62 ANALYTICAL METHODS/Geochemical Analysis (Including X-ray) The melee of X-radiation from copper can be reduced to the Ka peak and then directed by a series of diffraction gratings, collimators, and slits The main features of an XRD analyser include an X-ray source with collimators, slits, etc, a sample, and an X-ray detector (Figure 9) The source and detector are both rotated about the sample, an arbitrarily fixed point, and define the same angle (y) relative to the sample The angle between the source and the detector is thus 2y relative to the sample Diffraction occurs when X-rays, light, or any other type of radiation passes into, but is then bounced back out of, a material with a regular series of layers Diffraction occurs within the body of the material rather than from the surface (and so is quite different from reflection) Regular layers are a characteristic of all crystalline materials (minerals, metals, etc) Each rock-forming mineral has a well-defined set of these layers, which constitute the crystal lattice No two minerals have exactly the same crystal structure, so fingerprinting a mineral by its characteristic set of lattice spacings helps to identify minerals A radiation beam from a pure source has a defined wavelength, and the rays from such a pure source will be ‘in phase’ Constructive interference occurs only when all the outgoing (diffracted) X-rays are also in phase Destructive interference, the norm, occurs when the diffracted X-rays are no longer in phase Constructive interference occurs when the extra distance that X-rays travel within the body of the material is an integer (whole number) multiple of the characteristic wavelength of the incident X-ray (Figure 10) The geometry of the XRD equipment, the wavelength of the incident radiation, and the lattice spacing are all important in defining whether constructive interference occurs The key equation is known as the Bragg Law, which must be satisfied for constructive interference (‘diffraction’) to occur: 2dsiny ¼ nl, where d is the lattice spacing, l is the wavelength of the incident X-ray source, and n is an integer (typically one in many cases) The value of y, defined in Figure 9, is a function of the variable geometry of the XRD equipment X-ray diffraction is most commonly used on crushed (powered) rock samples to ensure homogeneity of the sample and randomness of the orientations of all the crystal lattices represented by different minerals This is known as X-ray powder diffraction XRD works by rotating the X-ray source and the detector about the sample from small angles (e.g 4 ) through to angles of up to 70 The low angles can detect large interlattice spacings (large values of d) while the high angles detect smaller interlattice spacings For CuKa radiation these angles equate to d-spacings from about 30 A˚ down to about 1.5 A˚ , covering the dominant d-spacings of practically all rock-forming minerals For a pure mineral sample, the diffraction peaks from different lattice planes with discrete d-spacings have different relative intensities This is a function of the details of the crystal structure of a particular mineral, but the maximum-intensity trace (peak) for many minerals has a low Miller Index value (a simple notation for describing the orientation of a crystal) For example, many clay minerals dominated by sheetlike crystal structures have (001) as the maximumintensity peak All other XRD traces have intensities that are fixed fractions of the intensity of the maximum-intensity trace The result for each pure mineral is a fingerprint of XRD peaks on a chart of intensity on the y-axis and 2y on the x-axis (Figure 11) This can be compared with collections of standards to identify the mineral Figure Basic elements of an X ray diffraction device An X ray source is directed at a sample at a controlled and variable angle (y) The X ray detector is at the equivalent angle on the opposite side of the pivot point The source and detector are at an angle of 180 2y to one another The source and detector are thus simultaneously rotated about the pivot point When diffrac tion occurs the X ray detector records a signal above the back ground The sample is usually a powder and preferably randomly orientated Figure 10 Diffraction from a crystal The incident X rays are in phase as they hit the mineral surface The grey line shows the path length difference between the two X rays Constructive interference occurs when the extra path length (2d siny) is an integral multiple (typically one) of the wavelength of the X rays Constructive interference leads to an X ray diffraction peak set against a low level of background noise