Can anybody tell me what do the terms area weighted domain size and volume weighted domain size physically mean. How to understand these two concepts of domain sizes physically.
Bertaut and Warren considered columns of cells along a given hkl direction and defined a P(M) distribution corresponding to the numerical proportion of columns having the length M (this being equivalent to the proportion of area at the extremity of the columns having the length M). The mean size <M> is the ratio of the volume of all the coherently diffracting domains to the surface of their projection on the (hkl) plane considered. That area-weighted domain size is the average of the P(M) distribution : <M> = S M P(M) / S P(M) (S for Summation between 0 and the maximal length).
From P(M), a volume-weighted distribution is defined as
G(M) = M P(M) / <M> (this being verified if S G(M) = S P(M) = 1).
The mean of G(M) is the volume-weighted domain size (if you
multiply the column area by its length, you obtain its volume) :
<M1> = S M G(M) / S G(M)Hope this is not even more confusing.
Integral breadth gives the volume-weighted size <M1>.
For some special size distributions P(M), there could be a direct relations between <M> and <M1>. For instance <M1> = 2<M> when the size distribution P(M) is Cauchy-like.
If I am not wrong again...
Armel
References : Bertaut F., C.R. Acad Sci. Paris, 228 (1949) 492. Bertaut E.F., Acta Cryst. 3 (1950) 14. Warren B.E. and Averbach B.L., J. Appl. Phys. 21 (1950) 585.
