Bulk Self-Diffusion in Single Crystal Alpha Hafnium-2.1% Zirconium
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AN ABSTRACT OF THE THESIS OF BERNARD ERIC DAVIS for the DOCTOR OF PHILOSOPHY (Name) (Degree) METALLURGICAL ENGINEERING in (MATERIALS SCIENCE) presented on p ic(10 (Major) (Date) Title: BULK SELF-DIFFUSION IN SINGLE CRYSTAL ALPHA HAFNIUM-2.1% ZIRCONIUM Abstract approved:Redacted for privacy Dr. William D. McMullen Coefficients for the diffusion of Hf181(43 day half-life, main gamma peak at 482 key) were measured in the [0001] and [1120] directions in oriented single crystals of HCP Hf-2. 1 wt % Zr over a temperature range of 1074 °C to 1610 °C. A lathe sectioning tech-, nique was used in conjunction with the thin-film solution. Self-diffusion coefficients at temperatures between 1220° C and 1610°C for diffusion parallel and perpendicular to the c axis, respec, tively, may be expressed as follows. D = 0.86 exp [(-88,400_± 3, 200) /RT] c sec lic = 0.28 exp [( -83, 200 ± 4, 800)/R,T]cm2/sec is These results are probably valid for lattice diffusion.They agree with rules-of-thumb applicable to the "normal" self-diffusion be- havior found in most metals but disagree with previously reported self-diffusion data for polycrystalline, alpha Hf, Zr and Ti which indicate anomalous self-diffusion behavior. Below 1220 0 C the Arrhenius plot bends upward and, because of scatter, the data are only approximated by the following expressions. -11 2 D = 7.1 x 10 exp [(-20, 300 6, 400) /RT] cm/sec Ilc -10 D =8. 9 x 10 exp [(-24, 900 ± 13,200)/RT] c sec c The low temperature results probably do not represent Harrison's type A diffusion but are significantly influenced by short-circuiting. A proposed explanation for the disparity between these results and those previously reported for polycrystalline, alpha Hf, Zr and Ti is based on the short-circuiting model of Lundy and Pawel. Measured DI /Di'ratios of approximately 1.5 for high- _Lc I lc temperature self-diffusion indicate that both basal and nonbasal vacancy mechanisms probably operate in the lattice. The anisotropy of the lattice self-diffusion is consistent with that of the other HCP metals for which single crystals have been studied in that DD for a metal of less than ideal c/a ratio D Et and in that the degree of anisotropy decreases as the temperature is increased. Bulk Self-Diffusion in Single Crystal Alpha Hafnium -2. 1% Zirconium by Bernard Eric Davis A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 1970 APPROVED: Redacted for privacy Associate Professor of Metallurgical Engineering in charge of major Redacted for privacy Head of /Apartment of Metallurgical Engineering Redacted for privacy Dean of Graduate School Date thesis is presented pi ii /1:51600 Typed by Donna L. Olson forBernard Eric Davis ACKNOWLEDGEMENTS This research could not have been performed without the con- siderable assistance of many kinds received from a great number of people.For any and all such help I am most grateful. My wife Helen, more than any other person, made this work possible by earning the principal income for our family and by her cooperation, assistance and encouragement. It is a pleasure to thank my thesis advisor Dr. William D. McMullen for his considerate and friendly manner as well as for faithful and sensible guidance based on broad technical experience and a sound understanding of both, theory and experiment. The graduate research fellowship which sponsored this investi- gation was awarded by the Albany Metallurgy Research Center (AMRC) at the U.S. Bureau of Mines station in Albany, Oregon. am grateful for the two-year, part -time, income and for the use of the excellent equipment and services at AMRC where most of the work was performed.I appreciate the many kinds of help and the friendly cooperation that was given by whomever was asked; perhaps half of the AMRC staff was at some time involved at least in some small way. Special thanks go to Mr. Hal J. Kelly, Project Coordinator, and to all the members of the Materials Science Projects Section at AMRC, who welcomed me into their organization, willingly loaned their equipment, cooperated, assisted and consulted concerning experimental problems. Among the members of the section, Mr. W. H. Barstow and Mr. C. W. Antrim deserve special mention for care of tube furnaces during two long anneals and for metallographic assis- tance, respectively.Essential services were rendered by the analy- tical laboratories; the library; the machine shop; the drafting group; the photographer, Mr. R. W. Nelson; the glass blower, Mr. R. H. Maier; and particularly the electrical and instrument shop whose staff, including Messrs. M. L. Fa.rlee, A. D. Bennett and H. K. Taylor, are especially thanked.The delicate lathe sectioning was performed with care by Mr. D. R. Stone and Mr. C. W. Yancey, skilled machinists.Valuable help and counsel were received on numerous occasions from Mr. J. C. White and Mr. P. A. Romans. Mr. M. P. Krug is thanked for his study of thermal expansion co- efficients. The hafnium used in the study was donated by Wah Chang Albany Corporation. As my former employer, Wall> Chang provided support and encouragement which carried me through my metallurgy courses. For these helpful policies of Mr. S. W. H. Yih, President, adminis- tered by Mr. S. A. Worcester, Technical Director, and Mr. E. F. Baroch, Director of Metallurgical Research, I am grateful. Mr. P. L. Rittenhouse, Group Leader, and members of his staff in the Zirconium Metallurgy Group at Oak Ridge National Laboratory (ORNL) kindly formed single crystals for the investigation free of charge from the hafnium donated by Wah Chang Albany Corpor- ation. Valuable help, both in consultations on radiological techniques and in services, was rendered by several members of the faculty and staff of the OSU Radiation Center.They included Drs. R. A. Schmidt, D. J. Reed, C. H. Wang and J. C. Ring le and Messrs. V. N. Smith, A. G. Johnson, T. V. Anderson and G. E. Paull. Several scientists who specialize in diffusion research were consulted concerning experimental techniques at the inception of the study.These persons, who graciously gave information and advice during personal discussions at their laboratories, are Drs. T. S. Lundy of ORNL, N. L. Peterson of Argonne National Laboratory, W. J. Frederick of the OSU Chemistry Department and Mr. Marvin Greene and Dr. A. P. Batra, then graduate and post-doctoral fellows, respectively, in the Physics Department of the University of North Carolina.Dr. Lundy was later consulted by telephone concerning my results.Dra. Fanny Dyment of Buenos Aires, who conducted an earlier investigation of self-diffusion in alpha hafnium, has been very gracious in carrying on a technical correspondence concerning her study and mine. A grant from the OSU Research Council covered expenses in- curred on the campus. SYMBOLS USED IN THE THESIS Symbol Description Units a Lattice parameter in the [112:0] direction A a' Lattice parameter for BCC phase A' A Specific activity counts /min /grin a Coefficient of linear thermal ex- pansion microin /in / °C at Surface concentration at initial time g atom/cm, 2 Lattice parameter in the [0001] direction 3 C Concentration g atom/cm V C Concentration gradient (a vector quantity) g atom/cm4 2 D Diffusion coefficient cm/sec D Diffusion coefficient for diffusion parallel to the c axis cm2 /sec D Diffusion coefficient for diffusion Jc perpendicular to the c axis cm2/sec D[0001] Diffusion coefficient for diffusion in the [0001] direction cm2/sec D. Frequency factor cm2/sec D.. Diffusion coefficient for flux in the i direction due to a gradient in the j direction cm2/s ec J Flux (a vector quantity) g atom/cm, 2/sec Component of flux in the x 2 direction g atom/cm/,sec Symbol Description Units K Structure factor of Sherby and Simnad (85) (none) Lm Latent heat of melting cal/g atom -2 M Slope of a penetration plot cm Q Activation energy cal/g atom or kcalfg atom Universal gas constant cal/g atom °C t Time sec T' Temperature °C T Absolute temperature °K Melting temperature °K V Chemical valence (none) x Penetration depth in x direction cm y Penetration depth in y direction cm z Penetration depth in z direction cm Dens ity g/cm3 Displacement magnitude (for a single movement of an atom in a diffusion mechanism) 0 Angle between diffusion direction and c axis degrees 0 Angle which displacement of i th atom makes with c axis degrees Subscripts Description Parallel to the c axis lc Perpendicular to the c axis Melting point 1 Mechanism dominant at high temperatures Mechanism dominant at low temperatures in D..) Flux direction in D..) Gradient direction TABLE OF CONTENTS Chapter Page I.INTRODUCTION Objectives 1 Background and Significance 1 Hafnium 1 Relation to Previous Research 6 Diffusion Coefficients 11 Theory 12 Fick's Second Law and the Thin-Film Solution 12 Diffusion in Crystal Lattices of Hexagonal Symmetry 15 Mechanisms for Diffusion 18 Lattice Diffusion Mechanisms and Anisotropy of Self-Diffusion in HCP Single Crystals 20 "Normal" vs Anomalous Self-Diffusion 23 Normal Self-Diffusion Behavior 23 Self-Diffusion in the Anomalous BCC and HCP Metals 24 Activation Energies Correlated with Physical Properties 26 Explanations for "Abnormal" Diffusion Behavior in the Anomalous BCC and HCP Metals 27 II.EXPERIMENTAL MATERIALS, PROCEDURES AND EQUIPMENT 35 Monocrystalline Hf -2. 1% Zr Source for Diffusion Specimens 36 Orientation and Removal of Diffusion Specimen Wafers 45 Surface Preparation and Examination of Diffusion Specimens 54 Application of Thin Radioactive Film 57 Diffusion Annealing