The solvent-fixed coordinate system applied to two-phase diffusion coatings resulting from a constant surface flux of so
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A N e a r l i e r p a p e r 1 t r e a t e d the c o n c e n t r a t i o n d i s t r i b u tion and d i m e n s i o n a l changes o c c u r r i n g , as the r e s u l t of diffusion, i n the i n s t a n c e w h e r e a solute is i n t r o duced to the s u r f a c e of a s o l v e n t u n d e r a c o n s t a n t flux b o u n d a r y condition s u c h as o c c u r s i n e l e c t r o p l a t ing. T h i s p a p e r extends that t r e a t m e n t to include the case in which a second p h a s e is f o r m e d as the r e s u l t of exceeding s o l u b i l i t y l i m i t s in the f i r s t phase f o r m e d . The n u m e r i c a l s o l u t i o n s for m u l t i p h a s e b i n a r y diff u s i o n coatings a r e c o m p l i c a t e d by two f a c t o r s : the i n i t i a t i o n of the s e c o n d phase and m o v e m e n t of the r e s u l t a n t p h a s e i n t e r f a c e . T h i s p a p e r p r e s e n t s methods for d e a l i n g with t h e s e f a c t o r s and a p p l i e s them in two example problems. As in the s i n g l e - p h a s e case, the use of the modified c o o r d i n a t e ~y g r e a t l y s i m p l i f i e s the c a l c u l a t i o n s . Since each i n c r e m e n t i n the ~y c o o r d i n a t e s y s t e m c o n t a i n s a n equal n u m b e r of m o l s of the s u b s t r a t e (solvent) component, e x p a n s i o n of the s p e c i m e n is c o m p e n s a t e d f o r and the p o s i t i o n of the t w o - p h a s e i n t e r f a c e , ~, can be m e a s u r e d r e l a t i v e to any c o n v e n i e n t point on the s p e c i m e n . In the following d i s c u s s i o n it is a s s u m e d that the diffusion c o e f f i c i e n t s , c o n c e n t r a t i o n s , and dim e n s i o n s a r e e x p r e s s e d in a way c o m p a t i b l e with the ~y c o o r d i n a t e s y s t e m * . T h e s e e x p r e s s i o n s a r e *In the ~y coordinatesystemequalincrementsof ~y containan equalnumber of molsof componentB,e.g. dn g = (NBS/v)dx = d~y whereS is a umt cross-sectionalareain sq. cm, Vis the localmolarvolumeof the solution,andN B ~sthe localmol fractionof componentB. Concentration,C, is measuredm termsof molarratiosof componentsA andB (C= n A/n g wherenA andna are respectively the numberof toolsof componentsA andB). A diffusionsystemdescnbedby the
DONALD L. CREIGHTON is Associate Professor with Mechanical and Aerospace Engineering,University of Missouri-Columbia,Columbia, MO 65201. ROBERT L. BENEDETTt is Branch Manager.Power Burst Facility, Systems Engmeering Branch, E.G. and G., Idaho National EngineeringLaboratory, Idaho Falls, ID. Manuscript submitted March t 1, 1977. METALLURGICALTRANSACTIONSA
~y coordinatecannothavea concentrationgradientof componentB. The concentration &stnbutionis thendescribedby the use of onlythe diffusioncoefficient of componentA, D~y " ~}c/~}t= a/b~y (19r ~c/a~y ) d i s c u s s e d , a l o n g with u s e of the ~y c o o r d i n a t e s y s t e m in g e n e r a l , in Ref. 1. The r e f e r e n c e d p a p e r 1 c o n t a i n s many d e t a i l s of the computation s
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