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Elastic constants of monocrystalline alloys of Pd-Rh and Pd-Ag between 4.2°K and 300°K
Volume 31A, number 5
ELASTIC
PHYSICS
CONSTANTS
OF
LETTERS
MONOCRYSTALLINE BETWEEN 4.2°K
AND
9 March 1970
ALLOYS 300°K
OF
Pd-Rh
AND
Pd -Ag
E. W A L K E R , J. O R T E L L I and M. P E T E R Institute of Physics of condensed Matter, University of Geneva, Switzerland Received 27 January 1970
The elastic properties of six monocrystalline Pd-Rh and Pd-Ag alloys have been measured. We find correlations with the magnetic susceptibility as predicted by a theoretical model.
In fig. 1 we show the e l a s t i c c o n s t a n t s of d i f f e r e n t a l l o y s of P d with Rh and Ag m e a s u r e d b e tween 4.2OK and 300°K on m o n o c r y s t a U i n e s a m p l e s . The c r y s t a l s w e r e grown in an induction f u r n a c e by the floating zone technique. T h e d e l a y of 10 Mc p u l s e s obtained f r o m an A r e n b e r g g e n e r a t o r was m e a s u r e d on the c y l i n d r i c a l s a m p l e s of 1 cm d i a m e t e r and 2 c m length, o r i e n t e d in the (110) d i r e c t i o n . The moduli ½ ( C l l + ¢19 + 2c44) (fig. l a ) and ½ ( C l l - c19) (fig. i-b-) a r ~ - s e e n to d e c r e a s e a s the (e/a)-~'~tio i n c r e a s e s (i. e. in p a s s i n g f r o m t h e Rh s i d e to t h e Ag side). Below 100°K, t h e s e m o d u l i show a m a x i m u m in t h e i r n e g a t i v e t e m p e r a t u r e coefficient a r o u n d p u r e Pd. T h i s s i n g u l a r i t y can b e c o r r e l a t e d with the a n o m a l o u s t e m p e r a t u r e b e h a v i o u r of the s u s c e p t i b i l i t y in the
s a m e t e m p e r a t u r e and c o n c e n t r a t i o n r a n g e [1]. Above 100OK, the two t e m p e r a t u r e c o e f f i c i e n t s a r e a p p r o x i m a t e l y t e m p e r a t u r e independant and show a m i n i m u m at the c o n c e n t r a t i o n Pd95 % Rh5%. T h i s i s the c o n c e n t r a t i o n w h e r e m a g h e t ic s u s c e p t i b i l i t y and s p e c i f i c h e a t [2-4] a r e known to show p r o n o u n c e d p e a k s . We did not o b s e r v e the m i n i m u m of ½ ( C l l + c12 + 2c44) r e p o r t e d by Rayne [5] although we m e a s u r e d s a m p l e s f r o m two d i f f e r e n t P d c r y s t a l s with i d e n t i c a l r e s u l t s . The modulus c44 (fig. l c ) shows a p r o n o u n c e d m i n i m u m a r o u n d p u r e P d , which d i s a p p e a r s r a t h e r slowly upon a l l o y i n g with Rh and Ag and does not s e e m to c o r r e l a t e with t h e s u s c e p t i b i U ty. The bulk modulus shows no a n o m a l i e s . The p o l y c r y s t a U i n e v a l u e s e x t i m a t e d f r o m o u r data
(140
3.|
0.93
• 30, 2.S
o3, z
0.2s
•~
(120
I1%
0.91
0.o---<..._
o0.21
2.$ t~O
I
2~0
I
300
I
I
tO0
I
I
I
Tempm'ature ('K) Fig. 1. Temperature dependence of elastic moduli for Pd-Rh and Pd-Ag monocrystalllne alloys. (a) ½ (c11 + c 12 ÷ 2c44); (b) shear modulus C' = ½ (Cll - c12); (c) shear modulus C = c44.
240
Volume 31A, number 5
PHYSICS LETTERS
a g r e e with the m e a s u r e m e n t s of B e l m a h i and al. [6]. F i s c h e r , et al. [7] have proposed a model predicting a correlation between susceptibility and e l a s t i c modulus, applicable to P d alloys. A c c o r d i n g to that model, a c o r r e l a t i o n should exist between X and ½ (Cll - c12) , but not b e tween X and c44. In the t e m p e r a t u r e coefficients, our m e a s u r e m e n t s show indeed the p r o p e r c o r r e l a t i o n for ½(Cll -c12) and not for c44. In the i n t e g r a t e d v a l u e s the c o r r e l a t i o n is not evident. This may b e due to the m o d e s t s i z e of the c o n t r i b u t i o n p r e d i c t e d by the model, or to s o m e s t r u c t u r a l effects. Note in this connection the m i n i m u m r e ported by H o a r e for the Debye t e m p e r a t u r e s . The c o r r e l a t i o n b e t w e e n ½(ell - c 12 ) and the a n o m a l y in the low t e m p e r a t u r e s u s c e p t i b i l i t y of Pd is p r e s e n t l y not understood.
CARBON-DIOXIDE
DISSOCIATION
9 March 1970
A detailed account of our work will be given in Helv. Phys. Acta. Support by the Swiss N a tional Science Foundation is g r a t e f u l l y acknowledged.
R e f erenGes 1. W. Treutmann (Thesis) Marburg 1968. 2. F.E. Hoare, J. C. Matthews and J. C. Walling, Proc. Roy. Soc. A 216 (1953} 502. 3. D.W. Budworth, F. E. Hoare and J. Preston, Proc. Roy. Soc. A 257 (1960) 250 4. F.E. Hoare and B. Yates, Proc. Roy. Soe. A 240 (1957) 42. 5. J.A. Rayne, Phys. Rev. 118 (1960) 1545. 6. O. Belmahi, M. Merck, E. Perreard, M. Peter, E. Walker and J. R. Schrieffer, Helv. Phys. Acta. 39 {1966) 336. 7. ~. Fischer, M. Peter and S. Steinemann, Helv. Phys. Acta. 42 (1969) 459.
IN A PULSED
CO2-N 2 LASER
MIXTURE
D. J. BOOTH and W. E. K. GIBBS
Australian Defence Scientific Service, Department of Supply, Defence Standards Laboratories, Maribyrnong 3032, Australia Received 31 December 1969
In a pulsed CO2-N2 laser discharge less than 3% of the CO2 was found to be dissociated. The effect of this dissociation on refractive-index gradients and on upper and lower laser level decay rates is discussed.
The effect of d i s s o c i a t i o n in a continuous c a r b o n - d i o x i d e l a s e r d i s c h a r g e has b e e n shown [1, 2] to be i n p o r t a n t to a detailed u n d e r s t a n d i n g of the l a s e r m e c h a n i s m s . F o r the c a s e of a pulsed d i s c h a r g e in CO2-N2 m i x t u r e s , w h e r e high s m a l l - s i g n a l gain has b e e n o b s e r v e d [3], i n t e r f e r o m e t r i c m e a s u r e m e n t s have shown that r a d i a l r e f r a c t i v e index v a r i a t i o n s of up to 1.8 × 10 -6 can o c c u r in a l a s e r a m p l i f i e r 1 m long and 25 m m i n t e r n a l d i a m e t e r which u s e d a gas m i x t u r e cons i s t i n g of 3 T o r r CO 2 and 3 T o r r N2 [4]. D i s s o c i a t i o n and the p r e s e n c e of d i s c h a r g e p r o d u c t s w e r e s u s p e c t e d a s c a u s e s of t h e s e v a r i a t i o n s and a l s o of i n c r e a s e d decay r a t e s [5]. This l e t t e r r e p o r t s m e a s u r e m e n t s of the d i s s o c i a t i o n p r o duced in a pulsed d i s c h a r g e which will help to c l a r i f y t h e s e questions.
The e x p e r i m e n t a l a r r a n g e m e n t c o n s i s t e d of an o i l - c o o l e d d i s c h a r g e tube 1 m long and 25 m m i n t e r n a l d i a m e t e r through which the gas m i x t u r e flowed at a velocity of 3 m / s to a v a c u u m pump. A p u l s e g e n e r a t o r that p e r m i t t e d the independent control of p u l s e d u r a t i o n and p u l s e c u r r e n t was u s e d to excite the discharge. The gas m i x t u r e used in these e x p e r i m e n t s c o n s i s t e d of 3 T o r r CO 2 and 3 T o r r N2, the p u l s e width was 130 ~t and the peak p u l s e c u r r e n t was v a r i e d in the r a n g e of 2A to 9A. P r e v i o u s e x p e r i m e n t s had shown that over this r a n g e of d i s c h a r g e conditions a s m a l l - s i g n a l gain in excess of 10dB/m could be achieved. The a m p l i f i e r was operated at a p u l s e r e p e t i t i o n f r e q u e n c y above the m i n i m u m r e q u i r e d for r e p r o d u c i b l e d i s c h a r g e conditions but low enough to e n s u r e that each p u l s e was 241
ELASTIC
PHYSICS
CONSTANTS
OF
LETTERS
MONOCRYSTALLINE BETWEEN 4.2°K
AND
9 March 1970
ALLOYS 300°K
OF
Pd-Rh
AND
Pd -Ag
E. W A L K E R , J. O R T E L L I and M. P E T E R Institute of Physics of condensed Matter, University of Geneva, Switzerland Received 27 January 1970
The elastic properties of six monocrystalline Pd-Rh and Pd-Ag alloys have been measured. We find correlations with the magnetic susceptibility as predicted by a theoretical model.
In fig. 1 we show the e l a s t i c c o n s t a n t s of d i f f e r e n t a l l o y s of P d with Rh and Ag m e a s u r e d b e tween 4.2OK and 300°K on m o n o c r y s t a U i n e s a m p l e s . The c r y s t a l s w e r e grown in an induction f u r n a c e by the floating zone technique. T h e d e l a y of 10 Mc p u l s e s obtained f r o m an A r e n b e r g g e n e r a t o r was m e a s u r e d on the c y l i n d r i c a l s a m p l e s of 1 cm d i a m e t e r and 2 c m length, o r i e n t e d in the (110) d i r e c t i o n . The moduli ½ ( C l l + ¢19 + 2c44) (fig. l a ) and ½ ( C l l - c19) (fig. i-b-) a r ~ - s e e n to d e c r e a s e a s the (e/a)-~'~tio i n c r e a s e s (i. e. in p a s s i n g f r o m t h e Rh s i d e to t h e Ag side). Below 100°K, t h e s e m o d u l i show a m a x i m u m in t h e i r n e g a t i v e t e m p e r a t u r e coefficient a r o u n d p u r e Pd. T h i s s i n g u l a r i t y can b e c o r r e l a t e d with the a n o m a l o u s t e m p e r a t u r e b e h a v i o u r of the s u s c e p t i b i l i t y in the
s a m e t e m p e r a t u r e and c o n c e n t r a t i o n r a n g e [1]. Above 100OK, the two t e m p e r a t u r e c o e f f i c i e n t s a r e a p p r o x i m a t e l y t e m p e r a t u r e independant and show a m i n i m u m at the c o n c e n t r a t i o n Pd95 % Rh5%. T h i s i s the c o n c e n t r a t i o n w h e r e m a g h e t ic s u s c e p t i b i l i t y and s p e c i f i c h e a t [2-4] a r e known to show p r o n o u n c e d p e a k s . We did not o b s e r v e the m i n i m u m of ½ ( C l l + c12 + 2c44) r e p o r t e d by Rayne [5] although we m e a s u r e d s a m p l e s f r o m two d i f f e r e n t P d c r y s t a l s with i d e n t i c a l r e s u l t s . The modulus c44 (fig. l c ) shows a p r o n o u n c e d m i n i m u m a r o u n d p u r e P d , which d i s a p p e a r s r a t h e r slowly upon a l l o y i n g with Rh and Ag and does not s e e m to c o r r e l a t e with t h e s u s c e p t i b i U ty. The bulk modulus shows no a n o m a l i e s . The p o l y c r y s t a U i n e v a l u e s e x t i m a t e d f r o m o u r data
(140
3.|
0.93
• 30, 2.S
o3, z
0.2s
•~
(120
I1%
0.91
0.o---<..._
o0.21
2.$ t~O
I
2~0
I
300
I
I
tO0
I
I
I
Tempm'ature ('K) Fig. 1. Temperature dependence of elastic moduli for Pd-Rh and Pd-Ag monocrystalllne alloys. (a) ½ (c11 + c 12 ÷ 2c44); (b) shear modulus C' = ½ (Cll - c12); (c) shear modulus C = c44.
240
Volume 31A, number 5
PHYSICS LETTERS
a g r e e with the m e a s u r e m e n t s of B e l m a h i and al. [6]. F i s c h e r , et al. [7] have proposed a model predicting a correlation between susceptibility and e l a s t i c modulus, applicable to P d alloys. A c c o r d i n g to that model, a c o r r e l a t i o n should exist between X and ½ (Cll - c12) , but not b e tween X and c44. In the t e m p e r a t u r e coefficients, our m e a s u r e m e n t s show indeed the p r o p e r c o r r e l a t i o n for ½(Cll -c12) and not for c44. In the i n t e g r a t e d v a l u e s the c o r r e l a t i o n is not evident. This may b e due to the m o d e s t s i z e of the c o n t r i b u t i o n p r e d i c t e d by the model, or to s o m e s t r u c t u r a l effects. Note in this connection the m i n i m u m r e ported by H o a r e for the Debye t e m p e r a t u r e s . The c o r r e l a t i o n b e t w e e n ½(ell - c 12 ) and the a n o m a l y in the low t e m p e r a t u r e s u s c e p t i b i l i t y of Pd is p r e s e n t l y not understood.
CARBON-DIOXIDE
DISSOCIATION
9 March 1970
A detailed account of our work will be given in Helv. Phys. Acta. Support by the Swiss N a tional Science Foundation is g r a t e f u l l y acknowledged.
R e f erenGes 1. W. Treutmann (Thesis) Marburg 1968. 2. F.E. Hoare, J. C. Matthews and J. C. Walling, Proc. Roy. Soc. A 216 (1953} 502. 3. D.W. Budworth, F. E. Hoare and J. Preston, Proc. Roy. Soc. A 257 (1960) 250 4. F.E. Hoare and B. Yates, Proc. Roy. Soe. A 240 (1957) 42. 5. J.A. Rayne, Phys. Rev. 118 (1960) 1545. 6. O. Belmahi, M. Merck, E. Perreard, M. Peter, E. Walker and J. R. Schrieffer, Helv. Phys. Acta. 39 {1966) 336. 7. ~. Fischer, M. Peter and S. Steinemann, Helv. Phys. Acta. 42 (1969) 459.
IN A PULSED
CO2-N 2 LASER
MIXTURE
D. J. BOOTH and W. E. K. GIBBS
Australian Defence Scientific Service, Department of Supply, Defence Standards Laboratories, Maribyrnong 3032, Australia Received 31 December 1969
In a pulsed CO2-N2 laser discharge less than 3% of the CO2 was found to be dissociated. The effect of this dissociation on refractive-index gradients and on upper and lower laser level decay rates is discussed.
The effect of d i s s o c i a t i o n in a continuous c a r b o n - d i o x i d e l a s e r d i s c h a r g e has b e e n shown [1, 2] to be i n p o r t a n t to a detailed u n d e r s t a n d i n g of the l a s e r m e c h a n i s m s . F o r the c a s e of a pulsed d i s c h a r g e in CO2-N2 m i x t u r e s , w h e r e high s m a l l - s i g n a l gain has b e e n o b s e r v e d [3], i n t e r f e r o m e t r i c m e a s u r e m e n t s have shown that r a d i a l r e f r a c t i v e index v a r i a t i o n s of up to 1.8 × 10 -6 can o c c u r in a l a s e r a m p l i f i e r 1 m long and 25 m m i n t e r n a l d i a m e t e r which u s e d a gas m i x t u r e cons i s t i n g of 3 T o r r CO 2 and 3 T o r r N2 [4]. D i s s o c i a t i o n and the p r e s e n c e of d i s c h a r g e p r o d u c t s w e r e s u s p e c t e d a s c a u s e s of t h e s e v a r i a t i o n s and a l s o of i n c r e a s e d decay r a t e s [5]. This l e t t e r r e p o r t s m e a s u r e m e n t s of the d i s s o c i a t i o n p r o duced in a pulsed d i s c h a r g e which will help to c l a r i f y t h e s e questions.
The e x p e r i m e n t a l a r r a n g e m e n t c o n s i s t e d of an o i l - c o o l e d d i s c h a r g e tube 1 m long and 25 m m i n t e r n a l d i a m e t e r through which the gas m i x t u r e flowed at a velocity of 3 m / s to a v a c u u m pump. A p u l s e g e n e r a t o r that p e r m i t t e d the independent control of p u l s e d u r a t i o n and p u l s e c u r r e n t was u s e d to excite the discharge. The gas m i x t u r e used in these e x p e r i m e n t s c o n s i s t e d of 3 T o r r CO 2 and 3 T o r r N2, the p u l s e width was 130 ~t and the peak p u l s e c u r r e n t was v a r i e d in the r a n g e of 2A to 9A. P r e v i o u s e x p e r i m e n t s had shown that over this r a n g e of d i s c h a r g e conditions a s m a l l - s i g n a l gain in excess of 10dB/m could be achieved. The a m p l i f i e r was operated at a p u l s e r e p e t i t i o n f r e q u e n c y above the m i n i m u m r e q u i r e d for r e p r o d u c i b l e d i s c h a r g e conditions but low enough to e n s u r e that each p u l s e was 241