD or a £ x + b £ x2 - £ xy = 0. (ll-l7)

**Equations**(l l-l6) and (l l-l7) arethe normal

**equations**. Simultaneous solution of these two**equations**yields thebest values of a and b, which can then be substituted into Eq. (ll-l4) to give the

**equation**of the line. The normal**equations**as written above can be rearrangedas follows: ...

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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

### Contents

Geometry of Crystals | 32 |

Directions of Diffracted Beams | 81 |

Intensities of Diffracted Beams | 107 |

Copyright | |

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### Common terms and phrases

absorption coefficient alloy atomic number austenite axes back-reflection body-centered Bragg angle Bragg law Bravais lattice calculated camera circle collimator constant copper cos2 counter counting rate cubic curve Debye ring Debye-Scherrer decreases determined diffracted beam diffraction lines diffraction pattern diffractometer diffractometer axis direction effect electron elements energy equation error example face-centered face-centered cubic factor film filter given grain hexagonal incident beam indices integrated intensity lattice parameter Laue method Laue spot martensite measured metal neutron normal obtained orthorhombic parallel percent phase photographic pinhole point lattice pole figure position powder pattern preferred orientation produced pulses random reciprocal lattice reciprocal-lattice reflecting planes relative rhombohedral rotation sample sheet shown in Fig shows sin2 0 values slit solid solution spacing specimen spectrometer sphere substance surface symmetry temperature tetragonal texture thickness transmission unit cell vector voltage wave wavelength x-ray beam x-ray diffraction x-ray tube zero zone