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Some properties of aluminum oxide in electrolytic solutions Urquhart, Helen Mary Ann 1949

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O i 7 Of' \ SOME PROPERTIES OF ALUMINUM OXIDE IN ELECTROLYTIC SOLUTIONS by H e l e n Mary Ann U r q u h a r t A t h e s i s s u b m i t t e d 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 t h e degree o f MASTER OF ARTS i n t h e Department o f PHYSICS 'The U n i v e r s i t y o f B r i t i s h Columbia A p r i l , 1949 A B S T R A C T By anodio oxidation, an aluminum plate oan be oovered with an amorphous or c r y s t a l l i n e oxide l a y e r , depending on the e l e c t r o l y t e used. The amorphous l a y e r , obtained i n a solution of oxalic or sulphuric aoid, has a porous structure. However, the pores do not go r i g h t down to the aluminum as has been shown by many investigators, but end i n a s o l i o i n s u l a t i n g l a y e r , the thickness of which may be determined by capacity measurements• Corresponding to a given temperature and aoid concentration of the e l e c t r o l y t i o s o l u t i o n and a given formation current density, there i s only one f i n a l capacity obtainable. Increasing the concentration, or temperature, or decreasing the current density, increases the f i n a l oapaolty obtainable. ACKNOWLEDGEMENT I wish to acknowledge the deepest g r a t i t u d e to Dr. A. J . Dekker who, through h i s c o n t i n u a l encouragement and personal i n t e r e s t i n t h i s problem, has made t h i s i n v e s t i g a t i o n both p r o f i t a b l e and enjoyable; to the N a t i o n a l Research Co u n c i l f o r f i n a n c i a l a s s i s t a n c e i n the form of a N a t i o n a l Research C o u n c i l Bursary; and to the Department of Physics and the U n i v e r s i t y of B r i t i s h Columbia, which have given me every opportunity, f i n a n c i a l and otherwise, to proceed toward t h i s degree, t r u l y l e a v i n g a l l l i m i t s to my progress to be determined by my own a b i l i t y , i n t e r e s t and e f f o r t . TABLE OF CONTENTS I. I n t r o d u c t i o n . . . . . . . . . . . . . 1 I I . A p p a r a t u s . • . . . . . . . . . . . . . . . . . . . • 4 I I I . E x p e r i m e n t a l R e s u l t s » • • . • . • • • • • . . . • & IV. D i s c u s s i o n 1. E x i s t i n g T h e o r i e s . . . . . . . • « » . • . • 15 2. D i s c u s s i o n o f E x p e r i m e n t a l R e s u l t s • • . . . 24 3. Suggested Theory f o r F o r m a t i o n o f Basic. L a y e r s o f Co n s t a n t T h i c k n e s s . . . . . 33 V. B i b l i o g r a p h y . f . . . . . . . . . . . . . . . . 39 SOME PROPERTIES OF ALUMINUM OXIDE IN ELECTROLYTIC SOLUTIONS I - INTRODUCTION By a n o d i c o x i d a t i o n an aluminum p l a t e can be c o v e r e d w i t h an amorphous o r c r y s t a l l i n e o x i d e l a y e r , depending on t h e e l e c t r o l y t e u s e d . The c r y s t a l l i n e l a y e r can be formed i n an aqueous s o l u t i o n o f a s u c c i n a t e , a c i t r a t e o r b o r i c a c i d . The s t r u c -t u r e o f t h i s l a y e r has been i d e n t i f i e d by Verwey (S) as i ^ - A l 2 0 q , a c u b i c f a c e - c e n t e r e d oxygen l a t t i c e i n which t h e c a t i o n s a r e d i s t r i b u t e d s t a t i s t i c a l l y o v e r a l l t h e i n t e r s t i c e s w i t h t h e o n l y r e s t r i c t i o n t h a t 70$ o f t h e aluminum i o n s occupy an o c t a h e d r o n h o l e and 30$ a t e t r a h e d r o n . Because o f t h e pronounced i n s u l a t i n g p r o p e r t i e s o f t h i s l a y e r , t h e c u r r e n t s t e a d i l y d e c r e a s e s d u r i n g f o r m a t i o n a t c o n s t a n t v o l t a g e . Hence t h e l i m i t t o t h e t h i c k n e s s o f a c r y s t a l l i n e l a y e r i s determined by t h e spark p o t e n t i a l o f t h e e l e c t r o l y t e . The amorphous l a y e r i s o b t a i n e d i n a s o l u t i o n o f o x a l i c , s u l p h u r i c o r p h o s p h o r i c a c i d . T h i s l a y e r has a porous s t r u c t u r e , t h e p o r e s h a v i n g a d i a m e t e r o f about 10*"^  cm. and b e i n g o r i e n t e d m a i n l y a t r i g h t a n g l e s t o t h e s u r f a c e . Dekker and Van G e e l (3) showed t h a t i f a p l a t e w i t h a porous l a y e r i s 2. t h e n o x i d i z e d i n b o r i c a c i d a c r y s t a l l i n e s t r u c t u r e forms i n t h e pores o f t h e amorphous l a y e r , and t h a t b o t h s t r u c t u r e s have t h e same d i e l e c t r i c c o n s t a n t . H i g h e r c u r r e n t d e n s i t y i n o x a l i c a c i d produces a d enser s t r u c t u r e o f t h e amorphous c o a t i n g . These pores do not go r i g h t down t o the aluminum as has been shown by many i n v e s t i g a t o r s , but end i n a v e r y s o l i d l a y e r t h a t seems t o be t h e base o f t h e porous p a r t . T h i s s o l i d l a y e r has i n s u l a t i n g p r o p e r t i e s as can be f o u n d f r o m c a p a c i t y measurements. Anderson (1) suggests, a method o f f o r m a t i o n o f t h e porous l a y e r , b a s i n g h i s t h e o r y on measure-ments o f Edwards and K e l l e r (4, 5)• A c c o r d i n g t o t h i s t h e o r y , t h e t h i n b a s i c l a y e r w i l l r e a c h an u l t i m a t e t h i c k n e s s f o r o x i d a t i o n a t c o n s t a n t v o l t a g e : t h e f i e l d s t r e n g t h i n t h e i n s u l a t i n g l a y e r d e c r e a s e s as t h e l a y e r grows, so t h a t t h e r a t e o f growth w i l l g r a d u a l l y d e c r e a s e u n t i l t h i s i s e q u a l t o t h e r a t e o f a t t a c k o f t h e a c i d . Now t h e r a t e o f a t t a c k i s d e t e r m i n e d by t h e c o n c e n t r a t i o n o f t h e s o l u t i o n and t h e t e m p e r a t u r e ; f o l l o w i n g Anderson's r e a s o n i n g , one would e x p e c t t h a t i f one o x i d i z e s a t c o n s t a n t c u r r e n t ( c o n s t a n t f i e l d s t r e n g t h ) and hence works w i t h a c o n s t a n t r a t e o f growth, t h a t t h e b a s i c l a y e r would c o n t i n u o u s l y i n c r e a s e w i t h t i m e , a s s u -ming te m p e r a t u r e and c o n c e n t r a t i o n o f t h e s o l u t i o n a r e cons-t a n t s . My i n v e s t i g a t i o n s do n o t b ear out t h i s t h e o r y , however. These o x i d e l a y e r s under c o n d i t i o n s o f v a r i e d tempe-r a t u r e , c o n c e n t r a t i o n o f t h e a c i d b a t h , and c u r r e n t d e n s i t y d u r i n g f o r m a t i o n , have been t h e s u b j e c t o f t h i s i n v e s t i g a t i o n , 3. w i t h t h e f o l l o w i n g r e p r o d u c i b l e r e s u l t s : 1* C o r r e s p o n d i n g t o a g i v e n t e m p e r a t u r e and a c i d c o n c e n t r a t i o n o f t h e HgSO^ b a t h , and a g i v e n c o n s t a n t c u r r e n t d e n s i t y , t h e r e i s o n l y one f i n a l c a p a c i t y o b t a i n a b l e . 2 . I n c r e a s i n g t h e c o n c e n t r a t i o n o f t h e H2 S (^4 D a t l 1 o r u s i n g a s t r o n g e r a c i d , i n c r e a s e s t h e f i n a l c a p a c i t y o b t a i n a b l e . 3. I n c r e a s i n g t h e c u r r e n t d e n s i t y d e c r e a s e s t h e f i n a l c a p a c i t y o b t a i n a b l e . 4 . I n c r e a s i n g t h e te m p e r a t u r e o f t h e b a t h i n c r e a s e s t h e f i n a l c a p a c i t y . The f o l l o w i n g f a c t s were a l s o o b s e r v e d : 1. 100$ c u r r e n t e f f i c i e n c y d u r i n g t h e f o r m a t i o n o f t h e o x i d e c o u l d n o t be o b t a i n e d w i t h t h e com-m e r c i a l A l samples a t hand (99*5$ A l w i t h Fe, Cu, and p o s s i b l y S i i m p u r i t i e s ) . 2 . The t h i c k n e s s o f an A l 2 0 q c o a t i n o x a l i c a c i d decays e x p o n e n t i a l l y f o r c o n d i t i o n s o f no c u r r e n t and no s t i r r i n g . 3. C o r r o s i o n o f t h e p l a t e s o c c u r r e d f o r c u r r e n t d e n s i t i e s above 4 m.a./cm.2 i n d i l u t e (1 .2$) H2SO4 s o l u t i o n . The c a p a c i t y was s t i l l measure-a b l e i n t h e s e c a s e s , i n d i c a t i n g an o x i d e l a y e r o v e r t h e p i t t e d s e c t i o n s ; t h e v a l u e o f t h e c a p a c i t y d i d not f a l l on t h e smooth c u r v e through c a p a c i t y f o r l o w e r c u r r e n t d e n s i t i e s . 4 . I I - APPARATUS The aluminum sample was c u t i n t o 5 cm. square p l a t e s w i t h a narrow s t r i p e x t e n d i n g above t h e b a t h , so t h a t l e a d s c o u l d be c l i p p e d onto t h e p l a t e . The p l a t e s were c l e a n e d i n s t r o n g KOH s o l u t i o n and t h e n washed i n d i s t i l l e d w a t e r . S i n c e t h e t h i c k n e s s o f t h e o x i d e l a y e r i 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 c a p a c i t y , a measure o f t h e c a p a c i t y i s t h e most d i r e c t way o f d e t e r m i n i n g t h a t t h i c k n e s s . However, the o x i d e l a y e r , £ s i s not a p e r f e c t d i e l e c t r i c , so i t s c a p a c i t y , G, i s e f f e c t i v e l y shunted by an ohmic r e s i s t a n c e . T h e r e f o r e an A.C. b r i d g e method o f measurement must be u s e d , i n w hich one compensates f o r t h e r e s i s t a n c e . The b r i d g e o p e r a t e s a t 60 c y c l e s and about 2 v o l t s . The p l a t e was hung i n a b eaker o f b o r i c a c i d oppo-s i t e s u f f i c i e n t t i n f o i l , and t h i s group was p l a c e d i n t h e A.C. b r i d g e as shown i n f i g . 1, The b r i d g e c o n s i s t s o f a " P h i l o -scope," which g i v e s a r e s i s t a n c e r a t i o , a s t a n d a r d v a r i a b l e -r e s i s t a n c e box, and a group o f pure c a p a c i t i e s . fl-c- f i g . 1. 5 Now the t o t a l c e l l i s measured as—vw—\\- but i s a c t u a l l y J_( \—Lvvvvvv—H V-L ftlx03 "fed r . t Tifefell However to avoid separation of measured C and R to a c t u a l values, the f o l l o w i n g was done: 1. The t i n f o i l c a p a c i t y was made so high as t o be n e g l i g l i b l e by u s i n g 10 sheets of t i n f o i l f o l d e d i n t o accordian p l e a t s and connected i n s e r i e s around the circumference of the beaker. The highest Al^O^ c a p a c i t y measured during the work was about 40 microfarads. Top view: *• Let c^ - c a p a c i t y of t i n f o i l and C = the t o t a l c, c a p a c i t y . _ i _ = -±- H , Q — 40 C c, Ct*HO Then c^ • .9# 0-^+40 f o r 2% accuracy i . e . C-L = 2000 microfarads. Now t o get the experimental value of the f o i l c a p a c i t y , two sheets of t i n f o i l were hung i n b o r i c a c i d s o l u t i o n , being equivalent to -j|—1|— Let C m be the cap a c i t y measured by the b r i d g e . _ L _ = J _ + _ i _ = _ 2 _ C c, c , So, = c , When the c a p a c i t y of an aluminum p l a t e i s measured, the two se c t i o n s of f o i l are connected, i n s e r i e s and the aluminum placed opposite them. 6. T h i s d o u b l e s t h e f o i l c a p a c i t y , so we have ^ cm = Gl = 2 0 0 0 m i c r o f a r a d s C m a 500 m i c r o f a r a d s T h e r e f o r e t h e measured f o i l c a p a c i t y s h o u l d be 500 m i c r o f a r a d s o r more f o r b e t t e r t h a n 2% a c c u r a c y . I n t h e a c t u a l e x p e r i m e n t , f o r two s i n g l e f o i l s , C m a 9,5 x 2 x 12.6 = 239 m i c r o f a r a d s So, f o r t h e f i v e p a i r s used, C„ s 1200 m i c r o f a r a d s m Thus we a r e a s s u r e d t h a t t h e t i n f o i l c a p a c i t y i s n e g l i g i b l e . 2. The s o l u t i o n and f o i l r e s i s t a n c e were measured; upon s u b t r a c t i n g t h a t r e s i s t a n c e f r o m t h e r e s i s -t a n c e measured by t h e b r i d g e , the c o r r e c t i o n f r o m s e r i e s t o p a r a l l e l , c a p a c i t y was f o u n d t o be n e g l i g i b l e . I t can be shown t h a t -J ^ -AAAA-VV*- ( b r i d g e ) and -vww— ( a c t u a l case) a r e r e l a t e d by The c o r r e c t i o n , c ^ R 2^ 2, i s t h a t w h i c h was fo u n d t o be n e g l i g i b l e i n t h i s c a s e . When t h e aluminum p l a t e was r e p l a c e d by a d u p l i -c a t e o f t i n f o i l , t h e f o i l and s o l u t i o n r e s i s t a n c e came t o about 24 ohms. However, t h e r e s i s t a n c e f o r t h e aluminum p l a t e measurements was about t h e same v a l u e , v a r y i n g f r om 23 t o 30 ohms. 7 . That leaves c*L , ( 7 ) = 0.01 f o r c s 40 mic r o f a r a d s . The same con c e n t r a t i o n of b o r i c a c i d s o l u t i o n was used throughout: a saturated b o r i c a c i d s o l u -t i o n plus s u f f i c i e n t ammonium hydroxide to make the s p e c i f i c c o n d u c t i v i t y 500 (ohm-cm.)"1 at 15° C. The su l p h u r i c a c i d from which the var i o u s concentrations were made was C P . (96.5$) w i t h s p e c i f i c g r a v i t y 1.84. R was continuously v a r i a b l e so t h a t e i t h e r current or voltage could be kept constant as d e s i r e d . The D.C. supply was checked f o r A.C r i p p l e by means of an o s c i l l o s c o p e . A.C. r i p p l e i s about 0.2$ of v o l t s D.C. V o l t s DC R i p p l e Measure Gain R i p p l e Measure Gain R i p p l e V o l t s AC AC/DC 40 200 280 .75 2.5 3.5 .15 .8 .084 .45 .62 .2$ .2$ .2$ Table 1. I l l - EXPERIMENTAL RESULTS 1. Dekker and Van G e e l (3) o b t a i n e d 100% c u r r e n t e f f i c i e n c y when o x i d i z i n g h i g h p u r i t y aluminum (99.99$) a t c o n s t a n t c u r r e n t i n b o r i c a c i d . I n our c a s e , -with c ommercial aluminum (99.5$), t h e r e was n o t i c e a b l e gas development on t h e anode, i n c r e a s i n g w i t h t i m e , i . e . , e f f i c i e n c y d e c r e a s i n g . See Graph 1. No t e m p e r a t u r e c o n t r o l seemed n e c e s s a r y i n t h i s c a s e , s i n c e we w i l l show t h i s e f f e c t c o u l d be due t o i m p u r i t i e s . 2. O x a l i c a c i d a t t a c k s t h e o x i d e c o a t . S i n c e c a p a c i t y , C = JLA , i t f o l l o w s t h a t i , b e i n g p r o p o r t i o n a l t o l a y e r ha d G t h i c k n e s s d, can be p l o t t e d on a t i m e graph t o show t h i s a t t a c k . A p l a t e was f i r s t o x i d i z e d a t 200 m.a./50 s q . cm. i n b o r i c a c i d , t h e n washed and p l a c e d i n a s a t u r a t e d o x a l i c a c i d s o l u t i o n , w h i c h was not s t i r r e d . The c a p a c i t y was measured i n t h e b a t h a t i n t e r v a l s as the c o a t was d i s s o l v i n g , w i t h r e s u l t s w h i c h f o l l o w . These r e s u l t s were used t o p l o t Graph 2. M i n u t e s G >f.) 3 6 .4 • .156 4 8 .6 .116 6 15.1 .066 7 16.4 .062 8 17.6 .057 9 18 . 9 .053 14 20.3 .049 18 21.2 .047 20 21.4 .047 The graph o f -± a g a i n s t t i m e appears t o be an e x p o n e n t i a l c u r v e . 9 . 3 . Working at 1 4 . 5 ° C, with a given concentration of sulph-uric acid, and keeping constant current density, only one f i n a l capacity was obtainable: 5 . 4 $ R^SO^, and 2 0 0 mils per 5 0 sq. cm.: Minutes C s e r i e s R s e r i e s "2*771 ] ohms I 2 7 . 2 2 5 , 4 " 2 6 . 2 2 5 . 0 „ . , - N 2 7 . 2 2 5 . 0 Table 3 . n 2 6 . 7 2 5 . 0 3' 2 6 . 5 2 4 . 8 5 2 6 . 5 2 4 . S 9 2 6 . 5 2 4 . 3 Average: 26.7 0.3 f . 4. Graph 3 shows sets of f i n a l capacities obtained, using current densities from 1 to 8 m.a./cm.2, using oxalic acid and various concentrations of sulphuric acid, but regulating the time of oxidation of the plates so that the same amount of charge passed through each. Note that no capacity was graphed for current density higher than 4 m.a./cm.2 in dilute (1.2$) sulphuric acid solution at 14° C. since the plates in this case corroded vi s i b l y . New solution did not change the results. Measurement of the capacity gave a value of the right order, but higher than expected, indicating no shorting of the oxide capacity. It was found upon increasing the temperature of the solution from 14° to 34° that corrosion did not occur. At 34° the capacity was 18. # microfarads compared with 16.1 microfarads at 14°. A capacity of about 15 microfarads would 10. be e x p e c t e d from t h e g r a p h . C o r r o s i o n s t i l l o c c u r e d a t 21.5° C. See T a b l e 5, page 11. 5. V a r y i n g t h e t e m p e r a t u r e o f the b a t h a f f e c t e d t h e f i n a l c a p a c i t y o b t a i n a b l e as shown on Graph 4 . C u r r e n t d e n s i t y o f 4 m i l s / c m . 2 was u s e d . T C (°C) 44 42 37 30 19.5 69.5 49.3 T a b l e 4 . 13 The c a p a c i t y f o r 13° C. was o b t a i n e d e a r l i e r f o r use i n Graph 3 . Table 5. $ H 2S0 4 15$ 9$ 5.4$ 2.3$ 1.19$ 4.8$ Oxalic acid (saturated) Moles/ l i t r e 2.71 1.63 .98 .416 .215 .869 Curr. R Dens, -fl-C R C R C R C •°- A f . R C -XL //f. R C R C 1 24.1 94.0 24.6 69.9 23.3 57.1 26.1 43.8 26.8 28.7 26.1 58.4 25.0 24.9 2 23.5 66i0 25.0 50.8 25.3 39.1 27.8 26.0 29.3 19.9 26.6 38.1 26.4 15.4 3 23.8 53.3 24.4 40.0 26.2 30.5 27.9 21.8 30.9 17.3 25.0 30.5 27.4 12.1 4 24.3 47.0 25.8 33.0 24.8 26.7 30.3 19.7 29.6 15.9 26.5 25.9 28.6 10.7 8 25.2 34.3 25.5 26.4 25.9 21.6 26.1 17.5 25.9 21.6 30.3 8.4 1 3 1 1 r 15. IV - DISCUSSION 1. EXISTING THEORIES; A d i s c u s s i o n o f t h e e x p e r i m e n t a l r e s u l t s i n v o l v e s a c o n s i d e r a t i o n o f t h e p r e s e n t t h e o r i e s o f f o r m a t i o n o f aluminum o x i d e i n e l e c t r o l y t i c s o l u t i o n s : t h e o r i g i n a l t h e o r y (Verwey - 8) r e q u i r e s aluminum m i g r a t i o n o n l y j and t h e o t h e r , r e c e n -t l y proposed by Anderson (1) and based on measurements by Edwards and K e l l e r (4,5), s u g g e s t s t h a t b o t h aluminum and oxygen m i g r a t i o n o c c u r . Now i t i s u n d i s p u t e d l y shown by X-ray a n a l y s e s t h a t aluminum has a f a c e - c e n t r e d c u b i c s t r u c t u r e w i t h a r, 4.04; and t h a t AI2O3 formed i n e l e c t r o l y t i c s o l u t i o n has t h e s t r u c t u r e o f tf-AL^O^, a c l o s e - p a c k e d f a c e - c e n t r e d oxygen l a t t i c e (a sa 3.95) w i t h t h e c a t i o n s d i s t r i b u t e d s t a t i s t i c a l l y o v e r t h e i n t e r s t i c e s , t h e o n l y r e s t r i c t i o n b e i n g t h a t 70$ o f t h e cations occupy an o.ctahedron h o l e and 30$ a t e t r a h e d r o n h o l e ( r e f . 8) . By t h e f i r s t t h e o r y , when aluminum i s made t h e anode i n an e l e c t r o l y t i c s o l u t i o n , oxygen i o n s c o l l e c t o v e r t h e s u r f a c e o f t h e anode i n t h i s o r d e r l y f . c c . arrangement. Then under t h e i n f l u e n c e o f t h e h i g h f i e l d ( l O ^ v . / c m . ) , A l i o n s d i f f u s e f r o m l a t t i c e p o s i t i o n s on t h e s u r f a c e o f t h e m e t a l t o i n t e r s t i t i a l p o s i t i o n s i n t h e oxygen i o n l a t t i c e . E l e c t r o n s i n t h e m e t a l , 'abandoned' by t h e m i g r a t i n g A l i o n s f l o w t h r o u g h t h e e x t e r n a l c i r c u i t and p r e s e r v e t h e c u r r e n t 16. c o n t i n u i t y ; w hich p r o c e s s can be c o n t r a s t e d w i t h t h e case o f 0 2 b e i n g l i b e r a t e d f r o m t h e anode s u r f a c e o f a m e t a l w h i c h does not f o r m an o x i d e , s i n c e t h e n i t i s t h e 2 e l e c t r o n s f rom each o f t h e oxygen i o n s t h a t f l o w i n t o t h e m e t a l . C o n t i n u e d growth o f t h e o x i d e l a y e r depends on t h e a b i l i t y o f t h e A l i o n s t o d i f f u s e t h r o u g h t h e oxygen l a t t i c e . I t appears t o me t h a t t h i s p r o c e s s p r e s e n t s one major problem: t h e problem o f t h e space v a c a t e d by m i g r a t i n g A l i o n s . P o s s i b l y more A l i o n s move up f r o m t h e m e t a l so t h a t t h e r e i s a g r a d u a l s h i f t i n g t h r o u g h t h e whole aluminum l a t t i c e . However, t h e r e i s no a p p r e c i a b l e f i e l d i n t h e aluminum l a t t i c e , t h e a p p l i e d p o t e n t i a l d i f f e r e n c e b e i n g c h i e f l y o v e r t h e o x i d e l a y e r and o n l y a v e r y s m a l l f r a c t i o n o v e r t h e e l e c t r o l y t i c s o l u t i o n ( c o n d u c t i v i t y 500 ohm-cm."^); and s i n c e l a t t i c e p o s i t i o n s a r e p o s i t i o n s o f minimum p o t e n t i a l f o r t h e i o n s , t h e i o n s a r e n o t l i k e l y t o assume t h e l o o s e r s t r u c t u r e o f t h e s h i f t i n g arrangement w i t h o u t a s t r o n g e x t e r n a l f i e l d . The o n l y o t h e r p o s s i b i l i t y seems t o be t h a t when a row o f A l i o n s have moved i n t o t h e oxygen l a t t i c e , t h e whole o x i d e l a t t i c e moves c l o s e r t o t h e m e t a l , w h i c h would be an e r r a t i c movement. Both t h e s e e x p l a n a t i o n s seem t o i m p l y a l e s s dense r e g i o n on t h e whole m e t a l s u r f a c e , which i s c o n t r a d i c t o r y t o t h e observed t e n a c i t y o f t h e o x i d e t o t h e m e t a l . Anderson's t h e o r y , on t h e o t h e r hand, l e a d s t o a v e r y c o n v i n c i n g e x p l a n a t i o n f o r t h i s t e n a c i t y . A c c o r d i n g t o h i s t h e o r y , one. out o f e v e r y t h r e e A l i o n s , h a v i n g a s m a l l r a d i u s o f 0.5 A, d i f f u s e s e a s i l y t h r o u g h t h e o x i d e l a t t i c e ; 17. i f t h e o t h e r two r e a r r a n g e s l i g h t l y , t h e r e i s s u f f i c i e n t room i n t h e m e t a l f o r a d j a c e n t oxygen i o n s t o jump i n under t h e i n f l u e n c e o f t h e s t r o n g e l e c t r i c f i e l d . The p o s i t i o n s v a c a t e d by t h e s e oxygen i o n s a r e t h e n f i l l e d by o t h e r s from f u r t h e r out i n t h e f i l m and t h e p r o c e s s i s r e p e a t e d u n t i l v a c a n t oxy-gen spaces a r e f i l l e d by i o n s from t h e e l e c t r o l y t e . The cur« r e n t t h e n i s c a r r i e d by outward d i f f u s i o n o f aluminum i o n s and i n w a r d s h i f t o f oxygen i o n s i n t h e r a t i o 1:2 ; o r i f i n w a r d s h i f t i n g o f oxygen i o n s i s t h e same as outward movement o f p o s i t i v e h o l e s , t h e n t h e c u r r e n t i s c a r r i e d 1/3 by p o s i t i v e i o n s and 2/3 by p o s i t i v e h o l e s . So growth t a k e s p l a c e b o t h a t t h e o x i d e - s o l u t i o n i n t e r f a c e and a t t h e o x i d e - m e t a l i n t e r f a c e , one m o l e c u l e o f A^O^ a t t n e f o r m e r f o r e v e r y 2 m o l e c u l e s a t t h e l a t t e r . So f a r i t has been assumed t h a t a l l t h e aluminum i s used t o f o r m o x i d e j but i n t r u t h t h i s i s o n l y so i n c e r t a i n e l e c t r o l y t i c s o l u t i o n s , such as b o r i c a c i d , i n which aluminum o x i d e i s not s o l u b l e . I n t h e s e s o l u t i o n s t h e c r y s t a l l i n e l a y e r o f t h e o x i d e forms u n i f o r m l y o v e r t h e whole s u r f a c e o f t h e m e t a l . In" o t h e r s o l u t i o n s / such as H^SO^, o x a l i c a c i d , and chromic a c i d , a l l t h e aluminum i s not used t o f o r m aluminum o x i d e ; and i n such c a s e s t h e l a y e r has been o b s e r v e d t o have a porous s t r u c t u r e . The pores have a d i a m e t e r o f about lCT^cm., and a r e o r i e n t e d m a i n l y a t r i g h t a n g l e s t o t h e s u r f a c e . (See e l e c t o n - m i c r o s c o p e m i c r o g r a p h , r e f . 3«) These pores do n o t go r i g h t t h r o u g h t o t h e aluminum as has been shown by many i n -v e s t i g a t o r s , b u t end i n a v e r y s o l i d l a y e r t h a t seems t o be t h e base o f the porous s e c t i o n . T h i s s o l i d l a y e r has i n s u l a t i n g p r o p e r t i e s as can be f o u n d f r o m c a p a c i t y measurements. The i m p o r t a n t f a c t i s t h a t aluminum o x i d e i s s o l u b l e i n t h e s e a c i d s , Anderson s t a t e s t h a t i n t h i s case t h e aluminum i o n s w hich m i g r a t e t o t h e s u r f a c e o f t h e o x i d e l a y e r do not combine w i t h oxygen t o f o r m more o x i d e , but form a s o l u b l e s u l p h a t e , f o r example, and go i n t o s o l u t i o n . C o n c e r n i n g t h e f a c t t h a t a porous s t r u c t u r e i s formed i n t h i s l a t t e r t y p e o f s o l u t i o n , Anderson s a y s : "Once t h e a c i d a t t a c k i s i n i t i a t e d a t a p o i n t , t h e r e i s e s t a b l i s h e d ,the e l e c t r i c a l f i e l d d i s t r i b u t i o n o f a charged p o i n t near a p l a n e . The aluminum i o n s and p o s i t i v e h o l e s w i l l d i f f u s e toward t h a t p o i n t which forms t h e base o f a p o r e . Thus we have t h e growth p r o c e s s e s t a k i n g p l a c e i n a s p h e r i c a l cap around t h e base o f t h e pore as c e n t r e . Pores a r e formed w i t h s u f f i c i e n t d e n s i t y t h a t t h e i r spheres o f a c t i o n j u s t o v e r l a p t h o s e o f a d j a c e n t p o r e s . The d i f f u s i n g i o n s move a l o n g r a d i u s v e c t o r s drawn from t h e base o f t h e pore t o t h e aluminum s h e e t . " The pro and con e v i d e n c e f o r t h e s e two t h e o r i e s , one o f aluminum m i g r a t i o n o n l y and t h e o t h e r o f b o t h aluminum and oxygen m i g r a t i o n , , seems t o be t h e f o l l o w i n g : 1. As a l r e a d y mentioned, t h e o b s e r v e d t e n a c i t y o f t h e o x i d e l a y e r t o t h e p a r e n t m e t a l i s b e t t e r e x p l a i n e d by Anderson's t h e o r y s i n c e t h e c o n s t a n t m i g r a t i o n o f oxygen i o n s i n t o v a c a n t m e t a l p o s i t i o n s as t h e y o c c u r keep's t h e two l a y e r s i n c l o s e c o n t a c t . 2. A s h o r t c a l c u l a t i o n o f volumes i n v o l v e d i n t h e Anderson t h e o r y shows t h e p r o p o s i t i o n i s f e a s i b l e : 19. 3 ° 3 A u n i t c e l l o f A l has a volume - ( 4 . 0 4 ) A , and c o n t a i n s 4 A l atoms. .*. Each A l atom i s a s s o c i a t e d w i t h a volume ^*°fr> 3 P - 1 6 . 5 A3. 4 3 A l atoms a r e a s s o c i a t e d w i t h volume o f 4 9 * 5 A 3 . A u n i t c e l l o f A 1 2 0 ^ has a volume ( 3 . 9 5 ) 3 13 and c o n t a i n 4 / 3 A I 2 O 3 m o l e c u l e s . .*. Each o x i d e m o l e c u l e i s a s s o c i a t e d w i t h a volume o f 46 A 3> Then i f t h r e e A l i o n s a r e removed, t h e space t h e y l e a v e ( 4 9 . 5 ^ 3 ) i s s u f f i c i e n t room f o r one m o l e c u l e o f o x i d e ; i . e . , one A l i o n i s s i m p l y removed by d i f f u s i o n t o t h e e l e c t -r o l y t e s u f f a c e , and th e o t h e r two remain t o form an o x i d e m o l e c u l e w i t h oxygen which i s a b l e t o jump i n t o t h e space p r o v i d e d due t o the h i g h f i e l d . N o t i c e , however, t h a t t h e space p r o v i d e d i s l a r g e r t h a n n e c e s s a r y . So a t t h i s p o i n t i t i s n e c e s s a r y t o p o i n t out t h e f o l l o w i n g d i s c r e p a n c y : Volume o f u n i t c e l l o f A l , ( 4 . 0 4 ) 3 £ 3 , c o n t a i n s 4 A l atoms. Weight o f u n i t c e l l = 4 x a t . wt. A l . x IH Weight o f 1 c c . A l = 4 x 2 7 x 1 . 6 7 x 1 0 " 2 i * ( 4 . 0 4 ) 3 x 1 0 - 2 / * -= 2 . 7 4 gms. T h i s i s i n agreement w i t h t h e a c c e p t e d d e n s i t y o f aluminum. S i m i l a r l y : Volume o f u n i t c e l l o f o x i d e i s ( 3 . 9 5 ) 3 A 3 , and c o n t a i n s 4 / 3 o x i d e m o l e c u l e s . Weight o f u n i t c e l l = 4 / 3 x 1 0 2 x I . 6 7 x 1 0 ~ 2 ^ gms. Wt. o f 1 c c o x i d e = 4 / 3 x 1 0 2 x 1 . 6 7 x IP" 2 2*-( 3 . 9 5 ) 3 x 1 0 " 2 4 = 3 . 7 gms. But. B u r g e r s ( 2 ) e x p e r i m e n t a l l y d e t e r m i n e d t h e 2 0 . d e n s i t y as 3*1 • Now t h e o x i d e may c o n t a i n a d s o r b e d water and a c i d m o l e c u l e s , w h i c h would e x p l a i n a d e n s i t y v a l u e b e i n g t o o low; as w i l l be seen l a t e r , p o r o s i t y w i l l a f f e c t measurements of t h e d e n s i t i e s o f l a y e r s formed i n c e r t a i n s o l u t i o n s ; and o f cou r s e i t i s v e r y d i f f i c u l t t o t a k e v e r y r e l i a b l e t h i c k n e s s measurements o f l a y e r s which a r e o n l y m i c r o n s i n t h i c k n e s s , e s p e c i a l l y when t h e aluminum must f i r s t be d i s s o l v e d o f f t h e l a y e r . 3. Another p i e c e o f e x p e r i m e n t a l e v i d e n c e f o r t h i s t h e o r y o f Anderson's i s t h e f a c t t h a t no v a l u e o f t h e e f f i c i -ency r a t i o i n e x c e s s o f 1.59 has y e t been o b s e r v e d w i t h e l e c t -r o l y t e s i n which t h e o x i d e i s s l o w l y s o l u b l e (Edwards and K e l l e r - 4). T h i s e f f i c i e n c y r a t i o i s the r a t i o o f t h e o x i d e formed t o t h e weight o f aluminum r e a c t i n g and b e i n g l o s t t o t h e s h e e t . I f a l l t h e aluminum r e a c t i n g appeared as o x i d e , t h e r a t i o would be 1.89. When Anderson c a l c u l a t e s t h e r a t i o i n t h e l i g h t o f h i s t h e o r y , he f i n d s a maximum p o s s i b l e v a l u e o f 1.59; Edwards and K e l l a r (4) e x p e r i m e n t a l l y have o b t a i n e d no v a l u e s above 1.46. 4. I t i s c e r t a i n l y t r u e a t l e a s t t h a t growth p r o c e s s e s do not t a k e p l a c e a t t h e t o p o f t h e o x i d e s e p a r a t i n g t h e p o r e s . Rummel (7) p a i n t e d t h i s p a r t and t h e n c o n t i n u e d o x i d a t i o n t o f i n d t h a t t h e new o x i d e was growing u n d e r n e a t h t h e p a i n t e d l a y e r . T h i s i s s u r e l y t o be e x p e c t e d , s i n c e t h e o x i d e between t h e pores i s so much t h i c k e r t h a n the t h i n l a y e r a t t h e base o f each pore t h a t t h e m i g r a t i o n due t o t h e f i e l d s t r e n g t h must be d i r e c t e d toward t h e bases o f t h e p o r e s . 2 1 . 5 » F i n a l l y t h e r e i s some e v i d e n c e f o r t h e f i r s t t h e o r y o f aluminum m i g r a t i o n a l o n e ; e v i d e n c e which depends on the a c c u r a c y o f t h e d e t e r m i n a t i o n s o f d e n s i t y o f t h e porous and s o l i d c r y s t a l l i n e l a y e r s : Dekker and Van G e e l ( 3 ) measured the r a t e o f change o f v o l t a g e d u r i n g o x i d a t i o n a t c o n s t a n t c u r r e n t i n b o r i c a c i d ; i . e . , f o r t h e s o l i d c r y s t a l l i n e l a y e r . Then t h e y formed a porous l a y e r on a n o t h e r p l a t e i n o x a l i c a c i d , a g a i n measuring t h e r a t e o f change o f v o l t a g e f o r the o x i d a t i o n i n b o r i c . I n t h i s second c a s e , assuming o n l y aluminum m i g r a t e s and t h a t t h e r e f o r e t h e o n l y f o r m a t i o n proceeds on t h e s u r f a c e , t h e y c o n s i d e r e d t h a t t h e b o r i c o x i d a t i o n was f i l l i n g t h e p o r e s . Then the r a t i o o f t h e two r a t e s o f change o f v o l t a g e i n b o r i c a c i d i s t h e r a t i o o f t h e pore a r e a t o t h e t o t a l a r e a o f t h e p l a t e . F o r a p a r t i c u l a r c u r r e n t d e n s i t y t h e y found t h e por e s were about 3 0 $ o f t h e t o t a l a r e a , which i s i n k e e p i n g w i t h t h e d e n s i t y r a t i o o f porous t o c r y s t a l l i n e l a y e r s o f 2 . 5 / 3 * 1 • Now i f Anderson ( 1 ) i s r i g h t , t h e n t h e second o x i d a t i o n i s not o n l y f i l l i n g t h e p o r e s , but i s a l s o f o r m i n g o x i d e a t t h e m e t a l - o x i d e i n t e r f a c e , one m o l e c u l e o f o x i d e on t h e s u r f a c e t o ev e r y two below. So a s l i g h t l y l o n g e r c a l c u l -a t i o n t h a n t h a t used above i s needed t o c o n v e r t t h e dv/dt r a t i o t o t h e a r e a r a t i o : F o r o x i d a t i o n o f t h e porous l a y e r i n b o r i c a c i d : When x cm.3 o f o x i d e a r e formed below, x / 2 cm.3 a r e formed i n t h e pores on t h e s u r f a c e . L e t t h e a r e a o f t h e pores be l / f o f t h e t o t a l a r e a A 22. o f t h e p l a t e ; i l e . , o u t s i d e a r e a = — ( i n s i d e a r e a ) . So x/2 cm. a r e formed on an a r e a A / f . Then t h i c k n e s s o f o u t s i d e l a y e r i s 1„ = v o l . / a r e a •8 = x f / 2 A whereas i n s i d e , x cm.3 a r e formed on a r e a A. Then t h i c k n e s s o f i n s i d e l a y e r i s 1^ = x/A Now t h e change i n v o l t a g e i s p r o p o r t i o n a l t o change i n t h i c k n e s s . T o t a l r a t e o f change = ^ - ( 1 T ) = 4-(3-i + 1«) d t 1 d t 1 s - ^ ( U + | l i ) = ( ! • § ) ^ M i ) - d_M. . I-- + r 2' d l So i r ( V A ) f f ) d (x ) f o r t h e p 0 r o u s l a y e r ( 1 ) . Fo r t h e s i m p l e b o r i c l a y e r w i t h no p o r e s , d s = d^/2 s i n c e o x i d a t i o n t a k e s p l a c e o ver t h e whole s u r f a c e i n t h i s c a s e . | _ ( 1 T ) = fed. • l ! ) - | d - d i ) So iL.(V R) oc 1 ^ _ ( l i ) f o r t h e b o r i c c r y s t a l l i n e layer, d t D 2 d t (2). E x p e r i m e n t a l l y , Dekker and Van G e e l found 4 _ ( V n ) = 12 d t o and ^ ( V A ) = 52. SO C M V b ^ = i f H t ^ * o r a P P r o x i m a t e l y » t t ( v B ) = £ ! t ( v A ) . Comparing f o r m u l a e (1) and (2) above: (1 + | ) = 6, and f = 10. So t h e pores a r e o f t h e t o t a l a r e a i n c o n t r a s t 1 0 1 w i t h Dekker and Van G e e l ' s v a l u e o f y t h w h i c h , however, was more i n k e e p i n g w i t h t h e d e n s i t y r a t i o o f y 2^* T n e d e n s i t y r a t i o has a l r e a d y been d i s c u s s e d . 24. 2. DISCUSSION OF EXPERIMENTAL RESULTS: 1. R e g a r d i n g o x i d a t i o n i n b o r i c a c i d : D u r i n g o x i d a t i o n i n b o r i c a c i d a t c o n s t a n t c u r r e n t d e n s i t y , t h e r a t e o f f o r m a t i o n s h o u l d be c o n s t a n t , as has been o b s e r v e d f o r h i g h p u r i t y aluminum, and w i t h 100$ c u r r e n t e f f i c i e n c y ( r e f . 3 ) . The c ommercial aluminum used i n t h i s i n v e s t i g a t i o n was o f 99*5$ p u r i t y , whereas t h a t mentioned above was 99.99$. T h i s seems t o be s u f f i c i e n t d i f f e r e n c e t o l o w e r t h e e f f i c i e n c y o f f o r m a t i o n as e v i d e n c e d by t h e d e v i a t i o n o f graph 1 f r o m a s t r a i g h t l i n e . Note t h a t t h e d e v i a t i o n becomes g r e a t e r as t h e l a y e r becomes t h i c k e r . An e x p l a n a t i o n may be as f o l l o w s : Assuming t h a t t h e oxygen l a t t i c e i s made up o f c l o s e -packed h a r d spheres i n a f a c e - c e n t e r e d c u b i c arrangement, t h e space t h r o u g h which t h e d i f f u s i n g aluminum i o n s must pass can be c a l c u l a t e d f r o m t h e d i m e n s i o n s o f t h e t r i a n g l e formed by t h r e e oxygen i o n p o s i t i o n s i n t h e c e n t e r s o f t h r e e a d j a c e n t .. cube f a c e s . E v e r y m i g r a t i n g aluminum i o n must pass t h r o u g h a s u c c e s s i o n o f t e t r a h e d r a l and o c t r a h e d r a l p o s i t i o n s , and i n o r d e r t o do so must pass t h r o u g h t h i s t r i a n g l e w hich i s t h e n t h e h i g h e s t p o t e n t i a l b a r r i e r t h a t must be passed; o t h e r w i s e t h e aluminum i o n s a r e r e l a t i v e l y u n h i n d e r e d s i n c e even i n a complete A l 2 0 ^ l a t t i c e t h e r e a r e many v a c a n t l a t t i c e p o s i t i o n s . The cube s i d e i s a = 3.95 T h e n b = i aV2 = 2 . 8 L So the maximum r a d i u s f o r undeformed oxygen spheres 25 i s ly = 1.4 X . b _ _ b _ . o 2 s i n 60° - r - 7 5 - 1 . 6 A Then c = r - ^ = 0 . 2 I , the r a d i u s of the l a r g e s t sphere which can pass between the oxygen i o n s . I f i t takes a f i e l d of 10^ v o l t s / cm. before o aluminum ions of r a d i u s 0 . 5 A can migrate through t h i s space, then i t seems l i k e l y that i m p u r i t y atoms such as a copper atom, having r a d i u s = 0.8 X , could not pass at a l l . As the l a y e r becomes thic k e r , , more of these ions which are incapable of d i f f u s i n g are incorporated i n the oxide l a t t i c e as i t grows from the bottom; and thus i t becomes i n c r e a s i n g l y more d i f f i -c u l t f o r the migrations to occur. Under these circumstances an appreciable e l e c t r o n i c current flows l i b e r a t i n g oxygen from the anode. f i g . 4. 2 . Regarding o x i d a t i o n i n s u l p h u r i c a c i d , which produces porous l a y e r s . Now Anderson (1) has s t a t e d t h a t when o x i d a t i o n i s c a r r i e d on at constant voltage i n s u l p h u r i c a c i d , the f i e l d strength decreases as the f i l m t h i c k n e s s i n c r e a s e s , and the r a t e of growth of the b a r r i e r l a y e r then diminishes u n t i l 26 e q u i l i b r i u m i s r e a c h e d between t h e r a t e o f a c i d a t t a c k and t h e r a t e o f growth. F o l l o w i n g t h i s r e a s o n i n g , one would expect t h a t i f o x i d a t i o n were c o n t i n u e d i n s u l p h u r i c a c i d s o l u t i o n w i t h c o n s t a n t c u r r e n t , t h a t t h e r a t e o f growth would be cons-t a n t , and t h a t t h e r e f o r e t h e unbroken b a s i c l a y e r below t h e pore s would c o n t i n u o u s l y i n c r e a s e i n t h i c k n e s s . That i s not t h e c a s e , however, I have found t h a t f o r a g i v e n a c i d c o n c e n t r a t i o n , t e m p e r a t u r e , and c o n s t a n t c u r r e n t d e n s i t y , o n l y one f i n a l c a p a c i t y i s o b t a i n a b l e ( t a b l e 2 ) ; i . e . , t h e t h i n b a s i c l a y e r w i l l n o t i n c r e a s e beyond a c e r t a i n t h i c k n e s s , no m a t t e r how l o n g t h e o x i d a t i o n p r o c e s s i s c o n t i n u e d . H e a v i e r c u r r e n t d e n s i t y r e s u l t s i n a t h i c k e r b a s i c l a y e r ; h i g h e r t e m p e r a t u r e o r h i g h e r a c i d c o n c e n t r a t i o n r e s u l t i n a t h i n n e r l a y e r (graphs 3 and 4) • S i n c e t h e t h i c k n e s s o f t h e o x i d e s e p a r a t i n g t h e pore s does i n c r e a s e w i t h t i m e , t h e c o n c l u s i o n n a t u r a l l y f o l l o w s t h a t growth i s c e r t a i n l y t a k i n g p l a c e a t t h e m e t a l - o x i d e i n t e r -f a c e as Anderson s u g g e s t s . I n o r d e r t h a t t h e unbroken l a y e r r e m a i n t h e same t h i c k n e s s t h e a c i d must be a t t a c k i n g t h e base o f t h e pores a t t h e same r a t e as t h e l a y e r i n c r e a s e s i n t h i c k -ness a t the m e t a l s i d e . The r e a c t i o n e q u a t i o n i n t h e s o l u t i o n c o u l d be w r i t t e n : H 2 S 0 4 -> 2 H r + S 0 4 " " S 04~"* H2° ~ * H l s o * 4 ° ~ ~ so t h e net r e s u l t i s s i m p l y : H ? 0 2H + + 0 27. There appear to be three possible reactions for oxide formation: a. The reaotion equation for oxide formation in borio acid must be: 1 8 H + + 6 Al***V 9 0~~-+ 3 A1 20 3 -+ 9 Hg* 1 molecule is produced on the surface for every 2 molecules next to the metal. b. The equation for oxide formation in sulphuric acid, using Anderson's pioture would be: 6 A l * % 9 + 18 £ Alg0 3+ 6 Hgt + Alg0 3+ 6 H*" «- 6 — * 2 A1+ 3 HgO the oxide produced on the surface going into the solution. o. Finally there could be this equation whioh represents the state of constant thickness of the thin layer beneath the pores; i.e., acid attack faster than i n the last equations given; as fast, in faot, as the oxide i s being formed: 6 Al"* +9 0 -+-18 H* —>- 3 Alg0 3+ 18 H^_> 6 AT**- 9 HgO The problem is vto.y at any time during oxidation equation (o) should be prefered over equation (b); i.e., why the; layer should dissolve as rapidly as i t i s formed after i t has attained a certain thiokness. Now I have noticed when forming these porous layers at constant current, that the voltage over the layer rises rapidly for about the f i r s t half minute, then drops as rapidly a volt or two before levelling off to beoome constant; this 28, c o u l d be i n t e r p r e t e d a s growth o v e r t h e whole s u r f a c e u n t i l a c r i t i c a l t h i c k n e s s i s r e a c h e d a t which t h i s r a p i d a c i d a t t a c k b e g i n s t o form p o r e s . The c o n c e n t r a t i o n o f aluminum i o n s w i l l be g r e a t e r a t t h e m e t a l - o x i d e i n t e r f a c e t h a n a t t h e s o l u t i o n -o x i d e i n t e r f a c e , as w i l l t h e c o n c e n t r a t i o n o f oxygen i o n s be g r e a t e r a t t h e l a t t e r i n t e r f a c e t h a n a t t h e f o r m e r . T h i s v a r i -a t i o n o f c o n c e n t r a t i o n o f i o n s w i l l a f f e c t t h e way t h e f i e l d v a r i e s t h r o u g h t h e o x i d e ; p o s s i b l y under g i v e n c u r r e n t , con-c e n t r a t i o n , and tempe r a t u r e c o n d i t i o n s t h e r e i s a c r i t i c a l t h i c k n e s s beyond w h i c h t h e o x i d e i s not s t a b l e under such f i e l d c o n d i t i o n s . I n o r d e r t o f i n d t h e way i n w h i c h t h e t h i c k n e s s o f the b a s i c l a y e r depends on c u r r e n t d e n s i t y , c o n c e n t r a t i o n and te m p e r a t u r e , d a t a f r o m t a b l e s 3 and 5 a r e used as f o l l o w s t o p l o t graphs 5, 6 and 7» From T a b l e 3: H 2S0 4 cone: 15$ 9% 5.4$ 2.3$ 1.19$; O x a l i c l o g I (ma) d (I) d(K) d (I) d (&) d (1) d ll) l o g 1 =0 33.8 45.5 55.8 72.6 111 128 l o g 2 =.301 48.3 62.6 81.4 122 160 238 l o g 3 =.477 59.7 79.6 104 146 184 264 l o g 4 =.602 67.7 96.5 119 162 200 299 l o g 8 =.903 92.9 120.5 147 182 — 380 T a b l e 6. These f i g u r e s a r e p l o t t e d on Graph 6, d v s . Log I , where d i s t h e f i n a l t h i c k n e s s o f t h e b a s i c l a y e r e x p r e s s e d i n Angstroms, and where I i s t h e c u r r e n t d e n s i t y . Note t h e n t h a t t h e v a l u e s o f d f o r c o n s t a n t c o n c e n t r a t i o n v a r y d i r e c t l y as the l o g o f t h e c u r r e n t d e n s i t y . 30 l o g I = * d ; c o n s t a n t f o r g i v e n c o n c e n t r a t i o n and t e m p e r a t u r e . From T a b l e 5: d (A) l o g - i -& 100 1000 o T 31.8 1.16 3.16 37.0 1.31 3.17 45.8 1.52 3.23 64.5 1.86 3.30 99.7 2.30 3.42 119.0 2.48 3.49 T a b l e 7. Graph 5 shows l o g d v s . ^ , which i s a s t r a i g h t l i n e e x c e pt f o r t h e l a s t 2 p o i n t s . So B l o g d = *p ; B = c o n s t a n t f o r g i v e n c o n c e n t r a t i o n and temperature.. Here i t may be u s e f u l t o p o i n t o ut t h e d i f f i c u l t y e n countered when o x i d i z i n g w i t h c u r r e n t s o v e r 4 m.a./cm. i n 1.2$ #2$®!+ a t 13° 0 . , which may have some b e a r i n g on t h e d e v i a t i o n f r o m a s t r a i g h t l i n e i n t h e above case f o r t h e l o w e r t e m p e r a t u r e s . Under t h e mentioned c o n d i t i o n s t h e p l a t e s c o r r o d e d v i s i b l y , b ut an o x i d e l a y e r s t i l l c o v e r e d t h e whole p l a t e , s i n c e a c a p a c i t y measurement was o b t a i n e d , a l t h o u g h t h e v a l u e d i d not l i e on t h e graph f o r l o w e r c u r r e n t d e n s i t i e s a t t h e same c o n c e n t r a t i o n and t e m p e r a t u r e . T h i s may be a t t r i b u -t a b l e t o s o l u b i l i t y p r o d u c t e f f e c t s , s i n c e i n some c a s e s d i l u t e s o l u t i o n s have been o b s e r v e d t o g i v e r i s e t o much more s e r i o u s e l e c t r o l y t i c c o r r o s i o n t h a n more c o n c e n t r a t e d s o l u t i o n s . A n o t h e r r e a s o n f o r e x p e c t i n g d e v i a t i o n s f o r t h i n n e r l a y e r s may be t h e f o l l o w i n g . The bases o f t h e pores can be 31 thought of as a ser ies of small plates set some distance from a s ingle large plate (the metal) ; when the plates are very-close together, the area must be the sum of the areas of the small p la tes ; but when the separation becomes large enough, the area f o r the capacity measurement approximates the area of the s ing le large p l a t e . T h i s would lead to deviat ions i n the d i r e c t i o n observed. From T a b l e 3, rearranging to keep current density constant, there i s the f o l l o w i n g r e l a t i o n between concentration ( i n m o l e s / l i t r e ) and thickness of the basic layer (expressed i n Angstroms): (See Graph 7) T a b l e 8. Cone. moles/ 10 d at d at d at d at ^2^4 l i t r e ~7Z 1 mil/cm§3 ma/cm2 4 ma/cm2 8 ma/cm2 15.0 % 2.71 6.07 33.8 59.7 67.7 92.9 9.0 % 1.63 7.85 45.5 79.6 96.5 120.5 5.4 % .98 10.1 55.8 104.0 119.0 147.0 2.3 % .416 15.5 72.6 146.0 162.0 182.0 1.19$ .215 21.6 111.0 I84.O 200.0 So d» where f » constant, f o r given temperature */c and current d e n s i t y . To summarize the experimental r e s u l t s : 1. F o r given temperature and current densi ty , d i s proport ional to 2. F o r given concentration and current densi ty , l o g d i s i n v e r s e l y proport ional to T, 3 . F o r given concentration and temperature, d i s proport ional to l o g I , where d refers to the thickness of the t h i n basic oxide layer u n d e r n e a t h t h e porous o x i d e s t r u c t u r e formed i n s u l p h u r i c a c i d . 3 . SUGGESTED THEORY FOR FORMATION OF BASIC LAYERS OF CONSTANT.  THICKNESS; Experiment has shown t h a t f o r g i v e n c o n c e n t r a t i o n o f s u l p h u r i c a c i d , t e m p e r a t u r e and c u r r e n t d e n s i t y , a b a s i c l a y e r o f c o n s t a n t t h i c k n e s s i s formed under t h e porous s t r u c t u r e and t h a t t h i s t h i c k n e s s i s p r o p o r t i o n a l t o the l o g a r i t h m o f t h e c u r r e n t d e n s i t y . I t i s proposed t o show by t h e f o l l o w i n g t h e o r e t i c a l c a l c u l a t i o n t h a t t h i s r e l a t i o n i s c o r r e c t . A. F i r s t some n u m e r i c a l v a l u e s must be c a l c u l a t e d . 1. C o n c e n t r a t i o n o f Al*" +*ions p e r c c . w i t h o u t f i e l d : S t r u c t u r e o f AI2O3 formed i n b o r i c a c i d i s o f t h e £>-type ( r e f . 9)> a f a c e - c e n t e r e d c u b i c l a t t i c e o f oxygen i o n s w i t h a s t a t i s t i c a l d i s t r i b u t i o n o f t h e A l i o n s o v e r o c t a h e d r o n and t e t r a h e d r o n h o l e s . The l a t t i c e parameter i s a =» 3.95 A*. Then, s i n c e t h e r e a r e on t h e average 8/3 A l ^ i o n s i n s i d e a cube o f s i d e a ( e q u i v a l e n t t o 4 0° i o n s ) , t h e c o n c e n t r a t i o n o f A l ^ ^ i o n s p e r c c . w i t h o u t a f i e l d i s n Q « 4.3 x 1 0 2 2 . 2. C o e f f i c i e n t /3 i n e l e c t r o l y t i c c u r r e n t f o r m u l a I « < e ^ , where F i s t h e f i e l d s t r e n g t h : A s t u d y o f t h e f . c c oxygen l a t t i c e shows t h a t one AT*** i o n must make 4 jumps t h r o u g h a l t e r n a t e o c t a h e d r o n and t e t r a h e d r o n p o s i t i o n s t o c o v e r a d i s -t a n c e a=3»95 A* i n one s p e c i f i c d i r e c t i o n . A p r o j e c t i o n o f t h i s p a t h l e a d s t o f i g . 5 f o r t h e 34. potential curve inside the oxide where b a a ~ 1 A. The a c t i v a t i o n energy U ' 6- ' f o r an octahedron-tetrahedron jump w i l l f i g . 5. for s i m p l i c i t y be assumed equal to that fo r a tetrahedron-octahedron Jump. I f the v i b r a t i o n frequenoy i s ^ s s l O 1 ^ , the p r o b a b i l i t y f o r a jump without an applied f i e l d i s Oe"^ 1* 1. With a strong f i e l d , assuming d i f f u s i o n and jumping against the f i e l d are n e g l i g i b l e i the p r o b a b i l i t y f o r an Al*** ion to jump i s _ 3eFb je-TJ/kT e 2 k T Assuming that there i s an e f f e c t i v e number of ions/ om.2 equal to N 0, the current/om. 2 inside the oxide, assuming no space charge, i s given by 1= N o.3e0e- u/ k T e 2 k T Now a volume of oxide with a oross-seotion of 1 cm. and b om. i n length oontains K Q ions; and therefore N o « > V H 0 » 1CT 8 x 4.3 x 1 0 2 2 - 4.3 x 1 0 1 4 Comparing with the experimental formula I - oc e ^ , we .see that & = 5.4.8 x l O " ^ 10-10 2 1..38 x l 0 " 1 6 x 300 a 1.74 x 10" 4 at room temperature, A f o r F i n e.s.u* g i v i n g /3 ~> 0.6 x 10~ 6 f o r F i n V/om. N.B. Verwey finds /3=0.7 x 10" 6 f o r F i n v/om. Gunthersohulzel finds 6 times as much, but that leads to i r~10~ 7 which i s the-o r e t i c a l l y impossible. I t i s too d i f f i c u l t to measure /3 ; ^•Gunthersohulze, A, & Beta, H., Z. Phys. 91, 70 (1934). 5 5 calculation i s to be prefered. 3. Height of the l a t t i c e potential barrier, U: We have I = bno.3e0e-U/kT e ^ From measurements of Dekker and Van Geel (3), oxi-dation in borio acid of 440 om.2 with, a atrrent of 200 m.a. gives at a voltage of 300 volts (1 e.s.u.) a capacity | 1 3 x 10-B o m . - l So thickness d- e A _ 8 x 440 x 13 x 10" 8 4n"C " 4TT = 3.64 x 10~5 om. So, in that oase, the f i e l d strength in e.s.u. i s * - r, ~ ? ~ — - 5 - 2.75 x 10 4 e*s*u;/om. 3.64 x 10~° Then e^ *" = e 4 , 7 8 <*120 Now I » |§£ 5ia. = l i 3 6 x 1 0 6 e*s.u./om.2 440 cm.2 . So a l l quantities but U i n the current equation are known. Solving for U: 9WlsX = 5.5 x 10 1 3 JJ ctSQ kT « .75 eY. N.B. Verwey oaloulatea from Gunthersohulze * s a value of 1.8 eV., which seems to agree very roughly with the fusion point. B. Now the f i e l d strength can be calculated as a function of x: Assume that only the AT*'* ions are mobile; then 1ft.e metal oxide interface can be considered as a source giving off metal ions. (If the motion of 0"" ions i n the opposite direc-tion i s taken into aocount, the metal-oxide interface oould be considered a souroe of metal ions and of positive holes. The 0— ourrent depends on the Al*"*^ current beoause the 0 ions 36. can o n l y move when the A l + + + i o n s jump f r o m t h e m e t a l i n t o t h e o x i d e , l e a v i n g h o l e s which t h e n move i n t h e same d i r e c t i o n as t h e A l + + + . ) I f , d u r i n g t h e t i m e c u r r e n t i s f l o w i n g , t h e c o n c e n t -r a t i o n o f A l + + + i o n s i s n ( x ) , we have I ( x ) - n ( x ) b 3 ei> e " U / k T e * F ( x ) * n e g l i g i b l e d i f f u s i o n t e r m (1) I ( x ) - n ( x ) - i / e l i F w i t h 3 ebOe*^/^ 2.6 x 10 f i g . 6. On t h e o t h e r hand, because o f p o s s i b l e space c h a r g e , we have g = hlH . 4 * l l e { n ( x ) n < 5) ( 2 ) assuming t h e number o f 0 ~ " i o n s remains t h e same as w i t h o u t a f i e l d . From (1) we have n(x) - L e " ^ * ) S u b s t i t u t e i n (2) , g i v i n g ". dF _ 12tre/I -/»F(x) „ \ - dx - T " ( 1 e - n o J OR f'dF „ /*121fe (PdF 1 ( i e " ' < - no ) / dx 12-nre •I Fe»FdF - I flF -L- flog(n 0e* F<> - I ) - l o g f n o e ^ - |)j no/3 L o * J T h i s g i v e s F as a f u n c t i o n o f x: 37 r, J*Fo 1 12iien 0Ac. 1.7 . i o 1 0x 9 pF J - e • f e - e p n 0 e - 7 Now suppose a t x • 0 t h e e f f e c t i v e d e n s i t y o f the aluminum i o n s i n t h e m e t a l i s m 0» Then I c - I - m0jreflP° or I = moe^ 0 S u b s t i t u t i n g t h i s f o r £ , we have n 0 — m© n o e 1 ^ " ^ ' - m0 " e P X When n 0 » m 0 , 1 = ( e ^ F - F o ) -W»?)ePx n« F o r t h o s e v a l u e s o f x f o r which px^ i s o f t h e o r d e r o f 1 o r s m a l l e r s we see t h a t we s h o u l d have ftW - /3F0 + px = 0 because we can omit B2. : n 0 and s i n c e flF0 • l o g — £ - . t h e n m0* • x = l l o g I ~ i l o g . m0tf - £F . p p p which means t h a t i f we assume s o l u t i o n o f t h e l a y e r b e g i n s when F r e a c h e s a c r i t i c a l v a l u e F ( b e i n g t h e same v a l u e i n a l l c a s e s where t h e c o n c e n t r a t i o n o f t h e s o l u t i o n i s t h e same), t h e n t h e c r i t i c a l v a l u e o f x » x w i l l be a l i n e a r f u n c t i o n o f l o g I , as found e x p e r i m e n t a l l y , where I i s t h e 3 & \ o x i d i z i n g c u r r e n t . 1 1 B i . e . x Q • — l o g I - — l o g m0tf - —F 0 p P P c Now p has been c a l c u l a t e d t o be 1.7 x 10^, so \ - .59 x l c T 1 0 , whereas t h e e x p e r i m e n t a l s l o p e (Graph 6) i s o f t h e o r d e r o f 1CT6 . Now t h e space charge o f A l + + + i o n s can o n l y be d i s t r i b u t e d o v e r t h e v a c a n t l a t t i c e p o s i t i o n s , n ot c o n t i n u -o u s l y t h r o u g h t h e o x i d e as has been assumed i n t h e p r o c e e d i n g t h e o r y , and t h i s f a c t may e x p l a i n why t h e r i g h t r e l a t i o n but wrong o r d e r has been o b t a i n e d . 39. Y - BIBLIOGRAPHY (I) Anderson, Soott Meonanism of E l e c t r o l y t i o Oxid-a t i o n of Aluminum, J . App. Phys. 15, 477 (1944). (2) Burgers, W. G., Claassen, A., Zernike, J . (3) Dekker, A.J., and Van Geel, W. Ch. (4) Edwards, J . D., and K e l l e r , F. (5) Edwards, J . D., and K e l l e r , F. (6) Mott, N. F., and Gurney, R. W. (7) Rummel, T. (8) Verwey, E. J . (9) Verwey, E. J i Z. Physik 74, 593 (1932). On tne Amorphous and C r y s t a l l i n e Oxide Layer of Aluminum, P h i l i p s Res. Reports 2, 313-319, (1947). Trans. Eleotroohem. Soo. 79, 180 (1940). Metals Teoh. T. P., 1710, (Apr. 1944). Eleotronio Processes i n Ionic C r y s t a l s , 2nd Ed. (1948) pp. 261, 267, Oxford Univ. Press, London.. Z. Physik 99, 518 (1936). Struoture of E l e o t r o l y t i o a l Oxide Layers on Aluminum, Z. K r i s t . Abt. A 91, 317-320 (1935). E l e c t r o l y t i o Conduction of a S o l i d Insulator at High F i e l d s ; Formation of the Anodio Oxide Film on Aluminum, Physioa, 2* 1059-1063, (1935). 

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