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Corrosion Chapter 16 / and Degradation of Materials P hotograph showing a bar of steel that has been bent into a horseshoe shape using a nut-and-bolt assembly. While immersed in seawater, stress corrosion cracks formed along the bend at those regions where the tensile stresses are the greatest. (Photograph courtesy of F. L. LaQue. From F. L. LaQue, Marine Corrosion, Causes and Prevention. Copyright 1975 by...

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Corrosion Chapter 16 / and Degradation of Materials P hotograph showing a bar of steel that has been bent into a horseshoe shape using a nut-and-bolt assembly. While immersed in seawater, stress corrosion cracks formed along the bend at those regions where the tensile stresses are the greatest. (Photograph courtesy of F. L. LaQue. From F. L. LaQue, Marine Corrosion, Causes and Prevention. Copyright 1975 by John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.) Why Study Corrosion and Degradation of Materials? With a knowledge of the types of and an understanding of the mechanisms and causes of corrosion and degradation, it is possible to take measures to prevent them from occurring. For example, we may S-204 change the nature of the environment, select a material that is relatively nonreactive, and/or protect the material from appreciable deterioration. Learning Objectives After careful study of this chapter you should be able to do the following: 1. Distinguish between oxidation and reduction electrochemical reactions. 2. Describe the following: galvanic couple, standard half-cell, and standard hydrogen electrode. 3. Compute the cell potential and write the spontaneous electrochemical reaction direction for two pure metals that are electrically connected and also submerged in solutions of their respective ions. 4. Determine metal oxidation rate given the reaction current density. 5. Name and briey describe the two different types of polarization, and specify the conditions under which each is rate controlling. 6. For each of the eight forms of corrosion and hydrogen embrittlement, describe the nature of the deteriorative process, and then note the proposed mechanism. 7. List ve measures that are commonly used to prevent corrosion. 8. Explain why ceramic materials are, in general, very resistant to corrosion. 9. For polymeric materials discuss (a) two degradation processes that occur when they are exposed to liquid solvents, and (b) the causes and consequences of molecular chain bond rupture. 16.1 INTRODUCTION To one degree or another, most materials experience some type of interaction with a large number of diverse environments. Often, such interactions impair a materials usefulness as a result of the deterioration of its mechanical properties (e.g., ductility and strength), other physical properties, or appearance. Occasionally, to the chagrin of a design engineer, the degradation behavior of a material for some application is ignored, with adverse consequences. Deteriorative mechanisms are different for the three material types. In metals, there is actual material loss either by dissolution (corrosion) or by the formation of nonmetallic scale or lm (oxidation). Ceramic materials are relatively resistant to deterioration, which usually occurs at elevated temperatures or in rather extreme environments; the process is frequently also called corrosion. For polymers, mechanisms and consequences differ from those for metals and ceramics, and the term degradation is most frequently used. Polymers may dissolve when exposed to a liquid solvent, or they may absorb the solvent and swell; also, electromagnetic radiation (primarily ultraviolet) and heat may cause alterations in their molecular structure. The deterioration of each of these material types is discussed in this chapter, with special regard to mechanism, resistance to attack by various environments, and measures to prevent or reduce degradation. CORROSION OF METALS Corrosion is dened as the destructive and unintentional attack of a metal; it is electrochemical and ordinarily begins at the surface. The problem of metallic corrosion is one of signicant proportions; in economic terms, it has been estimated that approximately 5% of an industrialized nations income is spent on corrosion prevention and the maintenance or replacement of products lost or contaminated as a result of corrosion reactions. The consequences of corrosion are all too common. Familiar examples include the rusting of automotive body panels and radiator and exhaust components. Corrosion processes are occasionally used to advantage. For example, etching procedures, as discussed in Section 5.12, make use of the selective chemical reactivity S-205 S-206 Chapter 16 / Corrosion and Degradation of Materials of grain boundaries or various microstructural constituents. Also, the current developed in dry-cell batteries is a result of corrosion processes. 16.2 ELECTROCHEMICAL CONSIDERATIONS For metallic materials, the corrosion process is normally electrochemical, that is, a chemical reaction in which there is transfer of electrons from one chemical species to another. Metal atoms characteristically lose or give up electrons in what is called an oxidation reaction. For example, the hypothetical metal M that has a valence of n (or n valence electrons) may experience oxidation according to the reaction Mn M ne (16.1) in which M becomes an n positively charged ion and in the process loses its n valence electrons; e is used to symbolize an electron. Examples in which metals oxidize are Fe Fe2 2e (16.2a) Al Al3 3e (16.2b) The site at which oxidation takes place is called the anode; oxidation is sometimes called an anodic reaction. The electrons generated from each metal atom that is oxidized must be transferred to and become a part of another chemical species in what is termed a reduction reaction. For example, some metals undergo corrosion in acid solutions, which have a high concentration of hydrogen (H ) ions; the H ions are reduced as follows: 2H 2e H2 (16.3) and hydrogen gas (H2) is evolved. Other reduction reactions are possible, depending on the nature of the solution to which the metal is exposed. For an acid solution having dissolved oxygen, reduction according to O2 4H 4e 2H2O (16.4) will probably occur. Or, for a neutral or basic aqueous solution in which oxygen is also dissolved, O2 2H2O 4e 4(OH ) (16.5) Any metal ions present in the solution may also be reduced; for ions that can exist in more than one valence state (multivalent ions), reduction may occur by Mn M(n e 1) (16.6) in which the metal ion decreases its valence state by accepting an electron. Or, a metal may be totally reduced from an ionic to a neutral metallic state according to Mn ne M (16.7) 16.2 Electrochemical Considerations Zn Zn2+ Acid solution Zinc e e H+ S-207 FIGURE 16.1 The electrochemical reactions associated with the corrosion of zinc in an acid solution. (From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) H2 H+ That location at which reduction occurs is called the cathode. Furthermore, it is possible for two or more of the reduction reactions above to occur simultaneously. An overall electrochemical reaction must consist of at least one oxidation and one reduction reaction, and will be the sum of them; often the individual oxidation and reduction reactions are termed half-reactions. There can be no net electrical charge accumulation from the electrons and ions; that is, the total rate of oxidation must equal the total rate of reduction, or all electrons generated through oxidation must be consumed by reduction. For example, consider zinc metal immersed in an acid solution containing H ions. At some regions on the metal surface, zinc will experience oxidation or corrosion as illustrated in Figure 16.1, and according to the reaction Zn2 Zn 2e (16.8) Since zinc is a metal, and therefore a good electrical conductor, these electrons may be transferred to an adjacent region at which the H ions are reduced according to 2e 2H H2 (gas) (16.9) If no other oxidation or reduction reactions occur, the total electrochemical reaction is just the sum of reactions 16.8 and 16.9, or Zn 2e 2H Zn Zn2 2e H2 (gas) Zn2 2H H2 (gas) (16.10) Another example is the oxidation or rusting of iron in water, which contains dissolved oxygen. This process occurs in two steps; in the rst, Fe is oxidized to Fe2 [as Fe(OH)2], Fe O2 Fe2 H2O and, in the second stage, to Fe 3 2Fe(OH) 2 2OH Fe(OH)2 (16.11) [as Fe(OH)3] according to O2 H2O 2Fe(OH)3 (16.12) The compound Fe(OH)3 is the all-too-familiar rust. As a consequence of oxidation, the metal ions may either go into the corroding solution as ions (reaction 16.8), or they may form an insoluble compound with nonmetallic elements as in reaction 16.12. ELECTRODE POTENTIALS Not all metallic materials oxidize to form ions with the same degree of ease. Consider the electrochemical cell shown in Figure 16.2. On the left-hand side is a piece of S-208 Chapter 16 / Corrosion and Degradation of Materials FIGURE 16.2 An electrochemical cell consisting of iron and copper electrodes, each of which is immersed in a 1M solution of its ion. Iron corrodes while copper electrodeposits. 0.780 V + V e e Voltmeter Fe Fe2+ Fe2+ solution, 1.0 M Cu2+ Cu Cu2+ solution, 1.0 M Membrane pure iron immersed in a solution containing Fe2 ions of 1M concentration.1 The other side of the cell consists of a pure copper electrode in a 1M solution of Cu2 ions. The cell halves are separated by a membrane, which limits the mixing of the two solutions. If the iron and copper electrodes are connected electrically, reduction will occur for copper at the expense of the oxidation of iron, as follows: Cu2 Fe Cu Fe2 (16.13) 2 or Cu ions will deposit (electrodeposit) as metallic copper on the copper electrode, while iron dissolves (corrodes) on the other side of the cell and goes into solution as Fe2 ions. Thus, the two half-cell reactions are represented by the relations Fe Cu 2 Fe2 2e Cu 2e (16.14a) (16.14b) When a current passes through the external circuit, electrons generated from the oxidation of iron ow to the copper cell in order that Cu2 be reduced. In addition, there will be some net ion motion from each cell to the other across the membrane. This is called a galvanic couple two metals electrically connected in a liquid electrolyte wherein one metal becomes an anode and corrodes, while the other acts as a cathode. An electric potential or voltage will exist between the two cell halves, and its magnitude can be determined if a voltmeter is connected in the external circuit. A potential of 0.780 V results for a copperiron galvanic cell when the temperature is 25 C (77 F). Now consider another galvanic couple consisting of the same iron half-cell connected to a metal zinc electrode that is immersed in a 1M solution of Zn2 ions (Figure 16.3). In this case the zinc is the anode and corrodes, whereas the Fe now becomes the cathode. The electrochemical reaction is thus Fe2 Zn Fe Zn2 (16.15) The potential associated with this cell reaction is 0.323 V. 1 Concentration of liquid solutions is often expressed in terms of molarity, M, the number of moles of solute per million cubic millimeters (106 mm3, or 1000 cm3) of solution. 16.2 Electrochemical Considerations V e e Voltmeter Fe2+ Fe Fe2+ solution, 1.0 M S-209 FIGURE 16.3 An electrochemical cell consisting of iron and zinc electrodes, each of which is immersed in a 1M solution of its ion. The iron electrodeposits while the zinc corrodes. 0.323 V + Zn Zn2+ Zn2+ solution, 1.0 M Membrane Thus, various electrode pairs have different voltages; the magnitude of such a voltage may be thought of as representing the driving force for the electrochemical oxidationreduction reaction. Consequently, metallic materials may be rated as to their tendency to experience oxidation when coupled to other metals in solutions of their respective ions. A half-cell similar to those described above [i.e., a pure metal electrode immersed in a 1M solution of its ions and at 25 C (77 F)] is termed a standard half-cell. THE STANDARD EMF SERIES These measured cell voltages represent only differences in electrical potential, and thus it is convenient to establish a reference point, or reference cell, to which other cell halves may be compared. This reference cell, arbitrarily chosen, is the standard hydrogen electrode (Fig. 16.4). It consists of an inert platinum electrode in a 1M FIGURE 16.4 The standard hydrogen reference half-cell. V Voltmeter Pt H+ solution, 1.0 M Hydrogen gas, 1 atm pressure Membrane S-210 Chapter 16 / Corrosion and Degradation of Materials Table 16.1 The Standard emf Series Standard Electrode Potential, V 0 (V) Electrode Reaction O2 Increasingly inert (cathodic) O2 Increasingly active (anodic) Au3 4H Pt2 Ag Fe3 2H2O Cu2 2H Pb2 Sn2 Ni2 Co2 Cd2 Fe2 Cr3 Zn2 Al3 Mg2 Na K 3e 4e 2e e e 4e 2e 2e 2e 2e 2e 2e 2e 2e 3e 2e 3e 2e e e Au 2H2O Pt Ag Fe2 4(OH ) Cu H2 Pb Sn Ni Co Cd Fe Cr Zn Al Mg Na K 1.420 1.229 1.2 0.800 0.771 0.401 0.340 0.000 0.126 0.136 0.250 0.277 0.403 0.440 0.744 0.763 1.662 2.363 2.714 2.924 solution of H ions, saturated with hydrogen gas that is bubbled through the solution at a pressure of 1 atm and a temperature of 25 C (77 F). The platinum itself does not take part in the electrochemical reaction; it acts only as a surface on which hydrogen atoms may be oxidized or hydrogen ions may be reduced. The electromotive force (emf) series (Table 16.1) is generated by coupling to the standard hydrogen electrode, standard half-cells for various metals and ranking them according to measured voltage. Table 16.1 represents the corrosion tendencies for the several metals; those at the top (i.e., gold and platinum) are noble, or chemically inert. Moving down the table, the metals become increasingly more active, that is, more susceptible to oxidation. Sodium and potassium have the highest reactivities. The voltages in Table 16.1 are for the half-reactions as reduction reactions, with the electrons on the left-hand side of the chemical equation; for oxidation, the direction of the reaction is reversed and the sign of the voltage changed. Consider the generalized reactions involving the oxidation of metal M1 and the reduction of metal M2 as n M1 M1 n M2 ne V0 1 M2 (16.16a) V0 2 ne (16.16b) where the V 0s are the standard potentials as taken from the standard emf series. Since metal M1 is oxidized, the sign of V 0 is opposite to that as it appears in Table 1 16.1. Addition of Equations 16.16a and 16.16b yields M1 n M2 n M1 M2 (16.17) and the overall cell potential V 0 is V0 V0 2 V0 1 (16.18) 16.2 Electrochemical Considerations S-211 For this reaction to occur spontaneously, V 0 must be positive; if it is negative, the spontaneous cell direction is just the reverse of Equation 16.17. When standard half-cells are coupled together, the metal that lies lower in Table 16.1 will experience oxidation (i.e., corrosion), whereas the higher one will be reduced. INFLUENCE OF CONCENTRATION AND TEMPERATURE ON CELL POTENTIAL The emf series applies to highly idealized electrochemical cells (i.e., pure metals in 1M solutions of their ions, at 25 C). Altering temperature or solution concentration or using alloy electrodes instead of pure metals will change the cell potential, and, in some cases, the spontaneous reaction direction may be reversed. Consider again the electrochemical reaction described by Equation 16.17. If M1 and M2 electrodes are pure metals, the cell potential depends on the absolute n n temperature T and the molar ion concentrations [M1 ] and [M2 ] according to the Nernst equation: (V 0 2 V V 0) 1 n [M1 ] RT ln n nF [M2 ] (16.19) where R is the gas constant, n is the number of electrons participating in either of the half-cell reactions, and F is the Faraday constant, 96,500 C/molthe magnitude of charge per mole (6.023 1023) of electrons. At 25 C (about room temperature), V (V 0 2 V 0) 1 n [M1 ] 0.0592 log n n [M2 ] (16.20) to give V in volts. Again, for reaction spontaneity, V must be positive. As n n expected, for 1M concentrations of both ion types (that is, [M1 ] [M2 ] 1), Equation 16.19 simplies to Equation 16.18. EXAMPLE PROBLEM 16.1 One half of an electrochemical cell consists of a pure nickel electrode in a solution of Ni2 ions; the other is a cadmium electrode immersed in a Cd2 solution. (a) If the cell is a standard one, write the spontaneous overall reaction and calculate the voltage that is generated. (b) Compute the cell potential at 25 C if the Cd2 and Ni2 concentrations are 0.5 and 10 3 M, respectively. Is the spontaneous reaction direction still the same as for the standard cell? S OLUTION (a) The cadmium electrode will be oxidized and nickel reduced because cadmium is lower in the emf series; thus, the spontaneous reactions will be Ni 2 Ni2 Cd 2e Cd2 Ni Cd Ni 2e Cd2 (16.21) S-212 Chapter 16 / Corrosion and Degradation of Materials From Table 16.1, the half-cell potentials for cadmium and nickel are, respectively, 0.403 and 0.250 V. Therefore, from Equation 16.18, V0 0.250 V ( 0.403 V) 0.153 V Cd (b) For this portion of the problem, Equation 16.20 must be utilized, since the half-cell solution concentrations are no longer 1M. At this point it is necessary to make a calculated guess as to which metal species is oxidized (or reduced). This choice will either be afrmed or refuted on the basis of the sign of V at the conclusion of the computation. For the sake of argument, let us assume that in contrast to part a, nickel is oxidized and cadmium reduced according to V V0 Ni Cd2 Ni Cd Ni2 (16.22) Thus, V (V 0 Cd V0 ) Ni 0.403 V RT [Ni2 ] ln nF [Cd2 ] ( 0.250 V) 0.0592 10 3 log 2 0.50 0.073 V Since V is negative, the spontaneous reaction direction is the opposite to that of Equation 16.22, or the same as that of the standard cell (Equation 16.21). THE GALVANIC SERIES Even though Table 16.1 was generated under highly idealized conditions and has limited utility, it nevertheless indicates the relative reactivities of the metals. A more realistic and practical ranking, however, is provided by the galvanic series, Table 16.2. This represents the relative reactivities of a number of metals and commercial alloys in seawater. The alloys near the top are cathodic and unreactive, whereas those at the bottom are most anodic; no voltages are provided. Comparison of the standard emf and the galvanic series reveals a high degree of correspondence between the relative positions of the pure base metals. Most metals and alloys are subject to oxidation or corrosion to one degree or another in a wide variety of environments; that is, they are more stable in an ionic state than as metals. In thermodynamic terms, there is a net decrease in free energy in going from metallic to oxidized states. Consequently, essentially all metals occur in nature as compoundsfor example, oxides, hydroxides, carbonates, silicates, suldes, and sulfates. Two notable exceptions are the noble metals gold and platinum. For them, oxidation in most environments is not favorable, and, therefore, they may exist in nature in the metallic state. 16.3 CORROSION RATES The half-cell potentials listed in Table 16.1 are thermodynamic parameters that relate to systems at equilibrium. For example, for the discussions pertaining to Figures 16.2 and 16.3, it was tacitly assumed that there was no current ow through the external circuit. Real corroding systems are not at equilibrium; there will be a ow of electrons from anode to cathode (corresponding to the short-circuiting of the electrochemical cells in Figures 16.2 and 16.3), which means that the half-cell potential parameters (Table 16.1) cannot be applied. 16.3 Corrosion Rates S-213 Table 16.2 The Galvanic Series Increasingly inert (cathodic) Increasingly active (anodic) Platinum Gold Graphite Titanium Silver 316 Stainless steel (passive) 304 Stainless steel (passive) Inconel (80Ni13Cr7Fe) (passive) Nickel (passive) Monel (70Ni30Cu) Coppernickel alloys Bronzes (CuSn alloys) Copper Brasses (CuZn alloys) Inconel (active) Nickel (active) Tin Lead 316 Stainless steel (active) 304 Stainless steel (active) Cast iron Iron and steel Aluminum alloys Cadmium Commercially pure aluminum Zinc Magnesium and magnesium alloys Source: M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reprinted with permission. Furthermore, these half-cell potentials represent the magnitude of a driving force, or the tendency for the occurrence of the particular half-cell reaction. However, it should be noted that although these potentials may be used to determine spontaneous reaction directions, they provide no information as to corrosion rates. That is, even though a V potential computed for a specic corrosion situation using Equation 16.20 is a relatively large positive number, the reaction may occur at only an insignicantly slow rate. From an engineering perspective, we are interested in predicting the rates at which systems corrode; this requires the utilization of other parameters, as discussed below. The corrosion rate, or the rate of material removal as a consequence of the chemical action, is an important corrosion parameter. This may be expressed as the corrosion penetration rate (CPR), or the thickness loss of material per unit of time. The formula for this calculation is CPR KW At (16.23) where W is the weight loss after exposure time t; and A represent the density and exposed specimen area, respectively, and K is a constant, its magnitude depending on the system of units used. The CPR is conveniently expressed in terms of either mils per year (mpy) or millimeters per year (mm/yr). In the rst case, K 534 to give S-214 Chapter 16 / Corrosion and Degradation of Materials CPR in mpy (where 1 mil 0.001 in.), and W, , A, and t are specied in units of milligrams, grams per cubic centimeter, square inches, and hours, respectively. In the second case, K 87.6 for mm/yr, and units for the other parameters are the same as for mils per year, except that A is given in square centimeters. For most applications a corrosion penetration rate less than about 20 mpy (0.50 mm/yr) is acceptable. Inasmuch as there is an electric current associated with electrochemical corrosion reactions, we can also express corrosion rate in terms of this current, or, more specically, current densitythat is, the current per unit surface area of material corrodingwhich is designated i. The rate r, in units of mol/m2-s, is determined using the expression r i nF (16.24) where, again, n is the number of electrons associated with the ionization of each metal atom, and F is 96,500 C/mol. 16.4 PREDICTION OF CORROSION RATES POLARIZATION Consider the standard Zn/H2 electrochemical cell shown in Figure 16.5, which has been short-circuited such that oxidation of zinc and reduction of hydrogen will occur at their respective electrode surfaces. The potentials of the two electrodes will not be at the values determined from Table 16.1 because the system is now a nonequilibrium one. The displacement of each electrode potential from its equilibrium value is termed polarization, and the magnitude of this displacement is the overvoltage, normally represented by the symbol . Overvoltage is expressed in terms of plus or minus volts (or millivolts) relative to the equilibrium potential. For example, suppose that the zinc electrode in Figure 16.5 has a potential of 0.621 V after it has been connected to the platinum electrode. The equilibrium potential is 0.763 V (Table 16.1), and, therefore, 0.621 V ( 0.763 V) FIGURE 16.5 Electrochemical cell consisting of standard zinc and hydrogen electrodes that has been short-circuited. e Zn Zn2+ Zn2+ solution, 1.0 M Pt 2H+ H2 H+ solution, 1.0 M Membrane 0.142 V H2 Gas, 1 atm pressure 16.4 Prediction of Corrosion Rates S-215 There are two types of polarizationactivation and concentrationthe mechanisms of which will now be discussed since they control the rate of electrochemical reactions. Activation Polarization All electrochemical reactions consist of a sequence of steps that occur in series at the interface between the metal electrode and the electrolyte solution. Activation polarization refers to the condition wherein the reaction rate is controlled by the one step in the series that occurs at the slowest rate. The term activation is applied to this type of polarization because an activation energy barrier is associated with this slowest, rate-limiting step. To illustrate, let us consider the reduction of hydrogen ions to form bubbles of hydrogen gas on the surface of a zinc electrode (Figure 16.6). It is conceivable that this reaction could proceed by the following step sequence: 1. Adsorption of H ions from the solution onto the zinc surface. 2. Electron transfer from the zinc to form a hydrogen atom, e H H 3. Combining of two hydrogen atoms to form a molecule of hydrogen, 2H H2 4. The coalescence of many hydrogen molecules to form a bubble. The slowest of these steps determines the rate of the overall reaction. For activation polarization, the relationship between overvoltage a and current density i is log a i i0 (16.25) where and i0 are constants for the particular half-cell. The parameter i0 is termed the exchange current density, which deserves a brief explanation. Equilibrium for some particular half-cell reaction is really a dynamic state on the atomic level. That is, oxidation and reduction processes are occurring, but both at the same rate, so that there is no net reaction. For example, for the standard hydrogen cell (Figure e 2 H+ 1 H+ H 3 H2 4 H2 H2 H2 H2 3 Zinc H e 2 H+ 1 H+ FIGURE 16.6 Schematic representation of possible steps in the hydrogen reduction reaction, the rate of which is controlled by activation polarization. (From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) Chapter 16 / Corrosion and Degradation of Materials 16.4) reduction of hydrogen ions in solution will take place at the surface of the platinum electrode according to 2H 2e H2 with a corresponding rate rred . Similarly, hydrogen gas in the solution will experience oxidation as H2 2H 2e at rate roxid . Equilibrium exists when rred roxid This exchange current density is just the current density from Equation 16.24 at equilibrium, or rred roxid i0 nF (16.26) Use of the term current density for i0 is a little misleading inasmuch as there is no net current. Furthermore, the value for i0 is determined experimentally and will vary from system to system. According to Equation 16.25, when overvoltage is plotted as a function of the logarithm of current density, straight-line segments result; these are shown in Figure 16.7 for the hydrogen electrode. The line segment with a slope of corresponds to the oxidation half-reaction, whereas the line with a slope is for reduction. Also worth noting is that both line segments originate at i0 (H2 /H ), the exchange current density, and at zero overvoltage, since at this point the system is at equilibrium and there is no net reaction. Concentration Polarization Concentration polarization exists when the reaction rate is limited by diffusion in the solution. For example, consider again the hydrogen evolution reduction reaction. When the reaction rate is low and/or the concentration of H is high, there is always +0.2 + + 2e FIGURE 16.7 For a hydrogen electrode, plot of activation polarization overvoltage versus logarithm of current density for both oxidation and reduction reactions. (Adapted from M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) 2H + 2 +0.1 H 0 ++ i0 (H2/H+) 2H 2e 0.1 Overvoltage, a (V) S-216 H2 0.2 0.3 0.001 0.01 0.1 1 10 Current density (logarithmic scale) 100 1000 S-217 16.4 Prediction of Corrosion Rates Depletion zone H H + H H + H H + + + H H + + + H H + H H + + H H H + H + H + H H + H H + H H + H + + + H + + + + H + + H Cathode + Cathode (a) ( b) FIGURE 16.8 For hydrogen reduction, schematic representations of the H distribution in the vicinity of the cathode for (a ) low reaction rates and/or high concentrations, and ( b) high reaction rates and/or low concentrations wherein a depletion zone is formed that gives rise to concentration polarization. (Adapted from M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) an adequate supply of hydrogen ions available in the solution at the region near the electrode interface (Figure 16.8a ). On the other hand, at high rates and/or low H concentrations, a depletion zone may be formed in the vicinity of the interface, inasmuch as the H ions are not replenished at a rate sufcient to keep up with the reaction (Figure 16.8b ). Thus, diffusion of H to the interface is rate controlling, and the system is said to be concentration polarized. Concentration polarization generally occurs only for reduction reactions because for oxidation, there is virtually an unlimited supply of metal atoms at the corroding electrode interface. Concentration polarization data are also normally plotted as overvoltage versus the logarithm of current density; such a plot is represented schematically in Figure 16.9a.2 It may be noted from this gure that overvoltage is independent of current density until i approaches iL ; at this point, c decreases abruptly in magnitude. Both concentration and activation polarization are possible for reduction reactions. Under these circumstances, the total overvoltage is just the sum of both overvoltage contributions. Figure 16.9b shows such a schematic -versus-log i plot. 2 The mathematical expression relating concentration polarization overvoltage density i is c 2.3RT log 1 nF i iL c and current (16.27) where R and T are the gas constant and absolute temperature, respectively, n and F have the same meanings as above, and iL is the limiting diffusion current density. Chapter 16 / Corrosion and Degradation of Materials FIGURE 16.9 For reduction reactions, schematic plots of overvoltage versus logarithm of current density for (a ) concentration polarization, and ( b) combined activation concentration polarization. Overvoltage, c + iL 0 Log current density, i (a) + 0 i0 Activation polarization Overvoltage, S-218 Concentration polarization iL Log current density, i (b) CORROSION RATES FROM POLARIZATION DATA Let us now apply the concepts developed above to the determination of corrosion rates. Two types of systems will be discussed. In the rst case, both oxidation and reduction reactions are rate limited by activation polarization. In the second case, both concentration and activation polarization control the reduction reaction, whereas only activation polarization is important for oxidation. Case one will be illustrated by considering the corrosion of zinc immersed in an acid solution (see Figure 16.1). The reduction of H ions to form H2 gas bubbles occurs at the surface of the zinc according to 2H 2e H2 (16.3) 2e (16.8) and the zinc oxidizes as Zn Zn2 No net charge accumulation may result from these two reactions; that is, all electrons generated by reaction 16.8 must be consumed by reaction 16.3, which is to say that rates of oxidation and reduction must be equal. Activation polarization for both reactions is expressed graphically in Figure 16.10 as cell potential referenced to the standard hydrogen electrode (not overvoltage) versus the logarithm of current density. The potentials of the uncoupled 16.4 Prediction of Corrosion Rates i0 (H+/H2) V (H+/H2) Electrochemical potential, V (V) 0 2H + 0.2 + 2e iC H S-219 FIGURE 16.10 Electrode kinetic behavior of zinc in an acid solution; both oxidation and reduction reactions are rate limited by activation polarization. (Adapted from M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGrawHill Book Company. Reproduced with permission.) +0.4 +0.2 2 0.4 VC + 2+ 0.6 2e Zn V (Zn/Zn2+) Zn 0.8 i0 (Zn/Zn2+) 1.0 10 12 10 10 10 8 10 6 10 4 10 2 1 Current density, i (A/cm2) hydrogen and zinc half-cells, V (H / H2) and V (Zn/Zn2 ), respectively, are indicated, along with their respective exchange current densities, i0 (H / H2) and i0 (Zn/Zn2 ). Straight line segments are shown for hydrogen reduction and zinc oxidation. Upon immersion, both hydrogen and zinc experience activation polarization along their respective lines. Also, oxidation and reduction rates must be equal as explained above, which is only possible at the intersection of the two line segments; this intersection occurs at the corrosion potential, designated VC , and the corrosion current density iC . The corrosion rate of zinc (which also corresponds to the rate of hydrogen evolution) may thus be computed by insertion of this iC value into Equation 16.24. The second corrosion case (combined activation and concentration polarization for hydrogen reduction and activation polarization for oxidation of metal M) is treated in a like manner. Figure 16.11 shows both polarization curves; as above, corrosion potential and corrosion current density correspond to the point at which the oxidation and reduction lines intersect. EXAMPLE PROBLEM 16.2 Zinc experiences corrosion in an acid solution according to the reaction Zn 2H Zn2 H2 The rates of both oxidation and reduction half-reactions are controlled by activation polarization. Chapter 16 / Corrosion and Degradation of Materials FIGURE 16.11 Schematic electrode kinetic behavior for metal M; the reduction reaction is under combined activationconcentration polarization control. V (H+/H2) i0 (H+/H2) Electrochemical potential, V S-220 iC VC V (M/M2+) i0 (M/M2+) iL Log current density, i (a) Compute the rate of oxidation of Zn (in mol/cm2-s) given the following activation polarization data: For Zn For Hydrogen V(Zn/Zn2 ) 0.763 V i0 10 7 A/cm2 0.09 V(H / H2) 0 V i0 10 10 A/cm2 0.08 (b) Compute the value of the corrosion potential. S OLUTION (a) To compute the rate of oxidation for Zn, it is rst necessary to establish relationships in the form of Equation 16.25 for the potential of both oxidation and reduction reactions. Next, these two expressions are set equal to one another, and then we solve for the value of i that is the corrosion current density, iC . Finally, the corrosion rate may be calculated using Equation 16.24. The two potential expressions are as follows: For hydrogen reduction, V(H VH / H2) H i i0H log and for Zn oxidation, VZn Now, setting VH V(H V(Zn/Zn2 ) Zn log i i0Zn VZn leads to / H2) H log i i0H V(Zn/Zn2 ) Zn log i i0Zn 16.5 Passivity S-221 And, solving for log i (i.e., log iC ) leads to 1 log iC [V(H Zn H / H2) 1 [0 ( 0.08) 0.09 V(Zn/Zn2 ) ( 0.763) H log i0H Zn ( 0.08)(log 10 log i0Zn ] 10 ) (0.09)(log 10 7)] 3.924 Or iC 10 3.924 1.19 10 4 A/cm2 And from Equation 16.24, iC nF r 1.19 10 4 C/s-cm2 (2)(96,500 C/mol) 6.17 10 10 mol/cm2-s (b) Now it becomes necessary to compute the value of the corrosion potential VC . This is possible by using either of the above equations for VH or VZn and substituting for i the value determined above for iC . Thus, using the VH expression yields V(H / H2) 0 VC ( 0.08 V) log H log iC i0H 1.19 10 4 A/cm2 10 10 A/cm2 0.486 V This is the same problem that is represented and solved graphically in the voltage-versus-logarithm current density plot of Figure 16.10. It is worth noting that the iC and VC we have obtained by this analytical treatment are in agreement with those values occurring at the intersection of the two line segments on the plot. 16.5 PASSIVITY Some normally active metals and alloys, under particular environmental conditions, lose their chemical reactivity and become extremely inert. This phenomenon, termed passivity, is displayed by chromium, iron, nickel, titanium, and many of their alloys. It is felt that this passive behavior results from the formation of a highly adherent and very thin oxide lm on the metal surface, which serves as a protective barrier to further corrosion. Stainless steels are highly resistant to corrosion in a rather wide variety of atmospheres as a result of passivation. They contain at least 11% chromium which, as a solid-solution alloying element in iron, minimizes the formation of rust; instead, a protective surface lm forms in oxidizing atmospheres. (Stainless steels are susceptible to corrosion in some environments, and therefore are not always stainless.) Aluminum is highly corrosion resistant in many environ- S-222 Chapter 16 / Corrosion and Degradation of Materials Electrochemical potential, V Transpassive FIGURE 16.12 Schematic polarization curve for a metal that displays an activepassive transition. Passive 2e 2+ + M M Active V (M/M2+) i0 (M/M2+) Log current density, i ments because it also passivates. If damaged, the protective lm normally reforms very rapidly. However, a change in the character of the environment (e.g., alteration in the concentration of the active corrosive species) may cause a passivated material to revert to an active state. Subsequent damage to a preexisting passive lm could result in a substantial increase in corrosion rate, by as much as 100,000 times. This passivation phenomenon may be explained in terms of polarization potentiallog current density curves discussed in the preceding section. The polarization curve for a metal that passivates will have the general shape shown in Figure 16.12. At relatively low potential values, within the active region the behavior is linear as it is for normal metals. With increasing potential, the current density suddenly decreases to a very low value that remains independent of potential; this is termed the passive region. Finally, at even higher potential values, the current density again increases with potential in the transpassive region. Figure 16.13 illustrates how a metal can experience both active and passive behavior depending on the corrosion environment. Included in this gure is the Sshaped oxidation polarization curve for an activepassive metal M and, in addition, reduction polarization curves for two different solutions, which are labeled 1 and 2. Curve 1 intersects the oxidation polarization curve in the active region at point A, yielding a corrosion current density iC (A). The intersection of curve 2 at point B is in the passive region and at current density iC (B). The corrosion rate of metal M in solution 1 is greater than in solution 2 since iC (A) is greater than iC (B) and rate is proportional to current density according to Equation 16.24. This difference in corrosion rate between the two solutions may be signicantseveral orders of magnitudewhen one considers that the current density scale in Figure 16.13 is scaled logarithmically. 16.6 ENVIRONMENTAL EFFECTS The variables in the corrosion environment, which include uid velocity, temperature, and composition, can have a decided inuence on the corrosion properties of 16.7 Forms of Corrosion S-223 Electrochemical potential, V FIGURE 16.13 Demonstration of how an activepassive metal can exhibit both active and passive corrosion behavior. i0 (1) i0 (2) B 2 1 A i0 (M/M2+) iC (B) iC (A) Log current density, i the materials that are in contact with it. In most instances, increasing uid velocity enhances the rate of corrosion due to erosive effects, as discussed later in the chapter. The rates of most chemical reactions rise with increasing temperature; this also holds for the great majority of corrosion situations. Increasing the concentration of the corrosive species (e.g., H ions in acids) in many situations produces a more rapid rate of corrosion. However, for materials capable of passivation, raising the corrosive content may result in an active-to-passive transition, with a considerable reduction in corrosion. Cold working or plastically deforming ductile metals is used to increase their strength; however, a cold-worked metal is more susceptible to corrosion than the same material in an annealed state. For example, deformation processes are used to shape the head and point of a nail; consequently, these positions are anodic with respect to the shank region. Thus, differential cold working on a structure should be a consideration when a corrosive environment may be encountered during service. 16.7 FORMS OF CORROSION It is convenient to classify corrosion according to the manner in which it is manifest. Metallic corrosion is sometimes classied into eight forms: uniform, galvanic, crevice, pitting, intergranular, selective leaching, erosioncorrosion, and stress corrosion. The causes and means of prevention of each of these forms are discussed briey. In addition, we have elected to discuss the topic of hydrogen embrittlement in this section. Hydrogen embrittlement is, in a strict sense, a type of failure rather than a form of corrosion; however, it is often produced by hydrogen that is generated from corrosion reactions. UNIFORM ATTACK Uniform attack is a form of electrochemical corrosion that occurs with equivalent intensity over the entire exposed surface and often leaves behind a scale or deposit. In a microscopic sense, the oxidation and reduction reactions occur randomly over the surface. Some familiar examples include general rusting of steel and iron and S-224 Chapter 16 / Corrosion and Degradation of Materials the tarnishing of silverware. This is probably the most common form of corrosion. It is also the least objectionable because it can be predicted and designed for with relative ease. GALVANIC CORROSION Galvanic corrosion occurs when two metals or alloys having different compositions are electrically coupled while exposed to an electrolyte. This is the type of corrosion or dissolution that was described in Section 16.2. The less noble or more reactive metal in the particular environment will experience corrosion; the more inert metal, the cathode, will be protected from corrosion. For example, steel screws corrode when in contact with brass in a marine environment; or if copper and steel tubing are joined in a domestic water heater, the steel will corrode in the vicinity of the junction. Depending on the nature of the solution, one or more of the reduction reactions, Equations 16.3 through 16.7, will occur at the surface of the cathode material. Figure 16.14 shows galvanic corrosion. Again, the galvanic series (Table 16.2) indicates the relative reactivities, in seawater, of a number of metals and alloys. When two alloys are coupled in seawater, the one lower in the series will experience corrosion. Some of the alloys in the FIGURE 16.14 Galvanic corrosion of a magnesium shell that was cast around a steel core. (Photograph courtesy of LaQue Center for Corrosion Technology, Inc.) 16.7 Forms of Corrosion S-225 table are grouped in brackets. Generally the base metal is the same for these bracketed alloys, and there is little danger of corrosion if alloys within a single bracket are coupled. It is also worth noting from this series that some alloys are listed twice (e.g., nickel and the stainless steels), in both active and passive states. The rate of galvanic attack depends on the relative anode-to-cathode surface areas that are exposed to the electrolyte, and the rate is related directly to the cathodeanode area ratio; that is, for a given cathode area, a smaller anode will corrode more rapidly than a larger one. The reason for this is that corrosion rate depends on current density (Equation 16.24), the current per unit area of corroding surface, and not simply the current. Thus, a high current density results for the anode when its area is small relative to that of the cathode. A number of measures may be taken to signicantly reduce the effects of galvanic corrosion. These include the following: 1. If coupling of dissimilar metals is necessary, choose two that are close together in the galvanic series. 2. Avoid an unfavorable anode-to-cathode surface area ratio; use an anode area as large as possible. 3. Electrically insulate dissimilar metals from each other. 4. Electrically connect a third, anodic metal to the other two; this is a form of cathodic protection, discussed presently. CREVICE CORROSION Electrochemical corrosion may also occur as a consequence of concentration differences of ions or dissolved gases in the electrolyte solution, and between two regions of the same metal piece. For such a concentration cell, corrosion occurs in the locale that has the lower concentration. A good example of this type of corrosion occurs in crevices and recesses or under deposits of dirt or corrosion products where the solution becomes stagnant and there is localized depletion of dissolved oxygen. Corrosion preferentially occurring at these positions is called crevice corrosion (Figure 16.15). The crevice must be wide enough for the solution to penetrate, yet narrow enough for stagnancy; usually the width is several thousandths of an inch. The proposed mechanism for crevice corrosion is illustrated in Figure 16.16. After oxygen has been depleted within the crevice, oxidation of the metal occurs at this position according to Equation 16.1. Electrons from this electrochemical reaction are conducted through the metal to adjacent external regions, where they FIGURE 16.15 On this plate, which was immersed in seawater, crevice corrosion has occurred at the regions that were covered by washers. (Photograph courtesy of LaQue Center for Corrosion Technology, Inc.) S-226 Chapter 16 / Corrosion and Degradation of Materials O2 O2 Cl OH e O2 + Na OH e + Na + M O2 Cl Cl Cl + M Cl O2 O2 OH OH OH Cl Cl + M + H Cl + M + H Cl + H + M + M Cl + M + H O2 + M Cl + M + M + M Cl + M + H Cl + M e FIGURE 16.16 Schematic illustration of the mechanism of crevice corrosion between two riveted sheets. (From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) are consumed by reductionmost probably reaction 16.5. In many aqueous environments, the solution within the crevice has been found to develop high concentrations of H and Cl ions, which are especially corrosive. Many alloys that passivate are susceptible to crevice corrosion because protective lms are often destroyed by the H and Cl ions. Crevice corrosion may be prevented by using welded instead of riveted or bolted joints, using nonabsorbing gaskets when possible, removing accumulated deposits frequently, and designing containment vessels to avoid stagnant areas and ensure complete drainage. PITTING Pitting is another form of very localized corrosion attack in which small pits or holes form. They ordinarily penetrate from the top of a horizontal surface downward in a nearly vertical direction. It is an extremely insidious type of corrosion, often going undetected and with very little material loss until failure occurs. An example of pitting corrosion is shown in Figure 16.17. The mechanism for pitting is probably the same as for crevice corrosion in that oxidation occurs within the pit itself, with complementary reduction at the surface. It is supposed that gravity causes the pits to grow downward, the solution at the pit tip becoming more concentrated and dense as pit growth progresses. A pit may be initiated by a localized surface defect such as a scratch or a slight variation in composition. In fact, it has been observed that specimens having polished surfaces display a greater resistance to pitting corrosion. Stainless steels are somewhat susceptible to this form of corrosion; however, alloying with about 2% molybdenum enhances their resistance signicantly. 16.7 Forms of Corrosion S-227 FIGURE 16.17 The pitting of a 304 stainless steel plate by an acid-chloride solution. (Photograph courtesy of Mars G. Fontana. From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) INTERGRANULAR CORROSION As the name suggests, intergranular corrosion occurs preferentially along grain boundaries for some alloys and in specic environments. The net result is that a macroscopic specimen disintegrates along its grain boundaries. This type of corrosion is especially prevalent in some stainless steels. When heated to temperatures between 500 and 800 C (950 and 1450 F) for sufciently long time periods, these alloys become sensitized to intergranular attack. It is believed that this heat treatment permits the formation of small precipitate particles of chromium carbide (Cr23C6) by reaction between the chromium and carbon in the stainless steel. These particles form along the grain boundaries, as illustrated in Figure 16.18. Both the chromium and the carbon must diffuse to the grain boundaries to form the precipitates, which leaves a chromium-depleted zone adjacent to the grain boundary. Consequently, this grain boundary region is now highly susceptible to corrosion. Intergranular corrosion is an especially severe problem in the welding of stainless steels, when it is often termed weld decay. Figure 16.19 shows this type of intergranular corrosion. FIGURE 16.18 Schematic illustration of chromium carbide particles that have precipitated along grain boundaries in stainless steel, and the attendant zones of chromium depletion. Cr23C6 precipitate particle Grain boundary Zone depleted of chromium S-228 Chapter 16 / Corrosion and Degradation of Materials FIGURE 16.19 Weld decay in a stainless steel. The regions along which the grooves have formed were sensitized as the weld cooled. (From H. H. Uhlig and R. W. Revie, Corrosion and Corrosion Control, 3rd edition, Fig. 2, p. 307. Copyright 1985 by John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.) Stainless steels may be protected from intergranular corrosion by the following measures: (1) subjecting the sensitized material to a high-temperature heat treatment in which all the chromium carbide particles are redissolved, (2) lowering the carbon content below 0.03 wt% C so that carbide formation is minimal, and (3) alloying the stainless steel with another metal such as niobium or titanium, which has a greater tendency to form carbides than does chromium so that the Cr remains in solid solution. SELECTIVE LEACHING Selective leaching is found in solid solution alloys and occurs when one element or constituent is preferentially removed as a consequence of corrosion processes. The most common example is the dezincication of brass, in which zinc is selectively leached from a copperzinc brass alloy. The mechanical properties of alloy the are signicantly impaired, since only a porous mass of copper remains in the region that has been dezincied. In addition, the material changes from yellow to a red or copper color. Selective leaching may also occur with other alloy systems in which aluminum, iron, cobalt, chromium, and other elements are vulnerable to preferential removal. EROSIONCORROSION Erosioncorrosion arises from the combined action of chemical attack and mechanical abrasion or wear as a consequence of uid motion. Virtually all metal alloys, to one degree or another, are susceptible to erosioncorrosion. It is especially harmful to alloys that passivate by forming a protective surface lm; the abrasive action may erode away the lm, leaving exposed a bare metal surface. If the coating is not capable of continuously and rapidly reforming as a protective barrier, corrosion may be severe. Relatively soft metals such as copper and lead are also sensitive to this form of attack. Usually it can be identied by surface grooves and waves having contours that are characteristic of the ow of the uid. 16.7 Forms of Corrosion S-229 FIGURE 16.20 Impingement failure of an elbow that was part of a steam condensate line. (Photograph courtesy of Mars G. Fontana. From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) The nature of the uid can have a dramatic inuence on the corrosion behavior. Increasing uid velocity normally enhances the rate of corrosion. Also, a solution is more erosive when bubbles and suspended particulate solids are present. Erosioncorrosion is commonly found in piping, especially at bends, elbows, and abrupt changes in pipe diameterpositions where the uid changes direction or ow suddenly becomes turbulent. Propellers, turbine blades, valves, and pumps are also susceptible to this form of corrosion. Figure 16.20 illustrates the impingement failure of an elbow tting. One of the best ways to reduce erosioncorrosion is to change the design to eliminate uid turbulence and impingement effects. Other materials may also be utilized that inherently resist erosion. Furthermore, removal of particulates and bubbles from the solution will lessen its ability to erode. STRESS CORROSION Stress corrosion, sometimes termed stress corrosion cracking, results from the combined action of an applied tensile stress and a corrosive environment; both inuences are necessary. In fact, some materials that are virtually inert in a particular corrosive medium become susceptible to this form of corrosion when a stress is applied. Small cracks form and then propagate in a direction perpendicular to the stress (see the chapter-opening photograph for this chapter), with the result that failure may eventually occur. Failure behavior is characteristic of that for a brittle material, even though the metal alloy is intrinsically ductile. Furthermore, cracks may form at relatively low stress levels, signicantly below the tensile strength. Most alloys are susceptible to stress corrosion in specic environments, especially at moderate stress levels. For example, most stainless steels stress corrode in solutions containing chloride ions, whereas brasses are especially vulnerable when exposed to ammonia. Figure 16.21 is a photomicrograph in which an example of intergranular stress corrosion cracking in brass is shown. The stress that produces stress corrosion cracking need not be externally applied; it may be a residual one that results from rapid temperature changes and uneven contraction, or for two-phase alloys in which each phase has a different coefcient of expansion. Also, gaseous and solid corrosion products that are entrapped internally can give rise to internal stresses. S-230 Chapter 16 / Corrosion and Degradation of Materials FIGURE 16.21 Photomicrograph showing intergranular stress corrosion cracking in brass. (From H. H. Uhlig and R. W. Revie, Corrosion and Corrosion Control, 3rd edition, Fig. 5, p. 335. Copyright 1985 by John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.) Probably the best measure to take in reducing or totally eliminating stress corrosion is to lower the magnitude of the stress. This may be accomplished by reducing the external load or increasing the cross-sectional area perpendicular to the applied stress. Furthermore, an appropriate heat treatment may be used to anneal out any residual thermal stresses. HYDROGEN EMBRITTLEMENT Various metal alloys, specically some steels, experience a signicant reduction in ductility and tensile strength when atomic hydrogen (H) penetrates into the material. This phenomenon is aptly referred to as hydrogen embrittlement; the terms hydrogen induced cracking and hydrogen stress cracking are sometimes also used. Strictly speaking, hydrogen embrittlement is a type of failure; in response to applied or residual tensile stresses, brittle fracture occurs catastrophically as cracks grow and rapidly propagate. Hydrogen in its atomic form (H as opposed to the molecular form, H2) diffuses interstitially through the crystal lattice, and concentrations as low as several parts per million can lead to cracking. Furthermore, hydrogeninduced cracks are most often transgranular, although intergranular fracture is observed for some alloy systems. A number of mechanisms have been proposed to explain hydrogen embrittlement; most of them are based on the interference of dislocation motion by the dissolved hydrogen. Hydrogen embrittlement is similar to stress corrosion (as discussed in the preceding section) in that a normally ductile metal experiences brittle fracture when exposed to both a tensile stress and a corrosive atmosphere. However, these two phenomena may be distinguished on the basis of their interactions with applied electric currents. Whereas cathodic protection (Section 16.9) reduces or causes a 16.8 Corrosion Environments S-231 cessation of stress corrosion, it may, on the other hand, lead to the initiation or enhancement of hydrogen embrittlement. In order for hydrogen embrittlement to occur, some source of hydrogen must be present, and, in addition, the possibility for the formation of its atomic species. Situations wherein these conditions are met include the following: pickling3 of steels in sulfuric acid; electroplating; and the presence of hydrogen-bearing atmospheres (including water vapor) at elevated temperatures such as during welding and heat treatments. Also, the presence of what are termed poisons such as sulfur (i.e., H2S) and arsenic compounds accelerates hydrogen embrittlement; these substances retard the formation of molecular hydrogen and thereby increase the residence time of atomic hydrogen on the metal surface. Hydrogen sulde, probably the most aggressive poison, is found in petroleum uids, natural gas, oil-well brines, and geothermal uids. High-strength steels are susceptible to hydrogen embrittlement, and increasing strength tends to enhance the materials susceptibility. Martensitic steels are especially vulnerable to this type of failure; bainitic, ferritic, and spheroiditic steels are more resilient. Furthermore, FCC alloys (austenitic stainless steels, and alloys of copper, aluminum, and nickel) are relatively resistant to hydrogen embrittlement, mainly because of their inherently high ductilities. However, strain hardening these alloys will enhance their susceptibility to embrittlement. Some of the techniques commonly used to reduce the likelihood of hydrogen embrittlement include: reducing the tensile strength of the alloy via a heat treatment; removal of the source of hydrogen; baking the alloy at an elevated temperature to drive out any dissolved hydrogen; and substitution of a more embrittlementresistant alloy. 16.8 CORROSION ENVIRONMENTS Corrosive environments include the atmosphere, aqueous solutions, soils, acids, bases, inorganic solvents, molten salts, liquid metals, and, last but not least, the human body. On a tonnage basis, atmospheric corrosion accounts for the greatest losses. Moisture containing dissolved oxygen is the primary corrosive agent, but other substances, including sulfur compounds and sodium chloride, may also contribute. This is especially true of marine atmospheres, which are highly corrosive because of the presence of sodium chloride. Dilute sulfuric acid solutions (acid rain) in industrial environments can also cause corrosion problems. Metals commonly used for atmospheric applications include alloys of aluminum and copper, and galvanized steel. Water environments can also have a variety of compositions and corrosion characteristics. Fresh water normally contains dissolved oxygen, as well as other minerals several of which account for hardness. Seawater contains approximately 3.5% salt (predominantly sodium chloride), as well as some minerals and organic matter. Seawater is generally more corrosive than fresh water, frequently producing pitting and crevice corrosion. Cast iron, steel, aluminum, copper, brass, and some stainless steels are generally suitable for freshwater use, whereas titanium, brass, some bronzes, coppernickel alloys, and nickelchromiummolybdenum alloys are highly corrosion resistant in seawater. Soils have a wide range of compositions and susceptibilities to corrosion. Com3 Pickling is a procedure used to remove surface oxide scale from steel pieces by dipping them in a vat of hot, dilute sulfuric or hydrochloric acid. S-232 Chapter 16 / Corrosion and Degradation of Materials positional variables include moisture, oxygen, salt content, alkalinity, and acidity, as well as the presence of various forms of bacteria. Cast iron and plain carbon steels, both with and without protective surface coatings, are found most economical for underground structures. Because there are so many acids, bases, and organic solvents, no attempt is made to discuss these solutions. Good references are available that treat these topics in detail. 16.9 CORROSION PREVENTION Some corrosion prevention methods were treated relative to the eight forms of corrosion; however, only the measures specic to each of the various corrosion types were discussed. Now, some more general techniques are presented; these include material selection, environmental alteration, design, coatings, and cathodic protection. Perhaps the most common and easiest way of preventing corrosion is through the judicious selection of materials once the corrosion environment has been characterized. Standard corrosion references are helpful in this respect. Here, cost may be a signicant factor. It is not always economically feasible to employ the material that provides the optimum corrosion resistance; sometimes, either another alloy and/or some other measure must be used. Changing the character of the environment, if possible, may also signicantly inuence corrosion. Lowering the uid temperature and/or velocity usually produces a reduction in the rate at which corrosion occurs. Many times increasing or decreasing the concentration of some species in the solution will have a positive effect; for example, the metal may experience passivation. Inhibitors are substances that, when added in relatively low concentrations to the environment, decrease its corrosiveness. Of course, the specic inhibitor depends both on the alloy and on the corrosive environment. There are several mechanisms that may account for the effectiveness of inhibitors. Some react with and virtually eliminate a chemically active species in the solution (such as dissolved oxygen). Other inhibitor molecules attach themselves to the corroding surface and interfere with either the oxidation or the reduction reaction, or form a very thin protective coating. Inhibitors are normally used in closed systems such as automobile radiators and steam boilers. Several aspects of design consideration have already been discussed, especially with regard to galvanic and crevice corrosion, and erosioncorrosion. In addition, the design should allow for complete drainage in the case of a shutdown, and easy washing. Since dissolved oxygen may enhance the corrosivity of many solutions, the design should, if possible, include provision for the exclusion of air. Physical barriers to corrosion are applied on surfaces in the form of lms and coatings. A large diversity of metallic and nonmetallic coating materials are available. It is essential that the coating maintain a high degree of surface adhesion, which undoubtedly requires some preapplication surface treatment. In most cases, the coating must be virtually nonreactive in the corrosive environment and resistant to mechanical damage that exposes the bare metal to the corrosive environment. All three material typesmetals, ceramics, and polymersare used as coatings for metals. CATHODIC PROTECTION One of the most effective means of corrosion prevention is cathodic protection; it can be used for all eight different forms of corrosion as discussed above, and may, 16.9 Corrosion Prevention _ + S-233 Current Rectifier Ground level Coated copper wire Gravel Current Steel pipe Mg anode Current Tank Backfill (a) Anode Earth environment Backfill ( b) FIGURE 16.22 Cathodic protection of (a) an underground pipeline using a magnesium sacricial anode, and (b) an underground tank using an impressed current. (From M. G. Fontana, Corrosion Engineering, 3rd edition. Copyright 1986 by McGraw-Hill Book Company. Reproduced with permission.) in some situations, completely stop corrosion. Again, oxidation or corrosion of a metal M occurs by the generalized reaction M Mn ne (16.1) Cathodic protection simply involves supplying, from an external source, electrons to the metal to be protected, making it a cathode; the reaction above is thus forced in the reverse (or reduction) direction. One cathodic protection technique employs a galvanic couple: the metal to be protected is electrically connected to another metal that is more reactive in the particular environment. The latter experiences oxidation, and, upon giving up electrons, protects the rst metal from corrosion. The oxidized metal is often called a sacricial anode, and magnesium and zinc are commonly used as such because they lie at the anodic end of the galvanic series. This form of galvanic protection, for structures buried in the ground, is illustrated in Figure 16.22a. The process of galvanizing is simply one in which a layer of zinc is applied to the surface of steel by hot dipping. In the atmosphere and most aqueous environments, zinc is anodic to and will thus cathodically protect the steel if there is any surface damage (Figure 16.23). Any corrosion of the zinc coating will proceed at an extremely slow rate because the ratio of the anode-to-cathode surface area is quite large. Corrosive environment Zinc coating (anode) Cathode region Zn2+ Zn2+ Zn2+ Zn2+ e e e e Steel FIGURE 16.23 Galvanic protection of steel as provided by a coating of zinc. S-234 Chapter 16 / Corrosion and Degradation of Materials For another method of cathodic protection, the source of electrons is an impressed current from an external dc power source, as represented in Figure 16.22b for an underground tank. The negative terminal of the power source is connected to the structure to be protected. The other terminal is joined to an inert anode (often graphite), which is, in this case, buried in the soil; high-conductivity backll material provides good electrical contact between the anode and surrounding soil. A current path exists between the cathode and anode through the intervening soil, completing the electrical circuit. Cathodic protection is especially useful in preventing corrosion of water heaters, underground tanks and pipes, and marine equipment. 16.10 OXIDATION The discussion of Section 16.2 treated the corrosion of metallic materials in terms of electrochemical reactions that take place in aqueous solutions. In addition, oxidation of metal alloys is also possible in gaseous atmospheres, normally air, wherein an oxide layer or scale forms on the surface of the metal. This phenomenon is frequently termed scaling, tarnishing, or dry corrosion. In this section possible mechanisms for this type of corrosion, the types of oxide layers that can form, and the kinetics of oxide formation will be discussed. MECHANISMS As with aqueous corrosion, the process of oxide layer formation is an electrochemical one, which may be expressed, for divalent metal M, by the following reaction4 : M O2 MO (16.28) Furthermore, the above reaction consists of oxidation and reduction half-reactions. The former, with the formation of metal ions, M M2 2e (16.29) occurs at the metalscale interface. The reduction half-reaction produces oxygen ions as follows: O2 2e O2 (16.30) and takes place at the scalegas interface. A schematic representation of this metal scalegas system is shown in Figure 16.24. For the oxide layer to increase in thickness via Equation 16.28, it is necessary that electrons be conducted to the scalegas interface, at which point the reduction reaction occurs; in addition, M2 ions must diffuse away from the metalscale interface, and/or O2 ions must diffuse toward this same interface (Figure 16.24).5 Thus, the oxide scale serves both as an electrolyte through which ions diffuse and as an electrical circuit for the passage of electrons. Furthermore, the scale may 4 For other than divalent metals, this reaction may be expressed as aM b O2 2 MaOb (16.31) 5 Alternatively, electron holes (Section 12.10) and vacancies may diffuse instead of electrons and ions. 16.10 Oxidation Metal (M) Oxide scale (MO) Gas (O2) S-235 FIGURE 16.24 Schematic representation of processes that are involved in the gaseous oxidation at a metal surface. M2+ O2 e M M2+ + 2e 1 O 22 O2 + 2e protect the metal from rapid oxidation when it acts as a barrier to ionic diffusion and/or electrical conduction; most metal oxides are highly electrically insulative. SCALE TYPES Rate of oxidation (i.e., the rate of lm thickness increase) and the tendency of the lm to protect the metal from further oxidation are related to the relative volumes of the oxide and metal. The ratio of these volumes, termed the PillingBedworth ratio, may be determined from the following expression6 : PB ratio AO AM M (16.32) O where AO is the molecular (or formula) weight of the oxide, AM is the atomic weight of the metal, and O and M are the oxide and metal densities, respectively. For metals having PB ratios less than unity, the oxide lm tends to be porous and unprotective because it is insufcient to fully cover the metal surface. If the ratio is greater than unity, compressive stresses result in the lm as it forms. For a ratio greater than 23, the oxide coating may crack and ake off, continually exposing a fresh and unprotected metal surface. The ideal PB ratio for the formation of a protective oxide lm is unity. Table 16.3 presents PB ratios for metals that form protective coatings and for those that do not. It may be noted from these data that protective coatings normally form for metals having PB ratios between 1 and 2, whereas nonprotective ones usually result when this ratio is less than 1 or greater than about 2. In addition to the PB ratio, other factors also inuence the oxidation resistance imparted by the lm; these include a high degree of adherence between lm and metal, comparable coefcients of thermal expansion for metal 6 For other than divalent metals, Equation 16.32 becomes PB ratio AO M aAM O (16.33) where a is the coefcient of the metal species for the overall oxidation reaction described by Equation 16.31. S-236 Chapter 16 / Corrosion and Degradation of Materials Table 16.3 PillingBedworth Ratios for a Number of Metals Protective Ce 1.16 Al 1.28 Pb 1.40 Ni 1.52 Be 1.59 Pd 1.60 Cu 1.68 Fe 1.77 Mn 1.79 Co 1.99 Cr 1.99 Si 2.27 Nonprotective K Li Na Cd Ag Ti Ta Sb Nb U Mo W 0.45 0.57 0.57 1.21 1.59 1.95 2.33 2.35 2.61 3.05 3.40 3.40 Source: B. Chalmers, Physical Metallurgy. Copyright 1959 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc. and oxide, and, for the oxide, a relatively high melting point and good high-temperature plasticity. Several techniques are available for improving the oxidation resistance of a metal. One involves application of a protective surface coating of another material that adheres well to the metal and also is itself resistant to oxidation. In some instances, the addition of alloying elements will form a more adherent and protective oxide scale by virtue of producing a more favorable PillingBedworth ratio and/ or improving other scale characteristics. KINETICS One of the primary concerns relative to metal oxidation is the rate at which the reaction progresses. Inasmuch as the oxide scale reaction product normally remains on the surface, the rate of reaction may be determined by measuring the weight gain per unit area as a function of time. When the oxide that forms is nonporous and adheres to the metal surface, the rate of layer growth is controlled by ionic diffusion. A parabolic relationship exists between the weight gain per unit area W and the time t as follows: W2 K1 t K2 (16.34) where K1 and K2 are time-independent constants at a given temperature. This weight gaintime behavior is plotted schematically in Figure 16.25. The oxidation of iron, copper, and cobalt follows this rate expression. In the oxidation of metals for which the scale is porous or akes off (i.e., for PB ratios less than about 1 or greater than about 2), the oxidation rate expression is linear; that is, W K3 t (16.35) where K3 is a constant. Under these circumstances oxygen is always available for reaction with an unprotected metal surface because the oxide does not act as a 16.10 Oxidation S-237 FIGURE 16.25 Oxidation lm growth curves for linear, parabolic, and logarithmic rate laws. Linear Weight gain per unit area, W Parabolic Logarithmic Time, t reaction barrier. Sodium, potassium, and tantalum oxidize according to this rate expression and, incidentally, have PB ratios signicantly different from unity (Table 16.3). Linear growth rate kinetics is also represented in Figure 16.25. Still a third reaction rate law has been observed for very thin oxide layers [generally less than 100 nm (1000 A)] that form at relatively low temperatures. The dependence of weight gain on time is logarithmic and takes the form W K4 log(K5 t K6) (16.36) Again, the K s are constants. This oxidation behavior, also shown in Figure 16.25, has been observed for aluminum, iron, and copper at near-ambient temperatures. CORROSION OF CERAMIC MATERIALS Ceramic materials, being compounds between metallic and nonmetallic elements, may be thought of as having already been corroded. Thus, they are exceedingly immune to corrosion by almost all environments, especially at room temperature. Corrosion of ceramic materials generally involves simple chemical dissolution, in contrast to the electrochemical processes found in metals, as described above. Ceramic materials are frequently utilized because of their resistance to corrosion. Glass is often used to contain liquids for this reason. Refractory ceramics must not only withstand high temperatures and provide thermal insulation but, in many instances, must resist high-temperature attack by molten metals, salts, slags, and glasses. Some of the new technology schemes for convering energy from one form to another that is more useful require relatively high temperatures, corrosive atmospheres, and pressures above the ambient. Ceramic materials are much better suited to withstand most of these environments for reasonable time periods than are metals. DEGRADATION OF POLYMERS Polymeric materials also experience deterioration by means of environmental interactions. However, an undesirable interaction is specied as degradation rather than corrosion because the processes are basically dissimilar. Whereas most metallic S-238 Chapter 16 / Corrosion and Degradation of Materials corrosion reactions are electrochemical, by contrast, polymeric degradation is physiochemical; that is, it involves physical as well as chemical phenomena. Furthermore, a wide variety of reactions and adverse consequences are possible for polymer degradation. Polymers may deteriorate by swelling and dissolution. Covalent bond rupture, as a result of heat energy, chemical reactions, and radiation is also possible, ordinarily with an attendant reduction in mechanical integrity. It should also be mentioned that because of the chemical complexity of polymers, their degradation mechanisms are not well understood. To briey cite a couple of examples of polymer degradation, polyethylene, if exposed to high temperatures in an oxygen atmosphere, suffers an impairment of its mechanical properties by becoming brittle. Or, the utility of polyvinyl chloride may be limited because this material may become colored when exposed to high temperatures, although such environments do not affect its mechanical characteristics. 16.11 SWELLING AND DISSOLUTION When polymers are exposed to liquids, the main forms of degradation are swelling and dissolution. With swelling, the liquid or solute diffuses into and is absorbed within the polymer; the small solute molecules t into and occupy positions among the polymer molecules. This forces the macromolecules apart such that the specimen expands or swells. Furthermore, this increase in chain separation results in a reduction of the secondary intermolecular bonding forces; as a consequence, the material becomes softer and more ductile. The liquid solute also lowers the glass transition temperature and, if depressed below the ambient temperature, will cause a once strong material to become rubbery and weak. Swelling may be considered to be a partial dissolution process in which there is only limited solubility of the polymer in the solvent. Dissolution, which occurs when the polymer is completely soluble, may be thought of as just a continuation of swelling. As a rule of thumb, the greater the similarity of chemical structure between the solvent and polymer, the greater the likelihood of swelling and/or dissolution. For example, many hydrocarbon rubbers readily absorb hydrocarbon liquids such as gasoline. The responses of selected polymeric materials to organic solvents are contained in Tables 16.4 and 16.5. Swelling and dissolution traits also are affected by temperature as well as characteristics of the molecular structure. In general, increasing molecular weight, increasing degree of crosslinking and crystallinity, and decreasing temperature result in a reduction of these deteriorative processes. Resistance to attack by acidic and alkaline solutions is, in general, much better for polymers than for metals. A qualitative comparison of the behavior of various polymers in these solutions is also presented in Tables 16.4 and 16.5. Materials that exhibit outstanding resistance to attack by both solution types include polytetrauoroethylene (and other uorocarbons) and polyetheretherketone. 16.12 BOND RUPTURE Polymers may also experience degradation by a process termed scission the severence or rupture of molecular chain bonds. This causes a separation of chain segments at the point of scission and a reduction in the molecular weight. As previously discussed (Chapter 8), several properties of polymeric materials, including mechanical strength, depend on molecular weight. Consequently, some of the 16.12 Bond Rupture S-239 Table 16.4 Resistance to Degradation by Various Environments for Selected Plastic Materials a Material Polytetrauoroethylene Nylon 6,6 Polycarbonate Polyester Polyetheretherketone Low-density polyethylene High-density polyethylene Polyethylene terephthalate Polyphenylene oxide Polypropylene Polystyrene Polyurethane Epoxy Silicone Nonoxidizing Acids (20% H2 SO4) Oxidizing Acids (10% HNO3) Aqueous Salt Solutions (NaCl ) Aqueous Alkalis (NaOH ) Polar Solvents (C2 H5OH ) Nonpolar Solvents (C6 H6) Water S U Q Q S U U Q S S S S S S U Q S Q S Q S S U U S S S S S S S S S S S S Q S S Q S S Q S S Q S S Q S S S S S S S S Q S Q Q Q Q U U U S S S S S S S S S Q S S S S S U S S U Q U Q S Q S S S S S S a S satisfactory; Q questionable; U unsatisfactory. Source: Adapted from R. B. Seymour, Polymers for Engineering Applications, ASM International, Materials Park, OH, 1987. Table 16.5 Resistance to Degradation by Various Environments for Selected Elastomeric Materials a Material Polyisoprene (natural) Polyisoprene (synthetic) Butadiene Styrenebutadiene Neoprene Nitrile (high) Silicone (polysiloxane) a WeatherSunlight Aging Alkali Dilute/ Concentrated Acid Dilute/ Concentrated Chlorinated Hydrocarbons, Degreasers Aliphatic Hydrocarbons, Kerosene, Etc. Animal, Vegetable Oils Oxidation Ozone Cracking D B NR A/C-B A/C-B NR NR D-B NR D B B NR NR C-B/C-B C-B/C-B C-B/C-B C-B/C-B NR NR NR NR D-B D-B D B D C A B NR A C C-B/C-B A/A B/B C-B/C-B A/A B/B NR D C-B NR C A D-B B B A A A A/A B/C NR D-C A A excellent, B good, C fair, D use with caution, NR not recommended. Source: Compound Selection and Service Guide, Seals Eastern, Inc., Red Bank, NJ, 1977. S-240 Chapter 16 / Corrosion and Degradation of Materials physical and chemical properties of polymers may be adversely affected by this form of degradation. Bond rupture may result from exposure to radiation or to heat, and from chemical reaction. RADIATION EFFECTS Certain types of radiation (electron beams, x-rays, - and -rays, and ultraviolet radiation) possess sufcient energy to penetrate a polymer specimen and interact with the constituent atoms or their electrons. One such reaction is ionization, in which the radiation removes an orbital electron from a specic atom, converting that atom into a positively charged ion. As a consequence, one of the covalent bonds associated with the specic atom is broken, and there is a rearrangement of atoms or groups of atoms at that point. This bond breaking leads to either scission or crosslinking at the ionization site, depending on the chemical structure of the polymer and also on the dose of radiation. Stabilizers (Section 14.12) may be added to protect polymers from ultraviolet damage. Not all consequences of radiation exposure are deleterious. Crosslinking may be induced by irradiation to improve the mechanical behavior and degradation characteristics. For example, -radiation is used commercially to crosslink polyethylene to enhance its resistance to softening and ow at elevated temperatures; indeed, this process may be carried out on products that have already been fabricated. CHEMICAL REACTION EFFECTS Oxygen, ozone, and other substances can cause or accelerate chain scission as a result of chemical reaction. This effect is especially prevalent in vulcanized rubbers that have doubly bonded carbon atoms along the backbone molecular chains, and which are exposed to ozone (O3), an atmospheric pollutant. One such scission reaction may be represented by URUCuCUR U FF HH O3 URUCuO F H OuCUR U F H O (16.37) where the chain is severed at the point of the double bond; R and R represent groups of atoms bonded to the chain that are unaffected during the reaction. Ordinarily, if the rubber is in an unstressed state, a lm will form on the surface, protecting the bulk material from any further reaction. However, when these materials are subjected to tensile stresses, cracks and crevices form and grow in a direction perpendicular to the stress; eventually, rupture of the material may occur. Apparently these cracks result from large numbers of ozone-induced scissions. The elastomers in Table 16.5 are rated as to their resistance to degradation by exposure to ozone. THERMAL EFFECTS Thermal degradation corresponds to the scission of molecular chains at elevated temperatures; as a consequence, some polymers undergo chemical reactions in which gaseous species are produced. These reactions are evidenced by a weight loss of material; a polymers thermal stability is a measure of its resilience to this decomposition. Thermal stability is related primarily to the magnitude of the bonding energies between the various atomic constituents of the polymer: higher bonding energies result in more thermally stable materials. For example, the magnitude of the CUF bond is greater than that of the CUH bond, which in turn is greater than Summary S-241 that of the CUCl bond. The uorocarbons, having CUF bonds, are among the most thermally resistant polymeric materials and may be utilized at relatively high temperatures. 16.13 WEATHERING Many polymeric materials serve in applications that require exposure to outdoor conditions. Any resultant degradation is termed weathering, which may, in fact, be a combination of several different processes. Under these conditions deterioration is primarily a result of oxidation, which is initiated by ultraviolet radiation from the sun. Some polymers such as nylon and cellulose are also susceptible to water absorption, which produces a reduction in their hardness and stiffness. Resistance to weathering among the various polymers is quite diverse. The uorocarbons are virtually inert under these conditions; but some materials, including polyvinyl chloride and polystyrene, are susceptible to weathering. SUMMARY Metallic corrosion is ordinarily electrochemical, involving both oxidation and reduction reactions. Oxidation is the loss of the metal atoms valence electrons; the resulting metal ions may either go into the corroding solution or form an insoluble compound. During reduction, these electrons are transferred to at least one other chemical species. The character of the corrosion environment dictates which of several possible reduction reactions will occur. Not all metals oxidize with the same degree of ease, which is demonstrated with a galvanic couple; when in an electrolyte, one metal (the anode) will corrode, whereas a reduction reaction will occur at the other metal (the cathode). The magnitude of the electric potential that is established between anode and cathode is indicative of the driving force for the corrosion reaction. The standard emf and galvanic series are simply rankings of metallic materials on the basis of their tendency to corrode when coupled to other metals. For the standard emf series, ranking is based on the magnitude of the voltage generated when the standard cell of a metal is coupled to the standard hydrogen electrode at 25 C (77 F). The galvanic series consists of the relative reactivities of metals and alloys in seawater. The half-cell potentials in the standard emf series are thermodynamic parameters that are valid only at equilibrium; corroding systems are not in equilibrium. Furthermore, the magnitudes of these potentials provide no indication as to the rates at which corrosion reactions occur. The rate of corrosion may be expressed as corrosion penetration rate, that is, the thickness loss of material per unit of time. Mils per year and millimeters per year are the common units for this parameter. Alternatively, rate is proportional to the current density associated with the electrochemical reaction. Corroding systems will experience polarization, which is the displacement of each electrode potential from its equilibrium value; the magnitude of the displacement is termed the overvoltage. The corrosion rate of a reaction is limited by polarization, of which there are two typesactivation and concentration. Polarization data are plotted as potential versus the logarithm of current density. The corrosion rate for a particular reaction may be computed using the current density associated with the intersection point of oxidation and reduction polarization curves. A number of metals and alloys passivate, or lose their chemical reactivity, under S-242 Chapter 16 / Corrosion and Degradation of Materials some environmental circumstances. This phenomenon is thought to involve the formation of a thin protective oxide lm. Stainless steels and aluminum alloys exhibit this type of behavior. The active-to-passive behavior may be explained by the alloys S-shaped electrochemical potential-versus-log current density curve. Intersections with reduction polarization curves in active and passive regions correspond, respectively, to high and low corrosion rates. Metallic corrosion is sometimes classied into eight different forms: uniform attack, galvanic corrosion, crevice corrosion, pitting, intergranular corrosion, selective leaching, erosioncorrosion, and stress corrosion. Hydrogen embrittlement, a type of failure sometimes observed in corrosion environments, was also discussed. The measures that may be taken to prevent, or at least reduce, corrosion include material selection, environmental alteration, the use of inhibitors, design changes, application of coatings, and cathodic protection. Oxidation of metallic materials by electrochemical action is also possible in dry, gaseous atmospheres. An oxide lm forms on the surface which may act as a barrier to further oxidation if the volumes of metal and oxide lm are similar, that is, if the PillingBedworth ratio is near unity. The kinetics of lm formation may follow parabolic, linear, or logarithmic rate laws. Ceramic materials, being inherently corrosion resistant, are frequently utilized at elevated temperatures and/or in extremely corrosive environments. Polymeric materials deteriorate by noncorrosive processes. Upon exposure to liquids, they may experience degradation by swelling or dissolution. With swelling, solute molecules actually t into the molecular structure. Scission, or the severance of molecular chain bonds, may be induced by radiation, chemical reactions, or heat. This results in a reduction of molecular weight and a deterioration of the physical and chemical properties of the polymer. IMPORTANT TERMS AND CONCEPTS Activation polarization Anode Cathode Cathodic protection Concentration polarization Corrosion Corrosion penetration rate Crevice corrosion Degradation Electrolyte Electromotive force (emf ) series Erosioncorrosion Galvanic corrosion Galvanic series Hydrogen embrittlement Inhibitor Intergranular corrosion Molarity Oxidation Passivity PillingBedworth ratio Pitting Polarization Reduction Sacricial anode Scission Selective leaching Standard half-cell Stress corrosion Weld decay REFERENCES ASM Handbook, Vol. 13, Corrosion, ASM International, Materials Park, OH, 1987. Craig, B. D. (Editor), Handbook of Corrosion Data, 2nd edition, ASM International, Materials Park, OH, 1995. Fontana, M. G., Corrosion Engineering, 3rd edi- tion, McGraw-Hill Book Company, New York, 1986. Fontana, M. G. and R. W. Staehle (Editors), Advances in Corrosion Science and Technology, Plenum Publishing Corp., New York. In seven volumes, 19701980. Questions and Problems Gibala, R. and R. F. Hehemann, Hydrogen Embrittlement and Stress Corrosion Cracking, ASM International, Materials Park, OH, 1984. Jones, D. A., Principles and Prevention of Corrosion, 2nd edition, Prentice Hall, Upper Saddle, NJ, 1996. Marcus, P. and J. Oudar (Editors), Corrosion Mechanisms in Theory and Practice, Marcel Dekker, Inc., New York, 1995. McEvily, A. J., Jr. (Editor), Atlas of Stress-Corrosion and Corrosion Fatigue Curves, ASM International, Materials Park, OH, 1990. Schreir, L. L. (Editor), Corrosion, Vol. 1, Metal/ S-243 Environment Reactions; Vol. 2, Corrosion Control, 3rd edition, Butterworth-Heinemann Ltd., Oxford, 1994. Schweitzer, P. A. (Editor), Corrosion and Corrosion Protection Handbook, 2nd edition, Marcel Dekker, Inc., New York, 1989. Schweitzer, P., Corrosion Resistance Tables, 4th edition, Marcel Dekker, Inc., New York, 1995. In three volumes. Uhlig, H. H. and R. W. Revie, Corrosion and Corrosion Control, 3rd edition, NACE International, Houston, TX, 1995. QUESTIONS AND PROBLEMS 16.1 (a) Briey explain the difference between oxidation and reduction electrochemical reactions. (b) Which reaction occurs at the anode, and which at the cathode? 16.2 (a) Write the possible oxidation and reduction half-reactions that occur when magnesium is immersed in each of the following solutions: (i) HCl, (ii) an HCl solution containing dissolved oxygen, (iii) an HCl solution containing dissolved oxygen and, in addition, Fe2 ions. (b) In which of these solutions would you expect the magnesium to oxidize most rapidly? Why? 16.7 16.8 16.3 Would you expect iron to corrode in water of high purity? Why or why not? 16.4 Demonstrate that (a) the value of F in Equation 16.19 is 96,500 C/mol, and (b) at 25 C (298 K), RT ln x nF 0.0592 log x n 16.5 (a) Compute the voltage at 25 C of an electrochemical cell consisting of pure cadmium immersed in a 2 10 3M solution of Cd2 ions, and pure iron in a 0.4M solution of Fe2 ions. (b) Write the spontaneous electrochemical reaction. 16.6 A Zn/Zn2 concentration cell is constructed in which both electrodes are pure zinc. The 16.9 16.10 Zn2 concentration for one cell half is 1.0M, for the other, 10 2M. Is a voltage generated between the two cell halves? If so, what is its magnitude and which electrode will be oxidized? If no voltage is produced, explain this result. An electrochemical cell is composed of pure copper and pure lead electrodes immersed in solutions of their respective divalent ions. For a 0.6M concentration, of Cu2 , the lead electrode is oxidized yielding a cell potential of 0.507 V. Calculate the concentration of Pb2 ions if the temperature is 25 C. An electrochemical cell is constructed such that on one side a pure nickel electrode is in contact with a solution containing Ni2 ions at a concentration of 3 10 3 M. The other cell half consists of a pure Fe electrode that is immersed in a solution of Fe2 ions having a concentration of 0.1 M. At what temperature will the potential between the two electrodes be 0.140 V? Modify Equation 16.19 for the case in which metals M1 and M2 are alloys. For the following pairs of alloys that are coupled in seawater, predict the possibility of corrosion; if corrosion is probable, note which alloy will corrode. (a) Aluminum and magnesium. (b) Zinc and a low-carbon steel. (c) Brass (60Cu-40Zn) and Monel (70Ni30Cu). S-244 Chapter 16 / Corrosion and Degradation of Materials Fe2 ions) if the corrosion current density is 1.15 10 5 A/cm2. (d) Titanium and 304 stainless steel. (e) Cast iron and 316 stainless steel. 16.11 (a) From the galvanic series (Table 16.2), cite three metals or alloys that may be used to galvanically protect nickel in the active state. (b) Sometimes galvanic corrosion is prevented by making an electrical contact between both metals in the couple and a third metal that is anodic to these other two. Using the galvanic series, name one metal that could be used to protect a copperaluminum galvanic couple. 16.12 Demonstrate that the constant K in Equation 16.23 will have values of 534 and 87.6 for the CPR in units of mpy and mm/yr, respectively. 16.13 A piece of corroded steel plate was found in a submerged ocean vessel. It was estimated that the original area of the plate was 10 in.2 and that approximately 2.6 kg had corroded away during the submersion. Assuming a corrosion penetration rate of 200 mpy for this alloy in seawater, estimate the time of submersion in years. The density of steel is 7.9 g/cm3. 16.14 A thick steel sheet of area 400 cm2 is exposed to air near the ocean. After a one-year period it was found to experience a weight loss of 375 g due to corrosion. To what rate of corrosion, in both mpy and mm/yr, does this correspond? 16.17 (a) Cite the major differences between activation and concentration polarizations. (b) Under what conditions is activation polarization rate controlling? (c) Under what conditions is concentration polarization rate controlling? 16.18 (a) Describe the phenomenon of dynamic equilibrium as it applies to oxidation and reduction electrochemical reactions. (b) What is the exchange current density? 16.19 Briey explain why concentration polarization is not normally rate controlling for oxidation reactions. 16.20 Lead experiences corrosion in an acid solution according to the reaction Pb KAi n (16.38) where K is a constant, A is the atomic weight of the metal experiencing corrosion, n is the number of electrons associated with the ionization of each metal atom, and is the density of the metal. (b) Calculate the value of the constant K for the CPR in mpy and i in A /cm2 (10 6 A/cm2). 16.16 Using the results of Problem 16.15, compute the corrosion penetration rate, in mpy, for the corrosion of iron in citric acid (to form H2 The rates of both oxidation and reduction half-reactions are controlled by activation polarization. (a) Compute the rate of oxidation of Pb (in mol/cm2-s) given the following activation polarization data: V(Pb/Pb2 16.15 (a) Demonstrate that the CPR is related to the corrosion current density i (A/cm2) through the expression CPR Pb2 2H For Lead 0.126 V i0 2 10 9 A/cm2 0.12 ) V(H For Hydrogen 0V i0 1.0 10 8 A/cm2 0.10 /H2) (b) Compute the value of the corrosion potential. 16.21 The corrosion rate is to be determined for some divalent metal M in a solution containing hydrogen ions. The following corrosion data are known about the metal and solution: For Metal M V(M/M ) 0.47 V i0 5 10 10 A/cm2 0.15 2 V(H For Hydrogen 0V /H2) i0 2 10 9 A/cm2 0.12 (a) Assuming that activation polarization controls both oxidation and reduction reactions, determine the rate of corrosion of metal M (in mol/cm2-s). Questions and Problems S-245 FIGURE 16.26 Plot of overvoltage versus logarithm of current density for a solution that experiences combined activationconcentration polarization at various solution velocities. Overvoltage v 5 > v4 > v 3 > v2 > v 1 Velocity v1 v2 v3 v4 v5 Log current density (b) Compute the corrosion potential for this reaction. 16.22 The inuence of increasing solution velocity on the overvoltage-versus-log current density behavior for a solution that experiences combined activationconcentration polarization is indicated in Figure 16.26. On the basis of this behavior, make a schematic plot of corrosion rate versus solution velocity for the oxidation of a metal; assume that the oxidation reaction is controlled by activation polarization. 16.23 Briey describe the phenomenon of passivity. Name two common types of alloy that passivate. 16.24 Why does chromium in stainless steels make them more corrosion resistant in many environments than plain carbon steels? 16.25 For each form of corrosion, other than uniform, do the following: (a) describe why, where, and the conditions under which the corrosion occurs; and (b) cite three measures that may be taken to prevent or control it. 16.26 Cite two examples of the benecial use of galvanic corrosion. 16.27 Briey explain why cold-worked metals are more susceptible to corrosion than noncoldworked metals. 16.28 Briey explain why, for a small anode-tocathode area ratio, the corrosion rate will be higher than for a large ratio. 16.29 For a concentration cell, briey explain why corrosion occurs at that region having the lower concentration. 16.30 Is Equation 16.23 equally valid for uniform corrosion and pitting? Why or why not? 16.31 (a) What are inhibitors? (b) What possible mechanisms account for their effectiveness? 16.32 Briey describe the two techniques that are used for galvanic protection. 16.33 Tin cans are made of a steel the inside of which is coated with a thin layer of tin. The tin protects the steel from corrosion by food products in the same manner as zinc protects steel from atmospheric corrosion. Briey explain how this cathodic protection of tin cans is possible since tin is electrochemically less active than steel in the galvanic series (Table 16.2). 16.34 For each of the metals listed below, compute the PillingBedworth ratio. Also, on the basis of this value, specify whether or not you would expect the oxide scale that forms on the surface to be protective, and then justify your decision. Density data for both the metal and its oxide are also tabulated. Metal Zr Sn Bi Metal Density (g/cm3) 6.51 7.30 9.80 Metal Oxide ZrO2 SnO2 Bi2O3 Oxide Density (g/cm3) 5.89 6.95 8.90 S-246 Chapter 16 / Corrosion and Degradation of Materials 16.35 According to Table 16.3, the oxide coating that forms on silver should be nonprotective, and yet Ag does not oxidize appreciably at room temperature and in air. How do you explain this apparent discrepancy? 16.36 Below, weight gain-time data for the oxidation of copper at an elevated temperature are tabulated. W (mg/cm2) 0.316 0.524 0.725 Time (min) 15 50 100 (a) Determine whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. (b) Now compute W after a total time of 450 min. 16.37 Below, weight gaintime data for the oxidation of some metal at an elevated temperature are tabulated. W (mg/cm2) 4.66 11.7 41.1 Time (min) 20 50 175 (a) Determine whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. (b) Now compute W after a time of 1000 min. 16.38 Below, weight gaintime data for the oxidation of some metal at an elevated temperature are tabulated. W (mg/cm2) 1.90 3.67 6.40 Time (min) 25 75 250 (a) Determine whether the oxidation kinetics obey a linear, parabolic, or logarithmic rate expression. (b) Now compute W after a time of 3500 min. 16.39 From a molecular perspective, explain why increasing crosslinking and crystallinity of a polymeric material will enhance its resistance to swelling and dissolution. Would you expect crosslinking or crystallinity to have the greater inuence? Justify your choice. 16.40 List three differences between the corrosion of metals and (a) the corrosion of ceramics, and (b) the degradation of polymers. Design Problems 16.D1 A brine solution is used as a cooling medium in a steel heat exchanger. The brine is circulated within the heat exchanger and contains some dissolved oxygen. Suggest three methods, other than cathodic protection, for reducing corrosion of the steel by the brine. Explain the rationale for each suggestion. 16.D2 Suggest an appropriate material for each of the following applications, and, if necessary, recommend corrosion prevention measures that should be taken. Justify your suggestions. (a) Laboratory bottles to contain relatively dilute solutions of nitric acid. (b) Barrels to contain benzene. (c) Pipe to transport hot alkaline (basic) solutions. (d) Underground tanks to store large quantities of high purity water. (e) Architectural buildings. trim for high-rise

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CHAPTER 3RISK AND RETURN: PART II(Difficulty: E = Easy, M = Medium, and T = Tough)True/FalseEasy:(3.4) SMLAnswer: b1.The slope of the SML is determined by the value of beta.Diff: Ea. Trueb. False(3.4) SMLAnswer: a Diff: E2.If you plotted
DeVry Fremont - FIN - 516
CHAPTER 4BOND VALUATION(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(4.1) Issuing bondsAnswer: b Diff: E1.If a firm raises capital by selling new bonds, the buyer is called the&quot;issuing firm,&quot; and the coupon rate is generally s
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CHAPTER 5BASIC STOCK VALUATION(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(5.1) Preemptive rightAnswer: a Diff: E1.The preemptive right gives current stockholders the right to purchase,on a pro rata basis, any new shares sold
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CHAPTER 6FINANCIAL OPTIONS(Difficulty: E = Easy, M = Medium, T = Tough)True-FalseEasy:(6.1) OptionsAnswer: a Diff: E1.An option is a contract which gives its holder the right to buy or sellan asset at a predetermined price within a specified per
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CHAPTER 7Accounting for Financial Management(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(7.1) Annual reportAnswer: a Diff: E1.The annual report contains four basic financial statements: the incomestatement; balance sheet; sta
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CHAPTER 8ANALYSIS OF FINANCIAL STATEMENTS(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(8.1) Ratio analysisAnswer: a Diff: E1.Ratio analysis involves a comparison of the relationships betweenfinancial statement accounts so as t
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CHAPTER 9FINANCIAL PLANNING ANDFORECASTING FINANCIAL STATEMENTS(Difficulty: E = Easy, M = Medium, T = Tough)True-FalseEasy:(9.2) Sales forecastAnswer: a Diff: E1.A typical sales forecast, though concerned with future events, willusually be base
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CHAPTER 10DETERMINING THE COST OF CAPITAL(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(10.1) Cost of capitalAnswer: a Diff: E1.The cost of capital should reflect the average cost of the varioussources of long-term funds a firm
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CHAPTER 11CORPORATE VALUATION AND VALUE-BASED MANAGEMENT(Difficulty: E = Easy, M = Medium, and T = Tough)True/FalseEasy:(11.1) Corporate valuation modelAnswer: b Diff: E1.The corporate valuation model cannot be used unless a company doesntpay di
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CHAPTER 12CAPITAL BUDGETING: DECISION CRITERIA(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:1(12.2) PV of cash flowsAnswer: b Diff: E.Because present value refers to the value of cash flows that occur atdifferent points in time
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CHAPTER 13CAPITAL BUDGETING: ESTIMATING CASH FLOWSAND ANALYZING RISK(Difficulty: E = Easy, M = Medium, and T = Tough)True-FalseEasy:(13.1) Relevant cash flowsAnswer: a Diff: E1.Any cash flow that can be classified as incremental is relevant in a
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CHAPTER 14REAL OPTIONS(Difficulty: E = Easy, M = Medium, and T = Tough)True/FalseEasy:(14.1) Real optionsAnswer: a Diff: E1.Real options exist when managers have the opportunity, after a projecthas been implemented, to make operating changes in
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CHAPTER 15CAPITAL STRUCTURE DECISIONS: PART I(Difficulty: E = Easy, M = Medium, T = Tough)True-FalseEasy:(15.1) Bankruptcy costsAnswer: a Diff: E1.Because creditors can foresee, to at least some extent, the costs ofbankruptcy, they charge a high
American International - ACCO - 3350
CHAPTER 2JOB ORDER COST ACCOUNTINGStudy Objectives Explain the characteristics and purposes ofcost accounting. Describe the flow of costs in a job order costaccounting system. Explain the nature and importance of a jobcost sheet.Study Objectives:
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Sample Multiple-Step Income StatementABC CompanyIncome StatementFor the Year Ended December 31, 2009SalesCost of goods soldGross profitOperating expenses:SellingAdministrativeTotal operating expensesIncome from operationsOther revenue and (exp
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Chapter1- 1CHAPTER1FINANCIAL ACCOUNTING ANDFINANCIALACCOUNTING STANDARDSACCOUNTINGIntermediateAccounting13thEditionKieso,Weygandt,andWarfieldChapter1-2Learning ObjectivesLearning Objectives1.Identifythemajorfinancialstatementsandothermeans
American International - ACCO - 3350
Chapter8-1CHAPTER8VALUATION OF INVENTORIES:VALUATIONA COST-BASIS APPROACHCOST-BASISIntermediateAccounting13thEditionKieso,Weygandt,andWarfieldChapter8-2Learning ObjectivesLearning Objectives1.Identifymajorclassificationsofinventory.2.Dis
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Chapter18-1CHAPTER1818REVENUE RECOGNITIONIntermediateAccounting13thEditionKieso,Weygandt,andWarfieldChapter18-2Learning ObjectivesLearning Objectives1.Applytherevenuerecognitionprinciple.2.Describeaccountingissuesforrevenuerecognitionatpoi
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Chapter24-1CHAPTER2424FULL DISCLOSURE INFULLFINANCIAL REPORTINGFINANCIALIntermediateAccounting13thEditionKieso,Weygandt,andWarfieldChapter24-2Learning ObjectivesLearning ObjectivesChapter24-3Full Disclosure in Financial ReportingFull Di
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Chapter 1 Financial Reporting and Accounting StandardsCHAPTER111FINANCIAL REPORTING AND ACCOUNTING STANDARDSThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the top
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Chapter 2 Conceptual Framework for Financial ReportingCHAPTER2CONCEPTUAL FRAMEWORK FOR FINANCIAL REPORTINGThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics
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Chapter 4 Income Statement and Related InformationCHAPTER441INCOME STATEMENT AND RELATED INFORMATIONThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in I
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Chapter 5 Statement of Financial Position and Statement of Cash FlowsCHAPTER5STATEMENT OF FINANCIAL POSITIONAND STATEMENT OF CASH FLOWSThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting S
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Chapter 7 Cash and ReceivablesCHAPTER771CASH AND RECEIVABLESThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discussions
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Chapter 8 Valuation of Inventories: A Cost-Basis ApproachCHAPTER881VALUATION OF INVENTORIES: A COST-BASIS APPROACHThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for t
University of Guelph - ECON - 2410
NAME:_STUDENT #: _Department of Economics and FinanceCollege of Management and EconomicsUniversity of GuelphECON*3620 - International TradeInstructor: Patrick MartinWinter 2012Assignment 1This first assignment (worth 5% of your mark) is due on Th
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Chapter 9 Inventories: Additional Valuation IssuesCHAPTER9INVENTORIES: ADDITIONAL VALUATION ISSUESThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in Inte
University of Guelph - ECON - 2410
University of Guelph - ECON - 2410
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Chapter 10 Acquisition and Disposition of Property, Plant, and EquipmentCHAPTER10101ACQUISITION AND DISPOSITION OF PROPERTY,PLANT, AND EQUIPMENTThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial R
University of Guelph - ECON - 2410
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Chapter 11 Depreciation, Impairments, and DepletionCHAPTER11111DEPRECIATION, IMPAIRMENTS, AND DEPLETIONThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics i
University of Guelph - ECON - 2410
ECON2310 (Martin, Goertz, and Adomait) Fall 2011ASSIGNMENT 4 for week 7 consists of 14 problems.Eight non-graded practice problems from chapters 7 &amp; 8. Unlike the other assignments we will have littletime to discuss these in labs as quiz 4 is the week
University of Guelph - ECON - 2410
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Chapter 12 Intangible AssetsCHAPTER12121INTANGIBLE ASSETSThis IFRS Supplement provides expanded discussions of accounting guidance under International Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discussions are
University of Guelph - ECON - 2410
ECON2310 (Martin, Goertz, and Adomait) Fall 2011ASSIGNMENT 5 for weeks 7 and 8 consists of two long problem on chapters 7-9, 14, and 15 to bediscussed in labs. Quizzes occur in week 9, November 7-11.This problems ties together the material in chapters
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Chapter 13 Current Liabilities, Provisions, and ContingenciesCHAPTER13CURRENT LIABILITIES, PROVISIONS, AND CONTINGENCIESThis IFRS Supplement provides expanded discussions of accounting guidance under International Financial Reporting Standards (IFRS)
University of Guelph - ECON - 2410
Econ*2410Name:_ Lab:_UNIVERSITY OF GUELPHCollege of Management and EconomicsDepartment of EconomicsECON*2410: INTERMEDIATE MACROECONOMICSWinter Semester 2007Homework assignment#1(Due date 01-30-2007)I. Multiple Choice Questions (5 points)1) The
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Chapter 14 Non-Current LiabilitiesCHAPTER14141NON-CURRENT LIABILITIESThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The dis
University of Guelph - ECON - 2410
Trade, exchange rates, budget balances and interest rates | The Economist1 of 2Log outhttp:/www.economist.com/node/21540300My accountDigital &amp; mobileNewslettersRSSJobsHelpFriday November 25th 2011World politicsBusiness &amp; financeEconomicsScie
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The Political and Social Consequences of the Black Death, 1348 1351By Walter S. ZapotocznyThe Black Death was one of the worst natural disasters in history. It swept over Europe and Asia andravaged cities causing widespread hysteria and death. The Blac
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Chapter 15 EquityCHAPTER15151EQUITYThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discussions are organized according t
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Chapter 16 Dilutive Securities and Earnings per ShareCHAPTER1616-1DILUTIVE SECURITIES AND EARNINGS PER SHAREThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the top
University of Guelph - ECON - 2410
ECON*2410 Fall, 2011Empirical Assignment, Due Date Friday, 25 NovemberAll sections have equal weightLabour MarketIn order to complete this task you need to determine which province has been assigned to youand what your particular start date is. Cons
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Chapter 17 InvestmentsCHAPTER17171INVESTMENTSThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discussions are organized a
University of Guelph - ECON - 2410
ECON*2410:GuidetoAssignmentFall,2011Instructor:D.PrescottTheassignmenthasaweightof25%inthefinalgradeandsoitisasubstantialpieceofappliedworkthatrequiresstudentstoretrievedatafromCANSIM,preparechartsandwriteareportthatexplainsthemethodsusedtopreparethe
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Chapter 18 RevenueCHAPTER18REVENUEThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discussions are organized according to
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Chapter 19 Accounting for Income TaxesCHAPTER19191ACCOUNTING FOR INCOME TAXESThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting.
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Chapter 20 Accounting for Pensions and Postretirement BenefitsCHAPTER20201ACCOUNTING FOR PENSIONSAND POSTRETIREMENT BENEFITSThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (
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Chapter 21 Accounting for LeasesCHAPTER21211ACCOUNTING FOR LEASESThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The discuss
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Chapter 22 Accounting Changes and Error AnalysisCHAPTER22ACCOUNTING CHANGES AND ERROR ANALYSISThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in Intermed
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Chapter 23 Statement of Cash FlowsCHAPTER23231STATEMENT OF CASH FLOWSThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IFRS) for the topics in IntermediateAccounting. The dis
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Chapter 24 Presentation and Disclosure in Financial ReportingCHAPTER24241PRESENTATION AND DISCLOSURE IN FINANCIAL REPORTINGThis IFRS Supplement provides expanded discussions of accounting guidance underInternational Financial Reporting Standards (IF