#### Experimental crystal structure determination, Physics tutorial

Introduction:

In general practice, to satisfy the Bragg's law for X-Ray diffraction, it is essential to vary either the angle of inclination of the specimen to the beam or the wavelength of radiation. The three standard processes of X-ray crystallography to be illustrated are the Laue method, the Rotating crystal method and the Powder method.

Definition:

The Experimental crystal structure determination is the experimental process to study the scattering of crystal based on the Ewald's simple geometric construction.

Laue method:

In the Laue process or method (figure shown below), a single crystal is mounted on a gonimeter that enables the crystal to be rotated via known angles in the two perpendicular planes, and maintained stationary in a beam of X-rays ranging in the wavelength from around 0.1 to 2.0 A. The crystal chooses out and diffracts those values of for which planes exits, of spacing'd' and glancing angle 'θ' satisfying the Bragg equation. A flat photographic film is positioned to receive either the transmitted diffracted beam or the reflected diffracted beam.

As represented in the figure above, the resultant Laue pattern comprises of a sequence of spots. Sharp well-defined spots on the film are good proof of a perfect crystal structure, while diffuse, broken or extended spots point out the lattice distortion, defects or other departures from the perfect crystal lattice. The Laue pattern reveals the symmetry of the crystal structure in the orientation employed; for illustration if a cubic crystal is oriented with a cube edge, that is, a [100] axis, parallel the incident beam, the Laue pattern will exhibit the four fold symmetry suitable to this axis.

Rotating Crystal Technique:

A small single crystal (around 1 mm dimension) is mounted on the gonimeter that, in turn, is firmly fixed to a spindle in such a way that the crystal can be rotated about a fixed axis in a beam of the monochromatic radiation. The specimen is generally oriented by one of the crystallographic axes parallel to the axis of rotation. The resultant variation in 'θ' brings different lattice planes into position for reflection and diffracted images are recorded on the photographic film positioned cylindrically, coaxial by the rotating spindle (figure shown below).

The diffracted beams will only take place all along those particular directions lying on the cones for which the accurate phase relationship as well holds for planes parallel to the other two coordinate axes. If the film is flattened out after development, such diffraction images will lie on a sequence of lines termed as layer lines.

Powder method:

In this method, a monochromatic X-ray beam is permitted to irradiate a small specimen of the substance grinded to a fine powder and contained in a thin-walled glass capillary tube. As the orientation of the minute crystal fragments is fully arbitrary, a certain number of them will lie with any set of lattice planes making precisely the right angle by the incident beam for reflection to take place. Moreover, these planes in the different crystallites are arbitrarily distributed about the axis of the incident beam in such a way that the corresponding reflections from all the crystallites in the specimen lie on the cone coaxial having the axis and by a semi-apex angle of twice the Bragg angle (that is, 2θ). The specimen is surrounded through a cylindrical film and two small parts of each and every cone are recorded as lines on the film. If the grain size is quite large (> 10-6 m) there is inadequate room in the irradiated volume for adequate crystallites to be in all possible orientations and the resultant powder lines will be instead 'spotty'. This spottiness can be removed by rotating the specimen throughout exposure this considerably raises the number of crystallites that can contribute to each and every powder line.

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