An Introduction to X-ray Crystallography, Second Edition by Michael M. Woolfson

By Michael M. Woolfson

A textbook for the senior undergraduate or graduate pupil starting a significant research of X-ray crystallography. it is going to be of curiosity either to these meaning to turn into specialist crystallographers and to these physicists, chemists, biologists, geologists, metallurgists and others who will use it as a device of their study. All significant facets of crystallography are covered--the geometry of crystals and their symmetry, theoretical and sensible facets of diffracting X-rays through crystals and the way the information might be analyzed to discover the symmetry of the crystal and its constitution. comprises fresh advances akin to the synchrotron as a resource of X-rays, equipment of fixing constructions from energy facts and the whole diversity of innovations for fixing constructions from single-crystal information. machine courses are supplied for accomplishing many operations of data-processing and fixing crystal buildings together with by way of direct equipment. those courses are required for plenty of of the examples given on the finish of every bankruptcy yet can be utilized to create new examples in which scholars can attempt themselves or one another.

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It is mathematically convenient to write the equation of a progressive wave in complex form as 7=r o exp[27iiv(r-x/c)] = Yo cos[27iv(r - x/c)] + i Yo sin[27tv(r - x/c)]. 3) Yo is the amplitude of the wave, the real part of the expression is the displacement and the ratio (imaginary part/real part) is the tangent of the phase of the wave motion at (x, t) with respect to that at the origin (0,0). With this nomenclature one can express the time dependence of the disturbance at P in fig. 4) y{26D, t) =/ 29 ^exp[27iiv(t - D/c) - i a j .

16) That this equation applies to identical scatterers is revealed by the factor 7/(20, D) appearing outside the summation. 17) where the scattering length for each of the scatterers now appears within the summation symbol. The phase-vector diagram for non-identical scatterers is shown in fig. 5 for the case n = 6. It will be evident that, although we refer to the scatterers as non-equivalent, we have assumed that they all have the same associated values of as. This is the usual situation with X-ray diffraction.

8 Symmetry elements We have noted that there are seven crystal systems each related to the type of unit cell of the underlying structure. In addition there are thirty-two crystal classes so that there are differing degrees of symmetry of crystals all belonging to the same system. This is associated with elements of symmetry within the unit cell itself and we shall now consider the possibilities for these symmetry elements. 2) and it was stated that there are thirty-two possible arrangements of symmetry elements or point groups.

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