Study of Randomly Oriented Polycrystalline Samples

Microstructural Study of Randomly Oriented Polycrystalline Samples 

In Chapter 5, we described in detail the effect on the diffiracted intensity s distribntion of the discrepancies between a crystal s mean stmcture and its actual structure. The quantitative study of these effects makes it possible to accurately determine the density of punctual defects, of dislocations or of stacking faults, the size of the grains, as well as the microstrain rate, etc. This type of analysis was developed in the second half of the 20 century and, due to the tremendous progress made by computers, became widespread in the late 1980s. In 1999, the International Union of Crystallography published a book describing most of the aspects of microstractirral analysis by X-ray diffraction on polycrystalline samples [SYN 99], 

Three different methods have been designed to quantitatively study structural volume defects. The integral breadth method, based on the theoretical considerations we discussed in Chapter 5, was introduced in 1918 by Scherrer [SCH 18] and generalized by Stokes and Wilson [STO 42], among others. Later on, Toumarie [TOU 56a, TOU 56b] followed by Wilson [WIL 62b, WIL 63] suggested a different analysis based on the variance of the intensity distribution. We described how Bertaut [BER 49] showed in 1949 that the Fourier series decomposition of the peak profile makes it possible to obtain the mean value and the distribution of the different effects that cause the increase in peak width. This method was further elaborated by Warren and Averbach [WAR 50, WAR 55, WAR 69]. 

Aside from a few authors [BER 93, GRO 98b, SAN 97] who still implement it, the variance method is hardly used anymore. This chapter will deal with the integral breadth method and the Fourier analysis. 

Regardless of which of the two methods is used, it is important to separate the tnicrostructural effects from the instrumental contribution in the peak profiles. We saw, in the first part of this book, how the different elements that comprise the instmment can modify the shape of the diffraction peaks. Obviously, microstructural analysis is easier when the instrument s contribution is small. However, this contribution has to be taken into account in order to extract the experimental profile, 

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Microstructural Study of Randomly Oriented Polycrystalline Samples 237... 

The samples studied in this section are zirconia films deposited on sapphire substrates. These films are produced by using a sol-gel method based on a dipping process which we have already described. After drying the sample and firing it at a low-temperature, we get a polycrystalline film comprised of randomly oriented nanocrystals (see section 7.2.1). A high temperature process, in this case, lasting one hour at 1,500°C, would yield a set of epitaxial islands of zirconia (see sectiorts... 

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