{"http:\/\/dx.doi.org\/10.14288\/1.0105465":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Applied Science, Faculty of","type":"literal","lang":"en"},{"value":"Materials Engineering, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Clayton, John Frederick","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2011-11-08T00:15:52Z","type":"literal","lang":"en"},{"value":"1963","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Master of Applied Science - MASc","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"An investigation into the variation of electrical resistance with temperature for high purity niobium and vanadium single crystals has been carried out.\r\nNiobium was studied over the temperature range -30\u00b0C to -146\u00b0C. It was found that in its highest purity there was little or no anomaly. At lower purities an anomaly in the region of -120\u00b0C was discovered which was attributed to oxygen or nitrogen or both changing their position on the lattice to one of higher strain energy because of changes in energy associated with the bonding between interstitials and the lattice.\r\nHydrogen doping of niobium produced an overall increase in resistivity. A drop in the resistance curve was noted at -100\u00b0C which was thought to be due to hydrogen, being mobile and non-bonded, moving off the high strain energy sites under the influence of thermal contraction. Hydrogen embrittlement was attributed to hydrogen occupation of high strain energy-sites.\r\nVanadium was found to have a slope change at.-170\u00b0 when tested between -130\u00b0C and -196\u00b0C. No definite explanation of this is suggested.\r\nUltrasonic testing of vanadium showed attenuation minima at -100\u00b0C and -170\u00b0C.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/38854?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"THE ELECTRICAL RESISTANCE OF NIOBIUM AND VANADIUM SINGLE CRYSTALS AT LOW TEMPERATURES by JOHN FREDERICK CLAYTON A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of 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 METALLURGY THE UNIVERSITY OF BRITISH COLUMBIA January 1963 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department O f M e t a l l u r g y  The University of British Columbia, Vancouver 8, Canada. ABSTRACT An investigation into the variation of e l e c t r i c a l resistance with temperature for high purity niobium and vanadium single crystals has been carried out. Niobium was studied over the temperature range -30\u00b0C ,o to -146 C. It was found that in i t s highest purity there was l i t t l e or no anomaly. At lower purities an anomaly in the region of -120\u00b0C was discovered which was attributed,to oxygen or nitrogen or both changing their position on the lat t i c e to one of higher strain energy because of changes in energy associated with the bonding between i n t e r s t i t i a l s and the l a t t i c e . Hydrogen doping of niobium produced an overall increase in r e s i s t i v i t y . A drop in the resistance curve was noted at -100\u00b0C which was thought to be due to hydrogen, being mobile and non-bonded, moving off the high strain energy sites under the influence of thermal contraction. Hydrogen embrittlenient was attributed to hydrogen occupation of high strain energy-sites. Vanadium was found to have a slope change at.-170\u00b0 when tested between -130\u00b0C and -196\u00b0C. No definite explana-tion of this i s suggested. Ultrasonic testing of vanadium showed attenuation minima at -100\u00b0C and -170\u00b0C. ACKNOWLEDGEMENT The author wishes to express his indebtedness to Dr. J.A. Lund for his supervision and guidance, to Mr. R.G. Butters for his invaluable technical assistance, and to Messrs. R. Richter and W. Cross for their co-operation i n the solution of mechanical problems. Single crystals grown by Mr. G.C. Howard were much appreciated, as was his help with the ultrasonic work. Of great assistance were the c r i t i c a l discussions held with Dr. E. Teghtsoonian, Mr. M.N. Shetty and other members of the department. Drs. R. Barrie and D.LI. Williams of the Physics Department were generous.of their time and assistance. Thanks are due to the Mines Branch of the Department of Mines and Technical Surveys for their generous loan of the vernier potentiometer. The author is very grateful to Mr. N. Brearley and the British Columbia Research Council for assistance in performing the ultrasonic testing and the use of their equipment. The work was financed by the National Research Council of Canada under Grant Number 7510=30. i i i TABLE OF CONTENTS Page 1. INTRODUCTION . 1 \u2022:\u2022 11 . REVIEW OF PREVIOUS WORK 3 A. The El e c t r i c a l Resistance of Metals. . . . . . 3 1. Matthiessen's Rule. . 5 2 . Resistance at High Temperature 6 3 . Resistance at Low Temperature 7 4. Effect of Change in Magnetic Properties 9 B. Previous Work on El e c t r i c a l Resistance . . . . 11 1. Alkali Metals 11 2 . Rare Earth. . . . . . . . . . . . . . . 13 3. Transition Metals . . . 15 4 . Bismuth . 17 C. Vanadium and Niobium IS 1. Vanadium. . 18 2 . Niobium 23 D. Internal Friction Measurements on Vanadium and Niobium . . . . . . . 23 111. EXPERIMENTAL . 25 A. Materials 25 1. High Purity Niobium Rod 25 2 . High Purity Vanadium Rod. . . . . . . . 25 3 . Hydrogen Gas. 26 B. Purification 26 C. Single Crystal Orientation . . . . . . . . . . 27 D. Addition of Hydrogen to Niobium. . . . . . . . 28 E. Annealing of Niobium 29 i v TABLE OF CONTENTS CONTINUED Page F. Specimen Preparation . . . . . . . 29 1. Machining. . . . . . . . . 29 2. Surface Preparation. . . 31 G. Resistance Measurements 32 1. Specimen Mounting. 32 2. Measurement of E l e c t r i c a l Resistance . . 37 3. Temperature Control and Measurement. . . 39 H. Ultrasonic Preparation 40 1. Specimen Preparation . . . . . . . . . . 40 2. Specimen Mounting 41 3\u00ab Procedure. . . . . . . 42 IV. EXPERIMENTAL OBSERVATIONS AND RESULTS. . 44 A. High Purity Niobium Specimens. . . . . . . . . . 44 1. Mechanical Polish Only . . . . . . . . . 44 2. Electropolished Specimens. . . . . . . . 48 3. Hydrogen Doped Specimens . 58 4. Summary of Results on Niobium. . . . \u2022 . \u2022 61 B. High Purity Vanadium Specimens. . . . . . . . 62 C. Ultrasonic Testing of High Purity Vanadium . . 68 V. DISCUSSION . 73 A. High Purity Niobium 73 1. E l e c t r i c a l Resistance Anomalies. . . . . 73 2. Increase i n Resistance during the Heating Cycle and on Standing at Room Temperature . . . . . . . . . . . 85 B. Vanadium . . . . . . . . . . . . 88 C. The Hydrogen Anomaly in Niobium . 91 D. Correspondence of Mechanical & Thermal Strain. 92 V TABLE OF CONTENTS .CONTINUED Page E. Hydrogen Embrittlement 94 F. Application to the Results of Harding on High Purity and Doped Single Crystals of Niobium . . . . . . . . . . . 97 1. High Purity Single Crystals of Niobium. 97 2. Hydrogen Doped Specimens. . . . . . . . 97 3. Oxygen Doped Specimens. . . . . . . . . 98 4. Nitrogen Doped Specimens. . . . . . . . 98 VI. CONCLUSIONS. . \u2022 o . . . o o \u00bb o o . o . \u00bb \u00bb . . . o . . 100 V l l . RECOMMENDATIONS FOR FUTURE WORK. . . . 102 V l l l . BIBLIOGRAPHY . 103 IX. APPENDIX . . 106 I. Change i n Resistance of Specimen due to Thermal Contraction. . . . . . . . . . . 107 II. Estimated Experimental Error . . . . . . . . . 108 v i FIGURES No. Page 1. Hypothetical Variation of Resistance with Temperature at various Impurity Contents 5 2. Variation of Resistance of Nickel with Temperature.... 9 3. Resistance versus Temperature for Bismuth 13 4. Resistance versus Temperature for Chromim 15 5. Resistance versus Temperature for Maganese 16 6. Resistance versus Temperature for Vanadium 19 7. Magnetic Susceptibility versus Temperature for 99.9% Vanadium 20 7.1\/ Resistance versus Temperature for 99.9% Vanadium 20 8. Variation of Anomaly Temperature with Chromium Content 22 9. Position of Niobium Specimen i n the Grips 32 10. Experimental Arrangement for Testing Single Crystals of Niobium 33 10A. Experimental Arrangement for Testing Single Crystals of Vanadium 35 10B. Schematic Diagram of Potentiometer Arrangement 37 10C. Schematic Diagram of Specimen Circuit 37 11. Variation of Ele c t r i c a l Resistance with Temperature for High Purity Single Crystals of Niobium under Load. (Specimen 1) 43 12. Ele c t r i c a l Resistance versus Temperature (Specimen 2) 45 13. El e c t r i c a l Resistance versus Temperature (Specimen 2) 4-7 14. Ele c t r i c a l Resistance versus Temperature (Specimen 3) 51 15. El e c t r i c a l Resistance versus Temperature (Specimen 3) 53 15A. Enlarged Sections of Figures 14 and 15 54 16. E l e c t r i c a l Resistance versus Temperature (Specimen 4) 56 v i i FIGURES CONTINUED No. Page 16A. Enlarged Section of Figure 16. . . . . 57 17. E l e c t r i c a l Resistance versus Temperature (Specimens 5 and 6 ) . . . . . . . . . . . . . 59 18. E l e c t r i c a l Resistance versus Temperature (Specimen 7) \u2022 60 19. E l e c t r i c a l Resistance versus Temperature (Specimen 8) 63 20. E l e c t r i c a l Resistance versus Temperature, (Specimen 8) . . . . . . . . . 64 21. E l e c t r i c a l Resistance versus Temperature (Specimen 9) 65 2 2 . E l e c t r i c a l Resistance versus Temperature (Specimen 10). 66 2 3 . E l e c t r i c a l Resistance versus Temperature (Specimen 10) 67 24. El e c t r i c a l Resistance versus Temperature (Specimen 10). 68 2 5 . E l e c t r i c a l Resistance versus Temperature (Specimen 11) 69 2 6 . Attenuation versus Temperature for Vanadium using Nonaq as Couplant (Specimen 12) 70 27. Attenuation versus\" Temperature for Vanadium using Hi-Vac Grease as Couplant (Specimen 13) . 71 28. Attenuation versus Temperature for Vanadium using Hi-Vac Grease as Couplant (Specimen 12) . 71 FIGURES CONTINUED No. Page 2 9 . The Two I n t e r s t i t i a l Sites i n a Body Centered Cubic Lattice 74 3 0 . Typical Cooling and Heating Curves for Niobium . . 85 3 1 . Percentage Reduction i n Area versus Temperature for Iron containing Hydrogen i n the Two States 94 32. Recovery of Ductility of Hydrogen Doped Niobium at Low Temperatures 97 3 3 . Resistance versus Temperature for Hydrogen Doped Niobium 97 } TABLES No. Page I. Analysis of As-Received Niobium . . 25 II. Analysis of As-Received Vanadium 26 III. I n t e r s t i t i a l Content of Zone-Refined Niobium . . . 27 IV. I n t e r s t i t i a l Content of Zone-Refined Vanadium. . * 27 V. Atomic Radii of the I n t e r s t i t i a l Elements. . . . . 75 THE ELECTRICAL RESISTANCE OF NIOBIUM AND VANADIUM SINGLE CRYSTALS AT LOW TEMPERATURES I. INTRODUCTION In view of the recent general interest in the body-centred cubic transition metals a considerable amount of work on the physical properties of Nb, V and Ta has been under-taken i n this department,1\"^ These studies have been mainly in the f i e l d of yield stress dependence upon temperature and the mode of deformation of single and polycrystalline specimens of the above metals. It was found that there was an anomalous dependence of yield stress upon temperature below room temperature for single crystals of Nb and V. Examination of the results of other workers for polycrystalline specimens also showed a similar effect. Yield stress vs. temperature plots gave two inter-1 seating curves whereas a plot of log yield stress vs. ^ gave two intersecting straight lines. The mechanism 2 responsible has not been definitely substantiated. Snowball proposed that different dislocation locking effects for each species of i n t e r s t i t i a l atom were responsible for the effect. Harding^ considered two mechanisms to explain his work on. Nb: 1. I n t e r s t i t i a l ordering involving the movement of i n t e r s t i t i a l s away from dislocations, which.Harding sub-sequently rejects. 2. Dislocation - solute interaction where the magnitude of the interaction of screw and edge disloca-tion with solute atoms varies differently with temperature. 2 At high temperature the screw dislocations are more easily released. As the temperature decreases and de-formation requires higher stresses both screw and edge dislocations acquire jogs. Movement of a jogged screw dislocation requires a diffusion process, thus edge dislocations become more easily moved eventually i.e. below the anomaly temperature. If 1. were the mechanism i t would be expected to affect electrical r e s i s i s t i v i t y . Previous workers have reported resistance anomalies in the form of slope changes in resistance vs. temperature curves i n V. >^ -*-9 This investigation was undertaken with the intention of verifying the previously reported work of Snowball, determining the. temperature dependence of e l e c t r i c a l resistance of Nb and the manner in which the addition of i n t e r s t i t i a l elements affects this relationship. Very low temperature measurements have been made on the tran-sition metals, in the temperature range 0 to 20\u00b0K, but l i t t l e has been reported in the way of detailed work from 20\u00b0K to room temperature. In the case of Nb the temperature range studied was -30\u00b0C to -146\u00b0C, and in the case of V i t was -130\u00b0C to -196\u00b0C. 3 \u2022II. REVIEW OF PREVIOUS WORK A. The E l e c t r i c a l \u2022Resistahce,-.,of Metals. ^ Resistance to the flow of an electric current i s usually regarded as being expressible i n the form of two terms; R = R t-. R i where R \u2014 total resistance Rj. \u2014 resistance due to thermal vibrations R^ \u2014resistance due to impurities The latter term may also be said to be the sum of two termsj \"impurity\" in practice i s any deviation from a perfect l a t t i c e . Thus R, ^ R , + R , 1 phys. chem. where R = resistance due to physical defects p hy s R. \u2014resistance due to chemical impurities chem Therefore \u2022\u2022 ., R \u2014R -*- R -t R 1 0 t phys chem ., This leads to the concept that chemical and e l e c t r i c a l purity are not synonymous as a metal containing very few foreign atoms but having undergone heavy deformation so as to contain a high concentration of vacancies, i n t e r s t i t i a l s and disloca-tions could have a higher r e s i s t i v i t y than the same metal in the annealed condition containing more foreign atoms. The f i r s t term i s due solely to thermal vibrations 4 interfering with electron flow by interaction with the l a t t i c e . Electron - phonon interaction is dependent upon temperature, being approximately proportional to at very low temperature and to T at higher temperatures. Thus at absolute zero there w i l l be no electron-phonon interaction and R \u2014R -r R. phys chem Depending upon the material and the amount of cold work, R would in general be expected to remain constant phys as the temperature decreased below room temperature, the physical defects being frozen into the l a t t i c e . The R chem term arises due to the presence of foreign atoms which also destroy the periodicity of the la t t i c e . In the case of . unworked single crystals R and R w i l l be roughly chem phys of the same magnitude, though this would not be so in a worked metal of high chemical purity where R , would be phys larger. Size and electronic structure play an important part, in.the determining of the magnitude of the effect that the fdreign atom w i l l have upon the r e s i s t i v i t y of the parent metal. Obviously a substitutional atom which i s very much larger or smaller than the parent la t t i c e atom w i l l have a greater disturbing effect upon the periodicity of the l a t t i c e than one that i s of approximately the same size. As would be expected a difference of electronic structure between the l a t t i c e and substitutional atoms also results in a pronounced effect. Cl) Matthiessen's Rule. This states that the contributions to r e s i s t i v i t y resulting from the addition of impurities are temperature i n -dependent i.e. the R vs. T curve retains i t s original slope and shape on the addition of impurity atoms but the position w i l l be elevated. The lower curve i s for a large specimen of a physically perfect\/ chemically pure, ideal metal. Such a specimen R Figure 1 Hypothetical Variation of Resistance R with Temperature at Various Impurity C ont ent s. would have R = 0 so i that at 0\u00b0K, R =0. Upon the addition of impurities the curve i s elevated and at 0\u00b0K where R^  = 0, R = R^  o R at 0 K i s known as the residual r e s i s t i v i t y and. i s due solely to impurities. Larger amounts of impurity continue to increase the residual r e s i s t i v i t y so 6 long as the impurity atoms remain in solid solution. Precipita-tion of a second phase results in a decrease in residual r e s i s t i v i t y . It i s found on closer inspection that R. i s not completely temperature independent but may vary with temperature in certain metals under certain conditions which w i l l be discussed below. In order that Matthiessen's Rule be obeyed two conditions must be f u l f i l l e d : (i) The addition of foreign atoms must not result i n a change in the effective number of free electrons in the metal. ( i i ) Scattering resulting from thermal vibrations of the l a t t i c e must be identical for solvent and foreign atoms.. These requirements are not met exactly but the rule provides a practical working basis for estimating the change in residual r e s i s t i v i t y due to the addition of foreign atoms in most cases. Exceptions are Cr and Co. (2) Resistance at High Temperatures Curves of R vs. T at temperatures above the Debye characteristic temperature usually give an almost linear plot. In the case of Cu, Ag, Au and W.the slope increases with increas-ing temperature. In the case of Pd, Pt, and Ta the slope decreases with increasing temperature. These, i n common with a l l the transition metals, have a relatively high r e s i s t i v i t y which is not due to a lack of s(conduction) electrons but 7 rather to the fact that there are vacant energy levels in the d band. The major part of the resisistivity;-of-transi-tion metals i s due to scattering of electrons from the s to the d. band taking place. It can be shown that the probability of such scatter taking place i s proportional to the density of energy states i n the d band in the energy range kT at the surface of the Fermi distribution. Pd and Pt have almost completely f i l l e d d bands thus the number of available energy levels into which electrons may be scattered decreases rapidly with increasing temperature. W, however, is not explainable on this basis as i t does not possess a nearly f u l l d band. (3) Resistance at Low Temperatures At temperatures well below the Debye temperature only lattice waves of long wavelength can be excited by the current carrying electrons which results in the electrons heing scattered through only small angles i.e. energy transfer i s limited. Theoretical consideration of this state of affairs leads to R being proportional to the f i f t h power of the temperature at very low temperature. In the case of divalent metals where electrons and holes are present, collisions between electrons can change the current, but the effect i s small compared to that due to scattering by la t t i c e waves at ordinary temperatures as both must be in states lying in the energy-range kT at the surface of the Fermi direction both before and after the c o l l i s i o n . Detailed analysis shows that R due to this cause in proportional to T^ and i s only of importance at very low temperatures. m It has been postulated R. \u00b0c T at low temperatures. 8 In the cases of Co, W and Rh, m =3.9, 4.2 and 5*1 respec-ti v e l y , indicating a complex situation. In the cases of Rh and I r there appears to be insufficient overlap in k space of the Fermi surfaces of the s and d electrons for s-d transitions to occur at low temperature, though there i s no discontinuous r e s i s t i v i t y change, which indicates a gradual shrinkage of the surfaces. In discussing the el e c t r i c a l conductivity of the transition metals Mott says that under the influence of latt i c e vibrations the probability that a conduction electron w i l l make a transition i s much greater for i t s passage into the d band than for i t to remain in the s band. Unoccupied d states are responsible for ferromagnetism or high paramagnetism and there i s a direct connection^ between magnetic and e l e c t r i c a l properties. In a magnetic f i e l d at suff i c i e n t l y low temperature the resistance w i l l decrease due to the fact that a l l un-occupied states (\"positive holes\") i n the d shell w i l l have a spin direction anti-parallel to the direction of magnetization which w i l l result in only half the conduction electrons being capable of making the s-d transition i.e. those with the anti-parallel spin direction. Above the Curie temperature a l l conduction electrons can go into the d band and a corresponding increase in R w i l l occur. F i l l i n g of these positive holes occurs when Au i s added to Pd but the resistance increases. Similar Pd - Ag alloys show a decrease in R i f Pd?40$ and hydrogen i s added, 9 thus indicating that electrons from hydrogen are f i l l i n g the holes and that the residual resistance effect of adding protons i s outweighed by the hole plugging, at least i n i t i a l l y . R w i l l start to increase as more hydrogen is added. (4) Effect of Change in Magnetic Properties Temperature (\u00b0C.) Figure 2. Variation of Resistance of Ni with Temperature I shows the observed change of resistance with temperature fdr'Ni.\" An extrapolation of the higher temperature portion of I gives II. Below 300\u00b0C. N i i s no longer paramagnetic. From theory IV would be the expected curve for paramagnetic Ni, which meets the observed curve at 0\u00b0K. Theory predicts III as being the curve for ferromagnetic Ni which coincides with I below about -100\u00b0C. Thus i t is to be expected that changes i n magnetic characteristics with temperature in a metal w i l l affect the R vs. T curve at or in the. region of the same temperature.^ Spin-disorder effects in metals and alloys were 10 discussed by Coles i n which he maintained that i f atoms in the metal possessed localised but randomly oriented spins this would lead to the scatter of conduction electrons resulting in a resistance effect. Thus i t would be expected that temperatures at which magnetic ordering took place would be also associated with anomalies in the R vs. . T curve in those metals with localised spins. This leads him to propose that Matthiessen's Rule i s composed of three terms, R^ , R^ and R due to spin disorder. The contribution from spin disorder should be temperature independent above the' Curie temperature. Klemens discusses the scattering due to extended 13 imperfections ^ using the Hunter and Nabarro method of treating electron scattering by a static strain f i e l d , namely that surrounding a dislocation. Low temperature l a t t i c e thermal conductivity i s limited by the scattering of phonons by electrons which can be used to derive a measure of electron-phonon coupling from experimental thermal conduction measurements. Derived from this i s an expression for the scattering of electrons by dislocations and stacking faults. Klemens derives expressions for the scattering of phonons by dislocations, grain boundaries and stacking faults. Hunter and Nabarro maintain that electrons are scattered only in an inhomogeneous strain f i e l d and i t i s strain rather than displacement which i s the governing factor controlling r e s i s t i v i t y . The expression obtained i s valid only for slowly varying strain f i e l d s . 11 Unfortunately electrons of Fermi energy have wavelengths of the order of the interatomic distance so that much of the scattering emanates from the dislocation core whose physical characteristics are inadequately described. It i s suggested that, as an unsatisfactory state of affairs exists with regard to explaining the fact that the major contribution to the increase in r e s i s t i v i t y upon deforma-tion i s due to point imperfections in some instances and to dislocations in others, when the dislocations are the larger contributor i t i s because stacking faults are formed. As there i s no dilatation associated with a stacking fault, perfectly free electrons cannot be influenced by i t ; results confirm that in noble metals at least, conduction electrons are far from free. B. Previous Work on E l e c t r i c a l Resistance Anomalies A general survey of a l l reported resistance anomalies occuring in metals, with the exception of semi-conductor effects, was undertaken because the mechanisms postulated as being responsible are not necessarily unique to one class of metals. (1) Alkali Metals 15 It was noted that the r e s i s t i v i t y of Na decreased i f the specimen were kept over a period of months, the conclusion being that annealing occurred. Lithium presented no anomalies. A slight anomalous bump of greater than 1\/3$ of t o t a l 12 15 resistance at 10-14\u00b0K was found i n a K'specimen. Testing of o a purer specimen yielded a 1% bump at 13.4 K, which was repeated i n third and fourth specimens. It was suspected i t s presence was due to Na so preparation of a specimen in K glass apparatus was undertaken which yielded no bump on testing from which i t was deduced that the anomaly was caused by very small numbers of impurity atoms. Ce showed anomalies at 4\u00b0 and 6\u00b0K in. one specimen and 15 at 4 and U K in another. If a specimen were cooled relatively slowly to liquid 0^  temperature i t was found that . o on warming a discontinuity occurred at =20 C in the form of a large drop in R. Extremely slow cooling gave a R vs. T o curve with a small bump at -20 C and no anomaly at a l l on heating, although the curve was displaced upwards slightly. However, the discontinuity could be a \"one-shot\" effect, though i t i s explained as an anomalous thermal contraction. The low temperature anomalies are attributed to Na. These small anomalies due to Na, which should merely give a temperature independent effect according to Matthi'essen's Rule, are not explained. 16 MacDonald noted an anomaly in the R vs. T curve of o 17 Rb at 180 K. Hedgcock did further work on this metal after i t had ..been shown a crystallographic change was not respon-sible for the effect. MacDonald had suggested some change in distribution of 5s and 4d electrons resulting in an increased probability of scatter of conduction electrons into the d 0 band at temperatures above 180 K. Any such change should be confirmable by magnetic susceptibility measurements as this 13 quantity i s proportional to the density of states at the Fermi level and a transition should result in an increase in paramagnetism above 180\u00b0K. No such increase i s found. 2+ There is considerable evidence to indicate that small amounts of 0^ can produce a marked change in the properties of Rb and i t i s suggested that 0^ i s also res-ponsible for the resistance anomaly. (2) Rare Earth Metals 25 Gadolinium, Dysprosium and Erbium a l l conform to the spin-disorder model in that a resistance anomaly i s found at the Curie temperature. As temperature decreases and Dy and Er become ferromagnetic small anomalies occur. Immediately below the Neel temperature in Dy and Er the resistance f a l l s less rapidly with temperature. Short range ordering is postulated as being responsible for th i s , though in what manner i s not clear. 25 Later work on Er single crystals was done with the resistance being measured para l l e l to the c axis and parallel to the a axis, Mand Rj\/. A complex magnetic la t t i c e exists above 53\u00b0K in this high.purity material. The two curves behave as shown. y Figure 3 14 Rj_ suffers a small slope change at the Neel point,, while R\\\\ shows a sharp increase, decreasing again at 53.5\u00b0K. Ordering or disordering of spins, or spin modification to another type of antiferromagnetism i s possibly responsible for bringing this about. 18 Annealed La shows an increase in R after being allowed to stand for 90 days due to a crystallographic trans-r formation from f.c.c. to h.c.p. j this transition was inhibited by extrusion of the specimen. Ce has a similar transformation to f.c.c. which i s thought to be a result of an electron shifting OS;-frbm a 4f to a 5d orbit. At approximately 12 K an anomaly-occurs which i s attributed to splitting of the lowest energy level of the ion by the f i e l d of i t s neighbours which results in the redistribution of electrons amongst the states. This becomes more pronounced with successive cycles. It is possible that level s p l i t t i n g may trigger 4f electrons to go to the 5d s h e l l , as this transition makes the transition to the condensed f.c.c. structure more l i k e l y . The onset of ferromagnetism is not ruled but as an explanation.' 18 Praseodymium shows an increase in R on successive 19 runs due to the h.c.p. modification being formed. However other work shows lower R on Later runs. An anomaly in the R curve i s also found in the form of an increase in the rate of f a l l of R with T between 6l\u00b0 and 95\u00b0K which has no corresponding magnetic susceptibility anomaly, although there o i s a broad peak in the specific heat vs. T curve between 60 and 100\u00b0K. Neodymium ^ ^ shows anomalies in the R vs. T 15 corresponding to magnetic transitions. It is concluded that the rare earths are very sensitive to presence of impurities. Rare earths react strongly with negative impurities such as 0, C, N and H and small amounts of these elements are believed to have pronounced effects upon the r e s i s t i v i t y of the solvent l a t t i c e . (3) Transition Metals The R vs. T curve for a recrystallised specimen Cr shows a pronounced cusped minimum at 35 + or - 2\u00b0C which 20 was thought due to an antiferromagnetic transformation Powder determination of the Neel temperature gave a value of 175\u00b0C. As many other metals showed a similar effect at the Neel temperature i t was thought and sub-sequently demonstrated that the internal strains present in the powder grains give the high Neel temperature. ! I ! I \u2022ao\u00b0c ao\u00b0c \\Ao\"c Figure 4 R vs. T for Cr It would be expected that below Tn the loss of spin disorder would reduce the resistance but this i s not the case. 21 0 It has been shown that below Tn 180 spin reversals occur every Ii+ unit cells which constitutes an antiphase arrangement 16 of magnetic spin domains which could cause the observed 2' resistance increase. Small chemically ordered domains From 65 to 35\u00b0C the curve departs from linearity, this being considered due to short range magnetic ordering. A p l a s t i c a l l y deformed specimen follows the broken line curve because, i t is suggested, plastic deformation smears out the Neel temperature. It i s known that Tn varies with hydrostatic stress. When a specimen is pla s t i c a l l y deformed the density of dislocations resulting i s thought to produce the same result, positive and negative pressures being found i n the strain f i e l d of a dislocation gives both increase and decrease i n the Tn value. Mn shows the i n i t i a l increase in R below Tn, then the curve f a l l s steeply probably due to ordering i n the spin system. are known to increase electron scatter. R 1 0 0 150 -Ordering in spin system 80\u00b0K Neel Temperature ~100\u00b0K 1 0 0 zoo 3 0 0 Temperature (\u00b0K) R vs. T curve for Mn 17 The impurity component of resistance for Cu shows a marked increase upon the addition of 2% Zn , but this shows no significant increase on plastic deformation although a large change in dislocation density has taken place. It i s therefore suggested that vanancies may be responsible for the increase in resistance. Bismuth. U N. Thompson found that the e l e c t r i c a l resistance of single crystals of Bi were very sensitive to small amounts of impurity. R was always measured twice at each temperature, the second time with the current reversed and different R values were usually observed due to thermal gradients, which procedure, was found to provide a very sensitive method of detecting the presence of such a gradient. Observations showed that in some cases Bi had a negative temperature coefficient of resistance which was not caused by a change in crystalline state or the precipitation of another phase. Jones explains this by noting that Bi possesses a Brillouin Zone of five electrons per atom so that the con-ductivity i s due to a few vanancies in the Zone and to electrons overlapping into the next Zone. Thus i t would be expected that the addition or removal of a few free electrons would have a pronounced effect upon ele c t r i c a l conductivity. On this basis impurities should have a marked effect upon 18 e l e c t r i c a l properties. Pb would increase the number of holes, Te and Se would increase the electrons, mixing the two would tend to produce a n u l l effect except upon Rchem. It i s suggested that the-addition of Pb or. Sn w i l l result in the. number of overlapping electrons being very small but: that these w i l l increase rapidly with temperature thus produced a negative coefficient in a certain temperature range when the increase in ^eff offsets the increased lat t i c e vibration. Vanadium and Niobium 1. Vanadium There has been reported a considerable amount of work on e l e c t r i c a l r e s i s t i v i t y anomalies in Loomis and 28 Carlson found an anomaly in e l e c t r i c a l conductivity with anomalies in la t t i c e constant, Young's Modulus, internal f r i c t i o n , thermal expansion and intensity of X-ray reflec-tions at similar temperatures. Hren and Wayman^ agreed with the exception of the Young's Modulus anomaly. 19 27 Rostoker,McPherson and Hansen measured the varia-tion of e l e c t r i c a l resistance of V wire of unspecified purity with temperature and obtained the curve below (Figure 6) -so -BO -40 -30 -ZO -to O +IO 420+30 Figure 6 E l e c t r i c a l Resistance versus Temperature for Vanadium. An anomaly of the step type occurs in the region of -30\u00b0C. Magnetic susceptibility experiments gave the curve below for 99-9$ Van Arkel Vanadium of the following composition C H N 0 Fe % .005 .001 .008 .020 .040 20 b v I I l-J I oo t(fo S.OO 3fl<3 Figure 7 Magnetic Susceptibility vs. Temperature for 99 .9$ V. X 3 0 a . r 0 2ifo T ( \u00b0 K ) Figure 7 . 1 Resistance vs. Temperature for 99.9$ V, Room temperature r e s i s t i v i t y was 23 t o r - 1 micron-ohm cm. An absolute accuracy of \u00b15$. was claimed with a very much higher relative accuracy. 26 Rostoker and Yamamata suggest that a l a t t i c e transition from b.c.c. to body centred tetragonal i s 21 responsible for the anomaly, but a l l efforts to find such a phase have failed. 26 Shull and Wilkinson used a neutron diffraction method in an effort to obtain a {lOO} reflection which would indicate magnetic ordering. No such reflection was found, leading to their conclusion that i f magnetic ordering were present the moment was of small magnitude. Cr and Co were added to V separately and 2% of the former or % of the latter resulted in a drop in the anomaly temperature of 15\u00b0C which evidences a magnetic origin for the anomaly, due to the onset of antiferro-magnetism, but this has not thus far been confirmed. With regard to the neutron diffraction evidence, a thermal neutron passes from one electron to another i n about 10\"^ sec, a Fermi electron requires 10\"^ sec; i f , therefore, the antiferromagnetic element i s subjected to -13 a process fluctuating more rapidly than 10 second neutron diffraction w i l l not reveal a (100) peak. Alloying was used by Taylor and Llewyllyn Smith -; i n an effort to explain the anomaly. Carefully prepared specimens from three sources were used for a series of experiments wherein the r e s i s t i v i t y was measured to 1$, the error residing mainly in variations in cross section area as the resistance was measured to ,005\/yU- ohms and the temperature to 1\/10\u00b0C. It was found that the source of material did not greatly affect results, but that the temperature at which 22 the anomaly occurred was dependent on a l l previous thermal and mechanical treatment. Anomaly Temperature 0 % Cr 2k% Figure 8 Variation of anomaly temperature with Cr content. Irregular variation of r e s i s t i v i t y with composition suggests that Nd(E) or ^eff i s responsible. Variation of Nd(E) i s known from magnetic susceptibility measurements and does not appear to be responsible. It is deduced therefore either that N \u201e_ must follow a different fine eff variation with composition, or that alloys cannot be described i n terms of a common conduction band, or that Matthiesson 1s rule i s grossly incorrect in these alloys. Plots of the resistance due to impurity above and below the anomaly temperature have the same form so that the mechanism for the variation of r e s i s t i v i t y with com-position does not appear to be simply related to the anomaly mechanism. If the lack of neutron diffraction peaks i s taken as f i n a l with regard to a density of states explanation, there remains the possi b i l i t y that hydrogen atoms order at the anomaly temperature (-46\u00b0C). There i s no hysteresis effect between heating and cooling and at -46\u00b0C only 23 hydrogen could move with sufficient dispatch to accomplish this. It i s thought the detailed variation of anomaly temperature with Cr content i s not simply related to Nd(E) or N g\u00a3\u00a3 but i s probably partially dependent upon interaction between neighbouring atoms. No.magnetic ordering effects have been found in the earlier members of the f i r s t transition group, in which category V i s found. . Variation of the Hall effect with temperature i s similar to the specific heat curves which suggests that changes in scattering mechanisms rather than N ^ are responsible for the observed temperature dependence of el e c t r i c a l properties. 2. Niobium No reported anomalies of R vs. T curves have been found for Nb. Nb has no discovered magnetic ordering effects and i s similar to V in i t s Hall effect behaviour. 0:. Internal Friction Measurements on Vanadium and Niobium The variation of internal f r i c t i o n with temperature of V containing various amounts of i n t e r s t i t i a l l y dissolved 27 oxygen and nitrogen has been reported . At frequencies of the order of 1 c.p.s. plots of logarithmic decrements of damping vs. temperature exhibit two sharp maxima between 150\u00b0 and 300\u00b0 which were ascribed to the reversible diffusion of 24 i n t e r s t i t i a l species. Changing the oxygen concentration changed the height of the lower temperature peak, whilst the higher temperature peak was similarly affected by changes i n the nitrogen concentration. Vacuum annealing at 1550\u00b0C for four hours substantially reduced the height of the lower temperature peak indicating that oxygen was removed, but no such effect was observed on the higher temperature peak. 29 Stanley and Werts* \u2022 reported that the damping peaks for nitrogen decreased with time, indicating that precipitation was occurring. Marx2^ et a l have carried out ultrasonic testing at 37 and 111 kilocycles on Nb between -160\u00b0C and 1000\u00b0C. Doping with 0 and N was done and peaks corresponding to o these two i n t e r s t i t i a l s noted i n the region of 400 C. Their results led them to the conclusion that the activation energy for the diffusion of 0 and N in Nb and other metals i s not constant with temperature. This could be due to the effective charge of an i n t e r s t i t i a l impurity i.e. i t s degree of ionization, varying with temperature in a transition metal. A change in degree of ionization would produce, a corresponding change in ionic radius of the solute atom which would alter the activation energy of diffusion. Such a change should be detectable by e l e c t r i c a l resistance measurements. 25 III. EXPERIMENTAL A. . Materials 1. High Purity Niobium Rod Centreless ground Nb rod 0 .200\" in diameter was obtained for this investigation from the Wah Chang Corporation. It was supplied in two production lots of comparable impurity content-. \u2022 TABLE 1 Analysis of As-Received Niobium. Element Parts per million C 60 0 55 N 45 H 2 Total 162 The average B.H.N, of the as-received material was 63 . No second phase was found upon metallographic examina-tion. 2 . High -Purity Vanadium Rod The Vanadium used in this investigation was supplied by Union Carbide Company i n the form of .25\" diameter rod the analysis of which i s given below. 26 TABLE II Element C 314 p.p.m. N 259 p.p.m. 0 0.068$ H 8.9 p.p.m. Snowball observed a second phase i n the as-received material which he accepted as being V^ C. 3. Hydrogen Gas Hydrogen was used to dope specimens of Nb. It was of commercial purity but was subject to the action of a \"Deoxo\" catalytic unit to remove oxygen and then passed through s i l i c a gel to ensure the absence of moisture before entering the doping furnace. B. Purification Niobium and Vanadium were both purified in a vertical floating-zone electron bombardment Zone-refiner, the technique of which has been completely described elsewhere^' ^ . Two passes were made on a l l single crystals grown; the drive was set to give a travel rate of 10 cm\/hr. and the _5 vacuum maintained was of the order of 10 mm. of Hg. Table III gives the estimated i n t e r s t i t i a l content of the Nb based on the as-received values and Harding's work\\ .27 material from the same batch being used in both investiga-tions . TABLE III I n t e r s t i t i a l Content of Zone-Refined Nb. Element Parts per Mill i o n C 50 N 30 0 40 H 2 Total. 122 V specimens were analysed by Ledoux and Company after two passes in the zone refiner and the results are given below. TABLE IV In t e r s t i t i a l Content of Zone-Refined V. Element Parts per Million C 136 '.N 318 0 160 H \u20227.2 Total 621 C. Single Crystal Orientation Nb single crystals were grown from a common seed and a l l had an axial direction of O-lOj. 28 Several Laue back reflection x-ray photographs were taken at intervals down a zone-refined rod in order to verify that, in fact, a single crystal had been produced. Such was found to be the case, though some crystals exhibited sub-structure effects in their x-ray photographs. Applying the same process to V i t was found that single crystals were produced of axial orientation approximately 20\u00b0 31 from \u00a3.00l0^:: Several of the V single crystals were radiographed and i t was found that they were highly subject to porosity, gas bursts as large in diameter as 3\/16\" being found. Great care had thus to be exercised in the selection of lengths from which specimens were to be prepared, though i n this type of work the presence of porosity in small amounts i s not of great importance. D. Addition of Hydrogen to Nb This process, referred to hereinafter as \"doping\" was solely applied to Nb and was accomplished by allowing the single crystal specimen to si t at elevated temperature in the presence of the gas, where absorption and diffusion occurred. 1 2 4 Details of the process are described elsewhere 3 9 . Hydrogen, having been purified, i s admitted to a vacuum annealing furnace of the horizontal type with a wheel mounted el e c t r i c a l furnace as the heat source. Flushing of the furnace i s accomplished by pumping down to 10 ^ mm. of Hg, allowing hydrogen to enter the furnace u n t i l atmospheric pressure i s attained whereupon the hydrogen valve is closed and the fore pump connected to remove the hydrogen. 29 This is done three times, ensuring complete flushing. As the hydrogen enters the furnace a pressure s l i g h t l y above that of the atmosphere i s maintained between the gas cylinder and the furnace to avoid contamination of the hydrogen. The specimen, having been previously placed in the furnace tube supported clear of the glass on Mo wire, i s then subject to a temperature of 1000\u00b0C. Varying periods of time were used on different specimens to attain varying hydrogen concentrations in the specimens. The gas reservoir held i t s pressure indefinitely, indicating that hydrogen leakage was of an insignificant quantity. Hydrogen's extremely rapid diffusion removed the necessity for any homogenisation period after doping. The furnace was merely switched off after the prescribed time period had elapsed and slowly rolled back from the specimen, giving a f a i r l y rapid cool. E. Annealing of Niobium Annealing was carried out in the same furnace, the furnace being evacuated to 10\"\"^ mm. of Hg. Unfortunately, the type of glass used in the construc-tion of the furnace has a maximum operating temperature of 1050\u00b0C, which i s marginal for the annealing of Nb. Specimens to be annealed were held at this temperature for 2k hours. F. Specimen Preparation 1. , Machining. In order that a practical value of el e c t r i c a l resistance be obtained from the specimen i t was necessary that i t be much 30 longer than the standard .125\" tensile specimen machined from these single crystals, or of approximately the same length but of smaller diameter. Machining problems were posed by both possibilities but in view of material savings i t was deemed advisable to adopt the latter alternative. Small diameter specimens were able to sustain only very small stresses at right angles to the specimen axis. In order that these stresses be minimised a hook shaped tool was used. The point of the hook was in the machining direction and thus the loading was largely compressive and down the axis of the specimen. A high angle of r e l i e f was ground on the tool bit -approximately 60\u00b0 . To further ease the right, angle load surface speeds as high as compatible with lathe performance were used(24.00 r.p.m. - 7.0 s.ft\/min) together with slow tool travel. Trichloroethylene was used as a lubricant. Lengths 2\" to 2-g\" long were cut from the single crystal using a fine bladed jeweler's saw, they were then centre d r i l l e d and mounted in a lathe. I n i t i a l cuts of .006\" were made, being reduced as the diameter of the specimen decreased so that at .120\" . 0 0 3 \" . cuts were taken, .001\" down to .100\" and .0005\" cuts below . 1 0 0 \" . Some specimens were machined to a diameter less than . 0 9 0 \" . Careful polishing followed with 0 through 0000 emery paper u t i l i s i n g high speed rotation of the specimen in the lathe coupled with light pressure. Both Nb and V specimens were prepared as above except V was found somewhat easier to machine. Because of the geometry of the apparatus the V specimens were shorter in length than 31 the ones of Nb. 2. Surface Preparation, (i) Niobium Following removal from the lathe the specimens were usually electro-polished in a solution of 85$ concentrate sulphuric acid and 15$ hydrofluoric acid (35$ strength). Rotation of the specimen round i t s axis during electropolishing by means of an electric s t i r r e r and rheostat was practiced i n an effort to give uniform removal of the metal. Where only . 0 0 3 \" , the amount necessary to remove machining deformation, was taken from the diameter, no anisotropy was observed. Electro-polishing was used to reduce cross-section area as much as possible - removal of up to . 0 2 0 \" from the diameter being accomplished - but this resulted in the formation of two ridges diametrically opposite one another, giving the cross-section roughly the form of an ellipse. A current density of 1 .15 amps per square inch was used. ( i i ) Vanadium This was electropolished in a solution of 40 cc. of concentrated sulphuric acid, 160 cc. of methyl alcohol and approximately 2 0 drops of.water. Using a current density of about 3 . 5 amps per square inch . 0 0 3 \" was removed from the specimen diameter. 32 G. Resistance Measurements 1. Specimen Mounting (1) Niobium Each end of the specimen was centre d r i l l e d and d r i l l e d and tapped to receive a 2-56 mild steel screw, the head of which was cleaned and a short length of copper wire 1\/32\" in diameter soldered on. Figure 9 The specimen could then be placed in s p l i t grips as shown i n Figure 9\u00b0 This assembly f i t t e d into the test j i g shown in Figure 10 which was bolted onto a Tinius Olsen tensile testing machine, the ends of the copper wires being soldered to the j i g as shown. Insulated potential leads soldered to the loops thus formed led off to the vernier potentiometer. The current in the cir c u i t was led down to the specimen via the d r i l l steel rod and the specimen grips, out at the bottom of the specimen and back up the stainless steel columns which comprised the compressive load bearing members of the j i g and thence through the structure of the Olsen testing machine to the vernier potentiometer. Loading was accomplished by means of the testing machine but was measured by a Detecto spring scale of 400 lb. capacity, this being considered a sufficiently accurate and 33 Potentiometer Leads Dewar Flask LOAD Stirrer Shaft Stainless Steel P i l l a r s Gontra-Pitch Vanes Grips Thermocouple ' ' Specimen Petroleum Ether Figure 10 Experimental Arrangement for Testing Single Crystals of Niobium 34 a more direct method than using the balance beam of the machine. In some of the i n i t i a l tests loads were applied to a given percentage of the yield stress of high purity Nb at the temperature of resistance measurement; in a l l other cases the load was of the order 8-12 lbs and was applied merely to hold the specimen i n position and maintain good e l e c t r i c a l contact. The cooling vehicle was petroleum ether contained in a Dewar flask and agitated by an e l e c t r i c a l l y driven s t i r r e r com-prised of two contra-pitch vanes on a common shaft. This arrange-ment was found to give thermal gradients down the specimen which were so small as to be undetectable by means of the thermocouple employed i n this work. Resistance measurements were made in the temperature range from -30\u00b0C. to - 145\u00b0C ( l l ) Vanadium As lower temperatures were required for this metal in view of previously reported work by Snowball-^, a different experimental set up was necessary where the specimen was not in a liquid bath. It was found that severe thermal gradients resulted in using the Nb j i g and this could be partially alleviated by (a) Reducing heat conduction losses (b) Mounting the specimen horizontally As no load was to be applied to the specimen the tensile testing machine was not required and horizontal mounting presented no problem. A j i g was made up consisting of an insulating board base and two right angles of brass secured to the base in each instance by two screws in a slot so that the distance between 35 Polystyrene Plug Dewar Flask Outer Container Cotton Batting Inner Container Current Leads Potentiometer Leads ^ : v Figure 1JQB. Experimental Arrangement for Testing Single Crystals of Vanadium. 36 the two uprights was adjustable. Each upright contained a slot and countersunk hole into which the shoulder of the specimen f i t t e d . Securing the j i g to the base of the brass container in which i t sat were two screws. This container had brass loops soldered to i t s base and sides to hold i t at a uniform distance, from the walls of the can i n which i t was placed. Cotton batting f i l l e d the space between the two vessels. The whole assembly was placed inside a Dewar flask, permitting liquid nitrogen to surround the outer can. Current entered and l e f t the specimen by means of copper wires soldered to screws, similar to the arrangement used for Nb specimens. Potential leads were, of absolute necessity arising from unavoidable thermal gradients, kept to a maximum of simplicity and a minimum of dissimilar metal contact by taking the form of two turns of fine copper wire twisted t i g h t l y round the specimen. Reduced contact of dissimilar metals was necessitated by the fact that were such contacts permitted indiscriminately, with the thermal gradients involved, sufficient thermoelectric e.m.f. could be generated to give an abnormaly high voltage drop when the current flowed in one direction and a negative voltage drop when the current was reversed. Even with the arrangement as described because of this effect two curves were required on each~ test with the current flowing in opposite directions. A l l leads were insulated e l e c t r i c a l l y . Thermal insulation at the top of the Dewar flask was by means of a tight l y f i t t i n g s p l i t polystyrene plug through which a l l leads, including the thermocouple, emerged via a common hole. 37 2. Measurement of El e c t r i c a l Resistance. This was accomplished by measurement of current and potential drop in the specimen, the current in the circuit being determined by measurement of the f a l l in potential across a standard resistance of 0.100 ohms. Procedure and equipment for resistance measurement were the same for Nb and V. (i) Circuit T o m e l?e\"bl'\"bt-ak\\C\u00a3N rh X Sharvciarct Call To Figure IOC Figures 10C\u00a3arid'5p give a schematic diagram of the experimental arrangement. Reversing switches were incorporated in the battery and standard c e l l connections so that the time delay when the current was reversed in the specimen circuit was reduced to a minimum. The galvanometer used was of the mirror type and was of a sensitivity compatible with that of the vernier potentiometer. Changing connections from the specimen to the standard resistance was done by a switch on the potentiometer. 38 Adjustment of the variable resistance was made in order to give a suitable value of current in the circuit at the outset, this being of sufficiently low value (approximately 6 m.a.) so that no significant heating occurred, ( i i ) Procedure After switching the batteries on and cooling to the required temperature the circuit was l e f t for 15 minutes to come to thermal and el e c t r i c a l equilibrium, after which i t was possible to standardise the battery against the standard c e l l . (a) In the case of Nb, where the procedure was accurate and the cooling slow, as the temperature approached the requisite value the current was measured, then the potential drop down the specimen, after which the temperature was taken again. When the temperature was at the requisite value, the potential drop was checked and recorded provided the standardiza-tion showed an error of no more than one division from zero. Four divisions error in the standardization were required to produce a discernable effect on the reading. From time to time during a run the current would be reversed. The reading thus produced did not, in general, l i e on the curve but the discrep-ancy was small and almost constant. Current values remained vi r t u a l l y constant during a run. (b) Vanadium specimens were cooled more rapidly and in addition two readings were required at each temperature, the second being for the curve with the current reversed. Reversing the current required re-standardization. When, as was frequently the case, cooling was rapid this meant that readings were made continuously and as fast as possible in order to have 39 sufficient points on the curves. 3 . Temperature Control and Measurement, (i) Niobium Petroleum ether was used as the medium and in conjunction with the contrapitch s t i r r e r this gave very stable thermal conditions. Cooling the petroleum ether was performed by liquid nitrogen which was pumped from a vacuum flask by means of a rubber bulb onto the surface of the petroleum ether. When the temperature was being reduced in decrements of the order of 1-2\u00b0C, as was usual, three minutes or less was sufficient for thermal and e l e c t r i c a l equilibrium to be attained in general; this was checked from time to time by allowing longer periods to elapse and noting any change in resistance that might occur. Heating was carried out by permitting the apparatus to stand, or, i f an accelerated rate were required, a copper heat sink was introduced into the petroleum ether. It was found that unstable thermal conditions were obtained when the compressive load bearing members were made from mild steel rod. These were removed and hollow p i l l a r s of stainless steel substituted which reduced heat conduction to a fraction of i t s former value. ( i i ) Vanadium Cooling was by conduction, the specimen being i n a i r . Adding liquid nitrogen to the vacuum flask resulted in a fast i n i t i a l rate of cooling which soon slowed to a reasonably steady rate but subsequently v i r t u a l l y ceased. This was a far from ideal method. A temperature di f f e r e n t i a l of as much as 2-3\u00b0C. 40 existed between ends of the specimen at times. Allowing the apparatus to stand produced an acceptable heating rate which could be accelerated by partial removal of the polystyrene plug from the top of the flask, ( i i i ) Temperature Measurement. In both instances the temperature was measured by means of a copper-constantan thermocouple using a melting ice cold junction. The e.m.f. generated was measured on a Pye port-able potentiometer. Winding the thermocouple around the middle of the specimen was found completely satisfactory. H. Ultrasonic Preparation 1. Specimen Preparation Parallelism i n ultrasonic testing poses a serious mech-anical problem in that very close tolerances are required -.0001\" per inch being stipulated. For a ferromagnetic material which can be held in a magnetic chuck the problem is not serious. Neither Nb nor V is ferromagnetic, however, so an alternative procedure was devised. Five slugs of V, a l l just under 0 . 5 \" in length, were mounted in bakelite. One was placed in the middle with the other four rad i a l l y surrounding i t with their nearest point of approach to the edge of the bakelite mount being 1\/16\" from i t s circum-ference. Thus mounted the specimens were machined in a specially manufactured collet. One side was machined very carefully, the f i n a l cut being .0005\" deep. Reversing the bakelite mount the other face was machined in the same manner. 41 Careful micrometer application showed the high spots. The mounted specimens were then polished on a coarse alumina wheel with the high spots held always furthest from the centre. This subjected the high spots to the increased cutting action of the faster portion of the wheel. This was continued u n t i l parallel faces were obtained to within the limits of accuracy imposed by the micrometer. The slugs were cut from the mould, the saw cuts being so positioned that a part of the slug side was exposed, the rest remaining in the bakelite. Having f i l e d a groove in the bakelite a thermocouple was placed in the groove and secured in such a manner that the junction rested against the slug. 2. Specimen Mounting Ultrasonic testing requires the use of a quartz trans-ducer coupled by some means to the specimen and usually to a brass cylinder 1\" deep and J\" in diameter which transmits the pulse from the generator to the transducer and also receives the reflected pulse back from the transducer, which signal then appears on an oscilloscope screen. This was modified by evaporating a film of copper onto the back of the transducer and soldering a very fine gold wire to this coating. Fisher \"Nonaq\" grease or Dow-Corning High Vacuum grease was used as a couplant and the transducer was wrung on to the V slug. This was placed in a hollow copper cylinder, being held firmly against the grounded base by means of a wad of tissue and a cork in the end of the cylinder. Cotton batting was wrapped around the cylinder and i t was placed in a can which in turn was 42 placed in a Dewar flask and surrounded by liquid nitrogen. 3. Procedure A Sperry ultrasonic amplifier was used which was equipped with a pulse comparator so that when the wave form from the specimen matched the internally generated envelope on the screen the d i a l reading gave a direct measure of the wave attenuation. Cooling was very rapid but adjustment of the pulse com-parator was also rapid so that with assistance to continuously measure the temperature i t was possible to obtain attenuation versus temperature curves. 44 IV EXPERIMENTAL OBSERVATIONS AND RESULTS The variation of electrical resistance with temperature has been observed for high purity single crystals of Nb and V at low temperatures. The effect upon resistance of adding hydrogen to Nb has been noted between =30\u00b0C. and-145\u00b0C. A, High Purity Niobium Specimens 1. Mechanical Polish Only. ._ I n i t i a l testing of the variation of el e c t r i c a l resistance with temperature was carried out on specimens which had been care-f u l l y turned on a lathe and polished down to 0000 emery paper. As resistance i s a bulk property i t was not deemed necessary to - . electropolish them. They thus possessed a thin deformed surface layer, i n a l l probability less than .001\". It was hoped to detect a resistance effect arising from dislocation movement and to this end a stress was applied to the specimen, usually after a test under no load. The load was not constant but was a given percentage of the yield stress at the test temperature, as previously measured^. Figure 11 shows curves 1,2, and 3 for specimen 1. These were obtained after the specimen had been rapidly cooled to -146\u00b0C. As the specimen heated slowly back towards room temp-erature el e c t r i c a l resistance measurements were made. A pronounced anomaly i n the region of -120\u00b0C. occurs i n 1 on the f i r s t test under load (70$ yield stress). Below the anomaly a change in slope occurred. Curve 2 shows a repeat of the test with the direction 46 of current flow reversed. No anomaly is observed and the slope change i s in the opposite direction and of comparable magnitude, thus indicating the slope change to be an extrinsic effect. An overall increase i n resistance is observed in spite of the apparatus having been completely undisturbed between tests. Curve 3 was conducted with the current i n the original direction and with the stress up to 90% of the yield stress. Again an anomaly was observed, but at a slightly higher temper-ature and of smaller magnitude. The slope change was as i n 1 but the overall value of resistance was higher than 1 and 2, indicating that the increase in resistance upon standing i s a genuine effect. Curve 3 commenced to rise quite sharply above -105\u00b0C. and fractured at -100\u00b0C. Figures 12 and 13 relate to specimen No.2 but the tests were conducted during the cooling portion of the cycle i.e. cooling was accomplished slowly and i n a uniform manner below -90 C. Curves 4 to 8 were a l l conducted under no load. Curve 4 showed a pronounced slope change and no anomaly, unless i t was of such size that the limited temperature range of the curve did not reveal i t . Curve 5 also exhibited a slope change of smaller magnitude but accompanied by an anomaly in the region of -110\u00b0C. An anomaly i s also seen on curve 6 but of apparently different character and smaller magnitude. The temperature of occurrence i s 5\u00b0 lower at -115\u00b0C. These anomalies are approx-imately .3% of the t o t a l resistance at the temperature of occur-rence. No slope change occurs in 7 where the current has been reversed; a small anomaly in the form of a b l i p appears. In curve 8 with the current flowing in the original direction and the resistance measured on the heating cycle a very small slope change appears at about -125\u00b0C. Loading to 90$ of the yield stres produced 9 wherein a reverse b l i p appears just prior to fracture as in 3, but no untoward increase in resistance appears unless i t is manifested in the anomaly. Curves 7 and 9 appear to have slope changes at ~80\u00b0C but this may be the usual overall curve of the resistance versus temperature curve. Specimen 2 showed the same overall increase in resistance upon standing as specimen 1, the resistance increasing approx-imately 2$ on standing for 24 hours. The increase on successive days i s of smaller magnitude. 2. Electropolished Specimens' Specimens which had been mechanically polished were electropolished to remove the deformed surface layer. Figure 14 shows R vs. T for specimen 3. This specimen was deformed torsionally quite severely during machining and thus possessed a distorted la t t i c e structure. Curve 10 shows the f i r s t cooling of this specimen. An anomaly occurs in the region of -122\u00b0C which is about .6$ of the to t a l resistance at -120\u00b0C. Subsequently a slope change appears. The heating cycle shows an increase in resistance but no anomaly. Curve 11 shows what appears to be slightly anomalous behaviour from -110\u00b0C to -120\u00b0C. (See enlarged portion of the curve in Figure 15A). There i s no slope change. The curve 52 obtained as the specimen slowly heats showed i n s t a b i l i t y in the region of -120\u00b0C. The anomaly persists in curve 12 (See Figure 15A) but i s now approximately .1% of the t o t a l resistance, as opposed to ,k% i n 10. The heating curve for 12 shows no anomalies of any description and i s only very slightly higher.than the cooling curve. Repeated cooling appears to enable the specimen to approach some form of equilibrium. Specimen 4 was deep machined without being subject to a deep electropolish, as was specimen 3\u00ab X-ray examination did not indicate a deformed layer, but sub-boundaries of 3-4\u00b0 misorienta-tion were present. The single crystal from which this specimen was produced was not of as high a purity as usual due to defective sealing of the zone refining apparatus leading to a poorer vacuum being obtained than was customary. Operation was usually at -6 -5 4-5 x 10 mm. of Hg, in this case i t was 10 mm. of Hg. Experimental d i f f i c u l t i e s were encountered in the testing of specimen 4 so that curve 13 i s the third cooling. Two small blips (approximately were observed at =108\u00b0C. and =116\u00b0C. (See Figure 16A). L i t t l e overall increase in resistance i s observed in the heating cycle but some trace of the cooling anomalies appears to persist. The cooling cycle was accomplished i n two parts on different days, thus i t s v a l i d i t y i s somewhat suspect. Specimen 4 was removed from the apparatus and annealed in a vacuum furnace for 24 hours at 1050\u00b0C. and 5 x 10~^ mm. of Hg after which i t was cooled quite rapidly by ro]ling back the furnace to achieve an a i r cool. F i g u r e 16 E l e c t r i c a l Be.sistance Versus Temperature (Specimen 4) 55 Curve 14 shows the behaviour of the annealed specimen. A very large blip (3%) in the curve appeared in the v i c i n i t y of =133\u00b0C. On repeating the test (15) an overall increase in resis-tance occurred and possible anomalous behaviour in the region of -120\u00b0C. Re-annealing the specimen produced curve 16 which exhibited no slope changes or anomalies. The heating cycle was commenced on the same day but only completed as far as -125\u00b0C, whereupon the specimen stood overnight, heating very slowly to -40\u00b0C. Re-cooling the following day to complete the curve produced apprec-iably higher resistance. The f i r s t part (April 17th.) of the heating curve diverged from the cooling curve, whilst the second part (April 18th.) had a slope very nearly parallel to the cooling curve, again indicating that some sort of equilibrium is being approached as the specimen is l e f t standing. Curves 14, 15 and 16 exhibit a step in the R vs. T curve o in the region of -97 C. similar to that reported by Rostoker et a l 2 7 . Specimen 5 was of exceptionally high purity as the re-built apparatus produced a vacuum of 10~^ mm. of Hg. A possible very small anomaly and a slight slope change at -124\u00b0C were the only departures from linearity. Figure 17 also shows curve 18 which was determined from specimen 6. Specimen 6 was made from the extreme end of a single crystal and i s thus of doubtful purity. Two steps or possibly very long blips were noted at =123\u00b0C. and -133\u00b0C. These were .5 and ,6% increases respectively 58 in t o t a l resistance. Specimen 7 was from the same crystal as specimen 5 and thus very pure. It was, however, heavily deformed during machining. Small twin blips were found in the region of -120\u00b0C. followed by a long b l i p or i t may be the curve i s straight to -128\u00b0C. and then takes a downward step of about . 5 $ . A v i r t u a l l y coincident curve (not shown) but with no anomalies, i s obtained from the heating cycle. Specimen 8 was also of high purity. Testing over a wide range of temperature produced only the previously observed slight slope change in the v i c i n i t y of -90\u00b0C. 3 . Hydrogen Doped Specimens. Hydrogen doping was carried out on the specimen to an estimated content of 3-400 p.p.m. of hydrogen. This produced an increase in resistance at ~120\u00b0C. of 2% approximately. A definite figure cannot be stated as the doping process necessi-tated the removal of the contacts and contact resistance would probably change significantly upon their replacement. Testing this doped specimen produced curve 2 1 . Heating to repeat a cooling range from -40 to -50\u00b0C. produced the effect shown, once more indicating an unstable equilibrium. A pro-nounced slope change at - 7 5\u00b0C is noted. From -101\u00b0C to -126\u00b0C a long reverse b l i p (3%) occurs. The end of this i s seen more clearly in the curve at the right of Figure 19 which is plotted on double scale and also has the heating cycle plotted. A slope change but no other anomalies was noted for the heating cycle. 61 Figure 21 shows the results of repeating the experiment with Specimen 8 a week later. A slope change and small reverse b l i p was noted at -65\u00b0C. This was followed by a loop and discontinuity at -100\u00b0C. The anomalies in the lower section of the curve are shown at the right of Figure 20 on double scale. The one occurring at -120\u00b0C. could be a reverse b l i p or a step and i s 1.1$ of the t o t a l resistance. A step anomaly occurs at -125\u00b0C. The two anomalies are possibly part of a long reverse blip. 4. Summary of Results on Niobium (1) No effect ascribable to dislocation movement was observed. (2) Relatively pronounced anomalies occur in the temperature range -110 to 130\u00b0C. (3) Other anomalies such as steps and slope changes, occur at other temperatures in various specimens but not con-sistently. (4) Pronounced slope changes seem to be associated with a deformed surface layer. (5) Of the specimens exhibiting anomalies in the v i c i n i t y of -120\u00b0C, blips tend to be found in deformed specimens and steps in undeformed specimens. (6) Specimens prepared under high vacuum, which i t is reasonable to suppose would be of high purity, exhibit l i t t l e or no anomalous behaviour. (7) Hydrogen doping produces a long reverse bl i p , or slope change and step. 62 (8) On being allowed to stand after the f i r s t cooling the resistance of the specimen increases. B. High Purity Vanadium Specimens. Electropolished single crystals of vanadium were tested between -130\u00b0 and -200\u00b0C. to determine the variation of elec-t r i c a l resistance with temperature i n this range. Owing to the temperature range employed the specimen was mounted in a i r leading to the presence of thermal gradients. It was thus necessary to measure the e l e c t r i c a l resistance with the current flowing both from right to l e f t and l e f t to right in the specimen. On the curves an arrow pointing upwards denotes a current flow from right to l e f t and a downward pointing arrow from l e f t to right. Curve 23 i n Figure 21 shows the results of cooling from o o o -145 C. to -185 C. Between =165 and -170 C. an apparent slope change i s observed and possibly a b l i p anomaly also. Curve 24 was obtained whilst heating the specimen and no apparent anomaly of any description appeared, though the scatter of points was wider than for the cooling curve. Figure 22 shows curve 25 which owing to mechanical problems was obtained in two parts, the second of which exhibited greater thermal gradient effect. The average curve (broken line) exhibits a slight slope change at -168\u00b0C. Specimen 10 was re-tested over a more comprehensive range, the results of which are shown in Figure 23- Curve 26 was obtained by cooling from -140 to -196\u00b0C. A large b l i p 68 ( 2 . 5 $ of the t o t a l resistance) extending over approximately 10\u00b0 from -162\u00b0C. was observed, which was accompanied by a change of slope. Cooling specimen 10 for the third time (Figure 24) produced no anomaly and a barely detectable slope change. Specimen 11 produced a definite slope change and a large (4$) blip. No doping was attempted on Vanadium. Vanadium thus appears similar to Niobium i n that anomalous behaviour i s encountered to a more marked degree on the f i r s t cooling that on subsequent ones; these effects would probably disappear after 4 or more cycles. The effects are not observed for the heating curves. C. Ultrasonic Testing of High Purity Vanadium. Single crystal slugs of V were tested between -30\u00b0 and -196\u00b0C. using a Sperry Ultrasonic Comparator operating at a frequency of 3*5 megacycles. Two types of couplant were used -Fisher Scientific Co's Nonaq grease and Dow-Corning*s Hi-Vac grease. Figure 26 shows the results obtained using Nonaq. Curve 29 i s the f i r s t cooling and the attenuation reaches a minimum at or about -173\u00b0C. At -196\u00b0C. the curve goes off the scale. Allowing the specimen to heat up produced curve 30 which followed 29 i n form, reaching a minimum at -175\u00b0C. but on extending the temperature range another minimum was observed in the v i c i n i t y of 90\u00b0C. Immediate re-cooling to give curve 31 gave minima about -103\u00b0C. and -176\u00b0C. Thus i t would appear that the cause 69 of the resistance anomaly i s also the cause of the attenua-tion minimum occurring about -170\u00b0C. The fact that another minimum appears above -100\u00b0C. indicates the advisability of extending the temperature range of the resistance measurements on V. The results using Hi-Vac grease were a l i t t l e more ambiguous. The f i r s t cooling of specimen 13 (Figure 2 7 , curve 32) reveals no.minimum in the v i c i n i t y of -100\u00b0C. but. the curve appears to be dropping towards a minimum of -170\u00b0C. when contact was- los t . A second attempt (curve 33) produced a not very distinct minimum about -100\u00b0C. followed by a peak which i s probably not, from i t s appearance, the result of the, in t r i n s i c properties of V. A minimum at -170\u00b0C. i s followed by an increase in attenuation to such an extent that the wave form amplitude had to be re-set. Heating gave no minimum in this region and a very diffuse one at -110\u00b0C. Figure 28 shows the continued work. A third cooling of the same specimen (curve 35) shows a minimum in the v i c i n i t y of -80\u00b0C. and another at -193\u00b0C; the heating which followed (curve 36) showed minima about -165\u00b0C. and -110 oC. Curve 37 was taken immediately, showing a broad minimum at -110\u00b0C and a much sharper one at -170\u00b0C. In general Hi-Vac does not seem to give results of as satisfactory reproducibility as does Nonaq, but both indicate that the physical behaviour which gives rise to the resistance anomaly also affects internal f r i c t i o n and that there is another 72 change of - this nature in the v i c i n i t y of -100 C. which should have been investigated e l e c t r i c a l l y . Repeated cooling and heating do not remove the minima 73 V DISCUSSION A. High Purity Niobium 1. E l e c t r i c a l Resistance Anomalies The experimental results on the variation of e l e c t r i c a l r e s i s t i v i t y of Nb with temperature indicate that some form of anomalous behaviour of this property occurs i n the v i c i n i t y of -120\u00b0C. In non-electropolished specimens having a deformed surface layer i t appears to be a slope change, sometimes assoc-iated with a bl i p (Figures 11,12). In electropolished specimens i t i s a step i n undeformed specimens (Figures 17,18)-' in deformed specimens i t i s a bl i p (Figures 14,15,18). Energy level s p l i t t i n g of electrons and changes i n magnetic ordering which are held accountable for many resistance anomalies would be revealed in magnetic susceptibility versus temperature curves. The uniform behaviour of these plots indicates that the effect does not originate in these phenomena. Hume-Rothery and Coles33 report no antiferromagnetic Curie temperature or antiferromagnetic behaviour of magnetic susceptibility or of specific heat for either Nb or V. Successive runs exhibit smaller anomalies and heating curves rarely show any effect. In view of this and the pre-ceding any change i n electronic structure, energy le v e l splitting or effects involving electrons must be ruled out as the hysteresis involved in such changes with temperature i s neglig-ib l e . Thus i t would appear that some form of equilibrium i s involved. 74 Preparation of the single crystals removes only 0, N and H. Substitutional impurities remain and C i s v i r t u a l l y unaffected i . e . the refining process i s one of out-gassing. Anomaly magnitude appears to be c r i t i c a l l y dependent upon the efficiency of this process. Running the zone-refiner at a higher vacuum than usual results in no anomaly in the curve (Figures 17,19)\u2022 Thus the anomaly appears to be associated with the presence of 0, N and H i n the material. Precipitation of a second phase in Nb of this purity has not been reported. Concentrations orders of magnitude higher are required^* 35, in a n y event, the precipitation of a second phase requires that the resistance decrease, not increase. It i s assumed, therefore, that C, 0, N and H are a l l . i n t e r s t i t i a l l y dissolved. There are two positions that an i n t e r s t i t i a l may adopt in a b . c c . l a t t i c e ; i t may enter The T position i s considerably larger than the 0, but with the possible exception of H considerable l a t t i c e strain i s involved in either. In t e r s t i t i a l s are therefore stress centres in the l a t t i c e and a change of position of i n t e r s t i t i a l s could be responsible for anomalies in the resistance versus temperature curve. . Calculations of the stress arising from the occupancy of a site by an i n t e r s t i t i a l are rendered d i f f i c u l t because: of the impossibility of assigning an exact radius to the inter-s t i t i a l atom ( i f i t is indeed an atom at a l l in l a t t i c e ; this i s open to question)\u201e Barrett-^ gives approximate values of r in Table V. These values are based on half the single bond lengths of the atoms involved. TABLE V G N C H r (kX) 0.74 0.74 0.77 O.46 It has been shown that the scattering of conduction \\ electrons resulting from l a t t i c e distortions surrounding imperfections is an order of magnitude greater than that due to the imperfection i t s elf37. Thus comparatively large effects are to be expected from low concentrations of i n t e r s t i t i a l s i f they are i n positions of high strain energy. Van Bur en ^  gives a method for calculating the stress due to dissolving a substitutional atom in a l a t t i c e which has been modified s l i g h t l y to and applied to i n t e r s t i t i a l l y dissolved impurities. The use of this i s further complicated by the fact that the 0 site i s not spherically symmetrical whilst the T site i s . The. formula gives the hydrostatic stress 1 0~rr arising at a distancerfrom the substitutional atom. Thus the value calculated for the 0 position w i l l be too large. cr - ^ IrgO _i_ ( 1 ) where \"v - Poisson's ratio and g Q \u00bb constant r =\u2022 distance from the stress centre Addition of an i n t e r s t i t i a l brings about a change i n volume given by A v * h. (2) 2G r^r where G =\u2022 Young's modulus In order to find A V i t i s necessary to know the size of.the i n t e r s t i t i a l s i t e . The radius, r , of the largest sphere to f i t i n an 0 site is given by 0.154 R, where R i s the atomic radius of Nb. The distance from the centre of the site to the next nearest neighbours i s given by 0.633 R. T holes are 0.291 R in radius. 0 site 0.154 R = 0.154 x 1.426 = 0.202 kX 0.633 R \u00bb 0.633 x 1.426 * 0.903 kX T site 0.291 R =0.291 x 1.426 - 0.415 kX 1. Stress Arising from the Presence of Interstitials (i) H on 0 sites 771 =\u2022 :\/: :^>r (.46 3 - .2023) = .374 kX 3 A V = S o ^ \u00bb28 6.76 x 106 * ! , 3 6 g 0 =AV x 6.76 x 10 6 x = 1.27 x 1 0 7 \u2022 28 0- = ^28 S \u00b0 1 r r .64 \" ft 73 = 1.78 x 10 6 x i _ ( i i ) H on T sites A V = | t r ( . 46 3 -.383 3) - 17.3 x IO\" 2 kX 3 3o A V x 3.28 x 107 56.74 x 10? \u00b0\"rr = ^ 8 . fo . 1 .64 r 3 = 7.9 x 10 5 x 1 -3 Similar ly ( i i i ) C on 0 Sites ^ 6 1 cTrr * 8.51 x 10 x - 3 r (iv) C on T Sites r 3 c T r r \u00bb 7.76 x IO 6 x 78 (v) 0 and N on 0 Sites 0~rr = 7.62 x 106 x i 3 (vi) 0 and N on T Sites 6 cr = 6.7 x 10 x The maximum value of 0~rr w i l l occur at the minimum value of r which is the radius of the i n t e r s t i t i a l . Thus i t is seen that distortions of high strain energy-are produced. With regard to the distortion on 0 sites, with the next nearest neighbour 0.9^3 kX from the stress centre i t is obvious that even the largest i n t e r s t i t i a l , C, of radius .77 kX, w i l l touch the next nearest neighbours. Thus on 0 sites dis-tortion to a f i r s t approximation is only of one row of atoms along the cube edge. On T sites the distortion i s spherically symmetrical, so that distortion of the 0 site might in fact be more easily accomplished than the distortion of a T site. It might be thought that thermal contraction of the lattice would result i n an increase in stress to such a point that the i n t e r s t i t i a l , i f on an unfavourable site, would move to one of lower strain energy. It.may be seen from Figure 29 that on the hard sphere atomic model there is no energy barrier to prevent an i n t e r s t i t i a l from moving from an 0 site to a T should strain energy render the original site unfavourable. Such a movement would, however, result in a decrease in the size of the stress centre, whereas the anomaly noted i s an increase in resistance. It may be argued that a re-distribution of stress could occur in such a manner as to increase the scattering effect even though the stress i s smaller. It i s possible that a high stress spread over a small area could result in a stress centre which was too small to be an effective scattering agent i f i t were smaller than the wave length of the conduction electrons. However, as i t i s found that dislocation cores scatter very 37 effectively , i n t e r s t i t i a l s in either position should also be capable of scattering conduction electrons as the stress distribution could not be concentrated i n an area less than that of a dislocation core. Bonding i s postulated as being the cause of inter-s t i t i a l movement from one site to another; the movement is such as to increase the strain energy, the increase i n strain energy being offset by a decrease in the energy required for bonding to give a decrease i n t o t a l energy. There i s considerable evidence to indicate that bond-ing occurs between the i n t e r s t i t i a l and the solvent atoms. 33 Hume-Rothery and Coles point out that i t is possible to calculate the size of the holes in a b.c.c. l a t t i c e a v a i l -able for i n t e r s t i t i a l occupation but when i t i s occupied by the i n t e r s t i t i a l bonding w i l l occur altering the effective size of the hole. It i s concluded from this that the more bonding that occurs the larger the size of i n t e r s t i t i a l which can be accommodated without excessive l a t t i c e strain. It is 80 therefore fruitless to place any great emphasis upon the preceding stress calculations other than to give a rough estimate of orders of magnitude. In discussing i n t e r s t i t i a l structures Kiessling39 states that i n t e r s t i t i a l compounds are true compounds stabilized by electron transfer from the i n t e r s t i t i a l to the metal l a t t i c e . The ratio of electron concentration to co-ordination number i s stated to be of fundamental importance in determining la t t i c e structure and that donor capacity increases from 0 to N to C. However, Rundle's^ 0 view of the bonding between inter-s t i t i a l s and metals in the form of compounds MX, where M i s the,metal and X i s H, C, 0 or N, i s that the bonds are very strong, directional and the X component has strong acceptor properties. Internal f r i c t i o n work by Powers and Doyle 40 has shown that in Nb where Zr appears as an impurity, ZrN i s formed as atom couples throughout the l a t t i c e . Hydrogen is rather a unique case and deserves separate consideration. It is generally conceded that H in metals is in the atomic fornM. However, Smith in his \" r i f t \" theory suggests H may be present as protons and Isenberg^ purports to prove thi s . Whether this i s valid or not H is the only i n t e r s t i t i a l to have appreciable mobility in the region of -100\u00b0C. and so i t is necessary to afford i t special attention, and w i l l be treated later. Considering the anomalies in the v i c i n i t y of -120\u00b0C. in electropolished specimens, undeformed specimens show a 81 step with the curve possessing the same slope prior to and after the discontinuity. This behaviour must be the result of an increase i n the number of stress centres or their effectiveness. Precipitation, ordering, or the formation of a new phase would produce a slope change instead of or in addi-tion to a step. Also a change of this nature would be slow to occur at these low temperatures. To account for the change of position to one of higher strain energy an overall decrease i n energy i s envisaged, being due to the change in bond energy. It i s known that in Fe, with a la t t i c e constant of 2.8606 kX the G atom normally i.e. at room temperature, occupies the smaller 0 si t e , producing very great strains. On the other hand, in Mo with a la t t i c e constant of 3.140 kX, the C atoms occupy the T s i t e . With the acceptor tendency of C in mind, i t would seem that 4 electrons are required for each C atom. In the T position one electron would come from each of the four nearest neighbours. Fe i s in a lower energy position with 2 electrons removed - i t s valency being 2 or 3, so that i t is conceivable that even with the lower strain energy this i s not a favourable position. In the 0 site each of the two nearest neighbours loses 2 electrons from the s she l l and in consequence are in lower energy states. As temperature decreases the p bonding orbitals of the i n t e r s t i t i a l s become denser and more directional so that i t i s found that in spite of la t t i c e contraction and the high strains produced the C remains in this position down to room 82 temperature. In the case of Mo, with a valency of 4> no such favour-able bonding exists i n the 0 site, 2 electrons from each of two nearest neighbours, being l i t t l e different from an energy view-point from 4 electrons donated by each of 4 neighbours. Because of strain energy the C w i l l go to the larger site. In the case of Mo, with a valency of 4, no such favourable bonding exists i n the 0 site, 2 electrons from each of two nearest neighbours being l i t t l e different from an energy view-point from 4 electrons donated by each of 4 neighbours. Because of strain energy the C w i l l go to the larger s i t e . In the case of Mb, with one 5 S electron, the T position i s definitely favoured for C from strain energy and bonding considerations, removing one outer electron from each of the four tetrahedral atoms. Thus C in Nb w i l l tend to occupy T sites and stay i n them. Oxygen has 6 outer electrons in i t s sh e l l and therefore w i l l require 2 more. At room temperature and above there w i l l be a s t a t i s t i c a l distribution of 0 between 0 and T sites as one electron from each 0 nearest neighbour i s desirable from, a bonding viewpoint but the lesser strain energy of the larger T site offsets this. On cooling down below room temperatures some 0 w i l l be on T sites and w i l l remain there as 0 has lost i t s mobility at room temperature. As cooling progresses and the bonds become more directional the 0 atoms w i l l reach a point where the higher bond energies involved offset the elastic strain energy and i n spite of the la t t i c e having con-tracted they w i l l be pulled into an 0 s i t e . It i s found that 83 repeated cooling produces steps of smaller magnitude at sli g h t l y lower temperatures e.g. -115, -117, -116.5\u00b0C. This indicates that were the specimen held at the step temperature for a longer period of time than was usually the case under test conditions a larger step would result. In some cases the steps are quite gradual which bears this out. Eventually after several cycles steps no longer tend to occur as a l l inter-s t i t i a l s have l e f t the unfavourable sites. Steps do occur on heating, but are of smaller magnitude and at higher temperatures indicating elastic strain energy does force some r e v e r s i b i l i t y in the process. N has 5 outer electrons and thus w i l l require 3 more. Because of the symmetry and the directional properties of the metallic bond i t i s probably energetically favourable to obtain these electrons in the form of cbvalent bonding with, the 6 octahedral atoms. The manner of functioning of the bonding mechanism i s tentative. Were the i n t e r s t i t i a l s to behave as acceptors a modified picture would result. It is quite conceivable that the i n t e r s t i t i a l s could move from 0 to T at the anomaly-temperature and that this could lead to a greater scattering of conduction electrons resulting from the spherical symmetry of the T site requiring more strain energy to accommodate an i n t e r s t i t i a l that the asymmetrical 0 site. Until more informa-tion i s obtained with regard to the positions adopted by i n t e r s t i t i a l s in b.c.c. l a t t i c e this must remain a moot point. The foregoing leads to the basic hypothesis that some 84 form of non-equilibrium distribution of i n t e r s t i t i a l s i s obtained in Nb when i t i s cooled f a i r l y rapidly from high temperature. Cycling between room temperature and low temperature gradually removes the anomalies as a psuedo equilibrium i s attained by. atoms on unfavourable sites moving to favourable ones due to the nature of the bond between the i n t e r s t i t i a l and the l a t t i c e . Marx finds a change i n activation energy of diffusion of 0 and N i n Nb. This could be attributed to a change in bonding. It i s noted (Figure 16) that an anneal followed by a rapid cool (at a greater rate than was obtained in the zone refiner) produced the largest anomaly. Re-annealing followed by a slow furnace cool produced no anomaly, but this could have been due to i n t e r s t i t i a l loss during annealing. Experimental work thus seems to indicate that inter-s t i t i a l s are frozen into non-equilibrium positions. Further support of this is lent by the formation of loops when.the cool-ing curves are interrupted or reversed (Figures 14 and 20). Deformed specimens which exhibit an anomaly do so i n the form of a b l i p (Curves 1,3,7,10 and 12). It i s thought that this i s a step i n i t i a l l y but that the vacancies present in the specimen as a consequence of the deformation suffered may migrate into the v i c i n i t y of the i n t e r s t i t i a l s and thus relieve some of the stress associated with the new position. The magnitude of the blips seem to be larger than the steps when the specimens are of the same general level of purity. This could be due to deformation causing more i n t e r s t i t i a l s to go to the lower strain energy sites so that upon reaching the anomaly temperature more i n t e r s t i t i a l s are moved to the higher 85 strain energy positions, or i t could be due to the bonding forces removing i n t e r s t i t i a l s from the close proximity of vacancies with which they are associated, giving a larger increase in strain energy than would occur were vacancies absent. The vacancies quickly re-arrange themselves to again provide stress r e l i e f and i n so doing change the step into a blip. It has been noted that in some instances a step denot-ing a decrease in strain energy occurs (Figures 16 and 19). This suggests stress r e l i e f by an i n t e r s t i t i a l changing i t s position under the influence of thermally engendered stress. 2. Increase in Resistance during the Heating Cycle and on Standing at Room Temperature. R T Figure 30 Typical Cooling and Heating Curves for Nb. Because of the method employed of measuring the potential drop down the specimen there i s a possi b i l i t y that the effect i s due to poor contact result-ing from the variation in thermal expansion of the mild steel screws and the Nb.. If this be the case, on reheating back to the starting point the resistance should return to the original value as the screws cannot turn and loosen mechanically owing to the wire soldered to the screw 86 head. The increase i n resistance commences as soon as the specimen i s on the heating portion of the cycle. This i s due to hysteresis in the T \u2014*-0 transition. If the heating i s carried out quickly the slope w i l l continue with i t s increased value through the test range. Slower heating gives a curve which decreases i t s slope at some point. Above this point the heating curve remains pa r a l l e l to the cooling curve. On even slower heating the stable slope value, par a l l e l to the cooling curve, appears at a lower temperature. On second cooling the effect i s very much smaller but i s usually present. A third cooling may produce l i t t l e or no increase i n resistance on heating. On standing at room temperature an increase in resistance i s observed, the rate of increase of which becomes progressively smaller. This and the above is thought to be due to the inter-s t i t i a l s approaching equilibrium i n their distribution. Cool-ing to -140\u00b0C. has the effect of changing the s t a t i s t i c a l distribution of i n t e r s t i t i a l s on 0 and T sites. By the laws of probability some i n t e r s t i t i a l on 0 sites w i l l not have received sufficient heat energy to break the bonds holding them to the 0 sites and so w i l l remain there. The effect i s dependent upon impurity content, very pure specimens which show l i t t l e or no anomaly also show almost identical heating and cooling curves. Normal specimens show increases of up to 2-3$ of the total resistance on standing. Hydrogen doped specimens show increases up to 25$. Specimen 3 Nov 3rd to Nov 7th Nov 7th to Nov 9th R inc. 3.0$ R inc. 0.8$ 8? R at cl20\u00b0Co 1.955 ohm 2.465 \" 2.865 \" It i s possible that precipitation on a micro scale or ordering of a certain type could increase the resistance. A study of the ordering processes in Cu^ Au has shown that during the i n i t i a l stages of ordering e l e c t r i c a l resistance does increase. Small unstable ordered regions-\"embryos\" are formed. It i s l i k e l y that stable neighbouring embryos are antiphase. Sykes and Jones44 show that the presence of antiphase domains i n a crystal destroys i t s homogeneity. When the domains are of a size comparable with the mean free path of conduction electrons, scattering w i l l result. When the domains are sufficiently small the r e s i s t i v i t y is the same as for a com-pletely disordered material. Small embryos i n i t i a l l y present act as scattering centres. Nuclei of high order increase the inhomogeneity and thus increase r e s i s t i v i t y . Subsequent nuclear growth removes disordered material and decreases the r e s i s t i v i t y . Nuclei are progressively smaller and their density in the metal larger as the temperature decreases. It has also been proposed that a limitation of electron mean free path by internal boundaries could occur which would cause an increase in resistance. These boundaries are grain, mosaic or dislocation boundaries. Seraphim46 has reported the formation of a super-Lattice Specimen 8 September 6th \" \" \" H doped \" 11th \" \u00bb \" \" \" \" 12th 88 of N i n Ta at a concentration of 65 p.p.m. At this low con-centration to be meaningful the super-lattice would have to consist of domains of ordering. They would be antiphase in a l l probability and increase e l e c t r i c a l resistance. Thus the increase in resistance could be due to either an increase in strain energy due to the i n t e r s t i t i a l movement or to small domains of local order formed which reduce the l a t t i c e regularity. Micro-precipitation or coupling of the type Zr - N are other alternatives which could also be considered. Before any mechanism could be chosen more work would be necessary. B. Vanadium The work done on V did not give results of comparable accuracy to those obtained from Nb. The method of testing was such as to give curves of differing slopes and positions with changing direction of current flow. An average of these provided an approximation to a curve representative of the true e l e c t r i c a l properties of the material. From this i t appeared that blips similar to those in Nb were found. Certainly a definite change in slope occurred'. The magnitude of the slope change decreased with the number of cycles to which the specimen was subjected, also similar to the behaviour in Nb with regard to the change of position of the inter-s t i t i a l u n t i l some pseudo equilibrium i s obtained. However, within the rather poor relative accuracy attained in this work there did not appear to be any increase in the resistance on standing. With regard to the previously reported anomaly in the \/ 89 o 23 28 v i c i n i t y of -30 to -50 C , i t would appear that this i s accompanied by similar anomalies in other properties, mech-anical and e l e c t r i c a l , so that a second phase being precipitated i s a possible explanation. The variation in temperature of the reported anomaly could be caused by varying purities, though i t i s unlikely this could be lowered to -170\u00b0G as the anomaly was reported at -46\u00b0C for electron beam refined material. No other reported magnetic susceptibility anomalies have been found. As the anomaly i s , or is accompanied by, a slope change, some change in l a t t i c e structure is to be held accountable. The slope change indicates an increased resistance and precipita-tion would cause a decrease. However, the previously mentioned arguments for Nb with regard to the increase i n resistance on standing apply equally well here, noting that the lower the temperature the more nuclei there are and the smaller in size. The change of slope indicates continuous formation of these nuclei. Some re v e r s i b i l i t y is indicated in that Snowball obtained the effect on heating. As with Nb, an equilibrium i s attained after 3 or more cycles. Unfortunately the effect of H doping was not investi-gated. The p o s s i b i l i t y that the slope change i s due to change of i n t e r s t i t i a l site i s an unlikely one in that a continuous change of site over a temperature range of at least 25\u00b0C would be required and there i s no obvious reason why this should occur. Precipitation appears to be a reasonable supposition in vanadium as i t has a higher impurity content than the Nb. 3 Snowball observed what he believed to be V C in the as received 90 vanadium at an analysis of 314 p.p.m. In the purified condi-tion 136 p.p.m. of C were found; thus i t is not inconceivable that V2C precipitate. Stanley and Werts29 reported that the damping peaks in vanadium ascribed to N decreased i n height with time, which they took to indicate precipitation. This could also be . explained by the N atoms taking up more stable positions i n the l a t t i c e as the peak could be due only to N atoms on certain sites. White and Woods^7 did work on many transition metals and found a slope change for vanadium at about -73\u00b0C which they feel may be due to the presence of oxygen. In recent work on i t was noted that 10 p.p.m. oL H caused embrittlement in the v i c i n i t y of -100\u00b0C. This could be linked with the attenuation minimum at this temperature. Ih doping with 0 i t was found the yield load on bend tests was proportional to temperature down to about -170\u00b0C, after which i t became invariant with temperature. This was true for con-centrations of 0 from 150 to 3100 p.p.m. This suggests again that there may be some connection between the slope change and the position of the i n t e r s t i t i a l on the l a t t i c e . This investigation on vanadium suffered from too small a temperature range of testing. Ultrasonic testing revealed two minima in the attenuation vs. temperature curve, one in v i c i n i t y of -170\u00b0C and one in v i c i n i t y of -100\u00b0C. As a slope change occurs at -170\u00b0C i t would have been of interest to determine whether one also was to be found at -100\u00b0C. Changes in the depths of these minima did occur but 91 owing to the limited time available i t was not possible to attain sufficient proficiency in the technique for even qualitative comparisons to be made. It i s of interest to note that the slope change noted by previous workers i s an increase in slope, this investigation reports a decrease in slope at a lower temperature. Combined, the two would give a long and large reverse b l i p of the type reported i n H doped Nb and to be discussed in the next section. Its size could be readily explained by the much higher inter-s t i t i a l content present in Nb. C. The Hydrogen Anomaly i n Nb. Hydrogen i s unique among the i n t e r s t i t i a l s i n that i t retains i t s mobility down to very low temperatures. This i s due in part to i t s small size but also the fact that i t does not bond as the other i n t e r s t i t i a l s do. Both Nb and V are exothermic occluders forming psuedo-metallic hydrides. In the concentrations involved i n the high purity specimen H will,be in solid solution. In the doped specimens H w i l l s t i l l be in solution but a portion of i t may be in the form of a psuedo-hydride which may be regarded as a loosely bonded compound. H on 0 and T sites w i l l be subject to stress, though at room temperature i t i s doubtful i f those H atoms on T sites w i l l be greatly stressed. As the specimen i s cooled. H, which w i l l diffuse i n any case, i s losing thermal energy but gaining stress energy. As the temperature i s approached at which H undergoes the 0 to T transition, some atoms w i l l make the tran-sit i o n at a higher temperature due to having acquired sufficient 92 thermal energy. This gives stress r e l i e f and an attendant lowering of resistance. Thus i t is found that the anomaly commences below about -100\u00b0C. and continues down to below -120\u00b0C. In this range the resistance is f a l l i n g steadily to a maximum of about 1% below the extrapolated to the temperature. This may occur because H on T sites has commenced to strain the l a t t i c e . While the T site i s larger, i t i s also spherically symmetrical and there are four atoms to be strained instead of two in the 0 site so the value of R riBes quickly. Heating does not show the effect. This increase in R is more probably due to the previously noted step occuring due to other i n t e r s t i t i a l s making the T-*\"0 transition which occurs in this region. D. Correspondence of Mechanical and Thermal Strain It was noted the difference i n temperature that the anomalies occurred in the yield point resistance curves could be possibly accounted for by corresponding thermal and mechanical strains. 1. Vanadium Yield Point anomaly - -125\u00b0C. Resistance anomaly - -170\u00b0C. The hypothesis i s that the effects occur each time at  equivalent strains. 93 Mechanical: H e l d Point stress At r i g h t angles to axis Y i e l d Point stress Strain = 6.5 x 104 p . s . i . 6.5 x 1CT x .36 N4 6.5 x .36 x 10 1.9 x 10 7 12.3 x 10-4 Thermal: oL * 7 x IO\" 6 inch\/inch\/\u00b0C. A T = 45\u00b0C . . \u2022 \u2022 Strain = 7 x IO\" 6 x 45 3.15 x 10-4 Temperature would also be expected to have an effect -at the higher temperature less s t r a i n would be expected to affect the t r a n s i t i o n as greater thermal energy i s available. However, the higher temperature anomaly i s the mechanical one where the st r a i n i s approximately four times the thermal s t r a i n . 2. Niobium Mechanical: Y i e l d Point stress Young's Modulus Stra i n = 4.2 x 10 p . s . i . 7 = 1.85 x 10' p . s . i . - 4.2 x 10 4 x .33 1.85 x 10? = 1.4 x 10-3 1.85 =* 7.55 x 10 -4 Thermal: oC = 6.9 x IO\" 6 inch\/inch\/\u00b0C. Strain = 1.38 x 10\"^ 94 The difference could be explained by a decrease i n com-p r e s s i b i l i t y of the atoms as.the temperature decreases. This correspondence i s possibly of significance but the discrepancy appears rather too large to be tolerated. E. Hydrogen Embrittlement Recent work by Baldwin and Adenis^ upon the effect of H on pure Fe has shown that when Fe containing H i s quenched from the austenitic region i t i s subject to time dependent fracture. When H was i n the state to produce t h i s effect i t was termed \"noxious\". In the absence of H (less than 1 p.p*m.) or when a H containing specimen had been slow furnace cooled no such effect was observed. H af t e r the slow furnace cool was said to be innocuous. A d u c t i l e to b r i t t l e to du c t i l e t r a n s i -t i o n was obtained with H i n the noxious state. -2.00 -\\0O 0 7-00 T (\u00b0C) Figure 31. Percentage Reduction i n Area versus Temperature for Fe containing H i n the Two States. 95 After quenching H into position an anneal of one hour at 315\u00b0C was sufficient to render the H innocuous. Rapid fracture of Fe containing noxious H produced the same strength as Fe containing no H. Slow testing i n a tensile machine of the same material produced a reduction i n area of only 27$ whereas H free Fe had a value of 61.5$ under the same circumstances. This suggests the H i s quenched onto 0 sites and occupies only T sites when allowed to come to equilibrium. The internal stresses arising from H occupying 0 sites results i n hydrogen embrittlement. H doped Nb shows exactly the same behaviour, as does V. The b r i t t l e area shows an increase in yield stress corresponding to decrease in d u c t i l i t y . H present on 0 sites, straining the l a t t i c e , would undoubtedly increase the yield stress and decrease the du c t i l i t y . As i t leaves the 0 sites and occupies the larger T sites an increase i n d u c t i l i t y and decrease i n strength would come about. To explain time dependent fracture on this model the diffusion of H must be invoked, particularly since the process occuring during annealing has an activation energy close to that of H diffusion in Fe. Baldwin and Adenis propose the mechanism of Zapffe and Sims50, or of Petch* 1. The formation of voids near the fracture surface seems to bear this out, but i t is not explained whey they only occur there; on the mechanism of Zapffe and Sims one would expect voids throughout the specimen. On the H leaving 0 sites mechanism i t i s proposed that 96 as the lattice undergoes thermal contraction there w i l l come a point when the H becomes unstable in the 0 site and vacates i t . It may then seek a T site or a dislocation array or some type of lattice imperfection. In the latter cases the presence of H is sufficient to cause microcracking. As the crack enlarges more H w i l l find low energy accommodation in i t and lead to increased cracking. This may be accomplished in the manner pro-posed by Petch. H on T sites, where the in ters t i t ia l is under less strain and is symmetrically surrounded by lattice atoms, is under less pressure to move and tends to remain where i t i s . When a stress is applied to a b.c.c. metal containing H in the 0 sites stress activated diffusion w i l l cause H movement to occur at higher temperatures and to move faster. Also micro-cracks w i l l enlarge and be more numerous so that the H w i l l have a shorter distance to cover before helping to initiate the spread of the crack. If the deformation is accomplished suf-ficiently rapidly H w i l l not have time to diffuse to the micro-crack areas and thus a ductile fracture w i l l occur. As H diffuses towards the cracks and becomes absorbed therein there w i l l be left in the lattice regions of metal com-paratively free of H which w i l l deform plastically as the cracks open on failure of the specimen. In this manner the voids found in the fracture region are formed. Although H w i l l diffuse to microcracks in regions away from the fracture the vigorous deformation accompanying fracture is required to pull the cracks into voids. 97 F. Application to the Results of Harding on High P u r i t y  and Doped Single Crystals of Niobium 4 1. High P u r i t y Single Crystals of Nb. These showed an anomaly i n the y i e l d stress versus temperature curve at about -105\u00b0C which indicate an increase i n strength of the material. This i s considered due t o the i n t e r -s t i t i a l s 0 and N making the T -\u00bb0 t r a n s i t i o n i n t h i s v i c i n i t y and the re s u l t i n g increase i n the associated stress centre providing greater d i s l o c a t i o n locking. D u c t i l i t y versus temperature curves do not show any appreciable effect at these low concentrations of i n t e r s t i t i a l s . 2. Hydrogen Doped Specimens. These exhibited a y i e l d stress anomaly around -120\u00b0C, again due to 0 and N. The temperature i s lowered because of interference with the T -*-0 t r a n s i t i o n from H already present on 0 s i t e s . -P z i o o r TEMPEPATUR& C\u00b0C) T E M \u00ab ? E R * T U R * ( \u00b0 C ) .. Figure 32. Recovery of Figure 33. Resistance vs. D u c t i l i t y of H Temperature for doped Nb at Low . N doped Nb. Temperatures. 98 The recovery of d u c t i l i t y demonstrated by H doped material i s due to thermal contraction and probably stress i n -ducing H to leave 0 sites. The R. vs. T. curve for H doped Nb (Figure 33) shows stress r e l i e f beginning about -100\u00b0C, at which temperature recovery of d u c t i l i t y commences and continues to -17p\u00b0C. when presumably a l l , or nearly a l l , H has l e f t the 0 sites and the curve follows the form which i t would possess were no H present. 3. Oxygen Doped Specimens The yield stress anomaly occurs at -110\u00b0C for 800 and 2000 p.p.m. 0, and at 2000 p.p.m. of 0 a d u c t i l i t y minimum occurs at -140\u00b0C. This indicates that strain energies at this high concentration of 0 are so great that the bond energy i s over-come and some 0 leaves the 0 si t e . Alternatively, at the high lat t i c e strains involved precipitation may occur. At 800 p.p.m. the % Reduction in Area commences to decrease sharply at -100\u00b0C. At lower concentrations this would occur at lower temperatures, say about -110\u00b0 to -120\u00b0C, indicating the 0 anomaly should occur hereabouts. 4. Nitrogen Doped Specimens The yield stress anomaly occurs at -110\u00b0C for 70 and 85 p.p.m. of N. In both instances d u c t i l i t y f a l l s off at -100\u00b0 o to -110 C. This implies that the higher temperature step or bl i p i s due to N and lower to 0. Harding also reported that on quickly warming a specimen from l i q u i d N? temperature to -146\u00b0C and allowing thermal 99 equilibrium to be established a yield stress value 1% higher than was usual was obtained. This is thought due to the fact that always there i s a s t a t i s t i c a l distribution of inter-s t i t i a l s between 0 and T sites. The rapid heating disturbed the equilibrium and some i n t e r s t i t i a l s are l e f t on 0 sites which would occupy T sites at equilibrium. The resulting hardening effect increases the strength of the material. 100 VI CONCLUSIONS 1. No effect attributable to dislocation movement was found in measurements of e l e c t r i c a l resistance. 2. Anomalies in the region of -120\u00b0C were found which were ascribed to 0 and N; the anomalies were indicative of an increase in resistance. 3. Anomalies were found in cooling curves, rarely in heating curves and tended to decrease in magnitude on cycling, indicating some sort of equilibrium was concerned. 4. Hydrogen doping showed hydrogen to behave d i f f e r -ently, producing anomalous behaviour commencing at about -100\u00b0C and indicating a decrease in resistance occurred. 5. The mechanism proposed concerned the occupancy of the two available i n t e r s t i t i a l sites, 0 and T, by oxygen, nitrogen and hydrogen. The mechanism was capable of explaining the mechanical phenomena of hydrogen embrittlement, time dependent fracture, low temperature recovery of d u c t i l i t y and the yield stress anomaly. 6. An increase i n resistance occurred on the heating portion of the cycle and when the specimen was l e f t to stand overnight. This could have been due to the T-*-0 mechanism or to others such as micro-precipitation or small domains of high order. 7. High purity single crystals of vanadium exhibited a change in slope i n the e l e c t r i c a l resistance versus:-; r curve 101 temperature curve at -170\u00b0C and was more in evidence on cooling rather than on heating. The effect was not -explainable on the basis of this investigation. 8. Ultrasonic testing of single crystals of high purity vanadium showed minima in the attenuation curves in the v i c i n i t y of -100\u00b0C and -170\u00b0C. 102 VII RECOMMENDATIONS FOR FUTURE WORK It i s f e l t that this work should be repeated measuring r e s i s t i v i t y rather than resistance; an extended temperature o range would also be advantageous - below -140 C for Nb and above -100\u00b0C for V. The effect of doping with oxygen, nitrogen and carbon should be determined, including measurement of residual resistance. Extended work in the ultrasonic f i e l d i s also recommended, particularly as i t could be put on a quantitative basis. Other b.c.c. metals tested in this manner would provide valuable comparative data. 103 VIII BIBLIOGRAPHY 1. Fraser, R.W., M.A.Sc. Thesis submitted in the Department of Mining and Metallurgy, University of B.C., November I960. 2. Lawson, V.B., M.A.Sc. Thesis submitted in the; Department of Mining and Metallurgy, University of B.C., A p r i l 1961. 3. Snowball, R.F., M.A.Sc. Thesis submitted in the Department of Mining and Metallurgy, University of B.C., October i960. 4. Harding, H.J., M.A.Sc. Thesis submitted in the Department of Mining and Metallurgy, University of B.C., September 1961. 5. Loomis, B.A., Carlson, O.JN. Iowa State College Report ISC - 1037 (1958) (unpublished). 6. Hren, J.A., and Wayman, CM. Trans. A.I.M.M.E. 218 (I960) 377. 7. White, G.K., Woods, S.B. P h i l . Trans. Roy Soc. (London) 251 (1959) 273. 8. Rostoker, W., and Yamamoto, A.S. Trans. A.S.M. 4J, (1955) 1002. 9. Burger, J.P., Taylor, M.A. Phys. Rev. Letters 6, (196i) 185. 10. Mott, N.F., Jones H., \"The Theory of the Properties of Metals and Alloys\", Dover Publications Inc., 1958. 11. Mott, N.F., Proc. Roy. Soc. A 15J5 (1936) 699. 12. Coles, B.R. Advances in Physics 2 (1958) 40. 13. Klemens, P.G. Can. J. of Phys. 3j> (1957) 441. 14. Thompson, N., Proc. Roy. Soc. A 15J5 (1936) 111. 15. MacDonald, D.K.C., Mendelssohn, K., Proc. Roy. Soc. A 202 (1950) 103. 16. MacDonald, D.K.C., P h i l . Mag 41 (1952) 479. 17. . Hedgcock, F.T., Can. J. of Phys. 3Jt (1956) II64. 18. James, N.R., Segvold, S., Spedding, F.H., Phys. Rev. 121 (1961) 1637. 19. Alsted, J.K., Colvin, R.V., Segvold, S., Spedding, F.H., Phys. Rev. 121 (1961) 1637-20. Dugdale, J.S., J. App. Phys. (U.S.A.) 32. (1961) 1238 21. Corliss et a l . Phys. Rev. Letters 3_ (1959) 211. 22. Burns, F.L., Quimby, S.L., Phys. Rev. 9_Z (1955) 1567-104. 23. Kemp et a l . Acta Met. 5_ (1957) 303. 24. Dauphines et a l . Proc Roy. Soc. A233 (1955) 214-25. Legvold et a l . Rev. of Mod. Phys. 25 (1953) 129. 26. Green et a l . Phys. Rev. 122 No.3 (1961) 827. 27. Rostoker, W. \"'The Metallurgy of Vanadium*. John Wiley (1958) 81. 28. Taylor, M.A. Llewyllyn Smith, CH. Physica 28 (1962) 453. 29. Marx, J.W., Baker, G,S,m Sivertsen, J.M. Acta Mer. 1 (1953) 193. 30. Chester, G,V,;! Adv, in Phys, 9-10 0960-61 ) 357. 31. Simpson, L. Private Communication, Department of Mining University of B.C., 32. MacDonald, D.K.C., Phil. Mag. \u00a32 (1951) 756. 33. Hume-Rothery, W., Coles, B.R., Adv. in Phys. (1954) 356. 34. Albrecht, W.M. et a l . Electrochem. Soc. J. 106 (1959) 981. 35. Eustice, A.L., Carlson, O.N. Met. Soc. A.I.M.E. Trans. 221. (1961) 876,;' 36. Barett, C.S., \"'Structure of Metals\", McGraw-Hill Publishing Co., (1952) 271. 37. Overhauser, K.S., Gorman, S., Phys. Rev. 102 (1956) 676. 38. Van Buren \"Imperfections in Crystalline Solids\", Van Norstand Inc. (1960) 89. 39. Kiessling, R., Powder Metallurgy 3 (1959) 177. 40. Kamber, K., Keefer, D., Wert, C.A., Aeronautical Research Laboratory Tech. Note 60-112 p.2. 41. Smith, D.P., \"Hydrogen in Metals\"', University of Chicago Press, (1948). 42. Isenberg, I., Phys. Rev. 79 (1950) 736. 43. Burns, F.P., Quimby, S.L. Phys. Rev. 97 (1959) 1567. 44. Sykes, J.P., Jones,F., Proc. Roy. Soc. A 166 (1938) 376. 45. MacDonald, D.K.C., Phil. Mag. 42 (1951) 756. 46. Seraphim D.P., Private Communication, I.B.M. Research Center, Poughke e ps ie, N.Y. 47. White, G.K. Woods, S.B., Proc. Roy. Soc. Phil. Trans. 251. (1959) 273. 105 48. Berlincourt, Ted G., Phys. Rev. 1J\u00b1 (1959) 969-49. Baldwin, W.M., Adenls, D.J.-P., Trans. A.S.M. 5Jt (196l) 381. 50. Zapffe and Sims, Trans. A.I.M.M.E. 1ZJL (1941) 225. 51. Petch, N.J., Stables, P., Nature 16j9_ (1952). 106 IX. APPENDIX 107 APPENDIX I Change In Resistance of Specimen due to Thermal Contraction Nb - Specimen 8 Length = 1.304\" Radius = .0475\" \u00b0^ = 7-1 x 10\"6\/\u00b0C Temperature drop -90 to -145\u00b0C = 55\u00b0C R =.0475 x 55 x 7.1 x IO\" 6 \u2014 19.25 x 10~6 2 6 Increase i n R = (.0475 - .0475 - 19-25 x 10 ) x 100$ .04752 = .09$ Considering the Length - R decreases 55 : ,-6 i l - 1.304 x x 7.1 x IO\" 6 = 71.5 x 10\" R decreases 7l\u00ab5 x 1C\"S 1.304 = .006$ Thus thermal contraction as such may be regarded as having negligible effect upon the e l e c t r i c a l oyer the temperature range considered. 108 Estimated Experimental Error A. . Niobium Relative accuracy of temperature measurement = \u00b1,2\u00b0C Equivalent error In R =\u2022 ^2 x 1 x 100 \u2022=\u2022 .200$ 2 .0 5 ' Error in current measurement: Error in standard resistance \u2014 0 \"'\" \" potential measurement = 4 x 100 = .060$ 6500 Error i n measurement of potential drop across specimen = 1 x 100 =\".050$ 2000 ===== Total Error = . 31$ The actual relative error w i l l be considerably smaller as compensation w i l l occur. B. Vanadium An accurate estimate i s not possible, scatter of points on the curves i s the only indication which can be used. 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