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3. H. Kolsky: Stress Waves in Solids, pp. 16-23, Dover Publishers, New York, 1963. 4. E. P. Papadakis: PhysicalAcoustics, vol. 4B, W. P. Mason, ed., pp. 269-328, Academic Press, New York, 1963. 5. R. Truell, C. Elbaum, and B. Chick: Ultrasonic Methods in Solid State Physics, pp. 190-276, Academic Press, New York, 1969. 6. W. P. Mason and H. J. McSkimrrdn: J. AppL Phys., 1947, vol. 19, pp. 940-46.

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Surface Structure Concepts in the Theory of Homogeneous Bubble Nucleation

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(MHz) Fig. 2 - - S u r f a c e wave attenuation v s f r e q u e n c y f o r v a r i o u s g r a i n s i z e s in F e - 3 pct Si s h e e t .

m a y a l s o be a t t r i b u t e d to d i s l o c a t i o n and m i c r o e d d y c u r r e n t m a g n e t i c damping, s which a l o n g with g r a i n s c a t t e r i n g , c a u s e a t t e n u a t i o n in the s a m p l e s . The d i s l o c a t i o n and m a g n e t i c l o s s e s a r e independent of D, but m a y c a u s e a f r e q u e n c y - d e p e n d e n t l o s s a s high a s f2; so that s u p e r p o s i t i o n of t h i s l o s s on the f o s c a t t e r i n g l o s s m a y r e s u l t in the o b s e r v e d f x a t t e n u a t i o n b e h a v ior. It i s not s i m p l y f o r t u i t o u s that the s u r f a c e wave d a t a show q u a l i t a t i v e a g r e e m e n t with the p r e d i c t i o n s of s c a t t e r i n g t h e o r y . Mason and M c S k i m m i n 6 have t r e a t e d the s c a t t e r i n g l o s s f o r )~ < D, and t h e y p r e d i c t that a t t e n u a t i o n o c c u r s when a c o u s t i c a l e n e r g y is r e f l e c t e d and r e f r a c t e d f r o m the m a i n b e a m path a s a wave l e a v e s one g r a i n and c r o s s e s the i n t e r f a c e into a n o t h e r . T h e i r a n a l y s i s shows that a s long a s ~ < T), the l o s s is i n d e p e n d e n t of the f o r m of the wave and is s i m p l y p r o p o r t i o n a l to the n u m b e r of i n t e r f a c e s c r o s s e d , i.e., to b -z. T h e i r a n a l y s i s d o e s not p r e c l u d e the wave having the f o r m of the R a y l e i g h wave, so the o b s e r v e d a g r e e m e n t is not s u r p r i s i n g . It m u s t b e r e - e m p h a s i z e d that only the m o s t g e n e r a l and q u a l i t a t i v e a g r e e m e n t b e t w e e n o u r d a t a and t h e o r y i s c l a i m e d . We f e e l h o w e v e r , that it can be v a l i d l y c o n c l u d e d that: 1) Surface u l t r a s o n i c s allow the d e t e r m i n a t i o n of g r a i n s i z e in s i l i c o n i r o n s h e e t , o t h e r f a c t o r s such a s g r a i n shape b e i n g h e l d c o n s t a n t . 2) The f r e q u e n c y and g r a i n s i z e d e p e n d e n c e o b s e r v e d f o r s u r f a c e w a v e s a r e c o n s i s t e n t with the q u a l i t a t i v e p r e d i c t i o n s of a c o u s t i c wave s c a t t e r i n g t h e o r y . 3) The o b s e r v e d f r e q u e n c y d e p e n d