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X-ray powder diffraction studies of LixMo0₂ Sacken, Ulrich Gustav von 1980

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X-RAY POWDER DIFFRACTION STUDIES OF L i x M o 0 2 by ULRICH GUSTAV VON/SACKEN B . S c , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We a c c e p t t h i s t h e s i s as con f o r m i n g to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1980 © U l r i c h Gustav von Sacken, 1980 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 D a t e ^ I O M . \^ ll&O i i ABSTRACT Debye-S c h e r r e r x - r a y powder photography i s used to s t u d y the dependence of the h o s t l a t t i c e parameters of LixMoC>2 (0 < x <_ 1) upon the l i t h i u m c o n t e n t (x) . The r e s u l t s i n d i c a t e t h a t the h o s t l a t t i c e expands c o n s i d e r a b l y as x i n c r e a s e s but t h a t the l a t t i c e reassumes i t s o r i g i n a l s t r u c t u r e when the l i t h i u m i s removed. I n t e r c a l a t i n g one e q u i v a l e n t o f l i t h i u m (x = 1) causes a c o n s i d e r a b l e (a.13%) i n c r e a s e i n the u n i t c e l l volume. T h i s e x p a n s i o n i s c o n f i n e d to d i r e c t i o n s p e r p e n d i c u l a r to the t u n n e l s through the M0O2 l a t t i c e . D e t a i l e d measurements are made o f the v o l t a g e V(x) of Li/Li xMoC>2 c e l l s . These and the x - r a y p a t t e r n s both i n d i c a t e t h a t LixMoC>2 o c c u r s i n t h r e e d i s t i n c t c o m p o s i t i o n a l phases w i t h approximate c o m p o s i t i o n s o f MoC»2f L i j Mo0 2 and LiMoC>2. F i r s t - o r d e r t r a n s i t i o n s i n v o l v i n g pronounced h y s t e r e s i s e f f e c t s are observed as the l i t h i u m c o n t e n t i s a l t e r e d . A b r i e f d i s c u s s i o n o f the e l e c t r o c h e m i c a l p r o p e r t i e s o f the LixMoC>2 system i n terms of a l a t t i c e gas model i s i n c l u d e d . i i i TABLE OF CONTENTS Page 1 I n t r o d u c t i o n 1 2 S t r u c t u r e 6 2.1 R u t i l e s t r u c t u r e 6 2.2 M0O2 s t r u c t u r e 11 3 X-ray D i f f r a c t i o n Theory 15 3.1 D i r e c t i o n o f the d i f f r a c t e d beams 16 3.2 I n t e n s i t y o f the d i f f r a c t e d beams 17 3.3 The Debye-Scherrer method 18 3.4 The e f f e c t s o f i n t e r c a l a t i o n 21 4 E x p e r i m e n t a l P r o c e d u r e s 22 4.1 M0O2 p r e p a r a t i o n and c h a r a c t e r i z a t i o n 22 4.2 C e l l c o n s t r u c t i o n 23 4.3 The V(x) cu r v e 27 4.4 Che m i c a l p r e p a r a t i o n o f L i x M o 0 2 compounds 36 4.5 E l e c t r o c h e m i c a l p r e p a r a t i o n o f Li x M o 0 2 compounds ....38 4.6 P r e p a r a t i o n and x - r a y i n g of Li x M o 0 2 specimens 39 4.7 Measurement o f L i x M o 0 2 d i f f r a c t i o n p a t t e r n s 40 5 R e s u l t s and D i s c u s s i o n 42 5.1 Phase t r a n s i t i o n s 42 5.2 U n i t c e l l parameters o f Li x M o 0 2 48 5.3 O r d e r i n g , s t r a i n e f f e c t s , and s u p e r l a t t i c e s 51 6 C o n c l u s i o n 55 B i b l i o g r a p h y 58 Appendix A - I n d e x i n g L i x M o 0 2 p a t t e r n s 60 Appendix B - The USGS program 67 Appendix C - The CALINE program 73 Appendix D - D i f f r a c t i o n p a t t e r n s o f M0O2, L i i M0O2 and LiMo02-81 -1 i v LIST OF TABLES Ta b l e Page I F r a c t i o n a l c o - o r d i n a t e s o f s i t e s i n T i 0 2 11 I I F r a c t i o n a l c o - o r d i n a t e s o f atoms i n the M0O2 u n i t c e l l ...13 I I I C o m p o s i t i o n a l ranges o f s i n g l e phases o f Li xMo02 44 IV H i g h - a n g l e l i n e s which can be i d e n t i f i e d from s t r o n g low-an g l e l i n e s 65 V M0O2 (Phase I) d i f f r a c t i o n p a t t e r n 82 VI LijMoCH (Phase I I ) d i f f r a c t i o n p a t t e r n 84 V I I LiMo02 (Phase I I I ) d i f f r a c t i o n p a t t e r n 86 V LIST OF FIGURES F i g u r e Page 1 Schematic r e p r e s e n t a t i o n o f a L i / L i x M o 0 2 c e l l 3 2 M e t a l s which form r u t i l e r e l a t e d metal d i o x i d e s 6 3 The t e t r a g o n a l u n i t c e l l o f T i 0 2 7 4 A s i n g l e o c t a h e d r a l TiOg u n i t 8 5 R u t i l e s t r u c t u r e viewed a l o n g the t e t r a g o n a l c - a x i s 9 6 I n t e r c a l a t i o n s i t e s i n the r u t i l e s t r u c t u r e 10 7 P o s i t i o n s of the o c t a h e d r a l and t e t r a h e d r a l s i t e s i n the M0O2 u n i t c e l l 12 8 R e l a t i o n between m o n o c l i n i c and p s e u d o - t e t r a g o n a l u n i t c e l l s o f M0O2 13 9 Atom p o s i t i o n s i n the M0O2 u n i t c e l l 14 10 Schematic r e p r e s e n t a t i o n of a Debye-Scherrer camera 19 11 F l a n g e c e l l , 25 12 C h a r g e - d i s c h a r g e c u r v e s o f a t y p i c a l c e l l 28 13 C u r r e n t v s . time a f t e r s t e p p i n g c e l l v o l t a g e 32 14 i s ( V ) e s t i m a t e d from r e s i d u a l c u r r e n t s 33 15 V v s . Qj o b t a i n e d by s t e p p i n g c e l l v o l t a g e 34 16 The n o r m a l i z e d V(x) c u r v e 35 17 M easuring l i n e p o s i t i o n 41 18 The phase I I to I t r a n s i t i o n 46 19 L i x M o 0 2 d i f f r a c t i o n p a t t e r n s 47 20 U n i t c e l l parameters v s . x 49 21 U n i t c e l l volume v s . x 50 22 P o s s i b l e one d i m e n s i o n a l arrangements o f i n t e r c a l a t e d l i t h i u m atoms 53 23 Two p o s s i b l e t h r e e - d i m e n s i o n a l arrangements o f the oc c u p i e d s i t e s f o r L i t M0O2 55 v i ACKNOWLEDGEMENTS F i r s t o f a l l , I would l i k e t o thank my s u p e r v i s o r Rudi H a e r i n g f o r the t i m e , the a d v i c e , and the p a t i e n c e w i t h which he has h e l p e d me t o complete t h i s p r o j e c t . I a l s o b e n e f i t e d from many u s e f u l d i s c u s s i o n s w i t h my co-workers James C h i u , Ross McKinnon and J e f f Dahn. Many o f the t e c h n i q u e s used t o pr e p a r e x - r a y specimens were deve l o p e d by Dave W a i n w r i g h t . I am g r a t e f u l t o E. P. Meagher f o r the use o f h i s copy o f the USGS program. The f i g u r e s were drawn by P e t e r Haas. I t i s a p l e a s u r e t o thank Rosanna Chui f o r her a s s i s t a n c e w i t h the t y p i n g o f t h i s t h e s i s . I am g r a t e f u l t o the N a t i o n a l Research C o u n c i l f o r f i n a n c i a l s u p p o r t i n the form o f a P o s t g r a d u a t e S c h o l a r s h i p . 1 1 I n t r o d u c t i o n In r e c e n t y e a r s much a t t e n t i o n has been f o c u s s e d on i n t e r c a l a t i o n systems because o f t h e i r p o t e n t i a l u s e f u l n e s s as h i g h enerqv d e n s i t y , r e c h a r g e a b l e b a t t e r i e s which f u n c t i o n a t ambient t e m p e r a t u r e s . The L i / T i S 2 b a t t e r y d e v e l o p e d by Exxon R e s e a r c h ^ was, u n t i l r e c e n t l y , b e i n g produced c o m m e r c i a l l y , B e l l L a b s 2 have been i n v e s t i g a t i n g the Li/VS2 system, and the Li/MoS2 b a t t e r y i s b e i n g developed by M o l i Energy^. A l l o f the s e a r e based on the i n t e r c a l a t i o n o f l a y e r e d t r a n s i t i o n m e t a l d i c h a l c o g e n i d e s , but many o t h e r m a t e r i a l s , some w i t h r a d i c a l l y d i f f e r e n t s t r u c t u r e s , a re known t o i n t e r c a l a t e . The s u b j e c t o f t h i s t h e s i s i s the Li/Mo02 i n t e r c a l a t i o n system, which can a l s o be used i n e l e c t r o c h e m i c a l c e l l s , but does not have a l a y e r e d s t r u c t u r e . A t r u e i n t e r c a l a t i o n system i s one which p e r m i t s the i n s e r t i o n o f a gues t s p e c i e s , such as l i t h i u m , i n t o a h o s t l a t t i c e w i t h o u t d i s r u p t i n g the h o s t s t r u c t u r e . In g e n e r a l the bonds o f the h o s t l a t t i c e a r e p r e s e r v e d and the s t r u c t u r a l d i s t o r t i o n s accompanying i n t e r c a l a t i o n a r e s m a l l enough t o p e r m i t the subsequent removal o f the i n t e r c a l a t e d g u e s t s and the r e t u r n of the h o s t l a t t i c e t o i t s o r i g i n a l s t a t e . I n t e r c a l a t i o n o c c u r s when i t i s t h e r m o d y n a m i c a l l y f a v o u r a b l e f o r g u e s t s to r e s i d e a t a c c e s s i b l e s i t e s i n the h o s t l a t t i c e , c o n s e q u e n t l y i n t e r c a l a t i o n h o s t s g e n e r a l l y have s t r u c t u r e s w i t h open c h a n n e l s or l a y e r s t h r o u g h which the g u e s t s can d i f f u s e from one s i t e t o 1 Exxon Research & E n g i n e e r i n g Co., Florham P a r k , N.J., U.S.A. 2 B e l l Telephone L a b o r a t o r i e s , I n c . , Murray H i l l , N.J., U.S.A. 3 M o l i Energy Co., Burnaby, B.C., Canada 2 the n e x t . I n t e r a c t i o n s w i t h the s u r r o u n d i n g h o s t l a t t i c e and i n t e r c a l a t e d g u e s t s o c c u p y i n g n e i g h b o r i n g s i t e s d e t e r m i n e the energy o f an i n t e r c a l a t e d g u e s t o c c u p y i n g a p a r t i c u l a r s i t e . T h i s energy i s commonly r e f e r r e d t o as the e f f e c t i v e s i t e e nergy. The number of a v a i l a b l e s i t e s s e t s an upper l i m i t t o the number o f g u e s t s which can be i n t e r c a l a t e d , but i f the i n t e r a c t i o n s among t h e s e a re s u f f i c i e n t l y r e p u l s i v e , o n l y a f r a c t i o n o f the a v a i l a b l e s i t e s can be o c c u p i e d . Phase t r a n s i t i o n s and o r d e r i n g e f f e c t s a r e t o be ex p e c t e d and have been o b s e r v e d i n s e v e r a l i n t e r c a l a t i o n systems. Not a l l i n t e r c a l a t i o n systems a r e s u i t a b l e f o r use i n e l e c t r o c h e m i c a l c e l l s . Only those i n t e r c a l a t i o n r e a c t i o n s which can be s e p a r a t e d i n t o redox h a l f - r e a c t i o n s p e r m i t the t r a n s f e r o f e l e c t r o n s t h r o u g h an e x t e r n a l c i r c u i t . For i n s t a n c e , the i n t e r c a l a t i o n o f l i t h i u m i n t o M0O2 c o u l d be w r i t t e n as x L i + Mo0 2 t L i x M o 0 2 (1-1) but i n an e l e c t r o c h e m i c a l c e l l , l i k e t he one d e p i c t e d i n F i g . 1, two s e p a r a t e h a l f - r e a c t i o n s o c c u r . At the anode, which c o n s i s t s o f l i t h i u m m e t a l , x L i t x L i + + xe ~ (1-2) and a t the cathode Mo0 2 + x L i + + x e " t L i x M o 0 2 (1-3) the open c i r c u i t v o l t a g e (V) of such a c e l l i s a measure o f the energy d i f f e r e n c e between l i t h i u m atoms i n the me t a l and the l o w e s t a v a i l a b l e s i t e energy i n the i n t e r c a l a t i o n h o s t . Because the s i t e energy depends upon how much l i t h i u m has a l r e a d y been i n t e r c a l a t e d , V = V ( x ) , where x i s the mole r a t i o o f l i t h i u m t o molybdenum i n the c a t h o d e , as i n eqn. 1-3. I f the c e l l i s s h o r t 3 M o 0 2 cathode Lithium metal Electrolyte (Li Br /PC) o - e-• = L i + e « Br" F i g . 1 - Schematic r e p r e s e n t a t i o n o f the d i s c h a r g e o f a Li/Li xMoC>2 c e l l . c i r c u i t e d s i t e s w i t h p r o g r e s s i v e l y h i g h e r e n e r g i e s a r e o c c u p i e d u n t i l a l l t h o s e w i t h e n e r g i e s lower than t h a t o f m e t a l l i c l i t h i u m a re f i l l e d . S i n c e V = V(x) the c o m p o s i t i o n o f the LixMoC>2 cathode can be c o n t r o l l e d by a p p l y i n g a s u i t a b l e DC v o l t a g e t o the c e l l . L i t h i u m i n t e r c a l a t i o n compounds have a l s o been pr e p a r e d by the d i r e c t r e a c t i o n o f h o s t s w i t h v a r i o u s c h e m i c a l r e a g e n t s as reviewed by Whittingham (1978a) . The s i m p l e s t of t h e s e t e c h n i q u e s i s the use o f n - b u t y l l i t h i u m (C/jHgLi) d i s s o l v e d i n hexane, which a c t s as a l i t h i u m donor when p l a c e d i n c o n t a c t w i t h a s u i t a b l e a c c e p t o r . 2 x C 4 H 9 L i + 2Mo0 2 -*• 2 L i x M o 0 2 + x C 8 H 1 8 (1-4) H i s t o r i c a l l y i n t e r c a l a t i o n has been a s s o c i a t e d o n l y w i t h 4 layered host structures. The connection i s so intimate that some sources r e s t r i c t the term " i n t e r c a l a t i o n " only to processes involving a lamellar host (Ebert, 1976). The i n t e r c a l a t i o n of graphite was f i r s t investigated more than one hundred years ago (Schafhautl, 1841), and since then many other layered i n t e r c a l a t i o n hosts including graphite oxide, boron n i t r i d e , the lamellar clays, and the t r a n s i t i o n metal dichalcogenides have been studied (Dines, 1974). Only recently have i n t e r c a l a t i o n hosts with nonlayered structures, p a r t i c u l a r l y the r u t i l e related compounds l i k e M0O2, been studied (Murphy et a l , 1978). X-ray d i f f r a c t i o n methods can be used to monitor the str u c t u r a l changes and phase t r a n s i t i o n s which generally occur in a host l a t t i c e as i t i s intercalated, but only a few systems, a l l with layered hosts such as L i / T i S 2 (Chianelli et a l , 1978) and Li/MoS2 (Wainwright, 1979), have been studied c a r e f u l l y in t h i s manner. Most of the published results have been obtained using f u l l y intercalated compounds prepared by reaction with n-butyllithium or other chemical reagents. Murphy et a l (1978) have reported the approximate structure of several intercalated r u t i l e related compounds, including LiMo02r prepared by n-b u t y l l i t h i a t i o n , but none of these have been studied in d e t a i l . The purpose of t h i s thesis i s to use x-ray d i f f r a c t i o n techniques to investigate structural changes and phase tr a n s i t i o n s in the Li xMo02 system, and to correlate these with observed electrochemical properties of Li/Mo0 2 c e l l s . The L i x M o 0 2 system i s e s p e c i a l l y interesting because unlike the quasi two-dimensional layered i n t e r c a l a t i o n compounds i t has a "tunnelled" host structure and i s almost one-dimensional in some 5 r e s p e c t s . 6 2 Structure MoO2 i s one of several materials (Fig. 2) commonly known as the r u t i l e - r e l a t e d metal dioxides, the structures of which are c l o s e l y related to the r u t i l e form of T i 0 2 (Rogers et a l , 1969). These structures are most e a s i l y understood in terms of the simple r u t i l e structure which exhibits the important features without any of the complicating structural d i s t o r t i o n s commonly found among the r u t i l e - r e l a t e d metal dioxides. T i V Cr Mn Nb Mo Tc Ru Rh Sn T a W Re Os I r Pt P b F i g . 2 - Metals which form r u t i l e - r e l a t e d dioxides (after Rogers et a l , 1969). 2.1 Rutile Structure Rutile has a tetragonal unit c e l l as i l l u s t r a t e d in F i g . 3. Each titanium atom i s co-ordinated by six oxygen atoms which l i e at the corners of an octahedron (Fig. A ) . These octahedral units are the basic building blocks of r u t i l e and related metal dioxides. Linear chains of edge sharing octahedra p a r a l l e l to 7 the tetragonal c-axis are cross linked by shared corners to give an equal number of p a r a l l e l tunnels, as i l l u s t r a t e d in Fi g . 5. F i g . 3 - The tetragonal unit c e l l of T i 0 2 ( r u t i l e ) . The numbers inscribed in the c i r c l e s are the f r a c t i o n a l atomic co-ordinates along the tetragonal c-axis (after Wyckoff, 1963). Along the centers of these tunnels there are two types of large s i t e s where intercalated guests might reside. According to the number of co-ordinating oxygen atoms these are c l a s s i f i e d as either octahedral or tetrahedral^ (Fig. 6). For each titanium atom there are two octahedral and two tetrahedral s i t e s , the positions of which are given in Table I. Each tunnel e s s e n t i a l l y consists of a st r i n g of alternating 4 This i s not meant to imply that the co-ordinating octahedra (tetrahedra) are regular. In fact they are irre g u l a r in both TiC"2 and M0O2. 8 Fi g . 4 - A single octahedral TiOg unit. octahedral and tetrahedral s i t e s . When viewed along the c-axis the strings of s i t e s and the strings of metal atoms at the centers of TiOg octahedra appear to l i e on two interpenetrating square grids as i l l u s t r a t e d in F i g . 5. Calculations by Kingsbury et a l (1968) indicate that in T i 0 2 the energy of the tetrahedral s i t e s i s lowest, but since these calculations are based upon a simple model which assumes the host l a t t i c e to be 100% io n i c , i t i s not clear that these s i t e s are preferred in other r u t i l e -related compounds such as Mo02, which i s a conductor. In addition to the large tetrahedral s i t e s at the centers of the tunnels, there are two types of smaller tetrahedral s i t e s (Fig. 6) at the edges and between the tunnels which may be 9 c a F i g . 5 - The r u t i l e structure viewed along the tetragonal c-axis. Chains of metal atoms (m) and channel s i t e s (s) l i e on interpenetrating square gri d s . important as loopholes through which i t i s possible for intercalated guests to d i f f u s e from one tunnel to the next. It i s u n l i k e l y that intercalated guests a c t u a l l y reside in these small s i t e s since calculations indicate that they have much higher energies (Kingsbury et a l , 1968) and experiments have shown that the d i f f u s i o n of intercalated lithium i s highly anisotropic, being at least 10^ times slower perpendicular to the c-axis than along i t (Johnson, 1964). Henceforth any mention of tetrahedral s i t e s refers only to the large tetrahedral s i t e s at the centers of the tunnels. 10 (a) (b) F i g . 6 - I n t e r c a l a t i o n s i t e s i n t h e r u t i l e s t r u c t u r e a) F o u r c h a i n s of e d g e - s h a r i n g o c t a h e d r a v i e w e d a l o n g t h e t e t r a g o n a l c - a x i s . E a c h l e t t e r c o r r e s p o n d s to a p a r t i c u l a r t y p e of s i t e . At t h e c e n t e r of e a c h c h a n n e l t h e r e a r e o c t a g e d r a l (A) and l a r g e t e t r a h e d r a l (B) s i t e s . S m a l l e r t e t r a g e d r a l s i t e s a r e s i t u a t e d a t t h e edges (C) and between c h a n n e l s ( D ) . b) A p e r s p e c t i v e v i e w of t h e same f o u r c h a i n s of o c t a h e d r a . To i l l u s t r a t e how t h e s i t e s a r e c o - o r d i n a t e d t h e oxygen atoms w h i c h c o - o r d i n a t e one of e a c h of t h e f o u r t y p e s of s i t e s a r e l a b e l l e d a c c o r d i n g l y . The s i t e s t h e m s e l v e s a r e a t t h e c e n t e r s of t h e s e c o - o r d i n a t i n g p o l y h e d r a . -11 T a b l e I - F r a c t i o n a l c o - o r d i n a t e s o f s i t e s i n T i 0 2 Type of s i t e F r a c t i o n a l c o - o r d i n a t e s (see F i g . 3) O c t a h e d r a l (1/2,0,1/2) (0,1/2,1/2) (1/2,0,0) (0,1/2,0) T e t r a h e d r a l (0,1/2,1/4) (0,1/2,3/4) (1/2,0,1/4) (1/2,0,3/4) 2.2 Mo0 2 S t r u c t u r e The Mo0 2 s t r u c t u r e i s a m o n o c l i n i c d i s t o r t i o n o f the s i m p l e r u t i l e s t r u c t u r e . Because o f m e t a l - m e t a l bonding the Mo atoms are d i m e r i z e d and the c o - o r d i n a t i n g o c t a h e d r a a re d i s t o r t e d , p r o d u c i n g a c o n s i d e r a b l e v a r i a t i o n i n 0-0 and Mo-0 bond l e n g t h s (Brandt & S k a p s k i , 1967). The s i t e s a r e a l s o d i s t o r t e d , so t h a t u n l i k e T i 0 2 where each o c t a h e d r a l ( t e t r a h e d r a l ) s i t e i s e q u i v a l e n t t o any o t h e r o c t a h e d r a l ( t e t r a h e d r a l ) s i t e , t h e r e a re now t h r e e t y p e s of o c t a h e d r a l and two t y p e s o f t e t r a h e d r a l s i t e s i n the c h a n n e l s ( F i g . 7 ) . However the b a s i c f e a t u r e s o f the r u t i l e s t r u c t u r e remain e s s e n t i a l l y unchanged. There a r e s t i l l two o c t a h e d r a l and two t e t r a h e d r a l s i t e s per m e t a l atom, and the s t r i n g s o f s i t e s s t i l l l i e i n open t u n n e l s , p a r a l l e l t o the s t r i n g s " of me t a l atoms a l o n g the m o n o c l i n i c a - a x i s ( F i g . 7 ) . Because the Mo0 2 s t r u c t u r e i s a d i s t o r t i o n o f the s i m p l e r u t i l e s t r u c t u r e i t a l m o s t f i t s a p s e u d o - t e t r a g o n a l u n i t c e l l . F i g . 8 i l l u s t r a t e s t he r e l a t i o n between the m o n o c l i n i c and p s e u d o - t e t r a g o n a l c e l l s . The p s e u d o - t e t r a g o n a l parameters (primed) f a c i l i t a t e comparisons between d i s t o r t e d and 12 • — Mo atoms (3 - Octahedral sites / \ - Tetrahedral sites F i g . 7 - The positions of the octahedral and tetrahedral s i t e s in the M0O2 unit c e l l . There are three types of octahedral s i t e s (A, B, C) and two types of tetrahedral s i t e s (D, E) in channels - p a r a l l e l to the monoclinic a-axis. The oxygen atoms have been omitted for c l a r i t y . undistorted r u t i l e structures, and are related to the monoclinic unit c e l l parameters (unprimed) in the following manner: a' = l/2(b + csing) (2-la) c' = a/2 (2-lb) Table II gives the f r a c t i o n a l co-ordinates (x,y,z) of the atoms in the monoclinic unit c e l l . According to Brandt & Skapski M0O2 belongs to the space group P2j/c (C?jh) consequently there are four equivalent positions for each point in the unit c e l l ^ : (x,y,z); (-x,-y,-z); (-x,1/2+y,1/2-z); (x,1/2-y,1/2+z) so only the positions of one Mo atom and two oxygen atoms need 5 These equivalent positions are not necessarily in the same unit c e l l as the point (x,y,z) from which they are calculated. In order to find the corresponding positions in the unit c e l l containing the o r i g i n a l point (x,y,z) i t may be necessary to add or subtract 1 from some of the f r a c t i o n a l co-ordinates u n t i l 0 < x,y,z < 1, as in Table I I . 13 MONOCLINIC PSEUDOTETRAGONAL F i g . 8 - The r e l a t i o n between the m o n o c l i n i c ( s o l i d l i n e s ) and p s e u d o - t e t r a g o n a l (dashed) u n i t c e l l s of M0O2. T a b l e I I - F r a c t i o n a l c o - o r d i n a t e s o f atoms i n M0O2 u n i t c e l l ( a f t e r Brandt & S k a p s k i , 1967) X y z Mol 0.232 0.992 0.016 Mo2 0.768 0.008 0.984 Mo3 0.768 0.492 0.484 Mo4 0.232 0.508 0.516 01 0.112 0.217 0.234 02 0.888 0.783 0.766 03 0.888 0.717 0.266 04 0.112 0.283 0.734 05 0.391 0.697 0.299 06 0.609 0.303 0.701 07 0.609 0.197 0.201 08 0.391 0.803 0.799 to be s p e c i f i e d . I n the same paper v e r y p r e c i s e u n i t c e l l p arameters (a,b,c,g) and the u n i t c e l l volume (V) a r e a l s o 14 g i v e n : a = 5.6109 A b = 4.8562 A c = 5.6285 A B = 120.95° V = 131.52 A3 The i n t e r c a l a t i o n o f l i t h i u m does not appear t o a l t e r any of the b a s i c f e a t u r e s of the M0O2 s t r u c t u r e , e s p e c i a l l y the open c h a n n e l s c o n t a i n i n g the o c t a h e d r a l s i t e s and the c h a i n s o f MoOg oc t a h e d r a s u r r o u n d i n g them. D i s t o r t i o n s o f the u n i t c e l l caused by the i n t e r c a l a t i o n o f l i t h i u m are d i s c u s s e d i n s e c t i o n 5.2. b F i g . 9 - Atom p o s i t i o n s i n the M0O2 u n i t c e l l . The numbers i n s c r i b e d i n the c i r c l e s a r e the f r a c t i o n a l c o - o r d i n a t e s a l o n g b. 15 3 X-Ray D i f f r a c t i o n Theory Debye-Scherrer x-ray powder photographs (li k e the ones in F i g . 19) of Li xMo02 samples were used to investigate the s t r u c t u r a l changes which occur in the Li xMo02 system during the i n t e r c a l a t i o n process. The positions of the l i n e s in these d i f f r a c t i o n patterns are dictated by the size and shape of the monoclinic unit c e l l , while the r e l a t i v e i n t e n s i t i e s of the l i n e s depend upon the atom positions within the unit c e l l . Although i t i s straightforward to calculate the d i f f r a c t i o n pattern for a given c r y s t a l structure, i t can be extremely d i f f i c u l t to do the reverse, that i s to determine the structure of a compound from i t s x-ray d i f f r a c t i o n pattern. In the case of the LixMoC>2 system th i s task i s s i m p l i f i e d considerably i f one assumes that i n t e r c a l a t i o n simply causes r e l a t i v e l y small d i s t o r t i o n s of the well known Mo0 2 structure. The d i f f r a c t i o n patterns of L i x M o 0 2 samples can in fact be interpreted in t h i s manner (see Appendix D). The p r i n c i p l e s of x-ray d i f f r a c t i o n theory are well established, so several important results presented in standard reference texts such as C u l l i t y (1956) and Klug (1974) w i l l be stated without proof. The primary purpose of t h i s chapter i s to discuss how the i n t e r c a l a t i o n of lithium can a l t e r the d i f f r a c t i o n pattern of the M0O2 host l a t t i c e . 16 3.1 D i r e c t i o n o f the d i f f r a c t e d beams When a monochromatic beam of x - r a y s impinges upon a c r y s t a l , t he p e r i o d i c n a t u r e o f the c r y s t a l causes d e s t r u c t i v e i n t e r f e r e n c e o f the s c a t t e r e d r a d i a t i o n i n a l l but a few s p e c i a l d i r e c t i o n s , a l o n g which d i f f r a c t e d beams can emerge. A l t h o u g h i t i s somewhat m i s l e a d i n g t h e s e d i f f r a c t e d beams a r e commonly c a l l e d " r e f l e c t i o n s " . Each o f thes e d i r e c t i o n s c o r r e s p o n d s t o a p a r t i c u l a r s p a c i n g (d) between a s e t o f p a r a l l e l e q u i d i s t a n t l a t t i c e p l a n e s a c c o r d i n g t o the Bragg law: d = x / 2 s i n e (3-1) where A = wavelength o f r a d i a t i o n 9 = Bragg a n g l e . 6 A c t u a l l y , eqn. (3-1) i s o n l y v a l i d f o r f i r s t o r d e r d i f f r a c t i o n from a p a r t i c u l a r s e t o f l a t t i c e p l a n e s ; i n g e n e r a l i t s h o u l d be w r i t t e n as d 1 = n X / 2 s i n 6 . However c r y s t a l l o g r a p h e r s p r e f e r t o c o n s i d e r h i g h e r o r d e r d i f f r a c t e d beams as f i r s t o r d e r beams from f i c t i t i o u s l a t t i c e p l a n e s w i t h 1/n the s p a c i n g o f the r e a l p l a n e s ( i . e . d = d'/n = x / 2 s i n e ) . Each s e t o f l a t t i c e p l a n e s and the c o r r e s p o n d i n g r e f l e c t i o n can be s p e c i f i e d by M i l l e r i n d i c e s ( h k l ) , which a r e a s e t o f i n t e g e r s i n v e r s e l y p r o p o r t i o n a l t o the f r a c t i o n a l i n t e r c e p t s o f the p l a n e s w i t h the t h r e e c r y s t a l l o g r a p h i c axes ( a , I D , and c i n the m o n o c l i n i c s y s t e m ) . M i l l e r i n d i c e s (nh,nk,nl) w i t h a common f a c t o r n r e p r e s e n t the f i c t i t i o u s p l a n e s p a r a l l e l t o t h e r e a l ( h k l ) p l a n e s , but w i t h o n l y 1/n the s p a c i n g . The s p a c i n g d ^ i between l a t t i c e p l a n e s w i t h i n d i c e s ( h k l ) i s determined by the 6 26 = a n g l e between i n c i d e n t and d i f f r a c t e d beams. 17 geometry of the unit c e l l . In p a r t i c u l a r , for a monoclinic unit c e l l 1 1 2 2 d h k l S l n 3 h 1 2 h l c o s B 2 + 2 a c ac + ( 3 - 2 ) b Because d^kl depends s o l e l y upon the unit c e l l parameters a,b,c and B , the directions in which d i f f r a c t e d beams may emerge depend only upon the geometry of the unit c e l l and are independent of the positions of the atoms within the unit c e l l . 3.2 Intensity of the d i f f r a c t e d beams The r e l a t i v e i n t e n s i t y I* (arbitrary units) of a p a r t i c u l a r r e f l e c t i o n i s given by the equation I' = I F h k l | 2 ( i + cos22e) - (3-3) where = structure factor for (hkl) r e f l e c t i o n 6 = Bragg angle. The p o l a r i z a t i o n factor (1 + cos 228) appears because an unpolarized beam of x-rays i s scattered a n i s o t r o p i c a l l y by electrons. Since electrons are by far the dominant x-ray scatterers, a l l d i f f r a c t e d beams have th i s angular dependence. The structure factor for a pa r t i c u l a r r e f l e c t i o n i s an interference term which takes into account the phase s h i f t s between radiation scattered in a p a r t i c u l a r d i r e c t i o n by d i f f e r e n t atoms within a unit c e l l . N F h k l = I fjexp[2wi(huj + kvj + lwj)] (3-4) j where N = # of atoms per unit c e l l (UJ,VJ,WJ) = f r a c t i o n a l co-ordinates of j'th atom f j = atomic scattering factor of j'th atom. As mentioned in the previous section, radiation scattered by 18 d i f f e r e n t u n i t c e l l s w i t h i n a c r y s t a l i n t e r f e r e s d e s t r u c t i v e l y e x c e p t i n t h e d i r e c t i o n s a l l o w e d b y t h e B r a g g l a w , so i t i s s u f f i c i e n t t o e x p r e s s F i n t e r m s o f t h e M i l l e r i n d i c e s o f t h e a l l o w e d r e f l e c t i o n s . X - r a y s s c a t t e r e d b y e l e c t r o n s b e l o n g i n g t o a s i n g l e atom a l s o i n t e r f e r e w i t h one a n o t h e r b e c a u s e t h e e l e c t r o n c l o u d i s s p r e a d o v e r a f i n i t e r e g i o n . T h i s e f f e c t i s r e p r e s e n t e d by t h e a t o m i c s c a t t e r i n g f a c t o r f = f ( s i n e / A ) w h i c h i s t a b u l a t e d i n m o s t r e f e r e n c e t e x t s ( e . g . C u l l i t y , 1 9 5 6 ) . The v a l u e o f f i s d e t e r m i n e d l a r g e l y b y t h e number o f e l e c t r o n s a s s o c i a t e d w i t h an a t o m , i n f a c t f o r f o r w a r d s c a t t e r i n g (e = 0 ° ) where t h e r e i s no d e s t r u c t i v e i n t e r f e r e n c e , f = # o f e l e c t r o n s . (3 -5 ) In g e n e r a l , t h e s c a t t e r i n g f a c t o r o f an a tom i s r o u g h l y p r o p o r t i o n a l t o i t s a t o m i c number Z , s o f i / f j - Z i / Z j ( 3 -6 ) f o r a n y g i v e n v a l u e o f s i n e / A . C o n s e q u e n t l y m o l y b d e n u m a t o m s a r e t h e d o m i n a n t s c a t t e r e r s i n a L i x M o 0 2 s a m p l e , and t h e l i t h i u m c a n g e n e r a l l y be o m i t t e d f r o m s t r u c t u r e f a c t o r c a l c u l a t i o n s s i n c e f L i / f M o < 3 / 4 2 . 3 . 3 The D e b y e - S c h e r r e r method D e b y e - S c h e r r e r x - r a y p h o t o g r a p h s a r e o b t a i n e d by m o u n t i n g a s p e c i m e n i n t h e s h a p e o f a t h i n r o d a l o n g t h e a x i s o f a c y l i n d r i c a l c a m e r a a s i l l u s t r a t e d i n F i g . 1 0 . A n a r r o w , n e a r l y m o n o c h r o m a t i c beam o f x - r a y s e n t e r s t h r o u g h t h e c o l l i m a t o r and i s d i f f r a c t e d b y t h e s p e c i m e n t o p r o d u c e r e f l e c t i o n s w h i c h a r e r e c o r d e d on a s t r i p o f f i l m a r o u n d t h e i n s i d e o f t h e c a m e r a . A 19 beam stop shields the film from undesirable r e f l e c t i o n s produced when the transmitted beam st r i k e s other parts of the camera. Ideally, the specimen consists of a very large number of small, randomly oriented c r y s t a l s . Usually, the specimen i s rotated slowly about the camera axis in order to e f f e c t i v e l y increase the number of c r y s t a l orientations in the sample. F i g . 10 - Schematic representation of a Debye-Scherrer camera (side view). The d i f f r a c t e d beams from many c r y s t a l s combine to form d i f f r a c t i o n cones, each of which corresponds to a certain spacing of l a t t i c e planes. The l i n e s on a Debye-Scherrer photograph are the intersections of these d i f f r a c t i o n cones with x— ray film beam stop 20 t h e f i l m . By m e a s u r i n g t h e p o s i t i o n o f a l i n e on t h e f i l m , t h e B r a g g a n g l e e and t h e d - s p a c i n g o f t h e c o r r e s p o n d i n g l a t t i c e p l a n e s c a n be d e t e r m i n e d . The " r e l a t i v e i n t e g r a t e d i n t e n s i t y " ( I ) o f a p a r t i c u l a r r e f l e c t i o n i s r o u g h l y e q u i v a l e n t t o t h e r e l a t i v e s t r e n g t h o f t h e c o r r e s p o n d i n g l i n e when v i s u a l l y c o m p a r e d t o n e i g h b o r i n g l i n e s on t h e f i l m . I = | F | 2 p ( 1 + c o s 2 2 e ) / s i n 2 e c o s e (3 -7 ) where p = m u l t i p l i c i t y f a c t o r . T h i s d i f f e r s f r o m t h e i n t e n s i t y o f a d i f f r a c t e d beam ( e q n . 3 -3 ) b y a f a c t o r p / s i n 2 0 c o s e . T h e L o r e n t z f a c t o r ( l / s i n 2 e c o s e ) a r i s e s f r o m g e o m e t r i c c o n s i d e r a t i o n s s p e c i f i c t o t h e D e b y e - S c h e r r e r m e t h o d . The m u l t i p l i c i t y f a c t o r i s p r e s e n t b e c a u s e c r y s t a l s u s u a l l y h a v e s e t s o f s y m m e t r y r e l a t e d e q u i v a l e n t l a t t i c e p l a n e s w h i c h h a v e i d e n t i c a l s t r u c t u r e f a c t o r s and d - s p a c i n g s , a l t h o u g h t h e i r M i l l e r i n d i c e s d i f f e r . T h e s e a r e known a s p l a n e s o f a f o r m and a r e d e n o t e d b y t h e M i l l e r i n d i c e s o f one t h e e q u i v a l e n t p l a n e s e n c l o s e d i n b r a c e s { h k l } . The m u l t i p l i c i t y f a c t o r f o r a g i v e n l i n e i s e q u a l t o t h e number o f e q u i v a l e n t p l a n e s w h i c h c o n t r i b u t e t o t h a t r e f l e c t i o n . T e m p e r a t u r e and a b s o r p t i o n e f f e c t s , w h i c h c a n n o t be p r e d i c t e d a c c u r a t e l y , c a u s e s i g n i f i c a n t a t t e n u a t i o n o f d i f f r a c t e d b e a m s , b u t b e c a u s e t h e s e e f f e c t s v a r y s l o w l y w i t h e , t h e r e l a t i v e s t r e n g t h s o f l i n e s c l o s e t o g e t h e r on t h e f i l m c a n be o b t a i n e d u s i n g e q n . 3 - 7 . 21 3 .4 The e f f e c t s o f i n t e r c a l a t i o n B e c a u s e l i t h i u m a toms a r e c o m p a r a t i v e l y weak x - r a y s c a t t e r e r s Li xMoC>2 d i f f r a c t i o n p a t t e r n s a r e i n s e n s i t i v e t o t h e L i a t o m s t h e m s e l v e s . H o w e v e r , t h e l a t t i c e d i s t o r t i o n s w h i c h g e n e r a l l y a c c o m p a n y t h e i n t e r c a l a t i o n p r o c e s s do a l t e r t h e d i f f r a c t i o n p a t t e r n o f t h e h o s t l a t t i c e . A s l o n g a s t h e l a t t i c e d i s t o r t i o n s a r e r e l a t i v e l y s m a l l , a s one w o u l d e x p e c t f o r an i n t e r c a l a t i o n s y s t e m , t h e d i f f r a c t i o n p a t t e r n w i l l n o t c h a n g e d r a s t i c a l l y . The r e l a t i v e l i n e i n t e n s i t i e s , w h i c h a r e d e t e r m i n e d by t h e a tom p o s i t i o n s , s h o u l d n o t c h a n g e much b e c a u s e t h e b o n d i n g o f t h e h o s t l a t t i c e r e m a i n s u n a l t e r e d ; t h e l i n e p o s i t i o n s a r e e x p e c t e d t o s h i f t i n r e s p o n s e t o t h e d i s t o r t i o n o f t h e u n i t c e l l . In p r i n c i p l e , t h e s e c h a n g e s i n t h e d i f f r a c t i o n p a t t e r n c a n be u s e d t o d e t e r m i n e how t h e u n i t c e l l p a r a m e t e r s and atom p o s i t i o n s o f t h e M0O2 h o s t l a t t i c e d e p e n d upon t h e amount o f l i t h i u m w h i c h h a s b e e n i n t e r c a l a t e d . 22 4 E x p e r i m e n t a l P r o c e d u r e s 4.1 M0O2 p r e p a r a t i o n and c h a r a c t e r i z a t i o n Two d i f f e r e n t methods were used t o s y n t h e s i z e M0O2 i n the l a b o r a t o r y . I n a d d i t i o n , some M0O2 was purchased d i r e c t l y from a c h e m i c a l s s u p p l i e r ( A t o m e r g i c ) . In a l l c a s e s the m a t e r i a l was i n powder form and gave x - r a y powder d i f f r a c t i o n p a t t e r n s c o n s i s t e n t w i t h the p r e v i o u s l y r e p o r t e d s t r u c t u r e o f M0Q2 (Brandt & S k a p s k i , 1967). The e l e c t r o c h e m i c a l p r o p e r t i e s o f the d i f f e r e n t b a t c h e s v a r i e d somewhat, p o s s i b l y because o f d i f f e r e n c e s i n p a r t i c l e s i z e and c r y s t a l p e r f e c t i o n . V e r y f i n e M0O2 powder was pre p a r e d by o x i d i z i n g s u p e r f i n e M0S2 powder" 7 under a stream o f oxygen and n i t r o g e n a t about 575°C to o b t a i n M0O3 MoS 2 + 7/202 -* M o 0 3 + 2 S 0 2 (4-1) and s u b s e q u e n t l y r e d u c i n g the M0O3 a t about 425°C under a stream of hydrogen and n i t r o g e n t o produce M0O2. M0O3 + H 2 -»• Mo0 2 + H 20 (4-2) T h i s i n d i r e c t s y n t h e s i s was used because a l t h o u g h the o x i d a t i o n o f M0S2 produces some M0O2 i t r a p i d l y c o n t i n u e s through a s e r i e s o f i n t e r m e d i a t e o x i d e s u n t i l o n l y M0O3 r e m a i n s . Incomplete o x i d a t i o n r e s u l t s i n a m i x t u r e o f M0S2 and v a r i o u s molybdenum o x i d e s , so the r e d u c t i o n p r o c e s s , which proceeds d i r e c t l y from M0O3 t o M0O2 and then t o molybdenum m e t a l ( M e l l o r , 1931), was used i n s t e a d t o produce f a i r l y pure Mo0 2. X-ray powder 7 Obtained from Molybond L a b o r a t o r i e s , Dandenong, V i c t o r i a A u s t r a l i a . P a r t i c l e s i z e l e s s than 5 m i c r o n s . 23 d i f f r a c t i o n p h o t o g r a p h s o f t h i s m a t e r i a l i n d i c a t e t h a t t r a c e s o f e i t h e r M0O3 o r Mo a r e p r e s e n t , a s m i g h t be e x p e c t e d . M0O2 was a l s o s y n t h e s i z e d by r e a c t i n g s t o i c h i o m e t r i c a m o u n t s o f M0O3 ( s y n t h e s i z e d a c c o r d i n g t o e q n . 4 -1 ) and Mo (Spex) a t 7 5 0 ° C i n an e v a c u a t e d q u a r t z t u b e ( M a g n e l i e t a l , 1 9 5 2 ) . Mo + 2M0O3 •+ 3 M o 0 2 ( 4 -3 ) M i c r o s c o p i c e x a m i n a t i o n r e v e a l s t h a t t h e M o 0 2 powder s y n t h e s i z e d a c c o r d i n g t o e q n . 4 - 3 c o n t a i n s r e l a t i v e l y l a r g e w e l l - d e v e l o p e d c r y s t a l l i t e s w i t h some f a c e s a s l a r g e a s 20 m i c r o n s a c r o s s . On t h e o t h e r h a n d , t h e M o 0 2 powder p r o d u c e d b y r e d u c i n g M0O3 w i t h h y d r o g e n c o n s i s t s o f h i g h l y p o l y c r y s t a l l i n e p a r t i c l e s w i t h few w e l l d e v e l o p e d c r y s t a l f a c e s . The p u r c h a s e d M o 0 2 a p p e a r s t o be s i m i l a r i n a l l r e s p e c t s t o t h a t s y n t h e s i z e d i n v a c u o . 4 . 2 C e l l c o n s t r u c t i o n The c a t h o d e s u s e d i n e l e c t r o c h e m i c a l c e l l s were p r e p a r e d b y f i r s t s u s p e n d i n g M o 0 2 powder i n p r o p y l e n e g l y c o l 8 , t h e n b r u s h i n g a s m a l l amount o f t h e s u s p e n s i o n o n t o an a l u m i n u m o r n i c k e l f o i l s u b s t r a t e , and f i n a l l y h e a t i n g t h e c o a t e d s u b s t r a t e t o 3 7 5 ° C u n d e r a s t r e a m o f n i t r o g e n f o r 20 min t o e v a p o r a t e and remove t h e p r o p y l e n e g l y c o l . The t h i n l a y e r o f M o 0 2 powder w h i c h r e m a i n s on t h e s u b s t r a t e a d h e r e s f a i r l y w e l l i f i t i s h a n d l e d g e n t l y . E a c h c a t h o d e g e n e r a l l y c o n s i s t e d o f 5 t o 10 mg o f M o 0 2 8 P r o p y l e n e g l y c o l was u s e d b e c a u s e i t i s v i s c o u s and v a p o r i z e s a t f a i r l y l o w t e m p e r a t u r e s . 24 c o v e r i n g a p p r o x i m a t e l y 1 c m 2 o f t h e s u b s t r a t e . A n o d e s were made o f 0 . 4 mm t h i c k l i t h i u m f o i l ( A l p h a ) u s e d a s r e c e i v e d . S i n c e l i t h i u m and L i x M o 0 2 c o m p o u n d s r a p i d l y d e c o m p o s e i n t h e p r e s e n c e o f o x y g e n and w a t e r (among o t h e r t h i n g s ) t h e c e l l s were a s s e m b l e d i n an i n e r t a r g o n a t m o s p h e r e u s i n g a Vacuum A t m o s p h e r e s g l o v e b o x . A I M s o l u t i o n o f L i B r i n p r o p y l e n e c a r b o n a t e ( a l s o known a s PC o r 1 , 2 - p r o p a n e d i o l c a r b o n a t e ) was u s e d a s t h e e l e c t r o l y t e . The PC ( E a s t m a n - K o d a k ) was d i s t i l l e d t w i c e , t h e n r u n t h r o u g h t h r e e c o l u m n s o f a c t i v a t e d a l u m i n a t o remove i m p u r i t i e s , and s u b s e q u e n t l y s t o r e d u n d e r a r g o n i n t h e g l o v e b o x . G a s c h r o m a t o g r a p h y r e v e a l e d t h a t t h i s p r o c e d u r e r e d u c e d t h e c o n c e n t r a t i o n o f p r o p y l e n e g l y c o l ( t h e m a j o r c o n t a m i n a n t ) f r o m more t h a n 500 ppm t o 6 ppm. The L i B r ( o b t a i n e d f r o m MCB) i s d e l i q u e s c e n t and was t h e r e f o r e vacuum f u s e d r i e d b e f o r e b e i n g e n t e r e d i n t o t h e g l o v e b o x where t h e e l e c t r o l y t e was t h e n m i x e d and s t o r e d . P o l y p r o p y l e n e s e p a r a t o r s ( C e l g a r d #3501) s o a k e d w i t h e l e c t r o l y t e were p l a c e d b e t w e e n t h e a n o d e and c a t h o d e , a s i l l u s t r a t e d i n F i g . 1 1 . B e f o r e b e i n g s o a k e d i n e l e c t r o l y t e , t h e s e p a r a t o r s were f i r s t s o a k e d i n two c o n s e c u t i v e b a t h s o f p u r i f i e d PC i n o r d e r t o remove a s u r f a c t a n t c o a t i n g and a n y a d s o r b e d i m p u r i t i e s . W i t h o u t t h e s u r f a c t a n t PC w i l l n o t wet p o l y p r o p y l e n e , b u t o n c e t h e s e p a r a t o r s a r e wet t h e s u r f a c t a n t i s no l o n g e r n e c e s s a r y and s h o u l d be removed b e c a u s e i t a p p a r e n t l y r e a c t s w i t h l i t h i u m . G a s t i g h t c a s e s c o n s i s t i n g o f two s t a i n l e s s s t e e l f l a n g e s h e l d t o g e t h e r b y n y l o n s c r e w s ( F i g . 11) were u s e d f o r t h e c e l l s . 25 F i g . 11 - Flange c e l l (exploded view). 26 V i t o n o - r i n g s were u s e d b e c a u s e o f t h e i r e x t r e m e l y l o w c o n d u c t i v i t y and b e c a u s e t h e y do n o t a b s o r b PC a s r e a d i l y a s some o t h e r m a t e r i a l s . T h e f l a n g e s were p r e c i s i o n m a c h i n e d so t h a t t i g h t e n i n g t h e b o l t s p r e s s e d t h e a n o d e and c a t h o d e t o g e t h e r w i t h e n o u g h f o r c e t o e n s u r e g o o d e l e c t r i c a l c o n t a c t b e t w e e n t h e M o 0 2 and t h e c a t h o d e s u b s t r a t e w h i l e a t t h e same t i m e c o m p r e s s i n g t h e o - r i n g s u f f i c i e n t l y t o make a g a s t i g h t s e a l . Once t h e s e " f l a n g e c e l l s " a r e a s s e m b l e d t h e y c a n be t e s t e d o u t s i d e t h e g l o v e b o x i n a n y d e s i r e d p o s i t i o n , and c a n w i t h s t a n d r o u g h h a n d l i n g - t h e i r o n l y d r a w b a c k i s t h a t t h e y a r e e a s i l y s h o r t e d s i n c e t h e f l a n g e s t h e m s e l v e s a r e t h e c e l l c o n t a c t s . B e s i d e s r e d u c i n g t h e 0 2 and H 2 0 l e v e l s i n t h e s y s t e m a s much a s p o s s i b l e , a d d i t i o n a l p r e c a u t i o n s were t a k e n t o p r e v e n t t h e o c c u r e n c e o f " s i d e - r e a c t i o n s " ( i . e . r e a c t i o n s o t h e r t h a n t h e one u n d e r i n v e s t i g a t i o n - e q n . 1-1) w h i c h c o n t r i b u t e t o t h e e l e c t r o c h e m i c a l p r o p e r t i e s o f t h e c e l l s and t h e r e b y o b s c u r e t h e p r o p e r t i e s o f t h e L i x M o 0 2 s y s t e m . In p a r t i c u l a r , c o r r o s i o n o f a l u m i n u m and s t a i n l e s s s t e e l p a r t s o f t h e c e l l , p r e s u m a b l y b e c a u s e o f a l l o y i n g w i t h l i t h i u m , was i n i t i a l l y o b s e r v e d . C o r r o s i o n o f t h e a l u m i n u m o c c u r r e d o n l y when V < 0 . 2 v o l t s , and s i n c e s u c h l o w v o l t a g e s were r a r e l y r e q u i r e d , t h i s r e a c t i o n was e a s i l y a v o i d e d b y m a i n t a i n i n g a s u f f i c i e n t l y h i g h c e l l v o l t a g e . When l o w v o l t a g e t e s t s were p e r f o r m e d n i c k e l s u b s t r a t e s , w h i c h a p p e a r e d t o r e m a i n i n e r t down t o V = 0 , were u s e d i n s t e a d o f a l u m i n u m . The r e a c t i o n w i t h s t a i n l e s s s t e e l was a v o i d e d by c o a t i n g b o t h i n s i d e s u r f a c e s o f t h e f l a n g e s w i t h s i l i c o n e h i g h -vacuum g r e a s e ( D o w - C o r n i n g ) , w i t h t h e e x c e p t i o n o f a s m a l l s p o t a t t h e c e n t e r o f e a c h f l a n g e w h i c h s e r v e d t o m a i n t a i n e l e c t r i c a l 27 c o n t a c t w i t h t h e a n o d e o r c a t h o d e . T h i s a v o i d e d t h e s i d e -r e a c t i o n b y p r e v e n t i n g t h e e l e c t r o l y t e f r o m c o m i n g i n c o n t a c t w i t h t h e s t a i n l e s s s t e e l . 4 . 3 The V ( x ) c u r v e The manner i n w h i c h t h e o p e n c i r c u i t c e l l v o l t a g e (V) d e p e n d s upon t h e l i t h i u m c o n t e n t o f t h e c a t h o d e (x) i s an i n v a l u a b l e a i d t o i n t e r p r e t i n g t h e x - r a y d a t a and t o w a r d s u n d e r s t a n d i n g t h e Li xMoC>2 s y s t e m , b u t u n f o r t u n a t e l y V ( x ) i s d i f f i c u l t t o m e a s u r e a c c u r a t e l y . An a p p r o x i m a t e g r a p h o f V ( x ) i s e a s i l y o b t a i n e d by c y c l i n g a f l a n g e c e l l ( i . e . c h a r g i n g and d i s c h a r g i n g i t b e t w e e n f i x e d v o l t a g e l i m i t s ) c o n t a i n i n g a w e i g h e d amount o f M0O2 a t a c o n s t a n t c u r r e n t w h i l e r e c o r d i n g t h e c e l l v o l t a g e * a s a f u n c t i o n o f t i m e . A s s u m i n g t h a t t h e n e t c h a r g e t r a n s f e r i s due e n t i r e l y t o t h e i n t e r c a l a t i o n o f l i t h i u m i n t o MoC*2r t h e l i t h i u m c o n t e n t o f t h e c a t h o d e a t a n y t i m e ( t ) i s e a s i l y c a l c u l a t e d . S e v e r a l s u c h c y c l e s o f a t y p i c a l c e l l w h i c h was r u n f o r 30 c o n s e c u t i v e c y c l e s a r e shown i n F i g . 1 2 . T h e s e were o b t a i n e d b y c o n t r o l l i n g t h e c u r r e n t w i t h a PAR m o d e l 173 g a l v a n o s t a t and a PAR m o d e l 175 u n i v e r s a l p r o g r a m m e r . The g r o s s f e a t u r e s o f t h e f i r s t c y c l e a r e r e p r o d u c e d q u i t e w e l l i n s u b s e q u e n t c y c l e s , i n d i c a t i n g t h a t t h e s y s t e m i s r e v e r s i b l e i n t h e s e n s e t h a t t h e h o s t l a t t i c e r e v e r t s t o i t s o r i g i n a l s t r u c t u r e when t h e i n t e r c a l a t e d l i t h i u m i s r e m o v e d . T h i s i s v e r i f i e d b y t h e d i f f r a c t i o n p a t t e r n s o f f u l l y r e c h a r g e d c a t h o d e m a t e r i a l , w h i c h m a t c h t h e p a t t e r n o f p u r e M o 0 2 ( s e e F i g . 1 9 ) . H o w e v e r , t h e s y s t e m i s o b v i o u s l y n o t t h e r m o d y n a m i c a l l y 28 I Discharge Recharge I , , , , O I 2 3 4 t (hrs) F i g . 12 - C h a r g e - d i s c h a r g e c u r v e s o f a t y p i c a l f l a n g e c e l l c o n t a i n i n g 7 mg o f M0O2 a t a c o n s t a n t c u r r e n t o f 0 . 5 mA. r e v e r s i b l e s i n c e t h e d i s c h a r g e and r e c h a r g e c u r v e s h a v e d i s t i n c t l y d i f f e r e n t f e a t u r e s . T h i s " h y s t e r e s i s " i s o b s e r v e d c o n s i s t e n t l y and i s d e f i n i t e l y a p r o p e r t y o f t h e L i x M o 0 2 s y s t e m . The c e l l s d i d n o t h a v e a n y s i g n i f i c a n t c a p a c i t y b e l o w 1 v o l t so c y c l i n g was g e n e r a l l y c o n f i n e d t o t h e 1-2 v o l t r a n g e . No s a t i s f a c t o r y e x p l a n a t i o n f o r t h e g r a d u a l l o s s o f c a p a c i t y e v i d e n t i n F i g . 12 h a s y e t b e e n f o u n d . I t may be due t o some d e c o m p o s i t i o n o f t h e L i x M o 0 2 c a t h o d e b u t no p r o d u c t s a t t r i b u t a b l e t o t h e d e c o m p o s i t i o n o f L i x M o 0 2 c o u l d be i d e n t i f i e d f r o m powder d i f f r a c t i o n p a t t e r n s o f c a t h o d e s w h i c h had b e e n c y c l e d r e p e a t e d l y . H o w e v e r , t h e p o s s i b i l i t y t h a t L i x M o 0 2 d e c o m p o s e s t o f o r m a m o r p h o u s p r o d u c t s r e m a i n s . W h e n e v e r c u r r e n t i s p a s s e d t h r o u g h a c e l l t h e m e a s u r e d 29 v o l t a g e ( V ) d i f f e r s f r o m t h e o p e n c i r c u i t v o l t a g e (V) b e c a u s e o f v a r i o u s k i n e t i c e f f e c t s . U n l i k e t h e o p e n c i r c u i t v o l t a g e , V d e p e n d s n o t o n l y u p o n t h e l i t h i u m c o n t e n t o f t h e c a t h o d e , b u t a l s o u p o n n u m e r o u s o t h e r f a c t o r s s u c h a s t h e p r o p e r t i e s o f t h e e l e c t r o l y t e , t h e d i f f u s i o n r a t e o f l i t h i u m t h r o u g h t h e M0O2 h o s t l a t t i c e , and t h e c o n d i t i o n s a t t h e a n o d e - e l e c t r o l y t e and c a t h o d e - e l e c t r o l y t e i n t e r f a c e s ^ . The i r r e p r o d u c i b i l i t y o f t h e v o l t a g e s a t w h i c h f e a t u r e s ( s u c h a s t h e p l a t e a u s on t h e r e c h a r g e ) i n t h e c h a r g e - d i s c h a r g e c u r v e s i n F i g . 12 o c c u r i s p r o b a b l y due t o c h a n g e s i n some o f t h e f a c t o r s w h i c h i n f l u e n c e V . Of t h e a f o r e m e n t i o n e d k i n e t i c e f f e c t s , t h e d i f f u s i o n o f l i t h i u m t h r o u g h t h e h o s t l a t t i c e d e s e r v e s s p e c i a l a t t e n t i o n , f o r i t a f f e c t s n o t o n l y t h e c e l l v o l t a g e b u t a l s o t h e h o m o g e n e i t y o f t h e c a t h o d e . So f a r we h a v e made t h e i m p l i c i t a s s u m p t i o n t h a t t h e c o m p o s i t i o n o f t h e c a t h o d e i s u n i f o r m , b u t t h i s i s o n l y t r u e i f t h e c e l l i s a t e q u i l i b r i u m . D e p e n d i n g upon w h e t h e r t h e c e l l i s b e i n g c h a r g e d o r d i s c h a r g e d , t h e s u r f a c e c o n c e n t r a t i o n o f l i t h i u m i n t h e c a t h o d e w i l l g e n e r a l l y be l e s s t h a n o r g r e a t e r t h a n t h e a v e r a g e l i t h i u m c o n t e n t . S i n c e t h e c e l l v o l t a g e d e p e n d s upon t h e s u r f a c e c o m p o s i t i o n r a t h e r t h a n t h e a v e r a g e c o m p o s i t i o n o f t h e c a t h o d e , t h e c e l l must be a l l o w e d t o e q u i l i b r a t e so t h a t x i s u n i f o r m b e f o r e t h e c o r r e s p o n d i n g V ( x ) c a n be m e a s u r e d a c c u r a t e l y . When c e l l s a r e c y c l e d a t f a i r l y h i g h r a t e s t h e i r a p p a r e n t c a p a c i t y i s r e d u c e d c o n s i d e r a b l y b e c a u s e o n l y t h e s u r f a c e o f t h e c a t h o d e i s b e i n g f u l l y c h a r g e d and d i s c h a r g e d . 9 F o r a d e t a i l e d d i s c u s s i o n o f t h e k i n e t i c s o f i n t e r c a l a t i o n c e l l s s e e M c K i n n o n ( 1 9 8 0 ) . 30 From t h e d a t a i n F i g . 1 2 , t h e n o m i n a l c o m p o s i t i o n o f t h e f u l l y d i s c h a r g e d c a t h o d e i s Lin.9M.oO2, b u t s i n c e t h e c o m p o s i t i o n i s p r o b a b l y n o n - u n i f o r m t h i s i s o n l y a l o w e r b o u n d on t h e maximum l i t h i u m c o n t e n t ( x m a x ) o f t h e M0O2 h o s t l a t t i c e . A n o t h e r f a c t o r w h i c h a f f e c t s t h e a c c u r a c y w i t h w h i c h x c a n be d e t e r m i n e d i s t h e p r e s e n c e o f s i d e - r e a c t i o n s w h i c h a p p e a r t o i n v o l v e t h e r e a c t i o n o f l i t h i u m w i t h i m p u r i t i e s i n t h e e l e c t r o l y t e o r w i t h PC i t s e l f * 0 . I f a c e l l i s l e f t a t o p e n c i r c u i t t h e v o l t a g e i s o b s e r v e d t o r i s e g r a d u a l l y a s i f t h e c e l l were b e i n g r e c h a r g e d a t a c u r r e n t i n t h e o r d e r o f 1 u A . T h i s " s e l f - r e c h a r g i n g " e f f e c t h a s a l s o b e e n o b s e r v e d i n L i / M o S 2 c e l l s ( W a i n w r i g h t , 1979) and i s p r e s u m a b l y due t o a s i d e - r e a c t i o n w h i c h g r a d u a l l y r e m o v e s l i t h i u m f r o m t h e c a t h o d e . E a c h o f t h e c y c l e s i n F i g . 12 h a s a d i s c h a r g e w h i c h t a k e s s l i g h t l y l o n g e r t h a n t h e c o r r e s p o n d i n g r e c h a r g e b e c a u s e t h e d i s c h a r g e i s p r o l o n g e d t o c o m p e n s a t e f o r t h e l i t h i u m w h i c h t h e s i d e r e a c t i o n r e m o v e s f r o m t h e c a t h o d e w h i l e t h e r e c h a r g e i s i n t u r n h a s t e n e d b y t h e " s e l f - r e c h a r g e " . The e f f e c t i s s m a l l a t h i g h r a t e s s u c h a s 0 . 5 mA b u t b e c o m e s q u i t e p r o n o u n c e d when c e l l s a r e c y c l e d a t l o w e r r a t e s , m a k i n g i t i m p o s s i b l e t o c a l c u l a t e x r e l i a b l y f r o m t h e n e t c h a r g e t r a n s f e r . A v o l t a g e - s t e p p i n g t e c h n i q u e was u s e d t o a c c o u n t f o r b o t h k i n e t i c and s i d e - r e a c t i o n e f f e c t s and t h u s m e a s u r e V ( x ) more a c c u r a t e l y . I t c o n s i s t s o f c h a r g i n g ( o r d i s c h a r g i n g ) a c e l l l ° B e s e n h a r d & E i c h i n g e r (1976) r e p o r t t h a t i n some c a s e s , s u c h a s t h e l i t h i u m i n t e r c a l a t i o n c o m p o u n d s o f g r a p h i t e , i n t e r c a l a t e d l i t h i u m r e a c t s w i t h PC t o f o r m L i 2 C 0 3 and p r o p e n e g a s . T h i s i s u n l i k e l y i n t h e c a s e o f L i x M o 0 2 f o r a l t h o u g h L * 2 C 0 3 ^ s i n s o l u b l e i n PC i t s c h a r a c t e r i s t i c l i n e s were n o t o b s e r v e d i n a n y o f t h e powder d i f f r a c t i o n p a t t e r n s . 31 c o n t a i n i n g a w e i g h e d amount o f M0O2 b y i n c r e m e n t i n g (or d e c r e m e n t i n g ) t h e c e l l v o l t a g e and t h e n a l l o w i n g t h e c e l l t o e q u i l i b r a t e u n t i l t h e c u r r e n t d e c a y s t o t h e s i d e - r e a c t i o n c u r r e n t ( i s ) . T h i s i s t h e c u r r e n t a t w h i c h a c e l l m u s t be d i s c h a r g e d t o c o u n t e r t h e s e l f - r e c h a r g i n g e f f e c t o f t h e s i d e -r e a c t i o n . A s s u m i n g t h a t i s i s a f u n c t i o n o f V o n l y , t h e c u r r e n t s h o u l d e v e n t u a l l y d e c a y t o i s r e g a r d l e s s o f w h e t h e r t h e c e l l i s b e i n g c h a r g e d o r d i s c h a r g e d , and t h i s i s i n f a c t o b s e r v e d ( s e e F i g . 1 3 ) . T h e r e f o r e t h e c u r r e n t a c t u a l l y due t o t h e i n t e r c a l a t i o n o f l i t h i u m ( i j ) i s g i v e n by i j ( t ) = i ( t ) - i s ( 4 -4 ) where i ( t ) i s t h e m e a s u r e d c u r r e n t t h r o u g h t h e c e l l a t t i m e t d u r i n g t h e e q u i l i b r a t i o n p e r i o d ( A t ) . C o n s e q u e n t l y t h e c h a r g e t r a n s f e r due t o t h e i n t e r c a l a t i o n o f l i t h i u m ( A Q j ) i s A Q i = A Q - i s A t ( 4 -5 ) where A Q i s t h e n e t c h a r g e t r a n s f e r m e a s u r e d a t t h e end o f t h e e q u i l i b r a t i o n p e r i o d . P o s i t i v e c u r r e n t and p o s i t i v e c h a r g e t r a n s f e r c o r r e s p o n d t o t h e c h a r g i n g o f t h e c e l l , h e n c e i s < 0 . B e c a u s e i s i s s m a l l , t y p i c a l l y l e s s t h a n 1 v A , k i n e t i c e f f e c t s a r e n e g l i g i b l e , s o a t t h e end o f t h e e q u i l i b r a t i o n p e r i o d t h e c e l l v o l t a g e i s e s s e n t i a l l y e q u a l t o V . The v o l t a g e - s t e p p i n g m e a s u r e m e n t s were t a k e n u s i n g a PAR m o d e l 173 p o t e n t i o s t a t e q u i p p e d w i t h a d i g i t a l c o u l o m e t e r t o s t e p t h e v o l t a g e and m o n i t o r b o t h t h e r e s u l t i n g c h a r g e t r a n s f e r and t h e c u r r e n t . A f t e r s t e p p i n g t h e v o l t a g e t h e c e l l was a l l o w e d t o e q u i l i b r a t e f o r a t l e a s t one d a y , u n t i l t h e c u r r e n t d r o p p e d b e l o w 1 y A , b u t b e c a u s e t h e c u r r e n t d e c a y s v e r y s l o w l y ( s e e F i g . 13) t h e r e s i d u a l c u r r e n t ( i r ) a t t h e end o f t h e 32 F i g . 13 - C u r r e n t v s . t i m e a f t e r t h e v o l t a g e o f a c e l l c o n t a i n i n g 3 . 5 mg o f M 0 O 2 i s s t e p p e d t o 1 . 3 5 v o l t s . The c u r r e n t d e c a y s t o t h e s i d e - r e a c t i o n c u r r e n t ( i s ) b o t h on c h a r g e and d i s c h a r g e . e q u i l i b r a t i o n p e r i o d i s n o t q u i t e e q u a l t o i s . The s i d e - r e a c t i o n c u r r e n t a s a f u n c t i o n o f V was e s t i m a t e d b y g r a p h i c a l l y a v e r a g i n g t h e r e s i d u a l c u r r e n t s , a s i l l u s t r a t e d i n F i g . 1 4 , w i t h t h e c o n s t r a i n t t h a t f o r a n y g i v e n v o l t a g e i r ( d i s c h a r g e ) < i s < i r ( r e c h a r g e ) . ( 4 -6 ) The e s t i m a t e d i s ( V ) was t h e n u s e d t o c a l c u l a t e AQj f o r e a c h v o l t a g e s t e p d u r i n g t h e c y c l e , t o g i v e t h e c u r v e i n F i g . 1 5 . A s e x p e c t e d , t h e l e n g t h o f t h e c h a r g e and d i s c h a r g e a r e n e a r l y t h e s a m e . F i n a l l y , we m u s t c o n v e r t t h e g r a p h o f V v s Q j t o a g r a p h o f V ( x ) . I d e a l l y , f o r e v e r y e l e c t r o n w h i c h p a s s e s t h r o u g h t h e 33 0.2n < w 0 - 0 2 H -0.4H o o ° 0 o 0 0 o o 1 r - o - ° — o — « — ? — ^ > »• • i — 1.2 1.4 -V 1.8 2.0 o °^ _ - ~" x V (volts) o o — X X X •*- x * x o — ( r o n recharge x x x - i r on discharge x x F i g . 14 - i s ( V ) estimated from the residual currents measured et the end of each e q u i l i b r a t i o n period during one complete voltage-stepping cycle of a c e l l containing 3.5 mg of M0O2. external c i r c u i t one lithium atom i s intercalated so x = (m/MF ) Qj (4-7) where m = mass of M0O2 in the c e l l M = formula weight of M0O2 F = Faraday's number Because some of the M0O2 powder i s e a s i l y dislodged when the cathodes are handled* m cannot be determined r e l i a b l y , so the proportionality constant (x/Qj) must be evaluated by an alternate method. Judging from the r e p r o d u c i b i l i t y of the features of the charge-discharge curves and the x-ray powder patterns, the cathodes seem to be in a well defined structural state of maximum lithium content ( x m a x ) when c e l l s are discharged to V £ 1 v o l t , so x was evaluated using x = [ xmax/0ld v)]Ql ( 4 -8 ) where Qi(lv) i s the t o t a l charge transfer due to in t e r c a l a t i o n when a c e l l i s discharged to 1 v o l t . From the charge-discharge cycles in F i g . 12 x m a x - 0.9, and according to Murphy et a l (1978) x m a x =. 1. The V(x) curve shown in F i g . 16 was 34 o — Qj on discharge x — Qj on recharge O -1.0 -2.0 CHARGE TRANSFER (coul) F i g . 15 - V v s . O i ( s o l i d l i n e ) o b t a i n e d b y s t e p p i n g t h e c e l l v o l t a g e . The d a s h e d l i n e shows t h e u n c o r r e c t e d c h a r g e t r a n s f e r 0 t o i l l u s t r a t e t h e s i d e r e a c t i o n e f f e c t s . T h e s e a r e e s p e c i a l l y p r o n o u n c e d a t l o w v o l t a g e s . o b t a i n e d u s i n g x m a x = 1 , and n o r m a l i z i n g t h e r e c h a r g e c u r v e t o g i v e x = 0 f o r t h e f u l l y r e c h a r g e d c e l l , s i n c e t h e x - r a y powder p a t t e r n s i n d i c a t e t h a t f u l l y r e c h a r g e d c a t h o d e s r e a s s u m e t h e o r i g i n a l M0O2 s t r u c t u r e . The d i s c r e p a n c y b e t w e e n t h e l e n g t h o f t h e c h a r g e and d i s c h a r g e i n F i g . 15 p r o b a b l y a r o s e b e c a u s e i s c o u l d n o t be m e a s u r e d a c c u r a t e l y e n o u g h t o f u l l y c o m p e n s a t e f o r t h e e f f e c t s o f t h e s i d e - r e a c t i o n . A l t h o u g h o n l y a c r u d e e s t i m a t e o f i s ( V ) i s p o s s i b l e f r o m t h e d a t a i n F i g . 1 4 , t h e V(x) c u r v e c a n n e v e r t h e l e s s be d e t e r m i n e d q u i t e a c c u r a t e l y b e c a u s e i t i s F i g . 16 - The n o r m a l i z e d V ( x ) c u r v e . 36 f a i r l y i n s e n s i t i v e t o t h e e x a c t f u n c t i o n a l d e p e n d e n c e o f i s upon V . A n y r e a s o n a b l e i s ( V ) w h i c h s a t i s f i e s c o n d i t i o n 4 - 6 s h i f t s none o f t h e d a t a p o i n t s i n F i g . 16 by more t h a n + 0 . 0 1 5 a l o n g t h e x a x i s . When F i g . 12 i s c o m p a r e d w i t h t h e f i n a l V ( x ) c u r v e i n F i g . 15 t h e k i n e t i c and s i d e - r e a c t i o n e f f e c t s on t h e f o r m e r a r e e v i d e n t . The t r u e r e c h a r g e c u r v e a c t u a l l y c o n s i s t s o f two d i s t i n c t p l a t e a u s o f e q u a l c a p a c i t y o v e r w h i c h t h e v o l t a g e r e m a i n s a l m o s t c o n s t a n t . A l s o t h e f e a t u r e s on t h e t r u e V ( x ) c u r v e o c c u r a t n o t i c e a b l y h i g h e r d i s c h a r g e and l o w e r r e c h a r g e v o l t a g e s b e c a u s e o v e r - p o t e n t i a l s due t o k i n e t i c e f f e c t s were a v o i d e d . 4 . 4 C h e m i c a l p r e p a r a t i o n o f L i x M o 0 2 c o m p o u n d s The c h e m i c a l p r e p a r a t i o n o f s i z e a b l e a m o u n t s o f LiMo02 by n - b u t y l l i t h i a t i o n was a t t e m p t e d i n t h e h o p e o f m e a s u r i n g x m a x a c c u r a t e l y , b u t t h e s e a t t e m p t s were u n s u c c e s s f u l b e c a u s e i n a l l c a s e s t h e p r o d u c t c o n s i s t e d o f a m i x t u r e o f Li^MoC»2 a n d LiMo02-S e v e r a l s a m p l e s were p r e p a r e d by t r e a t i n g a b o u t 1 gram o f M0O2 powder ( A t o m e r g i c ) w i t h a p p r o x . 8 ml o f 2 . 4 2 M n - B u L i i n h e x a n e ( A l p h a ) u n d e r an i n e r t a r g o n a t m o s p h e r e . The m i x t u r e was s t o r e d a t room t e m p e r a t u r e i n a s e a l e d s e p t u m b o t t l e f o r 1 t o 2 w e e k s , a f t e r w h i c h t h e e x c e s s l i q u i d was drawn o f f w i t h a s y r i n g e . The powder was t h e n r i n s e d w i t h h e x a n e t o remove t h e r e m a i n i n g n -B u L i . F i n a l l y , b e f o r e e n t e r i n g t h e s a m p l e i n t o t h e g l o v e b o x , t h e r e m a i n i n g h e x a n e was removed b y p u m p i n g . X - r a y d i f f r a c t i o n p a t t e r n s o f t h e s e s a m p l e s i n d i c a t e t h a t t h e y a r e a c t u a l l y m i x t u r e s o f L i ^ M o 0 2 and L i M o 0 2 ( s e e F i g . 1 9 ) . 37 A t f i r s t t h i s was t h o u g h t t o be due t o i m p u r i t i e s i n t h e h e x a n e w h i c h m i g h t c a u s e a p a r t i a l d e c o m p o s i t i o n o f t h e s a m p l e d u r i n g t h e r i n s e , b u t t h e same r e s u l t s were s t i l l o b t a i n e d e v e n when r i n s i n g was d i s p e n s e d w i t h . H e n c e we c o n c l u d e t h a t t h e r e a c t i o n o f n - B u L i w i t h M0O2 i s e i t h e r k i n e t i c a l l y o r t h e r m o d y n a m i c a l l y h i n d e r e d b e f o r e t h e M0O2 i s f u l l y i n t e r c a l a t e d . A k i n e t i c a l l y h i n d e r e d r e a c t i o n seems u n l i k e l y b e c a u s e r e a c t i n g n - B u L i w i t h M0O2 a t 4 0 ° C r a t h e r t h a n room t e m p e r a t u r e c a u s e d no v i s i b l e c h a n g e i n t h e d i f f r a c t i o n p a t t e r n . The m o s t l i k e l y e x p l a n a t i o n f o r t h e i n a b i l i t y o f n - B u L i t o f u l l y l i t h i a t e t h e s e Mo0 2 s a m p l e s i s t h a t n - B u L i i s s i m p l y n o t a s u f f i c i e n t l y p o w e r f u l r e d u c i n g a g e n t . N - b u t y l l i t h i a t i o n c a n i n t e r c a l a t e a h o s t l a t t i c e o n l y i f t h e r e a r e s i t e s a v a i l a b l e w i t h e n e r g i e s b e l o w t h e e n e r g y . o f t h e l i t h i u m a t o m s i n n -B u L i / h e x a n e . H e n c e , t r e a t i n g M0O2 w i t h n - B u L i i s e q u i v a l e n t t o d i s c h a r g i n g a Li/MoC>2 c e l l t o a c e r t a i n v o l t a g e (<j> ) w h i c h may be i n t e r p r e t e d a s t h e p o t e n t i a l o f t h e n - B u L i r e a c t i o n r e l a t i v e t o t h e L i / L i + e l e c t r o d e . A n t i c i p a t i n g t h e r e s u l t s o f s e c t i o n 5 . 1 , w h i c h i n d i c a t e t h a t t h e p l a t e a u i n V ( x ) a t 1 .3 v o l t s on d i s c h a r g e ( s e e F i g . 16) i s due t o a p h a s e t r a n s i t i o n f r o m L i tM0O2 ( p h a s e I I ) t o LiMo0 2 ( p h a s e I I I ) , t h e f a c t t h a t t r e a t i n g Mo0 2 w i t h e x c e s s n - B u L i p r o d u c e s a m i x t u r e o f t h e s e two p h a s e s l e a d s t o t h e c o n c l u s i o n t h a t tj> = 1 .3 v o l t s . P r e s u m a b l y , t h e e x a c t v o l t a g e a t w h i c h t h e t r a n s i t i o n o c c u r s w i l l d i f f e r s l i g h t l y b e t w e e n one p a r t i c l e and t h e n e x t , so some p a r t i c l e s c a n make t h e t r a n s i t i o n w h i l e o t h e r s do n o t . M u r p h y & C a r i d e s (1979) c l a i m t h a t <j> = 1 v o l t , b u t t h i s v a l u e i s p r o b a b l y l o w b e c a u s e i t was i n f e r r e d f r o m c o n s t a n t c u r r e n t d i s c h a r g e c u r v e s 38 o f L i/VSe2 and L i/VS2 c e l l s . K i n e t i c e f f e c t s , w h i c h t h e y d i d n o t c o n s i d e r , c o u l d be r e s p o n s i b l e f o r t h e 0 . 3 v o l t d i s c r e p a n c y . A l t h o u g h i t i s n o t c l e a r what g o v e r n s t h e e x a c t v o l t a g e a t w h i c h t h e t r a n s i t i o n f r o m p h a s e I I t o p h a s e I I I o c c u r s , f a c t o r s s u c h a s t h e s i z e and s t o i c h i o m e t r y o f i n d i v i d u a l p a r t i c l e s may be r e s p o n s i b l e . B e t t e r s t o i c h i o m e t r y o r l e s s v a r i a t i o n i n t h e p a r t i c l e s i z e o f t h e i r M0O2 may e x p l a i n why M u r p h y e t a l (1978) were a b l e t o o b t a i n p u r e LiMo02 by n - b u t y l l i t h i a t i o n . 4 . 5 E l e c t r o c h e m i c a l p r e p a r a t i o n o f L i xMo02 c o m p o u n d s M o s t L i xMo02 s a m p l e s were p r e p a r e d e l e c t r o c h e m i c a l l y by u s i n g e i t h e r c o n s t a n t - v o l t a g e o r c o n s t a n t - c u r r e n t t e c h n i q u e s t o c h a r g e and d i s c h a r g e f l a n g e c e l l s i n a c o n t r o l l e d m a n n e r , t h e r e b y c o n t r o l l i n g t h e l i t h i u m c o n t e n t o f t h e c a t h o d e . The c o n s t a n t - v o l t a g e t e c h n i q u e c o n s i s t s o f c h a r g i n g o r d i s c h a r g i n g a c e l l t o a p r e d e t e r m i n e d v o l t a g e ( I / ) b y c o n n e c t i n g i t i n s e r i e s w i t h a m i c r o a m m e t e r and a r e g u l a t e d DC v o l t a g e s u p p l y s e t a t t h e d e s i r e d v o l t a g e . The c e l l i s a l l o w e d t o e q u i l i b r a t e f o r a b o u t 24 h r s , a f t e r w h i c h t h e o p e n c i r c u i t c e l l v o l t a g e (V) i s e s s e n t i a l l y e q u a l t o V , s i n c e o n l y a s m a l l r e s i d u a l c u r r e n t ( 1 u A ) i s s t i l l f l o w i n g . T h e a p p r o p r i a t e b r a n c h o f t h e V ( x ) c u r v e , d e p e n d i n g upon w h e t h e r t h e c e l l was b e i n g c h a r g e d o r d i s c h a r g e d , c a n t h e n be u s e d t o d e t e r m i n e x f r o m t h e v o l t a g e , w i t h o u t a n y k n o w l e d g e o f t h e w e i g h t o f t h e M0O2 i n t h e c e l l . A n o t h e r b e n e f i t o f t h i s m e t h o d i s t h a t t h e r e s u l t i n g s a m p l e s a r e g e n e r a l l y h o m o g e n e o u s and t h e r e f o r e g i v e e x c e p t i o n a l l y c l e a r x - r a y p a t t e r n s . A c o n s t a n t - c u r r e n t t e c h n i q u e was u s e d t o p r e p a r e s a m p l e s 39 over ranges of x where dV/dx 0 because on these p l a t e a u s the v o l t a g e i s i n s e n s i t i v e to changes i n x . A f t e r c y c l i n g a c e l l s e v e r a l t imes at a c o n s t a n t c u r r e n t o f 0.5 mA between 1 and 2 v o l t s the c u r r e n t was i n t e r r u p t e d and the approximate l i t h i u m c o n t e n t o f the cathode was determined by e s t i m a t i n g Q j ( l v ) from the l e n g t h of the p r e v i o u s c y c l e and then u s i n g e q n . 4 - 8 . T h i s e s t i m a t e of x i s crude but s u f f i c e s because the p l a t e a u s a re m a n i f e s t a t i o n s of phase t r a n s i t i o n s i n the L i x M o 0 2 system (see s e c t i o n 5 . 1 ) , d u r i n g which the l i n e s i n the x - r a y d i f f r a c t i o n p a t t e r n s do not s h i f t . Only the i n t e n s i t i e s change d u r i n g phase t r a n s i t i o n s so e r r o r s i n x are u n i m p o r t a n t . 4 .6 P r e p a r a t i o n and x - r a y i n g of L i x M o 0 2 specimens L i x Mo02 specimens s u i t a b l e f o r t a k i n g D e b y e - S c h e r r e r photographs were prepared i n the g lovebox by a l l o w i n g c a p i l l a r y a c t i o n to draw a s l u r r y o f L i x Mo02 suspended i n e l e c t r o l y t e i n t o a t h i n w a l l e d Pyrex c a p i l l a r y ( o . d . < 0.3 mm) and then s e a l i n g the ends o f the tube wi th s i l i c o n e g r e a s e * * . T h i s p r o t e c t s the a i r s e n s i t i v e L i x Mo02 from the atmosphere when the specimen i s taken out o f the g lovebox to be x - r a y e d . S i n c e both the g l a s s and the e l e c t r o l y t e are amorphous they do not produce any d i f f r a c t i o n l i n e s and a l though they do cause some d i f f u s e low ang le s c a t t e r i n g most o f the L i x Mo02 l i n e s are e a s i l y r e s o l v e d . V e r y l i t t l e m a t e r i a l i s r e q u i r e d to make a spec imen . A drop o f e l e c t r o l y t e mixed wi th a few m i l l i g r a m s of L i x M o 0 2 r which may be scraped from the cathode s u b s t r a t e of a d i s s a s s e m b l e d c e l l or * * T h i s t e c h n i q u e i s d e s c r i b e d i n more d e t a i l by Wainwright (1979) . 40 taken from a sample prepared by n - b u t y l l i t h i a t i o n , i s s u f f i c i e n t . A f t e r a c a p i l l a r y has been loaded and sealed i t i s mounted on a specimen h o l d e r , which f i t s i n t o the x-ray camera, using e i t h e r Apiezon Q-grease or P l a s t i c e n e . The mounted c a p i l l a r y i s then a l i g n e d along the camera a x i s (see F i g . 10) and f i n a l l y , a s t r i p of no-screen x-ray f i l m (Kodak) i s placed around the i n s i d e perimeter of the camera. The e n t i r e process of pre p a r i n g and mounting a specimen takes l e s s than 20 min. The x-ray photographs were made with f i l t e r e d CuK« r a d i a t i o n from a P h i l i p s model PW 1009 x-ray g e n e r a t o r , using a Debye-Scherrer camera 11.483 cm i n diameter with a entrance a p e r t u r e of 1 mm. An exposure time of 3 hr was used, d u r i n g which the specimen was r o t a t e d s l o w l y to reduce the s p o t t i n e s s of the d i f f r a c t i o n l i n e s . Some of the Li xMo02 d i f f r a c t i o n p a t t e r n s obtained i n t h i s manner are shown i n F i g . 19. The q u a l i t y of these p a t t e r n s i s comparable to that of the d i f f r a c t i o n p a t t e r n of pure M0O2 ( F i g . 19a), i n d i c a t i n g t h a t no a p p r e c i a b l e decomposition occurred d u r i n g the exposure time. N o t i c e a b l e s h i f t i n g of the l i n e s was not observed unless the specimen was not sealed p r o p e r l y , or was s t o r e d o u t s i d e the glovebox f o r more than about 8 h r s . 4.7 Measurement of Li xMo02 d i f f r a c t i o n p a t t e r n s The p o s i t i o n (£) of a p a r t i c u l a r l i n e on the f i l m (see F i g . 17) was determined using a f i l m i l l u m i n a t o r equipped with a v e r n i e r s c a l e which could be read to +.005 cm. The corresponding Bragg angle 6 was c a l c u l a t e d using the r e l a t i o n 6 = 90°(£/L), 41 where L i s the distance between the centers of forward scattered and backscattered d i f f r a c t i o n rings. Film shrinkage, which generally amounted to less than 0.2% was corrected for by measuring the distance L for each f i l m . F i g . 17 - Measuring l i n e position (£). Line i n t e n s i t i e s were v i s u a l l y estimated to be either very strong (VS), strong (S), medium (M), f a i n t (F) or very f a i n t (VF). A v i s u a l estimate was used because in order to resolve many of the weaker l i n e s i t was necessary to overexpose the strong l i n e s , thereby making accurate i n t e n s i t y measurements poin t l e s s . 42 5 R e s u l t s end D i s c u s s i o n As d i s c u s s e d i n s e c t i o n 3.4, the x - r a y powder d i f f r a c t i o n p a t t e r n s of L i x M o 0 2 samples ca n , i n p r i n c i p l e , be used t o d e t e r m i n e how the s t r u c t u r e o f the M0O2 h o s t l a t t i c e changes as l i t h i u m i s i n t e r c a l a t e d . From th e s e changes one may a l s o be a b l e to i n f e r something about how the i n t e r c a l a t e d l i t h i u m atoms ar e a r r a n g e d i n the h o s t l a t t i c e . In p r a c t i c e , o n l y the v a r i a t i o n of the u n i t c e l l p arameters c o u l d be e x t r a c t e d from the e x p e r i m e n t a l d a t a . W i t h o u t a d i f f T a c t o m e t e r , the i n t e n s i t y o f the d i f f r a c t e d beams cannot be measured a c c u r a t e l y enough t o d e t e r m i n e how the atom p o s i t i o n s w i t h i n the u n i t c e l l change as l i t h i u m i s i n t e r c a l a t e d . The methods used t o i n d e x the x - r a y d i f f r a c t i o n p a t t e r n s and then o b t a i n the u n i t c e l l p arameters are d e s c r i b e d i n the a p p e n d i c e s . The f o l l o w i n g s e c t i o n s d i s c u s s the r e s u l t s o f t h i s a n a l y s i s . 5.1 Phase t r a n s i t i o n s The phase t r a n s i t i o n s d i s c u s s e d here are t r a n s i t i o n s between d i f f e r e n t c o m p o s i t i o n a l phases which o c c u r as l i t h i u m i s i n t e r c a l a t e d i n t o or removed from the h o s t l a t t i c e . X-ray powder d i f f r a c t i o n work has r e v e a l e d t h a t such t r a n s i t i o n s o c c u r i n s e v e r a l i n t e r c a l a t i o n systems. Some, l i k e L i x M o S 2 undergo i r r e v e r s i b l e phase t r a n s i t i o n s ( W a i n w r i g h t , 1979) w h i l e o t h e r s , n o t a b l y L i x V S e 2 e x h i b i t r e v e r s i b l e t r a n s i t i o n s (Murphy, 1979; W h i t t i n g h a m , 1 9 7 8 b ) i 2 . Because l i t h i u m i s such a weak x - r a y 1 2 T h i s i s not meant t o i m p l y t h a t the t r a n s i t i o n s are t h e r m o d y n a m i c a l l y r e v e r s i b l e , o n l y t h a t the r e v e r s e t r a n s i t i o n o c c u r s when the c e l l i s r e c h a r g e d . 43 s c a t t e r e r , x-ray d i f f r a c t i o n techniques cannot be used to d i s t i n g u i s h between d i f f e r e n t c o m p o s i t i o n a l phases un l e s s these phases have d i f f e r e n t host l a t t i c e s t r u c t u r e s . The d i f f r a c t i o n p a t t e r n of the host l a t t i c e i s u n a f f e c t e d u n l e s s the host l a t t i c e undergoes a s t r u c t u r a l phase t r a n s i t i o n c o n c u r r e n t l y with the c o m p o s i t i o n a l phase t r a n s i t i o n . Although i t i s c o n c e i v a b l e t h a t the s t r u c t u r e of a host l a t t i c e might remain v i r t u a l l y unchanged duri n g a c o m p o s i t i o n a l phase t r a n s i t i o n , i t i s c e r t a i n l y understandable that a change i n the l o c a l l i t h i u m content w i l l g e n e r a l l y cause a n o t i c e a b l e d i s t o r t i o n of the host l a t t i c e s t r u c t u r e , as i n the case of both L i x V S e 2 and Li xMoS2« During such a t r a n s i t i o n , the x-ray d i f f r a c t i o n p a t t e r n i s g e n e r a l l y a s u p e r p o s i t i o n of two d i s t i n c t d i f f r a c t i o n p a t t e r n s due to the two phases present i n the sample (see F i g . 18). The o n l y change which occurs as the t r a n s i t i o n proceeds i s that the d i f f r a c t i o n p a t t e r n of the i n i t i a l phase fades while the r e f l e c t i o n s due to the f i n a l phase become more i n t e n s e . The l i n e p o s i t i o n s do not change because the composition, and t h e r e f o r e the s t r u c t u r e , of both phases remains constant f o r the d u r a t i o n of the t r a n s i t i o n even though the average l i t h i u m content (x) i s changing. Only when a system c o n s i s t s of a s i n g l e homogeneous phase are the l i n e s expected to s h i f t . The s i m p l e s t method of checking i f phase t r a n s i t i o n s occur i n a l i t h i u m i n t e r c a l a t i o n system i s by studying the system's V(x) curve. During a phase t r a n s i t i o n dv/dx - 0 because the l o c a l l i t h i u m content i n both phases remains e s s e n t i a l l y c onstant f o r the d u r a t i o n of the t r a n s i t i o n * ^ s o the V(x) curve w i l l e x h i b i t a c h a r a c t e r i s t i c p l a t e a u over the range i n x where 44 the system i s a phase mixture. This e f f e c t has been observed in many systems including Li xMoS2 and L i x V S e 2 . The p o s s i b i l i t y that a plateau may occur in the absence of a phase t r a n s i t i o n i s remote because t h i s would require s i t e energies to be v i r t u a l l y independent of the l o c a l lithium content of the host l a t t i c e . The two plateaus in the V(x) curve of the Li xMo02 system (Fig. 16) indicate that LixMoC>2 occurs in three d i f f e r e n t compositional phases. These phases, which are l a b e l l e d I, I I , and I I I , have approximate compositions of M0O2, Li 1Mo02/ a n d L i M o 0 2 respectively and correspond to the steep portions of V(x). The compositional ranges over which these phases occur can thus be inferred from V(x) (see Table I I I ) . Within these single Table III - Compositional ranges of single phases of Li xMo0 2 I II III Discharge Recharge 0 < x < 0.25 0 < x < 0.15 0.46 < x < 0.75 0.44 < x < 0.60 0.95 < x < 1 0.95 < x < 1 phase regions the average lithium content (x) i s equal to the l o c a l lithium content of the host l a t t i c e ( i . e . Li xMo0 2 i s not only the average but also the microscopic composition of the sample), but for other compositions where the sample consists of a two phase mixture, t h i s does not apply. A sample of lithium content x in a mixed phase region does not contain any material with the microscopic composition Li xMo0 2. For example, a sample with a nominal composition of Lin.3Mo02 during discharge l^The thermodynamics of phase t r a n s i t i o n s in i n t e r c a l a t i o n systems are discussed in d e t a i l by McKinnon (1980). 4 5 a c t u a l l y c o n s i s t s o f m i x t u r e o f L i o . 2 5 M o 0 2 a n o " L * 0 . 4 6 M o O 2 * The presence o f a t r a n s i t i o n between phases I and I I i s c o n f i r m e d by the x - r a y d i f f r a c t i o n p a t t e r n s d e p i c t e d i n F i g . 18. Samples b ) , c) and d) are a l l phase m i x t u r e s , but a t d i f f e r e n t p o i n t s on the p l a t e a u . The p r o g r e s s i o n from a s t r o n g phase I I p a t t e r n and weak phase I p a t t e r n i n b) t o a weak phase I I p a t t e r n and s t r o n g phase I p a t t e r n i n d) i s c l e a r l y v i s i b l e . P a t t e r n s a) and e) d i f f e r s l i g h t l y from the c o r r e s p o n d i n g phase I I and phase I p a t t e r n s i n b) and d) because the s t r u c t u r e o f the h o s t l a t t i c e v a r i e s w i t h x i n the s i n g l e phase r e g i o n s , as d i s c u s s e d i n the next s e c t i o n . D i f f r a c t i o n p a t t e r n s o f a l l t h r e e phases are shown i n F i g . 1 9 . The i n t e r c a l a t i o n o f l i t h i u m i n t o M 0 O 2 i s c l e a r l y not a t h e r m o d y n a m i c a l l y r e v e r s i b l e p r o c e s s s i n c e d i f f e r e n t V(x) c u r v e s a r e o b t a i n e d f o r charge and d i s c h a r g e . The v o l t a g e s a t which the phase t r a n s i t i o n s o c c u r on d i s c h a r g e a re a p p r o x i m a t e l y 0 . 1 v o l t s lower than the v o l t a g e s a t which the c o r r e s p o n d i n g t r a n s i t i o n s o c c u r d u r i n g the r e c h a r g e . C o n s e q u e n t l y , the ranges i n c o m p o s i t i o n over which s i n g l e phases, e s p e c i a l l y phase I I , o c c u r depend upon whether l i t h i u m i s b e i n g i n t e r c a l a t e d or removed (see T a b l e I I I ) . A l t h o u g h the e x p e r i m e n t a l r e s u l t s p r e s e n t e d here do not e x p l a i n what causes t h i s " e l e c t r o c h e m i c a l h y s t e r e s i s " , we s u s p e c t t h a t i t may be analogous t o the h y s t e r e s i s commonly observed i n magnetic m a t e r i a l s . J u s t as a c o e r c i v e f o r c e i s r e q u i r e d t o n u c l e a t e domains and move g r a i n b o u n d a r i e s p a s t l a t t i c e d e f e c t s i n a magnetic system, an analogous " c o e r c i v e v o l t a g e " might be r e q u i r e d t o i n i t i a t e the f o r m a t i o n o f a new phase, and then move the phase b o u n d a r i e s 46 th r o u g h the LixMoC>2 i n t e r c a l a t i o n system, A) x = 0.58 phase I I b) x = 0.42 phase I & I I c) x a 0.28 phase I & I I d) x - 0.08 phase I & I I e) x = 0 phase I • 1 • 7 ' ( W •> 1 1 • '•fl • » ) • 34' 34' F i g . 18 - The phase I I t o I t r a n s i t i o n . Note the change i n r e l a t i v e i n t e n s i t y o f the low a n g l e d o u b l e t ( i n d i c a t e d by arrows) as the t r a n s i t i o n p r o c e e d s . Only a p o r t i o n o f the d i f f r a c t i o n p a t t e r n i s shown. The x v a l u e s f o r p a t t e r n s b ) , c ) , and d) are o n l y approximate because these samples were prepar e d u s i n g the c o n s t a n t - c u r r e n t t e c h n i q u e . F i g . 19 - Some L i MoO d i f f r a c t i o n p a t t e r n s a) Mo0„ ( p h a s e I ) X s a m p l e p r e p a r e d by r e a c t i n g Mo0_ and Mo i n vacuum b) MoO^ ( p h a s e I) sample p r e p a r e d by r e c h a r g i n g c e l l to 2.00 v o l t s c) L i S 8Mo0 ( p h a s e I I ) sample p r e p a r e d by r e c h a r g i n g c e l l t o 1.40 v o l t s d) ( p h a s e I I & I I I ) sample p r e p a r e d by t r e a t i n g Mo0 2 w i t h e x c e s s n - B u L i e) LiMoO- ( p h a s e I I I ) sample p r e p a r e d by d i s c h a r g i n g c e l l to 0.03 v o l t s 48 5.2 Unit c e l l parameters of LixMoC>2 The unit c e l l parameters of the host l a t t i c e for various values of x (in single phase regions) were determined by indexing LixMoC>2 d i f f r a c t i o n patterns, as described in Appendix A, and then using the USGS program described in Appendix B to refine the parameters. Indexing the d i f f r a c t i o n patterns i s f a i r l y d i f f i c u l t , in fact phase II and III patterns can be indexed in two ways and without quantitative i n t e n s i t y measurements i t i s impossible to select the correct indexing scheme. Fortunately t h i s does not seriously a f f e c t the interpretation of the r e s u l t s . The dependence of the unit c e l l parameters and volume upon x are depicted in Figs. 20 and 21. The parameters were obtained from the d i f f r a c t i o n patterns of Li xMo02 samples prepared by either charging or discharging c e l l s to a predetermined voltage, as described in section 4 . 4 , and l i k e V(x) the structure appears to change rev e r s i b l y within single phase regions. The structures of the individual constituents of phase mixtures could not be determined because too few l i n e s can be c l e a r l y resolved when two d i f f r a c t i o n patterns are superimposed. However, judging by the patterns depicted in F i g . 18, the structures of the individual constitutents appear to remain s t a t i c during the t r a n s i t i o n . Phase I and II structures exhibit a pronounced dependence upon x, unlike phase III which appears to have only a single well defined structure. This may be due to the comparatively narrow compositional range over which phase III occurs. The pseudotetragonal parameters calculated from the monoclinic phase 49 6.0 Phase I ° 5 5.8-ions 5.6J c a> E 5.4-Q Cell 5.2-Unit 5.0-4 8 o I22n a> |l20H 118 0.25 -fi f t 0.25 | Phase U 0.50 tt K*H 0.50 0.75 0.75 M OBJ, 0%D I F i g . 20 - U n i t c e l l p a r a m e t e r s v s . x. The two s e t s of p o i n t s f o r p hase I I and I I I c o r r e s p o n d to t h e two p o s s i b l e i n d e x i n g schemes. E r r o r b a r s i n d i c a t e t h e s e n s i t i v i t y of x t o a + 0.01 v o l t e r r o r i n t h e v o l t a g e . Square p o i n t s a t x = 0 a r e t h e u n i t c e l l p a r a m e t e r s of Mo0„ as g i v e n by B r a n d t & S k a p s k i ( 1 9 6 7 ) . 50 F i g . 21 - U n i t c e l l volume v s . x. The p o i n t s c o r r e s p o n d d i r e c t l y t o t h o s e i n F i g . 20. T h e r e i s no a p p r e c i a b l e d i f f e r e n c e i n t h e volume f o r t h e two p o s s i b l e i n d e x i n g schemes. 51 I I I p a r a m e t e r s a r e : a ' = 5 . 1 6 7 + . 0 0 3 A c ' = 2 . 7 8 2 + . 004 A B o t h i n d e x i n g s c h e m e s g i v e t h e same p s e u d o - t e t r a g o n a l p a r a m e t e r s b e c a u s e i n t e r m s o f t h e m o n o c l i n i c u n i t c e l l p a r a m e t e r s t h e y o n l y d i f f e r i n t h a t t h e v a l u e s o f b and c s i n f 3 a r e i n t e r c h a n g e d . T h e s e r e s u l t s a r e i n f a i r a g r e e m e n t w i t h M u r p h y e t a l ( 1 9 7 8 ) , who r e p o r t e d a ' = 5 . 1 3 ft and c ' = 2 . 7 8 A f o r L i M o 0 2 p r e p a r e d by n - b u t y l 1 i t h i a t i o n . The m a j o r e f f e c t o f i n t e r c a l a t i n g l i t h i u m on t h e s t r u c t u r e o f t h e h o s t l a t t i c e i s an e x p a n s i o n o f t h e l a t t i c e p e r p e n d i c u l a r t o t h e m o n o c l i n i c a - a x i s ( i . e . p e r p e n d i c u l a r t o t h e c h a n n e l s ) . B o t h b and c s i n B i n c r e a s e by ^5% when one e q u i v a l e n t o f l i t h i u m i s i n t e r c a l a t e d w h i l e t h e a - a x i s a c t u a l l y c o n t r a c t s s l i g h t l y a s x i n c r e a s e s , b u t o n l y i n p h a s e I. T h r o u g h o u t p h a s e I I and I I I a r e m a i n s e s s e n t i a l l y c o n s t a n t . The v o l u m e o f t h e u n i t c e l l i n c r e a s e s by a t o t a l o f ^13%. A s e x p e c t e d t h e o v e r a l l c h a n g e i n t h e s h a p e o f t h e u n i t c e l l i s r e l a t i v e l y s m a l l . 5 . 3 O r d e r i n g , s t r a i n e f f e c t s , and s u p e r l a t t i c e s To g a i n some i n s i g h t i n t o why p h a s e t r a n s i t i o n s o c c u r d u r i n g .the i n t e r c a l a t i o n o f L i x M o 0 2 and what t h e p h a s e s may a c t u a l l y b e , i t i s u s e f u l t o i n t e r p r e t t h e o b s e r v e d p r o p e r t i e s o f t h e L i x M o 0 2 s y s t e m i n t e r m s o f o r d e r i n g and s t r a i n e f f e c t s . The more g e n e r a l t h e o r e t i c a l a s p e c t s o f t h e s e t o p i c s a r e d i s c u s s e d i n d e t a i l b y M c K i n n o n ( 1 9 8 0 ) ; h e r e we w i l l o n l y b r i e f l y o u t l i n e how t h e y may a p p l y t o t h e L i x M o 0 2 s y s t e m . B e c a u s e t h e a tom p o s i t i o n s , p a r t i c u l a r l y t h e l i t h i u m atom 52 positions, cannot be determined using x-ray powder d i f f r a c t i o n techniques, the v a l i d i t y of t h i s interpretation cannot be ascertained. Nevertheless i t does provide some useful insi g h t s . The basic shape of the V(x) curve can be -explained simply in terms of one-dimensional ordering of the intercalated lithium atoms along the chains of s i t e s because of repulsive interactions between near neighbors. The intercalated lithium may be p a r t i a l l y ionic so e l e c t r o s t a t i c repulsion could be responsible for such an i n t e r a c t i o n . For s i m p l i c i t y we s h a l l assume that only one type of s i t e , either octahedral or tetrahedral, can be occupied and that a l l s i t e s of t h i s type are a l i k e . In such a system the s i t e s would f i r s t f i l l randomly but eventually, to minimize the repulsive interactions, the lithium atoms w i l l order, occupying every n'th s i t e along the chain. Once every n'th s i t e i s f i l l e d V(x) drops sharply because the remaining s i t e s are less favourable. The sharp drops in V(x) at x = h and x = 1 can be attributed to ordered states where every fourth and second s i t e , respectively, i s occupied (Fig. 22). If the repulsion between nearest neighbors i s strong enough the remaining s i t e s cannot be f i l l e d and the voltage drops to zero. However, short range e l e c t r o s t a t i c repulsions alone cannot account for f i r s t - o r d e r phase t r a n s i t i o n s . The observed phase t r a n s i t i o n s can be explained in terms of s t r a i n induced interactions due to the energy required to deform the host l a t t i c e . The s t r a i n energy required to deform the l a t t i c e in the v i c i n i t y of a given s i t e s u f f i c i e n t l y to accommodate a lithium atom w i l l depend upon the degree to which the l a t t i c e has already been distorted by intercalated atoms 53 o, o-@-o o- 0 - - 0 - - 0 - - 0 b) 0~O~O o- o~o~o~ o c) -o~@-o o--@--o~ o F i g . 22 - P o s s i b l e o n e - d i m e n s i o n a l a r r a n g e m e n t s o f i n t e r c a l a t e d l i t h i u m a toms a l o n g t h e c h a i n s o f s i t e s : a) r a n d o m l y o c c u p i e d s i t e s i n p h a s e I, b) e v e r y f o u r t h s i t e o c c u p i e d i n p h a s e I I and c) e v e r y s e c o n d s i t e o c c u p i e d i n p h a s e I I I . o c c u p y i n g n e a r b y s i t e s . Hence t h e s i t e e n e r g y i s a f f e c t e d b y a s t r a i n - m e d i a t e d i n t e r a c t i o n w i t h o t h e r o c c u p i e d s i t e s . M c K i n n o n (1980) shows t h a t f o r a t u n n e l l e d h o s t l a t t i c e s t r u c t u r e l i k e M0O2 t h e s t r a i n m e d i a t e d i n t e r a c t i o n c o n s i s t s o f two p a r t s : a l o n g r a n g e a t t r a c t i v e i n t e r a c t i o n and a s h o r t r a n g e i n t e r a c t i o n w h i c h i s a t t r a c t i v e a l o n g t h e t u n n e l s b u t r e p u l s i v e p e r p e n d i c u l a r t o t h e t u n n e l s . B e c a u s e o f t h e a t t r a c t i v e i n t e r a c t i o n s f i r s t - o r d e r p h a s e t r a n s i t i o n s , d u r i n g w h i c h l i t h i u m - r i c h and l i t h i u m - p o o r p h a s e s s e p a r a t e , a r e t o be e x p e c t e d . The t r a n s i t i o n f r o m p h a s e I t o I I c a n be i n t e r p r e t e d a s a t r a n s i t i o n f r o m a s t a t e w i t h r a n d o m l y o c c u p i e d s i t e s t o an o r d e r e d s t a t e w i t h e v e r y f o u r t h s i t e a l o n g t h e c h a i n s f i l l e d . The s e c o n d t r a n s i t i o n f r o m p h a s e I I t o I I I may c o r r e s p o n d t o a s i m i l a r t r a n s i t i o n t o an o r d e r e d s t a t e where e v e r y s e c o n d s i t e i s f i l l e d . I f t h e l i t h i u m a t o m s i n Li u MoC*2 r e a l l y do o c c u p y e v e r y f o u r t h s i t e a l o n g t h e c h a i n s t h e n t h e r e i s a p o s s i b i l i t y t h a t a s u p e r l a t t i c e s t r u c t u r e may f o r m . Two p o s s i b l e a r r a n g e m e n t s o f 54 the intercalated lithium atoms are shown in F i g . 23. Because of the strain-mediated repulsive interaction between occupied s i t e s in adjacent chains, one might expect a staggered arrangement as in b). Structure a) i s periodic over the indicated unit c e l l (with parameters a 0 , b 0, c D and g Q) but the arrangement of the occupied s i t e s in b) i s not. The presence of intercalated lithium atoms w i l l also a f f e c t the positions of nearby host l a t t i c e atoms so, for t h i s arrangement, the host l a t t i c e i t s e l f w i l l no longer be t r u l y periodic in the o r i g i n a l unit c e l l . Therefore an enlarged superlattice c e l l with parameters a = a Q , b = b Q, c = 2c 0, B = 3 D i s the true unit c e l l for structure b). However, since the host l a t t i c e atoms only s h i f t s l i g h t l y the host s t i l l remains almost periodic over the o r i g i n a l unit c e l l . Consequently the only expected difference between the d i f f r a c t i o n patterns of a) and b) would be the presence of some f a i n t "superlattice l i n e s " in pattern b). Except for these, a l l the l i n e s in the d i f f r a c t i o n pattern could be indexed in terms of the o r i g i n a l unit c e l l . The unexplained l i n e s observed in L i t M0O2 patterns (see Table VI) suggest that such a superlattice may ac t u a l l y form in phase I I . These l i n e s do not appear to be due to either impurities or decomposition products since they are observed consistently, but only in phase I I . One l i n e in p a r t i c u l a r , the fa i n t low angle l i n e corresponding to d = 5.5 A, suggests an enlarged unit c e l l , since the most widely separated l a t t i c e planes (the 101 planes) in M0O2 correspond to d = 4.9 ft. 55 F i g . 23 - Two p o s s i b l e t h r e e - d i m e n s i o n a l a r r a n g e m e n t s o f t h e o c c u p i e d s i t e s f o r L i ^ M o 0 2 a) t h i s a r r a n g e m e n t i s p e r i o d i c i n t h e i n d i c a t e d u n i t c e l l b u t p l a c e s l i t h i u m a t o m s i n a d j a c e n t c h a i n s c l o s e t o g e t h e r , b) t h i s a r r a n g e m e n t m a x i m i z e s t h e d i s t a n c e b e t w e e n o c c u p i e d s i t e s i n a d j a c e n t c h a i n s b u t i s no l o n g e r p e r i o d i c o v e r t h e i n d i c a t e d c e l l . 6 C o n c l u s i o n The p u r p o s e o f t h i s t h e s i s i s t o r e l a t e t h e e l e c t r o c h e m i c a l p r o p e r t i e s o f t h e Li xMoC>2 s y s t e m t o t h e s t r u c t u r a l c h a n g e s w h i c h a c c o m p a n y i n t e r c a l a t i o n . D e b y e - S c h e r r e r x - r a y powder p h o t o g r a p h y h a s b e e n u s e d t o d e t e c t p h a s e t r a n s i t i o n s and v a r i a t i o n s i n t h e u n i t c e l l p a r a m e t e r s . T h r e e d i s t i n c t c o m p o s i t i o n a l p h a s e s o f L i x M o 0 2 h a v e b e e n i d e n t i f i e d . B e c a u s e o f h y s t e r e s i s e f f e c t s t h e c o m p o s i t i o n a l r a n g e s o v e r w h i c h t h e s e o c c u r d e p e n d upon w h e t h e r t h e c e l l i s b e i n g c h a r g e d o r d i s c h a r g e d ( i . e . x i n c r e a s i n g o r d e c r e a s i n g , r e s p e c t i v e l y ) . On d i s c h a r g e ( r e c h a r g e ) p h a s e I 56 c o r r e s p o n d s t o 0 < x < 0 . 2 5 (0 < x < 0 . 1 5 ) , p h a s e I I c o r r e s p o n d s t o 0 . 4 6 < x < 0 . 7 5 ( 0 . 4 4 < x < 0 . 6 0 ) , and p h a s e I I I c o r r e s p o n d s t o 0 . 9 5 < x < 1 i n b o t h c a s e s . In g e n e r a l t h e h o s t l a t t i c e e x p a n d s a s t h e l i t h i u m c o n t e n t i n c r e a s e s (^13% f o r L i M o 0 2 ) . W i t h i n s i n g l e p h a s e r e g i o n s t h e s t r u c t u r e c h a n g e s r e v e r s i b l y , a s d o e s t h e v o l t a g e o f L i / M o 0 2 c e l l s . T h e f i r s t - o r d e r t r a n s i t i o n s ( w h i c h c o r r e s p o n d t o p l a t e a u s i n t h e c h a r g e - d i s c h a r g e c u r v e ) b e t w e e n t h e s e p h a s e s a r e a c c o m p a n i e d b y d i s c o n t i n u o u s s t r u c t u r a l c h a n g e s . H y s t e r e s i s e f f e c t s , p r o b a b l y due t o p h a s e b o u n d a r y s t r e s s e s , i n d i c a t e t h a t t h e t r a n s i t i o n s a r e n o t t h e r m o d y n a m i c a l l y r e v e r s i b l e . M o s t o f t h e o b s e r v a t i o n s c a n be u n d e r s t o o d q u a l i t a t i v e l y i n t e r m s o f a l a t t i c e g a s w i t h i n t e r a c t i o n s ; s t r a i n - m e d i a t e d a t t r a c t i v e i n t e r a c t i o n s b e t w e e n o c c u p i e d s i t e s c a u s e f i r s t - o r d e r p h a s e t r a n s i t i o n s and s h o r t r a n g e r e p u l s i v e i n t e r a c t i o n s c a u s e o r d e r i n g o f t h e i n t e r c a l a t e d l i t h i u m . A d d i t i o n a l work w i t h more p o w e r f u l e x p e r i m e n t a l t e c h n i q u e s i s r e q u i r e d b e f o r e t h e s t r u c t u r e o f t h e h o s t l a t t i c e c a n be f u l l y d e t e r m i n e d . D e b y e - S c h e r r e r p h o t o g r a p h y i s o f l i m i t e d u s e f u l n e s s w i t h a c o m p l e x s t r u c t u r e l i k e L i x M o 0 2 b e c a u s e o n l y t h e u n i t c e l l p a r a m e t e r s c a n be d e t e r m i n e d , and e v e n t h i s r e q u i r e s a s s u m p t i o n s a b o u t t h e f r a c t i o n a l c o - o r d i n a t e s o f t h e h o s t l a t t i c e a t o m s . I t w o u l d be r e a s s u r i n g t o a c t u a l l y d e t e r m i n e t h e p o s i t i o n s o f t h e h o s t l a t t i c e a t o m s i n p h a s e I I and I I I . T h i s c o u l d p r o b a b l y be d o n e w i t h a d i f f T a c t o m e t e r c a p a b l e o f a c c u r a t e l y m e a s u r i n g t h e l i n e i n t e n s i t i e s o f powder p a t t e r n s . A n o t h e r a d v a n t a g e o f a d i f f T a c t o m e t e r w o u l d be t h a t c a t h o d e s c o u l d be x - r a y e d i n s i t u u s i n g a t e c h n i q u e s i m i l a r t o t h e one 57 d e s c r i b e d by C h i a n e l l i e t a l ( 1 9 7 8 ) . S u c h a " d y n a m i c x - r a y d i f f r a c t i o n " t e c h n i q u e a v o i d s h a v i n g t o a s s e m b l e and t h e n d i s s a s s e m b l e a c e l l t o p r e p a r e e a c h x - r a y s p e c i m e n , t h e r e b y g r e a t l y s p e e d i n g t h e c o l l e c t i o n o f d a t a . B e c a u s e t h e h o s t l a t t i c e s t r u c t u r e i s q u i t e c o m p l i c a t e d i t m i g h t a l s o be u s e f u l t o h a v e i n t e r c a l a t e d s i n g l e c r y s t a l s f o r a d d i t i o n a l x - r a y d i f f r a c t i o n s t u d i e s b u t i t i s n o t c l e a r how t h e s e c o u l d be p r e p a r e d . P r e l i m i n a r y s t u d i e s i n d i c a t e t h a t s i n g l e c r y s t a l s a r e s h a t t e r e d when l i t h i u m i s i n t e r c a l a t e d , p r e s u m a b l y b e c a u s e o f p h a s e b o u n d a r y s t r e s s e s . U l t i m a t e l y , i t w o u l d be v e r y u s e f u l t o d e t e r m i n e t h e p o s i t i o n s o f t h e i n t e r c a l a t e d l i t h i u m a t o m s b u t t h i s w i l l r e q u i r e n e u t r o n d i f f r a c t i o n s t u d i e s s i n c e l i t h i u m i s s u c h a weak x - r a y s c a t t e r e r . Once t h e h o s t l a t t i c e s t r u c t u r e o f L i x M o 0 2 i s u n d e r s t o o d , d e t e r m i n i n g t h e p o s i t i o n s o f t h e l i t h i u m a t o m s by n e u t r o n d i f f r a c t i o n s h o u l d be s t r a i g h t f o r w a r d . 5 8 BIBLIOGRAPHY B e s e n h a r d , J . 0 . and E i c h i n g e r , G . (1976) J . E l e c t r o a n a l . Chem. 68 p . 1 B r a n d t , B . G . and S k a p s k i , A . C . (1967) A c t a C h e m . S c a n d . 2_1 p . 661 C h i a n e l l i , R. R . , S c a n l o n , J . C . and R a o , B . M. L . (1978) J . E l c h e m . S o c . 125 p . 1563 C u l l i t y , B e r n a r d D e n n i s (1956) E l e m e n t s o f X - r a y D i f f r a c t i o n , A d d i s o n - W e s l e y , R e a d i n g , M a s s . D i n e s , M. B . (1974) J o u r n a l o f C h e m i c a l E d u c a t i o n _51 p . 221 E b e r t , L . B . (1976) A n n u a l R e v i e w o f M a t e r i a l s S c i e n c e 6 p . 181 E v a n s ( J r . ) , H . T . , A p p l e m a n , D. E . and H a n d w e r k e r , D. S . (1963) A m e r i c a n C r y s t a l l o g r a p h i c A s s o c i a t i o n A n n u a l M e e t i n g , C a m b r i d g e , M a s s . , A b s t r a c t #E-10 J o h n s o n , 0 . W. (1964) P h y s . R e v . 136 p . A284 K i n g s b u r y , P . I., O h l s o n , W. D. and J o h n s o n , 0 . W. (1968) P h y s . R e v . 175 p . 1099 K l u g , H a r o l d P . and A l e x a n d e r , L e r o y E . (1974) X - r a y D i f f r a c t i o n  P r o c e d u r e s f o r P o l y c r y s t a l l i n e and A m o r p h o u s M a t e r i a l s , 2nd e d . , J . W i l e y & S o n s , New Y o r k M a g n e l i , A . , A n d e r s s o n , G . , B l o m b e r g , B . and K h i l b o r g , L . (1952) A n a l . C h e m . 24^  p . 1998 M c K i n n o n W. R. (1980) P h . D. T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a M e l l o r , J . W. (1931) A C o m p r e h e n s i v e T r e a t i s e on I n o r g a n i c and  T h e o r e t i c a l C h e m i s t r y , V o l . X I , J . W i l e y & S o n s , New Y o r k M u r p h y , D. W . , D i S a l v o , F . J . , C a r i d e s , J . N . and W a s z c z a k , J . V . (1978) M a t . R e s . B u l l . 13 p . 1395 M u r p h y , D . W. and C a r i d e s , J . N . (1979) J . E l c h e m . S o c . 128 p . 349 R o g e r s , D. B . , S h a n n o n , R. D . , S l e i g h t , A . W. and G i l l s o n , J . L . (1969) I n o r g . C h e m . 8 p . 841 S c h a f h a ' u t l , C . (1841) J . P r a k t . C h e m . 21. p . 129 W a i n w r i g h t , D. S . (1979) M. S c . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a W h i t t i n g h a m , M. S . (1978a) P r o g . S o l i d S t a t e Chem. 12 p . 41 59 Whi t t i n g h a m , M. S. (1978b) Mat. Res. B u l l . 13 p. 959 Wyckoff, Ralph W. G. (1963) C r y s t a l S t r u c t u r e s , V o l . I , 2nd ed., J . W i l e y & Sons, New York 60 Appendix A - I n d e x i n g Li xMoO? p a t t e r n s The f i r s t and most d i f f i c u l t s t e p towards e x t r a c t i n g u n i t c e l l parameters from powder d i f f r a c t i o n d a t a i s i n d e x i n g the d i f f r a c t i o n p a t t e r n ( i . e . i d e n t i f y i n g the M i l l e r i n d i c e s of the observed l i n e s ) . Once the p a t t e r n i s i n d e x e d , s u b s t i t u t i n g h, k, 1 and &hkl i n t o eqn. 3-2 f o r each observed l i n e g i v e s a system of e q u a t i o n s which can e a s i l y be s o l v e d f o r a, b, c and 6. S i n c e the observed d - s p a c i n g s ( d ^ g ) are s u b j e c t to e x p e r i m e n t a l e r r o r a l e a s t squares a n a l y s i s i s u s u a l l y used to r e f i n e the u n i t c e l l p a r a m e t e r s . I t i s i m p o r t a n t to note t h a t the e r r o r i n d 0 b s i s s t r o n g l y dependent upon e. From the Bragg law (eqn. 3-1) i t f o l l o w s t h a t Ad/A0 <* c o s e / s i n 2 e ( A - l ) hence the u n c e r t a i n t y i n d 0 b s due to the i n h e r e n t measurement e r r o r (A B) . i n the l i n e p o s i t i o n d e c r e a s e s as e i n c r e a s e s . T h e r e f o r e i t i s p a r t i c u l a r l y i m p o r t a n t to index " h i g h - a n g l e " l i n e s . In p r a c t i c e o n l y l i n e s i n the range 6 <. 45° were used because i t i s d i f f i c u l t t o index or even r e s o l v e any l i n e s i n the b a c k s c a t t e r i n g r e g i o n (see F i g . 1 9 ) * . A t r i a l and e r r o r approach i s g e n e r a l l y used to index m o n o c l i n i c and lower symmetry p a t t e r n s because no s i m p l e d i r e c t methods are a v a i l a b l e . To b e g i n w i t h , s e v e r a l l i n e s a r e a s s i g n e d t e n t a t i v e i n d i c e s and the u n i t c e l l parameters are c a l c u l a t e d on the b a s i s o f t h e s e . The r e s u l t i n g u n i t c e l l parameters are used to g e n e r a t e the e n t i r e t h e o r e t i c a l d i f f r a c t i o n p a t t e r n which i s then compared to the observed p a t t e r n . I f a r e a s o n a b l e f i t i s * T h i s i s because the number of l i n e s , the Ka s p l i t t i n g and the l i n e w i d t h s a l l i n c r e a s e w i t h e. 61 o b t a i n e d a d d i t i o n a l l i n e s a r e indexed and the u n i t c e l l p arameters may be r e f i n e d , o t h e r w i s e , i f the p a t t e r n s do not match, the e n t i r e p r o c e s s must be re p e a t e d u n t i l a s u i t a b l e i n d e x i n g scheme i s a r r i v e d a t . Computer programs which use such a p r o c e d u r e t o index d i f f r a c t i o n p a t t e r n s a r e a v a i l a b l e , but u n f o r t u n a t e l y t h e y a re u n s u i t a b l e f o r i n d e x i n g L i xMo02 p a t t e r n s . The problem w i t h L i x M o 0 2 i s t h a t because the system i s p s e u d o - t e t r a g o n a l the l i n e s i n the d i f f r a c t i o n p a t t e r n tend to be bunched c l o s e t o g e t h e r w i t h most o f them too weak-to be v i s i b l e (see the c a l c u l a t e d LiMo02 p a t t e r n l i s t e d a t the end of Appendix C ) . Co n s e q u e n t l y programs l i k e USGS (Appendix B) which do not take l i n e i n t e n s i t i e s i n t o account are i n c a p a b l e o f i n d e x i n g LixMoC>2 p a t t e r n s . On the o t h e r hand, more s o p h i s t i c a t e d programs which match i n t e n s i t i e s as w e l l as l i n e p o s i t i o n s r e q u i r e r e a s o n a b l y a c c u r a t e i n t e n s i t i e s ( l o b s ) such as can be o b t a i n e d u s i n g a d i f f r a c t o m e t e r . S i n c e I Q b s w a s o n l y d etermined q u a l i t a t i v e l y automated p r o c e d u r e s c o u l d not be used to compare c a l c u l a t e d and observed p a t t e r n s . L i x M o 0 2 p a t t e r n s were indexed by: 1) making an educated guess a t the i n d i c e s of ^ 10 l i n e s ; 2) c a l c u l a t i n g t e n t a t i v e u n i t c e l l parameters w i t h the USGS program on the b a s i s of these l i n e s ; 3) g e n e r a t i n g a t h e o r e t i c a l p a t t e r n w i t h the CALINE program; 4) m a n u a l l y c h e c k i n g t o see i f the t h e o r e t i c a l and observed p a t t e r n s match; 5) i n d e x i n g a d d i t i o n a l l i n e s i f the p a t t e r n s match or r e t u r n i n g to s t e p 1) i f th e y d o n ' t . 62 T h i s p r o c e s s i s q u i t e t e d i o u s so i t i s i m p o r t a n t t o s t a r t w i t h a r e a s o n a b l y good guess a t the i n d i c e s . The s i m p l e s t way of i d e n t i f y i n g l i n e s i s by comparing s e v e r a l p a t t e r n s of d i f f e r e n t c o m p o s i t i o n s w i t h i n a s i n g l e phase. S i n c e the l a t t i c e s t r u c t u r e changes c o n t i n u o u s l y i n s i n g l e phase r e g i o n s the l i n e s s h i f t g r a d u a l l y . By g r a p h i n g the l i n e p o s i t i o n s v s . x one can f o l l o w the motion of i n d i v i d u a l l i n e s i n response t o the changing l i t h i u m c o n t e n t . P r o v i d e d t h a t one o f the p a t t e r n s w i t h i n a phase has a l r e a d y been i n d e x e d , one can thus i d e n t i f y l i n e s i n the o t h e r p a t t e r n s . Phase I p a t t e r n s can be indexed u s i n g the M0O2 p a t t e r n as a r e f e r e n c e but f o r phase I I and I I I a d i f f e r e n t method must be used t o index a r e f e r e n c e p a t t e r n i n each of thes e phases. Phase I I and I I I r e f e r e n c e p a t t e r n s were indexed on the b a s i s o f s e v e r a l s i m p l i f y i n g a s s u m p t i o n s . The b a s i c r a t i o n a l e behind a l l o f these i s t h a t s i n c e Li xMoC>2 i s an i n t e r c a l a t i o n system the s t r u c t u r e o f the ho s t l a t t i c e cannot change r a d i c a l l y . One a s s u m p t i o n , which has a l r e a d y been i m p l i c i t i n the p r e c e e d i n g d i s c u s s i o n , i s t h a t the system can be indexed on the b a s i s of a m o n o c l i n i c u n i t c e l l . S e c o n d l y , the u n i t c e l l p arameters a re assumed to change o n l y s l i g h t l y ( i . e . <10%) . F i n a l l y , any changes i n the f r a c t i o n a l c o - o r d i n a t e s o f the host l a t t i c e atoms are assumed to have a n e g l i g i b l e e f f e c t on the l i n e i n t e n s i t i e s . T h i s l a s t assumption i s c r u c i a l because of the tremendous number of r e f l e c t i o n s which a re produced by a m o n o c l i n i c c r y s t a l . For i n s t a n c e the CALINE program g e n e r a t e s ^130 l i n e s ( c o u n t i n g r e f l e c t i o n s due to p l a n e s of a form o n l y once) i n the i n t e r v a l 0 _< 6 < 45° f o r M0O2 but of these o n l y 'MO 63 a r e s t r o n g enough to be v i s i b l e , a c c o r d i n g the the c a l c u l a t i o n , and o n l y 23 s e p a r a t e l i n e s can be r e s o l v e d i n the a c t u a l M 0 O 2 p a t t e r n (see Table V ) . U n l e s s the hundred odd v e r y weak r e f l e c t i o n s are assumed to r e m a i n weak a f t e r l i t h i u m i s i n t e r c a l a t e d i t would be a f o r m i d a b l e t a s k t o index LixMoC>2 p a t t e r n s w i t h o u t t h e a i d o f d i f f T a c t o m e t e r measurements and a s o p h i s t i c a t e d i n d e x i n g program. S e l f - c o n s i s t e n t i n d e x i n g schemes f o r r e f e r e n c e p a t t e r n s i n phase I I and I I I were e s t a b l i s h e d by f i r s t t e n t a t i v e l y i n d e x i n g s t r o n g , low a n g l e (0 < 20°) l i n e s and then u s i n g t h e s e t o c a l c u l a t e the expected d ^ k l f o r r e l a t e d s t r o n g l i n e s a t h i g h e r a n g l e s . I f the expected l i n e s a r e not observed then the low-angle l i n e s have not been indexed c o r r e c t l y and a d i f f e r e n t scheme must be used. O t h e r w i s e , i f l i n e s w i t h the expected d-s p a c i n g s a re observed they a re indexed s e l f - c o n s i s t e n t l y . In t h i s manner l o w - a n g l e l i n e s , which a re e a s i e r t o i n d e x , because t h e r e are fewer o f them, may be used t o index the h i g h a n g l e l i n e s which a re r e q u i r e d t o c a l c u l a t e a c c u r a t e u n i t c e l l p a r a m e t e r s . T h i s p r o c e d u r e i s bes t i l l u s t r a t e d w i t h a few examples. One group of l i n e s which can e a s i l y be indexed i n any Li xMo02 d i f f r a c t i o n p a t t e r n a re the (Okk) l i n e s w i t h k = 1,2,3. The ( O i l ) l i n e can be i d e n t i f i e d i m m e d i a t e l y because i t i s by f a r the most i n t e n s e l i n e and w e l l s e p a r a t e d from a l l o t h e r s t r o n g l i n e s . From e q u a t i o n 3-2 i t i s easy t o show t h a t d 0 1 1 = 2 d 0 2 2 = 3 d 0 3 3 (A-2) so i f , f o r example, we wish t o index the LiMoC>2 p a t t e r n l i s t e d i n T a b l e V I I I ; 64 3.602 A < d 0 1 1 < 3.690 A=>1.801 A < d 0 2 2 < 1.845 A =>1.201 A < d 0 3 3 < 1.230 A R e f e r r i n g to the observed p a t t e r n we can i d e n t i f y the (022) and (033) l i n e s : 1.820 & < d 0 2 2 < 1.833 A; 1.216 A < d 0 3 3 < 1.222 A. A second group of l i n e s which can be indexed once the (Okk) l i n e s have been i d e n t i f i e d a re the (Okl) l i n e s . These are expected to o c c u r i n c l o s e l y spaced ( O k l ) , ( 0 1 k ) p a i r s ( s i n c e f o r M0O2, d g k l ~ d 0 1 k ) a n d must s a t i s f y the r e l a t i o n 2 2 2 = ~T~  + ~T~  ( A _ 3 ) 9 d 0 3 3 d 0 k l d 0 1 k In f a c t , the ( 0 2 0 ) , (002) and ( 0 1 3 ) , (031) p a i r s can be i d e n t i f i e d w i t h c o n f i d e n c e s i n c e o n l y one s e t o f l i n e s s a t i s f i e s these c o n d i t i o n s , but t h e y can be indexed i n two ways because t h e r e i s no way o f d e t e r m i n i n g which member of a p a i r i s the (Okl) l i n e and which i s the (01k) l i n e . A d d i t i o n a l h i g h - a n g l e l i n e s were indexed u s i n g the (002) , (020) , (200) , (20~2) and ( 2 l l ) l i n e s . These are n e a r l y degenerate a t e = 18° f o r pure M0O2 but s p l i t as l i t h i u m i s i n t e r c a l a t e d . Once the ( 0 0 2 ) , (020) p a i r , which s h i f t to lower a n g l e s as l i t h i u m i s i n t e r c a l a t e d , have been i d e n t i f i e d , the t h r e e r e m a i n i n g r e f l e c t i o n s a re easy to s o r t o u t . The d - s p a c i n g s of some s t r o n g , h i g h - a n g l e l i n e s (see T a b l e IV) can be c a l c u l a t e d from these f i v e l i n e s u s i n g the f o l l o w i n g r e l a t i o n , which i s d e r i v e d from e q u a t i o n 3-2. 2 , 2 2 , 2 , , 1 r . fc - r k I /t = r h dkkl d h k l . 4 d 0 2 0 ) T h i s p a r t i c u l a r r e l a t i o n was used because o n l y two measured d-65 s p a c i n g s are r e q u r i e d , thus the u n c e r t a i n t y i n the c a l c u l a t e d v a l u e i s m i n i m i z e d . One can o f c o u r s e c a l c u l a t e any d ^ k l from the f i v e l i n e s above, but i f a c a l c u l a t i o n r e q u i r e s more than two measured d - s p a c i n g s the u n c e r t a i n t y i n the c a l c u l a t e d v a l u e i s o f t e n so l a r g e t h a t i t becomes d i f f i c u l t to c o r r e c t l y i d e n t i f y the observed l i n e s . T a b l e IV - H i g h - a n g l e l i n e s which can be i d e n t i f i e d from s t r o n g l o w-angle l i n e s u s i n g eqn. A-4 S t r o n g l i n e s 6 < 20° • R e l a t e d v i s i b l e l i n e s 20° < 6 < 45° ( O i l ) (022) (033) (020) (040) (002)& (020) (004) (013) (031) (024) (042) (022) (033) (200)&(020) (220) (240) (420) (20"2)&(020) (222) (242) (211)&(020) ( 2 3 l ) ( 4 0 2 ) Two i n d e x i n g schemes, c o r r e s p o n d i n g t o the two p o s s i b l e c h o i c e s f o r the (020) l i n e , produce t h e o r e t i c a l p a t t e r n s which are c o n s i s t e n t w i t h the observed phase I I and I I I p a t t e r n s (see Appendix D). In terms of the u n i t c e l l parameters the two i n d e x i n g schemes are e q u i v a l e n t to i n t e r c h a n g i n g the v a l u e s of b and c s i n 3 . For M 0 O 2 t h e y . a r e e q u i v a l e n t because 0 |b - c s i n B l < 0.03 A. A l t h o u g h the two schemes do g i v e s l i g h t l y d i f f e r e n t t h e o r e t i c a l p a t t e r n s , the d i f f e r e n c e s are too s m a l l to p e r m i t the i d e n t i f i c a t i o n o f the c o r r e c t i n d e x i n g scheme u n l e s s the i n t e n s i t i e s o f the l i n e s can be measured a c c u r a t e l y and the p o s s i b i l i t y o f changes i n the atomic c o - o r d i n a t e s i s d e a l t w i t h . 67 Appendix B - The USGS program T h i s program was w r i t t e n by Evans e t a l (1963) f o r the purpose o f u s i n g x - r a y powder d i f f r a c t i o n d a t a t o r e f i n e u n i t c e l l p a r a m e t e r s . G i v e n a s e t o f approximate u n i t c e l l parameters and the p o s i t i o n s o f the observed l i n e s ( 6 0 5 S ) , the program i s de s i g n e d to index the l i n e s and then produce a l e a s t squares r e f i n e m e n t of the parameters on the b a s i s of a l l the indexed l i n e s . T h i s i s a c c o m p l i s h e d by: 1) c a l c u l a t i n g l i n e p o s i t i o n s ( S c a l e ) from the g i v e n u n i t c e l l p a r a m e t e r s ; 2) comparing 6 0 b s w i t h e c a l c A n observed l i n e i s a s s i g n e d i n d i c e s i f t h e r e i s o n l y a s i n g l e c a l c u l a t e d l i n e and no o t h e r observed l i n e s w i t h i n a t o l e r a n c e T; 3) c a l c u l a t i n g A 9 = 6 c a i c - 0 o b s f o r each o f the indexed l i n e s ; 4) u s i n g the A 0 v a l u e s to perfor m a l e a s t squares a n a l y s i s t o o b t a i n r e f i n e d u n i t c e l l p a r a m e t e r s ; 5) r e p e a t i n g t h i s sequence o f s t e p s u s i n g the r e f i n e d u n i t c e l l p arameters o b t a i n e d i n s t e p 4) u n t i l the parameters remain c o n s t a n t . For the f i r s t c y c l e a maximum t o l e r a n c e , T = TOLMX i s a s s i g n e d . T h e r a f t e r , w i t h each subsequent c y c l e T i s reduced to 2a ( 6 ) u n t i l a minimum t o l e r a n c e (TOLMN) i s reached. I d e a l l y , as the parameters a re r e f i n e d and the t o l e r a n c e i s reduced, a d d i t i o n a l l i n e s can be indexed u n t i l e v e n t u a l l y , when a l l the l i n e s have been i n d e x e d , the parameters can be determined w i t h maximum p r e c i s i o n . The major drawback o f t h i s program i s t h a t i t does not d i s t i n g u i s h between weak and s t r o n g l i n e s . T h i s i s p a r t i c u l a r l y 68 troublesome i n the case o f LixMoC>2 because many l i n e s a r e too weak to be v i s i b l e . A l s o , because the LixMoC>2 system i s p s e u d o t e t r a g o n a l the l i n e s tend t o be bunched c l o s e t o g e t h e r . The a u t o m a t i c i n d e x i n g scheme i s unable t o cope w i t h t h i s s i t u a t i o n because any r e a s o n a b l e u n i t c e l l parameters produce so many c a l c u l a t e d l i n e s near the observed l i n e s t h a t , as f a r as the program i s co n c e r n e d , a f i t i s o b t a i n e d almost i m m e d i a t e l y so i t s i m p l y a c c e p t s the g i v e n u n i t c e l l p a r a m e t e r s . The f a c t t h a t the l i n e i n t e n s i t i e s do not f i t i s not ta k e n i n t o a c c o u n t . In o r d e r t o a v o i d t h i s problem the i n d e x i n g was done m a n u a l l y and the program was used o n l y t o o b t a i n a l e a s t squares r e f i n e m e n t . The program a c c e p t s a s s i g n e d i n d i c e s p r o v i d e d t h a t A6 f a l l s w i t h i n the t o l e r a n c e T; i f the t o l e r a n c e i s exceeded by a p a r t i c u l a r l i n e the assignment i s r e j e c t e d and the l i n e i s not i n c l u d e d i n the l e a s t squares a n a l y s i s . To i l l u s t r a t e how the parameters were r e f i n e d a p o r t i o n o f the o u t p u t produced d u r i n g the r e f i n e m e n t o f LiMoC>2 parameters ( u s i n g the p a t t e r n l i s t e d i n Ta b l e V I I I ) i s reproduced on the f o l l o w i n g pages. These r e s u l t s were o b t a i n e d u s i n g TOLMX = 0.3° and TOLMN = 0.05°. The c h o i c e o f TOLMN i s d i c t a t e d by the e x p e r i m e n t a l e r r o r i n 6 0 b s (+0.1°). Only narrow, h i g h - a n g l e l i n e s a r e used f o r the r e f i n e m e n t t o m i n i m i z e the e r r o r s , as d i s c u s s e d e a r l i e r i n Appendix A. LiMo02 i s the worst case because o n l y 17 s u i t a b l e l i n e s a r e a v a i l a b l e f o r the r e f i n e m e n t . About 20 l i n e s were used f o r most phase I and I I p a t t e r n s . The r e f i n e d parameters and the new v a l u e s o f 9 C a l c c o r r e s p o n d i n g t o each o f the indexed l i n e s a r e p r i n t e d out a f t e r each c y c l e . A complete s e t o f a l l 6 c a i c i s p r i n t e d a f t e r the f i n a l c y c l e but 69 t h i s has been omitted. The USGS program i t s e l f i s not l i s t e d here because i t i s too lengthy. CYCLE N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 USGS OUTPUT FOR LIM002 SCHEME I THETA TOLERANCE 0.30000 M0N0C K L D CALC D OBS LAMBDA 1 -2 2. 211904 2.210000 1.541800 1 0 2. 212229 2.210000 1.541800 2 2 1. 826096 1.827000 1.541800 1 -1 1. 718958 1.721000 1.541800 1 3 1. 644168 1.644000 1.541800 3 1 1. 622664 1.623000 1.541800 0 -4 1. 472339 1.473000 1.541800 0 2 1. 472628 1.473000 1.541800 3 -1 1. 455073 1.454000 1.541800 0 -2 1. 389999 1.390000 1.541800 3 3 1. 217397 1.219000 1.541800 2 -4 1. 217986 1.219000 1.541800 2 4 1. 160668 1.163000 1.541800 1 3 1. 149142 1.150000 1.541800 4 2 1. 149264 1.150000 1.541800 4 0 1. 135288 1.136000 1.541800 4 -2 1. 135243 1.136000 1.541800 RECIPROCAL CELL R C CORRECTIONS DIRECT CELL D C CORRECTIONS 0.20385420E+00 -0.31664777E-05 0.55592432E+01 -0.75721741E-03 0 -0 0 B THETA 20. 20. 24. 26. 27. 28. 31. 31. 31. 33. 39. 39. 41. 42. 42. 42. 42. .19509065E+00 0.19177353E+00 .10741738E-03 -0.23854330E-03 •51258240E+01 0.59094448E+01 LARGEST RESIDUAL REDUCED TO UNIT 0.28238297E-02 WEIGHT-0.10197 0.64449310E-02 CALC 39700 39388 97087 64549 96091 36473 57327 56636 99202 68349 2R929 26660 61990 13255 12703 76825 77032 ALPHA 90 0.0 0.0 90 0.0 -0.004 THETA OBS 20.41536 20.41536 24.95766 26.61140 27.96402 28.35832 31.55748 31.55748 32.01845 33.68344 39.22768 39.22768 41.51793 42.09392 42.09392 42.73505 42.73505 BETA 61 55.983 0.982 118 4.016 -0.984 THETA DIFF -0.01836 -0.02148 0.01321 0.03409 -0.00311 0.00641 0.01579 0.00P88 -0.02643 0.00005 0.06161 0.03893 0.10197 0.03864 0.03311 0.03320 0.03528 OBS 13 STANDARD ERROR UNIT WT OBS 0.02685 GAMMA 90 0.0 0.0 0.0 0.004 DEGREES 90 WEIGHT 00000 00000 00000 00000 1.00000 1.00000 1.00000 ,00000 .00000 ,00000 1.00000 1.00000 1 .00000 1.00000 1.00000 1.00000 1.00000 VOLUME 0.67299120E-02 0.11160970E-04 0.14859035E+03 0.24601746E+00 OF FREEDOM 13 CYCLE 2 uses OUTPUT FOR LIM002 SCHEME I N H K L D CALC D OBS LAMBDA THETA CALC 1 2 1 -2 2.212711 2.210000 1.541800 20.38924 2 2 1 0 2.212485 2.210000 1.541800 20.39140 3 0 2 2 1.827724 1.827000 1.541800 24.94708 4 3 1 -1 1.718823 1.721000 1.541800 26.64775 5 0 1 3 1.646095 1.644000 1.541800 27.92531 6 0 3 1 1.623668 1.623000 1.541800 28.34561 7 2 0 -4 1.473845 1.473000 1.541800 31.53731 8 2 0 2 1.473643 1.473000 1.541800 31.54210 9 2 3 -1 1.455601 1.454000 1.541800 31.97905 10 4 0 -2 1. 389811 1.390000 1.541800 33.68864 11 0 3 3 1.218482 1.219000 1.541800 39.24754 12 3 2 -4 1.218757 1.219000 1.541800 39.23700 13 0 2 4 1.161947 1.163000 1.541800 41.56392 14 2 1 3 1.150105 1.150000 1.541800 42.08914 15 0 4 2 1.150053 1.150000 1.541800 42.09152 16 2 4 0 1.135783 1.136000 1.541800 42.74515 17 2 4 -2 1.135814 1.136000 1.541800 42.74371 . rv D ^ H L r nrt RECIPROCAL CELL 0.20385432E+00 0.19509065E+00 0.19177347E+00 90 0.0 R C CORRECTIONS 0.17057147E-06 0.58421218E-07 -0.48156092E-07 0.0 DIRECT CELL 0.55592413E+01 0.51258259E+01 0.59094486E+01 90 0.0 D C CORRECTIONS -0.19073486E-05 0.19073486E-05 0.38146973E-05 0.0 LARGEST RESIDUAL REDUCED TO UNIT WEIGHT-0.04599 OBS 13 STANDARD ERROR THETA TOLERANCE - 0.05370 MONOC THETA OBS 20.41536 20.41536 24.95766 26.61140 27.96402 28.35832 31.55748 31.55748 32.01845 33.68344 39.22768 39.22768 41.51793 42.09392 42.09392 42.73505 42.73505 BETA 61 55.985 90 0.001 118 4.012 90 -0.004 JIT WT OBS 0.02685 THETA DIFF -0.02612 -0.02396 -0.01057 0.03635 -0.03871 -0.01271 -0.02017 -0.01538 -0.03940 0.00520 0.01987 0.00932 0.04599 -0.00478 -0.00240 0.01010 0.00867 GAMMA 0.0 0.0 0.0 0.0 DEGREES WEIGHT 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 • 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 VOLUME 0.67299120E-02 0.0 0.14859035E+03 0.0 OF FREEDOM 13 CYCLE 3 USGS OUTPUT FOR LIM002 SCHEME I N H K L D CALC D OBS LAMBDA THETA CALC 1 2 1 -2 2.212710 2.210000 1.541800 20.38925 2 2 1 0 2.212484 2.210000 1.541800 • 20.39142 3 0 2 2 1.827724 1.827000 1.541800 24.94708 4 3 1 -1 1.718822 1.721000 1.541800 26.64780 5 0 1 3 1.646096 1.644000 1.541800 27.92529 6 0 3 1 1.623668 1.623000 1.541800 28.34561 7 2 0 -4 1.473844 1.473000 1.541800 31.53732 8 2 0 2 1.473643 1.473000 1.541800 31.54210 9 2 3 -1 1.455600 1 1.454000 1.541800 31 .97908 10 4 0 -2 1.389809 1.390000 1.541800 33.68872 11 0 3 3 1.218483 1.219000 1.541800 39.24751 12 3 2 -4 1.218757 1.219000 1.541800 39.23700 13 0 2 4 1.161947 1.163000 1.541800 41.56392 14 2 1 3 1.150105 ' 1.150000 1.541800 42.08914 15 0 4 2 1.150053 1.150000 1.541800 42.09152 16 2 4 0 1.135783 1.136000 1.541800 42.74515 17 2 4 -2 1.135814 1.136000 1.541800 42.74371 RECIPROCAL CELL 0.20385420E+00 0.19509071E+00 0.19177347E+00 90 0.0 R C CORRECTIONS -0.96757049E-07 0.87633225E-07 0.30498214E-07 0.0 DIRECT CELL 0.55592432E+01 0.51258221E+01 0.59094467E+01 90 0.0 D C CORRECTIONS 0.19073486E-05 -0.38146973E-05 -0.19073486E-05 0.0 LARGEST RESIDUAL REDUCED TO UNIT WEIGHT-0.04599 OBS 13 STANDARD ERROR R C STNDRD ERRS 0.10089364E-03 0.64690175E-04 0.71213610E-04 0.0 DIRECT CELL VARIANCE-COVARIANCE MATRIX 0.75756716E-05 -0.91847221E-06 0.31532363E-06 0.0 -0.91847227E-06 0.28888835E-05 -0.12590972E-05 0.0 0.31531818E-06 -0.12590972E-05 0.72464509E-05 0.0 0.0 0.0 0.0 0.0 0.54289802E-06 -0.77610821E-07 0.96189888E-06 0.0 0.0 0.0 0.0 0.0 D C STNDRD ERRS 0.27523937E-02 0.16996716E-02 0.26919234E-02 0.0 THETA TOLERANCE «= 0.05371 MONOC THETA OBS 20.41536 20.41536 24.95766 26.61140 27.96402 28.35832 31.55748 31.55748 32.01845 33.68344 39.22768 39.22768 41.51793 42.09392 42.09392 42.73505 42.73505 THETA DIFF -0.02611 -0.02394 -0.01057 0.03639 -0.03873 -0.01271 -0.02016 -0.01538 -0.03937 0.00528 0.01984 0.00932 0.04599 -0.00478 -0.00240 0.01010 0.00867 BETA GAMMA 61 55.984 90 0.0 -0.001 118 4.016 90 0.004 JIT WT OBS 0.02685 2.079 0.54289836E-06 -0.77610878E-07 0.96189888E-06 0.0 0.36569929E-06 0.0 2.079 0.0 0.0 0.0 DEGREES 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ).0 WEIGHT 00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 00000 00000 1.00000 1.00000 VOLUME 67299120E-02 ,0 14859035E+03 ,0 OF FREEDOM 13 ROW 1 2 3 4 5 6 0.78144193E-01 73 Appendix C - The CALINE program T h i s program was w r i t t e n s p e c i f i c a l l y t o c a l c u l a t e the Debye-Scherrer powder p a t t e r n which would r e s u l t from any g i v e n h y p o t h e t i c a l s e t o f Li x M o 0 2 u n i t c e l l p a r a m e t e r s . The d- s p a c i n g and l i n e p o s i t i o n ( O f o r each s e t o f M i l l e r i n d i c e s ( h k l ) a r e c a l c u l a t e d u s i n g eqns. 3-1 and 3-2. Approximate l i n e i n t e n s i t i e s are c a l c u l a t e d a c c o r d i n g t o eqns. 3-4 and 3-7 u s i n g the f r a c t i o n a l c o - o r d i n a t e s o f oxygen and molybdenum atoms i n pure M0O2 (from Brandt & S k a p s k i , 1967) and the atomic s c a t t e r i n g f a c t o r s f o r CuKa r a d i a t i o n a t 6 = 20° ( C u l l i t y , 1956). Because o n l y approximate i n t e n s i t i e s a r e r e q u i r e d s c a t t e r i n g from i n t e r c a l a t e d l i t h i u m atoms, the atomic s c a t t e r i n g f a c t o r s ' dependance on 0, and the e f f e c t s of temperature and a b s o r b t i o n are not i n c l u d e d i n the i n t e n s i t y c a l c u l a t i o n . The program c a l c u l a t e s p o s i t i o n s , d - s p a c i n g s , and i n t e n s i t i e s f o r a l l ( h k l ) w i t h 0 £ h £ h m a x , 0 £ k £ k m a x , and - l m a x £ 1 £ l m a x ^ a n d then l i s t s the non-degenerate l i n e s w i t h d m i n S. d S. dmax * n t n e o r d e r i n which t h e y appear on the f i l m . In p r a c t i c e h m a x = k m a x = l m a x = 4, d m i n = 1.0 A, and d r a a x = 7.1 %. were used because o n l y l i n e s i n the r e g i o n 0 < 45° are o f i n t e r e s t . The f o l l o w i n g i s a l i s t i n g o f the program, w r i t t e n i n A l g o l W, t o g e t h e r w i t h the o u t p u t f o r parameters which f i t LIM0O2 (see Table V I I I ) . I t is not necessary to use negative values of h and k because (hkl), (Ekl) , (hk~l) and (Tiki) are a l l planes of the form {hkl}. C a l i n e COMMENT *** GIVEN MAXIMUM VALUES OF INDICES H,K,L *** *** AND MONOCLINIC LATTICE CONSTANTS A,B,C,BETAO *** *** THIS PROGRAM WILL LIST VALUES OF D(HKL) *** LYING BETWEEN SPECIFIED BOUNDS DMIN, DMAX INPUT REQUIRED I S : ### ### UNIT CELL PARAMETERS A,B,C,BETA ### SPECIFY SPRINT *** *** ### ### ###; BEGIN PROCEDURE LOADCOORD(REAL ARRAY F,U,V,W(*)); COMMENT ***ENTERS ATOMIC SCATTERING FACTOR AND FRACTIONAL *** *** COORDINATES OF ATOMS IN THE UNIT CELL *** BEGIN REAL FOR I:=0 BEGIN CASE I BEGIN BEGIN A: = END; BEGIN A: = END; BEGIN A: = END END; FOR J : = l BEGIN A f X f Y f Z ; UNTIL 2 DO + 1 OF 32.6; X:= 0.232; Y:= 0.992; Z:= 0.016 5.3; X:= 0.112; Y:= 0.217; Z:= 0.234 5.3; X:= 0.391; Y:=0.697; Z:= 0.299 UNTIL 4 DO F ( 4 * I + J) A; CASE J OF BEGIN BEGIN U (4*1 + J ) := X; V ( 4 * I + J) := Y; W(4*I + J) := Z END; BEGIN U(4*I + J) := -X; V ( 4 * I + J) := -Y; W(4*I + J) : = -Z END; BEGIN U(4*I + J) := -X; V ( 4 * I + J) := 0.5 + Y; W(4*I + J) := 0.5 - Z END; BEGIN U (4*1 + J) : = X; 75 V( 4 * I + J ) : = 0.5 - Y; W(4*I + J ) : = 0.5 + Z END END END END END; REAL PROCEDURE LYN(INTEGER VALUE H0,K0,L0); COMMENT ***CALCULATES D(HKL) FROM H,K,L *** *** REQUIRES GLOBAL VARIABLES A, B, C ,BETA ***; BEGIN REAL X,P; X:= (H0/A)**2 + (K0*SIN(BETA)/B)**2 + (LO/C)**2 - 2*HO*LO*COS(BETA)/(A*C); P:= X/(SIN(BETA)**2); IF X=0.0 THEN 0.0 ELSE SQRT(1/P) END; REAL PROCEDURE INTENSITY(REAL VALUE D; INTEGER VALUE H,K,L; REAL ARRAY F,U,V,W(*)); COMMENT ***PROCEDURE CALCULATES INTENSITY OF LINE***; BEGIN REAL S,C,C2,LOR,LAMBDA; INTEGER P; COMPLEX SF; LAMBDA:= 1.54178; S:= LAMBDA/(2*D); C:= SQRT(1 - S**2); C2:= 2*C**2 - 1; L0R:= (1 + C2** 2 ) / ( C * S * * 2 ) ; IF K=0 OR (H=0 AND L=0) THEN P:=2 ELSE P:=4; SF:=0; FOR N:=l UNTIL 12 DO BEGIN REAL THETA; THETA:= 2*PI*(H*U(N) + K*V(N) + L*W(N)); SF:= SF + F(N)*(COS(THETA) + IMAG(SIN(THETA))) END; ABS SF **2*P*LOR/100 END; REAL PROCEDURE POSITION(REAL VALUE D); COMMENT ***PROCEDURE CALCULATES POSITION OF LINE*** *** ON FILM FOR THETA = 5*L ***; BEGIN REAL S,C,LAMBDA; LAMBDA:= 1.54178; S:= LAMBDA/(2*D); C:= SQRT(1 - S**2); 180*ARCTAN(S/C)/(5*PI) END; COMMENT >>>>>> MAIN PROGRAM <<<<<<; INTEGER HMAX,KMAX,LMAX,VOL; REAL A,B,C,VEE,BETAO/BETA,DMIN,DMAX; REAL ARRAY F,U,V,W(1::12) ; LOADCOORD(F,U,V,W); HMAX:= 5; KMAX:= 5; LMAX:= 5; DMIN:= 1.0; DMAX:= 7.1; V0L:= (HMAX + 1)*(KMAX + 1)*(2*LMAX + 1 ) ; BEGIN INTEGER Q,R,S; RECORD LINE (INTEGER H,K,L; REAL D); REFERENCE (LINE) ARRAY INDEX(1::VOL); READ(A,B,C,BETAO); BETA:= PI*BETAO/180; VEE:= A*B*C*SIN(BETA); COMMENT *** CALCULATE LINE POSITIONS ***; FOR I:= 0 UNTIL HMAX DO BEGIN Q:= I*(KMAX + 1)*(2*LMAX + 1 ) ; FOR J:= 0 UNTIL KMAX DO BEGIN R:= Q + J*(2*LMAX + 1 ) ; FOR M:= -LMAX UNTIL LMAX DO BEGIN S:= R + M + LMAX + 1; . INDEX(S):= L I N E ( I , J , M , L Y N ( I , J , M ) ) ; END END END; COMMENT *** SORT LINES IN ORDER OF DECREASING BEGIN REFERENCE(LINE) TEMP; INTEGER COUNT; COUNT:= 1; WHILE COUNT = 0 DO BEGIN COUNT:= 0; FOR I:= 2 UNTIL VOL DO IF D(INDEX(I - 1))<D(INDEX(I)) THEN BEGIN TEMP:= INDEX(I); INDEX(I):= INDEX(I - 1 ) ; INDEX(I - 1):= TEMP; COUNT:= COUNT + 1 END END END; 77 COMMENT *** TABULATE RESULTS ***; BEGIN INTEGER I ; R_FORMAT:= "A"; R_D:= 3; R_W:= 10; I_W:= 5; WRITE("LATTICE PARAMETERS ARE:"); WRITE("A= " , A ) ; WRITE("B= " ,B) ; WRITE("C= " , C ) ; WRITE("BETA= ",BETAO); WRITE("V= ",VEE); WRITE (" " ) ; WRITE (" H K L D(HKL) A L(CM) INTENSITY"); WRITE (" " ) ; I : = 1; WHILE'D(INDEX(I))>DMAX DO I:= I + 1; WHILE D(INDEX(I))>DMIN DO BEGIN IF D(INDEX(I)) =D(INDEX(I + 1)) THEN W R I T E ( H ( I N D E X ( I ) ) , K ( I N D E X ( I ) ) , L ( I N D E X ( I ) ) , D ( I N D E X ( I ) ) , POSITION(D(INDEX(I))), I N T E N S I T Y ( D ( I N D E X ( I ) ) , H ( I N D E X ( I ) ) , K ( I N D E X ( I ) ) , L ( I N D E X ( I ) ) , F,U,V,W)); I:= I + 1 END END END END. C a l i n e o u t p u t f o r Li xMoO? LATTICE PARAMETERS ARE: A= 5.559 B= 5.126 C= 5.909 BETA= 118.070 V= 148.574 H K L D(HKL) A L(CM) INTENSITY 0 0 1 5.214 1.700 0.000 0 1 0 5.126 1.730 0.000 1 0 -1 4.906 1.808 0.000 1 0 0 4.905 1.808 326.394 0 1 1 3.655 2.435 29387.89 1 1 -1 3.544 2.513 981.297 1 1 0 3.544 2.513 52.292 1 0 -2 2.947 3.032 570.649 1 0 1 2.947 3.033 0.000 2 0 -1 2.780 3. 220 0.000 0 0 2 2.607 3.440 3237.677 0 2 0 2. 563 3.501 3398.352 1 1 -2 2.555 3.512 8.051 1 1 1 2.555 3.512 2.254 2 0 -2 2.453 3.663 4192.023 2 0 0 2.453 3.664 4997.102 2 1 -1 2.443 3.678 8735.262 0 1 2 2.324 3.875 128.596 0 2 1 2.300 3.916 234.095 1 2 -1 2.272 3.967 78.548 1 2 0 2.272 3.968 95.712 2 1 -2 2.213 4.078 965.706 2 1 0 2.212 4. 078 825.287 1 0 -3 1.953 4.650 0. 000 1 0 2 1.953 4.651 16.243 1 2 -2 1.934 4.698 912.750 1 2 1 1.934 4.698 133.691 2 0 -3 1.902 4.783 0. 000 2 0 1 1.901 4.784 0.000 2 2 -1 1.884 4.830 4.215 0 2 2 1.828 4.990 8954.172 1 1 -3 1.825 4.998 1085.036 1 1 2 1.825 4.998 80.081 3 0 -2 1.824 4.999 896.972 3 0 -1 1.824 4.999 0. 000 2 1 -3 1.783 5.124 4919.070 2 1 1 1.783 5.125 6422.832 2 2 -2 1.772 5.157 5127.910 2 2 0 1.772 ,5.158 5748.777 0 0 3 1.738 5.266 0.000 3 1 -2 1.719 5.329 0.104 3 1 -1 1.719 5.330 974.892 0 3 0 1.709 5.364 0.000 0 1 3 1.646 5.586 3749.131 3 0 -3 1.635 5.625 0.000 3 0 0 1.635 5.626 263.692 0 3 1 1.624 5.669 3882.273 1 3 -1 1.614 5.708 287.681 1 3 0 1.614 5.708 140.979 3 1 -3 1.558 5.932 1503.205 3 1 0 1.558 5.932 9.202 1 2 -3 1.553 5.951 11.224 1 2 2 1.553 5.951 28.583 2 2 -3 1.527 6.063 60.899 2 2 1 1.527 6.064 10.956 3 2 -2 1.486 6.248 891.554 3 2 -1 1.486 6.249 12.281 1 3 -2 1.478 6.286 54.250 1 3 1 1.478 6.287 0.887 2 0 -4 1.474 6.308 1711.487 2 0 2 1.473 6.309 2429.881 2 3 -1 1.456 6.396 4642.762 1 0 -4 1.439 6.478 638.789 1 0 3 1.439 6.479 0.000 0 2 3 1.438 6.481 77.479 0 3 2 1.429 6.529 37.475 2 1 -4 1.416 6.595 132.933 2 1 2 1.416 6.596 207.590 79 2 3 -2 1.402 6.671 70.354 2 3 0 1.402 6.672 195.041 4 0 -2 1.390 6.738 1892.948 1 1 -4 1.385 6.762 6.428 3 0 -4 1.385 6.762 631.548 1 1 3 1.385 6.762 78.922 3 0 1 1.385 6.764 0.000 3 2 -3 1.379 6.800 51.111 3 2 0 1.378 6.801 295.022 4 0 -3 1.343 7.006 0.000 4 0 -1 1.343 7.007 0.000 4 1 -2 1.341 7.016 5.232 3 1 -4 1.337 7.040 64.984 3 1 1 1.337 7.041 127.776 0 0 4 1.303 7.251 1660.770 4 1 -3 1.299 7. 280 1482.355 4 1 -1 1.299 7.281 1940.599 1 3 -3 1.286 7.367 297.911 1 3 2 1.286 7.367 21.630 0 4 0 1.281 7. 396 1611.444 2 2 -4 1.278 7.423 1096.288 2 2 2 1.277 7.424 1810.405 2 3 -3 1.271 7.468 1076.275 2 3 1 1.271 7.469 1474.801 0 1 4 1.263 7.521 126.341 1 2 -4 1.255 7.581 349.991 1 2 3 1.255 7.582 9.085 3 3 -2 1.247 7.636 83.001 3 3 -1 1.247 7.636 384.034 0 4 1 1.244 7.655 199.991 1 . 4 -1 1. 240 7.689 92.908 1 4 0 1.240 7.689 63.929 4 0 -4 1.226 7.789 170.990 4 0 0 1.226 7.790 410.086 4 2 -2 1.222 7.825 614.013 3 2 -4 1.219 7.848 1049.339 3 2 1 1.219 7.849 17.357 0 3 3 1.218 7.850 2667.157 4 1 -4 1.193 8.052 16.743 4 1 0 1.193 8.054 38.852 4 2 -3 1.190 8.079 15.343 4 2 -1 1.189 8.080 102.260 3 3 -3 1.181 8.146 652.387 3 3 0 1.181 8.147 24.316 2 0 3 1.180 8.158 0.000 1 4 -2 1.175 8.198 128.377 1 4 1 1.175 8.199 49.051 2 4 -1 1.164 8.297 11.318 0 2 4 1.162 8.313 1134.957 3 0 2 1.161 8.322 4.058 0 4 2 1.150 8.418 1389.630 2 1 3 1.150 8.419 1832.695 2 4 -2 1.136 8.548 1538.778 2 4 0 1.136 8.549 1747.224 1 0 4 1.134 8.563 72.865 3 1 2 1.132 8.582 5.456 80 2 3 -4 1.116 8.738 135.541 2 3 2 1.116 8.739 63.922 1 1 4 1.107 8.823 12.202 4 2 -4 1.106 8.834 1541.262 4 2 0 1.106 8.836 2600.117 1 3 -4 1.101 8.892 53.583 1 3 3 1.101 8.892 126.021 4 0 1 1.085 9.052 0.000 4 3 -2 1.078 9.129 15.162 3 3 -4 1.076 9.151 0.796 3 3 1 1.076 9.153 151.912 2 2 3 1.072 9.197 23.952 1 4 -3 1.071 9.203 121.235 1 4 2 1.071 9.203 39.245 2 4 -3 1.063 9.300 0.784 2 4 1 1.063 9.301 33.446 4 1 1 1.062 9.311 1487.445 3 2 2 1.057 9.360 77.687 4 3 -3 1.056 9.379 804.510 4 3 -1 1.056 9.380 1222.010 3 4 -2 1.049 9.463 402.647 3 4 -1 1.049 9.464 91.612 1 2 4 1.037 9.602 186.334 0 3 4 1.036 9.612 10.708 0 4 3 1.031 9.673 42.030 3 4 -3 1.009 9.968 16.291 3 4 0 1.009 9.969 246.978 81 Appendix D - D i f f r a c t i o n p a t t e r n s of MoO?, Li uMoO? and LiMoO? The f o l l o w i n g t a b l e s l i s t the observed d i f f r a c t i o n p a t t e r n s of phase I, II and I I I compounds together with the corresponding p a t t e r n s c a l c u l a t e d using the CALINE program. Two c a l c u l a t e d p a t t e r n s , corresponding to the two p o s s i b l e indexing schemes, are i n c l u d e d f o r phase II and I I I compounds. Only those . c a l c u l a t e d l i n e s which are inten s e enough that they should be v i s i b l e ( i . e . I c a l c > 2) are l i s t e d . Those l i n e s which were used f o r the USGS parameter refinement program are marked with a s t e r i s k s . T a b l e V - Mo0 2 (Phase I ) Sample p r e p a r e d by r e d u c i n g MoO~ under hydrogen. T h e o r e t i c a l p a t t e r n c a l c u l a t e d u s i n g a=5.611 K, b=4.856 K, c=5.628 A and 6=129.95 C a l c u l a t e d P a t t e r n Observed P a t t e r n ( h k l ) " c a l c ^ c a l c ^ dob.< &> "obs 100 3 4. 812 - 4. 843-4 740 VF 111 O i l 9 255 3. 3. 446 423 [ 3. 463-3 385 VS 102" 5 2. 814 2. 828-2 794 F 202 42 2. 445 211 86 2. 429 020 30 2. 428 • 2. 446-2 396 VS 002 27 2. 413 200- 48 2. 406 molybdenum (110)? 2. 236-2 215 VF 212 9 2. 184 2. 189-2 169 F 210 8 2. 156 2. 159-2 139 F 302" 122" 9 8 1. 1. 842 838 1. 843-1 829 M 213 45 1. 726 222" 48 1. 723 1. 726-1 714 S 113 9 1. 717 3 IT 10 1. 712 1 022 76 1. 712 1. 714-1 702 VS 220 53 1. 709 211 57 1. 698 1. 699-1 688 S 313 15 1. 545 031 013 34 31 1. 1. 535 527 \ 1. 538-1 520 M 322 9 1. 468 1. 468-1 460 F 204" 15 1. 407 402" 231 19 42 1. 1. 403 402 \ 1. 405-1 397 S ho 83 T3 c O o I > cu r H - 0 ; cd | H co o co O T3 fe > CO CO fe fe S fe > > > ON O 00 CM CM o I N o> oo CM m CO ON 00 r H O 00 < f CO o 00 oo ro ro CM CM CM CM r H r H r H r H O o r - l r H r H r H r H r H r H r H r H r H r H I I I I r H | r H 1 1 1 VO VO 1 m 1 1 vO 00 I I I I UO r H CO CM ON oo in <r O O r H o oo m <)- i -H 00 ro ro ro CO CM CM CM r H r H r H r H O o r H r H r H r H r H r H r H i—1 i -H r H i—1 r H r H fe fe o rC I I I o r  r H m v O i n O O ^ N N r N v J - v f l v N C O s f C T M H O O i n v f O O O O N r H r - 1 r H i—I O O O 00 < J C O O O C O O O C O C M C M C M C M C M C M C M C M r - l i — I r H CM m<r I-H oo <f CTi O0 CO OO CO N N o o o o o o o H r I i — I r H r H r H i — I r H r H r H r H v o i n c o m O N O O v D < t " C O < r v D O v o < r CM I—I r H I—I I—I I—I r H r H r H r H CM m m oor^ O i n N i—I CM i—I c M k f l - d - o l o o H k f l c n l c M O r - i ^ f c M K f l o o c o k | C M ( N O < f O c n O O O C M i — l i - H c M 0 0 C N < f 0 0 O C N C N r 0 C 0 C " C s l < f < j " < l " C N C N r H C M O O i — I C O < t - d - C M C M < t O C M O C M C O O O O < f CN O CN O <T CN T a b l e VI L i > M o 0 2 (Phase I I ) Sample p r e p a r e d by r e c h a r g i n g Li/MoC^ c e l l t o 1.55 v o l t s T h e o r e t i c a l p a t t e r n s c a l c u l a t e d u s i n g : ( i ) a = 5.580 A, b = 5.017 . " Q 1 " 1 1 n n n ° ( i i ) a = 5.581 A, b = 5.060 '. x = 0.470 ± .005 c = 5.783 A and 6 = 118 ..90' c = 5.757 A and B = 119.07°C a l c u l a t e d P a t t e r n ( i ) Observed P a t t e r n C a l c u l a t e d P a t t e r n ( i i ) ( h k l ) 013* " c a l c 35 d c a l c ^ 011 278 3. 564 11T 10 3. 501 107 5 2 . 889 002 30 2. 531 020 32 2. 509 207 42 2. 445 200 50 2. 443 2 IT 87 2. 438 021 2 2. 248 212* 10 2. 198 210* 8 2. 196 127 9 9 1. 894 302" 9 1. 830 022* 84 1. 782 113 10 1. 780 213 47 1. 757 211 62 1. 755 222* 50 1. 751 220* 56 1. 750 311 10 1. 718 1.600 } } } d o b s ^ 2.538-2.511 2.517-2.490 2.451-2.425 VS 1.868-1.854 VF 1.789-1.776 1.756-1.743 VS 1.606-1.596 obs d c a l c ^ > ''"calc (hkl) VF - ? VS - 3.562 278 o i l 3.511 10 i n 2.867 5 107 S • 2.530 33 020 S -• 2.507 30 002 1 ' 2.444 87 2 IT < 2.439 49 200 L 2.438 41 202" 2.259 2 021 VF ? r 2.197 8 210* M < I 2.196 9 217* 1.897 9 122 ? 1.829 9 307 S • 1.781 84 022* 1.768 10 113 ' 1.756 56 220 « 1.755 50 222 1.750 61 211 . 1.749 47 213 1.720 10 3 IT VF ? VF 1 M - 1.599 37 031* 8 5 c o o > CL) • S i l-H cXj a T3 •}< * -X * IcMlo-kfM * JL. okr -3< , * * * •?< O l s t C O | C O | C N H CM 1st Ico o s t t - i |co CN|st |cM C0|C0 CM O N OlcM co H H C N C O o o O O O i - l r - l s t o co co CM CM CM O CM co co s t CM s t St r - l CM CM o ro CM C N CM < t H c n s f s t o o CM CM CM C M <t St C O O C O O O CM CM CM St St <f IO ^ C O r - l i o C O V D CM r - l aivDvoaMn\oin<fONOvD<toinvo^HNin r - l r—t r—I r—I r—I r—I r—I r—I r—I i—I CM r - l r - l r—I t—I 00 V O io CM rH C M C O St St St O N CTl io St r H r H 00 C M O N O O O N C O C O C O V D O N oo 00 s t oo St C O co O N oo V O O N O N m m LO St St C M r H o oo r- C M C M CM C M r H O N O N m LO S t St s t s t co co C O CM CN C M C M CM CM CM C M CM CM CM r H r H r H r H r H r H r H O o r - l r - l r - l r - l r H r - l r H r H r H r H r H r H r H r H r H i—1 r H r H r H r H r H r H r H r H r H r H r H r H r H fe S fe fe fe fe > fe co r H ON r H VD CM VD VO oo O S t VO oo S t CN ON ON VO s t r H 00 CN CM r H ON LO S t s t CO CM CM CM CM r H r H r H r H O r H r H r H r H r H r H r H r H r H r H r H r H r H | CO ON 1 ON 1 CM 1 LO I CM 1 r H 1 CM S t oo O ON s t co ON O VD LO CM ON co CN r H o m S t s t CO CO CM CM CM r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H 00 O 00 L O C O oo L O s t s t L O L O s t s t s t s t co s t l—I LO I—I o O N s t co CO O N O N V O S t C N r H O O O O r H O N C O O O r ^ - O O N O N V O l O L O L O S t S t C M r H O O O v D C O C N C M C N C M C M C N C M C N C M C N C M r H i — I r H r^ - LO ON vO CO CO rH i—I CN LO S t VO ON vO L O O N v D i O O r ^ O s t s t v O O L O v O r H i—I i—I i—I i—I rH rH i—I i—I rH CM r H * * * * * r H r H | c o | c M | s t C N H k t l c M k t |00 | r H S t okr C N | C O CO r H CM O O co o o o r H r H o S t C N CM CO O CO C O CM CM CM l—1 s t C O s t s t o O C N CM CM S t CO VO VO ON 00 CN CM r H r H ON ON r H r H r H r H O O r H r H r H r H r H r H CO 00 LO r^- LO VO r H r H r H r H r H CM # * CN CO kM okt O S t r H s t S t CM CM O CM CM CM S t S t Table VII - LiMo0 9 (Phase I I I ) Sample prepared by d i s c h a r g i n g Li/MoC^ c e l l to 0.03 v o l t s T h e o r e t i c a l p a t t e r n s c a l c u l a t e d u s i n g ( i ) a = 5.559 A, b = 5.126 A, c ( i i ) a = 5.556 A, b = 5.215 A, c and 3 = 118.07 and (3 = 118.43 C a l c u l a t e d P a t t e r n ( i ) Observed P a t t e r n C a l c u l a t e d P a t t e r n ( i i ) (hkl) "''calc d c a l c '^ O i l 294 3.655 11T 10 3.544 002 32 2.607 020 34 2.563 207 42 2.453 200 50 2.453 2 IT 87 2.443 021 2 2.300 217* 10 2.213 210* 8 2.212 127 9 1.934 022* 90 1.828 113 11 1.825 302 9 1.824 213 49 1.783 211 64 1.783 227 51 1. 772 220 57 1. 772 3 IT* 10 1.719 013* 37 1.646 031* 39 1.624 317 15 1.558 322 9 1.486 } } } d o b S ^ > •""obs dcalc<*> "'"calc (hkl) 3 . 6 9 0 - 3 . 6 0 2 VS -• 3 . 6 5 5 2 9 4 0 1 1 3 . 5 6 4 1 0 1 1 T 2 . 6 2 0 - 2 . 5 9 1 S - 2 . 6 0 8 3 5 0 2 0 2 . 5 6 9 - 2 . 5 4 1 S - 2 . 5 6 3 3 1 0 0 2 1 " 2 . 4 5 2 8 8 2 I T 2 . 4 7 3 - 2 . 4 2 2 VS < 2 . 4 4 3 5 0 2 0 0 1 . 2 . 4 4 2 4 1 2 0 7 2 . 3 0 8 - 2 . 2 8 6 F - ? 2 2 1 - 2 . 2 0 Q M \ 2 . 2 1 2 8 2 1 0 * 2 . . 2 ^ 2 1 1 1 0 2 1 2 * 1 . 9 4 2 9. 1 2 7 8 3 3 - 1 . 8 2 0 VS \ 1 . 8 2 8 9 0 0 2 2 * 1 . T 1 . 8 2 2 9 3 0 7 1 . 8 0 4 1 1 1 1 3 ' 1 . 7 8 3 5 8 2 2 0 7 9 0 - 1 . 7 5 8 VS - 1 . 7 6 2 5 2 2 2 7 1 . 1 . 7 7 2 6 3 2 1 1 1 . 7 7 1 4 8 2 1 3 1 . 7 2 7 - 1 . 7 1 5 F -- 1 . 7 2 1 1 0 3 I T * 1 . 6 4 9 - 1 . 6 3 8 S - 1 , 6 4 6 4 0 0 3 1 * 1 . 6 2 8 - 1 . 6 1 7 S - 1 . 6 2 3 3 6 0 1 3 * 1 . 5 6 5 - 1 . 5 5 5 VF • ? 1 . 5 5 4 1 5 3 1 3 1 . 4 9 6 - 1 . 4 8 7 VF - 1 . 4 9 4 9 3 2 2 oo 87 o M M > W r Q cu O r H r O CO H o<! H co CN CN|<M<f|cN O O O O CN CN r H <|-00 s f S v O O N <f N H r H N- o H |co <f r H |co CN f<t N 0 < T i - H r H O C O C O C N C N C N r O O s t < t O N ( N ! N C M s f ^ D N O M O ^ D i n r - I O O i H v D o co |-cr |co CN O |CN <t co o her H |ro O O O CN CO <t <l" -3" CN i—I CN CN C- CO CO < t O COOOOCMCNOCN<J-<}- <t" <f < f N O N - J OO vDi—I oo i o m CM CO CN r H r H r H r H r H r H CN r H r H vO LO vO o> <f ON 00 r H OO r H O VO r H oo LO 00 CN m LO r H 00 O ON cr. oo r-^  | \ CN CN r H r H OO VO o- o- CO oo CO CN CN CN CN CN CN CN CN CN CN CN r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H r H t-H r H r H r H r H VO vO VO CN r H CO O O VD VO r H r H r H O O r H r H r H r H r H a S S fe a a fe fe fe > > > oo VO CO VO r H vo <t 00 ON CN r H VO •st- oo 00 CN CN CN CN r H r H r H r H r H r H r H r H | r H | r H 1 CN 1 r H VO O 00 CN LO VO ON 00 O OO CN CN VO •sT oo oo OO CN CN CN r H r H r H r H r H r H r H r H r H r H oo oo LO fe > oo oo ON oo a'fe a CN i-H ON O 00 LO r H O O I O r H I I LO <T 0O VO O O <(- 00 VO LO <t-r H r H r H VO r H CN * * kr CN H o o co CN CN CN O N O L O O O C O O N O N I — l O O t ^ i — I r H vO CN O N 00 C O C ^ O D N O O N C r i C O N N N N C M C N i H i H < f 0 O c n c n c n c N C N C N C N C N C N C N C N C N C N C N r H CN OO VO O O vO VO vO vO LO LO CO 0O O O CN VO O v O O N V O O O t ^ - L O O N V O r H O O i — l L O < f v O O t ^ -r H r H r H i — I r H r H r H r H r H i—I CN kr|cN|<r o <t|co|rH okr CN|CO I-H O N M - co O O O C N O i — I r H - J - C N C N O O O O O C N C N O O r H < t O O O O O < t < J - O C N C N C N C N < f < J - 0 0 0 l^ v r H <T 00 LO r-^  LO vD r H r H I—I r H r H CN LO * .* -X , |oo <r CN CO|CN Okl" O r H CO CN r H <f <t CN CN o- r H CO o o CN CN CN <f <f 

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