Studying the crystallographic orientation and determining epitaxy relations

Studying the crystallographic orientation and determining epitaxy relations 

If two crystals are placed side by side, it is possible to define vector relations that express the characteristic crystallographic directions of one of the ctystals in a set of coordinates defined by the cell of the other crystal. These are referred to as epitaxy relations. By extrapolation, when the grains that comprise a polyctystalUne film all have virtually the same orientation, it is possible to define ctystallographic axes specific to this orientation and to find the relation between these axes and those, for example, of the single ctystal on which the film is deposited. If the film and the substrate share the same ctystal nature, we are dealing with homoepitaxy, otherwise, it is referred to as heteroepitaxy. Epitaxy relations are three-dimensional and therefore they are usually written as follows  

In the following sections, we will show how we can find these relations from X-ray diffraction measurements. As we have just explained, in order for relations of this type to make sense, the crystals in the film must all be oriented the same way, which means that the film is a quasi-single crystal . As a result, the relevant techniques and vocabulary are often taken from single crystal diffraction. 

Consider a heteroepitaxial film on a single crystal substrate. For a given family of planes (hkl), specific to the crystal phase that comprises the film, when the sample is irradiated at an incidence angle enabling these (hkl) planes to diffract, each crystal within the film diffracts and contributes to the intensity of a peak located at the angle 20 given by the Bragg relation. 

An experimental illustration of this kind of measurement is shown in Figirre 7.13 [MAR 00]. The film in the example is comprised of zirconia crystals and has been deposited on a sapphire substrate cut parallel to the (l 12o) planes. 

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