Surface ultrasonic measurement of grain size of silicon iron sheet
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MHz. F r e q u e n c i e s b e l o w 6.75 MHz a r e not e m p l o y e d b e c a u s e t h e i r long w a v e l e n g t h b e c o m e s c o m p a r a b l e to the s h e e t t h i c k n e s s , and p r o p a g a t i o n of a R a y l e i g h wave is i m p o s s i b l e . In the m e g a h e r t z f r e q u e n c y r a n g e , the e l a s t i c wave is a t t e n u a t e d b y a n u m b e r of l o s s m e c h a n i s m s a s it p r o p a g a t e s along the s h e e t s u r f a c e . Of c h i e f i n t e r e s t is the s c a t t e r i n g l o s s which o c c u r s a s the wave c r o s s e s g r a i n b o u n d a r i e s . The a m o u n t of e n e r g y d i s s i p a t e d o r d i v e r t e d f r o m the i n i t i a l wave d e p e n d s upon the n u m b e r and type of s c a t t e r s e n c o u n t e r e d (i.e., g r a i n s i z e and shape) and upon d i f f e r e n c e s in a c o u s t i c i m p e d a n c e ( e l a s t i c m o d u l i and d e n s i t y ) b e t w e e n s c a t t e r e r s and m a t r i x . The a t t e n u a t i o n then s h o u l d p r o v i d e a m e a s u r e of g r a i n s i z e , shape, and c r y s t a l l o g r a p h i c t e x t u r e in a single phase polycrystalline material. F i g . 1 shows that ~ d e c r e a s e s a s b i n c r e a s e s and i n d i c a t e s that at any f r e q u e n c y , a p r o v i d e s a m e a s u r e of the g r a i n s i z e . F i g . 2 shows that a i n c r e a s e s r o u g h l y a s f to the f i r s t p o w e r . T h e p l o t s show t h a t s u r f a c e u l t r a s o n i c s d o e s p r o v i d e an e m p i r i c a l m e a s u r e of g r a i n s i z e . In a d d i t i o n to following an e m p i r i c a l c o r r e l a t i o n , the s u r f a c e wave a t t e n u a t i o n d a t a show at l e a s t 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 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 . The t h e o r y i s s u m m a r i z e d in a r e c e n t r e v i e w b y P a p a d a k i s , 4 w h e r e it is shown t h a t l o n g i t u d i n a l o r t r a n s v e r s e w a v e s t r a v e l i n g in bulk p o l y c r y s t a l line m a t e r i a l s should a t t e n u a t e a s s m . At low f r e q u e n c i e s (X >>s R a y l e i g h s c a t t e r i n g is o b s e r v e d , and n e q u a l s 3 and m e q u a l s 4. As f r e q u e n c y is i n c r e a s e d so t h a t X < s the diffusive s c a t t e r i n g r e g i o n is e n t e r e d , and n d e c r e a s e s to - 1 and m d e c r e a s e s to 0. Our data, f o r which k < D, show the ~)-1 g r a i n s i z e d e p e n d e n c e and a f r e q u e n c y d e p e n d e n c e of f l . (The d a s h e d c a l c u l a t e d c u r v e a = 100D -~ s h o w s the good f i t b e t w e e n t h e o r y and e x p e r i m e n t ) . The n o n - z e r o v a l u e of the f r e q u e n c y exponent m a y i n d i c a t e that o u r c o n d i t i o n s a r e not s u f f i c i e n t l y within t h e d i f f u s i v e r e gion f o r f r e q u e n c y - i n d e p e n d e n c e . L a c k of a g r e e m e n t
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