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Proton nuclear magnetic resonance line narrowing and tetragonal lattice distortion in SmH2+ξ (0 ⩽ ξ ⩽ 0.40)
Journal of AUoys and Compounds, 177 (1991) 83-91 JAL 0071
83
Proton nuclear magnetic resonance line narrowing and tetragonal lattice distortion in SmH2+x (0~
Ph. l'H6ritier INPG, URA 1109 CNRS, E N S de Physique de Grenoble, B.P. 46, 38402 St. Martin d ' H ~ e s Cedex (France)
(Received April 30, 1991; in final form July 3, 1991)
Abstract Proton magnetic resonance experiments have been made on samarium hydride samples SmH2+~ (0~
1. I n t r o d u c t i o n A s in t h e l a n t h a n u m h y d r i d e s , s a m a r i u m f o r m s a n o n s t o i c h i o m e t r i c d i h y d r i d e p h a s e , S m H 2 +x, o v e r a w i d e c o m p o s i t i o n r a n g e . A t r o o m t e m p e r a t u r e it h a s t h e C a F 2 - t y p e s t r u c t u r e a n d a c o n t i n u o u s s o l i d s o l u t i o n e x t e n d s f r o m x= -0.05 to x=0.34 [1 ]. H o w e v e r , t h e s e l i m i t s a r e s t r o n g l y i n f l u e n c e d b y the preparation conditions. F o r H : S m = 2, t h e h y d r o g e n a t o m s e n t e r t h e t e t r a h e d r a l s i t e s p r e d o m i n a n t l y , b u t f o r x > 0 t h e y a l s o h a v e t o fill o c t a h e d r a l s i t e s . D e p e n d i n g o n t h e w a y in w h i c h t h e o c t a h e d r a l s i t e s a r e o c c u p i e d , t w o i n t e r e s t i n g p h e n o m e n a are observed. When hydrogen atoms occupy these sites randomly, the proton s e l f - d i f f u s i o n p r o c e s s o c c u r s m o r e e a s i l y . H o w e v e r , if t h e o c c u p a t i o n o f t h e octahedral sites is not statistical, an ordered hydrogen sublattice and tetragonal metal lattice deformation are expected. We would like to report both effects here for the samarium hydrides.
2. E x p e r i m e n t a l d e t a i l s T h e s a m p l e s u s e d i n t h i s s t u d y a r e t h e s a m e a s d e s c r i b e d in ref. 2. T h e a c c u r a c y o f t h e i r a t o m i c r a t i o H : S m is _ 0 . 0 3 . T h e c o n t i n u o u s w a v e ( C w )
0925-8388/91/$3.50
© 1991 -- Elsevier Sequoia, Lausanne
84
nuclear magnetic resonance (NMR) experiment details are also in ref. 2. Debye X-ray diffraction patterns were used to obtain the structure and the lattice constant. A laboratory-made X-ray diffractometer (Fe Ka radiation, A= 1.93597/~) was used for this purpose [3]. It included a 0--20 goniometer and a liquid nitrogen (or helium) cryostat at the bottom of which the sample was glued onto a cold copper finger.
3. R e s u l t s and d i s c u s s i o n The proton Cw spectra obtained over a temperature range from about 78 K to 295 K indicated a lack of any changes for SmH2.oo and a linewidth narrowing onset at about 250 K for SmH2.12 (see Fig. 1). The temperature behaviour of the SmH2.ao and SmH2.4o spectra is more complicated. A single, narrow lorentzian-like line at room temperature broadens when the temperature is lowered, and near 250 K a composite system of broad and narrow resonance lines appears. Figure 1 shows the temperature dependence of the linewidth in the region where it could be determined with good precision. Below T ~ 2 5 0 K, the superposition of the two lines prevents further linewidth measurements. The resonance absorption derivative for SmH2.oo is shown in Fig. 2. Its shape can be well fitted by Abragam's proposed function [4]: b
] l" F - ( h - x)21 G ( h ) - 2ab(2~r)'/2 J-b exp[ 2a 2 J d x
(1)
where h = H - H o and a and b are the parameters. An example of the fit to the measured derivative of the absorption resonance line is shown in Fig. 3. By using the following relation [4]:
T 6!
2~o
2~0- 2~o
~8o
3oo
T(K) Fig. i. The temperature dependence of the proton resonance linewidth in SmH2.j2 (O), SmH2.3o (A) and SmH2.4o (V). Data are taken at a Larmor frequency of 15 MHz.
85
g .d o
~J 0.8 mT
H
-
H0
Fig. 2. An example of the absorption mode derivative spectrum of the 'H resonance in SmH2.0o at a resonance frequency of 5.96 MHz and T= 78 K. 52
m 2= a 2+ -3 b4 m4 = 3a 4 + 2a2b 2 +
(2)
--
5 t h e s e c o n d (m2) a n d f o u r t h (m4) m o m e n t s c a n be e s t i m a t e d . T h e y h a d to b e c o r r e c t e d f o r finite m o d u l a t i o n a m p l i t u d e [5] a n d t h e n v a l u e s o f m 2 = 8 . 5 - + 0 . 5 × 10 -2 mT 2 a n d m 4 = 186_+ 1 5 × 10 -4 mT 4 a r e o b t a i n e d . S i n c e t h e d a t a w e r e t a k e n a t r e l a t i v e low m a g n e t i c field ( - - 0 . 1 4 T), t h e d e m a g n e t i z a t i o n e f f e c t s [6, 7] o n l y i n f l u e n c e d t h e s p e c t r a t o a s m a l l e x t e n t . W e e s t i m a t e t h a t t h e i r c o n t r i b u t i o n t o t h e m o m e n t s is w i t h i n e x p e r i m e n t a l uncertainties. Experimentally obtained moments may be compared with c a l c u l a t e d o n e s u s i n g t h e Van Vleck f o r m u l a [8] a n d X - r a y d a t a f o r c r y s t a l l a t t i c e s t r u c t u r e . The s e c o n d a n d f o u r t h m o m e n t s d e r i v e d f o r t h e CaF2 t y p e o f s t r u c t u r e a r e [9 ]: C2ao
6
m2 = - (115.6 a2+2640 2/~+a
a f t + 1 0 7 5 f12)
86
u) C
.d 0
09 C w
0.8 mT
(H-H o )
Fig. 3. Comparison of the absorption derivative IH NMR lines obtained from experiment (broken line) and from a least-squares fit to eqn. (1) (solid line). Here, the experimental recording presented in Fig. 2 is reproduced without noise for better illustration of the agreement between the two lines. The fitting parameters a and b are 0.19 mT and 0.383 mT respectively.
m4 -
C4ao 12 - 2/3+a
( 4 . 4 7 × 106/!¢ a + 9 . 1 3 × 1 0 4 a 3 + 7 . 2 9 × 1 0 8 a 2 / 3 + 2 . 1 8 × 107afl 2
+ 3 . 5 3 × 105/32 + 5 . 3 9 × 1 0 3 a 2 + 2 . 5 6 × 1 0 6 a f t ) C2 = 3 . 5 8 2 X 1 0 - 6 ( n m 6 m T 2)
C4 = 3 . 9 6 ×
(3)
10 - ' 2 ( n m '2 m T 4)
where a and/3 are the probabilities of occupancy in octahedral and tetrahedral s i t e s r e s p e c t i v e l y . T h e c o n s t a n t s C2 a n d (?4 w e r e c a l c u l a t e d f o r p r o t o n s a n d the contribution of samarium nuclei moments has been neglected because of their low abundances and moments. The lattice constant a0 = 0.5358 nm was taken from X-ray experiments. Assuming a=0.03 and fl=0.985, we o b t a i n e d m2 = 8 . 5 × 1 0 - 2 m T 2 a n d m 4 = 1 8 8 . 5 × 10 - 4 m T 4, v a l u e s w h i c h a g r e e with the above-mentioned experimental values. Earlier work [10] on proton N M R s e c o n d m o m e n t a n a l y s i s f o r LaH2 g a v e a = 0 . 0 5 a n d / 3 = 0 . 9 7 5 . H e n c e , in b o t h c a s e s t h e h y d r o g e n a t o m s m o s t l y o c c u p y t e t r a h e d r a l s i t e s w i t h o n l y a f e w b e i n g l o c a t e d i n o c t a h e d r a l s i t e s . A l s o , in SmH2.,2 t h e l i n e s h a p e o f the 'H NMR resonance at low temperature can be described using eqn. (1) and the moments t h u s o b t a i n e d a r e m 2 = 1 0 . 6 _+ 0 . 5 × 1 0 - 2 m T ~ a n d m4=299+30× 1 0 - 4 m T 4. O n e t h e n o b t a i n s v e r y s i m i l a r c a l c u l a t e d v a l u e s of m2 = 10.6× 10 .2 mT 2 and m4=298× 10 . 4 m T 4 f o r a = 0 . 1 8 a n d / 3 = 0 . 9 7 ,
87 and a0 = 0 . 5 3 5 nm. It again indicates a v e r y large p e r c e n t a g e o f tetrahedral o c c u p a n c y and an increased probability of o c t a h e d r a l site o c c u p a n c y , n e c e s s a r y now to a c c o m m o d a t e the larger n u m b e r of h y d r o g e n a t o m s ( H : S m = 2 . 1 2 ) . The p r o t o n linewidth in SmH2 le, which is c o n s t a n t at low t e m p e r a t u r e , starts to n a r r o w in the vicinity o f 250 K (Fig. 1) owing to rapid thermally activated self-diffusion o f the protons. In this case, the linewidth 6H is related to the dipolar correlation time ~'d by the Kubo and T o m i t a [1 l] expression: ~-d=Cd(~H) - l tan ~ \6Ho] J
(4)
w h e r e for p r o t o n s C d = 3 . 2 × 1 0 -6 (S mT), and the rigid-lattice (~Ho) and m e a s u r e d (till) linewidths are given in milliTesla. Assuming, as c u s t o m a r y , that: 7d= ~'0 e x p (E/kT)
(5)
t h e n the activation e n e r g y E is d e t e r m i n e d from the plot of In Td VS. 1/7. B e f o r e applying the a b o v e equations, o n e has to take into a c c o u n t the fact that the entire linewidth is not related to the dipolar interaction. There is a c o n t r i b u t i o n f r o m d e m a g n e t i z a t i o n effects [ 6, 7 ] c a u s e d by the p a r a m a g n e t i s m of the s a m a r i u m hydride sample. This contribution has b e e n estimated from the t e m p e r a t u r e d e p e n d e n c e o f the m a g n e t i c susceptibility [7] and by det e r m i n i n g the m a g n e t i c field d e p e n d e n c e of the linewidths. Thus, the o b s e r v e d linewidths (Fig. 1) w e r e c o r r e c t e d by subtracting the m a g n e t i c field b r o a d e n i n g m e n t i o n e d above. A least-squares fit of the data to eqns. (4) and (5) t h e n yields E = 3 6 . 8 _ 3 kJ mol -~ and T 0 = 2 x l 0 ~1 s plus or m i n u s a f a c t o r o f 10. The t e m p e r a t u r e b e h a v i o u r of the p r o t o n s p e c t r a for SmH2.30 and SmH24o (Fig. 1) m a k e s their i n t e r p r e t a t i o n m o r e difficult than that o f SmH2.1e. Although their linewidths indicate a self-diffusion of the p r o t o n s , E and ~'0 c a n n o t be d e t e r m i n e d b e c a u s e a two-line s y s t e m is o b s e r v e d at low t e m p e r a t u r e s . A typical e x a m p l e o f the s u p e r p o s i t i o n of these lines at T= 238 K is s h o w n in Fig. 4 for SmH2.40. This s p e c t r u m can be d e c o m p o s e d into two s e p a r a t e lines if o n e a s s u m e s that one of the lineshapes is d e s c r i b e d b y eqn. (1) and the s e c o n d o n e is lorentzian. The effect of the d e c o n v o l u t i o n is shown in Fig. 5. The p a r a m e t e r s a and b o f the first lineshape are 1.7 × 1 0 - ~ m T and 5.36 × 1 0 : ~ m T respectively. The linewidth o f the lorentzian c o m p o n e n t (~HL ( m e a s u r e d b e t w e e n m a x i m a of the derivative of the a b s o r p t i o n line) is equal to 0.38 mT. The c o n t r i b u t i o n o f the lorentzian line to the w h o l e intensity of the s p e c t r u m is e s t i m a t e d to b e 0.58 (see A p p e n d i x A). At a still lower t e m p e r a t u r e (T= 78 K), the m o m e n t s o f the b r o a d line i n c r e a s e by a b o u t 1 5 % , (~HL is ~ 0 . 4 8 m T a n d the contribution o f the lorentzian line t o the total intensity r e m a i n s the same. A similar b e h a v i o u r is exhibited by the s p e c t r a o f the SmH2.ao sample. H o w e v e r , in this case, a b o u t 0.4 of the total intensity (at T= 78 K) can be d e s c r i b e d by the lorentzian lineshape, and the m o m e n t s o f the s e c o n d line are smaller t h a n t h a t o f SmH2.4o.
88
/+03020-
-12
-8
-~.
100 12 •-10 .-20 .-30 -/.,0 H_ Ho(lO4mT)
_---
Fig. 4. Comparison of the measured absorption derivative JH NMR spectrum for SmH2.40 with that obtained as a result of superposition of the two lines shown in Fig. 5 (solid line). The signal to noise ratio for the experimental spectrum (broken line) was similar to that shown in Fig. 2.
A
20i 104 -=
-
-L
J -10 -20 -30
H-Ho {104rnT} ----,,..
Fig. 5. The two resonance lines A and B resulting from the decomposition of the spectrum shown in Fig. 4. A is lorentzian in shape with ~HL= 0.38 mT whilst B is described by eqn. (1) with a = 0 . 1 7 mT and b = 0 . 5 3 6 mT.
T h e c h a n g e f r o m the one-line s p e c t r u m t o t h e m o r e c o m p l i c a t e d o n e w a s r e p o r t e d f o r 2D NMR in LaD2+x d e u t e r i d e s [12]. One n a r r o w a n d t w o b r o a d r e s o n a n c e s w e r e o b s e r v e d b e l o w 2 4 0 K f o r 2.28 < x < 2.48. T h e y h a v e b e e n a t t r i b u t e d to the f a c t t h a t d e u t e r i u m a t o m s e x p e r i e n c e d different crystalline e l e c t r i c field g r a d i e n t s in t h e o r d e r e d d e u t e r i u m sublattice. F o r SmH2+x it is difficult to a p p l y t h e s a m e a r g u m e n t since p r o t o n s a r e insensitive to t h e s e g r a d i e n t s . One p o s s i b l e e x p l a n a t i o n o f the two-line s y s t e m in SmH2.ao a n d SmH2.4o is t o a s s u m e t h a t b e l o w a b o u t 2 5 0 K the t w o p h a s e s m i g h t coexist. One o f t h e m m a y h a v e a n o r d e r e d s t r u c t u r e on t h e h y d r o g e n s u b l a t t i c e ( b r o a d line), whilst in the o t h e r o n e the h y d r o g e n a t o m s a r e still relatively
89
m o b i l e (lorentzian line). T h e o r d e r i n g w o u l d p r o b a b l y lead to a r e s t r i c t i o n of the p r o t o n diffusion as well as i n d u c i n g a c u b i c - t e t r a g o n a l t r a n s f o r m a t i o n o f t h e f.c.c, lattice o f t h e s a m a r i u m ions. In fact, s u c h a lattice d e f o r m a t i o n h a s b e e n o b s e r v e d b y us for a Smile 3o s a m p l e . At r o o m t e m p e r a t u r e we o b s e r v e d t h a t f o r the SmH2.~o s a m p l e the X-ray p a t t e r n is c h a r a c t e r i s t i c for the f.c.c, lattice with a lattice p a r a m e t e r ao = 0 . 5 3 6 5 nm. H o w e v e r , w h e n the t e m p e r a t u r e w a s l o w e r e d , a d e c r e a s e o f ao a n d an a s y m m e t r i c b r o a d e n i n g of t h e r e f l e c t i o n s at large a n g l e s w e r e d e t e c t e d . In Fig. 6, a typical e x a m p l e of the diffraction line in the vicinity o f O= 70 ° is s h o w n for T = 171 K. This reflection a r i s e s f r o m (333), ( 5 1 1 ) a n d ( 1 1 5 ) indices. W h e n t e t r a g o n a l d e f o r m a t i o n t a k e s place, the ( 3 3 3 ) line r e m a i n s u n c h a n g e d b u t the ( 5 1 1 ) a n d ( 1 1 5 ) lines are s u b j e c t to splitting. T h e lattice p a r a m e t e r s a n d c / a ratio d e d u c e d f r o m o u r X-ray s t u d i e s for T = 98 K are ao = 0 . 5 3 4 4 n m and Co = 0 . 5 3 6 2 (c:a = 1.003). F o r c o m p a r i s o n , K n a p p e et al. [13] r e p o r t e d v e r y similar v a l u e s of a 0 = 0 . 5 3 4 3 n m and Co = 5 3 6 5 n m (c:a = 1.004) o b t a i n e d at r o o m t e m p e r a t u r e f o r SMH2.33. H o w e v e r , in o u r s a m p l e the t e t r a g o n a l d e f o r m a t i o n o c c u r s at l o w e r t e m p e r a t u r e s . The X-ray d a t a t a k e n for SmH2.,2 indicate t h a t it r e m a i n s cubic b e t w e e n T = 12 K a n d T = 2 9 3 K. The result is in a g r e e m e n t with the c o n c l u s i o n s d r a w n f r o m b o t h o u r ' H NMR d a t a and electrical resistivity m e a s u r e m e n t s r e p o r t e d by Vajda et al. [ 14, 15 ]. H o w e v e r , the s i t u a t i o n is m o r e c o m p l i c a t e d for the SmH2.4o s a m p l e , w h e r e we did not o b s e r v e c l e a r e v i d e n c e o f t e t r a g o n a l d e f o r m a t i o n o f the m e t a l lattice. I n s t e a d of this, an i n c r e a s e in the w i d t h : h e i g h t ratio for the 0 = 70 ° reflection w a s o b s e r v e d b e t w e e n 112 K and 12 K. P r o b a b l y the s i m p l e s t e x p l a n a t i o n o f t h a t f a c t is to a s s u m e t h a t the t e t r a g o n a l d e f o r m a t i o n in SmH2.4o is s m a l l e r t h a n in SmH2.30. This is p r o m p t e d b y the X-ray d a t a in the LaH2+~ [16] a n d CeH2+~ [17] s y s t e m s , w h e r e a small t e t r a g o n a l d e f o r m a t i o n o f the crystal lattice w a s also o b s e r v e d . In particular, it w a s f o u n d t h a t the c:a ratio for H:Ln of a b o u t 2 . 4 0 is s m a l l e r t h a n t h a t
>-
69
70
71
Fig. 6. X-ray diffraction line of SmH2.30 at a b o u t 0 = 7 0 ° t a k e n at T = 1 7 1
K.
90 for the other hydrogen concentrations where a tetragonal deformation was d e t e c t e d . F i n a l l y , l e t u s m e n t i o n t h e r e c e n t p a p e r b y D a o u et a l . [ 1 8 ] o n X - r a y m e a s u r e m e n t s in S m H z + , . A l t h o u g h t h e y d o n o t r e p o r t o b s e r v a t i o n o f a t e t r a g o n a l p h a s e , a n o m a l i e s in t h e t h e r m a l e x p a n s i o n c o e f f i c i e n t s f o r x = 0 . 2 6 and x=0.45 w e r e s e e n . In s u m m a r y , t h e p r e s e n t i n v e s t i g a t i o n o f S m H z + x shows that for x = 0 and x = 0.12 the samarium hydrides display properties s i m i l a r t o t h o s e o f LaH2 +.~. [ 10 ]. H o w e v e r , t h e r e s u l t s f o r x = 0 . 3 0 a n d x = 0 . 4 0 i n d i c a t e a p h a s e t r a n s i t i o n in t h e v i c i n i t y o f T = 2 5 0 K w h i c h is m o s t p r o b a b l y owing to the ordering of the hydrogen sublattice.
Acknowledgment O.J.Z is g r a t e f u l t o t h e C N R S - - P A N e x c h a n g e p r o g r a m f o r p a r t i a l s u p p o r t of this work.
References 1 O. Greis, P. Knappe and H. MueUer, J. Solid. State Chem., 39 (1981) 49. 2 O. J. Zogat, M. Drulis and S. Idziak, Z. Phys. Chem. N.F., 163 (1989) 303. 3 M. Barberon, Doctoral Thesis, CNRS No. 702, Paris, 1973. 4 A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1961, p. 120. 5 E. R. Andrew, Phys. Rev., 91 (1953) 425. 6 L. E. Drain, Proc. Phys. Soc. (London), 80 (1962) 1380. 7 0 . J. Zogat, Phys. Status Solidi B, 117 (1983) 717. 8 J. H. Van Vleck, Phys. Rev., 74 (1948) 1168. 9 B. Stalifiski, C. K. Coogan and H. S. Gutowsky, J. Chem. Phys., 34 (1961) 1191. B. Nowak and O. J. Zoga], unpublished data, 1983. 10 D. S. Schreiber and R. M. Cotts, Phys. Rev., 131 (1963) 1118. 11 R. Kubo and K. Tomita, J. Phys. Soc. Jpn., 9 (1954) 888. 12 D. G. de Groot, R. G. Barnes, B. J. Beaudry and D. R. Torgeson, J. Less-Common Met., 73 (1980) 233. 13 P. Knappe, H. Mueller and H. W. Mayer, J. Less-Common Met., 95 (1985) 323. 14 P. Vajda, J. N. Daou and J. P. Burger, Phys. Rev. B, 40 (1989) 500. 15 P. Vajda, J. N. Daou and J. P. Burger, Z. Phys. Chem. N.F., 163 (1989) 637. 16 E. Boroch, K. Conder, Cai Ru-Xiu and E. Kaldis, J. Less-Common Met., 156 (1989) 259. 17 E. Kaldis, E. Boroch and M. Tellefsen, J. Less-Common Met., 129 (1987) 57. 18 J. N. Daou, P. Vajda and J. P. Burger, Solid State Commun., 71 (1989) 1145.
Appendix A When resonance lines are recorded as first derivatives, their intensities can be determined either by double integration or by using appropriate formulae. First integration gives the absorption, and the result of such a p r o c e d u r e f o r t h e d e r i v a t i v e s f r o m F i g . 4 is s h o w n in F i g . A 1 . T h e a r e a ( P ) under lines A and B is a measure of their intensities. In particular, I A = P A / (PA + P B ) is t h e r e l a t i v e i n t e n s i t y o f l i n e A ( h e r e t h e l o r e n t z i a n o n e ) .
91
A ,4 h~
-5.0
5.0 H-H o (10-1 mT)
Fig. A1. The absorption lines A and B obtained by integration of their first derivatives as shown in Fig. 5. A n o t h e r m e t h o d c a n be applied w h e n the lineshape f u n c t i o n s are known. In o u r case, we have:
PA = (27r/31/2)( ~HL)2g'm~,
(A1)
PB = 2ab(27r)~P2g'ma,
(A2)
w h e r e g'max is the m a x i m u m value of the first derivative and the formulae are valid for the lorentzian and eqn. (1) lineshape f u n c t i o n s respectively. In the latter, the a p p r o x i m a t i o n is v e r y g o o d for b / 2 a > 1.
83
Proton nuclear magnetic resonance line narrowing and tetragonal lattice distortion in SmH2+x (0~
Ph. l'H6ritier INPG, URA 1109 CNRS, E N S de Physique de Grenoble, B.P. 46, 38402 St. Martin d ' H ~ e s Cedex (France)
(Received April 30, 1991; in final form July 3, 1991)
Abstract Proton magnetic resonance experiments have been made on samarium hydride samples SmH2+~ (0~
1. I n t r o d u c t i o n A s in t h e l a n t h a n u m h y d r i d e s , s a m a r i u m f o r m s a n o n s t o i c h i o m e t r i c d i h y d r i d e p h a s e , S m H 2 +x, o v e r a w i d e c o m p o s i t i o n r a n g e . A t r o o m t e m p e r a t u r e it h a s t h e C a F 2 - t y p e s t r u c t u r e a n d a c o n t i n u o u s s o l i d s o l u t i o n e x t e n d s f r o m x= -0.05 to x=0.34 [1 ]. H o w e v e r , t h e s e l i m i t s a r e s t r o n g l y i n f l u e n c e d b y the preparation conditions. F o r H : S m = 2, t h e h y d r o g e n a t o m s e n t e r t h e t e t r a h e d r a l s i t e s p r e d o m i n a n t l y , b u t f o r x > 0 t h e y a l s o h a v e t o fill o c t a h e d r a l s i t e s . D e p e n d i n g o n t h e w a y in w h i c h t h e o c t a h e d r a l s i t e s a r e o c c u p i e d , t w o i n t e r e s t i n g p h e n o m e n a are observed. When hydrogen atoms occupy these sites randomly, the proton s e l f - d i f f u s i o n p r o c e s s o c c u r s m o r e e a s i l y . H o w e v e r , if t h e o c c u p a t i o n o f t h e octahedral sites is not statistical, an ordered hydrogen sublattice and tetragonal metal lattice deformation are expected. We would like to report both effects here for the samarium hydrides.
2. E x p e r i m e n t a l d e t a i l s T h e s a m p l e s u s e d i n t h i s s t u d y a r e t h e s a m e a s d e s c r i b e d in ref. 2. T h e a c c u r a c y o f t h e i r a t o m i c r a t i o H : S m is _ 0 . 0 3 . T h e c o n t i n u o u s w a v e ( C w )
0925-8388/91/$3.50
© 1991 -- Elsevier Sequoia, Lausanne
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nuclear magnetic resonance (NMR) experiment details are also in ref. 2. Debye X-ray diffraction patterns were used to obtain the structure and the lattice constant. A laboratory-made X-ray diffractometer (Fe Ka radiation, A= 1.93597/~) was used for this purpose [3]. It included a 0--20 goniometer and a liquid nitrogen (or helium) cryostat at the bottom of which the sample was glued onto a cold copper finger.
3. R e s u l t s and d i s c u s s i o n The proton Cw spectra obtained over a temperature range from about 78 K to 295 K indicated a lack of any changes for SmH2.oo and a linewidth narrowing onset at about 250 K for SmH2.12 (see Fig. 1). The temperature behaviour of the SmH2.ao and SmH2.4o spectra is more complicated. A single, narrow lorentzian-like line at room temperature broadens when the temperature is lowered, and near 250 K a composite system of broad and narrow resonance lines appears. Figure 1 shows the temperature dependence of the linewidth in the region where it could be determined with good precision. Below T ~ 2 5 0 K, the superposition of the two lines prevents further linewidth measurements. The resonance absorption derivative for SmH2.oo is shown in Fig. 2. Its shape can be well fitted by Abragam's proposed function [4]: b
] l" F - ( h - x)21 G ( h ) - 2ab(2~r)'/2 J-b exp[ 2a 2 J d x
(1)
where h = H - H o and a and b are the parameters. An example of the fit to the measured derivative of the absorption resonance line is shown in Fig. 3. By using the following relation [4]:
T 6!
2~o
2~0- 2~o
~8o
3oo
T(K) Fig. i. The temperature dependence of the proton resonance linewidth in SmH2.j2 (O), SmH2.3o (A) and SmH2.4o (V). Data are taken at a Larmor frequency of 15 MHz.
85
g .d o
~J 0.8 mT
H
-
H0
Fig. 2. An example of the absorption mode derivative spectrum of the 'H resonance in SmH2.0o at a resonance frequency of 5.96 MHz and T= 78 K. 52
m 2= a 2+ -3 b4 m4 = 3a 4 + 2a2b 2 +
(2)
--
5 t h e s e c o n d (m2) a n d f o u r t h (m4) m o m e n t s c a n be e s t i m a t e d . T h e y h a d to b e c o r r e c t e d f o r finite m o d u l a t i o n a m p l i t u d e [5] a n d t h e n v a l u e s o f m 2 = 8 . 5 - + 0 . 5 × 10 -2 mT 2 a n d m 4 = 186_+ 1 5 × 10 -4 mT 4 a r e o b t a i n e d . S i n c e t h e d a t a w e r e t a k e n a t r e l a t i v e low m a g n e t i c field ( - - 0 . 1 4 T), t h e d e m a g n e t i z a t i o n e f f e c t s [6, 7] o n l y i n f l u e n c e d t h e s p e c t r a t o a s m a l l e x t e n t . W e e s t i m a t e t h a t t h e i r c o n t r i b u t i o n t o t h e m o m e n t s is w i t h i n e x p e r i m e n t a l uncertainties. Experimentally obtained moments may be compared with c a l c u l a t e d o n e s u s i n g t h e Van Vleck f o r m u l a [8] a n d X - r a y d a t a f o r c r y s t a l l a t t i c e s t r u c t u r e . The s e c o n d a n d f o u r t h m o m e n t s d e r i v e d f o r t h e CaF2 t y p e o f s t r u c t u r e a r e [9 ]: C2ao
6
m2 = - (115.6 a2+2640 2/~+a
a f t + 1 0 7 5 f12)
86
u) C
.d 0
09 C w
0.8 mT
(H-H o )
Fig. 3. Comparison of the absorption derivative IH NMR lines obtained from experiment (broken line) and from a least-squares fit to eqn. (1) (solid line). Here, the experimental recording presented in Fig. 2 is reproduced without noise for better illustration of the agreement between the two lines. The fitting parameters a and b are 0.19 mT and 0.383 mT respectively.
m4 -
C4ao 12 - 2/3+a
( 4 . 4 7 × 106/!¢ a + 9 . 1 3 × 1 0 4 a 3 + 7 . 2 9 × 1 0 8 a 2 / 3 + 2 . 1 8 × 107afl 2
+ 3 . 5 3 × 105/32 + 5 . 3 9 × 1 0 3 a 2 + 2 . 5 6 × 1 0 6 a f t ) C2 = 3 . 5 8 2 X 1 0 - 6 ( n m 6 m T 2)
C4 = 3 . 9 6 ×
(3)
10 - ' 2 ( n m '2 m T 4)
where a and/3 are the probabilities of occupancy in octahedral and tetrahedral s i t e s r e s p e c t i v e l y . T h e c o n s t a n t s C2 a n d (?4 w e r e c a l c u l a t e d f o r p r o t o n s a n d the contribution of samarium nuclei moments has been neglected because of their low abundances and moments. The lattice constant a0 = 0.5358 nm was taken from X-ray experiments. Assuming a=0.03 and fl=0.985, we o b t a i n e d m2 = 8 . 5 × 1 0 - 2 m T 2 a n d m 4 = 1 8 8 . 5 × 10 - 4 m T 4, v a l u e s w h i c h a g r e e with the above-mentioned experimental values. Earlier work [10] on proton N M R s e c o n d m o m e n t a n a l y s i s f o r LaH2 g a v e a = 0 . 0 5 a n d / 3 = 0 . 9 7 5 . H e n c e , in b o t h c a s e s t h e h y d r o g e n a t o m s m o s t l y o c c u p y t e t r a h e d r a l s i t e s w i t h o n l y a f e w b e i n g l o c a t e d i n o c t a h e d r a l s i t e s . A l s o , in SmH2.,2 t h e l i n e s h a p e o f the 'H NMR resonance at low temperature can be described using eqn. (1) and the moments t h u s o b t a i n e d a r e m 2 = 1 0 . 6 _+ 0 . 5 × 1 0 - 2 m T ~ a n d m4=299+30× 1 0 - 4 m T 4. O n e t h e n o b t a i n s v e r y s i m i l a r c a l c u l a t e d v a l u e s of m2 = 10.6× 10 .2 mT 2 and m4=298× 10 . 4 m T 4 f o r a = 0 . 1 8 a n d / 3 = 0 . 9 7 ,
87 and a0 = 0 . 5 3 5 nm. It again indicates a v e r y large p e r c e n t a g e o f tetrahedral o c c u p a n c y and an increased probability of o c t a h e d r a l site o c c u p a n c y , n e c e s s a r y now to a c c o m m o d a t e the larger n u m b e r of h y d r o g e n a t o m s ( H : S m = 2 . 1 2 ) . The p r o t o n linewidth in SmH2 le, which is c o n s t a n t at low t e m p e r a t u r e , starts to n a r r o w in the vicinity o f 250 K (Fig. 1) owing to rapid thermally activated self-diffusion o f the protons. In this case, the linewidth 6H is related to the dipolar correlation time ~'d by the Kubo and T o m i t a [1 l] expression: ~-d=Cd(~H) - l tan ~ \6Ho] J
(4)
w h e r e for p r o t o n s C d = 3 . 2 × 1 0 -6 (S mT), and the rigid-lattice (~Ho) and m e a s u r e d (till) linewidths are given in milliTesla. Assuming, as c u s t o m a r y , that: 7d= ~'0 e x p (E/kT)
(5)
t h e n the activation e n e r g y E is d e t e r m i n e d from the plot of In Td VS. 1/7. B e f o r e applying the a b o v e equations, o n e has to take into a c c o u n t the fact that the entire linewidth is not related to the dipolar interaction. There is a c o n t r i b u t i o n f r o m d e m a g n e t i z a t i o n effects [ 6, 7 ] c a u s e d by the p a r a m a g n e t i s m of the s a m a r i u m hydride sample. This contribution has b e e n estimated from the t e m p e r a t u r e d e p e n d e n c e o f the m a g n e t i c susceptibility [7] and by det e r m i n i n g the m a g n e t i c field d e p e n d e n c e of the linewidths. Thus, the o b s e r v e d linewidths (Fig. 1) w e r e c o r r e c t e d by subtracting the m a g n e t i c field b r o a d e n i n g m e n t i o n e d above. A least-squares fit of the data to eqns. (4) and (5) t h e n yields E = 3 6 . 8 _ 3 kJ mol -~ and T 0 = 2 x l 0 ~1 s plus or m i n u s a f a c t o r o f 10. The t e m p e r a t u r e b e h a v i o u r of the p r o t o n s p e c t r a for SmH2.30 and SmH24o (Fig. 1) m a k e s their i n t e r p r e t a t i o n m o r e difficult than that o f SmH2.1e. Although their linewidths indicate a self-diffusion of the p r o t o n s , E and ~'0 c a n n o t be d e t e r m i n e d b e c a u s e a two-line s y s t e m is o b s e r v e d at low t e m p e r a t u r e s . A typical e x a m p l e o f the s u p e r p o s i t i o n of these lines at T= 238 K is s h o w n in Fig. 4 for SmH2.40. This s p e c t r u m can be d e c o m p o s e d into two s e p a r a t e lines if o n e a s s u m e s that one of the lineshapes is d e s c r i b e d b y eqn. (1) and the s e c o n d o n e is lorentzian. The effect of the d e c o n v o l u t i o n is shown in Fig. 5. The p a r a m e t e r s a and b o f the first lineshape are 1.7 × 1 0 - ~ m T and 5.36 × 1 0 : ~ m T respectively. The linewidth o f the lorentzian c o m p o n e n t (~HL ( m e a s u r e d b e t w e e n m a x i m a of the derivative of the a b s o r p t i o n line) is equal to 0.38 mT. The c o n t r i b u t i o n o f the lorentzian line to the w h o l e intensity of the s p e c t r u m is e s t i m a t e d to b e 0.58 (see A p p e n d i x A). At a still lower t e m p e r a t u r e (T= 78 K), the m o m e n t s o f the b r o a d line i n c r e a s e by a b o u t 1 5 % , (~HL is ~ 0 . 4 8 m T a n d the contribution o f the lorentzian line t o the total intensity r e m a i n s the same. A similar b e h a v i o u r is exhibited by the s p e c t r a o f the SmH2.ao sample. H o w e v e r , in this case, a b o u t 0.4 of the total intensity (at T= 78 K) can be d e s c r i b e d by the lorentzian lineshape, and the m o m e n t s o f the s e c o n d line are smaller t h a n t h a t o f SmH2.4o.
88
/+03020-
-12
-8
-~.
100 12 •-10 .-20 .-30 -/.,0 H_ Ho(lO4mT)
_---
Fig. 4. Comparison of the measured absorption derivative JH NMR spectrum for SmH2.40 with that obtained as a result of superposition of the two lines shown in Fig. 5 (solid line). The signal to noise ratio for the experimental spectrum (broken line) was similar to that shown in Fig. 2.
A
20i 104 -=
-
-L
J -10 -20 -30
H-Ho {104rnT} ----,,..
Fig. 5. The two resonance lines A and B resulting from the decomposition of the spectrum shown in Fig. 4. A is lorentzian in shape with ~HL= 0.38 mT whilst B is described by eqn. (1) with a = 0 . 1 7 mT and b = 0 . 5 3 6 mT.
T h e c h a n g e f r o m the one-line s p e c t r u m t o t h e m o r e c o m p l i c a t e d o n e w a s r e p o r t e d f o r 2D NMR in LaD2+x d e u t e r i d e s [12]. One n a r r o w a n d t w o b r o a d r e s o n a n c e s w e r e o b s e r v e d b e l o w 2 4 0 K f o r 2.28 < x < 2.48. T h e y h a v e b e e n a t t r i b u t e d to the f a c t t h a t d e u t e r i u m a t o m s e x p e r i e n c e d different crystalline e l e c t r i c field g r a d i e n t s in t h e o r d e r e d d e u t e r i u m sublattice. F o r SmH2+x it is difficult to a p p l y t h e s a m e a r g u m e n t since p r o t o n s a r e insensitive to t h e s e g r a d i e n t s . One p o s s i b l e e x p l a n a t i o n o f the two-line s y s t e m in SmH2.ao a n d SmH2.4o is t o a s s u m e t h a t b e l o w a b o u t 2 5 0 K the t w o p h a s e s m i g h t coexist. One o f t h e m m a y h a v e a n o r d e r e d s t r u c t u r e on t h e h y d r o g e n s u b l a t t i c e ( b r o a d line), whilst in the o t h e r o n e the h y d r o g e n a t o m s a r e still relatively
89
m o b i l e (lorentzian line). T h e o r d e r i n g w o u l d p r o b a b l y lead to a r e s t r i c t i o n of the p r o t o n diffusion as well as i n d u c i n g a c u b i c - t e t r a g o n a l t r a n s f o r m a t i o n o f t h e f.c.c, lattice o f t h e s a m a r i u m ions. In fact, s u c h a lattice d e f o r m a t i o n h a s b e e n o b s e r v e d b y us for a Smile 3o s a m p l e . At r o o m t e m p e r a t u r e we o b s e r v e d t h a t f o r the SmH2.~o s a m p l e the X-ray p a t t e r n is c h a r a c t e r i s t i c for the f.c.c, lattice with a lattice p a r a m e t e r ao = 0 . 5 3 6 5 nm. H o w e v e r , w h e n the t e m p e r a t u r e w a s l o w e r e d , a d e c r e a s e o f ao a n d an a s y m m e t r i c b r o a d e n i n g of t h e r e f l e c t i o n s at large a n g l e s w e r e d e t e c t e d . In Fig. 6, a typical e x a m p l e of the diffraction line in the vicinity o f O= 70 ° is s h o w n for T = 171 K. This reflection a r i s e s f r o m (333), ( 5 1 1 ) a n d ( 1 1 5 ) indices. W h e n t e t r a g o n a l d e f o r m a t i o n t a k e s place, the ( 3 3 3 ) line r e m a i n s u n c h a n g e d b u t the ( 5 1 1 ) a n d ( 1 1 5 ) lines are s u b j e c t to splitting. T h e lattice p a r a m e t e r s a n d c / a ratio d e d u c e d f r o m o u r X-ray s t u d i e s for T = 98 K are ao = 0 . 5 3 4 4 n m and Co = 0 . 5 3 6 2 (c:a = 1.003). F o r c o m p a r i s o n , K n a p p e et al. [13] r e p o r t e d v e r y similar v a l u e s of a 0 = 0 . 5 3 4 3 n m and Co = 5 3 6 5 n m (c:a = 1.004) o b t a i n e d at r o o m t e m p e r a t u r e f o r SMH2.33. H o w e v e r , in o u r s a m p l e the t e t r a g o n a l d e f o r m a t i o n o c c u r s at l o w e r t e m p e r a t u r e s . The X-ray d a t a t a k e n for SmH2.,2 indicate t h a t it r e m a i n s cubic b e t w e e n T = 12 K a n d T = 2 9 3 K. The result is in a g r e e m e n t with the c o n c l u s i o n s d r a w n f r o m b o t h o u r ' H NMR d a t a and electrical resistivity m e a s u r e m e n t s r e p o r t e d by Vajda et al. [ 14, 15 ]. H o w e v e r , the s i t u a t i o n is m o r e c o m p l i c a t e d for the SmH2.4o s a m p l e , w h e r e we did not o b s e r v e c l e a r e v i d e n c e o f t e t r a g o n a l d e f o r m a t i o n o f the m e t a l lattice. I n s t e a d of this, an i n c r e a s e in the w i d t h : h e i g h t ratio for the 0 = 70 ° reflection w a s o b s e r v e d b e t w e e n 112 K and 12 K. P r o b a b l y the s i m p l e s t e x p l a n a t i o n o f t h a t f a c t is to a s s u m e t h a t the t e t r a g o n a l d e f o r m a t i o n in SmH2.4o is s m a l l e r t h a n in SmH2.30. This is p r o m p t e d b y the X-ray d a t a in the LaH2+~ [16] a n d CeH2+~ [17] s y s t e m s , w h e r e a small t e t r a g o n a l d e f o r m a t i o n o f the crystal lattice w a s also o b s e r v e d . In particular, it w a s f o u n d t h a t the c:a ratio for H:Ln of a b o u t 2 . 4 0 is s m a l l e r t h a n t h a t
>-
69
70
71
Fig. 6. X-ray diffraction line of SmH2.30 at a b o u t 0 = 7 0 ° t a k e n at T = 1 7 1
K.
90 for the other hydrogen concentrations where a tetragonal deformation was d e t e c t e d . F i n a l l y , l e t u s m e n t i o n t h e r e c e n t p a p e r b y D a o u et a l . [ 1 8 ] o n X - r a y m e a s u r e m e n t s in S m H z + , . A l t h o u g h t h e y d o n o t r e p o r t o b s e r v a t i o n o f a t e t r a g o n a l p h a s e , a n o m a l i e s in t h e t h e r m a l e x p a n s i o n c o e f f i c i e n t s f o r x = 0 . 2 6 and x=0.45 w e r e s e e n . In s u m m a r y , t h e p r e s e n t i n v e s t i g a t i o n o f S m H z + x shows that for x = 0 and x = 0.12 the samarium hydrides display properties s i m i l a r t o t h o s e o f LaH2 +.~. [ 10 ]. H o w e v e r , t h e r e s u l t s f o r x = 0 . 3 0 a n d x = 0 . 4 0 i n d i c a t e a p h a s e t r a n s i t i o n in t h e v i c i n i t y o f T = 2 5 0 K w h i c h is m o s t p r o b a b l y owing to the ordering of the hydrogen sublattice.
Acknowledgment O.J.Z is g r a t e f u l t o t h e C N R S - - P A N e x c h a n g e p r o g r a m f o r p a r t i a l s u p p o r t of this work.
References 1 O. Greis, P. Knappe and H. MueUer, J. Solid. State Chem., 39 (1981) 49. 2 O. J. Zogat, M. Drulis and S. Idziak, Z. Phys. Chem. N.F., 163 (1989) 303. 3 M. Barberon, Doctoral Thesis, CNRS No. 702, Paris, 1973. 4 A. Abragam, The Principles of Nuclear Magnetism, Clarendon, Oxford, 1961, p. 120. 5 E. R. Andrew, Phys. Rev., 91 (1953) 425. 6 L. E. Drain, Proc. Phys. Soc. (London), 80 (1962) 1380. 7 0 . J. Zogat, Phys. Status Solidi B, 117 (1983) 717. 8 J. H. Van Vleck, Phys. Rev., 74 (1948) 1168. 9 B. Stalifiski, C. K. Coogan and H. S. Gutowsky, J. Chem. Phys., 34 (1961) 1191. B. Nowak and O. J. Zoga], unpublished data, 1983. 10 D. S. Schreiber and R. M. Cotts, Phys. Rev., 131 (1963) 1118. 11 R. Kubo and K. Tomita, J. Phys. Soc. Jpn., 9 (1954) 888. 12 D. G. de Groot, R. G. Barnes, B. J. Beaudry and D. R. Torgeson, J. Less-Common Met., 73 (1980) 233. 13 P. Knappe, H. Mueller and H. W. Mayer, J. Less-Common Met., 95 (1985) 323. 14 P. Vajda, J. N. Daou and J. P. Burger, Phys. Rev. B, 40 (1989) 500. 15 P. Vajda, J. N. Daou and J. P. Burger, Z. Phys. Chem. N.F., 163 (1989) 637. 16 E. Boroch, K. Conder, Cai Ru-Xiu and E. Kaldis, J. Less-Common Met., 156 (1989) 259. 17 E. Kaldis, E. Boroch and M. Tellefsen, J. Less-Common Met., 129 (1987) 57. 18 J. N. Daou, P. Vajda and J. P. Burger, Solid State Commun., 71 (1989) 1145.
Appendix A When resonance lines are recorded as first derivatives, their intensities can be determined either by double integration or by using appropriate formulae. First integration gives the absorption, and the result of such a p r o c e d u r e f o r t h e d e r i v a t i v e s f r o m F i g . 4 is s h o w n in F i g . A 1 . T h e a r e a ( P ) under lines A and B is a measure of their intensities. In particular, I A = P A / (PA + P B ) is t h e r e l a t i v e i n t e n s i t y o f l i n e A ( h e r e t h e l o r e n t z i a n o n e ) .
91
A ,4 h~
-5.0
5.0 H-H o (10-1 mT)
Fig. A1. The absorption lines A and B obtained by integration of their first derivatives as shown in Fig. 5. A n o t h e r m e t h o d c a n be applied w h e n the lineshape f u n c t i o n s are known. In o u r case, we have:
PA = (27r/31/2)( ~HL)2g'm~,
(A1)
PB = 2ab(27r)~P2g'ma,
(A2)
w h e r e g'max is the m a x i m u m value of the first derivative and the formulae are valid for the lorentzian and eqn. (1) lineshape f u n c t i o n s respectively. In the latter, the a p p r o x i m a t i o n is v e r y g o o d for b / 2 a > 1.