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Passivation of copper in alkaline chloride solutions Chow, Norman 1997

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PASSIVATION OF COPPER IN ALKALINE CHLORIDE SOLUTIONS  by  NORMAN CHOW B.A.Sc, University of British Columbia, 1991  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Metals and Materials Engineering)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA July 1997 © Norman Chow, 1997  In  presenting this  degree at the  thesis in  University of  partial  fulfilment  of  the  requirements  British Columbia, I agree that the  for  an advanced  Library shall make it  freely available for reference and study. I further agree that permission for extensive copying  of  department  this thesis for scholarly purposes may be granted or  by  his  or  her  representatives.  It  is  by the  understood  that  head of my copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  HE-TAL*,  AAJD  MAT&KJACC  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  feJ^-fA/seg/A/fr-  ABSTRACT Using polarization and impedance studies, the breakdown of passive films on copper in buffered alkaline sodium chloride was found to be caused by a loss of pH control at the metal surface. The loss of pH control was still observed when there was sufficient buffer species present to neutralize the total protons generated from the aqueous corrosion of copper. This indicates that the loss of pH control is a localized phenomenon. At the onset of passive film breakdown film defects were detected with the use of impedance modeling. The production of protons that accompany the local corrosion of copper to form HCuCV ions at these defect sites consumes all the conjugate base buffer species at the defects. The ensuing drop in local pH has a detrimental effect on the remaining oxide layer. The local acidic condition causes the precipitation of CuCl and hence prevents re-passivation.  Impedance modeling was successful in determining the thickness of the passive film in-situ. The passive film thickness was determined to be in the range of 7.0A to 108.8A, which is in line with published values from ex-situ XPS studies. The impedance modeling was also successful in identifyingfilmdefects at the onset of passive film breakdown.  TABLE OF CONTENTS  ABSTRACT  ii  TABLE OF CONTENTS  iii  LIST OF TABLES  vi  LIST OF FIGURES  vii  ACKNOWLEDGEMENTS  xiii  1 INTRODUCTION  1  2 LITERATURE REVIEW  2  2.1 THERMODYNAMICS  2  2.2 PASSIVE FDJVI CHARACTERISTICS  6  2.3 EFFECT OF HALDDES  9  2.4 EFFECT OF NON HALIDE COMPLEXING AGENTS  11  2.5 EFFECT OF BUFFER SPECIES  12  3 OBJECTIVE  14  4 EXPERIMENTAL  15  4.1 SOLUTION PREPARATION  15  4.2 SAMPLE PREPARATION  16  4.3 ELECTROCHEMICAL CELL SET-UP  18  4.4 POLARIZATION SCAN TECHNIQUES  19  4.5 AC IMPEDANCE SCAN TECHNIQUES  19  4.6 ROTATION SPEEDS  20  iii  5 RESULTS  21  5.1 POLARIZATION STUDIES  21  5.1.1 POLARIZATION BEHAVIOR - EFFECT OF BUFFER T Y P E  24  5.1.2 POLARIZATION BEHAVIOR - EFFECT OF BUFFER CONCENTRATION... 29 5.1.3 POLARIZATION BEHAVIOR - EFFECT OF ROTATION SPEED  36  5.2 A C IMPEDANCE SPECTROSCOPY STUDIES  45  5.2.1 THEORY OF IMPEDANCE FOR CAPACITORS A N D RESISTORS  47  5.2.1.1 IMPEDANCE OF CAPACITORS  47  5.2.1.1.1 FREQUENCY DEPENDENT IMPEDANCE OF CAPACITORS  49  5.2.1.1.2 TIME L A G B E T W E E N CURRENT AND V O L T A G E  50  5.2.1.2 IMPEDANCE OF RESISTORS  52  5.2.2 IMPEDANCE OF T H E PASSIVE FILM CIRCUIT M O D E L  52  5.2.3 V E C T O R REPRESENTATION OF IMPEDANCE  53  5.2.4 CALCULATION OF IMPEDANCE FOR A RANDLES CIRCUIT  55  5.2.5 PLOTTING IMPEDANCE DAT A  58  5.2.6 A C IMPEDANCE D A T A DURING PASSIVE FILM FORMATION A N D BREAKDOWN....:.:.....  60  6 DISCUSSION...:..:  75  :.::...;  6.1 POLARIZATION BEHAVIOR.....  75  6.2 A C IMPEDANCE - MODELLING OF T H E PASSIVE FILM  86  6.2.1 ANALYSIS OF IMPEDANCE RESULTS  91  6.3 CORRELATION OF FILM THICKNESS WITH PUBLISHED LITERATURE.. 100  iv  6.4 LIMITATIONS OF IMPEDANCE SPECTROSCOPY  101  6.5 MECHANISM OF PASSIVE FORMATION, GROWTH, AND BREAKDOWN 101 7 CONCLUSIONS 8 RECOMMENDATIONS FOR FUTURE WORK 9 REFERENCES APPENDIX I: MICROSOFT QUICKBASIC PROGRAM FOR CONTROLLING ELECTROCHEMICAL DEVICES FOR POLARIZATION EXPERIMENTS  103 105 106 109  APPENDIX II: MICROSOFT QUICKBASIC PROGRAM FOR CONTROLLING ELECTROCHEMICAL DEVICES FOR AC IMPEDANCE EXPERIMENTS 117 APPENDIX III: COMPARISON OF MEASURED IMPEDANCE DATA WITH MODELED IMPEDANCE RESULTS 127  LIST OF TABLES  Table 2.1 Thermodynamic Free Energy Data for Copper Species and Water  3  Table 4.1 List of Test Solutions  16  Table 5.1 Summary of Polarization Data for Different Buffer Types  29  Table 5.2 Summary of Polarization Data For Increasing Buffer Concentration  35  Table 5.3 Summary of Polarization Data Showing Effects of Rotation Speed  43  Table 5.4 Summary of Impedance Data for Copper in IM Sodium Chloride Buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM 67 Table 5.5 Summary of Impedance Data for Copper in IM Sodium Chloride Buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM 74 Table 6.1 Summary of Calculated Bicarbonate and Carbonate Concentrations  76  Table 6.2 Summary of Calculated Borate Concentrations  78  Table 6.3 Summary of Diffusion and Viscosity Data  80  Table 6.4 Calculated Diffusion Thicknesses  81  Table 6.5 Flux of Conjugate Base to Copper Surface  82  Table 6 6 Flux of Hydrogen Ions Produced During Passivation  84  Table 6.7 Summary of Impedance Results for Tests Conducted in IM NaCl Buffered to pH 10.5 with 0.01M Na B 0 Rotating at 50 RPM 98 2  4  7  Table 6.8 Summary of Impedance Results for Tests Conducted in IM NaCl Buffered to pH 10.5 with 0.01MNa B O Rotating at 5000 RPM 100 2  4  7  vi  LIST OF FIGURES  Figure 2.1 E-pH Diagram for Copper in Water at 25 °C ( V Reference Electrode)  = VSHE,  Standard Hydrogen 4  18  Figure 2.2 E-pH Diagram for Copper Showing Regions of Corrosion, Passivation, and Immunity at 25 °C 5 18  Figure 2.3 Illustration of a Passive Film on Copper  6  19  Figure 2.4 Polarization Curve of Copper at pH 11 Buffered with Borate  6  7  Figure 2.5 Cu-Cl-H 0 Equilibria at 25°C in the Presence of 0.67 Activity of CI" Ions. Situation Equivalent to 1M NaCl 10 2  27  Figure 4.1 Assembly of the Rotating Disk Electrode Specimen  17  Figure 4.2 Electrochemical Cell Set-Up  18  Figure 5.1 Typical Polarization Curve for Copper in 1M NaCl in a Buffered Alkaline Solution 23 Figure 5.2 Polarization Curve of Copper in 1M NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, and (2) 0.01M Sodium Borate at 23°C 25 Figure 5 3 Polarization Curve of Copper in 1M NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, and (2) 0.01M Sodium Borate at 23°C... 26 Figure 5.4 Polarization Curve of Copper in lMNaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.05M Sodium Bicarbonate/Carbonate, and (2) 0.05M Sodium Borate at 23°C. ........ 27 Figure 5.5 Polarization Curve of Copper in 1M NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.05M Sodium Bicarbonate/Carbonate, and (2) 0.05M Sodium Borate at 23°C : ..' 28  vii  Figure 5.6 Polarization Curve of Copper in IM NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, (2) 0.05M Sodium Bicarbonate/Carbonate, (3) 0.1M Sodium Bicarbonate/Carbonate, and (4) 0.5M Sodium Bicarbonate/Carbonate at 23°C 30 Figure 5.7 Polarization Curve of Copper in lMNaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, (2) 0.05M Sodium Bicarbonate/Carbonate, (3) 0.1M Sodium Bicarbonate/Carbonate, and (4) 0.5M Sodium Bicarbonate/Carbonate at 23°C 31 Figure 5.8 Polarization Curve of Copper in IM NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.001M Sodium Borate, (2) 0.01M Sodium Borate, and (3) 0.05M Sodium Borate at 23°C 32 Figure 5.9 Polarization Curve of Copper in lMNaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0:001M Sodium Borate, (2) 0.01M Sodium Borate, and (3) 0.05M Sodium Borate at 23°C 33 Figure 5.10 Polarization Curve of Copper in lMNaCl Buffered to pH 10.5 with 0.0 IM Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C 37 Figure 5.11 Polarization Curve of Copper in IM NaCl Buffered to pH 10.5 with 0.05M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C 38 Figure 5.12 Polarization Curve of Copper in IM NaCl Buffered to pH 10.5 with 0. IM Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C 39 Figure 5.13 Polarization Curve of Copper in IM NaCl Buffered to pH 10.5 with 0.5M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C: 40 Figure 5.14 Polarization Curve of Copper in lMNaCl Buffered to pH 10.5 with 0.01M Sodium Borate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C 41 Figure 5.15 Polarization Curve of Copper in lMNaCl Buffered to pH 10.5 with 0.05M Sodium Borate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C 42 Figure 5.16 Plot of Pitting Potential Versus Buffer Concentration For All Experiments Conducted 44 Figure 5.17 Electrical Circuit Model of a Passive Film In-Situ Figure 5.18 A Capacitor  46 47  viii  Figure 5.19 Charged Capacitor  48  Figure 5.20 Capacitor Charge and Discharge  49  Figure 5.21 Applied Voltage and Resulting Current for a Capacitor  51  Figure 5.22 Randies Circuit used to Model a Passive Film  52  Figure 5.23 Vector Representation of Impedance  54  Figure 5.24 Typical Bode Plot of Impedance Data  59  Figure 5.25 Bode Plot for Copper at -0.4 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  60  Figure 5.26 Bode Plot for Copper at -0.3 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  61  Figure 5.27 Bode Plot for Copper at -0.2 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  61  Figure 5.28 Bode Plot for Copper at -0.1 Vsce in lMNaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  62  Figure 5.29 Bode Plot for Copper at 0 Vsce in lMNaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM 62 Figure 5.30 Bode Plot for Copper at 0.1 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  63  Figure 5.31 Bode Plot for Copper at 0.2 Vsce in lMNaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  63  Figure 5.32 Bode Plot for Copper at 0.3 Vsce in lMNaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  64  Figure 5.33 Bode Plot for Copper at 0.4 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  64  Figure 5.34 Bode Plot for Copper at 0.5 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  65  ix  Figure 5.35 Bode Plot for Copper at -0.4 Vsce in lMNaCl buffered to pH 10.5 with 0.0IM Sodium Borate rotating at 5000 RPM  68  Figure 5.36 Bode Plot for Copper at -0.3 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM  68  Figure 5.37 Bode Plot for Copper at -0.2 Vsce in lMNaCl buffered to pH 10.5 with 0.0IM Sodium Borate rotating at 5000 RPM  69  Figure 5.38 Bode Plot for Copper at -0.1 Vsce in IM NaCl buffered to pH 10.5 with 0.0IM Sodium Borate rotating at 5000 RPM  69  Figure 5.39 Bode Plot for Copper at 0 Vsce in lMNaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM 70 Figure 5.40 Bode Plot for Copper at 0.1 Vsce in IM NaCl buffered to pH 10.5 with 0.0IM Sodium Borate rotating at 5000 RPM.  70  Figure 5.41 Bode Plot for Copper at 0.2 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM  71  Figure 5.42 Bode Plot for Copper at 0.3 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM..:......:.,  71  Figure 5.43 Bode Plot for Copper at 0.4 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM  72  Figure 5.44 Bode Plot for Copper at 0.5 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM..  72  Figure 6.1 Current Path Through Circuit Model at Low Frequencies  87  Figure 6.2 Current Path Through Circuit Model at High Frequencies  87  Figure 6.3. Circuit Model for a Passive Film with Large Defect Sites  92  Figure 6.4 Typical Bode Plot of Circuit Model of Passive Film with Large Defects  93  Figure 6:5 Simplified Large Defect Model for Low Frequencies.................:.:  95  Figure 6.6 Simplified Large Defect Modelfor High Frequencies.:........:.....:.........  96  Figure A l . Measured Versus Model Impedance for Copper at -0.4 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM 127 Figure A2. Measured Versus Model Impedance for Copper at -0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM 127 Figure A3. Measured Versus Model Impedance for Copper at -0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM 128 Figure A4. Measured Versus Model Impedance for Copper at -0.1 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM 128 Figure A5. Measured Versus Model Impedance for Copper at 0.0 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  129  Figure A6. Measured Versus Model Impedance for Copper at 0.1 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  129  Figure A7. Measured Versus Model Impedance for Copper at 0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  130  Figure A8. Measured Versus Model Impedance for Copper at 0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  130  Figure A9. Measured Versus Model Impedance for Copper at 0.4 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  131  Figure A10. Measured Versus Model Impedance for Copper at 0.5 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM...... 131 Figure A l 1. Measured Versus Model Impedance for Copper at -0.4 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM.............. 132 Figure A12. Measured Versus Model Impedance for Copper at -0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 132 Figure A13. Measured Versus Model Impedance for Copper at -0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 133 Figure A14. Measured Versus Model Impedance for Copper at -0.1 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 133  xi  Figure A15. Measured Versus Model Impedance for Copper at 0.0 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 134 Figure A16. Measured Versus Model Impedance for Copper at 0.1 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 134 Figure A17. Measured Versus Model Impedance for Copper at 0.2 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 135 Figure A18. Measured Versus Model Impedance for Copper at 0.3 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 135 Figure A19. Measured Versus Model Impedance for Copper at 0.4 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM......:... ... 136 Figure A20. Measured Versus Model Impedance for Copper at 0.5 Vsce in lMNaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM 136  xii  ACKNOWLEDGEMENTS  I would like to thank my supervisor, Dr. Desmond Tromans for his guidance, advice, and patience throughout this research. Many thanks also extend to the faculty members and my fellow students for making graduate studies an enjoyable experience. Financial support provided by PAPRICAN is greatly appreciated.  xiii  1 INTRODUCTION  The corrosion resistance of copper in alkaline solutions is dependent upon the formation of an electrochemically generated film of oxide or hydrated oxide. This film promotes passivity by acting as a diffusion barrier between the metal surface and the environment, thus impeding the corrosion kinetics. The quality of the protection provided by a passive film depends on its physical characteristics. A desirable passivefilmis stable, adherent, and relatively defect free. Under certain conditions a passivefilmis prone to breakdown and undergoes dissolution, thereby accelerating the corrosion rate of the metal substrate.  The anodic behavior of copper in alkaline solutions has been the subject of numerous studies" . It is well established that the corrosion resistance of copper is 1  17  dependent on the presence of a cuprous and cupric oxide (hydroxide) passive film. A review of recent publications has shown that the stability of the passive layer in alkaline solutions may be decreased by complexing agents and enhanced by buffer species.  Copper is widely used and readily available in very pure form. As such, the passivation of copper in alkaline solutions represents a model situation for the study of passivation in general. Examining the mechanisms of passivefilmformation, growth, and breakdown on copper in alkaline solutions may lead to practical solutions in preventing corrosion of metals and alloys that resultfromthe breakdown of passive films.  1  2 LITERATURE REVIEW  2.1 THERMODYNAMICS  Thermodynamic studies on the stability of metals in aqueous solutions was pioneered by Pourbaix via the construction of potential (E) - pH diagrams based on thermodynamic free energy data . These diagrams are useful in predicting the 18  predominant stable species at a given E and pH. As such, it is easy to predict as a first approximation whether the metal will be immune, corrode, or passivate under certain conditions. Given the thermodynamic data listed in Table 2.1, the E-pH diagram for copper in water as prepared by Pourbaix is shown in Figure 2.1 . This diagram shows 18  that CU2O and CuO are predominant in the pH ranges that are slightly acidic to slightly alkaline. Aqueous HCuOV ions can co-exist with Cu 0 and CuO at a slightly alkaline pH. 2  A simple diagram depicting the regions of immunity, corrosion, and passivation is shown in Figure 2.2 . It is important to note that E-pH diagrams are only a guide to predicting 18  passivation. The thermodynamic diagrams do not take into account kinetics or possible differences in local solution chemistry at the metal surface.  2  Table 2.1 Thermodynamic Free Energy Data for Copper Species and Water  SPECIES  AG° (KJ/mol)  Cu  0  Cu 0  -146.4  CuO  -127.2  Cu  +  50.2  2+  65.0  2  Cu  HCu0 "  -257.0  Cu0 -  -182.0  2  2  2  0 H  0  2  o  0  H 0  -228.6  2  2  3  Figure 2.1 E-pH Diagram for Copper in Water at 25 °C ( Hydrogen Reference Electrode) . 18  4  V = V  S  H  E ,  Standard  Figure 2.2 E-pH Diagram for Copper Showing Regions of Corrosion, Passivation, and Immunity at 25 °C . 18  5  2.2 PASSIVE FILM CHARACTERISTICS  It is generally agreed that the passive film on copper consists of a duplex structure of CU2O and CuO or Cu(OH) . According to Sato a less protective CU2O exists adjacent 2  to the metal which is encapsulated with a more protective CuO or Cu(OH)2 barrier layer as shown in Figure 2.3  19  Numerous potentiostatic studies have shown the presence of  two passive states corresponding to the anodic formation of Q12O and CuO or Cu(OH)2 " ' ' " - ' " . 1  6 8 10  14  16 20  23  For example, the polarization curve of copper in a pH 11 solution  buffered with borate (shown in Figure 2.4) shows an anodic peak of -0.26Vsse (silver/silver chloride/saturated potassium chloride reference electrode) corresponding to Cu 0 formation and an anodic peak at -0.03 Vsse corresponding to Cu(OH) formation. 6  2  2  Voltametric studies have shown that a thin layer of Cu 0 forms initially. This is followed 2  by growth of a thicker Cu 0 layer and then followed by growth of the CuO-Cu(OH) 2  2  layers ' . 5 11  BARRIER LAYER LESS PROTECTING LAYER METAL  Figure 2.3 Illustration of a Passive Film on Copper . 19  6  0.3  <  1—i—i—i—i—l—I j*Regionri)-^| ReoJonOE^  1  1—I  1 1—r  Region (H)  H  E  —0.21 Tofell  to  c  <D  "£o.i fi>  is  Tofell -05  0  05  Potential , E / V vs. SSE  Figure 2.4 Polarization Curve of Copper at pH 11 Buffered with Borate  7  1.0  Shirkhanzadeh et al describe the initial stages of passivation in terms of nucleation and growth processes. Discrete nuclei of Cu(I) species form on the surface, followed by the growth and coalescence of the Cu(I) surface nuclei to produce the initial CU2O monolayers . In-situ spectroelectrochemical studies by Pyun et al have shown that 15  hydroxides of Cu(I) and Cu(II) are first formed by anodic oxidation and then transformed to oxides upon aging . Studies by Marchiano et al revealed that at least three different 2  Cu(I) species are formed during CU2O formation. Thefirstis a soluble Cu(OH) ' species, 2  followed by aging to Cu(OH), followed by further aging to CU2O . Laz et al determined 3  that growth of the CuO oxide occurs via electrodissolution of and diffusion of Cu species through the passivating layer . This mechanism was also confirmed by Drogowska et al . 20  4  In addition, they found that the duplexfilmexhibits logarithmic growth kinetics . 20  Photopotential studies on the passivefilmhave shown that the CU2O behaves like a p-type semiconductor (with the presence of electron-holes in the lattice) and CuO behaves like an n-type semiconductor (with excess electrons in the lattice). As such, CuO has a higher electrical conductivity than Cu 0 ' . 20  25  2  X-ray photoelectron spectroscopy (XPS) studies of anodically formed oxides in an alkaline medium (Kautek et al) showed the presence of the dual Q12O and Cu(OH) layers 2  of a combined thickness of 40 A to 60 A . XPS studies on air formed oxides on copper 23  (Chawla et al) have shown a dual oxide structure in the range of 24 A thick . 26  Gravimetric, optical interference, and electrometric studies on air formed oxides have  8  shown that a visible discoloration is observed once the film thickness exceeds a range of 190 A to 380 A . 36  2.3 EFFECT OF HALEDES  Numerous studies have shown that the presence halides adversely affects the passive film. Thermodynamic calculations conducted by Tromans et al have shown that soluble copper chloride complexes can prevent passivation. The E-pH diagram depicting the predominant species in the presence of copper, chlorine, and water is shown in Figure 2.5 . This diagram clearly shows that the formation of soluble CuC^" complexes and non 27  protecting CuCl decreases the stability region of Q12O and CuO.  9  Figure 2.5 Cu-Cl-H 0 Equilibria at 25°C in the Presence of 0.67 Activity of CI 2  Ions. Situation Equivalent to 1M NaCl . 27  10  Drogowska et al found that the presence of sodium chloride in an alkaline solution has an adverse effect on the passive film by increasing the solubility of the passive film and promotes dissolution. Formation of the more soluble cuprous chloride (CuCl) or cupric chloride (CuCl2.3Cu(OH) ) suggests that the copper oxide/solution interface becomes 2  acidic during dissolution as shown in Figure 2.5 ' . Nishikata et al found that a 10 27  concentration of greater than 0.5M chloride ions caused pitting corrosion in an alkaline pH 11 solution. This pitting corrosion was attributed to a decrease in the stability of the passive film . Elser et al found that the formation of sub-monolayer halide complexes 6  prior to the formation of Cu 0 and CuO has a detrimental effect on passivity. In addition, 2  fluoride complexes were found to have the most detrimental effect on passivity. This is followed by chloride complexes, bromide complexes, and then iodide complexes . 17  Pitting investigations by Souto et al showed that pit initiation on copper begins via a random nucleation on the Cu surface in the presence of NaC10 . It was also found that 14  4  chloride ions hinder the performance of inhibitors. 4  2.4 EFFECT OF NON HALIDE COMPLEXING AGENTS  Studies by Milosev et al have shown that  SO4 ' 2  is an aggressive ion to copper. In  the presence of an inhibitor, adsorption of the sulfate ions on the surface of the copper competes with the adsorption of the inhibitor . Souto et al discovered that the presence 12  of Na2S04 causes defects in the passive film, and hence, promotes dissolution of copper through the passive layer . Potentiodynamic studies by Al-Kharafi et al found that sulfate 13  11  ions were less aggressive than chloride ions . Thermodynamic calculations conducted by 9  Tromans et al showed that the presence of ammonia decreases the stability region of CuO via the formation of a Cu(NJT3)„ ion . Studies conducted by Kinoshita et al showed that 2+  1  copper is more susceptible to pitting in the presence of N0 " ions . 28  3  2.5 EFFECT OF BUFFER SPECIES  Studies involving bicarbonate buffers have been contradictory. Most studies have found that HCO3" enhances passivation whereas others have shown that HCO3" is detrimental to passivation. Milosev et al found that the presence of a HCO3" buffer has an inhibitor effect on copper and resists attack of aggressive anions via a competition mechanism . Studies by Drogowska et al found that concentrations of greater than 12  0.05M NaHC03 improve the resistance of copper to localized corrosion . Similarly 4  Sanchez et al found that passivation is enhanced via the formation of copper carbonates in which the structure is dependent upon the H C 0 " concentration. Tromans et al found 5  3  that a higher concentration of a buffer species promote resistance to passive film breakdown by neutralizing surface protons generated by thefilmforming process . 1  Studies have also indicated that N a 2 C 0 enhances the passivefilmbetter than NaHCOs . 11  3  In addition, high fluid velocities at the copper surface enhances passivation . On the 16  contrary, studies conducted by Adeloju et al found that the initial formation of copper carbonates competes with the formation of CU2O and, as a result, has a detrimental effect  12  on passivation ' . Studies by Nishikata et al have found that the stability of the passive 7 21  layer-is lowered by the presence of carbonate ions . 6  There is general agreement that the presence of phosphate or borate buffers enhances passivation. Drogowska et al found that a high phosphate to chloride ratio results in the formation of a thin protective layer whereas a high chloride to phosphate ratio results in the precipitation of a thick porous deposit on the surface . Laz et al found 29  that phosphate ions enhance passivation via the formation of a protective copper phosphate species on the surface . Studies conducted by Al-Kharafi et al found that 20  phosphate ions promote resistance of copper to aggressive anions such as sulfates, chlorides, and iodides . De Chialvo et al found that borate buffers inhibit the formation of 9  CuCl during pit growth . 8  13  3 OBJECTIVE  Although there have been many studies conducted on copper in alkaline solutions, very few studies have been devoted to examining the mechanism of passive film formation, growth, and breakdown. This thesis is directed toward applying a combination of traditional and novel electrochemical techniques to determine the mechanisms of passive film breakdown. Polarization studies conducted in solutions of different buffer concentrations and under different fluid flow rates (via a rotating disk electrode) will provide clues on how changes in surface pH affect passive film breakdown. In addition, the use of AC impedance spectroscopy will allow the characteristics of the passive film to be modeled. As such, the film characteristics during film formation, growth, and breakdown can be determined in-situ. There have been no publications to date on the use of AC impedance spectroscopy to examine passivation of copper in alkaline solutions.  14  4 EXPERIMENTAL  4.1 SOLUTION PREPARATION  All test solutions were prepared from reagent grade chemicals and distilled water. Alkaline IM sodium chloride test solutions were prepared in IL batches by adding 58.45 grams of sodium chloride and the required buffer agent into a beaker and bringing the total volume to IL with distilled water. For solutions buffered with sodium carbonate and sodium bicarbonate a molar ratio of 1.45 sodium carbonate to sodium bicarbonate was added to bring the pH to near 10.5. For example, for a desired 0.01M buffer concentration, 0.7316 grams of sodium carbonate monohydrate (molecular weight of Na2C03.H 0 of 124.00 g/mole) and 0.3444 grams of sodium bicarbonate (molecular 2  weight of NaHC03 of 84.01 g/mole) would be added. For the solutions buffered with sodium tetraborate, 3.8142 grams of Na2B 0 (molecular weight 381.42 g/mole) would 4  7  bring the solution to a 0.01M buffer concentration.  The pH measurements were conducted via a two point calibrated Corning Model 125 pH meter with a combination glass pH electrode. Measured pH values of the prepared solutions were generally up to 0.3 pH value below 10.5 for solutions buffered with sodium carbonate and sodium bicarbonate, and up to 1.8 pH value below 10.5 for solutions buffered with sodium tetraborate. Further pH adjustments were made with small  15  incremental additions of 1M sodium hydroxide until a stable reading of pH 10.5 ± 0.05 was achieved. A list of the test solutions used in this research is shown in Table 4.1.  Table 4.1 List of Test Solutions  Solution No.  NaCl (M)  Na C0 (M)  1 2 3 4 5 6 7  1 1 1 1 1 1  0.0059 0.0296 0.0592 0.2959  2  3  NaHC0 (M)  Na B 0 (M)  3  2  4  0.0041 0.0204 0.0408 0.2041 0.001 0.010 0.050  1  7  Total Buffer Concentration (M)  PH  0.010 0.050 0.100 0.500 0.001 0.010 0.050  10.5 10.5 10.5 10.5 10.5 10.5 10.5  4.2 SAMPLE PREPARATION  Rotating disk electrode test specimens were prepared by machining copper blocks of greater than 99.96% purity to 11.3 mm diameter and 2 mm thickness disks. Each disk was subsequently mechanically polished to a 600 grit finish to ensure consistency of the surface finish. Prior to each test a disk was partially inserted into a recessed Teflon disk holder supplied with the EG&G model 616 rotating disk electrode. The Teflon disk holder was then turned over, rested on a flat Teflon block and pressed until the disk was perfectly flush with the rim. The spring loaded contact was connected to the back of the test specimen and the sample holder was connected to the main body of the rotating disk electrode as shown in Figure 4.1.  16  I A = DISK B = DISK HOLDER C = O-RINGS D = MAIN BODY E = SPRING F = CONTACT STUD G = SPINDLE H = SPINDLE COVER Figure 4.1 Assembly of the Rotating Disk Electrode Specimen  17  4.3 ELECTROCHEMICAL CELL SET-UP  The 750 mL Teflon electrochemical cell consisted of five pre-drilled inlets for the rotating disk electrode, two platinum mesh counter electrodes, a saturated calomel reference electrode (see), and a nitrogen purge tube. The test set-up is shown in Figure 4.2  Figure 4.2 Electrochemical Cell Set-Up  18  4.4 POLARIZATION SCAN TECHNIQUES  Polarization scans were conducted with the Solartron 1280 potentiostat, which was connected to an MS-DOS personal computer via a GPIB-488 interface. Software was written in Microsoft Quickbasic to control the Solartron 1280 and to acquire data from the experiments. Prior to each test, the rotation speed of the electrode was set from thefrontcontrol panel. Nitrogen purging was conducted for 30 minutes to remove dissolved oxygen from the cell. The working electrode was then polarized at a potential of-0.9 Vsce for 30 minutes to reduce the air formed oxide. The potential was then swept from -0.9 Vsce to +0.9 Vsce at a scan rate of lmV per second. The control software is listed in Appendix I.  4.5 AC IMPEDANCE SCAN TECHNIQUES  AC impedance scans were conducted with the combination of the Solartron 1280 potentiostat and the Solartron 1250frequencyresponse analyzer. The Solartron 1280 was used to polarize the test specimen to the desired test potential, whereas the Solartron 1250 was used to apply an external + lOmV sinusoidal potential over afrequencysweep such that the impedance could be measured. Both instruments were connected to an MS-DOS personal computer via a GPIB 488 interface and software was written in Microsoft Quickbasic to control the impedance experiments and to acquire the impedance data. Prior to each test, the rotation speed of the electrode was set from  19  the front control panel. Nitrogen purging was conducted for 30 minutes to remove dissolved oxygen from the cell. The working electrode was then polarized at a potential of-0.9 Vsce for 30 minutes to reduce the air formed oxide. The potential was then stepped to -0.4 Vsce and held at this potential for 5 minutes to allow the cell to stabilize. A ±10 mV sinusoidal potential was then superimposed over the polarization potential and impedance measurements were made over a frequency sweep from 65535 Hz to 0.1 Hz. Impedance scans were conducted at a range of polarization potentialsfrom-0.4 Vsce to 0.5 Vsce at 0. IV increments. A control software program for the impedance experiments is listed in Appendix II.  4.6 ROTATION SPEEDS  All polarization and AC impedance experiments were conducted at both 50 RPM and 5000 RPM. These rotation speeds were selected because the diffusion layer thickness is proportional to the inverse square root of rotation speed , and as such, the diffusion 34  layer thickness would be changed by a factor of 10.  20  5 RESULTS  5.1 POLARIZATION STUDIES  The general polarization curve of copper in a sodium chloride media buffered to an alkaline pH is characterized by several distinct regions as shown schematically in Figure 5.1. At the beginning of the potential sweep below the corrosion potential  (E ^) c o  (Region I), species in the aqueous solution are reduced. Protons are reduced to hydrogen gas and trace oxygen (not removedfromnitrogen purging) is reduced to water. The electrochemical reactions for the reduction of protons and oxygen are as follows:  2FT + 2e" -> H  5.1  2  0 + 4FT + 4e" -> 2H 0 2  2  5.2  Region II directly aboveEcoir is where copper actively corrodes as per the following reaction:  Cu -> Cu + e  5.3  +  21  Following the active corrosion regime, a fairly noticeable active-passive transition occurs (Region III). This has been observed in all polarization scans in this work under the specified conditions. After Region III, passivation occurs (Region IV). This is characterized by a sudden decrease in current (or corrosion rate) and is due to the formation of a thin, adherent oxide which acts as a diffusion barrier between the copper metal and the solution. The passive region contains a small peak (IV). From a review of publishedfindings,it is determined that the transition peak (III) corresponds to the formation of CU2O and peak (IV) corresponds to the anodic formation of CuO or Cu(OH) " ' ' " ' ' " . Possible passivation reactions are as follows, where Equation 5.4 1  6 8 10  14 16 20  23  2  represents peak III, and 5.5 and 5.6 correspond to peak IV.  2Cu + H 0 2  Cu 0 + 2FT + 2e" 2  5.4  Cu + H 0-> CuO + 2Ff + 2e'  5.5  Cu + 2H 0 -> Cu(OH) + 2FT + 2e"  5.6  2  2  2  With increasing potential, the pitting potential (Ep;) is reached. This is characterized by a t  sudden increase in current which is representative of passivefilmbreakdown. Epj is an t  important value in this study because it relates to the ability of the passivefilmto resist breakdown. A higher EpH value represents a higher resistance tofilmbreakdown, whereas a lower E H value represents a lower resistance tofilmbreakdown. The transpassive P  22  regime at the high potentials (Region V) characterized by a diffusion controlled mechanism represents the formation of a non-protective precipitate or film.  Log Current Density  Figure 5.1 Typical Polarization Curve for Copper in 1M NaCl in a Buffered Alkaline Solution.  The polarization behavior of copper in a 1M sodium chloride media buffered to an alkaline pH was studied under several conditions. The effects of buffer type, concentration, and rotation speed with a rotating disk electrode were studied. The results are shown in the following sections.  23  5.1.1 POLARIZATION BEHAVIOR - EFFECT OF BUFFER TYPE  The effects of buffer type are shown on the polarization curves in Figures 5.2 to 5.5. Polarization experiments were conducted in IM sodium chloride with identical concentrations of either a sodium bicarbonate/carbonate buffer or a sodium tetraborate buffer at identical rotation speeds. Each polarization curve of copper in a IM sodium chloride solution buffered with either sodium bicarbonate/carbonate or sodium tetraborate exhibited some form of passivation. Under identical test conditions, there was very little difference in the shape of the polarization curve between the sodium bicarbonate/carbonate buffer and the sodium tetraborate buffer. Other than the fact that the sodium bicarbonate/carbonate buffered solution continually had a higher corrosion potential than the sodium tetraborate buffered solutions, there was very little difference in the pitting potentials or the passive current densities. The higher corrosion potential for the solutions buffered with sodium bicarbonate/carbonate may be attributed to a small amount of carbon dioxide formation via Equation 5.7. Data of the corrosion potentials, pitting potentials, and the passive current densities are summarized in Table 5.1. The polarization data was reproducible as repeated experiments yielded near identical results.  C0 " + 2H+ -> C0 + 2H 0 2  3  2  2  24  5.7  Log Current Density (A/m2) 0.01 M Bicarbonate/Carbonate 50RPM  0.01 M Borate 50RPM  Figure 5.2 Polarization Curve of Copper in 1M NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, and (2) 0.01M Sodium Borate at 23°C.  25  Log Current Density (A/m2) 0.01 M Bicarbonate/Carbonate 5000RPM  0.01 M Borate 5000RPM  Figure 5.3 Polarization Curve of Copper in 1M NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, and (2) 0.01M Sodium Borate at 23°C.  26  Log Current Density (A/m2) 0.05M Bicarbonate/Carbonate 50RPM • • •  0.05M Borate 50RPM  Figure 5.4 Polarization Curve of Copper in IM NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.05M Sodium Bicarbonate/Carbonate, and (2) 0.05M Sodium Borate at 23' C  27  Log Current Density (A/m2) 0.05M Bicarbonate/Carbonate 5000RPM -  0.05M Borate 5000RPM  Figure 5.5 Polarization Curve of Copper in 1M NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.05M Sodium Bicarbonate/Carbonate, and (2) 0.05M Sodium Borate at 23°C  28  Table 5.1 Summary of Polarization Data for Different Buffer Types  Buffer Type  Rotation (RPM)  Corrosion Potential (Vsce)  Pitting Potential (Vsce)  Passive Current Density  0.0 IM Sodium Bicarbonate/Carbonate 0.0 IM Sodium Borate  50  -0.38  0.09  (AJm ) 1.6 x 10"'  50  -0.50  0.05  1.8 x 10"  0.0 IM Sodium Bicarbonate/Carbonate 0.01M Sodium Borate  5000  -0.40  0.11  9.3 x 10"  5000  -0.51  0.18  1.8 x 10'  50  -0.33  0.12  1.4 x 10"  50  -0.51  0.18  1.1 x 10"  5000  -0.41  0.58  3.6 x 10"  5000  -0.42  0.50  7.5 x 10"  0.05M Sodium Bicarbonate/Carbonate 0.05M Sodium Borate 0.05M Sodium Bicarbonate/Carbonate 0.05M Sodium Borate  2  1  1  1  1  1  1  1  Note: passive current densities are taken at -0.1 Vsce  5.1.2 POLARIZATION BEHAVIOR - EFFECT OF BUFFER CONCENTRATION  The effects of buffer concentration on the passivation of copper in IM sodium chloride buffered to pH 10.5 are shown clearly in Figures 5.6 to 5.9. Figure 5.6 shows the differences in polarization behavior between 0.0IM, 0.05M, 0.1M, and 0.5M sodium bicarbonate/carbonate buffered solutions at a pH of 10.5 and a rotation speed of 50 RPM. Figure 5.7 shows the difference between 0.01M, 0.05M, 0.1M, and 0.5M sodium bicarbonate/carbonate buffered solutions at 5000 RPM. Figure 5.8 shows the difference between 0.001M, 0.01M, and 0.05M sodium borate solutions running at 50 RPM.  29  Figure 5.9 shows the difference between 0.001M, O.OIM, and 0.05M sodium borate buffered solutions running at 5000 RPM.  Figure 5.6 Polarization Curve of Copper in 1M NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, (2) 0.05M Sodium Bicarbonate/Carbonate, (3) 0.1M Sodium Bicarbonate/Carbonate, and (4) 0.5M Sodium Bicarbonate/Carbonate at 23°C  30  0.9 0.8 0.7 Ofi 0.5  \" \  C r  / i - ^ ' i  /  0.4 \0.3  X 2  1  1  1  y - ^r  1  2  :  -\<^  -  2  _n  ~~  -~-—r  A  i f \ l  11-0.9 • 1_  Log Current Density (A/m2) 0.01 M Bicarbonate/Carbonate 5000RPM (A)  0.05M Bicarbonate/Carbonate 5000RPM (B)  0.1 M Bicarbonate/Carbonate 5000RPM (C)  0.5M Bicarbonate/Carbonate 5000RPM(D)  Figure 5.7 Polarization Curve of Copper in 1M NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.01M Sodium Bicarbonate/Carbonate, (2) 0.05M Sodium Bicarbonate/Carbonate, (3) 0.1M Sodium Bicarbonate/Carbonate, and (4) 0.5M Sodium Bicarbonate/Carbonate at 23°C  31  Log Current Density (A/m2) 0.001 M Borate 50RPM (A)  0.01 M Borate 50 RPM (B)  . 0.05M Borate 50 RPM (C)  Figure 5.8 Polarization Curve of Copper in IM NaCl, Rotating at 50 RPM, Buffered to pH 10.5 with (1) 0.001M Sodium Borate, (2) 0.01M Sodium Borate, and (3) 0.05M Sodium Borate at 23°C  32  .  1— 0.9 0.8 0.7 0.6  &5JOA •  5  -4 i  -3 i  -2 i  V  ^3 0>  -1 r- 1  1 °i -QjA i <crjri ti\  —j  2  V^0.W  ^r^^T  -0.4 -0.6-  \ \ '° 7  \  ;  -0.8 -  i-  Log Current Density (A/m2) 0.001 M Borate 5000RPM (A)  0.01 M Borate 5000RPM (B)  0.05M Borate 5000RPM (C)  Figure 5.9 Polarization Curve of Copper in IM NaCl, Rotating at 5000 RPM, Buffered to pH 10.5 with (1) 0.001M Sodium Borate, (2) 0.01M Sodium Borate, and (3) 0.05M Sodium Borate at 23°C  33  During each polarization test, the copper specimen remained bright and shiny until there was breakdown of the passivefilm.Following the passivefilmbreakdown a nonadherent blue-green precipitate formed. This precipitate continually spalled off the surface of the rotating copper disk. A sample of this precipitate was analyzed on the EDX and was shown to contain 40.12 atomic percent chlorine and 59.88 atomic percent copper. As such, it is fair to assume that the majority of this precipitate is cuprous chloride (CuCl). In each of the graphs shown in Figures 5.6 to 5.9 there is a clear and repeatable increase in pitting potential with increasing buffer concentration. At the higher buffer concentrations of 0.5M sodium bicarbonate/carbonate no passive film breakdown was observed and the specimen remained shiny throughout the test. The corrosion potentials, pitting potentials, and passive current densities for each test are summarized in Table 5.2.  34  Table 5.2 Summary of Polarization Data For Increasing Buffer Concentration  Rotation (RPM)  Corrosion Potential (Vsce)  Pitting Potential (Vsce)  Passive Current Density (A/m)  50  -0.38  0.09  1.6 x 10"  50  -0.33  0.12  1.4 x 10"  50  -0.33  0.33  1.8 x 10"  50  -0.43  no pitting  1.8  5000  -0.40  0.11  9.3 x 10"  5000  -0.41  0.58  3.6 x 10  5000  -0.36  0.65  7.6 x 10'  5000  -0.45  no pitting  8.1  0.00 IM Sodium Borate  50  -0.39  -0.08  1.9 x lO  0.0 IM Sodium Borate  50  -0.50  0.05  1.8 x 10"  0.05M Sodium Borate  50  -0.51  0.18  1.1 x 10"  0.00 IM Sodium Borate  5000  -0.31  -0.08  3.6  0.0 IM Sodium Borate  5000  -0.51  0.18  1.8 x 10'  0.05M Sodium Borate  5000  -0.42  0.50  7.5 x 10"  Buffer Type 0.0 IM Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.0 IM Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate  Note: passive current densities are taken at -0.1 Vsce  35  2  1  1  1  1  1  1  -1  1  1  1  1  5.1.3 POLARIZATION BEHAVIOR - EFFECT OF ROTATION SPEED  The effects of rotation speed on the passivation of copper in alkaline buffered 1M sodium chloride are shown in Figures 5.10 to 5.15. Figure 5.10 shows the polarization curves of the 0.01 sodium bicarbonate/carbonate buffered solution at pH 10.5 at rotation speeds of 50 RPM and 5000 RPM. Figure 5.11 shows the polarization curves for the 0.05M bicarbonate/carbonate buffered solution at 50 RPM and 5000 RPM. Figure 5.12 shows the polarization curves for the 0.1M bicarbonate/carbonate buffered solution at 50 RPM and 5000 RPM. Figure 5.13 shows the polarization curves for 0.5M bicarbonate/carbonate buffered solutions at 50 RPM and 5000 RPM. Figure 5.14 shows the polarization curves for the 0.01M sodium borate buffered solution at 50 RPM and 5000 RPM. Figure 5.15 shows the polarization curves for the 0.05M sodium borate buffered solution at 50 RPM and 5000 RPM.  36  Figure 5.10 Polarization Curve of Copper in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  37  Log Current Density (A/m2) 0.05M Bicarbonate/Carbonate 50 RPM  0.05M Bicarbonate/Carbonate 5000RPM  Figure 5.11 Polarization Curve of Copper in 1M NaCl Buffered to pH 10.5 with 0.05M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  38  -0.4 -0.5 \-0.6 -  I  4-1 :  1  Log Current Density (A/m2) 0.1 M Bicarbonate/Carbonate 50 RPM  0.1 M Bicarbonate/Carbonate 5000RPM  Figure 5.12 Polarization Curve of Copper in IM NaCl Buffered to pH 10.5 with 0.1M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  39  Log Current Density (A/m2) 0.5M Bicarbonate/Carbonate 50RPM  - 0.5M Bicarbonate/Carbonate 5000RPM  Figure 5.13 Polarization Curve of Copper in 1M NaCl Buffered to pH 10.5 with 0.5M Sodium Bicarbonate/Carbonate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  40  Log Current Density (A/m2) 0.01 M Borate 50RPM  0.01 M Borate 5000RPM  Figure 5.14 Polarization Curve of Copper in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Borate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  41  Log Current Density (A/m2) 0.05M Borate 50RPM  0.05M Borate 5000RPM  Figure 5.15 Polarization Curve of Copper in IM NaCl Buffered to pH 10.5 with 0.05M Sodium Borate Rotating at (1) 50RPM, and (2) 5000RPM at 23°C  From the polarization curves that compare the effects of rotation speed on the passivation behavior of copper in buffered alkaline IM sodium chloride, there is clearly an increase in pitting potential at the higher rotation speeds. The increase in pitting potential with increasing rotation speed is greater at the higher buffer concentrations. This indicates that the diffusion of the buffer species to the surface of the copper in alkaline IM sodium chloride plays an important role in the prevention of passive film breakdown. In addition, the passive current density increases with increasing rotation speed, which shows that  42  passivation follows a diffusion controlled mechanism. The corrosion potentials, pitting potentials, and passive current densities (datafromTable 5.2) are re-arranged in Table 5.3 to show the effects of rotation speed. A plot of pitting potential as a function of buffer concentration is shown in Figure 5.16 (note that tests performed in the 0.5M bicarbonate/carbonate buffered solution exhibited no passive film breakdown).  Table 5.3 Summary of Polarization Data Showing Effects of Rotation Speed  Buffer Type  0.0 IM Sodium Bicarbonate/Carbonate 0.01M Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate  50  Corrosion Potential (Vsce) -0.38  Pitting Potential (Vsce) 0.09  Passive Current Density (AJm ) 1.6 x 10'  5000  -0.40  0.11  9.3 x 10"  50  -0.33  0.12  1.4 x 10"  5000  -0.41  0.58  3.6 x 10"  50  -0.33  0.33  1.8 x 10"  5000  -0.36  0.65  7.6 x 10"  Rotation (RPM)  1  1  1  1  1  1  1  0.5M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.01M Sodium Borate  50  -0.43  no pitting  1.8  5000  -0.45  no pitting  8.1  50  -Q.50  0.05  1.8 x 10"  0.0 IM Sodium Borate  5000  -0.51  0.18  1.8x10"'  0:05M Sodium Borate  50  -0.51  0.18  1.1x10-'  0.05M Sodium Borate  5000  -0.42  0.50  7.5 x 10"'  Note: passive current densities are taken at -0.1 Vsce  43  1  0.7  0  -I  1  1  1  0  0.01  0.02  0.03  1  1  1  1  1  1  0.04  0.05  0.06  0.07  0.08  0.09  Buffer Concentration (M) — • — Bicarbonate/Carbonate 50RPM (A) —*— Borate 50RPM (C)  •  Bicarbonate/Carbonate 5000RPM (B)  -X— Borate 5000RPM (D)  Figure 5.16 Plot of Pitting Potential Versus Buffer Concentration For AH Experiments Conducted.  44  1 0.1  5.2 AC IMPEDANCE SPECTROSCOPY STUDIES  AC Impedance Spectroscopy (ACIS) is a relatively new electrochemical technique used to examine the electrochemical and physical properties of electrochemical systems. This technique was first used by Randies and Somerton in 1952 . In this thesis ACIS is 30  used as a tool to study the physical characteristics of the passive film in-situ. A passive film in-situ inherently has a certain amount of capacitance and resistance depending on it's physical characteristics. Thus, the passivefilmimpedes current flow in a similar fashion to an electrical circuit consisting of capacitors and resistors. With ACIS the capacitive and resistive components of the passivefilmcan be determined by measuring the electrical impedance of the cell over a frequency sweep. A small amplitude (± 10m V) sinusoidal potential perturbation superimposed over the polarization potential is applied such that an impedance measurement can be obtained without (or negligibly) affecting the equilibrium condition of the passivefilm.As such, the passivefilmcan be characterized by modeling the passivefilmwith an electrical equivalent circuit as shown in Figure 5.17.  45  C(film)  Metal  Solution  • Passive Film  R(solution)  R(Film) Electrical Model oF Passive Film  In-Situ Passive F8m  Figure 5.17 Electrical Circuit Model of a Passive Film In-Situ  The passive film is capable of charging and discharging with an applied A C potential, and thus has a certain amount of capacitance (known as the passive film capacitance, Cnim). In addition, the passive film has a certain resistance to current flow (represented by the passivefilmresistance, Rcim). Finally the electrolyte has a certain resistance (represented by the solution resistance, Ration). To understand the basics of ACIS it is necessary to discuss the theory of impedance for capacitors and resistors, the modeling of electrochemical cells with electrical equivalent circuits, and the use of these models to characterize the electrochemical and physical parameters of an electrochemical cell.  46  5.2.1 THEORY OF IMPEDANCE FOR CAPACITORS AND RESISTORS  Capacitors and resistors are physically differentfromone another and thus behave differently when an AC potential is applied. The theory of impedance of capacitors, resistors, and capacitor-resistor combinations will be described in order to clarify the subsequent presentation of the experimental AC impedance data.  5.2.1.1 IMPEDANCE OF CAPACITORS  A capacitor consists of two parallel conducting plates separated by an insulating material, known as a dielectric (Shown in Figure 5.18).  Conducting Parallel Plates  Insulating Barrier  Figure 5.18 A Capacitor  47  When a DC voltage is applied across a capacitor, the plates become charged (Figure 5.19) and thus prevent the passage of current. Hence, a capacitor has an infinite impedance when a DC voltage is applied. However, when the polarity of the charged plates alternate (e.g. when a sinusoidal voltage is applied) the capacitor discharges, thereby allowing current to pass (illustrated in Figure 5.20). In general, a capacitor has two important characteristics due to the charge-discharge effect when a sinusoidal voltage is applied. The first is frequency dependent impedance, and the second is a time lag between the resulting current and the applied voltage.  Figure 5.19 Charged Capacitor  48  Capacitor Discharge  Charged Capacitor  -©  •0 0 -  ©-  Current F l o w  No Current F l o w  Figure 5.20 Capacitor Charge and Discharge  5.2.1.1.1 FREQUENCY DEPENDENT IMPEDANCE OF CAPACITORS  As the frequency of the applied voltage across a capacitor is increased (i.e. as the polarity of the charged plates alternate at a faster rate), the capacitor discharges and then charges at a faster rate. Therefore, the higher the frequency of the applied voltage, the more current is allowed to pass resulting in a lower impedance. Equations 5.8 describes the relationship between the magnitudes of impedance for a capacitor and the frequency of the applied voltage.  5.8  capacitor  49  Where: Z,capacitor = Magnitude of Impedance For a Capacitor (Ohms)  co = Angular Frequency — 2 x n x Frequency (Hz) C= Capacitance (Farads)  5.2.1.1.2 TIME LAG BETWEEN CURRENT AND VOLTAGE  The charge-discharge effect of a capacitor is not instantaneous, but occurs over a short period of time. Thus, when a sinusoidal voltage is applied across a capacitor, the resulting current lags the applied voltage by a certain amount of time. Therefore, the resulting current is out of phase with respect to the applied voltage according to Equations 5.9 and 5.10 respectively.  V(t)  V sin(ft> t)  5.9  0  /(>) I sin(o) t + 0)  5.10  a  50  Where: V(t) = Applied Voltage I(t) = Measured Current V = Peak Voltage Q  I = Peak Current a  co = Angular Frequency t = Time 6 = Phase Angle (time lag)  For a capacitor the phase angle is always 90° or %I2 radians. In other words, when a sinusoidal voltage is applied across a capacitor the resulting current is always out of phase by 90° or Till radians. This is illustrated graphically in Figure 5.21.  / A*' \  *  \  e  / A""'-/  *  *•/  "*  4 vy  \  M  \  /  V  vy  Time Applied Voltage  Measured Current  Figure 5.21 Applied Voltage and Resulting Current for a Capacitor  51  5.2.1.2 IMPEDANCE OF RESISTORS  Resistors are simpler components compared to capacitors because the impedance response of a resistor is independent of frequency (or time). The impedance of a resistor is equal to the resistance. In addition, the measured current and applied voltage are in phase for a resistor. In other words, there is no time lag between the measured current and the applied voltage (0 = 0).  5.2.2 IMPEDANCE OF THE PASSIVE FILM C m C U I T MODEL  The basic electrical equivalent circuit used to model a passivefilmis called a Randies Circuit as shown in Figure 5.22 (and is equivalent to the situation in Figure 5.17).  C(film)  R(solution)  -A/VV R(film)  Figure 5.22 Randies Circuit used to Model a Passive Film  52  Since the Randies Circuit is composed of both capacitance and resistance, the impedance response of this circuit ought to be somewhere in between the impedance response of a purely resistive circuit and a purely capacitive circuit. Therefore, the impedance of the Randies Circuit will be dependent on the applied voltage, and the phase angle will be somewhere in between 0° and 90°.  5.2.3 VECTOR REPRESENTATION OF IMPEDANCE  Impedance is essentially a vector quantity consisting of the magnitude of impedance (a scalar quantity) and a direction (phase angle). This representation of impedance is called polar form. Impedance can also be represented by two component vectors consisting of a real component of impedance and an imaginary component of impedance, called rectangular form (see Figure 5.23).  53  Phase Angle  Real Impedance  Figure 5.23 Vector Representation of Impedance  I.  The real component of impedance represents the "in phase" resistance of the circuit, and the imaginary component of impedance represents the "out of phase" reactance of the circuit. A purely resistive circuit would have only resistance (real component of impedance) and no reactance (imaginary component of impedance), whereas a purely capacitive circuit would have only reactance and no resistance. Equations 5.11, 5.12, and 5.13 describe the relationship between polar form and rectangular form.  54  \z\ze = z'+jZ"  5.11  |Z| = y/Z' +Z" 2  2  0 = ARCTAN[^J  Where:  5.12  5.13  \Z\ = Magnitude of Impedance 6 = Phase Angle Z ' = Real Component of Impedance (Resistance) Z" = Imaginary Component of Impedance (Reactance) 7 = V^T  5.2.4 CALCULATION OF IMPEDANCE FOR A RANDLES CIRCUIT  With the electrical circuit model of the passive film (Randies Circuit) as shown in Figure 5.22, the passive film is represented by a parallel combination of a capacitor (Cf,i„,) and a resistor (Rfiim). As such, the impedance of this parallel circuit is calculated by the parallel circuit rule as follows:  55  1 (  1  ^  7  ]  resistor'  i  r  + 7 \  i  ]  5.14  capacitor J  =—  5.15  Where: Z - Impedance of the Passive Film fitm  By multiplying both the numerator and the denominator of Equation 5.15 by — - {jai C ), \ fiu film) film  the impedance of the passivefilm(Zfiim) can be rearranged to  R  rectangular form as shown by Equation 5.16.  CO ^film  5.16  ~ ^film'-'  film  OJ  2  + p2 f~<2 ^film^filmJ  C film ^  RfilmCfilmJ  By adding the series solution resistance (Relation) to the passivefilmimpedance, the impedance of the Randies Cell model ( Z  ce  n)  becomes (in rectangular form):  56  This cell impedance can be converted to polar form to allow for plotting simplicity without the need to deal with complex numbers. The cell impedance in polar form (magnitude \z  \ and phase angle 0) is calculated as follows:  cELL  V  R  solution  f  5.18  +a> + n2 2  RfilmCfilm  p2  y->2 ^filrn^filmJ  r  2  ^•film^filmJ.  c film a> + 2  RfilnPfilm) 0  =  ARCTAN  5.19  r  solution RfilmCfilm  co + 2  p2  r  2  ^film^filmJ  57  Note that in electrochemistry (as opposed to electrical engineering) the sign of the phase angle is reversed so that the phase lag can be plotted on the positive axis for simplicity.  co f  r \  6 = ARCTANf R  ^film  CO'  r>2  r^2  ^film^filmJ  v  5.20  +solution D  r<2  ^film^film  a> + p 2 2  r  2  5.2.5 PLOTTING IMPEDANCE DATA  Impedance data is plotted on what is called a Bode Plot. This is a dual y-axis plot of log magnitude of impedance and phase angle versus log frequency. A typical Bode plot is shown in Figure 5.24.  58  Figure 5.24 Typical Bode Plot of Impedance Data.  The typical Bode plot of the basic model of a passive film consists of two impedance plateaus and one phase angle peak. The first impedance plateau is seen at a lowfrequencyand is equivalent to the sum of the film resistance (Rf,im) and the solution resistance (Rsoiution)- This plateau is seen because the impedance of the passive film capacitance is very high at low frequencies (since Z  film cavacitor  = ——— ), thus the current ML film  only passes through R f , i and Rsoiution- The second impedance plateau is seen at a high m  frequency and is equal to Rsoiution- This is seen because at the highfrequencies,the impedance of Cf,i is very small and as such shunts Rf,im. At intermediatefrequencies,a m  phase angle peak is seen because the impedance of Cfum is significant.  59  5.2.6 AC IMPEDANCE DATA DURING PASSIVE FTLM FORMATION AND BREAKDOWN  Impedance data were obtained at increasing electrochemical potentials such that the physical characteristics of the passive film could be modeled in-situ during film formation and breakdown. These impedance scans were conducted at 0.1 Volt increments from -0.4 Vsce to 0.5 Vsce in a 1M sodium chloride solution, buffered to pH 10.5 with a 0.01M sodium borate buffer at both 50 RPM and 5000 RPM. The Bode plots for the impedance scans conducted in 1M sodium chloride, buffered to pH 10.5 with 0.01M sodium borate at 50 RPM are shown in Figures 5.25 to 5.34.  90  -0.4Vsce  80 70  in  E  60  o  9  50 40 30 20  en o  10 0 0  1  2  3  4  Log Frequency (Hz) - Impedance  Phase Angle  Figure 5.25 Bode Plot for Copper at -0.4 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  60  90 80 70 60  f  50 u 40 ^ 30  S  20 £ 10 0 -1  0  1  2  3  4  5  Log Frequency (Hz) Impedance Phase Angle  Figure 5.26 Bode Plot for Copper at -0.3 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  •  r 90  6-, -0.2Vsce  80 70 60  • •  50  0) Ul  • 40 c 30  ? •  20  ; ; 1 —i—fQ-^ -1 0  <  Phase  •• •  10 -H  1  1  1  i  2  3  4  — 0  5  Log Frequency (Hz) Impedance  Phase Angle  Figure 5.27 Bode Plot for Copper at -0.2 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  61  90  -0.1 Vsce  5-  80 70  (A  E : :  4  :  E  |  50  «T  40 ^  IS  a.  60  30 Si re 20 £  : :  1  "  10  7^—o-  1  1  0  1  2  1  i  ^— 0  3  Log Frequency (Hz) - Impedance  Phase Angle  Figure 5.28 Bode Plot for Copper at -0.1 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  j 90 80  OVsce  70  E  60 oi 2_ - 50 SI o> • 40 c  £  o U  c  (0  30 < in f 20 0 L  a.  01  E  o> o  10 1  — i  1  2  1—  • 0  3  Log Frequency (Hz) •knpedance  Phase Angle  Figure 5.29 Bode Plot for Copper at 0 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  62  0  1  2  3  4  Log Frequency (Hz) • Impedance  Phase Angle  Figure 5.30 Bode Plot for Copper at 0.1 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  90 80  0.2Vsce  70 _ 60  SP •a  50 £ 40  O)  |  0)  30 « 20 £ 10 - 1 0  1  2  3  4  0  Log Frequency (Hz) •Impedance  Phase Angle  Figure 5.31 Bode Plot for Copper at 0.2 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  63  90 80  0.3Vsce  70 _ 60  |  50 «T Ol  40 £ 30  8  20 £ 10 1  2  0  3  Log Frequency (Hz) -Impedance  Phase Angle  Figure 5.32 Bode Plot for Copper at 0.3 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  90  o—  0.4Vsce  5-  E  XZ  4  a u  3  a.  2  O E  --  70 _ --  60  |  40 --  20 a.  1 •  80  10 — ^ — : ' \ - '  0 0  1  2  —  H  0  3  Log Frequency (Hz) Phase Angle  - Impedance  Figure 5.33 Bode Plot for Copper at 0.4 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  64  j 90  0.5Vsce  80  in  - 70  E  60 f - 50 £ - 40 <c 30 in  TJ  at a.  jj  20  q  10  W -C  a.  - 0 0  1  2  3  4  Log Frequency (Hz) Phase Angle  • Impedance  Figure 5.34 Bode Plot for Copper at 0.5 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM.  The Bode plots shown in Figures 5.25 to 5.34 are used to characterize the passive film characteristics during formation and breakdown. During passive film formation (from -0.4 Vsce to -0.1 Vsce) there is a distinct difference between the lowfrequencyand the highfrequencyimpedance. This indicates that a passivefilmis present on the surface of the copper as the difference between the low frequency impedance and the high frequency impedance represents the passivefilmresistance. In addition, the phase angle shows a distinct peak. Thefrequencyin which the phase angle peak occurs increases with increasing potential in the passive region. In this potential range the sample remained bright and shiny. At a potential of 0 Vsce there is a noticeable drop in the low frequency impedance concurrent with a splitting of the phase angle peak to form a lower frequency  65  peak and a higher frequency peak. This occurs at the onset of the passive film breakdown as the polarization curve shown in Figure 5.14 indicate that the pitting potential is 0.03 Vsce under the tested conditions. At 0.1 Vsce a single phase angle peak is present at the higher frequency. This is concurrent with the rapid formation of a blue-green precipitate determined to be cuprous chloride from previous EDX analysis. At 0.2 Vsce and above, the passivefilmresistance drops to a negligible value and the phase angle peak disappears. In this potential range heavy corrosion is observed along with spalling of the blue-green precipitate from the surface of the copper. Passivefilmresistance, solution resistance, and phase angle peak datafromthese Bode plots are summarized in Table 5.4. With a conductance of 77.5 mmho/cm for IM sodium chloride , a surface area of 1 cm , 33  2  and a reference electrode distance of approximately 1 cmfromthe working electrode, the solution resistance is calculated to be 12.9 ohms. This is close to the measured solution resistance obtained from the impedance experiments. The slight increase in solution resistance at the higher potentials represents changes in local solution chemistry (possibly due to CuCl formation).  66  Table 5.4 Summary of Impedance Data for Copper in IM Sodium Chloride Buffered to pH 10.5 with 0.01M Sodium Borate rotating at 50 RPM  Buffer Type  0.0 IM 0.0 IM 0.0 IM 0.0 IM 0.0 IM 0.0 IM 0.01M 0.01M 0.01M 0.01M  Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate Sodium Borate  Rotation (RPM)  Potential (Vsce)  50 50 50 50 50 50 50 50 50 50  -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5  Passive F i l m Resistance (Ohms) 1874 1585 3511 2565 285 1000 24 18 22 24  Solution Resistance (Ohms) 12 12 12 12 14 15 17 14 16 20  Frequency of Phase Angle Peak (Hz) 14.7 18.9 297.6 619.7 29.8, 17569.3 5925.5 no peak no peak no peak no peak  The results of the impedance scans taken between -0.4 Vsce to 0.5 Vsce, at 5000 RPM in IM sodium chloride, buffered to pH 10.5 with 0.01M sodium borate are shown in Figures 5.35 to 5.44.  67  c  r  -0.4Vsce  80 70  W)  E  60 V  01  IS  o  : :  2  30  "  01  VI IS  20  ;,' 1 •„• 0  9  50 _o> oi 40  \  o  TJ  01  90  10 1  1  1  1  2  3  "  ;  0  Log Frequency (Hz) • Impedance  Phase Angle  Figure 5.35 Bode Plot for Copper at -0.4 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  90 80  -0.3Vsce +  7  0  60  _ |  50 £ oi 40 ^ 30 $ is  + 20 £ 10 0 1  2  Log Frequency (Hz) • • Phase Angle  • Impedance  Figure 5.36 Bode Plot for Copper at -0.3 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  68  90  -0.2Vsce  80 70 60 | 50 a at 40 | 30  3  20 £ 10 0  1  2  0  3  Log Frequency (Hz) • Impedance  Phase Angle  Figure 5.37 Bode Plot for Copper at -0.2 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  -*7—  in E  54,  90  -0.1 Vsce  --  70 _  :  --  Q.  E o  60 50  D  u e <o •a ai  80  f  V  40  *  '2  -  30  S IB  _ 20 £  1 -00  —i  1  1  2  H  1  3  10  0  Log Frequency (Hz) Phase Angle  • Impedance  Figure 5.38 Bode Plot for Copper at -0.1 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  69  90 OVsce  80 +  7  0  60  _ f  50 £  ui  + 40  |  + 30 3 + 20 £ 10 1  2  0  3  Log Frequency (Hz) • Impedance  Phase Angle  Figure 5.39 Bode Plot for Copper at 0 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  j 90 O.IVsce  - 80  5 E  JZ  O  re a.  - 70 - 60  4/  - 50  3  - 40 - 30  .".2-  E' Ul  o  01  Ul  - 20 : 1;-  Ol c <  01 0. fi n  - 10  • n'  - 0 0  1  2  3  Log Frequency (Hz) - Impedance  Phase Angle  Figure 5.40 Bode Plot for Copper at 0.1 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  70  0.2Vsce  5-  Log Impedance (Ohms)  90  r  1  • 80 70  43-  -60  f  • 50  «T  40 £  2j  30  20 £  1-  -1  0  8cs  —i 1  1  1  H  2  3  4  10 V- 0 5  Log Frequency (Hz) Impedance  Phase Angle  Figure 5.41 Bode Plot for Copper at 0.2 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  90  - r  • 80 70 _ 60 ? TJ  • 50 * - 40  |  30  S <s  20 £ 10 - 0 -1  0  1  2  3  4  5  Log Frequency (Hz) Impedance Phase Angle  Figure 5.42 Bode Plot for Copper at 0.3 Vsce in 1M NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  71  j 90 80 70  a? 50 o> 60  D)  40 £ 30  8  20 £ 10 -• 0 5  Impedance  Phase Angle  Figure 5.43 Bode Plot for Copper at 0.4 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  90  -r  - 80 70 _ 60 « 50 ]f 40 ^ 30  8 IB  20 £ 10 - 0 5 Impedance  Phase Angle  Figure 5.44 Bode Plot for Copper at 0.5 Vsce in IM NaCl buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM.  72  For the impedance results conducted at the higher rotation speeds (5000 RPM) there is a distinct difference between the impedance at the low frequencies and the impedance at the high frequencies during the stages of passive film formation (from -0.4 Vsce to 0.1 Vsce). This observed effect is consistent with the polarization scans (Figure 5.14) which indicate that the pitting potential is 0.17 Vsce. The frequency in which the phase angle peak occurs increases with increasing potential in the passive region up to a potential of -0.1 Vsce. At 0 Vsce and 0.1 Vsce there is a decrease in the frequency in which the phase angle peak occurs although the film still remains passive. This suggests that there is a change in thefilmcharacteristics resulting from changes in film capacitance. In this potential range of -0.4 Vsce to 0.1 Vsce the sample remained bright and shiny. At 0.2 Vsce there is a distinct drop in the low frequency impedance, accompanied by a sudden increase in the frequency of the phase angle peak. This is concurrent with the observed breakdown of passivation which is accompanied with the sudden generation of a blue-green cuprous chloride precipitate. At potentials between 0.3 Vsce and 0.5 Vsce the low frequency impedance remains low. In addition, a splitting of the phase angle is noted and is concurrent with the observed generation of a cuprous chloride precipitate. The impedance data from the high rotation speed tests are summarized in Table 5.5. Again the increase in solution resistance at potentials from 0.3 Vsce to 0.5 Vsce represents changes in local solution chemistry possibly due to CuCl formation.  73  Table 5.5 Summary of Impedance Data for Copper in IM Sodium Chloride Buffered to pH 10.5 with 0.01M Sodium Borate rotating at 5000 RPM  Buffer Type  Rotation (RPM)  Potential (Vsce)  0.01M Sodium Borate 0.0 IM Sodium Borate 0.01M Sodium Borate 0.0 IM Sodium Borate 0.01M Sodium Borate 0.0 IM Sodium Borate 0.0 IM Sodium Borate 0.01M Sodium Borate 0.0 IM Sodium Borate 0.01M Sodium Borate  5000 5000 5000 5000 5000 5000 5000 5000 5000 5000  -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5  Passive F i l m Resistance (Ohms) 2117 1000 3511 3511 6579 4806 81 208 731 534  74  Solution Resistance (Ohms) 17 9 9 9 9 9 9 14 32 43  Frequency of Phase Angle Peak (Hz) 13.8 36 183.3 233.6 120.1 33.6 2553.2 3.8, 16237.8 3.1, >100000 2.0, >100000  6 DISCUSSION  6.1 POLARIZATION BEHAVIOR  The increase in pitting potential with increasing buffer concentration and rotation speed clearly indicates that mass transport of the buffer species to the copper surface resists passive film breakdown. The mass transport of the conjugate base buffer species through the diffusion layer to copper surface can be calculated with the steady state diffusion equation derived from Fick's Law shown in Equation 6.1. This equation 1  ignores electrical migration effects, which are negligible with a 1M sodium chloride supporting electrolyte.  ,  DmllBl-IB].]  Where: J  = Flux of the Conjugate Base from the Bulk to the Surface (moles/m sec) 2  [B]  D  = Diffusion Coefficient (m /s) 2  [B]  [B] = Concentration of the Conjugate Base in the Bulk (moles/m) 3  b  [B] = Concentration of the Conjugate Base at the Surface (moles/m) = 0 (if consumed) 3  s  5 = Diffusion Layer Thickness (m)  75  For a sodium bicarbonate/carbonate buffer, at any given pH the concentration of the conjugate base (carbonate ion) and the conjugate acid (bicarbonate ion) can be calculated by solving Equations 6.2 and 6.3.  log  [ H C O ; V  -10.34+  6.2  [CO ' ] + [HCOl ] = Total Buffer Concentration 2  18  6.3  Using Equations 6.2 and 6.3 the carbonate and bicarbonate ion concentrations for all solutions containing a sodium bicarbonate/carbonate buffer were calculated and are summarized in Table 6.1.  Table 6.1 Summary of Calculated Bicarbonate and Carbonate Concentrations  Total Buffer Concentration (M) 0.01 0.05 0.1 0.5  pH 10.5 10.5 10.5 10.5  [HC0 ] (M)* 0.0041 0.0204 0.0409 0.2045 3  1M= 1000 moles/m'  76  [C0 ] (M)* 0.0059 0.0296 0.0591 0.2955 2  3  Sodium tetraborate buffer behaves slightly differently in that the tetraborate ion [B4O7 ']  is not predominant at low concentrations . Instead at low concentrations, the  [B4O7 ']  ion will dissociate to [H3BO3], [H B0 "], and [HB0 "] depending on the pH.  2  2  18  2  2  The actual concentrations of [H3BO3],  3  [H2BO3],  3  and  [HBO3 ] 2  for any given pH can be  determined by solving the following three equations and three unknowns:  [H BO~t  r  log  [H B0 ]. 3  3  [HBOlY  log  \ \ H  2  6.4 18  -9.21 + pH  2  6.5 18  -12.70 + pH  B O ; I  [H B0 ] + [H BO; ] + [HBO - ] = 4 •added [B 0 ~ ] 6.6 2  3  3  2  2  4  Using Equations 6.4 to 6.6 the [H B0 ], [H B0 "], and [HB0 '] concentrations 2  3  3  2  3  3  are calculated for the various concentrations tested in this work. The calculated results are summarized in Table 6.2. Since [H B0 '] has the highest concentration at pH 10.5, it 2  3  is considered to be the conjugate base.  77  Table 6.2 Summary of Calculated Borate Concentrations  Concentration of  PH  [Na B 0 ]added 2  4  7  (M) 0.001 0.01 0.05  10.5 10.5 10.5  (M)*  [H B0 ] (M)*  0.000194 0.001940 0.009699  0.003782 0.037822 0.189108  [H3BO3]  2  * 1M= 1000moles/m  3  [HBO3 ] 2  (M)* 0.000024 0.000239 0.001193  3  The diffusion layer thickness determined by rotating electrode experiments depends on the flow conditions (laminar or turbulent). The flow conditions are determined by the Reynolds Number which is calculated as follows:  6.7  Where: Re = Reynolds Number U = Maximum Radial Velocity (mis) I = Distance = Radius of the Disk Electrode (m) v = Kinematic Viscosity of the Electrolyte (m /s) 2  As a first approximation, a Reynolds Number less than 500,000 indicates laminar flow, whereas a Reynolds Number greater than 500,000 indicates turbulentflowfor flat plate conditions . 31  78  The maximum radial velocity can be calculated via the following equation : 32  U = y/2cor  6.8  Where: co = Angular Velocity (rad/s) r = Radius of the Disk Electrode (m)  For a maximum rotation speed of 5000 RPM, a radius of 0.00565 m, and a kinematic viscosity of 1.056 x 10" m /s for 1M NaCl , the Reynolds Number is calculated 6  2  33  to be 22,384. This suggests that the flow is laminar for all rotating disk conditions tested in this thesis.  Under laminar flow conditions the thickness of the diffusion layer (as determined by the diffusion of the conjugate base species to the surface of the copper) is determined by the modified Levich Equation (Equation 6.9). 34  1/2  79  6.9  Where: 8 = Diffusion Layer Thickness (m) D= Diffusion Coefficient of Conjugate Base (m/s) 2  v= Kinematic Viscosity of the Electrolyte (m /s) 2  co = Angular Velocity (rad/s)  Using the diffusion and viscosity data shown in Table 6.3, the diffusion layer thickness is calculated (using Equation 6.9) for the sodium bicarbonate/carbonate buffer solutions and the sodium borate buffered solutions at 50 RPM and 5000 RPM. The results are summarized in Table 6.4.  Table 6.3 Summary of Diffusion and Viscosity Data  Diffusion Coefficient of rC0 "l (m /s) Diffusion Coefficient of [H B0 "1* (m/sV Kinematic Viscosity of IM NaCl (m /s) * based on typical values for ions' 2  2  35  0.923 x 10" 1 x IC 1.056 xlO"  9  3  2  2  9  3  2  33  6  80  Table 6.4 Calculated Diffusion Thicknesses  Buffer Type  Rotation (RPM)  Sodium Bicarbonate/Carbonate Sodium Bicarbonate/Carbonate Sodium Borate Sodium Borate  50 5000 50 5000  Diffusion Layer Thickness (m) 2.22 x 10" 2.22 x 10" 2.31 x 10" 2.31 x 10"  6  7  6  7  Substituting the conjugate base data given in Tables 6.1 and 6.2 and the diffusion layer thickness data given in Table 6.4, into Equation 6.1, the influx of the conjugate base to the surface of the copper is calculated for all conditions tested in this thesis (assuming that [B] approaches zero). The results are summarized in Table 6.5. s  81  Table 6.5 Flux of Conjugate Base to Copper Surface  Buffer Type  Rotation (RPM)  Conjugate Base  Flux (moles/msec)  0.01M Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.01M Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.001M Sodium Borate  50  [C0 ]  2.46 x 10'  50  [C0 ]  1.23 x 10"  50  [C0 ]  2.46 x lO  50  [C0 ]  1.23 x 10"  5000  tco -]  2.46 x 10"  5000  [C0 ]  1.23 x 10"  5000  [C0 ]  2.46 x lO"  5000  [C0 ]  1.23  50  tH B0 ]  1.63 x 10"  0.01M Sodium Borate  50  [H B0 ]  1.63 x 10"  0.05M Sodium Borate  50  [H B0 ]  8.17 xlO"  0.001M Sodium Borate  5000  [H B0 ]  1.63 x 10"  0.01M Sodium Borate  5000  rH B0 ]  1.63 x 10"  0.05M Sodium Borate  5000  [H B0 ]  8.17 xlO"  2  3  2  3  2  3  2  3  3  2  2  3  2  3  2  3  2  2  2  2  2  2  3  3  3  3  3  3  z  3  2  -2  1  2  1  1  3  2  2  2  1  1  Thefluxof FT ions formed by the passivation reactions (Equations 5.4 to 5.6) be calculated from the passive current density using the following equation: 1  82  6.10 Where: J  = Flux of protons (moles/m sec) 2  H+  / = Passive Current Density (A/m ) 2  F = Faraday's Constant = 96500 A.sec/eq.mole  Using Equation 6.10, the flux of hydrogen ions formed during the passivation is calculated for all tests conducted in this thesis. The calculatedfluxof hydrogen ions are summarized in Table 6.6 (the flux of the conjugate base species are included for comparison).  83  Table 6.6 Flux of Hydrogen Ions Produced During Passivation  Buffer Type  Passive Current Density (A/m)  H Flux (moles/msec)  Conjugate Base Flux (moles/msec)  50  1.6 x 10:  1.7 x 10"  6  2.46 x 10"  50  1.4 x 10"'  1.5 x 10"  1.23 x 10"  50  1.8 x 10"'  1.9 x 10'  2.46 x 10"  Rotation (RPM)  +  2  2  2  1  3  0.0 IM Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.01M Sodium Bicarbonate/Carbonate 0.05M Sodium Bicarbonate/Carbonate 0.1M Sodium Bicarbonate/Carbonate 0.5M Sodium Bicarbonate/Carbonate 0.00 IM Sodium Borate  50  1.8  1.9 x 10"  1.23 x 10'  5000  9.3 x 10-'  9.6 x 10"  2.46 x 10"  5000  3.6 x 10"'  3.7 x 10"  1.23 x 10  5000  7.6 x 10  7:9 xlO'  2.46 x 10-'  5000  8.1  8.4 x 10"  1.23  50  1.9 x 10"'  2.0 x 10'  1.63 x 10'  0.0 IM Sodium Borate  50  1.8 x K)-  1.9 x 10"  1.63 x 10"  0.05M Sodium Borate  50  1.1 xlO'  UxlOf  8.17 x 10  2  0.00 IM Sodium Borate  5000  3.6  3.7 x 10"  1.63 x 10  2  0.01M Sodium Borate  5000  1.8 x 10-'  1.9 x 10'  1.63 x 10  0.05M Sodium Borate  5000  7.5 x 10"'  7.8 x 10"  6  2  6  5  6  6  11  6  5  6  1  1  2  _1  3  6  1  2  6  5  5  6  2  1  8.17x10''  As shown in Table 6.6 the influx of the conjugate base species is much greater than the out-flux of hydrogen ions generated during the passivation of copper. As such, it is unlikely that the small amount of protons generated during copper passivation (Equations  5.4 to 5.6) is the cause of the observed loss of pH control which accompanies passive film breakdown. Instead the breakdown of passivation must be caused by the localized generation of protons (decreasing the local pH) likely initiating at one or more defect sites in the passivefilm.According to Pourbaix, the HCuCV ion can co-exist with the passive CuO or Cu(OH)2 species . As such, the occurrence of Equation 6.11 at a defect site will 18  result in a large local current density (since there is no local passivation) and thus result in a large local generation of protons that will consume any conjugate base species in the vicinity.  Cu + 2H 0 = HCuO/ + 3FT + 2e 2  6.11  With a drop in the surface pH; cuprous chloride will precipitate via Equation 6.12. Published literature has shown that once CuCl is formed re-passivation can no longer take place as it becomes impossible to form a passive barrier layer over the CuCl film As 17  such, the formation of CuCl interferes with passivation regardless of the diffusion of the conjugate base species to the surface.  Cu + Cl" =CuCl + e'  85  6.12  6.2 AC IMPEDANCE - MODELLING OF THE PASSIVE FELM  The physical parameters of the passive film can be characterized by equating the measured impedance (shown on the Bodes Plots in Figures 5.25 to 5.44) of the cell to the impedance of the electrical circuit model (Figure 5 . 2 2 ) , and then mathematically deconvoluting the individual circuit components of the model. The electrical parameters of the passive film such as passive film resistance and capacitance are used to estimate the physical characteristics of the passive film in-situ.  The film resistance and the solution resistance are determined simply from the plateaus of impedance versus frequency plot. Since the impedance of the film capacitor is inversely proportional to the applied frequency (Equation 5.8), the impedance of the film capacitor is very large at low frequencies and very small at high frequencies. As such, at low frequencies current only passes through the film resistor (Kfam) and the solution resistor (Rsoiution) as shown in Figure 6 . 1 . At the high frequencies the passivefilmresistor is shunted, only allowing current to pass through the solution resistor (Figure 6.2). Therefore, thefilmresistance is equivalent to the impedance at the low frequencies minus the impedance at the high frequencies and the solution resistance is equal to the impedance at the high frequencies.  86  m  m  )  very high impedance  R(solution)  R(Film)  HVVV-  •AAAr current path  Figure 6.1 Current Path Through Circuit Model at Low Frequencies  current path  ^  C(Film)  very low impedance  : Resolution):: •AAAr R(Film)  Figure 6.2 Current Path Through Circuit Model at High Frequencies  87  The film capacitance is determinedfromthefrequencyat which the phase angle peaks. This is determined by differentiating the phase angle equation (Equation 6.13) with respect tofrequencyand equating this value to zero. The derivation is as follows:  de= 0  6.13  dm  Where:  0)  C film a> +p2 2  V  6 = ARCTAN f R  solution  f~il ^film^filmJ  (From Equation 5.20)  +-  p  r<2 ^film^film  w + 2  ^  Rfilnf^filmJ  6.14  ^—Arc tan(x) = -—'~T dx 1+x  Application of the chain rule to Equation 6.14 yields the following:  ^  —  ^solution"'  ^film^film  ^film  88  ^solution  U  6.15  By rearranging Equation 6.15:  Rfilm  ~*~ ^solution  ^•filtn^  f.  \f.  film^solutton  Therefore:  4-7?  D  j (-film  =  J  -"V/i/m D2  f. \ H  ^solution 2  n  Where: C^ = Film Capacitance (Farads) /m  Rfiim Film Resistance (Ohms) =  ^solution  =  ^ m a x  =  Solution Resistance (Ohms) Angular Frequency at the Phase Angle Peak (Hz)  For a parallel plate electronic capacitor, the relationship between the capacitance and dielectric thickness is determined by Equation 6.18 : 33  C=  KA  And  89  6.18  Where: C = Capacitance (Electrostatic Units) 1 Farad = 9 x 10 Electrostatic Units 11  K = Dielectric Constant A = Surface Area of the Conducting Plate (cm ) 2  d = Thickness of the Dielectric (cm)  Once the capacitance of the passive film is known, the in-situ passivefilmthickness can be estimated from the following equation:  Where: C  film  = Capacitance (Electrostatic Units) determined by Equation 6.17  1 Farad = 9x 10 Electrostatic Units 11  K = Dielectric Constant  19,33  = 11 -18 for Cu 0 and 18.1 for CuO 2  A - Surface Area of the Rotating Disk Electrode = 1 cm  2  d = Thickness of the Passive Film (cm)  90  6.2.1 ANALYSIS OF IMPEDANCE RESULTS  Using the impedance results, the thickness of passive films are calculated on the assumption that a CU2O/Q1O duplex film is present on the surface of the test specimens and that the dielectric constant for the passive layer is 18. In the 1M sodium chloride solution buffered to pH 10.5 with 0.01M sodium borate rotating at 50 RPM the film thickness values at -0.4 Vsce and -0.3 Vsce are calculated to be 2.2 A and 2.6 A respectively using the impedance data (Table 5.4). According to the polarization curve shown in Figure 5.14, these two potentials correspond to the active region and as such the thin film detected from the impedance scans may correspond to the electrical double layer. The double layer thickness is estimated to be 2.88 A, based on the assumption that the thickness of the electrical double layer is approximately equal to the radius of a solvated cuprous cation (a cuprous cation surrounded by water molecules ). Using a dielectric 33  constant for the electrical double layer of approximately 78.54 (estimated with dielectric constant for water ), the modeled thickness of the double layer is calculated to be 9.6 A 33  and 11.3 A at -0.4 Vsce and -0.3 Vsce respectively. Since these values are greater than the expected thickness of the electrical double layer, the impedance response at these potentials are likely caused by a composite effect of the electrical double layer and an adsorbed surface film (or possibly the electrical double layer and the diffusion layer). At -0.2 Vsce and -0.1 Vsce thefilmthickness increases substantially to 61.2 A and 108.8 A respectively. This is consistent with the passivation observed on the polarization plot. At 0 Vsce the passivefilmresistance drops by nearly ten fold and the phase angle splits into  91  two peaks (one at a low frequency and one at a high frequency). The splitting of the phase angle peak is caused by a dual impedance effect that is likely caused by the presence of large defect sites in the passivefilm.The impedance response of both the non defect sites and the defect sites results in two phase angle peaks. A possible circuit model for a passive film with large defect sites is shown in Figure 6.3. This model consists of two parallel Randies Circuits, with which the effect of the thin non-defective (and possibly non-protective)filmis represented by thefilmcapacitance and thefilmresistance positioned in a series array with the thick defectivefilmcapacitance and the defective film resistance.  C(film)  C(defed)  Solution  mr  •A/WR(solution)  1  thick defective film  R(film)  Rfdefect)  thin film In-Situ Passive Film with Large Defects  Electrical Model of Passive Film with Large Defects  Figure 6.3. Circuit Model for a Passive Film with Large Defect Sites  Since the defective portion of thefilmis much thicker than the non defective portion Cf,im would be much greater than Cd f t. As such, the impedance of Cf,im would be e ec  significant at low frequencies and the impedance of Cd f t would be significant at high e ec  92  frequencies (since  capacitor  ). A typical Bode plot for this type of circuit (shown in  co C  Figure 6.4) consists of three impedance plateaus and two phase angle peaks.  Impedance of Film Defect Model  1  2  3  Log Frequency (Hz) • Phase Angle  - Impedance  Figure 6.4 Typical Bode Plot of Circuit Model of Passive Film with Large Defects  The first impedance plateau which occurs at a low frequency is equivalent to the sum of the non defectivefilmresistance Rfiim, the defectivefilmresistance Rd f e  ec  t,  and the  solution resistance Rsoiution- This impedance plateau is seen because the impedance of both Cdefect Rdefect,  and Cfiim are very high at low frequencies, thus current only passes through R f ^ , and Rsoiution- As thefrequencyincreases, the impedance of the Cfiim decreases, and  93  thus shunts the Rf,im (note that the frequency is still low enough such that the impedance of the defectivefilmcapacitor is very high). At this point the second impedance plateau equivalent to the sum of R d f and Rsoiution occurs. In addition, thefirstphase angle peak e  ect  occurs because of the reactance effect of Cf,im. As the frequency increases even higher, the impedance of Cdefect decreases and, thus shunts the Rdefect- At this point the third impedance plateau, equivalent to the solution resistance occurs. This effect is seen because the impedance of Cdefect is very low at very high frequencies, and thus the Rdefect is shunted. In addition, the second phase angle peak occurs because of the reactance of Cdefect-  Deconvoluting the circuit components of the largefilmdefect model requires simplification of the double parallel circuit into simple Randies circuits such that the defect capacitance and thefilmcapacitance can be determined. The following steps describe the deconvolution of the circuit components of the large defectfilmmodel.  Step 1: Determine Ruim, Rdefect, and Rsoiutionfromthe impedance plateaus of the impedance versus frequency plot (Figure 6.4).  Step 2: Since Cfiim is much larger than Cdefect, the impedance of Cd f e  ec  t  is much higher than  the impedance of C f , i at lowfrequencies.As such, the double parallel circuit can be m  simplified to a simple Randies circuit for low frequencies as shown in Figure 6.5.  94  C(film)  CCfilm)  very high impedance at low frequencies  C(defect)  •A/W  R(defect) R(solution)  R(solution) R(film)  R(ctefect) R(film)  Figure 6.5 Simplified Large Defect Model for Low Frequencies  Step 3: Using the low frequency simplified circuit, and thefrequencyat which the first phase angle peak occurs, the defect capacitance can be calculated using Equation 6.20.  „  i  C«.  'film  =  Rfiim  I—;  W TJ2  ' film max n  60  +  ;  2  (^defect  +  ^solution)  —  /n  {^defect  , +  n  ,  6.20  ^solution J  Step 4: At the higher frequencies the impedance of the Cfiim becomes very small, therefore the double parallel circuit can be simplified to a simple Randies circuit as shown in Figure 6.6.  95  very low impedance at high frequencies C(film)  C(defect)  C(defed)  HWV-  HWv—  R(solution)  R(solution)  R(defect)  R(film)  R(defect)  Figure 6.6 Simplified Large Defect Model for High Frequencies  Step 5: Using the high frequency simplified circuit, and thefrequencyin which the second phase angle peak occurs, thefilmcapacitance can be calculated using Equation 6.21.  _  I  defect  ^defect ~ J"^2 T i " ^defect "ffl 1  solution  .  p max^ solution  From the impedance plateaus of the Bode plot taken at 0 Vsce (Figure 5.29), the non-defectivefilmresistance  (Rf,im)  is 258 ohms, the defectivefilmresistance  estimated to be 13 ohms, and the solution resistance (co - 2nf ) of thefirstphase angle peak (f  a  angle peak (fm  max  max  (Rgoiution)  (Rd f ) e  ect  is  is 14 ohms. The frequency  ) occurs at 29.8 Hz and the second phase  ) occurs at 17569.3 Hz. The non-defectivefilmcapacitance (Cfiim) and  the defectivefilmcapacitance (Cd f t) are calculated to be 6.73 x 10" Farads and 5  e ec  9.68 x 10" Farads respectively. As such the calculated effective thickness for the non 7  96  defective film is calculated to be 2.4 A and the effective thickness of the defectivefilmis 165.4 A. Again since the thickness of the non-defect region is so small, it likely corresponds to a composite effect of the electrical double layer (a local site of active corrosion) and a thin adsorbedfilm.The lower resistance of the defectivefilm(13 ohms) as compared to the non defectivefilm(258 ohms) reinforces the fact that the defective film is very porous. This also corresponds to the pitting potential of 0.03 Vsce as determinedfromthe polarization curve (Figure 5.14).  At 0.1 Vsce a single phase angle peak occurs at a highfrequencyof 5925.5 Hz. This corresponds to afilmthickness of 718.8 A. This thick porousfilmis likely composed of CuCl, which was observed at this potential. At potentials at and above 0.2 Vsce, the phase angle peak disappears and the impedance drops to the level of the solution resistance. This indicates that nofilmor precipitate is present and the copper surface is rapidly corroding.  The impedance results for the tests conducted in IM sodium chloride solution buffered to pH 10.5 with 0.01M sodium borate rotating at 50 RPM are summarized in Table 6.7.  97  Table 6.7 Summary of Impedance Results for Tests Conducted in 1M NaCl Buffered to pH 10.5 with 0.01M Na B 0 Rotating at 50 RPM 2  Potential Frequency at Rfflm (Vsce) Phase Angle (Ohms) Peak (Hz)  4  Rdefect  (Ohms)  7  ^solution  (Ohms)  Film Thickness (A)  2.2" , 9.6' 0 12 1862 14.7 12 0 2.6* , 11.3" 1573 18.9 61.2 12 3499 0 297.6 108.8 12 2553 0 619.7 2.4 & 165.4 14 258 13 29.8 & 17569.3 718.8 15 0 985 5925.5 0.1 0 17 7 0 no peak 0.2 0 0 14 4 no peak 0.3 0 16 0 6 no peak 0.4 0 0 20 4 no peak 0.5 Footnote *1: Using the dielectric constant of copper oxide Footnote *2: Using the dielectric constant of the electrical double layer -0.4 -0.3 -0.2 -0.1 0.0  Comments  1  1  2  2  thin film & electrical double layer thin film & electrical double layer passive film present passive film present passive film with large defects, onset of film breakdown thick non-protective CuCl no film, high corrosion rate no film, high corrosion rate no film, high corrosion rate no film, high corrosion rate  In the 1M sodium chloride solution buffered to pH 10.5 with 0.01M sodium borate rotating at 5000 RPM thefilmthickness values at -0.4 Vsce and -0.3 Vsce are calculated to be 2.6 A and 3.4 A respectively using the impedance data shown in Table 5.5 and the dielectric constant for copper oxide. Using the dielectric constant for the electrical double layer, these thickness values are calculated to be 11.3 A and 14.8 A respectively. Again this indicates that the impedance response at -0.4 Vsce and -0.3 Vsce is likely due to a composite effect of the electrical double layer and a thin adsorbed film. The polarization curve shown in Figure 5.14 shows that these two potentials are in the active region. In the passive regionfrompotentials -0.2 Vsce to -0.1 Vsce, the passivefilmgrows to 32.7 A  98  and then to 41.6 A. Still in the passive region from 0 Vsce to 0.1 Vsce the passive film thickness begins to decreasefrom29.3 A to 7.0 A. The passivefilmresistance remains high at 6570 ohms and 4997ohms respectively. At 0.2 Vsce (30mV above the pitting potential as shown on the polarization curve in Figure 5.14) there is a large drop in the passivefilmresistance to 72 ohms followed by an increase in thefilmthickness to 61.6 A. A large drop in passivefilmresistance in combination with an increase infilmthickness indicates that thefilmis porous. Since only a single phase angle peak is present, the defect sites in this porousfilmmust be small. From 0.3 Vsce to 0.5 Vsce the phase angle splits to a very lowfrequencypeak and a very highfrequencypeak. This is consistent with the precipitation of a very defective cuprous chloridefilm.At 0.3 Vsce, 0.4 Vsce, and 0.5 Vsce the thickness values of the thin surfacefilmare calculated to be 0.2 A, 0.6 A, and 0.4 A respectively (assuming a dielectric constant for copper oxide). Using a dielectric constant for the electrical double layer, these thickness values are calculated to be 0.9 A, 2.6 A, and 1.7 A respectively. Since these values are close to the estimated thickness of the electrical double layer (2.88 A), it is fair to assume that the non-defective region of the model represents the electrical double layer at these potentials. The thickness of the thick defective CuCl portion of thefilmat 0.3 Vsce, 0.4 Vsce, and 0.5 Vsce are 115.7 A, 1860.0 A, and 2777.4 A respectively.  The impedance results for the tests conducted in IM sodium chloride solution buffered to pH 10.5 with 0.01M sodium borate rotating at 5000 RPM are summarized in Table 6.8.  99  Table 6.8 Summary of Impedance Results for Tests Conducted in IM NaCl Buffered to pH 10.5 with 0.01M Na B 0 Rotating at 5000 RPM 2  Potential (Vsce)  4  7  Frequency at Rfiim Rdefect ^solution Phase Angle (Ohms) (Ohms) (Ohms) Peak (Hz)  Film Thickness  Comments  (A)  -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2  13.8 36.0 183.3 233.6 120.1 33.6 2553.2  2100 991 3502 3502 6570 4797 72  0 0 0 0 0 0 0  17 9 9 9 9 9 9  2.6*', 11.3" 3.4* , 14.8* 32.7 41.6 29.3 7.0 61.6  0.3 0.4 0.5  3.8 & 16237.8 3.1 & 100000 2.0 & 100000  185 674 453  9 25 38  14 32 43  0.9" , 115.7" 2.6* , 1860.0* 1.7* , 2777.4*  2  1  2  2  2  2  3  3  3  thin film & electrical double layer thin film & electrical double layer passive film present passive film present passive film present thin passive film present passive film with small defects, onset of film breakdown thick porous CuCl film thick porous CuCl film thick porous CuCl film  Footnote * 1: Using the dielectric constant of copper oxide Footnote *2: Using the dielectric constant of the electrical double layer Footnote *3: Thickness of the porous cuprous chloride film using a dielectric constant of 18  6.3 CORRELATION OF FILM THICKNESS WITH PUBLISHED LITERATURE  Using the impedance modeling technique derived in this thesis, the passive film thickness ranged from 7.0 A to 108.8 A under the conditions tested. These values are . very close to documented XPS studies conducted by Kautek et al who found that the thickness of a copper oxide anodically formed in an alkaline solution under specific conditions ranged from 40 A to 60 A . Similar studies conducted by Chawla et al found 23  that the thickness of an air formed oxide on copper is approximately 24 A. The calculated  100  film thickness values are also below the first optical interference thickness of approximately 190 A  36,38  . As such, this suggests that the method of using impedance data  to determine passive film thickness is approximately correct.  6.4 LIMITATIONS OF IMPEDANCE SPECTROSCOPY  It is rare that an electrochemical cell can be represented exactly by an ordinary ideal electrical circuit. Thus the usefulness of AC impedance spectroscopy relies on the accuracy with which the electrical circuit models the electrochemical cell. In most cases, fairly accurate models can be used to determine the simplified characteristics of the passive film. Interpretation also relies on the accuracy of the dielectric constant which may not be readily available in published literature (particularly for passivefilmswhich are hydrated oxides). Comparisons of modeled data with measured impedance data shown in Appendix III shows that the models used in this study are fairly accurate.  6.5 MECHANISM OF PASSIVE FORMATION, GROWTH, AND BREAKDOWN  Based on the results of the polarization and impedance studies, the process of film formation, growth, and breakdown on copper in buffered alkaline solutions is summarized. In the region of active corrosion a composite of the electrical double layer and a thin nonprotectivefilmin the range of 2.2 A to 3.4 A are present on the surface of the copper. In the passive region, afilmin the range of 7.0 A to 108.8 A thick forms on the surface  101  consisting of a protective CU2O/CUO duplex structure. The formation of defects in the passive film initiates the breakdown of the film. At the non protected sites copper corrodes forming HCuCV ions and r f ions. The generation of protons results in a drop in the local pH, and therefore causing further breakdown of the passivefilm.The low pH results in the precipitation of a non protective cuprous chloride on the surface of the copper. This cuprous chloride prevents re-passivation as a protective barrier layer cannot be formed.  102  7 CONCLUSIONS  Studies on the behavior of copper in buffered alkaline sodium chloride solutions were consistent with the following conclusions.  (1) Passive film breakdown on copper in buffered alkaline sodium chloride is a result of a loss of pH control at the surface of the metal. (2) The initial loss of pH control that causes passive film breakdown is still observed when there is sufficient conjugate base influx to neutralize the total hydrogen ions generated from the corrosion process. As such, the loss of pH control must be a localized phenomenon. (3) The initiation of passive film breakdown occurs when there are defects present in the passive film. (4) Copper corrodes in these defect sites forming HCUO2' ions and FT ions. The protons  generated in this defect site results in a drop in local pH. (5) In order to prevent the initiation of passive film breakdown, an excess buffer concentration is required to neutralize the drop in local pH. (6) There is little difference between the sodium bicarbonate/carbonate buffer and the sodium tetraborate buffer in preventing passive film breakdown of copper in alkaline sodium chloride solutions. Sodium bicarbonate/carbonate buffer solutions produce a higher corrosion potential that is possibly due to carbon dioxide formation.  103  (7) The loss of pH control results in the precipitation of a solid cuprous chloride. (8) Cuprous chloride prevents re-passivation regardless of the influx of the buffer species. (9) The passivefilmthickness can be accurately determinedfromAC impedance studies by determining thefrequencyat which the phase angle peaks. (10) Film defects can be detected with AC impedance studies by virtue of a phase angle shift and a drop infilmresistance.  104  8 RECOMMENDATIONS FOR FUTURE WORK  Using the techniques described in this thesis, it is recommended that the following work be conducted in the future.  (1) Using XPS studies to determine the thickness of anodically formed passivefilmsand AC impedance studies to determinefilmcapacitance, the dielectric constant for these passivefilmscan be determined for different metals and alloys. (2) Further work is suggested on using the polarization and AC impedance techniques described in this thesis to examine the passivation behavior of different metals and alloys.  105  9 REFERENCES [I] D. Tromans, R. Sun, Journal of the Electrochemical Society, Vol. 139, No. 7, p. 1945 (1992). [2] C. H. Pyun, S.M. Park, Journal of the Electrochemical Society: Electrochemical Science and Technology, Vol. 133, No. 10, p. 2024 (1986). [3] S.L. Marchiano, C. I. Eisner, A. J. Arvia, Journal of Applied Electrochemistry, 10, p. 365 (1980). [4] M. Drogowska, L. Brossard, H. Menard, Journal of the Electrochemcial Society, Vol. 139, No. 1, p. 39 (1992). [5] M. Perez Sanchez, R. M. Souto, M. Barrera, S. Gonzalez, R. C. Salvarezza, A. J. Arvia, Electrochimica Acta, Vol. 38, No. 5, p. 703 (1993). [6] A. Nishikata, M. Itagaki, T. Tsuru, S. Haruyama, Corrosion Science, Vol. 31, p. 287 (1990). [7] S. B. Adeloju, Y Y. Duan, British Corrosion Journal, Vol. 29, No. 4, p. 315 (1994). [8] M. R. G. De Chialvo, R. C. Savarezza, D. Vasquez Moll, A. J. Arvia, Electrochimica Acta., Vol. 30, No. 11, p. 1501 (1985). [9] F. M. Al-Kharafi, Y. A. El-Tantawy, Journal of the Electrochemical Society: Electrochemical Science and Technology, Vol. 128, No. 10, p. 2073 (1981). [10] M. Drogowska, L. Brossard, M. Menard, Corrosion, Vol. 43, No. 9, p. 549 (1987). [II] M. Perez Sanchez, M. Barrera, S. Gonzalez, R. M. Souto, R. C. Salvarezza, A. J. Arvia, Electrochimica Acta, Vol. 35, No. 9, p. 1337 (1990). [12] I. Milosev, M. Metikos-Hukovic, M. Drogowska, H. Menard, L. Brossard, Journal of the Electrochemical Society, Vol. 139, No. 9, p. 2409 (1992). [13] R. M. Souto, S. Gonzalez, R. C. Salvarezza, A. J. Arvia, Electrochimica Acta., Vol. 39, No. 17, p. 2619(1994). [14] R. M. Souto, M. Perez Sanchez, M. Barrera, S. Gonzalez, R C. Salvarezza, Electrochimical Acta., Vol. 37, No. 8, p. 1437 (1992).  106  [15] M. Shirhanzadel, G. E. Thompson, V. Ashworth, Corrosion Science, Vol. 31, p. 293 (1990). [16] S. B. Ribotta, M. E. Folquer, J. R. Vilche, Corrosion, Vol. 51, No. 9, p. 682 (1995). [17] C. I. Eisner, R. C. Salvarezza, A. J. Arvia, Electrochimica Acta., Vol. 33, No. 12, p. 1735 (1988). [18] Atlas of Electrochemical Equilibria in Aqueous Solutions, M. Pourbaix, NACE International Cebelcor, p. 158-165, 384-389, 449-455 (1974). [19] Passivity of Metals, R. P. Frankenthal, J. Kruger, Proceeding of the Forth International Symposium on Passivity, Electrochemical Society Inc., p. 43, 88 (1978). [20] M. M. Laz, R. M. Souto, S. Gonzalez, R. C. Salvarezza, A. J. Arvia, Electrochimica Acta., Vol. 37, No. 4, p. 655 (1992). [21] S. B. Adeloju, Y. Y. Duan, British Corrosion Journal, Vol. 29, No. 4, p. 309 (1994). [22] R. L. Deutscher, R. Woods, Journal of Applied Electrochemistry, Vol. 16, p. 413 (1985). [23] W. Kautek, J. G. Gordon, Journal of the Electrochemical Society, Vol. 137, No. 9, p. 2672 (1990). [24] S. Sathiyanarayanan, S. P. Manoharan, G. Rajagopal, K. 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[33] CRC Handbook of Chemistry and Physics, 70 Edition, R. C. Weast, D. R. Lide, M. J. Astle, W. H. Beyer, CRC Press, Inc., p. D256, E54-55, F84, F187-189 (1989). th  [34] Electrochemical Kinetics Theoretical and Experimental Aspects, K. J. Vetter, New York Academic Press, p. 190 (1967). [35] Self-Diffusion in Electrolyte Solutions, R. Mills, V. M. M. Lobo, Elsevier Science Publishing Company Inc., p. 317 (1989). [36] Metallic Corrosion Passivity and Protection, U. R. Evans, Edward Arnold and Co., p. 68-69 (1946). [37] Electrochemical Systems, J. Newman, Prentice-Hall Inc., Englewood Cliffs, NJ, p. 230 (1973). [38] Oxidation of Metals and Alloys, O. Kubaschewski, B.E. Hopkins, Butterworth and Co. Ltd, London, UK, p. 188-189 (1962)!  108  APPENDIX I: MICROSOFT QUICKBASIC PROGRAM FOR CONTROLLING ELECTROCHEMICAL DEVICES FOR POLARIZATION EXPERIMENTS  •1286 POLARIZATION PROGRAM BY NORMAN CHOW DECLARE SUB PAUSE (DELAY!) DECLARE SUB STATUSBYTE (SP%, BIT%()) DIMBIT%(7) CLS 'INITIALIZE BOARD AND DEVICE OPEN "GPIBO" FOR OUTPUT AS #1 OPEN "GPIBO" FOR INPUT AS #2 OPEN "C:\DATA\TEST.DAT" FOR APPEND AS #3 PRINT #1, "ABORTPRINT #1, "RESET" PRINT #1, "REMOTE" PRINT #1, "OUTPUT 12; BK4" 'INITIALIZE PAUSE (2) 'GENERAL PARAMETERS PRINT #1, "OUTPUT 12; BY1" 'STANDBY CE/OC PRINT #1, "OUTPUT 12; RR5" 'IK STANDARD RESISTOR PRINT #1, "OUTPUT 12; IL5" 'CURRENT LIMIT 200mA PRINT #1, "OUTPUT 12; EB1" 'ERROR BEEP OFF PRINT #1, "OUTPUT 12; PV.9" 'POLARIZATION VOLTAGE 9V PRINT #1, "OUTPUT 12; DGO" 'DVM DIGITS 5X9s PRINT #1, "OUTPUT 12; TR1" 'RECYCLE PRINT #1, "OUTPUT 12; OL1" 'LIMIT 'SWEEP PARAMETERS PRINT #1, "OUTPUT 12; VA.9" V1=.9V PRINT #1, "OUTPUT 12; TA1800" T1=1800SEC PRINT #1, "OUTPUT 12; VB-.9" 'V2=-.9V 'PRINT #1, "OUTPUT 12; TB10" T2=10SEC 'PRINT #1, "OUTPUT 12; VC 1" 'V3=.1V 'PRINT #1, "OUTPUT 12; TC10" T3=10SEC 'PRINT #1, "OUTPUT 12; VD.5" V4=.5V 'PRINT # 1, "OUTPUT 12; TD10" T4=l OSEC PRINT #1, "OUTPUT 12;DL1" 'DELAY=1SEC  109  PRINT #1, "OUTPUT 12; SMI" 'SEGMENTS 1 'ECI SCREEN DISPLAY PRINT # 1, "OUTPUT 12; UL3" LEFT WINDOW RE PRINT #1, "OUTPUT 12; UR5" 'RIGHT WINDOW POLARIZATION 'BEGIN PAUSE (2) PRINT #1, "OUTPUT 12; RU1;"'DVM RUN ON INPUT "PRESS [ENTER] TO POLARIZE SAMPLE", DUMMY PRINT #1, "OUTPUT 12; RUO;" 'DVM RUN OFF PAUSE (1) PRINT #1, "OUTPUT 12; PW1;" 'STANDBY TO ON PRINT #1, "OUTPUT 12; RU1;" 'DVM RUN ON PAUSE (2) INPUT "PRESS [ENTER] TO SWEEP", DUMMY CLS PRINT "CELL ON" 'PAUSE (1800) PRINT #1, "OUTPUT 12; RUO;" 'DVM RUN OFF PRINT #1, "OUTPUT 12; TR3;" 'TRIGGER SYNC PRINT #1, "OUTPUT 12; GP1;" 'GPIB LONG ON PAUSE (1) PRINT #1, "OUTPUT 12; RU1;" 'DVM RUN ON CLS PRINT "SWEEPING" PAUSE (5) PRINT #1, "OUTPUT 12; SW1;" 'RAMP SWEEP PAUSE (5) 'FOR 5 SECOND DELAY FLAG = 0 FLAG3 =0 CLS SCREEN 9 VIEW (80, 48)-(600, 272) WINDOW (-5, -l)-(5, 1) AREA =.01*.01 LOCATE 23, 32 PRINT "CURRENT DENSITY (A/m"; CHR$(253);")" LOCATE 6, 3 PRINT "P" LOCATE 7, 3 PRINT "O"  110  LOCATE 8, 3 PRINT "T" LOCATE 9, 3 PRINT "E" LOCATE 10, 3 PRINT "N" LOCATE 11, 3 PRINT "T" LOCATE 12, 3 PRINT "I" LOCATE 13, 3 PRINT "A" LOCATE 14, 3 PRINT "L" LOCATE 16, 1 PRINT "(Vsce)" LOCATE 22, 9 PRINT "10" LOCATE 22, 15 PRINT "10" LOCATE 22, 22 PRINT "10" LOCATE 22, 28 PRINT "10" LOCATE 22, 35 PRINT "10" LOCATE 22, 41 PRINT "10" LOCATE 22, 48 PRINT "10" LOCATE 22, 54 PRINT "10" LOCATE 22, 61 PRINT "10" LOCATE 22, 67 PRINT "10" LOCATE 22, 74 PRINT "10" LOCATE 21,10 PRINT "-5" LOCATE 21, 16 PRINT "-4" LOCATE 21, 23  PRINT "-3" LOCATE 21, 29 PRINT "-2" LOCATE 21,36 PRINT "-1" LOCATE 21, 43 PRINT "0" LOCATE 21, 50 PRINT " 1" LOCATE 21, 56 PRINT "2" LOCATE 21, 63 PRINT "3" LOCATE 21, 69 PRINT "4" LOCATE 21, 76 PRINT "5" LOCATE 20, 7 PRINT M.O" LOCATE 16, 7 PRINT "-0.5" LOCATE 12, 7 PRINT " 0.0" LOCATE 8, 7 PRINT " 0.5" LOCATE 4, 7 PRINT " 1.0" LINE(-5,-l)-(5,-l) LINE (-5, l)-(5, 1) LINE(5,-l)-(5, 1) LINE (-5, l)-(-5,-l) FOR I = -5 TO 5 LINE (I, -1)-(I, -.94) FORK = 2T0 9 XLOG = LOG(K) / LOG( 10) LINE (I + XLOG, -1)-(I + XLOG, -.97) NEXT K NEXT I FORJ = -l TO 1 STEP .1 LINE (-5, JM-4.9, J) NEXT J AREA =.01 * .01 PRINT #1, "ENTER 12"  112  INPUT #2, POLS, 1$ POL = VAL(POL$) I = VAL(I$) POL1 = POL VOLT1 = -POL1 CURR1 = LOG(ABS(I / (AREA))) / LOG(10) READDATA: FLAG = FLAG + 1 PRINT #1, "ENTER 12" INPUT #2, POLS, 1$ POL = VAL(POL$) I = VAL(I$) IF FLAG = 10 THEN 'SAVE 1 OUT OF 10 DATA POINTS IF POL < .25 AND ABS(I) > .0001 AND FLAG3 = 0 THEN PRINT #1, "OUTPUT 12; RR2;": FLAG3 = 1 WRITE #3, POL, I FLAG = 0 VOLT2 = -POL CURR2 = LOG(ABS(I / (AREA))) / LOGQ0) COLOR 5, 0 LINE (CURR1, VOLTl)-(CURR2, VOLT2), 11 VOLT1 = VOLT2 CURR1 = CURR2 END IF 'SERIAL POLL PRINT #1, "SPOLL 12" INPUT #2, SP% CALL STATUSBYTE(SP%, BIT%()) IF BIT%(2) o 1 THEN GOTO READDATA PRINT #1, "OUTPUT 12; PW0;" 'ON TO STANDBY CLOSE (3) 'AUTOSCALE LOG PLOT SCREEN 0 CLS OPEN "C:\DATA\TEST.DAT" FOR INPUT AS #4 AREA = .01 * .01 VMAX = -1000 VMTN= 1000 IMAX = -1000 IMIN = 1000 DO UNTIL EOF(4)  113  INPUT #4, V, I VOLT = -V CURR = LOGYABS(I / (AREA))) / LOG(10) IF VOLT < VMTN THEN VMTN = VOLT IF VOLT > VMAX THEN VMAX = VOLT IF CURR < IMIN THEN IMIN = CURR IF CURR > IMAX THEN IMAX = CURR LOOP CLOSE (4) VMTN = INT(VMTN * 10) / 10 VMAX = INT((VMAX * 10) + .5) / 10 VSCALE: IF INT(((VMAX - VMTN) * 10) / 4) * 4 <> INT((VMAX - VMTN) * 10) THEN VMTN = INT((VMTN* 10)- 1)/ 10 IF INT(((VMAX - VMTN) * 10) / 4) * 4 o INT((VMAX - VMTN) * 10) THEN VMAX = INT((VMAX * 10) + 1.5) / 10 IF INT(((VMAX - VMTN) * 10) / 4) * 4 o (VMAX - VMTN) * 10 THEN GOTO VSCALE IMIN = INT(IMIN) IMAX = INT(IMAX + 1) OPEN "C:\DATA\TEST.DAT" FOR INPUT AS #4 CLS SCREEN 9 VIEW (80, 48)-(600, 272) WINDOW (IMIN, VMTN)-(IMAX, VMAX) FLAG2 = 0 LOCATE 23, 32 PRINT "CURRENT DENSITY (A/m"; CHR$(253);")" LOCATE 6, 3 PRINT "P" LOCATE 7, 3 PRINT "O" LOCATE 8, 3 PRINT "T" LOCATE 9, 3 PRINT "E" LOCATE 10, 3 PRINT "N" LOCATE 11, 3 PRINT "T" LOCATE 12, 3 PRINT "I" LOCATE 13, 3  114  PRINT "A" LOCATE 14, 3 PRINT "L" LOCATE 16, 1 PRINT "(Vsce)" FOR I = IMTN TO IMAX LOCATE 22, ((65 / (IMAX - IMTN)) * (I - EvflN)) + 9 PRINT "10" LOCATE 21, ((65 / (IMAX - IMTN)) * (I - EVflN)) + 10 PRINT I NEXT I LOCATE 20, 7 PRINT VMTN LOCATE 16, 7 PRINT VMTN + (VMAX - VMIN) / 4 LOCATE 12, 7 PRINT VMIN + (VMAX - VMTN) / 2 LOCATE 8, 7 PRINT VMIN + (3 * (VMAX - VMTN) / 4) LOCATE 4, 7 PRINT VMAX LINE (IMTN, VMTN)-(IMAX, VMTN) LINE (IMTN, VMAX)-(IMAX, VMAX) LINE (IMAX, VMIN)-(IMAX, VMAX) LINE (IMTN, VMAX)-(JJVIIN, VMIN) FOR I = IMTN TO IMAX LINE (I, VMTN)-(I, VMIN + .06) FORK = 2T0 9 XLOG = LOG(K) / L O G 0 O ) LINE (I + XLOG, VMIN)-(I + XLOG, VMIN + .03) NEXT K NEXT I FOR J - VMTN TO VMAX STEP .1 LINE (IMIN, J)-(IMIN + .1, J) NEXT J INPUT #4, V, I VOLTl = -V CURR1 = LOG(ABS(I / (AREA))) / LOG(10) DO UNTIL EOF(4) INPUT #4, V, I VOLT2 = -V CURR2 = LOG(ABS(I / (AREA))) / LOG(10) COLOR 5, 0  115  IF V0LT2 < VOLT1 AND 2 * INT(FLAG2 / 2) = FLAG2 THEN FLAG2 = FLAG2 + 1 IF VOLT1 < VOLT2 AND 2 * INT(FLAG2 / 2) <> FLAG2 THEN FLAG2 = FLAG2 + 1 LINE (CURR1, VOLTl)-(CURR2, VOLT2), FLAG2 + 11 VOLT1 = VOLT2 CURR1 = CURR2 LOOP CLOSE (4) END'* **************************************************** SUB PAUSE (DELAY!) CONST SECONDSINDAY = 24& * 60& * 60& LOOPFINISH = TIMER + DELAY IF LOOPFINISH > SECONDSINDAY THEN LOOPFINISH = LOOPFINISH - SECONDSINDAY DO WHILE TIMER > LOOPFINISH LOOP ENDIF 'IF PAUSE DOES NOT OCCUR AROUND MIDNIGHT: DO WHILE TIMER < LOOPFINISH IF TIMER < 1 AND LOOPFINISH > 86399 THEN GOTO 123 LOOP 123 SUB STATUSBYTE (SP%, BIT%()) X% = SP% FOR 1% = 0 TO 7 Y% = X% MOD 2 BIT%(I%) = Y% X% = FIX(X% / 2) NEXT 1%  116  APPENDIX H: MICROSOFT QUICKBASIC PROGRAM FOR CONTROLLING ELECTROCHEMICAL DEVICES FOR AC IMPEDANCE EXPERIMENTS  '1286/1250 AC IMPEDANCE PROGRAM BY NORMAN CHOW DECLARE SUB PAUSE (DELAY!) DECLARE SUB STATUSBYTE (SP%, BIT%0) DIMBIT%(7) CLS 'INITIALIZE BOARD AND DEVICE OPEN "GPIBO" FOR OUTPUT AS #1 OPEN "GPIBO" FOR INPUT AS #2 OPEN "C:\DATA\AC\FILENAME.DAT" FOR APPEND AS #3 PRINT #1, "ABORT" PRINT #1, "RESET" PRINT #1, "REMOTE" 'RESET 1250 PRINT #1, "OUTPUT 6; TT2" 'INITIALIZE PAUSE (.5) PRINT #1, "OUTPUT 6; SM" 'SCROLL MINI STATUS PAUSE (.5) PRINT #1, "OUTPUT 6; SO0201" 'SOURCE VOLTS/AMPS PAUSE (.5) PRINT # 1, "OUTPUT 6; AU3" 'Ch 1 SHORT PAUSE (.5) PRINT #1, "OUTPUT 6; AU4" Ch 2 SHORT PAUSE (.5) PRINT #1, "OUTPUT 6; IP1, 1" 'INPUT CHANEL 1 FROM REAR PAUSE (.5) PRINT #1, "OUTPUT 6; IP2, 1" 'INPUT CHANEL 2 FROM REAR PAUSE (.5) 'RESET 1286 PRINT #1, "OUTPUT 12; BK4" 'INITIALIZE PAUSE (.5) PRINT #1, "OUTPUT 12; PWO" 'STANDBY PAUSE (.5)  117  PRINT #1, "OUTPUT 12; POO" 'P STAT PAUSE (.5) PRINT #1, "OUTPUT 12; RR3" TO OHM STANDARD RESISTOR* ******************** SRESIS = 10 'STANDARD RESISTOR* **************************************** PAUSE (.5) PRINT #1, "OUTPUT 12; IL6" 'CURRENT LIMIT 2 AMPS PAUSE (.5) PRINT #1, "OUTPUT 12; OL2" 'OVERLOAD WARNING PAUSE (.5) PRINT #1, "OUTPUT 12; BY1" 'CE /OC ON STANDBY PAUSE (.5) PRINT #1, "OUTPUT 12; PV.9" 'POLORIZATION VOLTAGE -0.9 VOLTS****************** PAUSE (.5) PRINT #1, "OUTPUT 12; PI1" 'POL I/P x 0.01 PAUSE (.5) PRINT #1, "OUTPUT 12; DG2" 'DIGITS 4x9 60 Hz PAUSE (.5) PRINT #1, "OUTPUT 12; TR1" 'TRIGGER RECYCLE PAUSE (.5) PRINT #1, "OUTPUT 12; DC1" 'DRIFT CORR. OFF PAUSE (.5) PRINT #1, "OUTPUT 12; PX9" 'PARI = POL PAUSE (.5) PRINT #1, "OUTPUT 12; PY5" 'PAR2 = I PAUSE (.5) PRINT #1, "OUTPUT 12; RH1" 'DATA OUTPUT HEADING OFF PAUSE (.5) 'PRINT #1 "OUTPUT 12' VX1" 'Vx io********************* 'PAUSE (.5) 'PRINT #1 "OUTPUT 121X1"'I X 10********************* 'PAUSE (.5) 'PRINT #1, "OUTPUT 12; FI1" 'LP FILTER ON**************** 'PAUSE (.5) 'DVM DISPLAY PRINT #1, "OUTPUT 12; GP0" 'GPIB OFF PRINT #1, "OUTPUT 12; TR1" 'DVM RECYCLE PRINT #1, "OUTPUT 12; RU1" 'DVM ON -  i  ••••'••.>/.•..  'SETUP 1250  118  .......  PRINT #1, "OUTPUT 6; OP3,l" TILE ALL PAUSE (.5) PRINT #1, "OUTPUT 6; FC" 'CLEAR FILE PAUSE (.5) PRINT #1, "OUTPUT 6; FS31" 'FILE SIZE 31 BLOCKS PAUSE (.5) PRINT #1, "OUTPUT 6; AMI" 'GENERATOR AMPLITUDE 1/100 VOLTS VOLT* * ******************* PAUSE (.5) PRINT #1, "OUTPUT 6; ML1" 'MINIMUM FREQUENCY .1 p^****************************  PAUSE (.5) PRINT #1, "OUTPUT 6; MA65535" 'MAX. FREQUENCY 65535 J-f 7 *  * * * * * * * * * * * * * * * * * * * * * * * * *  PAUSE (.5) PRINT #1, "OUTPUT 6; GS30" '30 DATA POINT §************************************ PAUSE (.5) PRINT #1, "OUTPUT 6; IS210" 'INTEGRATION TIME 210 SECONDS PAUSE (5) TURN CELL (1286) ON RUNNO = 0 'SET 1ST RUNNO TO 0 PRINT #1, "OUTPUT 12; ON0" 'POL V/I POTENTIAL POLARIZATION* ****************** PRINT #1, "OUTPUT 12; OL1" 'OVERLOAD LIMIT PRINT #1, "OUTPUT 12; VTO" 'AUTO V REJECT PRINT #1, "OUTPUT 12; BR1" 'BIAS REJECT MEASURE THEN ON PRINT #1, "OUTPUT 12; IL6" CURRENT LIMIT 2 AMPS PRINT #1, "OUTPUT 12; PW1" CELL ON PAUSE (300) "INITIAL POLARIZATION TIME  RERUN: IF RUNNO = 0 THEN PRINT #1, "OUTPUT 12; PV.4" 'POLARIZE TO - 4Vsce PAUSE (300) ENDIF IF RUNNO = 1 THEN PRINT #1, "OUTPUT 12; PV.3"' POLARIZE TO - 3Vsce PAUSE (300) END IF IF RUNNO = 2 THEN  119  PRINT #1, "OUTPUT 12; PV2"' POLARIZE TO -.2Vsce PAUSE (300) IF RUNNO = 3 THEN PRINT #1, "OUTPUT 12; PV.l" 'POLARIZE TO - lVsce PAUSE (300) END IF IF RUNNO = 4 THEN PRINT #1, "OUTPUT 12; PVO"' POLARIZE TO OVsce PAUSE (300) ENDIF IF RUNNO = 5 THEN PRINT #1, "OUTPUT 12; PV-.l"' POLARIZE TO lVsce PAUSE (300) IF RUNNO = 6 THEN PRINT #1, "OUTPUT 12; PV-.2"' POLARIZE TO 2Vsce PAUSE (300) IF RUNNO = 7 THEN PRINT #1, "OUTPUT 12; PV-.3" 'POLARIZE TO 3Vsce PAUSE (300) ENDIF IF RUNNO = 8 THEN PRINT #1, "OUTPUT 12; PV-.4"' POLARIZE TO 4Vsce PAUSE (300) ENDIF IF RUNNO = 9 THEN PRINT #1, "OUTPUT 12; PV-.5"' POLARIZE TO 5Vsce PAUSE (300) END IF 'RUN 1250 PRINT #1, "OUTPUT 6; OP2,l" 'GPffi FILE ALL PAUSE (.5) PRINT #1, "OUTPUT 6; SC2" 'LOG SCAN DOWN PAUSE (.5) PRINT #1, "OUTPUT 6; RE" 'ANALYZER RECYLE PAUSE (.5) PRINT #1, "OUTPUT 6; RG"' START GENERATOR PAUSE (.5) 'DOWNLOAD DATA •GRAPH CLS SCREEN 9  120  WIDTH 80, 43 COLOR 11, 0 LOCATE 3, 32 PRINT FILENMS LOCATE 4, 32 PRINT DATES;" "; TIMES COLOR 11, 0 •X-AXIS LABELLING FREQUENCY XMIN = -1 XMAX = 5 L = XMAX-XMIN STP = 18.5/L 1= 0 FOR XLABEL = XMIN TO XMAX STEP 3 LOCATE 41, 18 + INT((2.4 * I * STP) + .5) PRINT "10" LOCATE 40, 19 + INT((2.4 * I * STP) + .5) XLABS = STRS(XLABEL) PRINT XLABS 1=1 + 3 NEXT 'left y-axis, impedance YMTN = 1 'MINIMUM IMPEDANCE************************************* YMAX = 6'MAXIMUM IMPEDANCE* ******************************************* L = YMAX - YMIN STP=14/L 1= 0 FOR YLABEL = YMIN TO YMAX YLABS = STRS(YLABEL) IF YLABEL = YMAX THEN LOCATE 40 - INT((2.4 * I * STP) + .5), 14 PRINT "10" LOCATE 39 - INT((2.4 * I * STP) + .5), 15 PRINT YLABS ELSE LOCATE 39 - INT((2.4 * I * STP) + .5), 14 PRINT "10"  121  LOCATE 38 - INT((2.4 * I * STP) + .5), 15 PRINT YLAB$ END IF 1 = 1+1 NEXT 'right y-axis labelling, phase angle TMTN = 0 'MINIMUM PHASE TMAX = 90 'MAXIMUM PHASE ANGLE******************************* COLOR 9, 0 L = (TMAX-TMTN)/15 STP=14/L 1= 0 FOR YLABEL = TMTN TO TMAX STEP 15 LOCATE 39 - INT((2.4 * I * STP) + .5), 64 YLAB$ = STR$(YLABEL) PRINT YLAB$ 1 = 1+1 NEXT COLOR 11,0 LOCATE 42, 33 PRINT "Frequency, (Hz)" Yl$ = "IMPEDENCE" Y2$ = "PHASE ANGLE" FORI = 1 TO LEN(Y1$) LOCATE 14+ 1,9 PRINT MID$(Y1$, I, 1) NEXT I LOCATE 16 + LEN(Y1$), 6 PRINT "("; CHR$(234); "cm"; CHR$(253);")' COLOR 9, 0 FORJ= 1 TO LEN(Y2$) LOCATE 14 + J, 70 PRINT MTD$(Y2$, J, 1) NEXT J LOCATE 16 + LEN(Y2$), 68 PRINT "(DEG)" LOCATE 42, 1 COLOR 11, 0  122  WINDOW (0, 0)-(640, 350) VIEW (145, 29)-(496, 302) 'plot ticks  WINDOW (XMIN, YMIN)-(XMAX, YMAX) LINE (XMIN, YMTN)-(XMIN, YMAX) LINE (XMIN, YMAX)-(XMAX, YMAX) LINE (XMIN, YMIN)-(XMAX, YMIN) COLOR 9, 0 LINE (XMAX, YMAX)-(XMAX, YMIN) COLOR 11, 0 INCX = (XMAX - XMIN) / 100 INCY = (YMAX - YMIN) / 100 FOR XTICK = XMIN TO XMAX LINE (XTICK, YMIN)-(XTICK, YMIN + 3 * INCY) LINE (XTICK, YMAX)-(XTICK, YMAX - 3 * INCY) NEXT FOR XTICK = XMIN TO XMAX STEP 3 LINE (XTICK, YMIN)-(XTICK, YMIN + 5 * INCY) LINE (XTICK, YMAX)-(XTICK, YMAX - 5 * INCY) NEXT FOR YTICK = YMIN TO YMAX LINE (XMIN, YTICK)-(XMIN + 5 * INCX, YTICK) FORI = 2T0 9 YLOG = YTICK + 1 + LOG(I /10) / 2.3 LINE (XMIN, YLOG)-(XMIN + 3 * INCX, YLOG) NEXT NEXT 'plot the total impedance versus the frequency  READDATA 1: PRINT #1, "ENTER 6" INPUT #2, FREQ, REA, IMG REA = REA * SRESIS IMG = IMG * SRESIS WRITE #3, FREQ, REA, IMG FREQ1 = LOGTFREQ) / LOG(10) TIMP1 = LOG((REA 2 + IMG 2) .5) / LOG(10) PHAS1 = (ATN(-IMG/REA)) * (180 / 3.1415) FLAG2 = 0 A  A  A  123  RE ADD AT A2: FLAG1 = FLAG1 + 1 IF FLAG2 = 0 AND FREQ < 10 THEN PRINT #1, "OUTPUT 12; FI1" 'LOWPASS FILTERON*******************^ FLAG2 =1 END IF PRINT #1, "ENTER 6" INPUT #2, FREQ, REA, IMG REA = REA * SRESIS I M G = I M G * SRESIS  WRITE #3, FREQ, REA, IMG FREQ2 = LOGXFREQ) / LOG(10) TIMP2 = LOG((REA 2 + IMG 2) .5) / L O G 0 O ) PHAS2 = (ATN(-IMG / REA)) * (180 / 3.1415) WINDOW (XMTN, YMTN)-(XMAX, YMAX) LINE (FREQ1 - INCX, TIMP1 - INCY)-(FREQ1 + INCX, TIMP1 + INCY), 11 LINE (FREQ1 - INCX, TIMP1 + INCY)-(FREQ1 + INCX, TIMP1 - INCY), 11 TIMP1 =TIMP2 A  A  A  'right axis ticks  COLOR 9, 0 WINDOW (XMTN, TMTN)-(XMAX, TMAX) INCT = (TMAX - TMTN) / 100 FOR YTICK = TMTN TO TMAX STEP 15 LINE (XMAX, YTICK)-(XMAX - 5 * INCX, YTICK) NEXT i  'plot the phase angle versus the frequency  LINE (FREQ1 - INCX, PHAS1 - INCT)-(FREQ1 + INCX, PHAS1 + INCT), 9, B FREQ1=FREQ2 PHAS1 =PHAS2 'SERIAL POLL PRINT #1, "SPOLL 6" INPUT #2, SP% CALL STATUSBYTE(SP%, BIT%()) IF BIT%(2) o 1 THEN GOTO READDATA2 PARS = "C:\PJSCREEN /UON /PT /AC /M16 /CD /RN" SHELL PARS 'CALL INT860LD(5, INARY%(), OUTARY%0)  124  'END PLOT CLOSE (3) PRINT #1, "OUTPUT 12; PWO" 'ON TO STANDBY PAUSE (.5) PRINT #1, "OUTPUT 6; SG" 'GENERATOR STOP PRINT #1, "OUTPUT 6; BK" 'BREAK RUNNO = RUNNO + 1 PAUSE (60) ' PAUSE TIME BETWEEN RUNS IF RUNNO < 10 THEN FILENMS = "C:\DATA\POL.00" + LTRTM$(STR$(RUTsTNO))'************ ************** ELSEIF RUNNO > 9 AND RUNNO < 100 THEN FILENMS = "C:\DATA\POL.0" + LTR1M$(STR$(RUNN0))'*************************** ELSE FILENMS = "C:\DATA\POL." + LTRIM$(STR$(RUNNO))'**** ***************** ******* END IF OPEN FILENMS FOR APPEND AS #3 IF RUNNO < 9 THEN GOTO RERUN: END************************************************* SUB PAUSE (DELAY!) CONST SECONDSINDAY = 24& * 60& * 60& LOOPFINISH = TIMER + DELAY IE LOOPFINISH > SECOND SINDAY THEN LOOPFINISH = LOOPFINISH - SECOND SIND AY DO WHILE TIMER > LOOPFINISH LOOP ENDIF 'IF PAUSE DOES NOT OCCUR AROUND MIDNIGHT: DO WHILE TIMER < LOOPFINISH IF TIMER < 1 AND LOOPFINISH > 86399 THEN GOTO 123 LOOP 123 J2ND gygi**** ********************* ******************  SUB STATUSBYTE (SP%, BIT%()) X% = SP% FOR 1% = 0 TO 7 Y% = X%MOD2  125  BIT%(I%) = Y% X% = FIX(X%/2) N E X T 1% E N D STJB'************************************  126  A P P E N D I X m : C O M P A R I S O N OF M E A S U R E D I M P E D A N C E D A T A W I T H M O D E L E D IMPEDANCE RESULTS  Log Frequency (Hz) Impedance (measured) —  — • Impedance (model)  Phase Angle (measured) • • - - - - Phase Angle (model)  Figure A l . Measured Versus Model Impedance for Copper at -0.4 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  *1  1  r 90  _-0.3sce  54 ^  E /  •  —  \  *  A-  - — e 0  V  1  1  1  2  1  3  —  4  —  '  80 - 70 60 50 • 40 30 20 - 10 -0 5  Log Frequency (Hz) Impedance (measured)  — - — - Impedance (model) - • - Phase Angle (model)  Phase Angle (measured) - -  Figure A2. Measured Versus Model Impedance for Copper at -0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  127  -1  0  1  2  3  4  5  Log Frequency (Hz) — • Impedance (model)  Impedance (measured) —  Phase Angle (measured) - - - - - - Phase Angle (model)  Figure A3. Measured Versus Model Impedance for Copper at -0.2 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  u c a  a.  E  a> o  1  2  3  Log Frequency (Hz) Impedance (measured)  — - — - impedance (model)  — Phase Angle (measured)  Phase Angle (model)  Figure A4. Measured Versus Model Impedance for Copper at -0.1 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  128  m E  0 1 o e IB  Q.  E q 1  2  3  Log Frequency (Hz) Impedance (model)  Impedance (measured) Phase Angle (measured)  - Phase Angle (model)  Figure A5. Measured Versus Model Impedance for Copper at 0.0 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  1 VI  E  01 u c  IB  Ol  q  *1  90 80  0.1 Vsce  5  70  4  60  I,  50 40 < 30 8  — ^ 3  21 d r  f  H.  1  !• '  1  1  2  1  1  10 0  3  Log Frequency (Hz) Impedance (measured)  — - — - Impedance (model)  — Phase Angle (measured)  Phase Angle (model)  Figure A6. Measured Versus Model Impedance for Copper at 0.1 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  129  0.2sce  ,j  ^-p  1  T  2  .  3  j 90 80 70 • 60 50 40 30 20 - 10 - 0 5  fTJ, Ct> CD  C <  <u U) to s. 0.  Log Frequency (Hz) Impedance (measured)  — • — - Impedance (model)  Phase Angle (measured)  Phase Angle (model)  Figure A7. Measured Versus Model Impedance for Copper at 0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  90  0.3Vsce  80  f f, I  70 60 H50 40 30 S 20 £  I 10 0 1  2  3  5  Log Frequency (Hz) •Impedance (measured) —  Impedance (model) - Phase Angle (model)  Phase Angle (measured)  Figure A8. Measured Versus Model Impedance for Copper at 0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  130  1 tfl  0.4Vsce  5-  E  ••  4-  0)  7° 60 50 40 30 20 10 0  •-  3-  u e  10  2  I  1-  TV— —  --  —  E  at o  1  2  90 80  f  5. o.  <  2 £  3  Log Frequency (Hz) Impedance (measured)  Impedance (model)  Phase Angle (measured)  - Phase Angle (model)  Figure A9. Measured Versus Model Impedance for Copper at 0.4 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  E  0 1 u c n a E oi o  90 + 80 70 f 60 250 B 40 < + 30 | 20 S. 10 0  0.5 Vsce  \  -v-  \  1  \  A  1  2  3  Log Frequency (Hz) Impedance (measured)  • Impedance (model)  Phase Angle (measured)  - - Phase Angle (model)  Figure A10. Measured Versus Model Impedance for Copper at 0.5 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 50 RPM  131  Log Frequency (Hz) Impedance (measured) —  — - Impedance (model)  Phase Angle (measured) - - - - • • Phase Angle (model)  Figure A l l . Measured Versus Model Impedance for Copper at -0.4 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  Log Frequency (Hz) — • — • Impedance (model) Phase Angle (measured) - - • - - - Phase Angle (model)  Impedance (measured)  Figure A12. Measured Versus Model Impedance for Copper at -0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  132  0  1  2  3  4  5  Log Frequency (Hz) — - Impedance (model)  Impedance (measured) —  Phase Angle (measured) - - - - - - Phase Angle (model)  Figure A13. Measured Versus Model Impedance for Copper at -0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  0  1  2  3  4  5  Log Frequency (Hz) Impedance (measured)  — - — - Impedance (model)  Phase Angle (measured) -  Phase Angle (model)  Figure A14. Measured Versus Model Impedance for Copper at -0.1 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  -1  0  1  2  3  4  5  Log Frequency (Hz) Impedance (measured) — — - Impedance (model) Phase Angle (measured) - - - - - - Phase Angle (model)  Figure A15. Measured Versus Model Impedance for Copper at 0.0 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  -1  0  1  2  3  4  5  Log Frequency (Hz) Impedance (measured) —  — • Impedance (model)  Phase Angle (measured) - - - - - - phase Angle (model)  Figure A16. Measured Versus Model Impedance for Copper at 0.1 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  134  1  2  3  Log Frequency (Hz) Impedance (measured)  — - — - Impedance (model)  Phase Angle (measured)  Phase Angle (model)  Figure A17. Measured Versus Model Impedance for Copper at 0.2 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  90 80  0.3Vsce  f 60 S. 7 0  + 50 * 40 < •  1  0  1  1—  3  2  Log Frequency (Hz) Impedance (measured)  30 «  f20f 10  u  5  — - — - Impedance (model)  Phase Angle (measured)  Phase Angle (model)  Figure A18. Measured Versus Model Impedance for Copper at 0.3 Vsce in 1M NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  135  1  2  3  Log Frequency (Hz) • Impedance (measured) — Phase Angle (measured) - -  — - Impedance (model) - - - phase Angle (model)  Figure A19. Measured Versus Model Impedance for Copper at 0.4 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  r - - •• -i0  1  2  3  Log Frequency (Hz) Impedance (measured)  Impedance (model)  Phase Angle (measured)  Phase Angle (model)  Figure A20. Measured Versus Model Impedance for Copper at 0.5 Vsce in IM NaCl Buffered to pH 10.5 with 0.01M Sodium Tetraborate Rotating at 5000 RPM  136  

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