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4.3 Grain Boundary Diffusion

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4.3 Grain Boundary Diffusion Secondary Ion Mass Spectrometric Analysis of Oxygen Grain Boundary Diffusion in Magnesium-Oxide Bicrystals by Michael James Liberatore Submitted to the Department of Materials Science and Engineering in partial fulfillment of the requirements for the degree of Doctor of Science in Ceramics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 1995 © Massachusetts Institute of Technology 1995. All rights reserved. A"%- - - I A / I Author..................... ...,,-.. .- .............. Department of Materials Science and Engineering January 13, 1995 A :% Certifiedby.................. ..- :- .- ...... ........... ...... C te yernhardt J. Wuensch Professor of Ceramics Thesis Supervisor Accepted by.. ................ Carl V. Thompson.......... II Carl V. Thompson II Professor of Electronic Materials Chair, Departmental mittee on Graduate Students MASSACHUSETTS INSTI OF TECHNOLOGY JUL 2 01995 Science LIBRARIES Secondary Ion Mass Spectrometric Analysis of Oxygen Grain Boundary Diffusion in Magnesium-Oxide Bicrystals by Michael James Liberatore Submitted to the Department of Materials Science and Engineering on January 13, 1995, in partial fulfillment of the requirements for the degree of Doctor of Science in Ceramics Abstract Chemical vapor transport by HCl gas, a procedure that has been used successfully in the past for the growth of MgO single crystals has been adapted to the growth, for the first time, of high purity MgO [001] tilt boundaries of controlled orientation. Oxygen-18 bulk diffusion has been measureded in MgO as a function of tempera- ture from 1250 - 1500°C and as a function of partial pressure from 10-12 - 10+1 kPa. Oxygen grain boundary diffusion has been measured in low energy coincidence site (E5, (310), E13, (510)) and high energy (asymmetric 16°) [001] tilt grain boundaries in MgO. Diffusion coefficients were evaluated from 180 concentration gradients mea- sured with the aid of secondary-ion mass spectroscopy with a Cs+ primary ion beam. The bulk diffusivity of oxygen over the given temperature is given by the following Arrhenian relation: D = 2.9 x 10 - 4 exp -4.eV cm2 1250 - 1500°C kT sec 'The partial pressure dependence of oxygen diffusivity can be expressed as: D c P. 11 10-12 - 10+1 kPa 1500°C On the basis of this and other data available for the isotope effect and the change in anion self-diffusion with aliovalent cation doping, it was concluded that transport was most likely due so some form of interstitial mechanism. Structural analysis of a E13 boundary revealed that the grain boundary region in was no more than 1 nm thick and that facets form to accommodate small deviations from the ideal misorientation. Grain boundary diffusion analysis was also done. The product of the grain boundary diffusion coefficient and boundary width, 6 Db, for the E13 boundaries is given by the Arrhenian expression: Db = 2.8 x 10-810 exp- cm3 1250- 1500°C kT sec Enhanced diffusion of oxygen was also observed in the E5 boundaries. The oxygen dciffusivitiesin the E5 and E13 boundaries at 1300°C were found to be equal to within experimental error (13 - 6.1 x 10- 21 cm 2/s, E5 - 9.2 x 10- 21 cm 2/s, 1.4 x 10- 20 cm2/s). In the general, 160 boundary, diffusivities were enhanced by 1 - 2 orders of magnitude over the low energy boundaries. This is in accord with the empirical 'Borisov relation. for metals which observed that the logarithm of the quotient of the grain boundary and bulk diffusion coefficients is proportional to the boundary energy. 'Thesis Supervisor: Bernhardt J. Wuensch Title: Professor of Ceramics Acknowledgments I am indebted to so many people that it is impossible to fully express my gratitude in mere words. Firstly I would like to thank Prof. Bernie Wuensch for his patience and guidance over the last five years. Never one to criticize, he always seemed to find something positive to say in even the most trying of circumstances. Some of my favorite Bernieisms': "Don't be so apologetic, no one has ever done this before!", and "A thesis is just part of your education, it should not be your whole life". I would also like to thank Profs. Tuller, Chiang, and Vander Sande for being on my committee. Some of their suggestions/improvements were ones I would never have been able to come up with myself. I would like to thank all of those people, too numerous to mention, who made my life at MIT a little easier, especially Dr. A.N. Sreeram for all of his help and his friendship and Mr. John Martin, MIT SIMS guru, who was taken from us, without warning, August 15, 1994. Without his patient help most of the work in this thesis would not have been possible. Contents IL Introduction 13 2 Theory and Literature Review 17 2.1 Grain Boundarv Structure and Energy ..... ............ .......17 2.1.1 Description of a General Grain Boundary [12] ........ 17 2.1.2 Dislocation Models for Grain Boundaries . 19 2.1.3 Grain Boundary Energy ......... .45 2.2 Grain Boundary Segregation ........... .59 2.3 Bulk and Grain Boundary Diffusion ....... 72 2.3.1 Continuum diffusion. 72 2.3.2 Atomistics of Diffusion .......... 81 2.3.3 Literature Review - Diffusion in MgO . 83 3 Sample Preparation and Analysis 95 3.1 Preparation of Seed Bicrystals .......... .95 3.2 Source Powder Preparation ........... 102 3.3 Crystal Growth .................. 104 ... 3.3.1 Theory and Overview ........... ..... .... 104 3.3.2 Bicrystal Epitaxy ............. .114 3.4 Annealing ..................... 120 ... 3.4.1 Design of Annealing Experiments .... 120 ... 3.5 Secondary Ion Mass Spectrometry ........ .124 3.5.1 Principles of Operation .......... 126 ... 5 3.5.2 Experimental .... 130 3.6 Transmission Electron Microscopy ............ ........ .136 4 Results and Discussion 141 4.1 Bulk diffusion of Oxygen ................. 141 4.2 Grain Boundary Structure ................ 159 4.3 Grain Boundary Diffusion ................ 161 5 Summary and Suggestions for Future Work 186 5.1 Summary. ..... 186 5.2 Suggestions for Future Work ..... ..... 188 Bibliography 189 A Additional Raw Data 200 6 List of Figures 2-1 Creation of a General Grain Boundary ................. 18 2-2 Formation of a symmetric tilt boundary by introduction and polygo- nalization of lattice dislocations ...................... 21 2-3 Burgers circuit for E5 and symmetric tilt boundary ........... 22 2-4 One of the primary dislocation descriptions for the E5 boundary . .. 23 2-5 Determining the dislocation spacing in a symmetric tilt boundary . 25 2-6 The Z5 [210], 36.9 ° boundary in MgO. ................. 28 2-7 The 13 [510], 22.6° boundary in MgO .................. 29 2-8 Uniform primary dislocation spacing in E5 boundary .......... 32 2-9 Periodic perturbation of primary spacing in E17 boundary (indicated by arrows) ................................. 33 2-10 Crossed grid of screw dislocations in Gold twist boundary. From Schober and Balluffi, 1970 .....-. ................. 35 2-11 E5 twist boundary in MgO with tilt component, showing screw and edge dislocation arrays ........................... 39 2-12 High resolution micrograph of E5 tilt boundary in NiO with close-ups of core structures. From Merkle and Smith, 1987 .......... 44 2-13 Geometry used for computation of strain energy in and around dislo- cation core ................................. 46 2-14 Computation of EII ........................... 48 2-15 Triple junction method for measuring boundary energies. - Three boundaries meeting at a junction ..................... 53 7 2-16 Calculation of boundary energy by boundary/surface dihedral angle measurement ............................... 54 2-17 Energy of [001] symmetric tilt boundaries in NiO, as a function of misorientation parameter, 0. From Dhalenne, 1984 .......... 56 2-18 Auger spectra of grain boundary fractures in MgO doped with 2% LiF for as pressed samples, and samples annealed at 1315 C and 1540 C showing the decrease in fluoride concentration and the increase in calcium concentration. From Johnson et al., J. American Ceramic Society, 57 [8] 342-44 (1974) ........................ 64 2-19 Peak height ratios for Sc, Ca, and Si as a function of distance from grain boundary in MgO doped with 3000 ppm Sc, and annealed at 1200 C 165 hours, showing the extent of segregation. From Chiang et al., J. American Ceramic Society, 64 [7] 385 (1981) ........... 68 2-20 Concentration profiles in MgO grain boundaries measured using ded- icated STEM technique showing segregation of (a) Fe, Ca, Si, La, Kingery et al., J. Mat. Sci. 14 1766 (1979). (b) Ca, Si, Roshko et al. J. American Ceramic Society, 68 [12] C-331 (1985). ........ 71 2-21 Geometry of MgO bicrystal for mathematical analysis ......... 76 3-1 Hot pressing MgO single crystals between zirconia bricks ....... 97 3-2 Crystal Orientation for Hot Pressing (a) normal (b) staggered ... 98 3-3 Schematic of Hot Pressing Apparatus .................. 100 3-4 Schematic diagram of the Mg Oxidation Apparatus .......... 103 3-5 Ellingham diagram for the reaction MgO(s) + 2HCl(g) = MgCl2(g) + ° ° H2 0(g) in the context of AH , AS , and Kp ............... 107 3-6 Partial pressure of XY(g), Pxy, as a function of equilibrium constant, Kp at various total pressures, ZP, for the hypothetical 1:1 reaction X(s) + Y(g) = XY(g), from Alcock and Jeffes ................. 109 8 3-7 Productivity function PF, P,,y dK, as a function of K for the hypo- thetical 1:1 reaction X(s) + Y(g) = XY(g) from [17]. This plot applies to all 1:1 reactions. ......... 110 3-8 Apparatus for growth of MgO crystals by dynamic, open system CVT. 112 3-9 CVT crystal growth apparatus used in this study ............ 115 3-10 Closeup of growth chamber showing placement of crucible assembly in RF induction field. ......... 116 3-11 Controlled atmosphere tube furnace used for annealing diffusion spec- imens. ................................... 121 3-12 Oxygen partial pressure as a function of temperature for a range of CO/('0 2 mixtures ............................. 125 3-13 Depiction of atomic collisions in single knock-on (prompt) sputtering. 128 3-14 Sputtering as a result of a collision cascade (slow collisional sputtering), from Vickerman.
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