A Molecular-Dynamics Study of the Frictional Anisotropy on the 2-Fold

University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 9-16-2008 A Molecular-Dynamics Study of the Frictional Anisotropy on the 2-fold Surface of a d-AlNiCo Quasicrystalline Approximant Heather McRae Harper University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Harper, Heather McRae, "A Molecular-Dynamics Study of the Frictional Anisotropy on the 2-fold Surface of a d-AlNiCo Quasicrystalline Approximant" (2008). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/280 This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. A MolecularDynamics Study of the Frictional Anisotropy on the fold Surface of a dAlNiCo Quasicrystalline Approximant by Heather McRae Harp er A thesis submitted in partial fulllment of the requirements for the degree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Ma jor Professor David Rabson PhD William Matthews Jr PhD Brian Space PhD Matthias Batzill PhD Date of Approval Septemb er Keywords atomistic simulation quasicrystals nanotrib ology contact mechanics ap erio dicity c Copyright Heather McRae Harp er DEDICATION I would like to dedicate this work to my mom for doing everything she can to encourage me help me and make my life a little easier to Alan for reminding me that in the end its the money that matters and to Doug for putting up with me every day and helping me stay p ositive Without you guys I would not have b een able to nish this Thank you ACKNOWLEDGMENTS I would rst like to thank all of my committee memb ers for their time and patience This research was the combination of suggestions insights and help from many p eople Most imp ortantly I would like to thank my advisor Dr David Rabson for his continued supp ort Thank you to Dr Susan Sinnott and her research group at the University of Florida for all of their help and insight on measuring friction through molecular dynamics and allowing me the invaluable exp erience of sp ending a week in their lab Dr Sagar Pandit for freely oering his exp ertise in molecular dynamics and Dr Patricia Thiel at Ames National Lab oratory through which a p ortion of this research was funded The author would also like to acknowledge the use of the services provided by Research Computing University of South Florida TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv LIST OF ABBREVIATIONS vi ABSTRACT vii CHAPTER INTRODUCTION CHAPTER A DISCUSSION OF CONTINUUM CONTACT MECHANICS The Hertz Theory The JohnsonKendallRob erts Theory The DerjaguinMullerTop orov Theory The Tab or Parameter and Other Metho ds of Interp olating Between The ories CHAPTER AN EXAMINATION OF SOME TECHNIQUES USED TO PER FORM MOLECULARDYNAMICS SIMULATIONS AND SOME POPULAR PACKAGES Limitations on the Simulation of Quasicrystals Using Quasicrystalline Approximants WidomMoriarty Pair Potentials Using an Adamant Tip Averaging and Error Analysis MolecularDynamics Packages DL POLY NAMD Gromacs LAMMPS CHAPTER PRELIMINARY RESULTS CHAPTER FINAL RESULTS CHAPTER FUTURE WORK Comparison of Dierent Approximants Larger Simulations i Tailoring the Pair Potentials Creating and Using a More Realistic Tip Monitoring Phonon Propagation REFERENCES APPENDICES App endix A LAMMPS Workarounds A Obtaining Forces on FixedRigid Atoms A Bugs Noted With the LAMMPS Splining Routine A Using a Triclinic Box in a Data File App endix B Calculating an Appropriate Timestep App endix C Required Files C Data File C Potential File C Simulation Parameters File C CIRCE Submission Script App endix D Original Atom Unit Cell App endix E Previous Publication ii LIST OF TABLES Table Atomic Co ordinates for the Atom Approximant Unit Cell Table UnitCell Vectors for the Atom Approximant Unit Cell Table Sliding Velo cities and Required Sliding Times Table Table of Co ecients of Friction at Highest Compressions for the Ap e rio dic Sliding Direction Table Table of Co ecients of Friction at Highest Compressions for the Peri o dic Sliding Direction Table Table Showing the Ratio Between the Perio dic and Ap erio dic Frictional Co ecients Table C SimulationBox Vectors Table D Atomic Co ordinates for the Full Atom Approximant Unit Cell Table D UnitCell vectors for the Atom Approximant Unit Cell iii LIST OF FIGURES Figure Sphere on Disk Hertzian Contact Prole Figure Sphere on Sphere Hertzian Contact Prole Figure JKR Contact Prole Figure fold Surface Figure fold Surface Figure Bulk Bilayer Structure Figure WidomMoriarty Pair Potentials Figure Truncated WidomMoriarty Pair Potentials Figure Mean Squared Displacement Figure AdAd and AlAl Pairwise Interactions Figure AdX Pairwise Interactions Figure Delineation of the Simulation Groups Figure Ap erio dic Lateral Force Over Time Preliminary Results Figure Perio dic Lateral Force Over Time Preliminary Results Figure Ap erio dic Normal Force Over Time Preliminary Results Figure Perio dic Normal Force Over Time Preliminary Results Figure Normal vs Lateral Force Preliminary Results Figure Extended Normal vs Lateral Force Preliminary Results Figure Visualization of Current Simulation Box fold Face Figure Visualization of Current Simulation Box Figure Ap erio dic Temp erature Over Time Final Results iv Figure Perio dic Temp erature Over Time Final Results Figure Ap erio dic Lateral Force Over Time Final Results Figure Perio dic Lateral Force Over Time Final Results Figure Ap erio dic Normal Force Over Time Final Results Figure Perio dic Normal Force Over Time Final Results Figure Ap erio dic Normal vs Lateral Force Final Results Figure Perio dic Normal vs Lateral Force Final Results Figure Perio dic and Ap erio dic Normal vs Lateral Force Final Results Figure Sliding Velo city vs Co ecient of Friction Final Results Figure Atom Approximant Unit Cell Figure Atom Approximant Unit Cell Figure Ap erio dic Lateral vs Normal Force Figure Ap erio dic Temp erature vs Lateral Force Figure Perio dic Temp erature vs Lateral Force Figure Ap erio dic Temp erature vs Normal Force v LIST OF ABBREVIATIONS QC Quasicrystal LAMMPS Largescale AtomicMolecular Massively Parallel Simulator VMD Visual Molecular Dynamics NAMD Nanoscale Molecular Dynamics AFM Atomic Force Microscop e UHV UltraHigh Vacuum JKR JohnsonKendallRob erts DMT DerjaguinMullerTop orov STM ScanningTunneling Microscop e vi A MOLECULARDYNAMICS STUDY OF THE FRICTIONAL ANISOTROPY ON THE FOLD SURFACE OF A DALNICO QUASICRYSTALLINE APPROXIMANT Heather McRae Harp er ABSTRACT In Park et al demonstrated that the fold surface of a dAlNiCo quasicrystal exhibits an fold frictional anisotropy as measured by atomicforce microscopy b etween the p erio dic and ap erio dic directions It has b een well known that quasicrystals exhibit lower friction than their crystalline counterparts however the discovery of the frictional anisotropy allows for a unique opp ortunity to study the eect of p erio dicity on friction when chemical comp osition oxidation and wear are no longer variables The work presented herein is fo cused on obtaining an understanding of the mechanisms of friction and the dep endence of friction on the p erio dicity of a structure at the atomic level fo cusing on the dAlNiCo quasicrystal studied by Park et al Using the LAMMPS package to simulate the compression and sliding of an adamant tip see x on a dAlNiCo quasicrystalline approximant substrate we have demonstrated in preliminary results an fold frictional anisotropy but in more careful studies the anisotropy is found to b e much smaller The simulations were accomplished using WidomMoriarty pair p otentials to dene the interactions b etween the atoms The studies presented in this work have shown a clear velo city dep endence on the measured frictional resp onse of the quasicrystalline approximants surface The nal results show b etween a fold and fold anisotropy b etween sliding in the p erio dic and ap erio dic directions dep ending on the sliding velo city vii CHAPTER INTRODUCTION Quasicrystals were discovered in by Shechtman et al Since that rst icosahe dral metastable AlMn quasicrystal was discovered there have b een numerous quasicrys tals with various forbidden p oint group symmetries discovered and studied The ma jority of known quasicrystals contain icosahedral symmetry This class of quasicrystals are ap erio dic in all three dimensions Contrary to this the decagonal AlNiCo quasicrystal on which this work fo cuses contains two ap erio dic directions and a third p erio dic direction The indepth analysis in by Park et al showed that the fold face of decagonal Al Ni Co contained b oth p erio dic and ap erio dic surface order on the atomic scale as 72 11 17 predicted by the bulk structure This showed that dAlNiCo quasicrystals p ossess the unique prop erty of exp osing a surface containing a p erio dic arrangement of atoms along the fold axis with a A p erio dicity and p erp endicular to it an ap erio dic arrangement of atoms following a Fib onacci sequence This quickly prompted further study into the eect of p erio dicity versus ap erio dicity on the co ecient of friction It had b een

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