Voigt - function model in diffraction line-broadening analysis

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categorie: Engleza

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nivel: Liceu

1 Introduction
Phenomenological line-broadening theory of plastically deformed metals and alloys was developed almost 50 years ago (Warren and Averbach 1950; Warren 1959). It identifies two main types of broadening: the size and strain components. The former depends on the size of coherent
domains (or incoherently diffracting domains in a sense that they diffract incoherently to one [...]
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1 Introduction
Phenomenological line-broadening theory of plastically deformed metals and alloys was developed almost 50 years ago (Warren and Averbach 1950; Warren 1959). It identifies two main types of broadening: the size and strain components. The former depends on the size of coherent
domains (or incoherently diffracting domains in a sense that they diffract incoherently to one another), which is not limited to the grains but may include effects of stacking and twin faults and subgrain
structures (small-angle boundaries, for instance); and the latter is caused by any lattice imperfection (dislocations and different point defects).

The theory is general and was successfully applied to other
materials, including oxides and polymers. However, the parameters obtained need a careful assessment of their physical validity and correlation to the particular structural features of the
material under study. In different approaches (Krivoglaz and Ryaboshapka 1963; Wilkens 1984; Groma et al. 1988), the effects of simplified dislocation configurations on diffraction-line broadening
were modeled.

These theories were applied mainly to the plastically deformed copper single crystals and recently to the ('-precipitate-hardened nickel-base superalloy (Kuhn et al. 1991). These microscopic models correctly identify origins of broadening in the terms of physically recognized quantities.

As our understanding and ability to model complex systems develops further, it is expected that their application will gradually include other materials where different sources of line broadening usually occur simultaneously. The focus here is to study and compare methods of linebroadening analysis in the frame of phenomenological approaches.

The development of this research field began when Scherrer (1918) understood that small crystallites cause broadening of diffraction lines. However, more than quarter of a century elapsed
before a more complex and exact theory of line broadening was formulated by Stokes and Wilson (1944). They included the lattice strain as another source of broadening.

Shortly thereafter, a new impulse was given to the theory: Stokes (1948) adapted the Fourier-deconvolution method to obtain the purely physical broadened line profiles from the observed pattern. Instead of mere estimates of either average size of coherent domains or some measure of strain, through the developments of Bertaut (1949) and Warren and Averbach (1950; 1952), a more detailed analysis of complete lineprofile shape became possible.

Moreover, Wilson (1962a) introduced the analysis of the variance of profile, and Ergun (1968) the method of successive foldings. All those procedures pushed aside the integral-breadth methods because of the important advantage of model independence. Moreover, with a careful application, it was possible to obtain much more information, such as column-length distribution function, the behavior of strain as a function of the averaging distance in domains, etc.

However, they also have very serious drawbacks: in cases of large line overlapping, or weak structural broadening, the Stokes deconvolution method cannot be applied without severe errors. This limits application to a small number of specimens and to cubic crystal systems.
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