MATERIAL RESEARCH SOCIETY Short Course in Materials Science and Technology Course Notes CONP-871255—1-Draf t DE88 003768 ATOM PROBE MICROANALYSIS: Principles and Applications to Materials Problems T3 ° 8 T) . £ | ft | D 6 £ 3 r i I g - M.K.MUXER f illlHf I Ceramics Division, OaJt /{/<3T^ National Laboratory. 7^ 37831. USA 1 |l5oniiii G.D.W. SMITH S &s^s^|8| ^.^_ „, o, .,, ^ •sosls||I University of Oxford. g ssgS»^>I^ Oxford, OXI 3PH. Great Britain § 2 fe.a - f -g - I •* MASTER A ' . S *i O M u .. wa Sponsored by the Division of Materials Sciences, ^ si^Sf 1"= U.S. Department of Energy, ^lilli under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. u of im %zbm:ii is ACKNOWLEDGMENTS The authors thank Drs. J. Bentley and E.A. Kenik, of Oak Ridge National Laboratory, Ms. K.L. More of Oak Ridge Associated Universities, Dr. A. Cerezo of Oxford University and Dr. M.G. Hetherington of Massachusetts Institute of Technology for their assistance and helpful discussions in drafting this manuscript. The authors would also like to give special thanks to K.F. Russell for her technical assistance in producing this manuscript. Sponsored by the Division of Materials Sciences, U.S. Department of Energy, under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc and by the Materials Research Society. CONTENTS CHAPTER 1. HISTORICAL BACKGROUND AND GENERAL INTRODUCTION 1.1. FIELD EMISSION AND FIELD-IONIZAT1ON 1-1 1.2. FIELD-ION MICROSCOPY 1-2 1.3. THE ATOM PROBE 1-7 1.4. REFERENCES 1-10 CHAPTER 2. PHYSICAL PRINCIPLES OF FIELD ION MICROSCOPY 2.1. THE MACROSCOPIC ELECTRIC FIELD DISTRIBUTION IN THE MICROSCOPE ^-1 2.2. THE OVERALL GAS SUPPLY FUNCTION, AND FIELD ADSORPTION 2-4 2.2.1. Supply of gas atoms to the specimen surface 2-4 2.2.2. Field adsorption 2-6 2.3. FIELD IONIZATION 2-7 2.3.1. Experimental observations. 2-7 2.3.2. Basic theory 2-8 2.3.3. Field ionization in the presence of adsorbed gas atoms. 2-11 2.4. FIELD DESORPTION AND FIELD EVAPORATION 2-11 2.4.1. Experimental Observations 2-13 2.4.2. Classical Theory of Field Desorption and Field Evaporation. 2-15 2.4.2.1. Image hump model 2-15 2.4.2.2. Charge exchange model 2-18 2.4.2.3. Weak or Zero Bonding Case: Equivalence to Field lonization. 2-20 2.4.3. Post-ionization theory of high charge states 2-23 2.4.4. Ion tunnelling 2-23 2.4.5. Field Evaporation of Alloys 2-23 2.4.6. Image gas interactions 2-25 2.5. ION TRAJECTORIES, IMAGE PROJECTION, MAGNIFICATION, RESOLUTION AND IMAGE CONTRAST 2-26 2.6. MECHANICAL STRESSES ON THE SPECIMEN, WORKING RANGE, AND OPTIMUM WORKING CONDITIONS FOR THE FIM. 2-26 2.7. REFERENCES 2-26 CHAPTER 3. FIM IMAGE INTERPRETATION 3.1 CRYSTALLOGRAPHY, SYMMETRY AND INDEXING 3_-, 3.2 DETERMINATION OF FEATURE MORPHOLOGY 3_-| 3.2.1. Image Projection 3_1 3.2.2. Regional and Local Magnification 3.3 3.2.3. Indirect Magnification Effect 3.5 3.2.4. Analysis of Linear Features 3_5 3.2.5. Analysis of Planar and Three-dimensional Features 3.7 3.3. IMAGE CONTRAST FROM PERFECT METAL CRYSTALS 3..7 3.4. IMAGE CONTRAST FROM LATTICE DEFECTS IN PURE METALS 3-8 3.4.1. Point Defects and Point Defect Clusters 3-8 3.4.1.1. Vacancies 3-8 3.4.1.2. Interstitials 3-9 3.4.2. Line defects 3-9 3.4.2.1. Perfect dislocations 3-11 3.4.2.2. Dislocation loops and dipoles 3-11 3.4.2.3. Partial dislocations and stacking faults 3-11 3.4.2.4. Artifacts associated with dislocation observation in the FIM 3-13 3.4.3. Interfaces 3-13 3.4.3.1. Low angle grain boundaries 3-13 3.4.3.2. High angle grain boundaries 3-13 3.4.3.3. Twin boundaries 3-18 3.5. IMAGE CONTRAST FROM ALLOYS, ORDERED AND MULTI-PHASE MATERIALS 3-18 3.5.1. Metallic solid solutions 3-18 3.5.2. Ordered alloys 3-20 3.5.3. Multi-phase materials 3-20 3.5.4. Interface Segregation Effects. 3-30 3.6. IMAGE CONTRAST FROM SEMICONDUCTORS AND OTHER MATERIALS 3-30 3.7. SURFACE PHENOMENA 3-35 3.7.1. Surface reconstruction 3-35 3.7.2. Adsorption studies 3-35 3.7.3. Thin films 3-37 3.7.4. Biological molecules 3-37 3.8. ARTIFACTS 3-37 3.8.1. Pseudospirals 3-37 3.8.2. Streaks 3-38 3.8.3. Field corrosion 3-38 3.8.4. Field induced migration 3-38 3.9. COMPUTER SIMULATION OF FIM IMAGES 3-40 3.9.1. Crystal structure identification 3-40 3.9.2. Crystal defects 3-40 3.9.3. Ordered alloys 3-41 3.9.4. Modulated microstructures 3-41 3.10. CONTRAST EFFECTS IN FIELD DESORPTION MICROSCOPY 3-42 3.10.1. Zone line effects 3-42 3.10.2. Contrast from individual image rings 3-45 3.10.3. Contrast from lattice defects and two-phase materials 3-45 3.11. REFERENCES 3-45 CHAPTER 4. TYPES OF ATOM PROBES 4.1. INTRODUCTION 4-1 4.2. TIME-OF-FLIGHT ATOM PROBE 4-1 4.3. ENERGY-COMPENSATED ATOM PROBE 4-4 4.4. MAGNETIC SECTOR ATOM PROBE 4-8 4.5. IMAGING ATOM PROBE 4-8 4.5.1. Field-ion Mode 4-15 4.5.2. Spectrum Mode 4-17 4.5.3. Ungated or Desorption Mode 4-18 4.5.4. Time-Gated Mode 4-18 4.5.5. Ramped Mode 4-20 4.5.6. Field-ion Tomography 4-20 4.6. PULSED LASER ATOM PROBE 4-20 4.7. COMBINED INSTRUMENTS 4_23 4.8. REFERENCES 4_24 CHAPTER S. INSTRUMENTATION 5.1. INTRODUCTION 5_1 5.2. VACUUM SYSTEM 5_1 5.2.1. Vacuum and pumping systems 5_1 5.2.2. Specimen transfer systems 5_] 5.2.3. Image Gas 5_4 5.3. SPECIMEN MANIPULATOR 5_4 5.4. SPECIMEN COOLING SYSTEM 5_6 5.5. HIGH VOLTAGE AND HIGH VOLTAGE PULSE GENERATOR 5_8 5.5.1. High voltage pulser 5-10 5.5.2. 50 ohm load and pickoff 5_1] 5.6. FIELD-ION IMAGING SYSTEM 5_H 5.6.1. The microchannel plate and phosphor screen assembly 5-13 5.6.2. Probe aperture 5-15 5.6.3. Image recording and processing 5-15 5.7. ELECTROSTATIC LENSES 5_T5 5.7.1 Einzel lens 5-16 5.7.2. Energy compensating or Poschenreider lens 5_15 5.8. SINGLE ATOM DETECTOR 5_18 5.8.1. MicroChannel plate detector 5-20 5.8.2. Channeltron detector 5_2i 5.8.3. Copper-beryllium mesh detector 5_2i 5.9. IMAGING ATOM PROBE DETECTOR 5_2i 5.10. PREAMPLIFIER-DISCRIMINATOR 5_23 5.11. HIGH SPEED DIGITAL TIMING SYSTEM 5_23 5.12. MICROCOMPUTER CONTROLLED TIMING SYSTEM 5_24 5.13. IMAGING ATOM PROBE TIME GATING SYSTEM 5_24 5.14. REFERENCES 5_25 CHAPTER 6. METHODS OF ATOM PROBE ANALYSIS AND DATA REPRESENTATION 6.1. INTRODUCTION 6_-j 6.2. METHODS OF ATOM PROBE ANALYSES 6-1 6.2.1. Single atom identification 6-1 6.2.2. Selected area analysis 6-3 6.2.3. Random area analysis 6-5 6.3. SPATIAL CONSIDERATIONS 6-5 6.3.1. Geometrical considerations 6-5 6.3.2. Lateral resolution 6-7 6.3.3. Depth resolution 6-10 6.4. DATA REPRESENTATION 6-10 6.4.1. Ion-by-ion display of mass-to-charge ratio 6-10 6.4.2. Mass spectrum 6-10 6.4.3. Time spectrum 6-17 6.4.4. Character plots 6-17 6.4.5. Composition profiles 6-18 6.4.6. Ladder diagrams 6-19 6.4.7. Cumulative profiles 6-21 CHAPTER 7. FACTORS AFFECTING PERFORMANCE 7. INTRODUCTION 7-1 7.1. VOLTAGE AND TEMPERATURE SETTINGS: PREFERENTIAL EVAPORATION AND RETENTION OF ATOMS 7-1 7.2. ION PILE-UP 7-6 7.3. EVAPORATION RATE 7-6 7.4. PULSE REPETITION RATE 7-6 7.5. HYDRIDE, COMPLEX AND MOLECULAR ION FORMATION 7-7 7.6. IMAGE GAS EFFECTS 7-7 7.7. ALIGNMENT OF THE MASS SPECTROMETER 7-9 7.8. PEAK DECONVOLUTION PROCEDURES IN A LINEAR TOFAP 7-9 7.9. MINIMUM DETECTION LIMITS 7.9 7.10. REFERENCES 7_1T CHAPTER 8. STATISTICAL ANALYSIS OF ATOM PROBE DATA 8.1. INTRODUCTION 8-1 8.2. RAW DATA TECHNIQUES 8-2 8.3. FREQUENCY DISTRIBUTIONS 8-3 8.4. MARKOV CHAIN 8-3 8.5. CONTINGENCY TABLES 8-6 8.6. CROSS-CORRELATION 8-7 8.7. POWER SPECTRUM 8-7 8.8. AUTOCORRELATION 8-7 8.9. REFERENCES 8-11 CHAPTER 9. CASE STUDIES AND SPECIAL TYPES OF ANALYSES 9.1. DEGREE OF ORDER AND SITE OCCUPATION PROBABILITY 9_1 9.1.1. Determination of the degree of long range order 9.4 9.1.2. Determination of the site occupation probability 9_4 9.2. REFERENCES 9-7 APPENDICES Ai APPENDIX A A2 Common acronyms APPENDIX B A3 Useful constants and conversion factors APPENDIX C A4 Stereographic projections and F2M simulations APPENDIX D A14 Interplanar spacing and relative prominence of planes APPENDIX E A15 Angles between planes in cubic crystals APPENDIX F A17 General form of the 24 angle-axis pairs for cubic coincident site lattice orientation relationships APPENDIX G A21 Crystal structure and lattice parameters of the elements at 20°C APPENDIX H A22 Index of commonly occurring charge states for the elements APPENDIX I A23 Examples of complex ion species observed in atom probe analysis APPENDIX J A24 Image hump model predictions of low temperature evaporation fields and charge states for the elements, and comparison with experimental values APPENDIX K A26 Post ionization model predictions of charge states of the elements versus field strength APPENDIX L A30 Quadratic-cubic and quartic-quintic moving average smoothing factors APPENDIX M A31 Specimen preparation methods APPENDIX N A34 Table of electropolishing conditions APPENDIX O A35 Percentage points of the x2 distribution APPENDIX P A36 Table of isotope abundances 1-1 CHAPTER ONE HISTORICAL BACKGROUND AND GENERAL INTRODUCTION The term "Atom Probe" is used to describe an instrument in which a field-ion microscope (FIM) is combined with some form of sensitive mass spectrometer for elemental analysis of a selected area of the imaged region of the specimen.