Mg-rich coatings: A new paradigm for Cr-free corrosion protection of Al aerospace alloys

Environmentally acceptable alternative coatings to chromate pigments and pretreatments for the corrosion control of Al alloy 2024 T-3, commonly used in aircraft, were designed, formulated, and tested as primer coatings to provide protection using particulate Mg-rich pigmentation. The system was designed by analogy to pigmented Zn-rich primer coatings used for the protection of steel. In the current study, four coating polymer systems were examined as possible candidates as polymer matrices for Mg-rich cathodic protect coatings. Mg-rich primers were formulated with ∼50-micron average particle size magnesium powder, near to the critical pigment volume concentration (CPVC) for this system. Top-coated scribed coatings systems have been subjected to Prohesion^™ exposure in dilute Harrison’s solution for up to 5000 hr. These coatings are the first nonchromated coatings to satisfy 3000 hr of such exposure and remain shiny and undamaged in the scribe area, only showing damage at about 4800 hr. The corrosion byproducts generated in the scribe areas during Prohesion exposure were examined by energy dispersive X-ray analysis (EDXA), and the local pH of the coating determined by the nature of the salt formed as a function of exposure conditions and time, did not cause Al corrosion. Presented at the 81 st Annual Meeting of the Federation of Societies for Coatings Technology, November 12–14, 2003, in Philadelphia, PA.     

Testing and evaluation of nonchromated coating systems for aerospace applications

The advanced corrosion resistant aircraft coatings program (ACRAC) is part of the Air Force strategy to improve performance and reduce environmental impact of coatings used on Air Force weapon systems. The program addresses the Air Force near and mid-term strategies to eliminate chromate corrosion inhibitors and reduce steps in the outer mold line coating process. Evaluation of the coating process (surface preparation, conversion coating, primer, topcoat) as a system is a key feature of the ACRAC program. Results to date indicate that the current-state-of-the-art nonchromated coating systems are significantly less effective than those with chromate. A chromate conversion coating is required for the nonchromate primer system to meet minimum requirements. Sol–gel-process based conversion coatings can replace chromate conversion coatings provided a chromated primer is used. Several approaches to incorporating inhibitors into sol–gel coatings are discussed. Electrochemical methods for testing coating performance are discussed and a new procedure based on impedance spectroscopy for evaluating active damage repair is presented.     

Properties of ketimine/acetoacetate coated aluminum substrates

Based on ketimine/acetoacetate coating technology, a new two-component high solids primer for aerospace use has been developed. The objective was to formulate a chromate-free primer that may be applied to all relevant aluminum surfaces, particularly after chromate-free pretreatment. During development, interesting indications of good adhesion and good corrosion resistance were found. For confirmation and in order to optimize the primer, research was focused on the interfacial performance of the coatings on typical aerospace substrates. In this paper, therefore, the nature of the substrates, including their pretreatments, is discussed with initial emphasis on the nitric acid pickling pretreatment, used in place of chromate pretreatments with their desirable properties. Although aging in relevant electrolytes of such pretreated aluminum leads to an increase of the thin oxide layer by further hydration normally influencing negatively interfacial performances, cross cut adhesion values of the primer, or the primer/topcoat, before and after aging in several electrolytes, were good on clad as well as on non-clad material. This was confirmed by microscopic morphology assessment during similar aging processes of the coating/substrate systems. The hydration of the nitric acid pickled layer was not found in the presence of primer, with or without topcoat. Using electron energy loss spectroscopy, indications of a distinct chemical bond between the primer and the nitric acid pickled aluminum were revealed. Electrochemical impedance measurements, determining film resistances of the various coated panels, also showed good responses when the primer was pigmented with a selected chromate-free inhibitor. Finally, in line with the previous indications and due to the special interfacial performance, in the presence of chromate-free pretreated substrates, filiform corrosion resistance with chromate alternative pigmentation approaches that of chromated primers.     

Trimethylsilane-based pretreatments in a Mg-rich primer corrosion prevention system

A trimethylsilane-based coating was investigated as a pretreatment for Al-2024 T3 in a novel Mg-rich primer corrosion prevention system. SiC-based thin films were deposited onto Al substrates by plasma-enhanced chemical vapor deposition (PECVD). A screening study of the pressure (P) dependence of films deposited at 350 °C showed an increase in growth rate from 0.6 to 1.9 Torr. A second screening study where P was fixed at 1.9 Torr and temperature (T) was varied from 125 to 550 °C showed decreasing growth rates with increasing temperature with an apparent transition around 300 °C. Electrochemical impedance spectroscopy (EIS) of the SiC-based films on Al-2024 after exposure to a corrosive environment (i.e., dilute Harrison solution) indicated that samples coated using SiC-based films exhibit higher low frequency impedance (i.e., 100–1000× higher) than bare Al-2024 with open circuit potential remaining 0.1 V higher for the former suggesting the SiC-based films slow the corrosion process. A Mg-rich primer was coated onto the SiC on Al-2024 with the galvanic function of the system determined by EIS. As compared to SiC on Al-2024, a similar behavior for the low frequency impedance was observed for the Mg-rich primer-coated samples with some films exhibiting 1E + 8 Ω at 0.1 Hz indicating a strong barrier property. Initial gas jet erosion using acrylic media indicates the Mg-rich primer coatings are removed in preference to the Si–C films—the first step toward demonstrating a permanent pretreatment. When successfully developed and optimized, the value of such a hard, protective coating is the reduction of a three-component coatings system (i.e., pretreatment, primer, and topcoat) to a two-component system (i.e., primer and topcoat).     

An organically modified zirconate film as a corrosion-resistant treatment for aluminum 2024-T3

Current coating systems for aircraft corrosion protection are based on a traditional chromate surface treatment, primer, and topcoat. The Air Force is seeking environmentally benign corrosion-resistant surface treatments for aluminum-skinned aircraft as a replacement for environmentally hazardous surface treatments involving chromates. Performance of replacement treatments must be able to satisfy the durability needed for dramatically extended lifetimes, be compatible with present and future environmental requirements, and be easily integrated into current primer/topcoat paint systems.

Organically modified zirconate sol–gel films were investigated as an environmentally compliant replacement for chromated surface treatments, which included functionalized components to tailor the chemistry at both the aluminum oxide substrate/surface treatment interface and the surface treatment/topcoat interface. Sol–gel films were applied to aluminum 2024-T3 alloy coupons, and the resulting film chemistry was investigated. FTIR was used to identify organic components in the film and X-ray photoelectron spectroscopy was used to investigate the interface chemistry. The result of the chemically modified sol–gel synthesis was a coating in which a concentration gradient was formed at the surface, which is discussed. The corrosion protection attributes of these films was also studied and the electrochemical evaluation of sol–gel films will be discussed, both as stand-alone coatings and as part of a full coating system.

Organically modified sol–gels exhibited significantly better protection in terms of barrier properties in comparison to a typical chromate-based processes. The resulting data from evaluations of sol–gel produced coatings show promise towards the goal of producing a robust chemical interaction/bonding of such corrosion-resistant coatings on the surface of aluminum-skinned aircraft without the use of environmentally hazardous chromate agents.     

EIS study of environmentally friendly coil coating performances

The corrosion protection of metal structures by the application of organic coatings is obtained using complex paint cycles. The metal pretreatment as well as primer, intermediate and top coat are the usual layers composing the protection system. Although chromate pretreatment processes and chromate containing primers are widely used, they require highly toxic chromic acid solutions, with consequent effluent disposal and ecological problems. This fact pushed many research laboratories to develop new chromium-free pretreatments and primer inhibitors. Electrochemical impedance spectroscopy (EIS) proved to be a very useful technique to study the protection properties of the organic coating because of the possibility of evaluating the corrosion process on the metal substrate and to measure the electric and dielectric characteristics of the coating. In this study, new chromium-free pretreatments and new primers containing ecological inhibitors were applied to steel substrates coated using an Al-Zn alloy. The results were compared with those obtained using traditional protection systems. The characterization of the complete system (pretreatment and primer) in sodium sulfate solution clearly showed the different water uptake behavior of the two primers, which highlights the better barrier properties of the one containing phosphate. However the corrosion protection of the primer containing chromates is also due to the inhibitive action of the chromates. Hence such a type of primer better withstands the presence of defects in the coating. Moreover the presence of environmentally friendly pretreatments do not worsen the corrosion protection which appears comparable to that observed when chromatation is employed.     

Aluminum alloy 2024-T3 protection by magnesium-rich primer with chromate-free metal salts

This research examines novel Mg- and metal salt-rich primer formulations with low Mg metal pigment loading. The chromate-free metal salts were incorporated to assist in the passivation, corrosion inhibition, and pH buffering of the aluminum substrate. The total pigment volume concentration (PVC) in the examined coatings ranged from 6 to 20%, which is far below its critical pigment volume concentration (CPVC) as well as that of traditional Mg-rich primers (PVC ≈ 45%). The formulations were applied to aluminum alloy (AA) 2024-T3 panels and coated with a polyurethane topcoat. Non-pigmented and Mg-rich primer controls were used for comparison. The coating systems were subjected to accelerated weathering by ASTM B117 salt spray chamber and removed periodically for analysis by electrochemical impedance spectroscopy (EIS) and electrochemical noise measurements (ENM). Corrosion potential was also measured. Conventional, macroscopic examination was used to rank coating performance.The present findings support the significance of CO₃ compounds in the protection of aluminum and its alloys by Mg-rich primers. It is proposed that the addition of Li₂CO₃ and Mg(NO₃)₂ to the primer facilitate the production of Mg(OH)₂ and MgCO₃ precipitates to improve protection. Anti-corrosion and anti-blistering effects were observed for formulations containing Li₂CO₃, Mg(NO₃)₂, and a low percentage of Mg metal particulates. The Mg(NO₃)₂ appears to reduce blistering while the Li₂CO₃ enhances defect protection. These effects are demonstrated throughout 1600 h of exposure to salt spray. Continued optimization presents the opportunity to design and implement unique cathodic protection plus corrosion inhibitor coating systems for use on aluminum substrates.     

Monitoring of a military vehicle coating under Prohesion exposure by embedded sensors

Two-layered organic coatings protect metallic structures against corrosion by reducing the transport of water, ions, and oxygen from the environment to the substrate and storing species that provide corrosion inhibition. The topcoat and the primer provide the former and latter, respectively, with the primer also providing adhesion between the topcoat and the substrate. A standard testing method for coatings is the ASTM G85 Prohesion^® test. This test involves alternating between a wet exposure of 1-h salt spray at 25 °C and a dry exposure of 1-h air at 35 °C. Apart from visual inspection, conventional monitoring of coating properties is achieved by ex situ electrochemical tests under immersion in a suitable electrolyte. In situ monitoring during a Prohesion^® test was performed for a military vehicle coating system using embedded sensors located between the topcoat and primer. In situ results associated with the dry and wet exposures are presented from electrochemical impedance spectroscopy and electrochemical noise measurements. In situ single-frequency impedance measurements were used to monitor the water uptake/loss associated with the exposures of the test conditions. Ex situ monitoring was also performed for comparison with the in situ embedded sensor monitoring.     

The influence of Ce-based coatings as pretreatments on corrosion stability of top powder polyester coating on AA6060

Cerium-based conversion coatings (CeCCs) are one of the most prospective alternatives to the widely used chromate conversion coatings (CCCs) due to their anticorrosion efficiency, environmentally friendly nature and low cost. In this work, the CeCCs on AA6060 were prepared by immersion into aqueous cerium salt solutions at room temperature, and subsequently post-treated in heated phosphate solution. The effect of counter ion (nitrate and chloride) on the coating properties was studied testing CeCCs as sole or conversion layers for the top polyester coating. Since the 60 μm thick polyester coating was applied, an artificial defect of 0.8 mm hole was introduced to faster assess the differences between pretreatments. The system with CCC pretreatment was used as reference. Corrosion properties were investigated in 0.5 M NaCl solution by electrochemical impedance spectroscopy while the adhesion strength was measured by NMPR (N-methyl-2-pyrrolidone) and pull-off tests. As shown, the post-treated chloride-based CeCC offered better protection than crack-free thin nitrate-based CeCC, when used as sole coatings. On the other hand, it was brought to evidence that in combination with top powder polyester coating, the CeCC deposited from nitrate solution exhibited better protection compared to protective system pretreated with chloride-based one. Excellent polyester coating adhesion was found independently on aluminium surface pretreatment.     

Heterogeneous hydrogen evolution on corroding Fe-3 at.% Si surface observed by scanning electrochemical microscopy

Corrosion behavior of Fe-3 at.% Si alloy in 0.01 mol dm⁻³ HCl solution was investigated by using scanning electrochemical microscopy (SECM) as well as general electrochemistry. The rate of corrosion coupled with hydrogen evolution was initially 0.44 A m⁻² but decreased significantly with time. Localized hydrogen evolution on the specimen surface was probed by an SECM system in which a force sensor was mounted to determine the probe height from the specimen surface. SECM images revealed that hydrogen evolution took place heterogeneously on the specimen surface depending on crystallographic orientation of substrate single grains in the initial stage and then became relatively homogeneous. Finally, a heterogeneous hydrogen distribution corresponding to the appearance of localized corrosion sites was observed.     

Next generation of aircraft coatings systems

The current generation of aircraft coatings had its basis in the polymer technologies of the 1970s and the use of chromate-based metal pretreatments and primers. There have been some incremental improvements in the epoxy and polyamide oligomers used in the primers as well as the isocyanates and flexible polyols used in topcoats, plus increases in the volume solids of the coatings to continue minimally meeting environmental requirements, but no truly new technologies have been developed and applied to aircraft coatings since that time. However, because of increasing economic and environmental pressures, this situation will soon change. Also, the U.S. Air Force is seeking a coating system that will have an ultimate lifetime of 30 years for maintenance cost control and fleet sustainability. The first change in the present coatings system will be in the pretreatments plus primers that currently constitute the metal protection system for the high strength Al alloys used for aircraft. For military aircraft, these alloys will continue to be Al 2024 T-3 and Al 7075-T6, heat-treated metals that have phase-separated regions rich in reactive metals such as Cu, Mg, and Zn. There are several new technologies now under consideration for such metal protection including conductive polymers as primers without Cr-based metal pretreatments, sol-gel based pretreatments and primers, plasma polymer metal pretreatments, and organo-modified aluminum oxide particles. Each of these technologies has shown some promise for Cr replacement, but each presently has a weakness that needs to be corrected for immediate usage. For the topcoat system, fluorinated polyols and improved use of UV-absorbers and light stabilizers will probably be the first changes implemented, with ceramer and other new crosslinking systems the most likely next polymer matrix candidates. The target for the entire coatings system is to have drastically improved wet-adhesion due to a covalently bonded system that has a gradient in composition that goes continuously from metal to metal oxide to mixed metal oxide/organic polymer to high-performance UV-stable organic polymer. The materials cost for such a system may be quite high, but the maintenance cost savings will much more than offset these costs. Presented at the 25th FATIPEC Congress, Sept. 19–22, 2000, in Turin, Italy. Department of Polymers & Coatings, Fargo, ND 58105.     

Advanced chrome-free organic–inorganic hybrid pretreatments for aerospace aluminum alloy 2024-T3—application of novel bis-ureasil sol–gel precursors

Effective pretreatment of aluminum alloys is very critical to success of protective coating systems for aerospace applications. While chromate-based pretreatments have been very successful for corrosion protection, they have been a target for replacement due to the increasingly stricter regulatory requirements arising from toxicity and carcinogenic nature of Cr(VI) used in such pretreatments. Among many approaches to develop alternative systems, the organic–inorganic hybrid (OIH) coatings based on sol–gel technology has advanced rapidly. We have successfully developed OIH coating systems by using suitably tailored organosilane precursors and sol–gel processing conditions. A series of novel bis-ureasil precursors have been developed and employed as organic precursor of OIH systems. Statistical design of experimental methodology (DoE) has been used to study and optimize compositional and process parameters using multifactor analysis of variance (ANOVA) analysis method. The corrosion resistance study (Potentiodynamic polarization, salt-spray corrosion test) shows that by proper choice of sol–gel precursors, cross-linkers, and reaction conditions, very dense, adherent and protective hybrid coatings, comparable in performance to chromate-based ones, can be obtained for aerospace aluminum alloy 2024-T3. This paper was awarded the Southern Society A.L. Hendry Award for best student paper. The paper was presented at FutureCoat! 2008, sponsored by Federation of Societies for Coatings Technology, held October 14–16, 2008, in Chicago, IL.     

A dipping E-coating for Mg alloys

Mg alloys are becoming more and more important structural materials in automotive industry. However, most commercial Mg alloys require coating protection because of their poor corrosion performance. In this paper, a self-deposited “electroless” E-coating process for Mg alloys is presented. By utilizing the unique electrochemistry of Mg, a thin film is rapidly formed on the surface of Mg alloys by simply dipping in an E-coating bath. The new developed dipping technique does not need a current or potential that is essentially required in a normal E-coating process. It is believed that the surface alkalization effect of Mg is responsible for the deposition of the “electroless” E-coating pre-film while the diffusion of hydroxyls in the porous film is governing the film growth. The rapidly formed pre-film can offer sufficient corrosion protection for Mg alloys in a chloride-containing environment or a phosphating bath in a paint line. The stability of the film can be significantly improved by the curing process. It is found that the coating performance is influenced by the type of Mg alloy and the surface pretreatment. The dipping coating can also act as a base for further powder-coating.     

A novel approach to heal the sol-gel coating system on magnesium alloy for corrosion protection

Sol-gel-based coatings exhibit high potentiality to be as an alternative to toxic chromate coatings for surface pre-treatment of metals and alloys. However, as soon as even small defects appear in the coating, the coating cannot stop the development of corrosion process. Present work demonstrates the possibility to use zinc nitrate as healing agent to repair the organic silane coatings in NaCl solution. The zinc nitrate was added to the 0.005 M NaCl solution where AZ91D magnesium alloy coated with organic silane coating was immersed. The healing process and the healing mechanism were investigated by electrochemical measurements and scanning electron microcopy coupled with energy dispersive spectroscopy. The results demonstrated the introduction of zinc nitrate to the electrolyte could stop the development of corrosion process of the coating system and a remarkable recovery on corrosion resistance could be obtained. This effect may be attributed to the formation of zinc oxide/hydroxide on the defective areas, hindering the corrosion activities.     

Nanostructured coatings approach for corrosion protection

Nanostructured surface treatment coatings based on the Self-assembled Nanophase Particle (SNAP) approach were investigated as potential replacement for chromate-based surface treatments on aircraft aluminum alloys. In the traditional sol–gel method, hydrolysis-condensation processes are followed by condensation polymerization upon film application. This process sequence provides a low temperature route to the preparation if thin coatings which are readily applied to most metallic substrates. The recent discovery of a method of forming functionalized silica nanoparticles in situ in an aqueous sol–gel process, and then cross-linking the nanoparticles to form a thin film, is an excellent example of a nanoscience approach to coatings. This Self-assembled Nanophase Particle (SNAP) process can be used to form thin, dense protective organic surface treatment coatings on Al aerospace alloys. The ability to design coating components from the molecular level upward offers tremendous potential for creating multifunctional coatings.

The important components of Al alloy corrosion inhibition by chromate are storage and release of Cr^VI species, inhibition of cathodic reactions (primarily oxygen reduction), and inhibition of attack at active sites in the alloy. Unlike chromate-based treatments, current SNAP coatings provide barrier-type corrosion resistance but do not have the ability to leach corrosion inhibitors upon coating damage and minimize corrosion of the unprotected area. In this study, organic inhibitors were tested for corrosion protection of aluminum alloys in combination with the (SNAP). Scanning Vibrating Electrode Technique, anodic polarization, electrochemical impedance spectroscopy, and salt spray test were used to study this new approach for chromate replacement.     

The role of chromate in filiform corrosion inhibition

This paper is part of a study on filiform corrosion (FFC) on aluminum alloy 2024-T3 and focuses on the surface characterization of corroded samples. Untreated samples were used as well as samples which had undergone pretreatments including polishing, surface etching and chromated conversion coatings (CCC). These samples were coated with both pigmented and non-pigmented epoxy-based coatings. Scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectroscopy (TOF-SIMS) analysis was used to investigate the nature of the surface as well as optical images to gauge the rate of FFC advancement. FFC corrosion rates decreased on samples which had received a surface etching pretreatment and a chromate conversion coating. Pigmented coatings reduced the rate of FFC further and led to two different types of corrosion surface morphology. On pretreated samples, the corrosion appeared deeper and pit-like, possibly due to an enhanced polymer-substrate bond. On untreated samples, widespread FFC developed. SEM and EDX analysis of various intermetallic particles (IMPs) on all samples, inside and outside of corroded regions, revealed that Cr from pigments was found deposited on Cu-containing intermetallics in corroded areas while Fe/Mn-containing particles were free from all pigment traces. These results suggest that the Cr deposition on Cu particles hinders the cathodic reduction of oxygen necessary for FFC advancement. For this reason, the coating pigments proved, under FFC conditions, to be a more effective inhibitor than the Cr originating from a chromate conversion coating.     

Addition of carbon black NIR absorber to galvanised steel primer systems: Influence on NIR cure of polyester melamine topcoats and corrosion protection characteristics

Near infrared (NIR) is becoming a popular option for rapid cure of coatings in the coil coating industry particularly where fast line speeds are required. The technology has the potential to reduce the cure time of a 20 μm polyester coating on a galvanised steel substrate from around 30 s via conventional heating methods down to <10 s under the lamps. Previous work suggested that the ideal situation in this case is to have a topcoat which is slightly transparent to NIR and an absorbing substrate to heat the coating from the substrate outwards in a two stage process which separates solvent removal from cross linking and film formation. This can be taken further by tinting the primer layer with a pigment that absorbs in the NIR region. In this study spectroscopy was used to show that a coated steel system could appear white in the visible region because of the reflectance of TiO₂ but the NIR absorption could be altered by adding absorbing pigments such as carbon black. Lamp settings could be reduced by 20% to achieve equivalent cure with tinted primer systems. The potential degradation in corrosion protection afforded by carbon-black containing pigments at various loadings was assessed for model organic coatings applied to galvanised steel specimens. In situ scanning Kelvin probe studies showed that rates of corrosion-driven coating delamination by cathodic disbondment remained unchanged by pigment loadings of up to 3.5 wt%.     

Effective corrosion protection of 8090 alloy by cerium conversion coatings

Conversion treatments based on immersion in Cr(VI) aqueous solutions are key technologies that combine low cost, easy application and high performance. However, they are environmentally problematic due to their carcinogenity and genotoxicity. Among the potential alternatives, treatments based on rare-earth compounds have drawn attention due to the stability of their oxides and their environmental acceptability. Despite the amount of work published, there is not yet an industrially suitable alternative treatment for aircraft aluminium alloys that is able to provide the required corrosion protection. A common feature of these alloys is the high level of copper in their chemical composition. Although the presence of copper in an alloy may enhance cerium deposition, high copper content alloys (AA2024, AA7075) have proven the most difficult to protect with Ce conversion coatings.In the present work, a commercial 8090-T8 aluminium alloy containing 1.15 weight percent (wt.%) Cu was coated with a Ce conversion coating at room temperature from a Ce bath without prior pretreatment of the specimens. Polarisation curves revealed that the presence of a cerium conversion coating (CeCC) reduces by two orders of magnitude the corrosion rate of the AA8090 alloy in a sodium chloride solution. Impedance measurements exhibited capacitive behaviour for the CeCC up to 216 h, showing that the cerium layer protects the bare alloy in the aggressive solution.Electrochemical tests have therefore revealed that these conversion layers afford long-lasting protection; withstanding up to 168 h in Salt Spray test.     

The roles of macrosegregation and of dendritic array spacings on the electrochemical behavior of an Al-4.5 wt.% Cu alloy

The microstructural pattern and the solute redistribution of as-cast aluminum alloys play an important role on the resulting corrosion behavior. However, of the main aluminum alloys, Al-Cu alloys have the lowest negative corrosion potential. The purpose of this work was to evaluate the electrochemical behavior of an Al-4.5 wt.% Cu alloy solidified under unsteady-state heat flow conditions. This evaluation was carried out through the analysis of both potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS) tests in a 0.5 M NaCl solution at 25 °C. The experimental segregation profile obtained in the solidification experiment was characterized by positive and negative copper content regions at the bottom and the top of the casting, respectively. Likewise, in conventional foundry practice, in a same casting both positive and negative copper segregation regions may occur. Such casting can exhibit different corrosion responses at different locations. The influences of solute redistribution during solidification, the magnitude of dendritic spacing and hence of the Al-rich phase and of Al₂Cu particles distribution along the casting on the corrosion resistance, were examined in samples collected along the casting length. The corrosion rate and impedance parameters (obtained from an equivalent circuit analysis) are also discussed.