The lattice parameters of α-manganese at low temperatures

Volume 24A. number 4

THE

LATTICE

PHYSICS LETTERS

PARAMETERS

OF

13 February 1967

~t-MANGANESE

AT

LOW TEMPERATURES

J. A. C. MARPLES Atomic Energy Research Establishment, Ha*well, Berks., England Received 17 January 1967

The lattice parameter of or-manganese has been determined as a function of temperature from 4°K to 30O°K. The most interesting feature of the results is a change in expansion coefficient from negative to positive with increasing temperature at the N~el point. s - m a n g a n e s e has a complex b.c.c. A 12 s t r u c t u r e with 58 a t o m s p e r unit cell. At low t e m p e r a t u r e s it i s a n t i - f e r r o m a g n e t i c with a N6el t e m p e r a t u r e of 95°K and many a n t i - f e r r o m a g n e t i c s u b s t a n c e s a r e known to exhibit a change in the t h e r m a l expansion coefficient at the N6el t e m p e r a t u r e . P r e v i o u s l y , White [1] has m e a s u r e d the e x p a n s i o n coefficient at low t e m p e r a t u r e s d i l a t o m e t r i c a l l y but his s y s t e m a t i c r e s u l t s w e r e c o n fined to below 30°K although a few m e a s u r e m e n t s w e r e made at higher t e m p e r a t u r e s . Below 30°K his r e s u l t s were well r e p r e s e n t e d by: A l / l = = -(1.45 ± 0.06) x 10 -8 T2, giving r,~= 2.9 x 1 0 - 8 T , and in addition he obtained ct = -5, + 10 and 25 × × 10 -7 OK-1 at 65, 75 and 85°K r e s p e c t i v e l y . It was of i n t e r e s t t h e r e f o r e to study in m o r e detail the change f r o m negative to positive expansion coefficient. F u r t h e r , the low t e m p e r a t u r e p r o p e r t i e s of plutonium, studied in this l a b o r a t o r y [2], show some m a r k e d s i m i l a r i t i e s to those of a - m a n g a n e s e and the i n v e s t i g a t i o n of the lattice

oK 2S I

i

44,S I

6 0 64 I I

77 I

86 --I

93 I

96 I

!X

-8"8805

i

e.,:9:l I

i

,

I

;J

3

4

I

l

I

i

I tIi

S

6

7

8

J 9

T 2 x tO 3

Fig. 2. Ot-Mn lattice parameter versus temperaturesquared.

1.90 i

I.I1¢

|.o

?I

410

I

.fO

I

1210

'

,~0

i

/ °

121

0

i

/ °

I"~MPt RATUflE

eK

Fig. 1. ct-Mn lattice parameter versus temperature.

p a r a m e t e r s of the l a t t e r was thus of i n t e r e s t on this count also. The X - r a y c r y o s t a t [2] we have used is b a s e d on a design by M a u e r and Bolz [3] adapted to fit a s t a n d a r d Hilger and Watts d i f f r a c t o m e t e r . The s p e c i m e n was a p o l y c r y s t a l l i n e plate of e l e c t r o deposited m a n g a n e s e supplied by J o h n s o n Matthey Ltd., containing: m a g n e s i u m , 5ppm; silicon, 5ppm; and copper, lppm as the only s i g nificant i m p u r i t i e s . The plate was ground flat and then etched with h y d r o c h l o r i c acid before loading. T h e r m o c o u p l e s , fastened to the back of the I m m thick s p e c i m e n , were used to control and to m e a s u r e the t e m p e r a t u r e to an a c c u r a c y of * l ° K below 100°K a n d , 2°K above this. The r e s u l t s obtained a r e shown in fig. 1. The 207

Volume 24A, number 4

PHYSICS LETTERS

m o s t o b v i o u s f e a t u r e of t h e m i s t h e m a r k e d change in expansion coefficient at the N6el temperature. The behaviour below this is quite well r e p r e s e n t e d by:

a = (8.88102 + 0.00006) - (14.3 ± 1.0) × I0 -8 T 2 , i.e., Aa/a= -(1.61±0.11)× 10-8T 2, or a = = -(3.22 ± 0.22) × 10-8 T, as shown in fig. 2, in good agreement with White's data [I] below 30°K but not with his reported positive thermal expansion coefficients occurring in the 75-85°K range. Above the N~el temperature the expansion coefficient is positive, becoming linear at about 150°K with ot = 18.5 × 10-6°K - I . The apparently simple form of the expansion coefficient below the Ndel temperature is probably fortuitous since the observed value is actually the difference between the positive lattice and

VIBRATIONAL POPULATION-INVERSION FROM THE CONTINUOUS-MIXING K. G. A N L A U F , D. H. M A Y L O T T E ,

13 February 1967

electron contributions and negative magnetic contribution. Further discussion of the magnetic term in the expansion coefficient is limited by the considerable uncertainty in the calculations of the exchange coupling involved. The author would like to thank Dr.J.A. Lee for his encouragement and for many helpful discussions.

References 1. G.K.White, Proc. Phys. Soc. 86 (1959) 159. 2. J . A . L e e et al., Institute of Metals. Third Intern. Conf. on Plutonium, London. November 1965, p a p e r 9. 3. F . A . M a u e r and L . H . B o l z , J. Res. Natl. Bur. Stand. 65C (1961) 22.

OF

AND STIMULATED EMISSION CHEMICAL REAGENTS

P . D . P A C E Y a n d J . C. P O L A N Y I

Department of Chemistry, University of Toronto 5, Canada Received 19 J a n u a r y 1967

We have maintained, continuously, a "complete vibrational population inversion" in the m o l e c u l a r product of t h r e e r e a c t i o n s : {i) H + C12 --~ HC1 + Cl, (ii) H + Br2--. HBr + Br, and (iii) C1 + HI -~HCI + I. Reactions (i) and (iii) gave r i s e to continuous stimulated e m i s s i o n with gains of 1.6%/metre and 5 % / m e t r e , r e s p e c tively. It h a s b e e n s u g g e s t e d t h a t t h e f r e s h l y - f o r m e d p r o d u c t s of c h e m i c a l r e a c t i o n s m i g h t c o n s t i t u t e t h e w o r k i n g m a t e r i a l f o r a " c h e m i c a l l a s e r " [1,2]. T w o v a r i e t i e s of v i b r a t i o n a l p o p u l a t i o n i n v e r s i o n were distinguished; "partial" and "complete" population inversion. Recently Kasper and Pimentel [3] s u c c e s s f u l l y o p e r a t e d a p u l s e d c h e m i c a l laser dependent on partial vibrational inversion; a n " e x p l o s i o n l a s e r " i n H2 + C12. T h e p r e s e n t w o r k i s p a r t of a s t u d y of p r o d u c t energy-distribution in simple exchange reactions [4]. In e a r l i e r s t u d i e s of t h e H + C12 r e a c t i o n ( r e a c t i o n (i), t a b l e 1) i t w a s f o u n d t h a t t h e p r o b a b i l i t y of r e a c t i o n t o f o r m HC1 i n v i b r a t i o n a l l e v e l v, w r i t t e n kv, i n c r e a s e d b y o v e r t w o o r d e r s of magnitude from the highest possible level, Vma x = 6, d o w n t o v = 3, a n d t h e n l e v e l e d off t o g i v e kv = 3 ~ k v = 2 . T h e p o p u l a t i o n s , Nv, i n v = l 208

a n d v = 0 s u g g e s t e d t h a t kv = 2 ~ kv = 1 - 0.1 k v=O, b u t t h e d e r i v a t i o n of t h e s e k v f r o m t h e o b s e r v e d Nv w a s s h o w n to b e u n c e r t a i n o w i n g t o t h e s e n s i t i v i t y of t h e r e s u l t t o t h e m o d e l u s e d f o r v i b r a t i o n a l r e l a x a t i o n [4]. In a n a t t e m p t t o e s t a b l i s h t h e kv's i n t o t h e s e low v i b r a t i o n a l s t a t e s we h a v e t a k e n t w o e x p e r i mental paths. (1) W e h a v e r e p e a t e d o u r e a r l i e r e x p e r i m e n t s i n a f l o w s y s t e m c o n s i s t i n g of a 4 in. d i a m e t e r pyrex pipe with three sapphire observation wind o w s a t 2¼ i n . s e p a r a t i o n a l o n g t h e l i n e of flow. V i b r a t i o n a l p o p u l a t i o n s , Nv, h a v e b e e n m e a s u r e d at successive "times" along the tube (~ 10-3 sec i n t e r v a l s ) a n d h a v e b e e n corrected f o r t h e e f f e c t of r e l a x a t i o n . T h e p o p u l a t i o n d i s t r i b u t i o n r e c o r ded at the first observation window is listed as A i n t a b l e 1. E x t r a p o l a t i o n of t h e d a t a b a c k t o z e r o