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Effects of lattice vibrations on proton blocking
Volume 31A, number 8
PHYSICS L E T T E R S
EFFECTS
OF
LATTICE
VIBRATIONS
20April 1970
ON P R O T O N
BLOCKING
R. M. MUELLER and W. WHITE Nuclear-Chicago Corporation, DesPlaines, Illinois 60018 USA Received 9 M~rch 1970
Proton blocking patterns for crystals of nearly identical structure, lattice parameter, and atomic *~umber show marked differences in appearance which are ascribed to differences in vibrational amplitudes.
It has been shown that lattice v i b r a t i o n s modify the a n g u l a r y i e l d s of heavy c h a r g e d p a r t i c l e s s c a t t e r e d f r o m c r y s t a l s [1-5]. I n c r e a s e d v i b r a t i o n d e c r e a s e s both p l a n a r and axial widths, with the l a t t e r being somewhat m o r e s e n s i t i v e to v i b r a t i o n . In this l e t t e r we p r e s e n t c o m p a r a t i v e s t u d i e s for m e t a l s at r o o m t e m p e r a t u r e which d e m o n s t r a t e these facts, and, m o r e i m p o r t a n t l y , suggest a method which could lead to the d e t e r m i n a tion of (for example) r e l a t i v e v i b r a t i o n a l a m p l i t u d e s for m a t e r i a l s of s i m i l a r s t r u c t u r e . The d e m o n s t r a t i o n c o n s i s t s of a c o m p a r i s o n of p r o ton blocking p a t t e r n s for m e t a l s which have n e a r l y identical s t r u c t u r e , atomic n u m b e r Z, and l a t tice p a r a m e t e r ao, but which differ m a r k e d l y in t h e r m a l p r o p e r t i e s . T h r e e c a s e s a r e given (1) Cr and ~' brass, (2) Rh, Pd and Ag and (3) Pt and Au. The pertinent parameters are given in table 1. Representative values of (ux~½, the x-component of the rms vibration amplitude, have been taken from ref. 6 or in the case of fl'
a
Table 1
ao l
(u21A>
2.88
~0.065
bcctfl,29Cu30Zn
2.94
~0.099
45Rh 46Pd fce 147Ag
3.80 3.89 4.09
N0.060
|24Cr
-
-
aT(AI o
0.15
~0.074 N0.091
fcc ~ 78Pt
3.92
N0"062 I
(79Au
4.08
N0.084
0.13
0.11
Fig. 1. Proton blocking pattern near the [111] axis of (a) a platinum and (b) a gold single crystal. These and other patterns of this study were made with protons of 150 keV incident energy. The film discriminates against energies of less than 50 keV [8].
431
Volume 31A: number 8
PHYSICS L E T T E R S
b r a s s c a l c u l a t e d [6] f r o m the Debye t e m p e r a t u r e [7]. The CsC1 type s t r u c t u r e of # ' b r a s s is effectively bcc for this c o m p a r i s o n since p r o t o n s cannot distinguish b__et,ween Cu and Zn. In case where (u2) ~ is s m a l l the p a t t e r n s have a d i s t i n c t l y different a p p e a r a n c e f r o m those corr, esponding to a s i m i l a r s t r u c t u r e of l a r g e r (U-~x)7. F o r example (fig. 1), the p a t t e r n for P t exhibits a g r e a t e r spot to line p r o m i n e n c e and g r e a t e r detail than the p a t t e r n for the l a r g e r v i b r a t i o n c a s e exemplified by Au. The situation is s i m i l a r and as m a r k e d for the other c a s e s studied. P a t t e r n s for Rh show v e r y strong spots r e l a t i v e to those for Pd and Ag, although the spots for Pd a r e only slightly m o r e p r o m i n e n t than in the Ag case. However the p a t t e r n for P d does show m o r e detail than that for Ag. T h e s e o b s e r v a t i o n s suggest that the depth and s h a r p n e s s of detail may be m o r e significant than the spot to line p r o m i n e n c e . One would expect ( u n c o r related) v i b r a t i o n to s m e a r p l a n a r and axial p o t e n t i a l s (which a r e well s e p a r a t e d for a static lattice) and to c a u s e blocking l i n e s for c l o s e l y spaced p l a n e s to b e c o m e indistinct. T h e s e effects will2~epend upon the r e l a t i v e m a g n i t u d e s of a o, (Ux)~ and the T h o m a s - F e r m i r a d i u s a T F and we suspect, (in view of the Pd-AK_dqta) may l i m i t r a t h e r quickly with i n c r e a s i n g (u~) z . The view that the difference between p a t t e r n s a r e a t t r i b u t a b l e to v i b r a t i o n r a t h e r than other s t r u c t u r a l d i f f e r e n c e s has b e e n c o r r o b o r a t e d by
432
20 April 1970
a c o m p a r i s o n of blocking p a t t e r n s for a Au c r y s tal b o m b a r d e d u n d e r identical conditions at t e m p e r a t u r e s of 140°K and 300OK. I n c r e a s e d detail and spot to line p r o m i n e n c e were noted for the lower t e m p e r a t u r e case. The e x a m i n a t i o n of blocking p a t t e r n s for m o r e than 15 other m a t e r i a l s including c o m pounds, leads us to b e l i e v e that the o b s e r v a t i o n s a r e quite g e n e r a l . Quantitative d e t e r m i n a t i o n s will need account for effects of depth, surface condition, s t r a i n , s t r u c t u r a l complexity, degree of c o r r e l a t i o n of v i b r a t i o n and e n e r g y dependence. We wish to thank Dr. C. S. B a r r e t for encour a g e m e n t in this work and for the u s e of the c r y s t a l of ~' b r a s s .
References 1. J. Lindhard, Dansk Vid. Selsk. Mat. -fys. Med. 34 Nr. 1 (1965). 2. J. U. Andersen, Dansk. Vid. Selsk. Mat.-fys. Med. 36 Hr. 7 (1967). 3. C. Erginsoy, Phys. Rev. Letters 15 (1965) 360. 4. A. F. Tulinov, Soy. Phys,-Usp. 8 (1966) 864. 5. J.U. Andersen and E. Uggerh6j, Can. J. Phys. 46 (1968) 517. 6. K. Lonsdale, Int. tables for X-ray crystail. Vol. III (Kynoeh, Birmingham. England, 1962). 7. D.R. Chipman, J. Appl. Phys. 31 (1960) 2012. 8. C. S Barrett. M. Barrett, R.M. Mueller and W. White J. Appl. Phys., to be published.
PHYSICS L E T T E R S
EFFECTS
OF
LATTICE
VIBRATIONS
20April 1970
ON P R O T O N
BLOCKING
R. M. MUELLER and W. WHITE Nuclear-Chicago Corporation, DesPlaines, Illinois 60018 USA Received 9 M~rch 1970
Proton blocking patterns for crystals of nearly identical structure, lattice parameter, and atomic *~umber show marked differences in appearance which are ascribed to differences in vibrational amplitudes.
It has been shown that lattice v i b r a t i o n s modify the a n g u l a r y i e l d s of heavy c h a r g e d p a r t i c l e s s c a t t e r e d f r o m c r y s t a l s [1-5]. I n c r e a s e d v i b r a t i o n d e c r e a s e s both p l a n a r and axial widths, with the l a t t e r being somewhat m o r e s e n s i t i v e to v i b r a t i o n . In this l e t t e r we p r e s e n t c o m p a r a t i v e s t u d i e s for m e t a l s at r o o m t e m p e r a t u r e which d e m o n s t r a t e these facts, and, m o r e i m p o r t a n t l y , suggest a method which could lead to the d e t e r m i n a tion of (for example) r e l a t i v e v i b r a t i o n a l a m p l i t u d e s for m a t e r i a l s of s i m i l a r s t r u c t u r e . The d e m o n s t r a t i o n c o n s i s t s of a c o m p a r i s o n of p r o ton blocking p a t t e r n s for m e t a l s which have n e a r l y identical s t r u c t u r e , atomic n u m b e r Z, and l a t tice p a r a m e t e r ao, but which differ m a r k e d l y in t h e r m a l p r o p e r t i e s . T h r e e c a s e s a r e given (1) Cr and ~' brass, (2) Rh, Pd and Ag and (3) Pt and Au. The pertinent parameters are given in table 1. Representative values of (ux~½, the x-component of the rms vibration amplitude, have been taken from ref. 6 or in the case of fl'
a
Table 1
ao l
(u21A>
2.88
~0.065
bcctfl,29Cu30Zn
2.94
~0.099
45Rh 46Pd fce 147Ag
3.80 3.89 4.09
N0.060
|24Cr
-
-
aT(AI o
0.15
~0.074 N0.091
fcc ~ 78Pt
3.92
N0"062 I
(79Au
4.08
N0.084
0.13
0.11
Fig. 1. Proton blocking pattern near the [111] axis of (a) a platinum and (b) a gold single crystal. These and other patterns of this study were made with protons of 150 keV incident energy. The film discriminates against energies of less than 50 keV [8].
431
Volume 31A: number 8
PHYSICS L E T T E R S
b r a s s c a l c u l a t e d [6] f r o m the Debye t e m p e r a t u r e [7]. The CsC1 type s t r u c t u r e of # ' b r a s s is effectively bcc for this c o m p a r i s o n since p r o t o n s cannot distinguish b__et,ween Cu and Zn. In case where (u2) ~ is s m a l l the p a t t e r n s have a d i s t i n c t l y different a p p e a r a n c e f r o m those corr, esponding to a s i m i l a r s t r u c t u r e of l a r g e r (U-~x)7. F o r example (fig. 1), the p a t t e r n for P t exhibits a g r e a t e r spot to line p r o m i n e n c e and g r e a t e r detail than the p a t t e r n for the l a r g e r v i b r a t i o n c a s e exemplified by Au. The situation is s i m i l a r and as m a r k e d for the other c a s e s studied. P a t t e r n s for Rh show v e r y strong spots r e l a t i v e to those for Pd and Ag, although the spots for Pd a r e only slightly m o r e p r o m i n e n t than in the Ag case. However the p a t t e r n for P d does show m o r e detail than that for Ag. T h e s e o b s e r v a t i o n s suggest that the depth and s h a r p n e s s of detail may be m o r e significant than the spot to line p r o m i n e n c e . One would expect ( u n c o r related) v i b r a t i o n to s m e a r p l a n a r and axial p o t e n t i a l s (which a r e well s e p a r a t e d for a static lattice) and to c a u s e blocking l i n e s for c l o s e l y spaced p l a n e s to b e c o m e indistinct. T h e s e effects will2~epend upon the r e l a t i v e m a g n i t u d e s of a o, (Ux)~ and the T h o m a s - F e r m i r a d i u s a T F and we suspect, (in view of the Pd-AK_dqta) may l i m i t r a t h e r quickly with i n c r e a s i n g (u~) z . The view that the difference between p a t t e r n s a r e a t t r i b u t a b l e to v i b r a t i o n r a t h e r than other s t r u c t u r a l d i f f e r e n c e s has b e e n c o r r o b o r a t e d by
432
20 April 1970
a c o m p a r i s o n of blocking p a t t e r n s for a Au c r y s tal b o m b a r d e d u n d e r identical conditions at t e m p e r a t u r e s of 140°K and 300OK. I n c r e a s e d detail and spot to line p r o m i n e n c e were noted for the lower t e m p e r a t u r e case. The e x a m i n a t i o n of blocking p a t t e r n s for m o r e than 15 other m a t e r i a l s including c o m pounds, leads us to b e l i e v e that the o b s e r v a t i o n s a r e quite g e n e r a l . Quantitative d e t e r m i n a t i o n s will need account for effects of depth, surface condition, s t r a i n , s t r u c t u r a l complexity, degree of c o r r e l a t i o n of v i b r a t i o n and e n e r g y dependence. We wish to thank Dr. C. S. B a r r e t for encour a g e m e n t in this work and for the u s e of the c r y s t a l of ~' b r a s s .
References 1. J. Lindhard, Dansk Vid. Selsk. Mat. -fys. Med. 34 Nr. 1 (1965). 2. J. U. Andersen, Dansk. Vid. Selsk. Mat.-fys. Med. 36 Hr. 7 (1967). 3. C. Erginsoy, Phys. Rev. Letters 15 (1965) 360. 4. A. F. Tulinov, Soy. Phys,-Usp. 8 (1966) 864. 5. J.U. Andersen and E. Uggerh6j, Can. J. Phys. 46 (1968) 517. 6. K. Lonsdale, Int. tables for X-ray crystail. Vol. III (Kynoeh, Birmingham. England, 1962). 7. D.R. Chipman, J. Appl. Phys. 31 (1960) 2012. 8. C. S Barrett. M. Barrett, R.M. Mueller and W. White J. Appl. Phys., to be published.