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University of Nevada Reno Knoop of Microhardness Anisotropy on The University of Nevada Reno Knoop Microhardness Anisotropy on the Cleavage Plane of Single Crystals with the Calcite Structure A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Metallurgical Engineering By Thomas Wong May, 1^91 MINES LIBRARY Thesis Approval Tfcsi $ ilb3 The M.S. thesis of Thomas Wong is approved by: Dr. Richard C. Bradt (Thesis Advisor, Dean, Mackay School of Mines) Dr. Denny A. Jones (Chairperson, Chemical/Metallurgical Engineering Department) Dr. Kenneth W. Hunter (Dean, Graduate School) University of Nevada Reno May, 1991 ii Copyright Note In presenting this thesis in partial fulfillment of the Master of Science degree reguirements, I agree that the library may make its copies freely available for inspection. I further agree that extensive copying of this thesis is allowed for all who are interested in this research. Please send all inquires to the following addresses: Current Address 69 Galen Place Reno, NV 89503 U.S.A. Permanent Address 28-D Jalan Bukit Assek 96000 Sibu, Sarawak Malaysia Signature: Thomas Wong May, 1991 in Acknowledgements Every worthwhile accomplishment of my life has been achieved with the help of many benevolent individuals. The completion of this thesis is no exception. I owe my deepest gratitude to Dr. Richard C. Bradt for his valuable guidance throughout the research. His wit and insightful suggestions have made my experience most enjoyable. Besides him, I owe my sincere appreciation to Dr. Dhanesh Chandra and Dr. Malcolm J. Hibbard for their advice and objective criticism as members of my committee. I also wish to thank my colleagues: Debashis Dey, Young Han and Hong Li for sharing their expertise in computer programming, instruction in the use of lab equipment and experimental techniques. Mr. Martin Jensen also deserves special acknowledgement for his assistance to obtain the carbonate single crystals for measurement, and with the scanning electron microscopy. My desire to pursue a Master's degree is largely inspired by my previous instructors. Dr. John W. Patterson at Iowa State University, Dr. Peter J. Hansen at Northwestern College, and Mrs. Sarada Menon at the Sacred Heart Secondary School are the three persons I am especially indebted to. Finally, I thank my caring parents, Mr. and Mrs. Wong Kee Chiek, for their encouragement and financial support throughout all of my educational endeavors. IV Table of Contents List of Figures .......................................... vii List of Tables ............................................ x Abstract .................................................. xi I. Introduction and Statement of the Problem ........... 1 II. Review of the Literature ............................ 4 (1) Physical Properties of the Rhombohedral Carbonate Single Crystals ................................. 4 A. Crystal Structure ............................ 5 B. Physical Appearance and Mohs' Hardness ....... 5 C. Cleavage ..................................... 7 D. Lattice Dimensions ........................... 11 E. Dislocations and Slip Systems ................ 11 F. Twinning ...................................... 14 (2) Microhardness Indentation Measurements .......... 20 A. Fundamentals of Hardness Testing ............. 20 (3) Knoop Microhardness Anisotropy .................. 22 A. Effective-Resolved-Shear-StressModel ......... 22 (4) Indentation Load/Size Effect .................... 28 A. The Classical Meyer's Law .................... 28 B. The Normalized Meyer's Law ................... 3 0 v III. Experimental Procedures ............................. 33 (1) Samples and Sample Preparations ................. 33 (2) Crystallographic Orientation Determinations ..... 35 (3) Knoop Indentation Measurements .................. 35 (4) Scanning Electron Microscopy .................... 37 IV. Results and Discussion .............................. 39 (1) Experimental Observations ....................... 39 A. Knoop Microhardness Profiles ................. 40 B. Anisotropy of Microhardness .................. 46 C. Scanning Electron Microscopy ................. 55 (2) Deformation Mechanisms .......................... 55 (3) Effective-Resolved-Shear-Stress Diagrams ........ 59 (4) Indentation Load/Size Effect .................... 64 A. The Classical Meyer's Law .................... 64 B. The Normalized Meyer's Law ................... 68 V. Summary and Conclusions ............................. 82 Appendix A: Knoop Indentation and Microhardness Data ..... 85 Appendix B: Effective-Resolved-Shear-Stress Values ....... 91 Appendix C: Knoop Software ................................ 94 References ................................................ 95 vi List of Figures II-l Crystal Structure of Calcite ...................... 6 II-2 Relationship of the Cleavage Rhombohearon to the True Rhombohedral Unit Cell ....................... 10 II-3 Critical-Resolved-Shear-Stress Deformation Model ... 13 II-4 Transformation of the Twinned Crystal Lattice ...... 16 II-5 Geometry of Twinning ............................... 17 II-6 Enlarged View of a Knoop Indenter and Impression on a Test Block ................................... 23 II—7 ERSS Model Showing the Knoop Indentation and the Cylinder of Deformation ................... 2 5 III- l Geometric Relation between the (1011) Cleavage Plane and the Morphological Unit Cell ............. 3 6 III- 2 Assignment of the Angles on the (1011) Cleavage Plane .................................... 38 IV-1 Knoop Microhardness Profiles on the (1011) Cleavage Planes for Test Loads of (a) 25 g, (b) 50 g, (c) 100 g, and (d) 200 g ................ 41 IV—2 Knoop Microhardness Profiles on the (1011) Cleavage Planes of (a) Magnesite (b) Smithsonite, (c) Siderite, (d) Dolomite, (e) Rhodochrosite, (f) Calcite 1 ..................................... 47 vii IV-3 A Plot of the Anisotropy of Microhardness versus the Indentation Test Load, P ...................... 54 IV—4 SEM Photomicrographs of (a) Calcite and (b) Repre- sentative of the Other Five Carbonate Single Crystals at 400X Magnification and for the 200 g Test Load ................................... 56 IV-5 A Plot of the M-0 Bond Length versus the Lattice Volume of the Calcite-Structure Carbonates ........ 58 IV-6 (a) ERSS Diagrams of_(a)_the {2021}<0112> Slip Systems, (b) the_jf 1011}<Ioi2> Slip Systems, (c) the £0001}<2110> Slip Systems, (d) the {2021}<1102> Slip Systems ......................... 60 IV—7 ERSS Diagrams of the {Ioi2}<1012> Twin Systems .... 65 IV-8 Logarithmic Plots of P versus d to Illustrate the Linear Relationship between log (P) and log (d) ........................................... 66 IV-9 A Plot of the Exponents or n-values versus the A Coefficients of the Classical Meyer's Law ......... 69 IV-10 Plots of P% versus d to Illustrate the Linear Relationship between P^ and d ..................... 72 IV-11 The True Microhardness Profiles on the (1011) Cleavage planes .................................... 73 IV-12 Logarithmic Plots of P versus (d/dQ) to Illustrate the Linear Relationship between log (P) and log (d/dQ ) ............................ 74 Vlll IV-13 A Plot of the Meyer's Law Exponents or n-values versus the A0 Coefficients of the Normalized Meyer's Law ....................................... 77 IV-14 A Plot of the Critical Indentation Load, Pc , versus the Meyer's Law Exponents or n-values ...... 79 IV-15 A Plot of the Critical Indentation Load, Pc , versus the Characteristic Indentation Size, dQ .... 80 IV-16 A Plot of the Meyer's Law Exponents or n-values versus the Characteristic Indentation Size, dQ .... 81 IX List of Tables II-l The Rhombohedral Calcite and Dolomite Groups ...... 4 II-2 Physical Appearances and Mohs' Hardnesses of the Carbonate Minerals ............................ 7 II-3 Hexagonal Morphological and Standard Unit Cell Indices ............................................. 9 II-4 Lattice Dimensions ................................ 11 II-5 Reported Slip Systems for Calcite and Dolomite .... 14 II- 6 Reported Twin Systems for Calcite and Dolomite .... 19 III- l Sources of the Carbonate Single Crystals .......... 34 IV- 1 The A and n Parameters of the Classical Meyer's Law and the Linear Regression Coefficients, R 2 .... 67 IV-2 The True Hardness, H0, the Difference between the Diagonal Lengths due to Elastic Recovery, de, and the Linear Regression Coefficients; R 2 ............. 70 IV-3 The A0 and nQ Parameters of the Normalized Meyer's Law and the Linear Regression Coefficients, R 2 .... 75 IV-4 The Critical Indentation Loads, Pc, in grams for (a) Magnesite, (b) Smithsonite, (c) Siderite, (d) Dolomite, (e) Rhodochrosite, and (f) Calcite 1 ....................................... 76 x Abstract Knoop microhardness profiles were determined on the (1011) cleavage planes for a series of natural rhombohedral carbonate single crystals, including calcite, magnesite, rhodochrosite, siderite, smithsonite, and the structurally related dolomite. Indentation test loads of 25 g, 50 g, 100 g, and 200 g were utilized. The resulting deformation features were examined using scanning electron microscopy (SEM). Twinning was observed in the calcite sample only. The physical properties of the other carbonate samples were considered to account for their deformation. The primary slip systems, in particular, were applied through the effective- resolved-shear-stress (ERSS) concept: F (cos S + sin a) ERSS = --- cos 6 cos <p --------------- A 2 which has been advanced by Brookes and co-workers. This concept explained the shapes of the microhardness
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