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The tensile deformation of pure vanadium single crystals at low temperatures Snowball, Robert Forrester 1960

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THE TENSILE DEFORMATION OF PURE VANADIUM SINGLE CRYSTALS AT LOW TEMPERATURES by ROBERT FORRESTER SNOWBALL A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of MINING AND METALLURGY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Mining and Metallurgy THE UNIVERSITY OF -BRITISH COLUMBIA October I960 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Mining and Metallurgy Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. November l ^ t h , i960 Date ABSTRACT An i n v e s t i g a t i o n of the low temperature t e n s i l e properties of vanadium sin g l e c y r s t a l s was c a r r i e d out, using zone-refined metal. Single c r y s t a l s of predetermined a x i a l [ l l O ] o r i e n t a t i o n were grown by a melt s o l i d i f i c a t i o n technique, using an e l e c t r o n beam, floating-zone r e f i n e r . Tensile specimens were prepared from these single c r y s t a l s . A p l o t of y i e l d stress versus t e s t temperature was found to be discontinuous and consisted of two curves which intersected at -125° C. The p l o t of log y i e l d stress versus r e c i p r o c a l temperature y i e l d e d two s t r a i g h t l i n e s which also intersected at -125° C. The s l i p system was i d e n t i f i e d as ^1^^112^ , which i s d i f f e r e n t from that found f o r i r o n s i n g l e c r y s t a l s . X-ray, metallographic and e l e c t r i c a l resistance data indicate that the phenomenon i s p r i m a r i l y a y i e l d point e f f e c t . The r e s u l t s of t e n s i l e t e s t s performed on s i n g l e c r y s t a l s at a very low s t r a i n r a t e , and on p o l y c r y s t a l l i n e specimens indi c a t e d that the temperature dependence of y i e l d stress i s i t s e l f o r i e n t a t i o n dependent. Three possible explanations of the unusual temperature dependence of y i e l d jstress are given' (1) A change i n deformation mechanism occurs, f o r example, from s l i p t o twinning. (2) A minor ordering r e a c t i o n occurs. (3) A change i n the mechanism by which d i s l o c a t i o n s are unlocked from t h e i r atmospheres occurs; f o r example, two impurity atmospheres surrounding d i f f e r e n t d i s l o c a t i o n s , each impurity showing a separate temperature dependence of y i e l d s t r e s s . ACKNOWLEDGMENT The author wishes to thank Dr. J.A. Lund and Professor W0tio Armstrong for their supervision and encouragement, and Mr. RBQ* Butters for his technical assistance during this investigation. The author is also indebted to Dr. E„ Teghtsoonian and R.W. Fraser for many helpful discussions. The work was financed by the Defence Research Board, under D.R.B. Grant 7510=36, 'The Effect of Strain Rate and Temperature on the Deformation Behaviour of Body<=Centered-Cubic Metals „« 1 TABLE OF CONTENTS Pag® X o INTRODUCTION o o o o o o o o o o o o o o o o o o o o o o 3. I I o A REVIEW OF PREVIOUS WORK . . . . . . . . o . 3 I I I . EXPERIMENTAL O o . 0 . 0 . 0 . . 0 . 0 0 0 0 0 . 0 . 0 0 1 7 A. Materials „ „ . . . . . o . . o . « » . o o . » o 17 B o P u r i f i c a t i o n 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 17 1. Comstructiom of the Zone Refi&er . „ . . „ . 1? (a) Power Supply o o . o o o o o . o o o o o 18 (b) Furnace o o o o o o o . o o o o o o o o l o (c) Vacuum System 0 0 0 0 0 0 0 0 0 0 0 0 0 21 2 . Operation of the Ze&e Refiner . . . . . 0 . . 21 3 . P u r i t y ©f the Zone-Refined-Metal . . . . . . 22 C. Single C r y s t a l Growth and Orie n t a t i o n „ . . . „ . 23 D. Specimen Preparation o o . o o o o o . o o o o o 25 l o Machining o o o ' o o o o o . o o o o . o o o o 25 2 0 Electropolishirag, o o o o . o o o o o . o o o 2 5 3 o X—Ray o o o o o o o o . o o o o o o o o o o o 2 5 4. Preparation of Polycrystallime Specimens . . 26 E. Testing Procedure „ . „ „ . . 0 . . . . . . . . . 2 7 1 . Gripping and Mounting of Test Specimeas . . „ 2 ? 2 . Temperature Measurement . . . . . . . . . . . 2 9 3 o Temperature Control O . . o o o . o . . . o ' o 2 9 Uc Test Procedure 0 o o o o o . o o o o o o o . 3 0 IV. EXPERIMENTAL RESULTS „ . . . . . . . . . . . . . . . . . 33 A. Single C r y s t a l s <= Rate of S t r a i n 0 o 0 5 5 / m i a , . . . 33 l o Yield. Stress 0 0 0 0 0 o o o o o o o o o 0 0 3 3 2 o Fl®w Stress o o o o o o o o o o o o o o o 0 0 ZjjO 3 o El0B.g*ib i®& 0 0 0 0 0 0 0 0 0 0 0 0 «« o o o o / i O B . Single Crystals - Rate of S t r a i n 0 , 0 0 2 2 / m i ® . '• . . Uh C. P o l y c r y s t a l l i n e Specimens - Rate of S t r a i a O o 0 5 5/mill 0 0 0 0 . 0 0 0 0 0 0 0 0 D. Analysis ®f the Deformation Mechanism . „ . . . . kl 1 * S l i p Systoifi 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bff 2 o Twi nn i n g o o o o o o o o o o o o o o o o o o 57" E. The C r i t i c a l Resolved Shear Stress . . . „ . „ „ 57 F. E l e c t r i c a l Resistance . . . . . . . . . . . . . . . 59 G o Microhardness o o o o o o o o o o o o o o o o o o 65 V o . DISCUSSION o o o o o o o o o o o o o o o o o o o o o o o 66 A o Review of Results „ „ „ o o o o o . o o o o o o o 66 B o Possible Mechanisms 0 0 o o . o o o o o o o o o o . 67 1 . Change ira Deformation Mechanism . . . . . . . 6 ? 2 . Ordering Process o o . o o o . o . o . o o o 69 3 o D i s l o c a t i o n Breakaway , „ „ . . . „ . . . . . 7 0 VIo CONCLUSIONS o O O O O O O O O O O O O O O O O O O O O O 74 V I I . RECOMMENDATIONS FOR FUTURE WORK . . . . . . . . . . . . 7 6 V I I I . B I B L I O G R A P H Y o o o o o o o o o . o o o . o o o o o o o 7 7 I X o A P P E N D I C E S o o o o o o o o o o o o o o o o o o o o o . 8 0 No. FIGURES Pafes 1„ Temperature dependence ©f the t e n s i l e properties of vanadium from Clough and Pavl©vie^„ . 0 <> . . o ° o . 9 2. Tensile properties ©f b©mb=reduced vanadium at lew temperatures, a f t e r Leomis and Carlsea^ 0 0 o . . . 12 3. Tensile preperties ef cr y s t a l ~ b a r vanadium at lew temperatures a f t e r Leomis and Carl s e s ^ „ 0 <, . o o o o 13 4« E f f e c t »f i n t e r s t i t i a l impurities ©n the ductile-t©= b r i t t l e t r a n s i t i o n ©f bomb=reduced vanadiumj a f t e r Loorais and Carlson . o . o o o . o o o o o o o o o o o 16 5o Constructien ©f the 60 Photograph ©f the assembled z©ae refimer and power S"UPP l y o o o o o o o o o o o o o o o o o o o o o o o o o 20 7o Photograph ©f vanadium sin g l e c r y s t a l s grown b y the melt«=solidif ication=z©ne=ref i n i n g technique o o o o o o 23 8„ Laue photograph near the tep end ©f V~14 o o o o o o o 24 9o Laue photograph near the bottom end ©f V-14 o o o o o o 24 10o Laue photograph of machined and electr o p o l i s h e d tensile specimen o o o o o o o o o o o o o o o o o o o o 26 I I , Jaws f o r gripping specimens o o o o o o o o o o o o o o 28 12a Photograph of mounted specimen, ready f o r t e n s i l e t© St l£lg o o o o o o o o o o o o o o o o o o o o o o o o 2S 13. T y p i c a l load=elongati©n curves at d i f f e r e n t temperatures 31 14o T y p i c a l broken specimens0 Left to r i g h t : p o l y c r y s t a l l i n e specimen (<=122„5°C), s i n g l e c r y s t a l (=196°C), sing l e c r y s t a l (24°C) „ „ o o 0 o o o „ o . „ 32 15. Y i e l d stress VS temperature f o r s i n g l e c r y s t a l s „ „ „ 0 34 16. Y i e l d stress VS r e c i p r o c a l temperature f o r s i n g l e C I*y 3 *t a Is 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 17. Log p l o t of S y VS r e c i p r o c a l temperature f o r s i n g l e CryStalS O O O O O O O O O O O O O O O O O O O O O O O O 3^  18o S y VS temperature f o r annealed molybdenum, a f t e r FlSh©F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 39 19o Flow stress VS temperature f o r s i n g l e c r y s t a l s 0 . 0 0 . 41 20. Flow st r e s s VS r e c i p r o c a l temperature f o r s i n g l e Cry St alS o o o o o o o o o o o o o o o o o o o o o o o o Page 2 1 . Log plat of flow stress VS reciprocal temperature for single crystals o o o o o o o o o o o o o o o o o o 43 2 2 o Percent elongation VS temperature for single crystals „ 45 2 3 o Sy VS temperature for single crystals „ <> o 0 o „ o o » 46 2 4 o Sy VS reciprocal temperature f o r single crystals . . . 46 2 5 o Sy V S temperature for polycrystalline metal 0 0 0 . . . 48 2 6 0 Sy VS reciprocal temperature for polycrystalline metal„ 46 2 7 . Orientation ©f pulled tensile specimens „ 0 o o 0 . . 0 §0 2 8 o [llo] photograph of broken specimen tested at 2 4 ° C ( V 0 S T $ ) O O O O O O O O O O O O O O O O O O O O O O O O 5 1 2 9 o Specimen of Figure 2 8 rotated 3 5.3° towards [boij.' Note the 3-fold symmetry of the ( l l l j direction „ . „ . „ „ 51 3 0 o fjioj photograph of broken specimen tested at < = *183 C (VO7T/4.) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 3 1 0 Specimen of Figure 3 0 rotated 3 5 » 3 ° towards (OOlJ . Note the 3-fold symmetry of the |Ll l ] direction . . . . 5 2 3 2 0 A and B , s l i p traces from specimens above the trans-it i o n temperature. Figure 3 2 A is V 0 8 T 3 , tested at 2 4 ° C , Figure 3 2 B i s V 0 9 T 5 , tested at ~ 5 0 ° C . Unetched X l 2 5 o o o o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 000 5 "4* 33o A and B , s l i p traces from specimens below the trans-i t i o n temperature. Figure 3 3 A i s V 0 7 T 4 , tested at = 1 8 3 ° C , Figure 3 3 B i s VO4T5, tested at ~ 1 9 6 8 C „ Unetched X 1 2 5 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 34, Standard Stereographic projection for the cubic system, showing the orientation of a standard tensile specimen with respect to the projection . . . . . . . . . 56 3 5 o Fundamental quantities in the resolution of simple tOUSl©!! o o o o o o o o o o o o o o o o o o o o o o * 5 ^ 36. Scr VS temperature for single crystals . . . . . . . . 60 3 7 . Scr VS reciprocal temperature for single crystals . . . 6 1 380 Log Scr VS reciprocal temperature for single crystals „ 6 2 390 E l e c t r i c a l resistance VS temperature for a single Cl?]^ S t a l l O O O O O O O O O C O « O O O O O O O O O O O O 3^ 4 0 . Enlargement of the c r i t i c a l region of Figure 39 . . . . 64 41. Hypothetical leg plot of S Cr VS I/^, . . <, 72 APPENDIX II 1, Circuit diagram of the ne refiner as used im this 1.11V© S11. gelt !• n . o o o e e o o » o 6 o o o o o o o o o e o 63 TABLES No. Page I. Typical impurity contents of commercial grade vanadium metal, as used in ether investigatieias . . . . , 6 II. Analysis of as-reeeived vanadium . . . . . . . . . . . . 17 III. Comparison of high purity vanadium metal 22 I. Appendix I. «= The results of tensile tests 0 „ . . .-<> o 81 I. Appendix III - The results of resistance measurements . . 90 I. Appendix IV = The results of micro-hardness measurements. 94 .THE TENSILE DEFORMATION OF PURE VANADIUM SINGLE CRYSTALS AT LOW TEMPERATURES Io INTRODUCTION The increasing demand for materials suitable for extreme elevated temperature service has directed investigators to many new fields in- recent years„ Exhaustive studies of ferrous and non-ferrous alloy systems-have been made, yielding materials which f a l l far short of the stringent requirements of the high temperature field. More recently, the fields of ceramics, cermets and refractory metals have come into the foreground.Although preliminary results are very encouraging, these fields are s t i l l in infancy, and a great deal of fundamental work is re-quired before a clear understanding-of the behaviour of these materials is achieved. This investigation is part of a programme concerning the be-haviour of refractory metals. More specifically, i t is a fundamental study of the tensile properties of vanadium metal. Vanadium metal has been an article of commerce for several years^", used principally as a ferrous and non-ferrous alloying addition. Two serious limitations prevent i t s extensive use as a refractory base metal; i t has a -low melting point (1900 - 25°C) relative to many other refractory metals and, more serious, the oxide which forms on the surface of vanadium and ductile vanadium-base alloys has aineltingpoint of 675°C. I t is s t i l l , however, a metal of interest becauseof i t s relatively low density (6.1 /cc)y its-high electricalresistivityy its good chemical corrosion resistaneej- its- relatively high hotstrength-at intermediate temperatures up to 500*C,i and its relative abundanceo351 ^ . 2 A survey of the literature indicates that, despite the interest in vanadium, surprisingly l i t t l e is known of its physical metallurgy. The objectives of this work were to study the temperature de-pendence of the tensile properties, and ductile-to-brittle transition behaviour of high purity vanadium single crystals and polycrystalline metal. It was proposed to perform these tests at various strain rates, and independently to evaluate in this manner the effect of strain rate on the low temperature tensile properties of vanadium. 3 II. A REVIEW OF PREVIOUS WORK The pronounced transition from ductile-to-brittle behaviour is most common in metals having the body-centered cubic structure, primarily because these metals exhibit a strong temperature and strain-rate de-pendence of yield strength. The condition for the occurrence of brittle or cleavage failure is that the yield strength must exceed the cleavage fracture strength, a condition which may be brought about -by lowering the temperature or increasing the strain rate, Wessel P H has reviewed the literature concerning the theoretical aspect of the ductile-to-brittle transition and has summarized i t in the following manner. Cottrell and Bilby^ and Fisher 1^ describe yielding as the break-ing away of dislocations-from atmospheres of impurity atoms, which i t is believed tend to form as a result of the migration of interstitial and other Impurity atoms to the vicinity of dislocations, and there to exert a 'locking' effect on such dislocations; This concept of yielding does not require any prior plastic deformation. Since pre-yield plastic strain does occur;the concept of catastrophic yielding resulting only from the breaking loose of feasd-Read sources from pinning atmospheres cannot adequately explain the yield phenomena encountered in body-centered cubic metals. It is believed that the pre-yield plastic strain is due to the breaking away of an appreciable number of dislocations prior to the elastic limit. These dislocations * are subsequently piled up on grain boundaries, impurity atoms or other barriers. 4 At high temperatures, the yield point is the result of the piled up dislocations being released, and more dislocation sources breaking away from anchoring atmospheres, resulting in the cataclysmic release of dislocations which causes the load to drop and results in the familiar upper and lower yield points. At low-temperatures, the stress level just prior to yielding is very high, and, because of the increased resistance to plastic deformation, higher localized stresses are required to enable piled-up dislocations to break through or away from barriers. As a result, high localized stresses can exist in front of piled up dislocations. These stresses can, in fact, be so high that they exceed the cohesive strength of the metal, and result in microcracking. Where material is more favorably oriented for flow, the piled up dislocations can result in plastic deformation. During the subsequent abrupt yielding, the microcracks grow in size and number, and eventually a stable crack forms which will propagate and result in brittle failure. The abruptness of the transition from a flow-producing yield to a crack-producing yield is dependent on the particular metal and its chemical and metallurgical condition. In general, most body-centered cubic transition metals exhibit a higher tendency for sharp yielding at low temperatures. Among the metals which exhibit this phenomenon are vanadium, niobium, chromium, moly-Tarrtelu»n bdenum, tungsten and iron, "gawbalitm has not shown brittle behaviour in tension as low as 4.2°K. There are large variations in transition temperatures encountered and many variables appear to have a large influence. The most important information contained in the literature con-cerns the; influence on properties of the intrinsic contents of the im-5 purity elements; hydrogen, nitrogen, carbon and oxygen. A limited amount of published data exists concerning the individual effects of these impurities, with the exception of hydrogen, for which more data is 5 9 available, , The term 'interstitial impuriteo' w i l l be applied to hydrogen, nitrogen, carbon and oxygen in the text which follows, although i t is recognized that oxygen is normally a substitutional impurity. A considerable volume of results based on studies of the tensile and impact properties of vanadium is now available in the literature, although the results are contradictory and inconclusive in some cases. This is due largely to the fact that the materials' used- in each case were of different purities, and the results cannot, therefore, be compared on a rigorous basis. A l l previous investigations with the exception of the work by Loo mi s and Carlson^ were carried out using a commercial or sub-commercial 5 grade of metal, and one paper reported the effect of contaminating commercial vanadium with hydrogen. Typical analyses of material used by previous workers is given in Table I. It is clear from the foregoing discussion that the purity of the metal must be known i f the results are to be of value. TABLE I TYPICAL IMPURITY CONTENT OF VANADIUM METAL USED BY OTHER INVESTIGATORS Ref. Type C(wt%) N(wt%) 0(wt$) H(wtfi) Fe Si Ca A l W Ref 0 3 Arc Melted 0.09 0.07 0.057 0.0004 0.005 0.005 0.02 3 4 Bomb-Reduced .03-.07 .02-.04 ,05-.12 .001^ .004 4 5 Bomb-Reduced 0.2 0.01 0.02 0.003 0.015 0.01 0.02 5 7 Bomb-Red Extruded .13 .009 .03 -.002 0.2 0.05 0.1 0.1 7. 8 Bomb-Reduced .036-. 047 ."O47-.083 ,030-.070 .0028-.0059 . . , 8 9 Bomb-Reduced .08 . 02 . 02 . 006 0,02 0.02 0.02 9 9 C r y s t a l Bar .024 . 005 . 01 .001 0.02 0.02 0.02 9 10 Arc Cast .029-.094 .032-.060 .043-.110 .001-.004 10 ON 7 The tensile properties of vanadium, in common with other body-centered cubic transition metals are sensitive to a number of factors, including the interstitial content pf the metal, the type and alignment of the specimen in a tension test, the strain rate and the type of testing machine used. • In general, an increase in the interstitial content or strain rate increases the yield strength of the metal. A 'soft' tensile machine, such as a heavy hydraulic unit tends to give a lower value of yield strength,^ since the upper yield point may be suppressed by the internal motion of the machine. A 'hard.' machine such as one having a screw-driven cross-head does not tend to suppress yielding phenomena. „ The other major factor involved is the alignment-of the specimen.^"* Mis-alignment, which is more difficult to avoid with sheet specimens than cylindrical, shouldered specimens, will also cause suppression of the yield phenomenon. For these reasons, probably less significance should be attached to strength values reported which are based on data obtained from soft machines using sheet specimens or where B# particular attention was paid to specimen alignment through the use of a universal-type of gripping mechanism. This applies especially to investigators who used standard bomb-reduced vanadium of norma! impurity content, and reported 1 '8 considerable ductility with no heterogeneous yielding phenomenon. Previous investigations of the variation of tensile properties of vanadium with temperature in the range between 25°C and -196°C have yielded contradictory results which may be roughly divided into three 3 8 10 categories: (!) Those showing no abnormal behaviour, 3 ' (2) those i 9 / \ showing abnormal temperature dependence of yielding,- and (3) those showing c A q abnormal ductility behaviour. * 9 7 8 3 Considering the first group, Pugh studied the tensile properties of sheet specimens for constant strain rate and at temperatures between 78° and 1500°K„ Specimens were cut from arc-melted, rolled and annealed metal, ofthe purity indicated in Table I 0 Evaluation was made in terms of ultimate-tensile strength, 0»2 percent yield strength', strain hardening and rate sensitivity of the flow stress. He concluded that vanadium has a temperature dependence of tensile properties which is characteristic of body-centered-cubic metals, with the following features, (1) a high temperature sensitivity at low temperatures, (2) the occurrence of dis-continuous yielding at low and intermediate temperatures, and the appear-ance of minima in strain rate sensitivity and elongation > and maxima in strain hardening and strength relationship at about 700°K, indicating 8 strain aging behaviour, Clough and Pavlovic studied the flow, fracture and twinning of commercially pure vanadium. They performed tensile tests in the temperature range from 200° to -196°C, and V-notch Gharpy tests in the temperature range 150° to -100°C, Bomb-reduced metal, of the purity indicated in Table I was used,. Tensile tests, made from round, threaded-end specimens-exhibited a five-fold increase in yield strength (using a 0,2 percent offset)j a three-fold increase in ultimate tensile strength, and a ductile-to-brittle transition over this range of temperature, as shown in Figure 1. The variation of yield strength was correlated to Fisher's application of the Cottrell-Bilby theory of yielding. 1 1 It should be noted that Clough and Pavlovie used a hydraulic tensile machine, and any heterogeneous yielding phenomena were probably obscured, Charpy tests indicated that both |lOo| and |llo) are active cleavage habit planes. Mechanical-twins were-formed by impact loading at test temperatures of -78°C and lower. These twins were found to occur on £ll2} planes, apparently only within one or two grains of a cleaved surface. Temperature, C 0 -4-oo -3oo -200 - loo o too Temperature , F 2 0 o 5oo 4oo Figure 1. Temperature dependence ©f the Tensile Properties ©f Vanadium From Cloiigh and Pavlovic Farrell has recently published a paper concerning the properties of unalloyed vanadium consolidated by vacuum consumable-electrode arc melting, hot extrusion and cold working. The results presented include short-time tensile properties for bar and sheet in the temperature range from 1100° to -196°C, yield point and strain aging phenomena, notched-bar tensile properties, true stress-true strain curves, the strain hardening coefficient and exponent, elastic modulus, work-hardening characteristics, bend and Erichsen test data, and crystal orientations determined by X-Ray studies. The results of Farrell"s tensile tests are of wide interest, particularly with regard to yield-point phenomena. Almost a l l tests were performed using a Baldwin-Lima-Hamilton Universal Testing machine. Load-elongation curves were recorded autographically. In a l l cases, fully c y l i n d r i c a l annealed cylindrio specimens displayed distinct upper and lower yield points, whereas sheet tensile specimens which had been given identical cold working and annealing treatment showed no evidence of similar be-haviour. The lack of a distinct yield point for sheet specimens was con-sidered to be due to (a) load eccentricity and/or (b) the use of a 'soft" hydraulic tensile machine. To resolve this problem the following tests were mades Sheet specimens of identical preparation-were tested in a "soft" (hydraulic) machine and a 'hard' (Instron screw-driven) machine. The curves from"the soft machine showed no yield phenomena, whereas the curves from the 'hard' machine showed distinct upper and lower yield points. Specimens were then prestrained in the 'soft 8 machine to 3 percent elonga-tion to remove any eccentricity that may have existed. To relieve the stresses introduced by prestraining, the specimens were annealed in the 11 machine, under a load of 1000 to 2000 pounds per square inch. Subsequent testing showed distinct, though slight, yield phenomena. It may therefore be assumed that suppression of yield phenomena may be caused both by load eccentricity and the use of a 'soft' machine. Consider now the second group of investigations (i.e. those showing abnormal temperature dependence of yielding). Loomis and Carlson^ studied the tensile properties of vanadium between room temperature and -196<i>C. The materials used were bomb reduced and crystal bar metal, of the purities indicated in Table I, Figures 2 and 3 illustrate the data of Loomis and Carlson; Figure 2 for bomb-reduced metal, and Figure 3 for crystal-bar metal. No explanation' was given for the rapid increase in yield- strength encountered at -80°C for bomb-reduced metal and at -100°C for crystal bar metal. Further discussion of this paper will appear later in the present thesis with- regard to the anomalous ductility behaviour encountered. A-consideration of the third group of investigations (i.e. those showing abnormal ductility behaviour) shows that three independent in-5 6 9 vestigators^' ' 7 found a ductile-brittle-ductile transition, that is, a \ c ductility minimum, Roberts and-Rogersy used cylindrical wire specimens and f o i l specimens of the nominal purity shown in Table I. After hydro-genation to 0.042, 0.062 and 0.045 weight percent hydrogen, the specimens were tested in tension. The reduction in area of the hydrogenated cy-lindrical' specimens showed a minimum at approximately room temperature. Unhydrogenated vanadium showed no sharp ductility change to -196"C. The mechanism whereby-hydrogen causes this phenomenon, according to Roberts1 and Rogers,5 is not as yet understood. Magnus son and Baldwin ' -'evaluated the effect of strain rate on the ductility minimum at a hydrogen content of 80 parts per million, and reported that at high strain rates (19000 in/in/min) no minimum is encountered, and at liquid nitrogen temperatures the metal Temperature, C =250 -200 =150 -100 -50 0 50 100 150 Temperature ,*F Figure 2 0 Tensile properties ©f bomb-reduced vanadium at lew temperatures, a f t e r L©@mis and Carlson^ Temf>eri>ture , °C =175 -160 -120 -80 =40 Pr s p o r t i a n a l l i m i t deduction in area S t r a i n rat 0, D06 i n /in„/ nin RecrJ7St-all)Lzed aft 2U10|Ft220uJ: 48 haurs -300 =250 =200 =150 =100 =50 0 50 100 150 Temperature , Figure 3„ Tensile properties ©f crystal=bar vanadium at l®w temperatures a f t e r Loomis and CarlsoB^ 14 sustains mora than 30 percent reduction i n area before fracture„ At low s t r a i n rates (0o05 in/in/min), they report a d u c t i l i t y minimum at about •=100° C, with a subsequent recovery of the reduction i n area to a value of 15 per cent at -196°C 0 The r e s u l t s of these in v e s t i g a t i o n s ' -4e- considered by some t o indicate that the low temperature b r i t t l e n e s s of vanadium may be associated with hydrogen embrittlement, rather than d u c t i l e - t o - b r i t t l e 13 t r a n s i t i o n behaviour,, ' o Loomis and Carlson found a progressive decrease i n reduction i n area from room temperature to =70°C, and a f a i r l y sharp t r a n s i t i o n of the elongation curve between =60° and -70°C f o r bomb-reduced metal (Figure 2)„ With c r y s t a l bar vanadium they found a sharp t r a n s i t i o n from d u c t i l e - t o -b r i t t l e behaviour f o r both elongation and reduction i n area values between =100° and =120°C, They also found a d u c t i l i t y minimum f o r crystal«.bar vanadium at temperatures of =150° and =180°C o A comparison of the d u c t i l i t y curves f o r the bomb-reduced and cr y s t a l - b a r vanadium of Loomis and Carlson also gives a q u a l i t a t i v e idea of the e f f e c t of p u r i t y on the t r a n s i t i o n temperature. Bend test data on bomb-reduced metal obtained by Loomis and Carlson^ showed a sharp t r a n s i t i o n from d u c t i l e - t o - b r i t t l e behaviour at =60° to =70°C, i n good agreement-with the t e n s i l e data discussed e a r l i e r . At low temper-ature a s l i g h t increase i n d u c t i l i t y was observed, although not so pronounced as that observed for•tension t e s t s of the" c r y s t a l bar metal, loomis and Carlson also-used bend t e s t s t o evaluate the e f f e c t of i n t e r s t i t i a l s on the transition-temperature. Figure 4 i l l u s t r a t e s these r e s u l t s , ' Bend t e s t s on the higher p u r i t y c r y s t a l bar m a t e r i a l shewed'that the t r a n s i t i o n was below -150°C, From the foregoing discussion, i t i s evident that the cause of the d u c t i l i t y change found in vanadium (and other body-centered-cubic metals), 15 and the effect that impurities, testing temperature and grain boundaries have on i t are not clearly understood„ Tensile tests at temperatures be-•tween room temperature and -196°C are rather exiguous and the results of different investigators are not in good agreement„ Also, apparently no investigation has been carried out previously using single crystals of vanadiumo i Of the work reviewed in this paper, only that of Loomis and Carlson and that of Clough and Pavlovic is of use as a basis of reference in the present study. In a l l other cases mentioned1*3*5=7,10,12 e ^ n e r ^he range 2 of temperature studied was above room temperature or the data were not sufficiently detailed between room temperature and =196°C,, Further reviews ©f previous werk used is the analysis ©f the data obtained in the present work will be made in the appropriate section of the thesis. 0.1 0.2 0.3 0„4 I n t e r s t i t i a l Addition, weight percent Figure 4. E f f e c t of i n t e r s t i t i a l impurities en the ductile~t©=>brittle t r a n s i t i o n of bomb- , reduced vanadium, a f t e r Loomis and Carlsoa 17 III. EXPERIMENTAL A. MATERIALS The vanadium used in this investigation was supplied by Union Carbide Metals Company and was prepared by the bomb: reduction of V3O5 by 2 calcium „ The as-received material was analysed for interstitial im-purities, with the results shown in Table II. TABLE II ANALYSIS OF AS-RECEIVED VANADIUM Element Wt$ C 0.0275 N 0.0048 0 0.0510 H 0.00032 The as-received metal was in the annealed condition, and metallographic examination showed the presence of a second phase which resembled in a l l characteristics a phase identified by Clough and Pavlovic as V2C. The metal used in this investigation was taken entirely from one production batch, and was supplied in the form of 1/4-inch diameter rod. B. PURIFICATION Purification of the as-received metal was carried out in a vertical floating-sone electron bombardment unit similar to the one described by Calverly, Davis and Lever^. 1. Construction of the Zone Refiner The zone refiner was built entirely by the technical staff of the Department of Mining and Metallurgy of the University of British Columbia, 18 and the details of construction and assembly are shown in Figures 5 and 6. (a) Power Supply The power supply consists essentially of a 2300 volt d.c. power supply, with a current stabilizer. It supplies 2300 volts d.c. at 300 milliamps (i.e. 690 watts). The circuit details, as well as suggested modifications are given in Appendix II. A relay is incorporated to cut off the power in case of overload, the cathode is supplied from a trans-former delivering up to 10 amps at 11 volts from a Variac-controlled mains input. Automatic control of the power input is attained by emmission control, in which the bombardment current is kept constant by automatically adjusting the cathode temperature. Manual control of the power input is also possible^ by direct connection to the cathode supply variac. Details of the control system are shown in Appendix II. (b) Furnace It is convenient to ground the specimen and to operate the cathode at a high-negative potential, and the cathode leads and beam-forming plates must therefore be electrically insulated from each other and from the rest of the apparatus. The electrode system is suspended inside a 2>-foot long by 7-inch diameter pyrex tube, and is attached to the top plate- by the main support rods (10, Figure 5). Movement of the specimen is facilitated by an 0-Ring vacuum seal in the top plate, through which a central drive rod protrudes (2, Figure 5). The drive-rod is connected to the main crosshead (8) and specimen ( l ) . The*whole assembly is pulled upward by a motor-driven gearing 19 ASSEMBLY 1. Specimen 2. Driven Parts 3. Specimen Holders k. Power Leads 5. Filament and Beam-Focus plate Holders 6. Beam-Focus plates 7. Filament 8. Main Crosshead 9. Radiation Shield 10. Main Support Rods SECTION A-A SCALE a» 1/2 F. S. 11. Stabilizer Rods IS. Drive Mechanism 13- Pyrex Tube lh. Ionization Gauge 15. Thermocouple Gauge 16. Gas Inlet Valve 17. Cold Trap 16. Mercury Diffusion Pump 19. Stand Figure 5o Construction of the Zone Refiner 20 Figure 6. Photograph of the Assembled Zone Refiner and Power Supply arrangement (12) which allows travel speeds of 50, 25, 10, and 5 centi-meters per hour. The cathode or filament (7),the shape of which is shown in Section A-A, Figure 5, is made from 0.010 inch diameter tungsten wire, and is attached by screws to the filament and beam-focus plate holders (5, Figure 5), Connection of this type allows quick replacement of a broken filament. The purpose of the beam-focus plates (6) is to form a narrow zone, which is important if a uniform cross-section of the refined specimen is desired. 21 The heated zone of the furnace i s surrounded by a molybdenum r a d i a t i o n s h i e l d (9) (Figures 5, 6,) to protect the glass and to reduce the r a d i a t i o n glare. Provision f o r viewing the specimen i s made by mounting a glass microscope s l i d e i n the front of the r a d i a t i o n s h i e l d . The specimen i s r i g i d l y attached to the crossheads by screw-clamp specimen holders (3). The specimen i s mounted i n two sections, so that no l a t e r a l forces e x i s t i n the specimen,, The furnace i s also equipped with a gas i n l e t valve, and su i t a b l e gas pressure-measuring devices. (c) Vacuum System The vacuum system i n t h i s apparatus consists of an Edwards l i q u i d nitrogen cold t r a p i n se r i e s with an Edwards 35 l i t e r per second, two stage mercury d i f f u s i o n pump. This i s connected to a Duo-Seal fore pump (rated at 50 l i t e r s per minute, free a i r capacity) by a one inch diameter high pressure hose„ This system provides an operating vacuum of 1 0 = s ndllimeters of mercury, a f t e r only 15 to 20 minutes of pumping time. 2. Operation o f the Zone Refiner The-specimen i s mounted i n two sections i n the manner previously described so that f u s i o n does not cause a l a t e r a l d e f l e c t i o n of the specimen. When the desired operating vacuum has been reached, the filament i s h e a t e d - t o a -high temperature and allowed to outgas f o r a period of ten to f i f t e e n minutes.-The high voltage i s then turned on and the specimen i s heated slowly, thereby allowing surface outgassing to take place. The two sections are then welded together. The specimen may then be zone-r e f i n e d . Care must be exercised i n choosing the correct voltage and current s e t t i n g s , so that a. stable molten zcne i s assured. Because of the high 22 vapor pressure of vanadium at i t s melting point, i t was necessary to open the system a f t e r each pass and remove layers of deposited metal from the r a d i a t i o n s h i e l d s arid beam-focus p l a t e s . I t was also necessary to change the viewing glass r e g u l a r l y . Each bar of vanadium, eight inches long, was given f i v e zone-refining passes. The appearance of the metal a f t e r 5 passes was a reasonably smooth and very lustrous bar, 3, P u r i t y of the Zone-Refined Metal The p u r i t y of the zone-refined vanadium bars was s u b s t a n t i a l l y higher than that used by any previous i n v e s t i g a t o r whose work i s reported i n the l i t e r a t u r e . The r e s u l t s of analysis on three bars appear i n Table 3, For reference purposes, these analyses are compared to that of very high-p u r i t y c r y s t a l bar vanadium prepared by Carlson and Owen^0 using an iodide r e f i n i n g process. The two types of metal are of almost exactly the same t o t a l i n t e r s t i t i a l impurity content; the d i f f e r e n c e l i e s p r i n c i p a l l y i n carbon and nitrogen, TABLE III COMPARISON OF HIGH PURITY VANADIUM METAL Specimen Treatment Wt. C % Impurity N 0 H As Received Bomb-reduced 0,0275 0.0048 0.0510 0.00032 V-16 Zone-Refined-5 passes 0.0066 0.0064 0.0090 0.00042 V-06 Zone-Refined-6 passes 0.0082 0.0089 0.0060 0.0028 V-13 Zone-Refined=6 passes 0.0056 0.0091 0.0050 0.0006 Ref. 30 Iodide Refined 0.015 0.0005 0.004 0.001 The zone-refined metal i s a l s o compared i n Table I I I to the as-received material obtained f o r t h i s i n v e s t i g a t i o n . The impurities most e f f e c t i v e l y 23 removed are carbon and oxygen, while nitrogen and hydrogen concentrations do not appear to be appreciably affected by zone r e f i n i n g . C. SINGLE CRYSTAL GROWTH AND ORIENTATION Single c r y s t a l s were grown i n the zone r e f i n e r , using a melt-so lidification-zone»refining technique. Zone-refined bars were seeded with a vanadium single c r y s t a l rod whose a x i a l d i r e c t i o n was £ll6j . This c r y s t a l was obtained by p r e f e r e n t i a l growth during the five-pass zone-r e f i n i n g process of one of the bars. A f t e r one pass, (giving the bars, e f f e c t i v e l y , s i x zone-refining passes) the c r y s t a l was examined by the Laue b a c k - r e f l e c t i o n X-Ray technique to be c e r t a i n that the bar was, i n f a c t , a single c r y s t a l over the whole length. Figure 7 shows f i v e s i n g l e c r y s t a l s grown by the above technique, while Figures 8 and 9 show Laue pictures of one of the bars. Figure 8 was taken at the top end of the bar, and Figure 9 at the bottom end. Figure 7. Photograph of Vanadium Single Crystals Grown by the M e l t - S o l i ^ i f i c a t i o n - Z o n e - R e f i n i n g Technique 2L Figure 9. Laue photograph near the bottom end of V-14. 2 5 D. SPECIMEN PREPARATION 1 . Machining The single c r y s t a l bars as shown i n Figure 7 were cut into f i v e equal lengths of approximately 1 . 2 5 inches using a jeweller's saw. The pieces were then mounted i n a lathe and c a r e f u l l y machined to the shape of t e n s i l e specimens with a gauge section approximately 0 . 8 to 1 inch long and one-eighth inch i n diameter. The maximum depth of cut taken i n a single pass on the lathe was 0 . 0 0 3 inches. The machined specimens were then polished with 0 0 0 emery paper while mounted i n the lathe. 2 . E l e c t r o p o l i s h i n g A f t e r machining, a l l specimens were el e c t r o p o l i s h e d f o r ten minutes removing a layer of approximately 0 . 0 0 2 inches from the surface of the specimen. The s o l u t i o n used was a mixture of U0 cc of concentrated sulphuric a c i d , 1 6 0 cc of methyl alchohol and approximately 2 0 drops of water. A p o t e n t i a l of 1 2 , 5 v o l t s gave a current of 1 .5 amps, and provided very s a t i s f a c t o r y surface f i n i s h . 3. X-Ray Laue photographs of randomly selected specimens were taken to be sure that-any e f f e c t s of machining had been completely removed. A t y p i c a l reproduction i s shown i n Figure 1 0 . 26 Figure 10. Laue Photograph of machined and electropolished t e n s i l e specimen. 4, Preparation of P o l y c r y s t a l l i n e Specimens Two zone-refined bars were used to make ten p o l y c r y s t a l l i n e specimens. After the bars had been cut i n t o lengths, they were severely deformed by l a t e r a l compression i n a hydraulic press. This treatment was followed by machining i n a lathe, taking deep cuts and thereby encouraging furt h e r deformation. A f t e r the usual mechanical p o l i s h i n g i n the lathe, the specimens were annealed at 900°C f o r four hours. The specimens were then electropolished, etched and examined metallographically, to be c e r t a i n that complete r e c r y s t a l l i z a t i o n had occurred, and that the grain s i z e was r e l a t i v e l y uniform. Since only a semi-quantitative analysis of the t e n s i l e behaviour of these specimens was planned, no p a r t i c u l a r attention was paid to the a c t u a l grain s i z e or the degree of preferred o r i e n t a t i o n . It i s i n t e r e s t i n g to note that there was no evidence of the second phase (V 2C) mentioned e a r l i e r i n t h i s paper. 27 E. TESTING PROCEDURE I. Gripping and Mounting of Test Specimens The design of the grips used to hold t e n s i l e specimens i n t h i s work are shown i n Figure llo The grips were threaded into the mounting device as shown i n Figure 12, which i s a photograph of a mounted specimen, ready f o r t e s t i n g . The mounting device was of a universal-type construction, equipped with r o l l e r bearings set at 9 0 " to each other, thus ensuring u n i a x i a l t e n s i l e loading of the specimens. The mounting device was suspended from the lower (movable) cross-head of the t e n s i l e machine, with the upper jaw attached to the load c e l l by means of a long s t e e l rod which projected through-the crosshead (Figure 12). By using t h i s method, the whole mechanism, plus an e l e c t r i c a l l y driven s t i r r e r , could be immersed i n a Dewar f l a s k containing the appro-p r i a t e r e f r i g e r a n t . The f l a s k was placed on a plywood s h e l f provided f o r that purpose (Figure 12), 28 Figure 12. Photograph of mounted specimen, ready f o r t e n s i l e t e s t i n g 29 i 2. Temperature Measurement Temperatures were measured with a copper-constantaa thermocouple which had been c a l i b r a t e d and feumd correct at ream temperature and l i q u i d nitrogen temperature. The thermecouple i s rated by the manufacturer"^^ as accurate t o 2 2 per cent between -185° and -60°C, and 1 1-1/2 percent be-tween -60°C and 100°C. The thermocouple was attached to the surface of a l l specimens by means of a f i a e wire. 3. Temperature Control Test temperatures of -196° and -183°C were achieved by immersing the mounted specimens i n a Dewar f l a s k f i l l e d with l i q u i d nitrogen and l i q u i d oxygen, r e s p e c t i v e l y . Test temperatures between room temperature and ~1A0°C were achieved by immersing the mounted specimens i n a f l a s k f i l l e d with petroleum ether, and cooled by a small, e x t e r n a l l y fed v e s s e l f i l l e d with l i q u i d nitrogen. Temperatures were measured at the s t a r t of the t e s t , at the y i e l d point and at the end of the t e s t . The temperatures taken at the beginning and end of the t e s t were only used to determine the t o t a l change over the length of the t e s t . Test temperatures between -183° and -140°C were achieved by submerging the mounted specimens i n l i q u i d nitrogen. When equilibrium had beea reached the f l a s k was removed, the nitrogen was poured out, and the empty f l a s k was replaced. The apparatus and specimen were allowed to warm at- a heating rate which was found by measuremeot to be 1°C per minute. Since t e n s i l e t e s t s required about two to three minutes; the temperature-variation was not more than-t 1 05 degrees. Again, the temperature takea at the y i e l d point was used i n subsequent c a l c u l a t i o n s . 30 4. Teat Procedure The tensile machine used in this work was a 10,000 pound capacity } Instron screw-driven unit, with the gripping mechanism modified as previously shown. Mounted specimens were immersed in the coolant for a period of 10 to 15 minutes prior to testing. A l l polycrystalline, and most single crystal specimens were tested at a crosshead speed of 0.05 inches per minute. Nine single crystal specimens were tested at a crosshead speed of 0.002 inches per minute. A l l load-elongation curves were recorded autographically. Typical curves for various temperatures are shown in Figure 13. Specimens" after testing were carefully packaged and retained for subsequent nwtallographic and X-Ray examination. Typical broken specimens are shown in Figure 14. The-results of a l l tensile tests were calculated and tabulated and appear in Appendix I. Specific procedures used in other parts of the experimental work are described in the appropriate section of the thesis. Figure 13•„ T y p i c a l Load=Elongation Curves at Di f f e r e n t Temperatures Figure 14. T y p i c a l broken specimens, Left to r i g h t : p o l y c r y s t a l l i n e specimen (-122.5°C) s i n g l e c r y s t a l (-196°C), single c r y s t a l (24°C) 33 IV. EXPERIMENTAL RESULTS A proaounced temperature dependence ef the meehanieal pro-perties of the zone-refined vanadium was observed. The dependence of the yield stress, flew stress and percent elongation was determined over the temperature range from 25°C to -196°C. A. SINGLE CRYSTALS - RATE OF STRAIN 0.055/min. 1. Yield Stress Figure 15 shows the upper yield stress as a function, of tempera-ture. The- plot of yield- stress against temperature did not yield a con-tinuous curve of the classical type (dotted line.Figure 15) in which a reduction i n temperature- results in a continuous increase in yield stress as suggested by the data of Clough and Pavlovic^ (Figure 2). In the present investigation- two- smooth curves werev found which intersected at approximately '-i.lt25*Cy* 'inplyiKg"-thmt there are two diff erent- temperature deDendencies of the yield stress, applying over different ranges of low temperatures. That this i s , in fact, the case is illustrated by replotting the yield'stress (8y) versus temperature data in the following forms: (a) 8 T versus reciprocal absolute temperature (Figure 16), and (b) a log plot of Sy versus reciprocal absolute temperature (Figure 17). It is inaediately obvious that a plot of Sy versus Vx doos not yield a straight line, but rather two distinct intersecting curves. The points en-the- leg plot of Sy vs. V«p> en the other hand j can be fitted to two intersecting -straight lines with relatively minor deviations from a linear correlation at a l l temperatures-except those in the region of the intersection. i / T (V° K x 1 0 3 ) Figure 16. Y i e l d Stress VS Reciprocal Temperature f o r Single Crystals 36 37 There are currently twe seheels ef theight concerning the tempera-ture dependence ef y i e l d stress. Zener and Helleman^ en the basis ef tests predict a thermally-activated process obeying approximately an equation of the form RT where P = a reaction parameter 6 - s t r a i n rate Q = 'activation energy' for flow The equation which Zener^ postulated w i l l be presented i n d e t a i l shortly. 11 20 Fisher interpreted" the G o t t r e l l - B i l b y theory of- yielding as indicating that-yie ld stress- should"be a function of the form m By ( / Q 2)= constant where G = shear modulus. Zener's theory is based on the assumption that Q i s r e l a t i v e l y insensitive to changes i n strain rate and temperature, whereas Fisher's theory i s based on the assumption that G, the shear modulus is independent of temperature. Zener and Holloman"'"^ i l l u s t r a t e d that the tensile flow stress, 8 y , of s t e e l could be expressed i n terms of two variables only; £ , the s t r a i n , and the parameter P mentioned previously. Since, by Zener's theory, P-e£e /RT, i t may be deduced that i f Q i s r e l a t i v e l y insen-s i t i v e to changes i n 6 and T o v e r the range of temperature studied, then Sy. should be approximately equal to e V T , that is 5 y <w OVT. i f s t r a i n (£) and s t r a i n rate (£) are held constant. I f log 8 .^ were then 38 plotted against reciprocal temperature, a straight line would result. 16, 17 1 8 Previously published results of tensile tests for steel, molybdenum, 19 and tungsten a l l body-centered cubic metals, have indicated that the Zener hypothesis' is correct in the temperature range over which yield strength is found to be particularly temperature sensitive. Fisher 1 1 illustrated that the tensile flow stress, C y , of steel may be expressed in terms of the temperature and shear modulus only, in the manner described previously. According to Fisher's theory, a plot of 5y against reciprocal temperature should yield a straight line. This postulate was supported by considerable low temperature tensile data obtained for iron and molybdenum by other investigates, and interpreted 11 by Fisher . The data f i t s Fisher's theory extremely well at temperatures above -140°C, but show marked deviations at temperatures below -140°C. This appeared to'be true for both molybdenum and iron. The departure from Fisher's calculated curve closely resembles the curves found in the present investigation, as is evidenced by Figure 18, Clough and Pavlovic plotted their data in both ways, and found that Fisher's theory was obeyed, and that Zener's theory gave a systematic deviation from linearity. It should be remembered, however, that this work is subject to suspicion, since the methods of specimen preparation and mounting, as well a s the type of tensile machine used apparently obscured the yield phenomena. 9 Loomis and Carlson made no attempt to correlate their data in anyway, but an attempt by the author to-do so has indicated that any agreement"with Fisher's theory is out of the question. A reasonable degree of agreement with the Zener hypothesis was found,.but the limited number of experimental points involved made precise correlation difficult. 39 The r e s u l t s of the present i n v e s t i g a t i o n imply that the mechanism responsible f o r the temperature dependence of the y i e l d point changes abruptly at a temperature between -125° and -132°C. This suggests that i n a narrow temperature range, a change takes place i n the process or processes by which Frank-Read sources become un-pinned from t h e i r surrounding impurity atmospheres, rel e a s i n g d i s l o c a t i o n loops which may then t r a v e l through the l a t t i c e . Three possible mechanisms whereby the curve of Figure 15 may be explained are given l a t e r i n t h i s t h e s i s . i 1 r 0 100 200 300 400 500 600 Absolute Temperature °K Figure 18. Sy versus temperature f o r Annealed Molybdenum, a f t e r F i s h e r l l ho 2. Flow Stress The d e f i n i t i o n o f flow stress i s much more d i f f i c u l t than that of y i e l d stress and f o r the purposes of t h i s work i t i s defined as the point at which the sudden load-drop a f t e r y i e l d i n g i s stopped or slowed, and at which gross p l a s t i c flow begins. The load elongation curve of every c r y s t a l tested i n t h i s work displayed a r e l a t i v e l y high y i e l d point (see Figure 13). For high temperature specimens the flow stress was taken as the lowest point reached immediately following y i e l d i n g . For low tempera-ture specimens, t h i s was not possible, since no minimum point was reached. In a l l cases, however, the curve underwent a change i n slope a f t e r dropping sharply from -the-upper y i e l d point. In these cases, the flow stress was taken at the i n t e r s e c t i o n of l i n e s drawn along the trace of the sharp drop a f t e r y i e l d i n g and' along the trace of the curve a f t e r the slope change. The r e s u l t s of these flow stress measurements are p l o t t e d i n Figures 19, 20 and 21. I t i s evident from those graphs, that the phenomenon responsible f o r the-pronounced d i s c o n t i n u i t y found i n the curves f o r y i e l d strength v i r t u a l l y disappeared or was obscured immediately a f t e r y i e l d i n g occurred.- The most noticeable change i s that the log plot of flew stress against r e c i p r o c a l temperature i s no longer l i n e a r . I t may, therefore, be concluded'that the dual nature of the y i e l d stress versus temperature r e l a t i o n s h i p i s concerned p r i m a r i l y with the high y i e l d point phenomenon. 3. Elongation Corresponding* t o the very sharp r i s e - i n y i e l d strength i n the temperature range between -105° and -125°C (Figure 15), i s a sharp decrease i n d u c t i l i t y (Figure 22). Figure 22 i s a p l o t of percent elongation versus temperature; • Considerable spread i n the elongation values at any given temperature i s exhibited. This i s due to the fa c t that the specimens were Temp ( 6C) Figure 19. Flew Stress VS„ Temperature f o r Single C r y s t a l s 140 130 : — 120 — 110 — 100 90 80 70 60 — 50 40 30 20 10 0 1 I I I I I I I I Rate of S t r a i n = 0.055 /min I i i 1 1 U U J il k k I L I I L ii 0 1 2 3 4 5 "5 7 " 8 ~ 3 — 1 6 " — H — E — 1 3 — H — 1 5 — I E " Figure 20. Flow Stress VS Reciprocal Temperature f o r Single Crystals s i n g l e c r y s t a l s , and much of the deformation occurred i n the area immediately adjacent to the f r a c t u r e . To c l a r i f y the r e l a t i o n s h i p , an average value of percent elongation f o r each temperature was p l o t t e d , and superimposed on the i n d i v i d u a l specimen points. B, SINGLE CRYSTALS - RATE OF STRAIN 0.0022/min. Nine sin g l e c r y s t a l s were tested at a rate of s t r a i n lower by a 2.5 f a c t o r of ^ 8$©- than the previous rate i n order to determine at least qual-i t a t i v e l y the e f f e c t of s t r a i n rate on the y i e l d point behaviour. The c r y s t a l s were tested only at temperatures which were i n the region o f the i n t e r s e c t i o n of the two l i n e s i n Figure 17. The r e s u l t s ©f these t e s t s are- shown i n Figures 23 and 2/+. A d i s c o n t i n u i t y of the type ob-served at the-higher s t r a i n rate i s -also p l a i n l y v i s i b l e i n t h i s y i e l d point data, although the small number of specimens used f o r t h i s part of the work -"'make^it' unreasonable "to draw rigorous conclusions'. The r e s u l t s indicate-that the-aforementioned mechanism change'is-not grossl y affected by changes-in rate of s t r a i n - o f the order involved i n t h i s work, fhe value of the y i e l d strength at a l l temperatures was s l i g h t l y lower at the lower s t r a i n r ate, as i t would be reasonable to expect. C. POLYCRYSTALLINE SPECIMENS - RATE OF STRAIN 0-.055/min. Seven p o l y c r y s t a l l i n e specimens were tested at a s t r a i n rate of 0.055 in/min. i n order t o determine q u a l i t a t i v e l y the" e f f e c t of i n t r o -ducing g r a i n boundaries-and more random o r i e n t a t i o n . A high*degree ©f preferred'orientation existed i n the specimens a f t e r deformation and annealing"treatments-.- This would be expected, since' the bars from which -the polycrystalline-specimens- were' machined were o r i g i n a l l y single - c r y s t a l s . Evidence o f preferred o r i e n t a t i o n was the appearance of broken specimens, which i n some cases showed a fr a c t u r e s i m i l a r to those found f o r single •G-O -200 o -175 -150 =125 ¥ o Rate ef S t r a i n = 0 o05/mia 0 — A r i f h r n e - f i c averages O - J£ypeoVnervte»l p o f n ^ i -75 -100 Temp (°C) Figure .22. Percent Elongation VS Temperature f o r Single Crystals -50 -25 8H 80 70 60 •H SO fX 8 5(L_ t o 40 Rate ©f S t r a i n = 0.0022/min Rate of S t r a i n = 0.05/min 301 -160 -150 46 -110 -140 -130 -120 Temp. (°C) Figure 23. S y VS Temperature f o r Single Crystals -100 -90 80, 70 60 CQ P , ?5 C | oO 4 0 L . 30| e ©f S t r a i n Rate,©f S t r a i n = 0.0022/min. 0.05/min. 1 -7 g d V T ( V o K ) (io3) Figure 24. 8 y VS Reciprocal Temperature f o r Single Crystals 47 c r y s t a l s (See Figure 14). Figures 25 and 26 show the r e s u l t s ©f p l o t t i n g y i e l d stress versus temperature and r e c i p r o c a l temperature. The l i m i t e d amount ©f data indicates that the e f f e c t i s g r e a t l y reduced i n p o l y c r y s t a l l i n e m a t e r i a l . The s l i g h t e f f e c t evident may be due to the high degree ©f preferred o r i e n t a t i o n present i n the p o l y c r y s t a l l i n e specimens. I f t h i s i s true, the y i e l d stress versus temperature proper-t i e s of vanadium are probably strongly o r i e n t a t i o n dependent. The data presented i n d i c a t e that the y i e l d stress of p o l y c r y s t a l l i n e metal i s much more-temperature-sensitive-at'low temperatures (below the sing l e c r y s t a l t r a n s i t i o n temperature)•than .is the y i e l d stress ©f s i n g l e c r y s t a l s , Elongation data f o r p o l y c r y s t a l l i n e specimens i s not presented because of l a r g e . s c a t t e r i n proportion to the number of t e s t s made. D. ANALYSIS OF THE DEFORMATION MECHANISM 1. S l i p System The-operative s l i p plane was found t© be a plane i n the ( l l O ^ zone, always within a few degrees ©f 41121 . This i s d i f f e r e n t from the r e s u l t s 21 22 of other investigators ' working with single c r y s t a l s of i r o n . S t e i j n 21 22 and Brick and Cox e t . a l . made extensive studies of s l i p i n single c r y s t a l s of i r o n and found that s l i p always occurred i n O-ll) d i r e c t i o n s •» planes i n the { l l l ^ zone, but not always on planes of low i n d i c e s . This was ref e r r e d t© as 'banal' ©r non-crystallographic s l i p . A theory ©f s l i p i n body-centered cubic metals, based on a hard sphere model, was pro-21 posed by S t e i j n and Brick . In the model, s l i p on high index planes could be resolved-into s l i p on planes of the forms |llo| and |ll2j . P a r t i c u l a r ' high-index planes would require a d e f i n i t e proportion ©f atom movements of each type. T(°C) Figure 25. 8V vs. Temperature f o r Poly-crystalline Metal I/ T (103) l/o K Figure 26. 8V ve I/_ f o r P o l y c r y s t a l l i n e Metal 49 It was thought i n i t i a l l y that the dual nature of the y i e l d stress curve was caused simply by a change i n the deformation system at lew temperatures. This was proved to be f a l s e on the basis of Laue back r e f l e c t i o n photographs. The complete o r i e n t a t i o n s of the specimens were found from Laue photographs. The a x i a l d i r e c t i o n s o f the specimens were (lioj, and the o r i e n t a t i o n of a l l specimens was found to be that shown i n Figure 27. The O-l-O d i r e c t i o n appeared p a r a l l e l to the knife edge of the broken specimen and the |00l] d i r e c t i o n appeared perpendicular to the knife edge. Hereinafter, Laue photographs which have been taken with the X-ray beam p a r a l l e l to the [llo] d i r e c t i o n w i l l be denoted as ' [llo] photographs • and photographs-taken with the X-ray beam p a r a l l e l to the [oOl] d i r e c t i o n w i l l be denoted as ' JoOl] photographs'. Specimens-tested at temperatures both above and below the t r a n s -i t i o n temperature were examined very c a r e f u l l y . X-ray photographs ©f a [llo3 typewere taken-©f"each specimen examined-(Figures 28 and'30). Be-cause of possible ambiguity concerning the s i m i l a r i t y between [llcQ photo-graphs and jpoij photographs, advantage of the more obvious 3 - f o l d symmetry of the ( i l l ] d i r e c t i o n was taken. This was accomplished by photographing the specimen a f t e r i t had been rotated t h r o u g h - 3 5 . 3 ° from a p o s i t i o n i n which the jlioj d i r e c t i o n was p a r a l l e l to the X-ray beam. The r e s u l t s of these photographs are shown i n Figures 29 and 3 1 o Angular measurements of s l i p traces indicated t h a t the glide e l l i p s e was at an angle of approximate-l y 5 5 ° to 6 0 ° to ( l l O ) planes (that i s ; the set of planes perpendicular to [llo] and-the-specimen a x i s ) . These measurements were made from the s l i p traces shown i n Figures 32 and 3 3 . The low index planes {llO} |Ll2j and { l 2 3 } are generally considered most l i k e l y t© be operative s l i p planes f o r a body-centered cubic s t r u c t u r e ^ These planes are also the most l i k e l y 50 0 [no] *\po\] Figure 27. Orientation of Pulled T e n s i l e Specimens 51 Figure 28. [ l i d ] Photograph of broken specimen tested at 2UCC (V08T5) Figure 29. Specimen of Figure 28 rotated 35.3° towards ( b o i j . Note the 3~t®ld symmetry of the j l l l ] d i r e c t i o n . Figure 30. llo} Photograph of broken specimen tested at-183°C (V07T4) 53 21,22,27-29 s l i p planes i n cases where non-crystall©graphic s l i p s i s be-l i e v e d to occur. In the present work i t was found that s l i p occurred only on the (112) and (112) planes. This was proven by the following crysta11©graphic an a l y s i s , using the stereographic p r o j e c t i o n shown i n Figure 34. Examination of Figures 27 and 34, (the specimen o r i e n t a t i o n and the stereographic p r o j e c t i o n , r e s p e c t i v e l y ) showed that the (001) plane, the !£llO) plane and the s l i p plane a l l l a y i n the same zone, namely the [ l i b ] zone. Therefore, planes of the |llo| form could not cau3e s l i p i n t h i s system. I f |l!0} planes were active s l i p planes, they would have to be ( O i l ) or (101), operating i n the ( i l l ] d i r e c t i o n . I f these planes were-operative, the k n i f e edge ©f the deformed specimens would have to be oriented-at 90° to the p o s i t i o n i n which i t i s a c t u a l l y found, both above andbelow the t r a n s i t i o n . The p o s s i b i l i t y of planes of the form {L23^  serving as s l i p planes was also eliminated by a s i m i l a r a n a l y s i s . If {123} planes were s l i p planes, the (Llo) r e f l e c t i o n would not appear p a r a l l e l to the k n i f e edge, but rather o f f s e t b y 10.9°. This was not found to-be the case; the (110) r e f l e c t i o n was always p a r a l l e l to the knife edge. In summary, the operative s l i p system was found to be ( i l l ] {l-^} over the whole range of temperature studied. Deformation was found to ©ccur i n the [lio] zone, with (112) and (112) planes as the only oper-ative s l i p planes. The measured angles of s l i p traces were s l i g h t l y higher f o r the h i $ i temperature specimens (Figure 32) than f o r the low temperature s p e c i -mens (Figure 33). This was probably due to the extensive -elongation which the high temperature specimens underwent. The d i s t o r t i o n of size and shape of the Laue spots of Figures 28 and 29 (high temperature specimens) was probably also a r e s u l t of the extensive deformation of the high tempera-54 Figure 32B Figure 32. Slip traces from specimens above the transition temperature. Figure 32A is V08T3, tested at 24°C, Figure 32B is V09T5, t e s t e d at -50°C. Unetched, X125. Figure 33A Figure 33B Figure 33. Slip traces from specimens below the transition temperature. Figure 33A is V07T4, tested at -lS^'C. Figurt 33B is V04T5, tested at -196"C, Unetched X125 Figure 34. Standard Stereographic Projection f o r the cubic system, showing the o r i e n t a t i o n of a standard t e n s i l e specimen with respect to the p r o j e c t i o n . 57 2, Twinning 8 Twins i n vanadium have been observed by ©ne i n v e s t i g a t o r and were reported as occurring on -^12 J planes which i s the common twin plane f o r body-centered cubic metals. Exhaustive examination f a i l e d to r e v e a l any markings o n specimens- i n t h i s work which could unambiguously be designated as twins. However, since the observed s l i p planes were found to be the same as the preferred twin planes, i t i s possible that s l i p and twin markings could ©ccur c o i n c i d e n t a l l y , and might therefore be i n d i s t i n g u i s h -able. It i s possible that a change i n deformation mechanism from s l i p to twinning could ©ccur, and be responsible f o r the anomolous y i e l d be-haviour exhibited by vanadium sin g l e c r y s t a l s . A recent paper by Adams, 31 Roberts and Smallman concerning the properties of niobium at very low temperatures reported the occurrence of large numbers of twins at very low temperatures or very high s t r a i n r a t e s . However, niobium was found to twin ' r e l u c t a n t l y • . Twinning i n vanadium may be of a s i m i l a r nature, E. THE CRITICAL RESOLVED SHEAR. STRESS The r e s o l u t i o n of simple tension i n terms of the s l i p system i s accomplished i n the manner described below, with reference to Figure 35, 26 which shows the fundamental q u a n t i t i e s involved i n the c a l c u l a t i o n . The s l i p d i r e c t i o n f o r bedy-centered cubic metals i s $ ! l ) , and i s a f f e c t e d by neither-composition nor temperature. The active s l i p planes do depend" on these q u a n t i t i e s ; and can be any of the planes of the form {no}, {112} ©r £23}, as long as the 8 l i p plane belongs to'the zone of the s l i p d i r e c t i o n . Let A be the area of the specimen, then A i s the cross-"JosY s e c t i o n a l area of the s l i p plane. The force F i s resolved i n the f l l l j r F [UVW] F Figure 35. Fundamental q u a n t i t i e s i n the r e s o l u t i o n of simple tension,2° di r e c t i o n ' and i s equal to F eos^ , where \ i s the angle between [ i l l ] and the tension a x i s . Therefore: 5 "° °° = F cos Q cos A y I By the analysis of the previous sec t i o n , the s l i p planes are (112) and (112), and from t h i s , the angles <p and % are 54°42* and 35° 18», The values ©f the c r i t i c a l resolved shear st r e s s are given i n Appendix I and shewn g r a p h i c a l l y i n Figures 36, 37 and 38. F. ELECTRICAL RESISTANCE The p o s s i b i l i t y that a minor ordering or disordering r e a c t i o n at the ' t r a n s i t i o n ' temperature was the cause ©f the unusual temperature dependence of y i e l d stress was examined by means of e l e c t r i c a l resistance measurements taken between -196° and 0°C. A l l resistance measurements were made on a t e n s i l e specimen mounted i n the t e s t i n g machine, im such a way that stress could be a p p l i i d . Measurements were taken on a Vernier potentiometer, and -are accurate to * 0.2%. The r e s u l t s are recorded i n Figures 39 and 40, and i n Appendix .III. Although a minor slope change was encountered at 106*K (-173°C), i t i s not believed that t h i s i s s u f f i c i e n t evidence for" ordering. A s i m i l a r 2 change i n slope'of the r e s i s t i v i t y curve was encountered by Rostoker between -20* and -35°C, and Loomis and Carlson^ (for bomb-reduced metal) between -70° and -80°C. The difference i n the nature of the curve ob-tained i n the present work i s believed to be due to the higher p u r i t y of the metal used f o r these experiments. The p o s s i b i l i t y of stress-induced ordering was examined by means of e l e c t r i c a l ' r e s i s t a n c e measurements taken at a given temperature and at d i f f e r e n t l e v e l s ©f s t r e s s . No appreciable change i n r e s i s t i v i t y between zero stress and the y i e l d point was found. 100 Figure 38 S c r VS Reciprocal Temperature f o r Single Crystals 450 6 3 Temperature ( 8K) Figure 3 9 o E l e c t r i e a l Resistance Versus Temperature f o r a Single C r y s t a l 60 70 80 90- 100 110 120 130 140 150 160 170 180 Temp. (°K.) Figure 40. Enlargement of the C r i t i c a l Region of Figure 39. 65 G. MICROHARDNESS Microhardness measurements were made on every zone r e f i n e d bar im an e f f o r t " t o - e s t a b l i s h some r e l a t i o n s h i p between impurity content and microhardnesso The purpose was to determine the uniformity of the zone r e f i n i n g process. Considerable hardness v a r i a t i o n from bar to bar was encountered^; however, -hardness measurements were made on broken specimens polished a f t e r mounting i n l u c i t e , and a combination of the unavoidable misallignmemt during mounting, and the var i a b l e p l a s t i c deformation present i n the tested specimens i s believed to be the cause of most of the d i f f e r e n c e s . The hardness measurements made on specimens tested at high temperatures i s not considered r e l i a b l e f o r these reasons. It should be-noted that hardness i s an orientation-dependent property. The value of the KHN f o r as-received vanadium was about 130-135, and f o r zone-refined metal about 105-110. Results of microhardness measurements are tabulated i n Appendix IV. The d i f f e r e n c e s i n hardness encountered d i d not appear to be r e f l e c t e d - i n the t e n s i l e r e s u l t s to•any s i g n i f i c a n t extent. A-number of cases were encountered where specimens taken from a 'hard' bar were p u l l e d at the same"temperature as specimens taken from-a ' s o f t ' bar, but i t was found that-neither type of specimen had con s i s t e n t l y higher or lower y i e l d strength than the other type.. 66 V. DISCUSSION The present i n v e s t i g a t i o n has shown that high p u r i t y vanadium i n the form of s i n g l e c r y s t a l s , conforms to the same general pattern of t e n s i l e behaviour as other body-centered cubic r e f r a c t o r y metals i n that i t d i s plays a very strong temperature dependence of y i e l d strength, and a d u c t i l e - t o - b r i t t l e (or s e m i - b r i t t l e ) t r a n s i t i o n . It i s now necessary t o examine those f a c t o r s which may explain the abnormal temperature de-pendence of y i e l d strength exhibited by the s i n g l e c r y s t a l s , and which may account f o r the d e t a i l e d d i f f e r e n c e s between vanadium metal and the other body-centered cubic r e f r a c t o r y metals. A. REVIEW OF RESULTS The anomolous temperature dependence of the upper y i e l d stress of vanadium was found to be a thermally acti v a t e d process, as evidenced by Figure 17 which shows the p l o t of log y i e l d stress against r e c i p r o c a l temper-ature. This behaviour i s p r i m a r i l y a y i e l d i n g phenomenon, since a plot of flow s t r e s s (Figures 19, 20, 21) against temperature did not show nearly as much departure from a smooth curve as d i d a p l o t of y i e l d stress (Figures 15, 16, 17). Further, the flow stress data d i d not give a l i n e a r l o g a r i t h -mic p l o t . P o l y c r y s t a l l i n e specimens tested under s i m i l a r conditions showed a much l e s s obvious anomaly (Figures 25, 26) and therefore the y i e l d be-haviour i s believed to be dependent upon specimen o r i e n t a t i o n . Single- c r y s t a l s tested at a lower s t r a i n - r a t e exhibited the ab-normal behaviour very c l e a r l y (Figures 23, 24), although the d i s c o n t i n u i t y occurred at a -lower stress and temper ature. The y i e l d s t r e s s , therefore, i s also s t r a i n - r a t e dependent; an increase i n s t r a i n rate r e s u l t i n g i n an increase i n ' t r a n s i t i o n ' temperature. 67 X-ray data i n d i c a t e that the s l i p system d©es mot change ©ver the range ©f temperature studied, s® therefore the change i n the tempera-ture dependence of y i e l d stress i s not associated with a simple change of s l i p system. 9 Loomis and Carlson studied a s i n g l e c r y s t a l of cr y s t a l - b a r vanadium at- low temperatures' by means of a Weissenberg camera i n order to determine'whether or not any form of a l l o t r o p i c transformation occurred. They reported that no change occurred to -115°C (the d u c t i l e - t o - b r i t t l e t r a n s i t i o n occurred at -110°C), X-ray d i f f r a c t i o n data presented by Loomis and Carlson i n d i c a t e d that vanadium exists i n the body-centered cubic form down-to -180°C. On the basis of t h i s data, i t may be assumed that no c r y s t a l l o g r a p h i c change takes place i n the range of temperature studded which could account f o r the abnormal temperature dependence of the y i e l d s t r e s s . B. POSSIBLE MECHANISMS The above discussion r e s t r i c t s the possible mechanisms by which a d i s c o n t i n u i t y i n the temperature dependence of y i e l d stress can be explained-. Three a l t e r n a t i v e mechanisms are -suggested: (1) a change i n deformation mechanism| f o r example, from s l i p to twinning, (2) a minor ordering or d i s o r d e r i n g - r e a c t i o n , or (3) a change i n the-manner i n which dislocation-becomes unlocked at the y i e l d s t r e s s . Each of these poss-i b i l i t i e s w i l l be discussed more c r i t i c a l l y i n the f o l l o w i n g t e x t . 1. Change i n Deformation'Mechanism The shape of the-plot of log y i e l d stress against r e c i p r o c a l temperature suggests the presence of two d i f f e r e n t thermally activated processes; with the higher temperature process having a higher a c t i v a t -ion energy. At the t r a n s i t i o n temperature the process having the higher a c t i v a t i o n energy (presumed to be s l i p ) i s replaced by a process with the lower a c t i v a t i o n energy (presumed t© be twinning)„ Adams, Roberts 31 and Smallman found evidence of gross twinning i n p o l y c r y s t a l l i n e niobium 22 21 at very low temperatures; Cox* Home and Mehl and S t e i j n and Brick found evidence of large amounts of twinning i n i r o n single c r y s t a l s at =196°C. In a l l cases reported, the twinning was accompanied by audible c l i c k s in-the specimen, and 'jerks' i n the l i n e a r portion of the load-elongation curve. In the present i n v e s t i g a t i o n the same observations were made at -196°C and-183°C,, but no evidence of twinning could be found on metallographic examination of the broken specimens. However since the s l i p plane i d e n t i f i e d i n vanadium s i n g l e c r y s t a l s , and the twin plane- (112) reported by-dough 1 and Pavlovie are coincident, i t i s possible- that a combination -of s l i p traces -and -twins were- present, even though repolishing--and etching" f a i l e d "to provi'de-adequate-evidence that 31 t h i s was so."AdamsyRoberts' and Smallman reported-that most"©f~the twinning i n niobium occurred during the very e a r l y stages of p l a s t i c de-formation. In the present i n v e s t i g a t i o n , no low temperature t e s t s were interrupted f o r the purpose ©f specimen examination, because of the d i f f i c u l t y i n removing an unbroken specimen from the machine without s p o i l i n g the ele c t r o p o l i s h e d surface. Since considerable p l a s t i c de-formation- occurred before f r a c t u r e , even at =196°C, i t i s possible that v i s i b l e evidence of twinning was obscured by s l i p l i n e s . Adams e t . a l . also reported a standard pattern of behaviour ®f a l l specimens pulled at 20°K'j (a) that small amounts ©f s l i p interspersed between extensive bursts of twinning occurred in-the e a r l y stages of deformation,- (b) that a pre-ponderance" o f s l i p with'only -occasional twinning occurred as deformation was c o n t i n u e d a n d - (c )• that the c r y s t a l s displayed an " a b i l i t y to- work-harden while- deforming 'by s l i p ; - B y ' t h i s - standard, any twinning which may have ta ken place' i n low temperature specimens may w e l l have -been obscured by subsequent s l i p deformation. 69 A theory of twinning i n i r o n c r y s t a l s by Biggs and P r a t t ^ de-20 veloped from the G o t t r e l l - B i l b y theory claims that twin nucleation i s more d i f f i c u l t than twin propagation 0 The suggestion was made that twin nucleation i s caused by a s t r e s s concentration which i s brought about by the release of a -burst of - s l i p as a Frank-Read- source - breaks away from i t s atmosphere, causing-the rapid piling-up of d i s l o c a t i o n s . Twins, once formed, may themselves act as b a r r i e r s , allowing f u r t h e r p i l i n g - u p of d i s l o c a t i o n s and fur t h e r twin nucleation. When most of the Frank-Read sources have been released from t h e i r atmospheres, s l i p w i l l no longer occur i n bursts, and twin nucleation w i l l ' no longer be p o s s i b l e . A"mechanismof' t h i s type ; could- w e l l account for-the heavy appear-ance- of the s l i p l i n e s at low temperatures, Figure 33, and f o r the d i s -continuous temperature dependence of the y i e l d s t r e s s . T h e - q u a l i f i c a t i o n must be-made, however, that twins i n niobium were not found u n t i l the temperature was reduced below -196°C; and not i n abundance u n t i l 20°K was reached. Further i t must be remembered that i n the present i n v e s t i g a t i o n no concrete evidence that gross twinning had taken place was found, even though -jerks i n the load-elongation curves, and corresponding audible c l i c k i n g noises occurred i n many of the specimens tested at temperatures lower than =165°C. 2, Ordering Process The-occurrence of a minor slope change i n the plot of e l e c t r i c a l resistance versus temperature- could p o s s i b l y be due to an ordering or disord e r i n g reaction, -although i t i s not considered likely-because-of the extremely small' number of- impurity atoms-available to p a r t i c i p a t e i n the reaction,' The ordering process i s thought" t© be the occupation ©f pre-fe r r e d i n t e r s t i t i a l s i t e s by atoms say, f o r example, of carbon. It i s suggested that t h i s -situation may jbe brought about-by-contraction of the l a t t i c e due t® applied stress and thermal contraction, such that at the t r a n s i t i o n temperature, the occupied s i t e s become to© small to accommodate the impurity atoms,- which are then forced to take up new ordered positions i n the l a t t i c e . That- t h i s type of reaction occurred would be m©st d i f f i c u l t ' to prove, p a r t i c u l a r l y since i t - i s - u n l i k e l y that r e s i s t i v i t y measurements would detect- an' ordering reaction of such small magnitude, A'mechanism of thi s " t y p e could, however, explain p a r t i a l l y the l e g p l o t of y i e l d stress versus reciprocal-temperature. The change could be considered analogous to an a l l o t r o p i c transformation, i n that i t would-be v i r t u a l l y d i f f u s i o n l e s s (a necessary condition because of the improbability of d i f f u s i o n taking place at the low temperatures involved). I t would merely involve the t r a n s f e r of i n t e r s t i t i a l atoms from one s i t e t o an adjacent or n e a i l y adjacent ©ne of more sui t a b l e dimensions. Since the change i n slope of the r e s i s t i v i t y curve was found to occur below the t r a n s i t i o n (-170°C), thus allowing the transformation to take place before the change i s noticeable, t h i s mechanism i s not impossible. For the reasons stated e a r l i e r , however, i t would appear u n l i k e l y . 3. D i s l o c a t i o n Breakaway The C o t t r e l l - B i l b y theory of y i e l d i n g i n i r e n ^ ^ postulates the migration of impurity atoms to Frank-Read sources where they form atmos-pheres. When an applied stress exceeds the pinning force, the d i s l o c a t i o n loops break away from the atmospheres; thereby causing the heterogeneous y i e l d i n g c h a r a c t e r i s t i c s found i n body-centered cubic metals. A-mechanism which could explain the temperature dependence of y i e l d s t r e s s of vanadium s i n g l e c r y s t a l s found i n t h i s i n v e s t i g a t i o n r e -quires t h a t - t w o - i n t e r s t i t i a l impurity species form atirospheres around d i s l o c a t i o n sources. 71 I t i s assumed that each impurity species has an independent locking e f f e c t ©n d i s l o c a t i o n s which i t surrounds„ Thus i t can be con-sidered that the e f f e c t of ©ne impurity on the temperatures dependence of y i e l d i n g i n vanadium i s d i f f e r e n t from that of any other impurity,, Figure 41 i s a hypothetical plot of the y i e l d stress-temperature r e l a t i o n -ship due to each of two a r b i t r a r y i n t e r s t i t i a l species assuming the Zener h y p o t h e s i s ^ a p p l i e s . I t i s probable that the v e r t i c a l p o s i t i o n of each of the two l i n e s w i l l be dependent on the r e l a t i v e concentrations of the two species. The slope of any l i n e w i l l be c h a r a c t e r i s t i c of the impurity/ and determined by f a c t o r s such as atomic diameter and p o s s i b l y valency. According to Figure 41» the s t r e s s necessary to overcome the l o c k i n g e f f e c t of ©ne species (impurity A) i s l e s s at high temperatures (above T^) than the stress necessary to unlock d i s l o c a t i o n s from im-p u r i t y B. At temperatures less- than Tx, the reverse i s true, and the minimum stress required to i n i t i a t e y i e l d i n g i s determined by the locking e f f e c t of- impurity B„ This implies that a temperature may e x i s t f o r c e r t a i n relative•concentrations of the two impurities at which the locking e f f e c t of ©ne impurity becomes les s s i g n i f i c a n t than that of the other impurity,- leading to a d i s c o n t i n u i t y i n a p l o t of y i e l d stress versus tempe rature, A number of observations i n the present work give strong support to t h i s suggested mechanism. Among those experimental data which t h i s hypothesis explains s a t i s f a c t o r i l y are the following? 1, The anomaly found i n the temperature dependence of y i e l d ' s t r e s s i n the-present work, 2. The s c a t t e r of the r e s u l t s observed i n the v i c i n i t y of the i n t e r s e c t i o n of the two s t r a i g h t l i n e s i n Figure 17. This s c a t t e r would be expected i n a region where-the-stress to f r e e d i s l o c a t i o n s pinned by e i t h e r of two impurities i s of the same magnitude. Hence, very minor 72. 73 v a r i a t i o n s i n the p u r i t y @f specimens test e d im t h i s region (which v a r i a t i o n s were i d e n t i f i e d ) could r e -s u l t i n higher or lower values of y i e l d s t r e s s . 3. The percent elongation versus temperature curves (Figure 22). This curve has two regions of tempera-' ture i n which d u c t i l i t y appears to be dropping r a p i d l y , corresponding i n each case to a rapid r i s e i n y i e l d stress (Figure 15). This observation i s ex p l i c a b l e i n terms of the dual-impurity hypothesis, but does not f i t with the ordering mechanism suggested e a r l i e r . I t i s notable that'the d i s c o n t i n u i t y i n the temperature dependence of y i e l d stress, which was marked i n the present work, was not found by other i n v e s t i g a t o r s working with vanadium. This may w e l l be associated with the unusually low carbon content of the zone-refined metal employed i n t h i s study. The'vanadium used by other workers contained from 4 to 20 times as much carbon, whereas the'nitrogen and hydrogen contents were generally of the same order. This suggests the p o s s i b i l i t y that ( r e -f e r r i n g to Figure 41) i f impurity B i s carbon; the curve en the l o g p l o t f o r carbon would'be s u b s t a n t i a l l y higher f o r the vanadium used by other workers then f o r that used i n the present study. This i n turn permits the speculation that the corresponding l i n e f o r another impurity (nitrogen, f o r example) l i e s below that f o r carbon at a l l temperatures down to =196°C f o r other i n v e s t i g a t i o n s , but that i n the present work, carbon may be the c o n t r o l l i n g impurity at temperatures below about -125°C. By way of semi-quantitative v e r i f i c a t i o n of t h i s postulate, the y i e l d s tress values obtained -by other workers were generally higher at the lower temperatures, but s i m i l a r at the higher temperatures, r e l a t i v e to those obtained by the present i n v e s t i g a t o r . It should be noted that carbon and nitrogen are used as examples only i n the above discussion, and that i t i s by no-means proven that these are the dominant impurities i n t h i s mechanism. VI. CONCLUSIONS 1. A z o n e - r e f i n i n g - m e l t - s o l i d i f i c a t i o n technique f o r the growth of vanadium Single c r y s t a l s of pre-determined o r i e n t a t i o n has been per-fec t e d . Crystals 1/4-inch i n diameter and up to 7 inches i n length have been' grown. The c r y s t a l s were ®f more uniform c r o s s - s e c t i o n a l area than those reportedly grown by workers using other metals, and the surface q u a l i t y was approximately equivalent to that obtained by e l e c t r o p o l i s h i n g . 2. Vanadium exhibits a marked temperature dependence of y i e l d s t r e s s , as do other body-centered cubic metals. With vanadium single c r y s t a l s , however, an unusual r e l a t i o n s h i p between temperature and y i e l d s t r e s s was encountered, i n that a d i s c o n t i n u i t y i n the p l o t was found between -125° and =130°C. This abnormality d i d not appear i n nearly as pron-ounced a fashion on a p l e t of flow stress versus temperature f o r the metal, and therefore the anomaly Is believed to be associated p r i m a r i l y with the i n i t i a t i o n of y i e l d i n g . 3. X-ray data proved that deformation occurred i n the system ^.13^ | l l 2 ^ , over the whole range of temperatures studied. Therefore the d i s -c o n t i n u i t y on the y i e l d stress p l o t could not have been caused by a change i n s l i p system. 4. The r e s u l t s of e l e c t r i c a l resistance measurements indicated the p o s s i b i l i t y that a very minor ordering process was responsible f o r the anomaly, but i t was considered u n l i k e l y ©n the basis of the magnitude ©f the ordering r e a c t i o n . 5. The p o s s i b i l i t y of a change i n deformation mechanism from s l i p t© twinning was examined' thoroughly, and, although no indisputable evidence ©f gross twinning was found, the"mechanism i s s t i l l p o s s i b l e . The de-formation-plane i d e n t i f i e d f o r specimens tested both above and below the t r a n s i t t e n temperature was (112), which i s also reported as the twin plane f o r vanadium. The coincidence of the s l i p and twin planes could mean that both were present i n low temperature specimens, but were i n -d i s t i n g u i s h a b l e . 6. D i s l o c a t i o n locking due to atmospheres of more than one impurity was proposed as a possible explanation of the observed r e s u l t s . I t depends on the formation of two impurity atmospheres around dislocation, each of which gives r i s e to a separate temperature dependence of y i e l d s t r e s s . The data of another i n v e s t i g a t o r 1 1 suggests that a s i m i l a r d i s c o n t i n u i t y occurs i n molybdenum, and several other metals. 7. The c r i t i c a l resolved shear stress on the (112) planes f o r a vanadium sin g l e c r y s t a l whose1 a x i a l d i r e c t i o n i s J l l C - J was found to be 11,250 p s i at room temperature. 76 VII. RECOMMENDATIONS FOR FUTURE WORK It i s f e l t that a great deal might be gained by an e f f o r t t® v e r i f y ©r r e j e c t e i t h e r the dual-impurity mechanism ®r the deformation mechanism as described i n the dis c u s s i o n preceding. This could be accomplished by means of c o n t r o l l e d impurity contents and/or c o n t r o l l e d impurity ratios i n vanadium and other body-centered cubic t r a n s i t i o n metals, i n c l u d i n g i r o n . A-more c r i t i c a l study should be made of the l©w-temperature behavi©ur of other body-centered eubic r e f r a c t o r y metals i n general, both by reference to the work of previous i n v e s t i g a t o r s , and by experiment. Emphasis was not placed ©nether metals i n the present work, i n view of the o r i g i n a l o b j e c t i v e s . The recommendation would include studies of high p u r i t y p o l y c r y s t a l l i n e metals and c a r e f u l metallographic studies. 77 V I I I . BIBLIOGRAPHY 1. Kinzel, A.B, - Vanadium Metal - A new Article ©f Commerce, Metal Progress, £8 (1950) 315. 2. Rostoker, W. - The Metallurgy of Vanadium, John Wiley and Sons, Inc., New York, (1958) 39. 3 . Pugh, J.W. - Temperature Dependence of the Tensile Properties of Vanadium, Journal of Metals, 9,. No. 10, Section 2, (1957) 1243-1244. 4. Tietz, T„E„, Wilcox, B„A0, and Wilson, J.W., Mechanical Properties and Oxidation Resistance of Certain Refractory Metals, SRI Project SU-2430, Final Report, Stanford Research Institute, 30 Jan. 59, 188. 5. Roberts, B.W. and Rogers, H.C. = Observations on Mechanical Properties of Hydrogenated Vanadium, Journal of Metals, 8, No. 10 (1956) 1213-1215. 6. Magnusson, A, and Baldwin, W.H., Jr., - Low Temperature Brittleness, Technical Report No. 34, ©n Contract N6onr-273/I. f®r office of Naval Research, March 1956. 7. Lacy, C.E., and Beck, C.J., Properties of Vanadium Consolidated by Extrusion, Transactions, A.S.M., £8, (1956), 579-594. 8. Clough, W.P. and Pavlovic, A.S. - The Flow, Fracture and Twinning of Commercially Pure Vanadium, Transactions, A.S.M., 52 Preprint 125, Aug. 1958. 9. Loomis, B.A., and Carlson, O.N., - Investigation of the Ductile-to-Brittle Transition in Vanadium, paper presented at the Reactive Metals Conference, May 27-29, 1958. 10. Farrell, J.W., - The Mechanical Properties of Unalloyed Vanadium -Technology Department Report, Union Carbide Metals Co., May 31, I960. 11. Fisher, J.C., - Application of Cottrell's Theory of Yielding to Delayed Yield in Steel. Transactions, A„S.M., 4J7 (1955) 451-462. 12. Schwartzberg, F.R., Ogden, H.R., and Jaffee, R.I,, Ductile-to-Brittle Transition in the Refractory Metals DMIC Report H i , Battelle Memorial Institute, 1959, 17-24, 13. Brown, C.M, - Rare Metals Handbook, Reinhold Publishing Corporation, New York, 1954, 594-596. 78 14. C a l v e r l y , A., Davis, M„, and Lever, R„F 0, The Floating-Zone Melting of Refractory Metals by Ele c t r o n Bombardment, Journal of S c i e n t i f i c Instruments, 3J±, (1957), 1^2-147. 15» Catalogue: Wheelc© Instruments, Barker-Colman Co„, Rockford, 111,, U.S,A,, p. 5, . . . 16. Zener, C. and Holloman, J,H., E f f e c t of S t r a i n Rate Upon the P l a s t i e Flow of S t e e l , Journal of Applied Physics, 1£, (1944) 22. 17. Holloman, J„H, S and Zener, C,, Conditions of Fracture i n S t e e l , Transactions, American I n s t i t u t e of Mining, M e t a l l u r g i c a l and Petroleum Engineers, 158, (1944) 283. 18. Bechtold, J.H., The e f f e c t of Temperature on the Flow and Fracture C h a r a c t e r i s t i c s of Molybdenum, Transactions, American I n s t i t u t e of Mining, M e t a l l u r g i c a l and Petroleum Engineers, 197. (1955) 1469. 19. Bechtold, J.H„, and Shewmon, P.G., Flow and Fracture C h a r a c t e r i s t i c s of Annealed Tungsten. Transactions, A.S.M., 4J7 (1955) 451, 20. C o t t r e l l , A.H., and B i l b y , B.A., D i s l o c a t i o n Theory of Y i e l d i n g and S t r a i n Aging i n Iron, Proceedings Royal Society, London, A62 (1949) 49. 21. S t e i j n , R.P., and Brick, R.M., Flow and Fracture of Single Crystals of High P u r i t y F e r r i t e , A.S.M. Preprint No. 36, 1953. 22. Cox, J . J . , Horne, G.T. and Hehl, R.F., S l i p , Twinning and Fracture i n Single C r y s t a l s of Iron, Transactions, A.S.M,, 4J9 (1956) Preprint No, 1, 23. C u l l i t y , D.B., Elements of X-ray D i f f r a c t i o n , Addison-Wesley Publishing Co. Inc., Reading, Mass. (1956) 72-73. 24« Barrett, C.S., Ansel, G., and Mehl, R.F., S l i p , Twinning and Cleavage i n Iron and S i l i c o n F e r r i t e , Transactions, A.S.M., 2j5 (1937) 702. 25, Fahrenhorst, N., and Schmid, E„, On the P l a s t i c Deformation of a n d -i r o n C r y s t a l , Z e i t s c h r i f t f u r Physik, 7_8 (1932) 383, 26, Opinsky, A.J., and Smoluchowski, R. The Crystallographic Aspect of S l i p i n Body-Centered Cubic Single C r y s t a l s , Journal of Applied Physics, 22 (1951) 1488. 27, Taylor, G.I., and Elam, C.F. The D i s t o r t i o n of Iron C r y s t a l s , Proceedings. Royal Society. London. A112 (1926) 337, 28, Taylor, G„I„, The Deformation of Crystals of B-Brass, Proceedings, Royal Society, London, A118. (1928) 1, 29, Chen, N.K., and Maddin, R., P l a s t i c i t y of Molybdenum Single C r y s t a l s , Transactions, A.I.M.E., 19J., (1951) 937. 79 3 0 . Carlson, O.N., and Owen, C 0V. Preparation of High Pu r i t y Vanadium Metal by the Iodide Refining Process, I n s t i t u t e f o r Atomic Research and Department of -Chemistry, Iowa State University, Paper presented at the Electro-Chemical Society Meeting, Chicago, May 1 9 6 0 . 31o Adams, M.A., Roberts, A 0C„, and Smallman R.E., Y i e l d and Fracture i n P o l l y c r y s t a l l i r a e Niobium.Acta M e t a l l u r g i c a , 8 , No. £ ( I 9 6 0 ) 3 2 8 - 3 3 7 . 3 2 . Biggs, W„D„, and Pra t t , P o L „ , <a£~Iron at Low Temperatures, Aeta Metallurgica, 6 , ( 1 9 5 8 ) 6 9 4 . 3 3 . C o t t r e l l , A o H 0 , D i s l o c a t i o n s and P l a s t i c Flow i n C r y s t a l s , Oxford U n i v e r s i t y Press, London, 1 9 5 3 s 1 3 4 = - 1 4 5 . 3 4 . Wessel, E.T., Abrupt Y i e l d i n g and the D u c t i l e - t o - B r i t t l e T r a n s i t i o n i n Body-Centered Cubic Metals, Journal of Metals, £, No. 7 Section 2 ( 1 9 5 7 ) 9 3 0 - 9 3 5 . IXo APPENDICES  APPENDIX I TABLE I THE RESULTS OF TENSILE TESTS J « o -p <* Q H • r l • Q q 0 -p ^ •H 0 •H — ' • H T H 1-3 o OH <*> —- I • O ^ H (X. • H n ftp co o COCO I £ g t*4 P , i CO H • H n P , P> I * Q O r-i CO w n AS U % V V05T1 14/6/60 .119 1.111 .825 1.06 20 3.41 28.48 22.50 23.85 23.22 24.84 11.25 V05T2 14/6/60 .120 1.130 .832 .900 -196 12.98 8.17 106.19 115.04 102.65 115.04 54.25 V05T3 14/6/60 .137 1.474 .760 .875 -183 11.11 15.13 91.59 98.37 78.02 98.37 46.39 V05T4 14/6/60 .134 1.410 .770 .980 20 3.41 27.27 21.99 24.45 24.11 26.24 11.53 V04T1 2/7/60 .115 1.038 .709 .890 20 3.41 25.52 23.80 26.30 25.72 27.55 12.40 V07T1 2/7/60 .118 1.093 .895 1.115 20 3.41 24.58 20.59 23.60 22.87 25.16 11.13 V04T4 2/7/60 .119 1.112 .915 .947 -183 11.11 3.49 93.53 101.80 98.20 101.80 48.01 V07T4 2/7/60 .120 1.130 .842 .923 -183 11.11 9.61 94.69 100.00 97.35 100.00 47.16 V04T5 2/7/60 .120 1.130 .992 1.050 -196 12.98 5.84 109.29 116.81 109.73 116.81 55.09 V07T5 2/7/60 ,116 1.056 .785 .862 -196 12.98 9.80 85.23 96.78 92.80 96.78 45.64 Faulty V08T1 26/7/60 .115 1.038 .815 1.056 24 3.37 29.57 17.82 21.39 21.00 23.70 10.09 V08T3 26/7/60 .123 1.188 .919 1.195 24 3.37 30.03 18.52 22.73 22.14 25.08 10.72 V08T5 26/7/60 .108 0.916 1.100 1.190 24 3.37 8.18 19.65 22.93 22.93 25.55 10.81 V09T1 26/7/60 .116 1.056 .840 1.056 -50 4.48 25.71 28.60 33.05 32.39 34.09 15.59 V09T3 26/7/60 .118 1.093 .825 1.036 -50 4.48 25.57 30.19 33.21 32.11 36.87 15.66 V09T5 26/6/60 .119 1.112 .857 1.049 -50 4.48 22.40 32.82 35.07 34.53 36.15 16.54 V04T2 27/7/60 .119 1.112 .772 .986 -50 4.48 27.72 33.09 35.70 34.08 36.33 16.84 V07T2 27/7/60 .122 1.169 .845 1.079 -50 4.48 27.69 32.93 34.90 33.19 34.47 16.46 V04T2 27/7/60 .122 1.169 .777 D.N.M. -109 6.09 D.N.M D.N.M D,N,M D.N.M D.N.M D.N.M Faul t y ¥07T3 27/7/60 .120 1.130 .840 1.070 -109 6.09 27.38 46.90 53.36 51.59 53.36 25.17 V10T1 27/7/60 .112 0.985 .807 1.090 -109 6.09 35.06 35.53 49.14 45.99 49.14 23.17 V10T3 27/7/60 .123 1.189 ,806 .962 -109 6.09 19.35 47.10 54.75 50.46 54.75 25.82 V10T5 27/7/60 .110 0.950 .820 .987 -109 6.09 20.36 44.53 50.11 48.63 50.11 23.63 V11T1 27/7/60 .120 1.130 .834 .995 -196 12.98 19.30 D.N.M D.N.M D.N.M D.N.M D.N.M.011 ©m V11T3 27/7/60 .116 1.056 .825 .892 -196 12.98 8.12 100.38 112.69 104.17 112.69 53.15 V11T5 27/7/60 .121 1.150 .853 .995 -196 12.98 16.64 D.N.M D.N.M. D.N.M D.N.M D.N.M O i l ©a V11T2 28/7/60 .113 1.003 .832 .911 -196 12.98 9.49 113.66 118.64 99.70 118.64 55.95 V10T2 3/8/60 .104 0.849 .788 .893 -125 6.76 13.32 71.85 75.38 61.25 75.38 35.55 V10T4 3/8/60 .122 1.169 .851 .963 -125 6.76 13.16 62.45 65.53 55.69 65.53 30.90 V09T2 3/8/60 .120 1.130 .784 .913 -125 6.76 16.45 70.80 73.89 63.72 73.89 34.85 ¥09T4 3/8/60 .114 1.020 .851 .952 -128 6.90 V12T1 4/8/60 .121 1.150 .814 . 9 1 9 -140 7.52 V12T3 4/8/60 .122 1.169 .764 ,882 -140 7.52 V12T4 4/8/60 .118 1.093 .802 ,910 -140 7.52 V06T1 5/8/60 .114 1.020 .815 .933 -121 6.58 V12T2 5/8/60 .114 1,020 .780 .903 -121 6.58 V11T4 5/8/60 .119 1.112 .852 .995 -121 6.58 V06T2 5/8/60 .116 1.056 .798 .895 -133 7.14 V06T3 5/8/60 .1225 1.178 .848 .933 -165 9.26 V06T4 29/8/60 .117 1.075 .806 D.N,M D.N.M D.N.M V06T5 29/8/60 .117 1.075 .841 D.N.M -165 9.26 V08T4 29/8/60 .113 1.003 .845 D.N.M -164 9.17 V02T1 29/8/60 .1205 1.140 .800 .924 -157 8.62 V02T2 29/8/60 .110 0.950 .811 D.N.M -128 6.90 V02T3 29/8/60 .116 1.056 .822 D.N,M -130 6.99 V13T2 29/8/60 .1165 1.066 .868 D.N,M -138.5 7.43 V13T3 30/8/60 .1135 1.011 .967 D,N,M -133.5 7.17 P e l y c r y s t a l l i n e Specimens at 0.055/mis. V15T2 30/8/60 .116 1.056 .866 D„N.M -122.5 6.64 V15T3 30/8/60 .1215 1.159 .833 D.N.M -101 5.81 V15T4 30/8/60 .120 1.130 .906 D.N.M -62 4.74 V16T5 30/8/6Q .119 1.112 .757 ,880 -136.5 7.33 V16T3 30/8/60 .116 1.056 .760 D,N,M -136.5 7.33 V16T4 30/8/60 .121 1.150 .793 1.080 -159.5 9.02 V15T5 30/8/60 .117 1.075 .882 1.057 -63 4.76 Single Crystals at 0.0022/min. V14T1 31/8/60 .118 1.093 .949 1.075 -157 8.62 V14T2 31/8/60 .1205 1.140 6914 1.020 -142 7.63 V14T3 31/8/60 .116 1.056 .890 D.N,M -137 7.35 V14T4 31/8/60 .121 1.150 .952 1.075 -134,5 7.22 V14T5 31/8/60 .1205 1.140 .971 1.079 -128 6.90 11.86 78.43 81.37 68.63 81.37 38.37 12.33 77.39 80.09 66.43 80,09 37.77 15.44 74.85 77.59 70.15 77.59 36.59 13.46 78.68 81.98 65.87 81,98 38.66 14.47 71.57 74.41 65.69 74.41 35.09 15.76 60.78 63.73 57.84 63.73 30,06 16.78 52.16 57.82 55.85 57.82 27.27 12.15 73.86 76.99 70.27 76.99 36.31 10.02 86.16 89.39 86.16 89.39 42.16 D.N,M, D.N.M D,N,M D.N.M D.N.M. D.N.M O i l i n grips * 22 71.63 74.92 73.02 74.42 35.10 Faulty Sp. * 15 85.74 88,14 78.36 88.14 41.57 15.50 77.19 81.67 74.82 81.67 38.52 * 18 66.32 69.16 64.11 69.16 32.62 * 18 67.80 71.97 62.50 71.97 33.94 * 18 69.42 72.61 64.63 72.61 34.24 * 18 73.18 76.58 63.91 76.58 36.12 64.39 67.61 64.30 67.61 * 23 53.49 56.60 53.67 56.60 - 24 33.98 40.27 40.27 41.59 16.24 69.24 73.29 69.24 73.29 * 16 67.23 71.97 69.13 71.97 36.19 88.70 93.91 86.09 93.91 19.84 36.28 41.49 40.93 42.79 13.27 73.19 80.15 71.73 80.15 37.80 11.59 71.93 74.82 59.04 74.82 35.29 * 10 63.45 65.25 59.19 65.25 30.77 12.92 65.22 66.35 54.78 66.35 31.29 11.12 59.65 62.37 53.07 62.37 29.41 VBT4 31/8/60 .1165 1.066 .958 D.N.M - 99.5 5.76 *D.N.M 32.83 39,68. 39=12 39.68 18.71 V13T5 31/8/60 .119 1.112 1.009 D.N.M =132.5 7.12 * 10 54.86 59.35 52.16 59.35 27-99 V13T1 31/8/60 .114 1.020 . 972 D.N.M =118 6.45 * 11 41.18 45.69 44.12 45.69 21.55 V02T4 31/8/60 .119 1.112 .819 .890 =134.5 7.22 8.66 58.72 62.59 55.85 62.59 29.52 ± Elongation estimated fro® Lead-Elongation curve AVERAGE ELONGATION DATA Avg. E l . % 20°C 27.53 ~50°C 25.81 =109*C 25.54 =121°C 15.67 =125°C 14.31 -128°C 14.93 -133.5°C 16.05 -140°C 14.80 -165°G 13.50 -183°C 9.41 -196°C 8.28 Bo THE CALCULATION OF STRESS AND ELONGATION EXAMPLE V05T1 (tasted at 20°C) STRESS Sy = y i e l d stress P = lead - 264 l b s . A = area = l„lllxl0 = 2 i n 2 - 264 = 23,850 lbs l o l l l x l O " 2 i n 2 ELONGATION E = % elengatiom 1 kc = i n i t i a l gauge length I f = f i n a l gauge length E = I f - l i n x 100 1 i n 0 = 1.060 - 0o825 8 8 28.48% 0.825 C. THE MAXIMUM ERROR IN YIELD STRESS MEASUREMENTS EXAMPLE 1 V05T1 (tested at 20°C) Estimated maximumerrer i n measuring Ps P = 264 ! 1 US • 264 1 oDhf> Estimated maximum err©r i n measuring A d • Oi'119 t 0.0005 A - .7852 (.119) 2 ! 0.001 = (1.111) ( 1 0 = ? ) t .001 (1.111) (10° 2) 1 9% T e t a l maximum err©r i n 8 % 8 - 23,850 2h ! 9.4% i s 2 = 23,850 1 2220 lbs i n 2 85 EXAMPLE 2 V05T2 (tested at =196°C) Estimated maximum er r o r i n measuring Ps P = 1300 - 10 l b s 0 = 1300 - 0.8 % Estimated" maximum e r r o r i n measuring As d = 0ol20•* 0.0005 im. A = . 7 8 5 2 (0.120)2 i 0.001 - 1 . 1 3 0 x 1 0 ° 2 * 0 . 0 0 1 - 2 + = 1.130 x 10 - 8.9% T o t a l maximum erro r i n 5 s 6 = P/ A = 1300 - 0.8 1.130 x H T 2 1 8 . 9 = 115,040 1 9 . 7 % - 115,040 * 11,160 lbs i n 2 It-should be remembered the values stated are maximum values, and i n nearly a l l cases, the accuracy would be much better. D. THE PROBABLE ERROR IN YIELD STRESS MEASUREMENTS  EXAMPLE V05T1 P = 2 6 4 - 1 - 264 - 0.4% •A = .7852 (.119) 2 * .0002 -1.111 x 10~ 2 = 1.8% Probable error i n 8 8 = 264 * 0o4% ( 1 . 1 1 1 ) ( K r 2 ) * 1.8% = 23850 * 2.2% = 23850 * 525 p s i . EXAMPLE, 2 V05T2 P - 1300 i 10 lbs $ 1300 - 0.8 % A = (.7852)(0.120)2 - 0.0002 -• 1.130 x 10 2 - 1.77% Probable error in 8 : 8 = 1300 * M = 115,040 - 2.57% (1.130)(10°2) - 1.77 8 = 115,040 - 2960 psi E. CALCULATION OF CRITICAL RESOLVED SHEAR STRESS 8cr = cos (p cos ^ P = Angle between perpendicular to slip plane and tension axis A = Angle between jlll} and tension axis P = load P/ => yield stress • 8 y A = area EXAMPLE V05T1 (tested at room temperature) 8 y = 23,850 psi. - 35°18» - 54°42« Cos"^ = 0.81614 Cos $ » 0.57786 S c r = 23,850 (O.8I614) ( 0.57786) =  11,250 psi. 67 APPENDIX II The Zone Refiner A. ELECTRICAL SYSTEM Figure 1 shews the c i r c u i t diagram f o r the zone r e f i n e r . It c l o s e l y resembles the one designed by Galverley, Davis and L e v e r a n d uses the same current c o n t r o l system, that i s by emission c o n t r o l , i n which the filament temperature controls the emission current, M e d i f i c a t i e n to'Power Supply There -are-a-number of-ways i n which a pewer system of the type used i n t h i s work could be g r e a t l y improved. The f i r s t and most important i s i n the current s t a b i l i z a t i o n . The present system contains a time l a g which arises from-the time i t takes f o r the filament to change teaperature. The modification suggested by C a l v e r l y , Davis and L e v e r ^ i s to supply the high voltage from a constant current souree; In -this system, the bombardment current i s kept constant by a d j u s t i n g the high voltage, A nuaber-of minor improvements which could b* made are: the use of very hieh speed relays t o shut o f f - t h e high voltage when a short c i r -c u i t occurs, the use of smaller and mere compact transformers, both te deerease the weight and increase the e f f i c i e n c y of operation; the use of a single thyratron-tube i n the c o n t r o l c i r c u i t , since i t was found i n the present work that only one of them operated-at any one time. However they were-found to alternate, and i n changing, they often caused the high voltage to cut out, r e s u l t i n g i n annoying delays. B. FURNACE SYSTEM •It i s f e l t by- the author that the -existing design of the furnace pert of the zone r e f i n e r i s u n s a t i s factory and should be r e b u i l t i n the manner described below. Rather than have 2 brass plates suspended by a Figure 1„ C i r c u i t Diagram ef the Zene Refiner as used i n t h i s investigation,, 89 large pyrex tube as was the case i n the present werk, the whole assembly sheuld be mounted en one plate which serves as the base and leads to the vacuum system. A b e l l j a r should be used f o r the vacuum chamber. This would greatly f a c i l i t a t e working around and on the apparatus. The drive should consist of a down-driven worm gear. This i s u s e f u l f o r two reasons: (1) a zone which moved upwards ( i . e . the specimen moves down) would provide a more stable zone, and (2) a worm gear drive would provide a much more uniform movement. It i s f e l t that the present system of specimen mounting, filament type, beam-focus pla t e s and r a d i a t i o n shields are s a t i s f a c t o r y except that i t would be convenient to have a r e f l e c t e d view of the molten zone, since metals with high vapor pressures very qu i c k l y deposit a layer of vaporized metal onto the viewing glass, thus obscuring the zone. 90 APPENDIX III RESISTANCE MEASUREMENTS TABLE I THE RESULTS OF RESISTANCE MEASUREMENTS Vernier fX volts (pet.) Potentiometer I R T JOl Volts (Current) (amps) (p. ohms) (°K) Remarks 116.7 7877.3 .78773 148.1 126.0 130.0 7916.9 .79169 164.2 136.0 140.6 7785.5 .77855 180.6 145.0 151.0 7794.7 .77947 193.7 150.0 161.7 7952.0 .79520 203.3 158.5 171.2 7816.9 .78169 219.0 166.0 181.0 7891.3 .78913 229.4 173.5 190.3 7820.8 .78208 243.3 185.5 195.4 7733.1 .77331 252.7 189.0 200.0 7492.8 .74928 266.9 197.0 213.8 7573.9 .75739 282.3 206.0 233.8 7773.2 .77732 300.8 216.0 252.5 7772.1 .77721 324.9 229.0 281.2 7794.4 .77944 360.8 250.5 300.0 6960.0 .69600 431.0 269.5 57.5 8050.1 .80501 71.4 75.5* 64.1 8944.6 .89446 71.7 75.5 78.5 8963.3 .89633 87.6 87.0 93.7 8980.2 .89802 104.3 97.0 108.1 8977.2 .89772 120.4 111.0 114.3 8974.9 .89749 127.4 112.0 131.0 8972.4 .89724 146.0 121.0 137.0 8974.6 .89746 152.7 126.5 146.8 8968.2 .89682 163.7 131.5 154.4 8965.6 .89656 172.2 137.0 161.5 8965.3 .89653 180.1 141.0 168.7 8965.6 .89656; 188.2 146.0 174.1 8965.6 .89656 194.2 150.0 176.6 8966.9 .89669 196.9 152.0 184.6 8966.7 .89667 205.9 156.5 193.2 8967.2 .89672 215.5 160.0 206.3 8964.4 .89644 230.1 168.0 213.4 8964.3 .89643 238.1 172 iO 220.9 8967.4 .89674 246.3 174.5 Run 1 No Load Run 2 Load = 40,000 psi. & Ne load 9 1 Vernier Potentiomet or I R P v o l t s )l v o l t s (Current) (amps) ohms) Remarks (psi) S t r e s s ( p s i ) 51,4 7074.5 .70745 72.7 0 Run 3 54.0 7374.2 .73742 73.2 10,000 No lead to 48.8 6600.0 .66000 73.9 20,000 y i e l d stress 118.8 16059.2 1.60592 74.0 30,000 at constant 119 o 6 16154.9 1.61549 74.0 40,000 temperature 117 o 4 15726.7 1.57267 74.7 50,000 ( l i q u i d N 2 • 120„6 16207.7 1,62077 74.4 60,000 -196°G) 121.2 16227.7 1.62277 74.7 70,000 121.4 16236.5 1,62365 74.8 80,000 121.4 16239.3 1.62393 74.8 90,000 122.1 16173.6 1.61736 75.5 100,000 T(°K) 116.1 15734.4 .157344 73.8 75.0 Run 4 127.6 15665.6 .156656 81.5 83.0 load » 142.0 15660.8 .156608 90.7 88.0 70,000 p s i 162.5 15632.0 .156320 104.0 99.5 196.9 15688.7 .156887 125.5 111.0 56.0 7761.6 .77616 72.2 78.5 Ron 5 74.0 7400.0 .74000 100.0 93.0 No load 76.9 7215.5 .72155 106,6 100.0 (Repeat) 85.9 7258.0 .72580 118.4 106.0 93.1 7443.2 .74432 125.1 113.0 102.6 7403.7 .74037 138.6 119.5 106.0 7130.0 .71300 148.7 126.0 114*5 7186.7 .71867 159.3 130.5 124.4 7224.2 .72242 172.2 139.5 139.9 7183.8 .71838 194.7 150.5 147.9 7176.9 .71769 206,1 159.0 160.8 7225.8 .72258 222.5 166.5 179.2 7330.0 .73300 244.5 177.0 185.2 7259.8 .72598 255.1 183.0 186.9 6926.2 .69262 268.5 194.0 194.8 6925.9 .69259 281.3 198.5 203.0 6924.0 .69240 293.2 204.5 216.6 7103.7 .71037 304.9 215.0 237.5 7279.8 .72798 326.2 227.0 260.0 7569.9 .75699 343.5 238.0 278.8 7663.5 .76635 363.8 251.0 291.5 7641.5 .76415 381,5 263.0 298.3 7334.3 .73393 406.4 274.0 92 Bo CALCULATION OF ELECTRICAL RESISTANCE The resistance measurements war© set up such that ©ne set-©f leads measured the current passing through the specimen and a standard resistance of 0.01 ©hm, while the ©ther set ©f leads-measured the p o t e n t i a l D J#Vp = p o t e n t i a l voltage (micr©<=v©lts) /We s current voltagee (micro=v®Its) I • ts current i n amps R = resistance i n micro ©hms SAMPLE CALCULATION JJNp (measured) <= 116.7 J& v o l t s /LWc (measured) = 7877.3 >B& v o l t s 1 = 7877.3 x 1 0 ° 6 = 0.78773 amps 0.01 R " 116o7 = 126.0 micro-©hms 0.78773 C. CALCULATION OF MAXIMUM ERROR IN RESISTANCE MEASUREMENTS R - jWp ~ I ~ Maximum fo E r r o r i n R = fo e r r o r i n /UVp + fo error i n I. Maximum fo e r r o r i n I «= fo e r r o r i n f$Ie + % e r r o r i n R 0 Maximum fo e r r o r i n JUVC = 0.2% (estimated) Maximum fo e r r o r i n R =0.2% at a temperature of 150°K R i s approximately 150 fi ohms. Therefore E r r o r i n R 5 3 = 0 . 3 ^ ©hms 15 + fo err©r i n temperature at. 150°K i s •= 2% Therefore error i n T = * 3°K .93 These error values are probably much tee large, simce the err o r i s temperature measurement i s compensating„ 94 APPENDIX IV MICROHARDNESS KHN TABLE I THE RESULTS OF MICROHARDNESS MEASUREMENTS 14.229 L/ i 2 L = load (kgms) 1 = length ef indentation (am) ± Values taken from Departmental Tables Specimen Avg. Filar Length(mm) KHN Units V02T3 7 7 5 . 3 0 . 3 6 8 105.1 V04T3 738 o 4 0.351 115.5 V05T3 775.0 0.368 105.1 V06T3 733.2 0.348 117.5 V07T3 691.3 0.328 132.3 * V08T3 735.2 0.349 116.8 ± V09T3 - 6 6 4 . 0 0.315 143.4 & V10T3 784.5 0.373 102.3 V11T3 784.6 0.373 102.3 V12T3 7 5 6 . 6 0.359 110 0 4 V13T3 815.3 0.387 95.01 V14T3 773.7 0.368 105.1 V15T3 676.0 0.321 138.1 V16T3 685.4 0.326 133.9 As Received 687.1 0.326 133.9 Remarks polycrystalline p®lycrystalline p©lycrystalline ± Results invalid because ©f extensive defermation which specimens underwent. 

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