Grain Size Distribution of Aluminum

Patterson, Burton Roe

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and . Therefore ^S-)proj = J/^e'^i'^^^ ^i' (^-2«> The values of | cos y .\ must be calculated individually for each line set, e.g. for i = 1: I I '^ZT ZT °^ (h k £) I cos Yi I = . ^'' '^ --'y I h+q -, k I /(l+q^)(h^+k^+i^) (D-29) Entering the expressions for n- and | cos y-I- i = 1,6 in Eq . (D-28) , and applying the scale factor yields 242 (Vproj = t '\; ][|h+q^k| + |h-q^k| + |q^k+q^M 4vii +k'^+,r + |q^k-q2?,| + |h+q2£ | + |h-q2p. I ] (D-30a) Due to symmetry, the positive octant of possible o...rientations is representative of the rest of a specimen and Eq . (D-30a) is further simplified. Noting this and Eq. (D-17), V'proj A' >- -^ ^ rj^ 4/h^+k^+£'^ [2(h+q^k+q2f |+|h-q^k| + Iq-j^k-q^.?. | + |h-q2f. I ] (D-30b) For specimens aoproximating the planar system (q, = 1) or linear system (q^ = 1), Eqs . (D-30a) and (D-30b) are further reduced. Thus, for a specimen on which (P.) , '^ ^ A a (P.), and (P.) have been measured, (P.) may be cal- culated for any otlier section plane.

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