Stable matrix defects

Data from single-variable mechanical property studies have characterised the matrix defect term as being due to two components stable matrix... 

Apart from these, there are volume defects that cannot conveniently be described in any other terms. The most important of these consist of regions of an impurity phase—precipitates—in the matrix of a material (Fig. 3.39). Precipitates form in a variety of circumstances. Phases that are stable at high temperatures may not be stable at low temperatures, and decreasing the temperature slowly will frequently lead to the formation of precipitates of a new crystal structure within the matrix of the old. Glasses, for example, are inherently unstable, and a glass may slowly recrystallize. In this case precipitates of crystalline material will appear in the noncrystalline matrix. 

There are two overriding considerations to keep in mind when discussing diffusion in solids the structure of the matrix across which diffusion occurs and the defects present. In a normal crystalline solid, diffusion is mediated by the defects present, and the speed of diffusion will vary significantly if the predominant defect type changes. This is because diffusion involves the movement of a species from a stable position, through some sort of less stable position or bottleneck, to another stable position. Any disorder in the solid due to defects will make this process easier. 

The second defect of LQ factorization is important for sparse matrices. In fact, dense matrices require double the computational effort of Gauss factorization. If the matrix is sparse, this gap may become larger and a dramatic filling of the factorized matrix may occur. The advantages of LQ factorization are a stable solution of an underdimensioned system (if the system is standardized), and the easy and safe removal of all linear combinations among equations. 

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