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Creep deformation of stoichiometric uranium dioxide single crystals Sturrock, William Robert 1962

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CREEP DEFORMATION :OF STOICHIOMETRIC URANIUM DIOXIDE SINGLE CRYSTALS by WILLIAM ROBERT STURROCK A Thesis.Submitted i n P a r t i a l F u l f i l m e n t of the Requirements f o r the Degree of Master of A p p l i e d Science i n the Department of METALLURGY We accept t h i s t h e s i s as conforming t o - the•standard r e q u i r e d from candidates f o r the degree of Master of A p p l i e d Science Members of the Department of M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA February, 1962 In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Metallurgy  The University of B r i t i s h Columbia, Vancouver 8, Canada. Date February 20, 1962 ABSTRACT Rectangular beams of high d e n s i t y s i n g l e - c r y s t a l UO were 2 prepared from l a r g e grains of fused UOg- They were deformed under constant l o a d i n f o u r - p o i n t bending i n hydrogen at temperatures from 13^0 t o li+20°C. The r e s u l t s appear t o f i t a creep equation of the form C ( ^ _ j l exp(.Q/RT) max SS where e = steady-state creep r a t e ( ) = -.v = r e s o l v e d shear s t r e s s i n <^ 01]^  d i r e c t i o n s max SS " <£>11? Q n | 1 ; L 1 J p l a n e s Q = 118 + 23 kcal/mole C = constant ; and 3 <^  n <[ k i n the regions of s t r e s s and temperatures examined. F a i n t s l i p l i n e s were .observed. ACKNOWLEDGEMENTS Thanks are due t o Pro f e s s o r W. M. Armstrong f o r h i s able d i r e c t i o n . o f t h i s research, and t o a l l the S t a f f and Graduate Students of the Department of M e t a l l u r g y f o r t h e i r a s s i s t a n c e , p a r t i c u l a r l y . Mr. Wayne I r v i n e f o r h i s h e l p f u l advice and d i s c u s s i o n s and Mr. A r v i d L a c i s f o r p reparing many of the specimens and a l l of the drawings. Most of the equipment used was loaned through the courtesy of Atomic • Energy of Canada (UO^ Research Contract #105-B5) w h ° a l s o k i n d l y provided the spectroscopic analyses. F i n a n c i a l a s s i s t a n c e was g r a t e f u l l y r e c e i v e d from NRC Metals Research Grant AECB 7-TABLE OF CONTENTS I INTRODUCTION 1 I I DEFORMATION AND CREEP IN CRYSTALLINE NONMETALS 2 I I I STRUCTURE ; OF UOg k IV PRIOR INVESTIGATIONS OF U0 2 DEFORMATION .' A P o l y c r y s t a l l i n e 5 B S i n g l e C r y s t a l s 6 V THEORY AND METHODS PERTINENT TO THIS INVESTIGATION ' A Creep i n Bending 7 B M a t e r i a l s , A n a l y t i c a l and P r e p a r a t i v e Methods 1. Uranium Dioxide (a) P o l y c r y s t a l l i n e 11 (b) S i n g l e C r y s t a l s 13 2. A n a l y t i c a l Methods 15 3. Specimen P r e p a r a t i o n l6 VI EXPERIMENTAL PROCEDURE AND DATA A Bend Creep Machine 1. Furnace and Temperature C o n t r o l l8 2. Creep Apparatus 18 • 3 • Measuring Devices 20 B Procedure 1. Constant Load, Constant Temperature 21 2. Constant Load, V a r i a b l e Temperature 22 3. V a r i a b l e Load, Constant Temperature 22 C Re s u l t s 1. Stoichiometry. 23 2. Density '. . 23 3- O r i e n t a t i o n 23 k. Constant Load, Constant Temperature (a) P o l y c r y s t a l 2k (b) S i n g l e c r y s t a l s 26 5- Constant Load, V a r i a b l e Temperature 29 6. V a r i a b l e Load, Constant Temperature. . . . . . 29 7- Sources of E r r o r s (a) Temperature 29 (b) Resolved shear s t r e s s 29 (c) Others 32 V I I ANALYSIS AND INTERPRETATION A S t r e s s Dependence 33 B Temperature Dependence 35 V I I I SUMMARY AND CONCLUSIONS 38 IX SUGGESTIONS FOR FUTURE RESEARCH 39 X APPENDICES Appendix I The Uranium-Oxygen System 0^ Appendix I I Stresses i n Bending 1^ Appendix I I I Growth !Attempts Appendix IV Stoic h i o m e t r y at Temperature k8 Appendix V Summary of R e s u l t s 9^ Appendix VI C a l c u l a t i o n of Resolved Shear S t r e s s . . . . 51 X I REFERENCES 52 LIST OF ILLUSTRATIONS Figure Page 1 F l u o r i t e type u n i t c e l l k 2 'Schematic constant t e n s i l e l o a d creep t e s t 7 3 F i r s t batch of fused uranium d i o x i d e showing two-phase i n c l u s i o n s ik h Second batch of fused uranium d i o x i d e 15 5 Slabs and rough-cut specimens of fused uranium d i o x i d e . l6 6 . Schematic of creep apparatus 19 7 Diagram.of e l e c t r i c a l system 20 8 Bend creep machine 21 9 Typical-Laue X-ray of uranium d i o x i d e s i n g l e c r y s t a l . . . 2k 10 Constant l o a d , constant temperature . 25 11 P l a s t i c a l l y deformed uranium .dioxide 27 12 Edge view of specimen showing s l i p : l i n e s ' o h b o t h . s i d e s . of n e u t r a l a x i s 28 13 Edge-view of s l i p l i n e s a t compression s u r f a c e . . . . 28 Ik Constant l o a d , v a r i a b l e temperature 30 15 V a r i a b l e l o a d , constant temperature 31 16 Constant temperature, l o g r e s o l v e d shear s t r e s s 3^  17 . Arrhenius p l o t showing e f f e c t of temperature on s t r a i n r a t e 36 18 S h i f t e d Arrhenius p l o t 37 AI The Uranium-Oxygen system ., . hO A I I . l Simple beam k2 A l l . 2 Stress d i s t r i b u t i o n i n bending kk LIST OF TABLES Table Page I A n a l y s i s of Uranium Dioxide used i n t h i s i n v e s t i g a t i o n . . 12 I I Oxygen-Uranium r a t i o s 23 I I I D e n s i t i e s 23 1 I INTRODUCTION The Canadian nuclear power program i s based on the use.of uranium •dioxide f u e l and heavy water moderator. N a t u r a l uranium d i o x i d e has many advantages as a nuclear f u e l s i n c e i t has a r e l a t i v e l y low cost and i s e a s i l y processed i n t o h i g h d e n s i t y shapes by powder m e t a l l u r g i c a l methods. I t i s i s o t r o p i c and f r e e from the low temperature phase changes of m e t a l l i c uranium. However, i t s r e f r a c t o r y nature and low thermal c o n d u c t i v i t y cause h i g h thermal gradients w h i c h . r e s u l t i n c r a c k i n g and d i s i n t e g r a t i o n . There f o r e , i t would be d e s i r a b l e t o know the e f f e c t of g r a i n boundaries, g r a i n s i z e and d e n s i t y on the high-temperature d u c t i l i t y of p o l y c r y s t a l l i n e m a t e r i a l . This can of course be accomplished by examining the e f f e c t of changing these v a r i a b l e s on p o l y c r y s t a l l i n e specimens.:. But t h i s approach i s not without i t s d i f f i c u l t i e s s i n c e , i f one changes g r a i n s i z e , the d e n s i t y changes as w e l l , not t o mention pore s i z e and shape. I n the study of the p l a s t i c behaviour of metals, much has been le a r n e d from the t e s t i n g . o f s i n g l e - c r y s t a l s . Therefore, i t was f e l t t h a t i n order t o understand b e t t e r the p l a s t i c behaviour of p o l y c r y s t a l l i n e U0 2, an examination of s i n g l e c r y s t a l s would be of i n t e r e s t . To t h i s end, t h i s i n v e s t i g a t i o n has been concerned w i t h the creep of s i n g l e c r y s t a l s of U0 2 at high temperatures. S p e c i f i c a l l y , the measurement of cen t r e - p o i n t d e f l e c  t i o n r a t e s of s t o i c h i o m e t r i c s i n g l e c r y s t a l s of U0 2 under constant l o a d i n bending at temperatures of 13U0°C t o lU20°C has been performed. The r e s u l t s show th a t creep i n bending i n v o l v e s s l i p on ^ - l l } .. •• planes i n the ^ 110^ d i r e c t i o n s , the r a t e depends on the r e s o l v e d shear s t r e s s to the exponent n, where 3 n ^ ^> a n <^ the apparent a c t i v a t i o n energy i s 118 + 23 k i l o c a l o r i e s f o r the o v e r a l l creep process. 2 I I DEFORMATION AND CREEP IN CRYSTALLINE NON-METALS Ceramists . have long been i n t e r e s t e d i n the mechanical p r o p e r t i e s of r e f r a c t o r y m a t e r i a l s at a l l temperatures. However, recent requirements f o r s t r u c t u r e s t h a t w i l l w i t h s t a n d temperatures f a r above the s e r v i c e l i m i t of m e t a l l i c s o l i d s has s t i m u l a t e d research i n t o the mechanical p r o p e r t i e s of non-metallic s o l i d s at h i g h temperatures f o r such d i v e r s e a p p l i c a t i o n s as t u r b i n e components, r e - e n t r y cones and nuclear f u e l s . Deformation s t u d i e s at low temperatures (temperatures l e s s than approximately \ mp) are hindered by the inherent b r i t t l e n e s s of non-metallic m a t e r i a l s . Problems such as specimen f a b r i c a t i o n , g r i p p i n g and p o r o s i t y which i n the case of ( m e t a l l i c m a t e r i a l s are r e l a t i v e l y minor i n nature, become serious o b s t a c l e s i n the t e s t i n g of ceramic m a t e r i a l s . Nonetheless, the nature of the mechanical behaviour of i o n i c c r y s t a l s a t room temperature i s perhaps b e t t e r understood than metal c r y s t a l s because o f , as p o i n t ed 'out by J . J . G i l m a n ^ , the r e l a t i v e l y simple chemical b i n d i n g i n them and the f e a s i b i l i t y of d i r e c t o b s ervation of d i s l o c a t i o n s i n the transparent i o n i c c r y s t a l s . High temperature (T>g-mp) deformation studies on ceramic (2) m a t e r i a l s , w h i l e e x p e r i m e n t a l l y no l e s s d i f f i c u l t ' have been more w i d e l y performed since, i n g e n e r a l , the d u c t i l i t y of ceramics increases w i t h i n c r e a s  i n g temperature. Much of the work has d e a l t w i t h the time-dependent deform a t i o n of ceramics; t h a t i s , the deformations produced under constant l o a d or constant s t r e s s , the former being the more common l o a d i n g technique. And s i n c e pure s i n g l e c r y s t a l s of ceramics, i n p a r t i c u l a r r e f r a c t o r y oxides, have only r e c e n t l y been a v a i l a b l e , most of such creep s t u d i e s have been (3) performed on p o l y c r y s t a l l i n e m a t e r i a l s . For example ,Chang has examined 3 the creep of p o l y c r y s t a l l i n e Al^O^ and BeO and the e f f e c t of a d d i t i o n s on ' (k) the creep r a t e . Parr et a l . ' s t u d i e d the creep of s i l i c o n n i t r i d e and s i l i c o n c a r b i d e , and S c o t t et a l . ^ examined p o l y c r y s t a l l i n e UOg- T e n s i l e creep t e s t s of long, t h i n sapphire s i n g l e c r y s t a l s have been performed by Wachtman^ and he found t h a t creep occurs by s l i p on the (0001) plane i n the (ll2oJ d i r e c t i o n . I l l STRUCTURE OF UO g Uranium d i o x i d e i s a dark brown t o b l a c k c r y s t a l l i n e s o l i d possessing the f l u o r i t e (CaF 2) s t r u c t u r e shown i n Figure 1, w i t h a l a t t i c e 7 F i g u r e 1 F l u o r i t e type u n i t c e l l : ( A f t e r A z a r o f f ) parameter of 5.1*68 A° and t h e o r e t i c a l d e n s i t y of 10.968 gm/cc at 2 6 ° C . ^ There are equivalent i n t e r s t i t i a l s i t e s at the body centre and edge centres of the u n i t c e l l (U^Og) making a t o t a l of one i n t e r s t i t i a l s i t e per uranium a t o m . ^ UOg Q w i l l r e a d i l y p i c k up oxygen above about 200°C to form s t a b l e U^Og. However, at room temperature, n o n - s t o i c h i o m e t r i c oxide w i l l c o n s i s t of the two phases U0,_,+x and U^O^. ^ 1 0 T h e r e i s a l s o evidence t h a t m a t e r i a l s o l i d i f i e d from the melt at 2800°C can e x i s t as a s i n g l e phase, w i t h the f l u o r i t e s t r u c t u r e , as UO-^  gc ' ^ e ^ 2 " ^ P n a s e diagram i s i n Appendix I . 5 IV PRIOR INVESTIGATIONS OF U0 2 DEFORMATION A. P o l y c r y s t a l l i n e As p o i n t e d out above, most of the work on r e f r a c t o r y oxides has been done on p o l y c r y s t a l l i n e m a t e r i a l s , and U0 2 i s no exception. One of the (12) f i r s t such s t u d i e s examined the e f f e c t of p a r t i c l e s i z e of fused U0 2 on the b u l k d e n s i t y of s i n t e r e d compacts and the f l e x u r a l s t r e n g t h i n k-point bending at temperatures ranging from room temperature t o 1000°C. The f l e x u r a l s t r e n g t h was found t o decrease w i t h i n i t i a l p a r t i c l e s i z e , and t o inc r e a s e w i t h t e s t temperature, and the r a t e of change of s t r e n g t h w i t h temperature decreases w i t h i n c r e a s i n g p a r t i c l e s i z e and as the s i n t e r e d d e n s i t y decreases. Two i n v e s t i g a t i o n s have been c a r r i e d out r e c e n t l y u s i n g creep under 3-point bending at high temperatures. S c o t t , H a l l a n d . W i l l i a m s ^ ) found t h a t n o n - s t o i c h i o m e t r i c uranium d i o x i d e deformed p l a s t i c a l l y at about 800°C, but th a t s t o i c h i o m e t r i c d i o x i d e d i d not deform p l a s t i c a l l y under l600°C. The creep r a t e s f o r UO were found t o obey the expression e = A s i n h (^) exp (-Q/RT) ( l ) where e i s the s t r a i n - r a t e , & the s t r e s s and T the absolute temperature. A and £ are m a t e r i a l constants. Values of Q are quoted as 65 k c a l f o r U 02 16' ^ 2 k C a l f ° r U°2 06 a n d k c a l f o r U 02 00' p e r m o l e * (13) The second i n v e s t i g a t i o n by Armstrong, I r v i n e and Martinson on s t o i c h i o m e t r i c U0 2 shows t h a t UOg 0 Q w i l l deform p l a s t i c a l l y at 1250°C," the creep r a t e can be represented by the expression e = A exp (-Q/RT)«£n (2) 6 where e i s the steady s t a t e s t r a i n r a t e , & i s the a p p l i e d t e n s i l e s t r e s s and A and n are m a t e r i a l constants. They found t h a t Q i s 91 t 8 k c a l and n = 1.0, f o r s t r e s s e s below about 10,000 p s i and f o r high d e n s i t y (93$ t h e o r e t i c a l ) m a t e r i a l . B. S i n g l e C r y s t a l s (lU) , One other i n v e s t i g a t i o n . ...besides the present one, has under taken t o use s i n g l e c r y s t a l s of UO^. Small c r y s t a l s were m e t a l l o g r a p h i c a l l y p o l i s h e d and then deformed i n compression at temperatures ranging from 700° t o 1900°C. The most a c t i v e s l i p plane at a l l temperatures was ^100^, w i t h { l l O ^ and | j-ll^ becoming more a c t i v e as the temperature was increased. 7 V THEORY AND METHODS PERTINENT TO THIS INVESTIGATION A. Creep i n Bending By f a r the gr e a t e s t amount of creep data have been obtained f o r metals from u n i a x i a l t e n s i o n t e s t s under constant l o a d . The time dependence of s t r a i n at constant temperatures of such a t e s t i s shown i n F i g u r e 2. PRIMARYJ SECONDARY TERTIARY FRACTURE j ELASTIC \ 1 RECOVERY TRANSIENT STRAIN PERMANENT STEADY-STATE STRAIN PLASTIC STRAIN INITIAL ELASTIC AND PLASTIC STRAIN TIME F i g u r e 2 Schematic constant t e n s i l e l o a d creep t e s t at constant temperature. Dotted l i n e shows behaviour i f speciment i s unloaded during t e s t , ( a f t e r Finnie-'-5) The secondary stage of minimum . s t r a i n r a t e may o f t e n be very prolonged and i s the s e c t i o n most amenable t o experimental study. At constant temper ature, the steady-state s t r a i n r a t e i s a f u n c t i o n o n l y of s t r e s s and may be represented by e = k<£ n (3) where e i s the s t r a i n r a t e , (£ the s t r e s s , and k and n are m a t e r i a l constants. 8 The temperature dependence of the s t r a i n r a t e may be represented by e = A exp (-Q/RT) (k) where R i s the gas constant, T the absolute temperature, and.A a m a t e r i a l constant. As p o i n t e d out by D o r n ^ ^ , Q , the observed a c t i v a t i o n energy, does not n e c e s s a r i l y represent the a c t i v a t i o n energy f o r a s i n g l e process, but may be an a p p r o p r i a t e l y weighted average of the a c t i v a t i o n energies of a l l o p e r a t i v e processes g i v i n g r i s e t o creep. The lower l i m i t of temperature i s , of course, determined by the s m a l l e s t s t r a i n r a t e t h a t can be detected; the upper l i m i t , b e i n g deter mined by the furnace components. I n t h i s case,, t h a t temperature range i s about 1250°C t o li4-25°C. Specimens of constant r e c t a n g u l a r c r o s s - s e c t i o n have the most convenient shape t o cut ( s i n c e diamond a b r a s i v e wheels must be used) from the raw m a t e r i a l s a v a i l a b l e . Therefore, bend, r a t h e r than say t e n s i l e , t e s t i n g of p r i s m a t i c beams of uniform c r o s s - s e c t i o n was chosen f o r t h i s i n v e s t i g a t i o n , and f o u r - p o i n t l o a d i n g was chosen over t h r e e - p o i n t l o a d i n g f o r reasons o u t l i n e d i n Appendix I I . The s i m p l i f i c a t i o n of the experimental problems by the use of bending i n . t h e place of t e n s i o n , however, comes at a p r i c e . The e x p e r i  mentally measured q u a n t i t i e s are only i n d i r e c t l y r e l a t e d t o those of the t e n s i o n t e s t and s e v e r a l s i m p l i f y i n g assumptions must be made. An a n a l y s i s of the use of bending to determine the p r e c i s e t e n s i l e p r o p e r t i e s of ceramic bodies at room temperature has been given (17) by Duckworth ' and he recommends, on the b a s i s of h i s a n a l y s i s , t h a t k-point l o a d i n g on a r e c t a n g u l a r specimen w i t h a reduced s e c t i o n f o r the gauge le n g t h should be used. He a l s o recommends th a t s t r a i n should be 9 measured i n both the upper and lower f i b r e s , thus a v o i d i n g e r r o r s i n t r o d u c e d by assumption h below. The centre s e c t i o n of beam loaded i n f o u r - p o i n t bending has a c t i n g on i t a constant bending moment. (See Appendix I I . ) Timoshenko ' s ^ ^ a n a l y s i s of creep i n bending i s b r i e f l y as follows." F i r s t the f o l l o w i n g assumptions are made: (1) C r o s s - s e c t i o n s remain plane; (2) Each l o n g i t u d i n a l f i b r e i s i n a c o n d i t i o n of simple t e n s i o n or compression; (3) . The creep equation (3) holds f o r t e n s i o n and compression a considerable time a f t e r the l o a d has been a p p l i e d ; (h) Moduli i n t e n s i o n and compression are equal. Then he shows t h a t f o r a r e c t a n g u l a r beam of width b and height h ( < * ) =^(£2+ 1 ) (5) v max ;SS 21 3n where ( & ) = s t r e s s at the outer f i b r e s i n steady s t a t e max SS M = a p p l i e d bending moment n = exponent i n equation (3) I = moment of i n e r t i a about n e u t r a l a x i s . Timoshenko then gives the d i f f e r e n t i a l equation of the d e f l e c t i o n curve: dx' where d^y + 2kt / ^  Nn: . + 2kt /h sn /2n+lNn n , ; s r i = - I T ( <\ax) SS = - — ( 2 l ) ( ^ n ~ ) M ^ y = d e f l e c t i o n x = distance along beam h = height of beam t ='time k = constant i n equation (3) n = exponent i n equation (3) 10 I n the case of a beam loaded i n pure bending (M = const.) as i s the centre s e c t i o n of a beam i n f o u r - p o i n t l o a d i n g (see Appendix I I ) , equation (6) can be i n t e g r a t e d along the length; o f the beam ( i . e . w i t h respect t o x) from x = 0 t o x = m (where m i s the l e n g t h o f the centre s e c t i o n ) to g i v e : + km 2 , ^ .n y = ~T~ ( ) q q t (T) . n max t>o The d e f l e c t i o n r a t e r e l a t i v e t o the p o i n t of l o a d a p p l i c a t i o n then i s 2 ^ ' $2. = y = + 1SL. ( cf ) n (8) dt " h max SS The maximum s t r a i n i n the outer f i b r e s i s given by Smax = k ( 9 ) • where ^ i s the r a d i u s of curvature; the curvature and d e f l e c t i o n (y) of a beam bent i n a c i r c u l a r arc are r e l a t e d by do) Combining equations (9) and (10), and d i f f e r e n t i a t i n g w i t h respect t o time e = %-y (11) max m Then s u b s t i t u t i o n of y i n equation (8) y i e l d s e = + Uk(<** ) 1 (12) max " v wmax'SS v ' The e l a s t i c maximum f i b r e s t r e s s i s < ^ m a x = 2 l • <13> 11 and comparing t h i s w i t h equation (5) shows t h a t K max'SS maxv 3 n ' ^ ' Therefore e max + «*r<s- ( ^ ) i n (15) I max 3n J Thus a p l o t of l o g e versus l o g £ (/C being the i n i t i a l maximum max max e l a s t i c s t r e s s ) should y i e l d a s t r a i g h t l i n e of slope n. (19) Hoff suggested t h a t the creep expression c o u l d be w r i t t e n as e = f(<tf ) e"Q/ R T (16) Therefore combining equations (h) and (15) we get e = C ( ^ i ) T exp(-Q/RT) (IT) L m a x 3n J where C combines constants. B. M a t e r i a l s , A n a l y t i c a l and P r e p a r a t i v e Methods 1. Uranium Dioxide (a) P o l y c r y s t a l l i n e : Specimens of t h i s m a t e r i a l were obtained from s i n t e r e d p e l l e t s , l i k e those used as r e a c t o r f u e l , s u p p l i e d by Atomic Energy of Canada. The d e n s i t y was 96 per cent of t h e o r e t i c a l (IO.96 g/cc) and the g r a i n s i z e averaged 6 microns. The spectrographic a n a l y s i s i s given i n Table I. 12 TABLE I ANALYSIS OF URANIUM DIOXIDE USED IN THIS INVESTIGATION ELEMENT POLYCRYSTAL SINGLE CRYSTAL ppm #6 ppm #15 ppm #16 ppm Ag - - - - A l 2 10 15 Au - - - B 2 - - r Ba - - - Be - - - B i - - - ~ c Ca 35 15 15 20 \ Cd - - - — r Cr 5 - 3 3 • Cu 20 - - Fe • ho 6 10 10 - Mg 15 - - Mn 2 - - Mo - 35 - Na 150 nd nd nd ' N i 20 - - i 1 Fb . 3 - - - S i 9 5 - 2 ' Sn - • - - r T i l 2 1 1 V - - - W _ 6 _ _ Y - - -Zn 3 l 2 2 Zr - - 10 7 ( 1 H tf> CO o H p< O ?H P O (U ft 13 (b) S i n g l e c r y s t a l s : I n i t i a l l y i t had been hoped t o grow s i n g l e c r y s t a l s by,a f l o a t i n g - z o n e technique u s i n g e i t h e r i n d u c t i o n or r e s i s t a n c e h e a t i n g . However, considerable experimental d i f f i c u l t y was encountered because of the r e f r a c t o r y nature of uranium d i o x i d e . (See Appendix I I I . ) S i n g l e c r y s t a l s , 'however, are a v a i l a b l e commercially from at l e a s t two sources. Spencer Chemical Company,,Kansas C i t y , Mo., w i l l supply " . . . c r y s t a l s of UOg of at l e a s t 3/l6 i n c h i n diameter, but i t should be noted t h a t t h i s i s a c r y s t a l l i n e {s±c\ m a t e r i a l and not necessar i l y s i n g l e c r y s t a l s " . M a t e r i a l of t h i s s i z e range would be too s m a l l f o r the type of bend t e s t specimen used i n t h i s i n v e s t i g a t i o n . The second source, Norton Company, Chippewa, Ontar i o , however, s u p p l i e d r a t h e r l a r g e s i n g l e c r y s t a l s of UO^, some of which were over 2 inches l o n g and'an i n c h i n diameter. The f u s i o n by Norton Company i s c a r r i e d out i n an e l e c t r i c arc furnace w i t h g r a p h i t e e l e c t r o d e s , y i e l d i n g 800-1000 l b s of p o l y c r y s t a l l i n e product from 3 A- of a ton of raw m a t e r i a l . T h e . p o l y - c r y s t a l l i n e mass i s broken up and l a r g e g r a i n s ( s i n g l e c r y s t a l s ) are found i n c e r t a i n l o c a t i o n s of the p i g . The sample c r y s t a l r e c e i v e d from Norton Company was examined and found t o be s a t i s f a c t o r y f o r creep t e s t i n g . On the b a s i s of t h i s , a l a r g e q u a n t i t y was ordered. The c r y s t a l s subsequently r e c e i v e d appeared to have a r a t h e r d u l l m o t t l e d s u r f a c e , were d i f f i c u l t t o cut without c r a c k i n g , and, on examination under the microscope, were found t o have a l a r g e q u a n t i t y of two-phase i n c l u s i o n s as shown i n F i g u r e 3-Ik Figure 3 F i r s t batch of fused uranium d i o x i d e , showing the two-phase i n c l u s i o n s (U80X) These i n c l u s i o n s were q u a l i t a t i v e l y i d e n t i f i e d by X-ray d i f f r a c t i o n to be f r e e uranium metal and uranium mononitride. The a n a l y s i s i s shown i n the column l a b e l l e d #6 of Table T . The second l o t was found t o be s a t i s f a c t o r y i n a l l r e s p e c t s : the general appearance was much cle a n e r , i t cut e a s i l y and no i n c l u s i o n s c o u l d be observed (See Figure k). The spectrograph!c a n a l y s i s of c r y s t a l s #15 and #16 are i n Table X. The s u p p l i e r ' s a n a l y s i s i s o/u = 1.995 - 2.03 Carbon = 0.01$ max. Nitrogen= 0.10$ max. 15 Figure k Second batch of fused uranium d i o x i d e (U8ox) 2. A n a l y t i c a l Methods D e n s i t i e s of the various specimens were determined by measuring the weight l o s s of the specimen on immersion i n carbon t e t r a c h l o r i d e . S t o i c h i o m e t r y was determined by measuring the weight-loss on annealing i n dry hydrogen f o r a t l e a s t one hour at 1000°C. The hydrogen was f i r s t passed through p a l l a d i n i z e d c a t a l y s t , then through a tube of s i l i c a g e l a t room temperature, and f i n a l l y through another tube of s i l i c a g e l immersed i n l i q u i d n i t r o g e n t o remove the l a s t t r a c e s of moisture. As a f u r t h e r p r e c a u t i o n the specimens were quenched from 1000°C to room temp erature by p u l l i n g the boat c o n t a i n i n g them from the hot zone t o the c o o l 16 end of the tube. O r i e n t a t i o n s were determined by the standard technique of Laue (21) back r e f l e c t i o n . v ; The specimen was p o s i t i o n e d w i t h the major a x i s v e r t i c a l so t h a t the i n c i d e n t beam was p a r a l l e l t o the s h o r t e s t dimension of the specimen. With a specimen-to-film distance of 3 cm and u n f i l t e r e d molybdenum r a d i a t i o n (1+OkV, 10 ma) an exposure of 10 minutes was needed. 3 • Specimen P r e p a r a t i o n The l a r g e as-received c r y s t a l s were mounted i n P l a s t e r of P a r i s and cut i n t o slabs of two t o three mm i n t h i c k n e s s i n a d i r e c t i o n t h a t would y i e l d slabs of maximum l e n g t h . The slabs were mounted on t r a n s i t e w i t h water-glass f o r c u t t i n g i n t o bars i n a d i r e c t i o n t h a t would y i e l d the g r e a t e s t number of specimens as shown i n F i g u r e 5• Figure 5 Slabs and rough-cut specimens of fused uranium d i o x i d e IT The as-cut bars were approximately two mm by three ram and 25 mm i n l e n g t h . A l l . c u t t i n g was done w i t h a diamond abrasive wheel (Felker-Di-Met) u s i n g water as coo l a n t . The bars were then ground t o a thic k n e s s of about 1.8 mm u s i n g a s l u r r y of 600 mesh alundum i n d i l u t e w a ter-soluble coolant on a c a s t - i r o n l a p . The f i n a l width of about 2.75 mm and f i n a l l e n g t h of 22-5 mm were accomplished i n the same manner. P o l i s h i n g of the surfaces was c a r r i e d out i n the f o l l o w i n g sequence: f i r s t 2/0 and h/0 carborundum paper w i t h kerosene as dust suppressor, f o l l o w e d by one-micron diamond paste on s i l k - c o v e r e d g l a s s . A l l specimens were given the same p o l i s h i n order t o h o l d surface c o n d i  t i o n s constant. A l l specimens, separated by bubbled alumina, were pla c e d i n two alumina boats and.heated f o r t e n hours at l600°C i n a hydrogen atmosphere. C o o l i n g of the furnace took 36 hours w i t h the maximum c o o l i n g r a t e of o 150 C per hour o c c u r r i n g i n the f i r s t hour. For metallographic examination of any surface the same procedure as described above i s used, f o l l o w e d by i ~ micron diamond paste. The f i n a l p o l i s h , was achieved by usi n g a d i l u t e s l u r r y of "L i n d e B" alumina i n 30$ hydrogen peroxide on Beuhler " M i c r o c l o t h " . Surfaces were etched by immersion i n f r e s h l y prepared s o l u t i o n of 30$ hydrogen peroxide and concentrated s u l p h u r i c a c i d i n the r a t i o of 9:1 r e s p e c t i v e l y , f o r 10 t o 30 seconds. 18 VI EXPERIMENTAL :PROCEDURE AND DATA A. Bend Creep Machine •1. Furnace and Temperature C o n t r o l The furnace c o n s i s t e d of fou r v e r t i c a l l y mounted "Globar" r e s i s t a n c e elements surrounded by r e f r a c t o r i e s enclosed i n a sheet metal c o n t a i n e r on the v e r t i c a l sides and " T r a n s i t e " on the upper and lower ends. The temperature was measured by a platinum-platinum + 10$ rhodium thermocouple enclosed i n an alumina p r o t e c t i o n tube which i s o l a t e d the thermocouple from the hydrogen atmosphere. The thermocouple was checked p e r i o d i c a l l y against another r e l a t i v e l y l i t t l e - u s e d thermocouple and m i l l i v o l t m e t e r which i n t u r n had been c a l i b r a t e d a t the m e l t i n g p o i n t of l e a d (327°C). The thermocouple s i g n a l was f e d , "through temperature - compensating l e a d s , t o a Wheelco Model h02 i n d i c a t o r - c o n t r o l l e r ( s e r i a l #95K3600), which maintained the iHxperature w i t h i n + 3°- 2. Creep Apparatus The creep apparatus i s i l l u s t r a t e d i n F i g u r e 6. I t c o n s i s t e d e s s e n t i a l l y o f : a notched tube f o r supporting the bend specimen; a co n c e n t r i c l o a d i n g tube w i t h a chamfered inner surface a t the t i p , which a p p l i e d two equal loads at equal d i s t a n c e s from the centre of the beam; and, at the centre of the l o a d i n g tube, a d e f l e c t i o n rod, w i t h sapphire t i p , which t r a n s m i t t e d the ce n t e r p o i n t d e f l e c t i o n t o the transducer and d i a l gauge. The l a t t e r two devices were attached t o the l o a d i n g tube so th a t the d e f l e c t i o n i s measured r e l a t i v e t o the p o i n t of l o a d a p p l i c a t i o n . Another tube c o n c e n t r i c w i t h and outside of the support tube and sealed at the ends permitted the use of a c o n t r o l l e d atmosphere. The f l e x i b l e s e a l s f o r the l o a d i n g tube and d e f l e c t i o n r o d were made from p o r t i o n s of t o y b a l l o o n s . F i g u r e 6 Schematic of Creep Apparatus 1 D i a l Gauge 80 Rubber stopper 2 I r o n core 9 Loading tube* 3 Transducer 10 Support tube* k Weight n Furnace tube 5 F l e x i b l e s e a l 12 Specimen 6 D e f l e c t i o n r o d * 13 Thermocouple p r o t e c t i o n tube* 7 Gas i n l e t ik Globar r e s i s t a n c e element 15 Gas o u t l e t * "Purox" r e c r y s t a l l i z e d alumina 20 The weights necessary t o provide the d e s i r e d l o a d c o n s i s t e d of two small containers of t e s t - l e a d whose t o t a l weight e q u a l l e d the d i f f e r e n c e of the c a l c u l a t e d l o a d minus the sum of the weight of the l o a d i n g tube and a l l the devices attached t h e r e t o . The creep runs were performed w i t h a hydrogen atmosphere p u r i f i e d by a p a l l a d i n i z e d c a t a l y s t and magnesium p e r c h l o r a t e dryer. 3- Measuring Devices The v e r t i c a l movements of the d e f l e c t i o n r o d were t r a n s m i t t e d t o the i r o n - c o r e of a l i n e a r variable-impedance transducer, which i n t u r n sent a vol t a g e change pro p o r t i o n a l t o the amount of v e r t i c a l movemehtobf the core, t o a d i r e c t reading measuring b r i d g e . ( P h i l i p s PR-93OO, S e r i a l #LO65*0 as shown i n Fi g u r e 7- Continuous p l o t t i n g of d e f l e c t i o n w i t h time Transducer Chart Recorder Philips PR 2210/21 Bridge ^ Oscillator Philips P R - 9 3 0 0 F i g u r e 7 Diagram of e l e c t r i c a l system was obtained by connecting the output of the b r i d g e t o a s t r i p - c h a r t recorder ( P h i l i p s PR2210 A/21, S e r i a l #D1763). Both the bri d g e and recorder were powered through a constant v o l t a g e transformer t o minimize 21 the e f f e c t of l i n e v o l t age f l u c t u a t i o n s . The d i a l gauge (R.S. S t a r r e t t Company, No. 656-611) was used t o c a l i b r a t e the continuous p l o t by t a k i n g readings at various time i n t e r v a l s . The general arrangement of the bend creep machine i s shown i n Figure 8. Figure 8 Bend creep machine B. Procedure 1. Constant Load, Constant Temperature The prepared specimen was i n s e r t e d i n t o the s l o t of the support tube and the l a t t e r c a r e f u l l y p l a c e d i n s i d e the furnace tube. The complete l o a d i n g assembly was then lowered t o w i t h i n a f r a c t i o n of an i n c h of the specimen, as i n d i c a t e d by the d e f l e c t i o n r o d which was placed i n contact w i t h the centre of the beam. Therefore, the beam was never subjected t o the weight of the l o a d i n g assembly (l660 gms) but 22 o n l y t o the weight of the d e f l e c t i o n r o d during the warmup p e r i o d . The whole assembly was checked f o r l e a k s , and then f l u s h e d w i t h hydrogen before t u r n i n g on the power t o the furnace. Notless than one hour a f t e r the d e s i r e d temperature had been reached ( t o allow the furnace t o come t o temperature e q u i l i b r i u m ) the l o a d was s l o w l y a p p l i e d by lowering the l o a d i n g tube, and the - zero-point reading taken on:'the d i a l gauge. Further readings were taken on the dial-gauge at i n t e r v a l s t o c a l i b r a t e the c h a r t . A t o t a l of four s i n g l e - c r y s t a l specimens were t e s t e d i n t h i s manner, numbers h, 3, 8 and 9> a"t 1^00°C and a t a l o a d c a l c u l a t e d t o y i e l d a maximum e l a s t i c f i b r e s t r e s s of 5000 p s i (see Appendix I I f o r d e t a i l s ) . 2. Constant Load, V a r i a b l e Temperature The i n i t i a l procedure was as described i n s e c t i o n 1 above, and the i n i t i a l c o n d i t i o n s were always lU00°C and 5000 p s i . However, once steady-state creep had been e s t a b l i s h e d , the temperature was r a i s e d or lowered t o a new value. The time taken f o r the change was always l e s s than 15 minutes. Temperatures chosen were 13^0, 1360, 138O and lU20°C as w e l l as lU00°C. Three specimens were t e s t e d i n t h i s manner: numbers 5, 15 and 16. 3- V a r i a b l e Load, Constant Temperature Again the i n i t i a l procedure was as desc r i b e d above (except t h a t the weights were added a f t e r the l o a d i n g tube was lowered), but i n t h i s case, the l o a d was changed by adding or s u b t r a c t i n g the necessary.weights t o vary the maximum f i b r e s t r e s s from 5000 t o 6000, 6000 t o 7000, and 7000 t o 5000 p s i , a l l at lU00°C. One specimen only was t e s t e d i n t h i s manner, number 17• 23 C. Re s u l t s 1. S t o i c h i o m e t r y The 0/U r a t i o at the t e s t temperature w i l l be determined by the p a r t i a l pressure of oxygen i n the system. See Appendix IV f o r an estimate of the r a t i o . R a t i o s were determined, however, on a few specimens: TABLE I I 0/U R a t i o + .002 Sample 1 2 As r e c e i v e d 2.000 2.00^ Annealed 2.009 2.000 A f t e r creep 2.000 2. Density D e n s i t i e s of the samples taken were a l l g r e a t e r than 99$ of t h e o r e t i c a l d e n s i t y (10.968 gm/cc); three are shown i n Table I I I . TABLE I I I gr D e n s i t i e s n/cc + ,0.005 Sample 1 2 , 3 As r e c e i v e d Annealed 10.905 IO.956 IO.958 IO.97U IO.895 IO.931 3 • O r i e n t a t i o n s A t y p i c a l Laue X-ray i s shown i n Figure 9- The o r i e n t a t i o n of the pole of the major a x i s of each specimen used i s "shown i n the i n s e r t Figure 9 Typical Laue X-ray of uranium dioxide single c r y s t a l i n Figure 16, with an estimated accuracy of + 2° . The £l-ll) standard projection i s used. In two cases, s p l i t spots were observed, but repeated attempts could not reproduce t h i s effect i n either case. h. Constant Load - Constant Temperature (a) Polycrystal: Three p o l y c r y s t a l l i n e specimens were deformed i n four- point bending and a representative deflection curve for one i s shown i n Figure 10, for comparison with the s i n g l e - c r y s t a l curves. Tertiary Figure 10. Constant load — Constant temperature 26 creep always began a f t e r a d e f l e c t i o n of about 0.01 inches, and cracks c o u l d be observed on the surface of the bar. (b) S i n g l e c r y s t a l s The d e f l e c t i o n curves of two of the fou r t e s t e d i n t h i s manner are shown i n Fi g u r e 10, and the a c t u a l numbers used t o c a l c u l a t e . the d e f l e c t i o n r a t e s are given i n Appendix V. The curves were not re p r o d u c i b l e i n the i n i t i a l r e g i o n because of the method of l o a d i n g used, the d i f f i c u l t y i n o b t a i n i n g an exact zero-point reading on the gauge, and because some s e t t l i n g and d i g g i n g - i n of the l o a d i n g tube occurred. The f o u r - p o i n t bending r e s u l t e d i n deformation t a k i n g p l a c e over a grea t e r l e n g t h of the beam, as compared t o t h r e e - p o i n t bending, (See Fi g u r e 11), but the same degree of u n i f o r m i t y was not obtained i n a l l cases. Therefore, no absolute values of s t r a i n are a v a i l a b l e . Thus, only steady-state d e f l e c t i o n .rates and s t r a i n r a t e s ( c a l c u l a t e d as shown i n Appendix V) are r e p o r t e d . Wo t e r t i a r y creep was observed i n any runs, which were terminated before the specimen f e l l out of the support tube; and although some r a t h e r l a r g e d e f l e c t i o n s were obtained, no c r a c k i n g whatsoever was observable. Specimens which had a met a l l o g r a p h i c p o l i s h on one edge before deformation- were examined a f t e r creep. These showed very f a i n t l i n e s on both sides of, but i n c l i n e d to, the n e u t r a l a x i s and not extend i n g through the n e u t r a l a x i s . These l i n e s , which c o u l d be removed by p o l i s h i n g , are shown i n Figures 12 and 13- The same l i n e s were looked f o r but not observed on the upper and lower s u r f a c e s . - J U3 O Figure 11 P l a s t i c a l l y deformed uranium d i o x i d e 1 Three-point 2 Three-point 3 Four-point k Four-point 5 Four-point 6 Four-point 7 Four-point 8 Four-point 9 Four-point 10 Four-point 11 Four-point l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g l o a d i n g p o l y c r y s t a l l i n e s i n g l e c r y s t a l p o l y c r y s t a l l i n e c r y s t a l #4 c r y s t a l #3 c r y s t a l #5 c r y s t a l #8 c r y s t a l #9 c r y s t a l #l6 c r y s t a l #17 c r y s t a l #15 F i g u r e 12 Edge view of specimen showing s l i p l i n e s on both sides of n e u t r a l a x i s (6ox) Figure 13 Edge view of s l i p l i n e s at compression surface. P i t s are p o l i s h i n g a r t i f a c t s . (7W) 29 5• Constant Load, V a r i a b l e Temperature From the above r e s u l t s i t was then assumed t h a t once steady- s t a t e s t r e s s c o n d i t i o n s had been obtained, they would p r e v a i l over r e l a t i v e l y long times. Thus, i t was p o s s i b l e t o vary the temperature, without otherwise d i s t u r b i n g the system, t o examine the e f f e c t of temperature on the r a t e s . The r e s u l t s obtained are again given i n Appendix V, and two of the three curves are p l o t t e d i n F i g u r e Ik. 6. V a r i a b l e Load, Constant Temperature In t h i s case the i n i t i a l c o n d i t i o n s again were l400°C and a l o a d c a l c u l a t e d f o r a £ of 5000 p s i . Steady-state creep was e s t a b l i s h e d as shown i n Fi g u r e 15, then a d d i t i o n a l weight was added to incr e a s e the s t r e s s . This was done f o r two i n c r e a s e s , and f i n a l l y weight was removed t o r e t u r n t o the o r i g i n a l c o n d i t i o n . The i n i t i a l and f i n a l r a t e s at 5000 p s i were e s s e n t i a l l y the same, as shown i n Appendix V. 7- Sources of E r r o r s i n the R e s u l t s (a) Temperature Through t he use of a r e l a t i v e l y l i t t l e - u s e d thermocouple, assumed t o be constant w i t h time, the temperatures were r e p r o d u c i b l e t o + 5°j however, t h i s r eference thermocouple was not c a l i b r a t e d over the range of temperatures used i n t h i s i n v e s t i g a t i o n . (b) Resolved shear s t r e s s This c a l c u l a t i o n i n v o l v e d three l i n e a r measurements and two weight measurements g i v i n g an estimated maximum e r r o r of + 10$, but t h i s i s overshadowed by the e f f e c t of the + 2° accuracy of the o r i e n t a t i o n determination. 5000 6000 7000 5000 Time (hrs) 1 1 T = I 4 0 0 ° C Gauge Calc. 17 © ^ max psi 1 0 Figure 15 5 10 15 20 25 Var iable load — Constant Temperature 32 (c) Others For reasons given i n s e c t i o n h(h) above, no absolute values of s t r a i n are a v a i l a b l e . I t should be p o i n t e d out as w e l l t h a t f r i c t i o n at the support p o i n t s has been neglected. This would have the e f f e c t of superimposing a t e n s i l e s t r e s s on the bent specimens. I d e a l l y at l e a s t one support p o i n t should be a r o l l e r support. Therefore s t r e s s e s w i l l be r e p o r t e d as the i n i t i a l maximum f i b r e s t r e s s . (See Appendix I I f o r a n a l y s i s of s t r e s s r e d i s t r i b u t i o n . ) However, a l l runs were performed i n the same manner and thus can be r e l a t e d one t o the other by slopes as i s done i n s e c t i o n V I I . One must be c a u t i o u s , however, i n drawing conclusions from values of i n t e r c e p t s . 33 V I I ANALYSIS AND INTERPRETATION A. S t r e s s Dependence With a l l e x t e r n a l v a r i a b l e s h e l d constant, the steady-state r a t e s v a r i e d by a f a c t o r of f i v e . Thus the more or l e s s random o r i e n t  a t i o n s of the specimens must be determining the r a t e s . The obvious approach i s t o c a l c u l a t e the maximum r e s o l v e d shear s t r e s s and p l o t the data according t o equation 15, on l o g - l o g s c a l e s . The c a l c u l a t i o n s were performed as shown i n Appendix VI and are p l o t t e d i n F i g u r e l6. The i — l l i n e s d e l i n e a t e the range caused by the +2° accuracy of the o r i e n t a t i o n determination. The s o l i d l i n e drawn through the p o i n t s was c a l c u l a t e d by the method of l e a s t squares, g i v i n g equal weight t o a l l p o i n t s , and has a slope of 3-^ - Lines w i t h slopes of four and three are drawn i n f o r comparison. The two p o i n t s which, i f removed from the p l o t would then r e s u l t i n a l i n e of about slope = k, are #8 and #17 at 7000 p s i . However, there i s no obvious reason why those two should be any l e s s r e l i a b l e than other p o i n t s , and t h e r e f o r e the slope appears t o be l e s s than f o u r . This p a r t i c u l a r r e s u l t may be of s i g n i f - icance s i n c e F i n n i e and H e l l e r x ' come t o the c o n c l u s i o n , based on a (23") (l6) t h e o r e t i c a l d e r i v a t i o n of Weertman^ ~" and on experimental work by Dorn (both on steady-state creep at h i g h temperatures and low s t r e s s e s i n fee me t a l s ) , t h a t the s t r e s s exponent should be equal to f o u r ; t h a t i s e = K6 (18) where e^ i s the steady creep r a t e at hig h temperatures and low s t r e s s e s , K i s a m a t e r i a l constant, and ^ i s the a p p l i e d s t r e s s . C h r i s t y ^ ^ p o i n t s out t h a t e s s e n t i a l l y the same ideas may be a p p l i e d t o i o n i c m a t e r i a l s . 35 Thus, si n c e n i n t h i s i n v e s t i g a t i o n appears t o "be l e s s than f o u r , the o v e r a l l creep behaviour c o u l d i n v o l v e , i n a d d i t i o n t o s l i p , some other processes. B. Temperature Dependence The steady-state r a t e s when p l o t t e d as l o g r a t e versus r e c i p r o c a l absolute temperature have the form shown i n F i g u r e 17, f o r the $000 p s i runs. The slopes of the three s e r i e s #5> #15> and #16 were c a l c u l a t e d independently by the method of l e a s t squares and were found t o be w i t h i n + 20$ of t h e i r mean value. Since *-20$ i s not an unreasonable experimental e r r o r f o r an a c t i v a t i o n energy determination, i t was assumed t h a t the same a c t i v a t i o n energy was i n v o l v e d . Therefore the three curves were s h i f t e d v e r t i c a l l y r e l a t i v e t o the s t r a i n - r a t e a x i s so t h a t the highest r a t e of each at 1^00°C co i n c i d e s w i t h the t h i c k - w a l l e d c i r c l e i n F i g u r e 18. The c a l c u l a t e d a c t i v a t i o n energy from the slope of t h i s l i n e then, i s 118 + 23 k c a l per mole. I t must be emphasized again t h a t t h i s i s an observed a c t i v a t i o n energy f o r the o v e r a l l process. Nonetheless, i t does l i e at the upper end of the range reported(5) f Q r the a c t i v a t i o n energy of s e l f - d i f f u s i o n of i n s t o i c h i o m e t r i c U0 Q (95 t o 120 kcal/mole). 36 200 A 100 80 60 4 0 2 0 X .3 • o o •8 17 • • A s 0 1 5 Q 16 ^ max-5000 psi • 5-907 5-977 6 050 6124 I I I I 6-200 I 0 V T ° K _J 1420 1400 1380 1360 1340 T ° C F i g u r e 17 Arrhenius p l o t showing e f f e c t of temperature on s t r a i n r a t e 200 100 10 O 15 A 5 Q 16 Q=ir8t23kcal — • T — x: /VS. m O • CD 5- 907 I 5-977 I 6 050 6124 6-200 I I | I04/T°K 1420 1400 F i g u r e 18 1380 1360 1340 T S h i f t e d Arrhenius p l o t °c V I I I SUMMARY AND CONCLUSIONS S t o i c h i o m e t r i c s i n g l e - c r y s t a l s of randomly o r i e n t e d uranium d i o x i d e have been deformed i n bending at low s t r e s s e s and high temper atures t o o b t a i n steady-state creep r a t e s . I n the regions of s t r e s s and temperature examined, the r e s u l t s appear t o f i t the r e l a t i o n s h i p : n C ( ^maAs - P ( " ^ ) where steady-state creep r a t e [K )„„ 1 *X ; '-.= r e s o l v e d shear s t r e s s i n <JD11> d i r e c t i o n s :°max^SS ; > &ll> o n ^ p l a n e s Q 118 + 23 kcal/mole constant; and 3 ^ n <C h Since f a i n t s l i p l i n e s were observed, s l i p must be i n v o l v e d i n the o v e r a l l process, but may not be the only process s i n c e n appears t o be l e s s than f o u r . 39 IX SUGGESTIONS FOR FUTURE RESEARCH C e r t a i n l y the f i r s t q u e s t ion t o be answered i s , does n =.kl More runs c o u l d be performed i n the same ranges of temperature and s t r e s s t o provide a s t a t i s t i c a l l y more s a t i s f a c t o r y p i c t u r e . The range of st r e s s e s then c o u l d n a t u r a l l y be extended t o determine the l i m i t s of a p p l i c a b i l i t y of the assumed s t r e s s dependence. I f the f o u r - p o i n t bending i s continued, i t i s suggested t h a t the l o a d i n g be reversed so th a t the d e f l e c t i o n s ( s t i l l r e l a t i v e to the two inner l o a d s , which are now supports) can be measured r e l a t i v e t o a s t a t i o n a r y reference p o i n t at the lower end. The lo a d s , at the ends of the beam, would be a p p l i e d from the top. P o s s i b l y d i s l o c a t i o n d e n s i t i e s and arrangements c o u l d be c o r r e l a t e d w i t h deformation by et c h i n g and X-ray techniques. P o l y - g o n i z a t i o n a f t e r creep deformation would be an i n t e r e s t i n g extension of t h i s r e s earch. ko APPENDIX I- THE URANIUM-OXYGEN SYSTEM The uranium oxygen system i s d i f f i c u l t t o i n v e s t i g a t e owing, t o the complex nature of the oxides formed and t h e i r extreme i n s t a b i l i t y . The r e s u l t s of va r i o u s i n v e s t i g a t o r s are summarized i n the.phase diagram. t— < UJ a. 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 / 1. r u o 2 + x + u 5 o . 3 i • | r U4°9± X ! uu 2 + x A /G i A 5 ! ! i i • ! / U4°9 i I 1 1 X l \ \ Y + 1 •O 1 o j / \\ \ 3 1 / B A B . A 1 uo2-t °9 , D L M w n D U n n i • BLACKBURN A BLACKBURN o RRftMvni n ! — 6R0 • ARO NVOLO NSON I 1 A ! 1 1 2.0 2.1 2.2 2.3 2.4 2.5 0/U ATOM RATIO 2.6 2.7 F i g u r e A l ( a f t e r Seddon ) APPENDIX I I STRESSES IN BENDING ( l ) Three-point bending A simply supported beam c a r r y i n g a s i n g l e concentrated l o a d at the•centre has a uniform shear s t r e s s along i t s l e n g t h which changes s i g n at the centre . The bending moment v a r i e s l i n e a r l y from the supports t o a maximum at the centre . Thus the maximum e l a s t i c f i b r e s t r e s s occurs i n the outer f i b r e s at the centre of the beam. There are a l s o contact s t r e s s concentrations i n the f i b r e s immediately below the a p p l i e d l o a d . (2) Four-point bending .A simply supported beam c a r r y i n g two equal concentrated ..loads at equal distances from the supports has, i n the centre s e c t i o n , zero shear s t r e s s , and constant bending moment as shown i n Figure A I I . 1 . The maximum e l a s t i c f i b r e s t r e s s 0>) i s d i s t r i b u t e d over the centre p o r t i o n of the beam. The contact s t r e s s e s again occur under the l o a d s . k2 m —> <—d -> P o LdtfL t p h C o Shear Bending ™ Moment F i g u r e A-II-1 Simple beam: two equal concentrated loads at equal d i s t a n c e s from supports 1 = 18.65 mm d = U.375 mm m = 10.00 mm Thus the use of f o u r - p o i n t bending, by d i s t r i b u t i n g the maximum s t r e s s e s u n i f o r m l y along the centre l e n g t h of the beam, a c t u a l l y r e s u l t s i n the t a k i n g of a more r e p r e s e n t a t i v e sample of the m a t e r i a l . I n t h i s i n v e s t i g a t i o n the used was c a l c u l a t e d from equation ( b ) . That i s , the t o t a l l o a d t o be used f o r a given beam was c a l c u l a t e d u s i n g ( ^ ) b h 2 W = 2P = (c) 3d . The s t r a i n - r a t e was c a l c u l a t e d u s i n g equation ( l l ) of the t e x t , kh • e = -g y (d) max m which assumes the centre s e c t i o n i s bent i n t o a c i r c u l a r a r c . I f the value of m from f i g u r e A I I . 1 , i s s u b s t i t u t e d i n equation ( d ) , and i f h i s i n m i l l i m e t r e s and y i n inches, then Anax = ( 1 " 0 1 5 ) h y . ( e) (3) S t r e s s r e d i s t r i b u t i o n i n beams undergoing creep At the i n s t a n t the l o a d i s a p p l i e d , the beam undergoes an instantaneous e l a s t i c (and p l a s t i c ) d e f l e c t i o n . I n i t i a l l y before the beam has had time t o creep the s t r e s s d i s t r i b u t i o n i s t h a t given by e l a s t i c c o n s i d e r a t i o n s and i s shown as the s t r a i g h t l i n e i n Fi g u r e A I I . 2 . The maximum f i b r e s t r e s s at the i n s t a n t of l o a d i n g w i l l then be given by equations (a) or ( b ) . hk F i g u r e A.II.2 S t r e s s d i s t r i b u t i o n i n bending ( a f t e r . F i n n i e and H e l l e r ( 2 2 ) ) Under the a c t i o n of the a p p l i e d s t r e s s the m a t e r i a l of the beam creeps. I f the m a t e r i a l deforms i n a t e n s i l e t e s t according t o equation (3) of the t e x t e = K<5" n ( f ) the i n i t i a l creep r a t e s i n the f i b r e s i n response to the l i n e a r e l a s t i c s t r e s s d i s t r i b u t i o n w i l l not be p r o p o r t i o n a l ( i f n > l ) t o t h e i r distances from the n e u t r a l a x i s . However, t h i s s i t u a t i o n would r e s u l t i n a s e c t i o n t h a t was not plane and i n order to maintain a plane s e c t i o n the s t r e s s i n f i b r e s near the n e u t r a l a x i s i n c r e a s e s . Some time a f t e r the l o a d i s a p p l i e d , a s t a t e of s t r e s s d i s t r i b u t i o n i s reached i n which the s t r a i n r a t e s i n a l l f i b r e s become p r o p o r t i o n a l t o t h e i r d i s t a n c e s from the n e u t r a l a x i s . This d i s t r i b u t i o n i s shown i n Figure A . I I . 2 . f o r v a r i o u s n's. Thus ^ ^max^SS K^ ^ m a x ^ e l a s t i c where K i s given b y ^ " ^ Assuming the creep law i n equation ( f ) k6 . APPENDIX I I I GROWTH:ATTEMPTS During the i n i t i a l stages of t h i s research program attempts were made t o grow s i n g l e c r y s t a l s of U 0 2 from the melt "by u s i n g the f l o a t i n g zone technique so s u c c e s s f u l l y a p p l i e d t o many metals. .However, UOg has a me l t i n g p o i n t of 2800°C, a thermal c o n d u c t i v i t y of 0.003 cal/cm,sec,°C, an e l e c t r i c a l c o n d u c t i v i t y of about 10" 2(Cicm)~^ at 500°C, and a vapour pressure of about 1 mm Hg at i t s m e l t i n g p o i n t . Thus i t i s a formidable task indeed. As ser i o u s experimental work began, r e p o r t s were r e c e i v e d of attempts of others t o accomplish the same end, a l l more or l e s s u n s u c c e s s f u l . However some experimental attempts were made and these w i l l be b r i e f l y o u t l i n e d . 1) I n d u c t i o n h e a t i n g : i f UOg i s heated above room temperature, i t s e l e c t r i c a l c o n d u c t i v i t y r a p i d l y i n c r e a s e s , and r e p o r t s i n d i c a t e d t h a t UO2 c o u l d be i n d u c t i v e l y heated above 1000°C. A one-turn c o i l of copper p l a t e was f a b r i c a t e d and connected ,to a P h i l i p s (output: 5KW, 800Kc) 1 i n d u c t i o n u n i t . A rod of s i n t e r e d UO2, about y^ " square was enclosed i n a Vycor tube so that, an argon atmosphere c o u l d be maintained, and was heated w i t h an oxy-gas t o r c h t o at l e a s t 1000°C. The tube c o n t a i n i n g the UO2 was lowered q u i c k l y i n t o the powered c o i l . S e v e r a l attempts were made, but no heati n g e f f e c t s were observed. 2) Resistance h e a t i n g : Attempts were made t o operate a narrow tungsten f i l a m e n t , bent t o the shape of a h a i r - p i n , at temperatures c l o s e t o i t s m e l t i n g p o i n t , t o melt a narrow zone of UO2 at the center of the c i r c u l a r bend. The f i l a m e n t and r o d of, again, s i n t e r e d UOg, were surrounded w i t h c o n c e n t r i c molybdenum r a d i a t i o n s h i e l d s and about 1000 watts of power were ^7 needed t o heat the f i l a m e n t t o 3000 C. This furnace was enclosed i n a p r o t e c t i v e atmosphere of argon. During s e v e r a l runs, some m e l t i n g of the •corners of the r o d was observed. However, heat t r a n s f e r c o n s i d e r a t i o n s 1 i n d i c a t e d t h a t the f i l a m e n t must be p l a c e d as c l o s e as p o s s i b l e t o the r o d without touching i t , and must be operated almost at i t s m e l t i n g p o i n t . Observations of the molten areas obtained showed t h a t a very narrow zone only ( K. 5mm) would be p h y s i c a l l y s t a b l e under the i n t e r a c t i o n s of the surface t e n s i o n and g r a v i t y . I f r e s i s t a n c e h e a t i n g w i l l ever be a f e a s i b l e technique, i t w i l l be w i t h f i l a m e n t s of higher m e l t i n g p o i n t m a t e r i a l s (say TaC, or WC), si n c e a small i n c r e a s e i n l i n e v o l t a g e t o the transformer supplying the high c u r r e n t - low v o l t a g e power t o the tungsten f i l a m e n t operated c l o s e t o i t s m e l t i n g p o i n t w i l l cause i t t o melt. 1+8 APPENDIX IV STOICHIOMETRY AT TEMPERATURE The oxygen pressure i n e q u i l i b r i u m w i t h U 0 2 + x at any temperature (25) may be estimated from / v r f -33000^ /31x\ P Q 2(atm) = 76 exp T o K J e x p ^ ^ j j I f the temperature i s 1300°C (1573°K) and x =0, then the pressure of oxygen o i n e q u i l i b r i u m w i t h s t o i c h i o m e t r i c U 0 2 i s 5 x 10 atmospheres. Assuming a l l oxygen i s converted t o water vapour by the p a l l a d i n i z e d c a t a l y s t , and t a k i n g a dew p o i n t of -50°C ( f o r the anhydrone used, the dew poi n t i s -80°C) which corresponds t o .00001+ atm water vapour, the p a r t i a l pressure of oxygen may be estimated from K where K f o r 1300°C = 1+.91 x 10" 6(atm)2, Thus PO 2{K(% 2O ]/ [%1 '(1+.91 x 10"6 )(!+ x 10" 5A 2 74 20 x 10" 2 2 atm o _ i p And even a dew p o i n t of +50 C gives a Pn of on l y 10 atm; t h e r e f o r e at 2 temperatures used the uranium d i o x i d e was s t o i c h i o m e t r i c . ^9 APPENDIX V SUMMARY OF EXPERIMENTAL RESULTS I n the f o l l o w i n g t a b l e , the symbols used a r e : h = the height i n m i l l i m e t e r s b = the width i n m i l l i m e t e r s <5^  = max. f i b r e s t r e s s , p s i (see Appendix I I ) T = t e s t temperature i n °C d^ = d e f l e c t i o n (gauge) inches x 10 at time t t ^ , t g = time from beginning i n hours dg = d e f l e c t i o n (gauge) inches x 10^ at time t g ^ d = dg - d^, inches x 105 £±t = t g - t , hours d = A d / ^ t , inches x 10^ per hour e = (l.015)(h)d, i n / i n x 10^ per hour (see Appendix I I ) I n some cases i t was not p o s s i b l e , due t o the l e n g t h of the runs , t o o b t a i n a gauge reading at the s t a r t ( o r / f i n i s h ) of a steady-state r e g i o n and t h e r e f o r e the d e f l e c t i o n had t o be c a l c u l a t e d u s i n g a c h a r t c a l i b r a t i o n of 22.8 x 10 inches per d i v i s i o n . Values obtained i n t h i s manner are marked *. The p o i n t s p l o t t e d as "calc " i n Fi;g-S'.10.,. Ik':,. 15 were obtained the same way. ; # Orig ,ln h b T d l * l d2 \ A d A t ' A e k w 15 c 02 1.82 2.76 5000 11+00 3^ 9 15 2149 66 1700 51 33.3 bl.5 3 N 15 c 03 1.85 2.65 11 365* 15 836 23 471 8 59-0 110 5 N 15 D 01 1-70 2.1+5 n 360 •21 ^01 24 l4i 3 47.0 81.1 " 1360 542 26 825 44 283 18 15.7 27.1 i t il+OO 828 44.50 1283 55.50 455 11. 41.4 71.4 " •1420 1304 .55-75 1459 58 155 2.25 69.0 119 " 1360 1497 58.50. 1788 69.25 291 10.75 27.0 46.6 1400 1788 60.25 2055 75 267 5.75 46.5 80.3 8 H 16 B 01 1.80 2.72 11 288 35 1182* 80 894 45 19.9 36.1+ 9 N 16 B 02 I.76 2.1+5 • 11 125 26 3^ 7 44.75 222 18.75 11.9 21.0 16 N 20 B 02 •1.65 3.25 11 445 11 719 16 274 5 54.8 91.9 13^0 763 17.25 867 24 104 6.75 15.4 25.8 " 1360 867 .24.25 1186* 31+ 319 9.50 33.6 56.2 1400 1270 37 1626 42.75 356 5-75 62.0 104 1360 1647 43 1957 59 310 16 19.4 32.5 1420 1983 59-75 62 2080 6I.50 93 1.50 62.0 io4 " i4oo 2125 2248 65.25 123 3.25 37-8 63.4 17 N 21 A 02 1.75 3.05 " I I 458* I.50 861 11.50 1+03 10 1+0.3 71.6 6000 11 1050 12.75 1199 14.25 149 1.50 99-3 177 7000 I I 1482 15.75 1722 17.25 240 I.50 160 , 284 5000 I I 1722 17.25 1873 20.50 151 4.25 35-5 63.O 15 N 22 B 02 1.85 3.10 " I I 127 16 502 33.50 375 17.50 21.5 1+0.3 " 1420 502 33.50 777 38.75 275 5.25 52.4 98.3 " 1360 803 39 1038 56.50 235 17.50 13-4 25.2 " 1400 1080 58.75 1370 69.25 290 10.50 27.6 51.8 1420 1372 69.50 1^ 35 70.75 63 I.25 50.4 94.5 51 APPENDIX VI CALCULATION OF RESOLVED SHEAR.STRESS I n the t a b l e below ^ i s the great c i r c l e angle from [piJ^ pole t o the.pole of the major a x i s Q i s the great c i r c l e angle from ( i l l ) p o l e t o the pole of the major a x i s t—* I = /\ cos cos 9 ' max v £ as defined i n Appendix I I max f c o s ^ 9 cos9 cos^cos9 T^ 011> l o g T e 15 38 .788 59 •515 .1+06 2030 3.308 1+0.3, 51-8 8 36 .809 67 •319 .316 1580 3-199 36.1+ 9 36 .809 65 .k23 .3U2 1710 3.23^ 21.0 3 ko .766 51 .629 .1+82 21+10 3-382 110. h ki • 755 50 .6k3 .^ 85 2425 3.385 61.5 5 37 •799 53 .602 .1+81 21+00 3.381 81. l,7l.l+, 80.3 91.9,101+, 63.1+ L6 52 .616 3^ • 731 .1+50 2250 3.352 L7 50 .6U3 k6 .695 .¥+7 2235 2680 3120 3-3^ 9 3-^ 28 3-^ 95 71.6,63.0 177 281+ 52 XI REFERENCES ( 1 ) Gilman, J - Mechanical P r o p e r t i e s of I o n i c C r y s t a l s , i n Prog, i n Ceram. S c i . , J.E. Burke, ed., 1 (1961), lk6. ( 2 ) Kingery, W.D., P r o p e r t y Measurements at High Temperatures, ( 1 9 5 9 ) , 1^9- (3) Chang, R., High Temperature Creep and A n e l a s t i c Phenomena i n P o l y c r y s t a l l i n e R e f r a c t o r y Oxides, J.Nuc.Mat., 2 ( 1 9 5 9 ) , m - (4) P a r r , N.L., et a l . , P r e p a r a t i o n , M i c r o s t r u c t u r e and Mechanical P r o p e r t i e s of S i l i c o n N i t r i d e , i n S p e c i a l Ceramics, P. Popper, ed., ( i 9 6 0 ) , 1 0 2 . (5) S c o t t , R., H a l l , A.R., and W i l l i a m s , J . , The P l a s t i c Deformation of Uranium Oxides Above 80QQC, J . N u c l . Mat., 1 ( 1 9 5 9 ) , 39- (6) Wachtman, J.B., Creep of C r y s t a l l i n e NOnmetals, i n Creep and Recovery, ASM Trans., h$A ( 1 9 5 ? ) , 3^ !+ • (?) A z a r o f f , L.V., I n t r o d u c t i o n t o S o l i d s (i960), 360. (8) Swanson, H.E. and Fyuot, R.K., Standard X-Ray D i f f r a c t i o n Powder P a t t e r n s , NBS C i r c u l a r 539> I I ( 1 9 5 3 ) , 3 4 - (9) Aronson, S., and B e l l e , J . , Nonstoichiometry i n Uranium D i o x i d e , Jour. Chem.Phys., 29 ( 1 9 5 8 ) , 1 5 1 . ( 1 0 ) Gronvold, F., High Temperature X-Ray Study of Uranium Oxides i n the UOp - U3OA Region, J . Inorg. and Nuc. Chem., l ( 1 9 5 5 ) , 357- (11) Anderson, J.S., et a l . , Decomposition of Uranium Dioxide at i t s M e l t i n g P o i n t , Nature, 26 Mar. ( i 9 6 0 ) , 9 1 5 . (12) Burdick, M.D., and Parker, U.S., E f f e c t of P a r t i c l e S i z e on Bulk D e n s i t y and Strength P r o p e r t i e s of U 0 P Specimens, ' J.Amer.Ceram.Soc, 39 ( 1 9 5 6 ) , 1 8 1 . (13) Armstrong, W.M., I r v i n e , W., and Martinson, R., Creep Deformation of S t o i c h i o m e t r i c UOp , t o be p u b l i s h e d i n Jour. Nuc. M a t e r i a l s . (14) Rapperport, E.J., and Huntress, A.M*, Def o r m a t l ^ ^ C r y s t a l Uranium Dioxide from 7 0 0 ^ t o 1900°C, Nuclear Metals Inc., NMI - 1242 ( i 9 6 0 ) . 53 (15) F i n n i e , I . , S t r e s s A n a l y s i s i n the Presence of Creep, Appl. Mech. Rev., 13 (I960), 705. (16) Dorn, J.E., The Spectrum of A c t i v a t i o n Energies f o r Creep, i n Creep and Recovery, ASM Trans., ^9A (19577, 255. (17) Duckworth, W.H.,Precise T e n s i l e P r o p e r t i e s of Ceramic Bodies, Jour. Amer.Ceram. &oc.} 34 (1951), 1. (18) Timoshenko, S., Strength of MateriaJs, Part I I , (1956), 527- (19) Hoff, N.J., Mechanics A p p l i e d t o Creep T e s t i n g , SESA Proceed., XVII (1958), 1- (20) S c o t t , J . J . , Fused Uranium Oxide, paper d e l i v e r e d Amer.Ceram.Soc., Toronto (1961). (21) C u l l i t y , B.D., Elements of X-Ray D i f f r a c t i o n , (1956), 215. (22) F i n n i e , I . , and H e l l e r , W.R., Creep of Engineering M a t e r i a l s , (1959), 80,. (23) Weertman, J . , Theory of Steady-State Creep Based on D i s l o c a t i o n Climb, J.Appl.Phys., 26 (1955), 1213. (2U) Seddon, B.J., Uranium Ceramics Data Manual, UKAEA, DEG Report 120R (I960), 32. (25) Webster,.A.H., and B r i g h t , N.F., The E f f e c t s of Furnace Atmosphere on the S i n t e r i n g Behaviour of Uranium D i o x i d e , Department of Mines and T e c h n i c a l Surveys, Ottawa, Research Report R2 (1958). 

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