REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 70, NUMBER 12 DECEMBER 1999

A superconducting quantum interference device magnetometer systemfor quantitative analysis and imaging of hidden corrosion activityin aircraft aluminum structures

A. Abedi and J. J. FellensteinDepartment of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235

A. J. LucasNCI Information Systems, Inc., Suite 505, 131 Russell Parkway, Warner Robins, Georgia 31088

J. P. Wikswo, Jr.Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235

~Received 31 March 1999; accepted for publication 12 September 1999!

We have designed and built a magnetic imaging system for quantitative analysis of the rate ofongoing hidden corrosion of aircraft aluminum alloys in planar structures such as intact aircraft lapjoints. The system utilizes a superconducting quantum interference device~SQUID! magnetometerthat measures the magnetic field associated with corrosion currents. It consists of a three-axis~vector! SQUID differential magnetometer, magnetic, and rf shielding, a computer controlledx-ystage, sample registration, and positioning mechanisms, and data acquisition and analysis software.The system is capable of scanning planar samples with dimensions of up to 28 cm square, with aspatial resolution of 2 mm, and a sensitivity of 0.3 pT/Hz1/2 ~at 10 Hz!. In this article we report thedesign and technical issues related to this system, outline important data acquisition techniques andcriteria for accurate measurements of the rate of corrosion, especially for weakly corroding samples,and present preliminary measurements. ©1999 American Institute of Physics.@S0034-6748~99!04312-9#

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I. INTRODUCTION

The detection of ongoing hidden corrosion and measument of its rate are extremely important to military and comercial aircraft for both safety and economic reasons. Wthe increase in the number of aging aircraft, for example,risk of structural weakening and failure due to undeteccorrosion-related damage is increasing. Addressing potesafety concerns requires not only the measurement of eing corrosion damage, typically through nondestructive teing ~NDT!, but also measurement of the rates of ongocorrosion and how these rates are affected by environmefactors. Although standard electrochemical instrumentstechniques are well suited for studying corrosion on theposed surface of samples, they are of little use for crevichidden corrosion, where the corrosion activity is governedthe restricted nature of the inaccessible chemical envirment surrounding the corroding surfaces. Since an invaexamination would alter the chemical environment and affthe rate and distribution of corrosion in such situations,perconducting quantum interference device~SQUID! magne-tometers provide a powerful technique for nondestructiquantitative analysis of corrosion rates and for studyingspatiotemporal variations of corrosion activity. FurthermoSQUID magnetometers can detect hidden corrosion fromonset, long before there has been sufficient material losdeposition of corrosion products to allow its detectionother noninvasive techniques. The unrivaled sensitivitySQUID magnetometers promises the possibility for quanttive analysis of corrosion at realistic rates and in typical

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vironments without the need for time-consuming field-tecoupons or unrealistic accelerated tests. The abilitySQUIDs to rapidly scan large areas with high sensitivmakes them ideal for many magnetic imaging application1

Previous qualitative studies have shown that SQUmagnetometers have the sensitivity to detect noninvasivthe magnetic field associated with corrosion currents in vous metal-acid and metal-salt environments.2–4 These studieswere done using strong corrosive solutions to produce hrates of corrosion and focused primarily on geometrwhich were intended to maximize the magnetic field genated by corrosion and to simplify its interpretation. Nevetheless, they presented the possibility of the use of SQUfor noninvasive studies of hidden corrosion. Other studhave demonstrated the possibility of the use of SQUIDscyclic voltametry,5 and for evaluation of electrochemical reactivity of materials, such as 304 stainless steel.6 The firstSQUID magnetometer specifically designed for corrosstudies was constructed by Quantum Magnetics~San Diego,CA! with a spatial resolution of the order of 1 mm and sesitivity of 3 pT/Hz1/2 ~at 1 Hz!.7 The system was operated ia nonshielded laboratory environment and was equipwith a nonmagnetic stage and computer control. A uniqfeature of this system was that the detection coil array woriented at 45° with respect to the dewar axis, and the dewas mounted at a 45° angle upon a cradle. A 180° rotatiothe dewar about its axis would change the coil axis frovertical to horizontal, allowing for measurement of eithertwo orthogonal field components. With the coil axis in th

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4641Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

horizontal position, the sample could be oriented so thatcorroding surface was vertical, thereby preventing problefrom bubble accumulation associated with high corrosirates.

Since the background field and environmental nowere reported to be the limiting factors for SQUID corrosiostudies,3 the first qualitative studies at Vanderbilt were coducted using a high-resolution magnetometer and magnshield system,8,9 which was originally designed for measuring the magnetic fields from isolated biological tissue, suas the heart, and for the nondestructive evaluation~NDE! ofmaterials. These studies focused on detection and imaginmagnetic fields due to corrosion of aircraft aluminualloys.10–13

The system we describe in this article was designed scifically for high-resolution, long-term, noninvasive, anquantitative spatiotemporal analysis of the rate of hiddcorrosion in aircraft aluminum alloys in planar structuresuch as aircraft lap joints. Since our primary goal wasstudy actual or simulated lap joints, we designed the sysfor these realistic sample geometries, rather than those omized to produce a large magnetic field. Within this costraint, we would also be able to examine any other placorrosion geometries. As with our earlier system, we choto include a magnetic shield so that we could detect corsion in realistic and, in particular, weakly corrosive enviroments. Long-term magnetic studies of ongoing corrosionquire accurate and repeatable sample positioning; hencesample registration and positioning mechanism was desigwith this in mind. This mechanism also allows for parallelong-term study and imaging of multiple samples. In tharticle, we report the design and technical issues relatedthis system and submit a representative sample of prelinary data.

II. MAGNETIC IMAGING SYSTEM

As shown in Fig. 1, the magnetic imaging system cosists of a vector SQUID magnetometer, magnetic andshielding, a computer controlledx-y stage, sample registration and positioning mechanisms, and data acquisition aanalysis software. All the scanning and data acquisitionrameters are controlled through the computer software twe developed. Planar samples~up to 2832832 cm! arescanned under the magnetometer by the sample scanningregistration system. The system is automated to scan

FIG. 1. The magnetic imaging system consists of a three-axis~vector!SQUID differential magnetometer, magnetic and rf shielding, a compucontrolledx-y stage, sample registration and positioning system, and dacquisition and analysis capability.

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sample at user-defined intervals and produces a serietwo-dimensional raster images of components of magnfield above the corroding sample. Each scan provides anage of the spatial distribution of the magnetic field within ttime required to complete a raster scan. Appropriate analtechniques are then used to quantify the rate of hiddenrosion, and to examine the spatiotemporal characteristicits associated currents. The following sections discussdetails of the system design and components.

A. SQUID magnetometer

The custom-built vector SQUID magnetometer~Con-ductus Instrumentation and Systems Division, San DieCA, now Tristan Technologies, Inc.! was designed to provide high field sensitivity~300 fT/Hz1/2 at 10 Hz!, with spa-tial resolution of approximately 2 mm for corrosion studieIt is a three-axis, first-order differential magnetometer stem; each axis uses a pair of 2-mm-diameter pickup cseparated vertically by a 3 cmbaseline. As shown in Fig. 2the z-component~vertical axis! pickup coils form an axialgradiometer configuration, whereas thex- and y-component~horizontal axes! pickup coils form planar gradiometers.14

The SQUID is controlled by a flux-locked loop~FLL!,mounted adjacent to the magnetic shield, and the SQUcontroller ~iMAG !, which provides for the tuning of theSQUID, SQUID reset, trapped flux removal~by heating theSQUIDs!, dc offset, low and high pass filtering, and ampfication. Furthermore, these functions can be controlledexternal GPIB commands. The minimum operational dtance between thez pickup coil and room temperature ismm.

Although a Dewar design7 ~described above! seemed at-tractive, it has the disadvantage that the increased compleof the dewar and the need for a larger magnetic shield dmatically increases the cost of the system. Therefore, sour system was designed mostly to deal with small corrosrates, where the bubble problem is not significant, our cventional design for the Dewar allowed for more efficieuse of the shielded volume and reduced the cost of thetem by a significant factor.

B. Sample scanning and registration system

The sample scanning system, illustrated in Fig. 3, wdesigned to provide repeatable scans with positioning ac

rtaFIG. 2. The first-order differential vector magnetometer used in this sysutilizes 2-mm-diameter pickup coils and a 3 cmbaseline. Thez ~vertical!coils form an axial gradiometer, while thex andy ~horizontal! coils form aplanar gradiometer. The minimum coil-to-room temperature distancemm.

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4642 Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Abedi et al.

racy of better than 0.1 mm, and to minimize the noise duethe stage motors and electronics. Furthermore, for paralong-term study of multiple samples, the kinematic designthe system allows for removal and repositioning of sampto their original location under the magnetometer with eand accuracy. The details of the scanning system arecussed below.

1. Computer-controlled stage

The main component of the scanning system is an opframex-y stage~Model 318122AT, Daedal Division, ParkeHannifin Corp., Harrison City, PA!, with 46 cm of travel ineach horizontal direction, driven by two stepper moto~S57102MO, Daedal!. Each stepper motor is connected tomicrostepping drive amplifier~Zeta Drive, Daedal! con-trolled by a computer controlled indexer~AT6400, Daedal!.Each axis of the stage is equipped with magnetic proximswitches that set the end-of-travel limits of the stage, adefine the home position; because of the shield and thetance between the SQUID and the stage, the magneticof these switches is below system noise. The home posiwhich is the reference point from which all distances ameasured, is always approached from the positive endtravel limits with a preset velocity and acceleration, to ensthe reproducibility of scans to better than 0.1 mm.

2. Sample scanning track

Since the stage has ferromagnetic components andstepper motors generate magnetic noise, they were ploutside of the magnetic shield, approximately 1.5 m frommagnetometer, and their control electronics were shieldea separate Faraday cage. As shown in Fig. 3, a 157 cm311cm nonmagnetic and nonconductive track~to avoid inductivecoupling of powerline fields into the shield!, was fabricatedof 1.3-cm-thick G-10 fiberglass epoxy. The track is attachat one end to the stage tower assembly, while the other efree to slide upon the glass surface of the scanning ta~described later! beneath the magnetometer. The rigid tratranslates the force of the stage to the sample holderscans the sample under the magnetometer. A self-positiolatching mechanism alongside the track was designed tothe sample holder at a specified location near the end oftrack during scans. This location was selected to centersample holder with respect to the magnetometer when

FIG. 3. The sample scanning and registration system consists of a compcontrolledx-y stage, which scans the sample over the scanning table vrigid track. The system was designed to allow for repeated removalrepositioning of multiple samples with positioning and scanning accuracbetter than 0.1 mm:~1! track, ~2! sample holder,~3! scanning table,~4!support rods,~5! z stage,~6! x-y stage,~7! stepper motor,~8! stage tower,~9! pulley system.

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stage is at the home position. The track serves as theform upon which the sample holder slides in and out ofshield via a pulley, drum, and kevlar cord mechanism.precision laboratory jack~Model 281, Newport Corp., IrvineCA! on top of the stage provides vertical height adjustmand leveling of the track with respect to the scanning tab

3. Sample holder and kinematic design

The design of the sample holders varies in complexdepending on sample size, shape, and the desired envment~i.e., temperature, humidity! for each corroding samplebut all sample holders have a standard kinematic mounplate by which they attached to the track. As seen in Figthe plate has a beveled hole, a beveled slot, and an overshole that match threaded holes in the carriage that slalong the track; two beveled screws, A and B, and one wout a bevel, C, hold the plate to the carriage in a kinemamanner.

As long as the sample~s! are fixed rigidly to the sampleholder, the sample holder can be removed from the carriaand at a later time, easily repositioned to its original locatiThis feature allows for parallel and long-term scanningmultiple samples, each mounted on their own sample hol

4. Scanning table

The scanning table, which provides a smooth, lofriction surface upon which track and sample holder slidea 85-cm-diameter nonmagnetic disk made of 1.3-cm-thG-10, reinforced underneath for rigidity, and with a 6-mmthick piece of plate glass on top. The table is held insidemagnetic shield by three 2.5-cm-diameter aluminum rowhich pass through the bottom of the shield and transferweight of the table to its support structure under the shieSpecial care has been made to avoid physical contacttween the magnetic shield and the scanning system tovent stage-induced vibrations of the shield. Another presion laboratory jack~Model 281, Newport! allows for

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FIG. 4. The kinematic design of the sample-holder plate allows for accurepositioning of the samples with respect to the scanning system. A carruns along the scanning track and has three matching threaded holesfor mounting the sample-holder plate. The beveled screw A is tightefirst, then the beveled screw B, and finally the nonbeveled screw C.

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4643Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

movement of the scanning table in thez direction and is usedfor fine adjustments of the Dewar-to-sample distance. Thadjustable legs steady the support structure after the hehas been set.

C. Magnetic shield

As shown in Fig. 5, the custom-built magnetic shieconsists of three concentric cylinders made of high permability Amumetal® ~Amuneal Manufacturing Corp., Philadelphia, PA!. The outer cylinder has a diameter of 106 cand a height of 127 cm. Each cylinder is separated fromnext by a 5-cm-gap defined by aluminum bar or ring spacwhich is filled with styrofoam packaging pellets and sanbags to reduce the amplitude of the natural modes of vibtion of the shield. The shield has access ports for saminsertion/removal, observation, liquid cryogen filling, scaning table legs, and cabling; the observation and cryofilling ports have removable, three-layer shielded coveThree large lids on top of the shield provide full access tointerior. The shield assembly weighs approximately 500and is supported by a custom-built wooden structure, whallows the use of forklift or floor jacks to move the shield

The shielding factors reported by the manufacturer w51 dB for dc, and 70 dB for ac~measured at 30 Hz!. Theshield was de-Gaussed in our laboratory by 27 turns ofgauge wire that entered the shield from the observationand exited from the sample insertion/removal port and cried a peak current of 63 A at 60 Hz. The magnitudemagnetic field measured inside the shield with fluxgate mnetometer, after de-Gaussing, was below the detection l

FIG. 5. The schematic diagram of the custom-built magnetic shield.shield consists of three concentric Amumetal® cylinders. The spacetween the cylinders is filled with packaging pellets and sandbags to reshield vibrations;~1! magnetic shield;~2! liquid-cryogen-fill port with cap;~3! observation port with cap;~4! sample in/out port;~5! electronic cableport; ~6! scanning-table-leg ports;~7! shield support frame;~8! vibrationisolation pads.

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of the magnetometer~i.e., less than 1027 T!, hence the dcshielding factor measured after de-Gaussing was more66 dB.

The SQUID is supported in the center of the shield byframework of G-10 and aluminum that provides for kinmatic positioning of the Dewar, as well as adjustmentrotation and tilt to simplify alignment of the SQUID coilwith the scanning coordinate system. Figure 6 illustrates hthe SQUID magnetometer, magnetic shield, and the samscanning system are integrated in the magnetic imagingtem.

1. Vibration isolation

Mechanical vibrations of the shield produce timvarying magnetic fields, which can be sensed by the magtometer and may severely affect the quality of data, escially when measuring weak magnetic fields such as thassociated with corrosion currents. Hence, the shieldmechanically isolated from the sample-scanning systemprevent contact-induced vibrations. To reduce the coupto ground vibrations, the shield base was supported atsites with damping pads. At each site, a vertical stack of153730.6 cm vibration isolation pads~Isolation Technolo-gies, NY!, separated by 1.2-mm-thick aluminum sheets, pvided the desired damping factor. The scanning stage ron four 63630.6 cm Vibex pads sandwiched between tfloor and 6-mm-thick aluminum plates.

III. DATA ACQUISITION

All stepper motor and data acquisition parameterscontrolled through software that we wrote using LabVIEW~National Instruments™, Austin, TX! and Motion Toolbox®~Compumotor Division, Parker Hannifin Corp., RohnePark, CA!. The system is capable of data acquisition in fodifferent modes. The continuous and the stop-and-go rascan modes produce surface images. The stationary t

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FIG. 6. The SQUID is supported in the center of the shield by a framewof G-10 and aluminum. The kinematic design of the frame simplifiesadjustment of rotation and tilt of the pickup coils with respect to the scning coordinate system. The shield is mechanically isolated from the sning system to prevent contact-induced vibrations.

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4644 Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Abedi et al.

base mode allows for temporal data acquisition from a scific location above the sample, and the raster time-bmode allows for repetitive data acquisition along a specscan line. The effects of high-frequency noise are reduthrough oversampling and averaging by the data acquisisoftware. Low- and high-pass filtering, gain, dc baseline,other SQUID parameters are set through the SQUID contler.

A. Data acquisition modes

1. Stop-and-go raster scan mode

In the stop-and-go raster scan mode, the user selectmaximum and minimum travel limits, and the step sizeeach scan axis; the software selects the specified grid pwithin this area. The scanning system positions the samunder the magnetometer at the specified grid points, waitsan operator-specified time prior to data acquisition for avibrational transients to die down, and acquires the specinumber of samples at the desired rate. The average of tsamples is then recorded. This approach has the advantaease in programming, but the greater disadvantages ofspeed, agitation of corrosive solutions due to numeracceleration/deceleration periods, and increased cumulapositioning error, and hence is seldom used.

2. Continuous raster scan mode

In the continuous raster scan mode, data are acquirethe sample is scanned under the magnetometer at a conspeed along the fast axis of the scanning system. To mmize backlash and vibrations, and to allow room for acceration of the stage to the desired speed, the scan line stamm outside the scan area. The acceleration of the motocontrolled by the software to ensure that the samplereach the desired scanning speed within the first 2.5 mmtravel. To provide a consistent starting point for data acqsition, the motor indexer confirms that for each scan linedesired constant speed has been achieved, and then trithe data acquisition as the initial sampling locationreached. To ensure accurate spatiotemporal sampling,acquisition is carried under hardware control, using the AMIO onboard timing circuitry, rather than the main CPclock of the computer. To minimize any hysteresis in tpositioning of the sample due to friction between the glsurface of the scanning table and the Teflon feet of theriage, and to minimize the associated vibrations, dataacquired only as the sample is pulled under the magnetoter rather than pushed. After each scan line, the sampthen moved one step along the perpendiculary axis andpushed back to the startingx coordinate. The process is repeated until the desired scan area has been covered.

3. Stationary time-base mode

In this mode, the desired location of the sample is potioned under the magnetometer and data acquisition isducted for the user-defined duration, sampling rate~up to 6kHz for each SQUID channel!, and decimation factor.

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4. Raster time-base mode

The raster time-base mode is similar to the continuoraster scan mode with the exception that the sample ispeatably scanned along thex axis at a fixedy coordinate. Atthe end of each scan line, data acquisition is delayed fouser-specified period of time before repeating the same sThis mode is especially useful for tracking rapid changesthe field over a particular region of the sample.

B. Spatial and temporal sampling

In imaging that utilizes spatial scanning of SQUID manetometers, there are a number of variables that affect imresolution. There are tradeoffs between spatial and tempresolution, and scanning speed. To obtain the best imagis important to understand the relationship and limitationsthese variables. We will analyze these in only one dimsion; the results are directly applicable to two-dimensioimages. The relevant variables are listed in Table I.

1. Spatial domain

We will consider the object that we are imaging to besource of magnetic field, for example a distribution of curent or magnetization. The image we obtain is a map ofmagnetic field measured by the magnetometer. The obO(x), has a spatial frequency spectrum, 0(k), for spatialfrequencies lower than the object cutoff frequencykoc. Weassume that there is no information fork.koc, i.e.,

0~k!'0, for k.koc. ~1!

If the cutoff is not sharp, a 3 dBpoint can specifykoc and theother cutoff frequencies used in this analysis.

For our measurements, the SQUID magnetometesome distance from the object. Because of the finite sizethe sensor and the attenuation of magnetic field with distafrom the object, the magnetometer acts as a spatial low-pfilter.15–18 Thus we can only obtain information for spatifrequencies lower than the magnetometer cutoff frequenkmc. The spatial response of the magnetometer is givenh(k), where we assume that

h~k!'0, for k.kmc. ~2!

TABLE I. Variables used for the analysis of spatial and temporal sampl

Variable Name Units

v Speed of stage ~mm/s!Nd Decimation factor ~dimensionless!N0 Oversampling factor ~dimensionless!

Temporalf mc Magnetometer low-pass cutoff frequency ~s21!f N Nyquist temporal sampling frequency ~points/s!f a Actual temporal sampling frequency ~points/s!

Spatialkic Image low-pass cutoff spatial frequency ~mm21!kN Nyquist spatial sampling frequency ~points/mm!kd Desired spatial sampling frequency ~points/mm!ka Actual spatial sampling frequency ~points/mm!koc Object cutoff spatial frequency ~mm21!kmc Magnetometer cutoff spatial frequency ~mm21!

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4645Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

FIG. 7. Imaging in the spatial frequency domain;~a! the frequency spectrum of an object. The minimum object spatial frequencykminocis limited by the

physical dimensions of the object,Dxmax. The size and distribution of the smallest features within the object,Dxmin , determines the shape and value of tmaximum object cutoff frequencykmaxoc

; ~b! the frequency response of magnetometer. The minimum magnetometer spatial cutoff frequencykminmcis

determined by the dimensions of the scan area. The maximum magnetometer spatial cutoff frequencykmaxmcis set primarily by the larger of the pickup coi

diameter or liftoff~i.e., the magnetometer spatial resolution!. ~c! The resulting image frequency spectrumi (k) is the product of the object and magnetometspectra.

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The image,I (x), is the sampled magnetic field obtaineby the scanned magnetometer. In the spatial frequencymain, the imagei (k) is given by

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The spatial cutoff frequency of the image,kic , determined byboth koc andkmc, as shown in Fig. 7, provides a conveniemeasure of the highest spatial resolution achievable withmagnetometer. The spatial sampling used to record theage must obey the Nyquist theorem, in that

kN>2kic'2kmc. ~5!

2. Temporal domain

In cases where the magnetometer is scanned at astant velocity relative to the object, the spatial frequencare manifest at the time of recording as temporal frequencThe challenge is to understand how to relate the tempand spatial frequencies and to avoid aliasing of either imor noise at the time of recording.

For simple magnetometers, it is reasonable to assthat the temporal cutoff frequency,f c , is the highest temporal frequency of information that could be present whilecording the image, as determined by the antialiasing filterthe data acquisition system or the magnetometer. Accordto the Nyquist theorem, to prevent data aliasing, at leastsamples must be made per cycle at the cutoff frequency.Nyquist temporal frequency,f N , is the minimum samplingfrequency set by the Nyquist limit, i.e.,

f N52 f mc. ~6!

In practice the actual temporal sampling frequency,f a , islarger thanf N by the oversampling factorN0 , or

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For a scan at velocityv, the Nyquist spatial frequencykN , is the Nyquist temporal frequency divided by scannivelocity

kN52p f N /v. ~8!

The actual spatial sampling frequency,ka , is the actual tem-poral sampling frequency divided by the stage speed

ka52p f a /v. ~9!

If ka is greater than the desired spatial frequency,kd , theextra samples can be eliminated by decimating the sigOne way to do this is to average groups of points, therereducing the number of samples in the image. The numbepoints to be averaged is simply

ka /kd5Nd , ~10!

which defines the decimation factor. If the temporal noisethe signal is incoherent, the signal-to-noise ratio will be iproved by a factor ofANd. Note that if the scanning velocityis set too high for a chosen sampling frequency,f a , andcutoff frequency,f mc, it is possible for the resulting spatiasampling frequency to violate the Nyquist limit in space. Itimportant to confirm that

ka.2kmc. ~11!

Table II shows an example of the settings used for the abvariables in a typical scan.

In imaging of samples where the magnetic field chanin time, the goal is to optimize not only the spatial resolutiobut also the temporal resolution of the scanned image.effective temporal resolution provided by sequential imagdepends on the time it takes to scan the entire image;hence, increasing the speed of the scan improves its tempresolution. However, for a given spatial resolution, thecrease in speed of the stage results in an increase inrequired sampling frequency. Since the data acquisition chas a maximum analog-to-digital conversion rate, there isupper limit to the scanning frequency, and hence the scning speed. At this regime, a further increase in speed m

4646 Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Abedi et al.

TABLE II. Example of the settings used for a typical SQUID scan.

1 Magnetometer low-pass filter set at 500 Hz f mc5500 s21

2 Nyquist temporal sampling frequency is 1 kHz@Eq. ~6!# f N51000 points/s3 Oversample by a factor of 2 N0524 Actual temporal sampling frequency set to 2 kHz@Eq. ~9!# f a52000 points/s5 Stage speed is set at 30 mm/s v530 mm/s6 Nyquist spatial sampling frequency is 33.3 points/mm@Eq. ~6!# kN533.3 points/mm7 Actual spatial frequency is 66.7 points/mm ka566.7 points/mm8 For a pickup coil with a radius of 1 mm positioned less than

1 mm from the sample, the cutoff frequency is 3.8 mm21,akmc53.8mm21

9 Confirm that the actual spatial frequency is at least twice thecoil cutoff spatial frequency@Eq. ~11!#

ka.7.7 points/mm

10 From knowledge of the sample and the SQUID, the desiredspatial frequency is set at 2 points/mm

kd52 points/mm

11 The decimation factor is 33 Nd533

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result in spatial undersampling and loss of spatial resolutFurthermore, increasingf a requires either a reduction of thoversampling and decimation factors or a wider magnetoter bandwidth, which reduces the signal-to-noise ratio. Csequently there are tradeoffs between spatial and tempresolution and signal-to-noise ratio, and for each systemshould optimize the above factors to achieve the desiredtiotemporal resolution and sensitivity.

C. System stability and long-term studies

1. Factors affecting signal stability

Corrosion of aluminum can be a slow process: in typi40 year service lifetime, a military aircraft may lose throucorrosion 10% of the thickness of a 1.2 mm thick fuselaskin, and that only in selected areas. The electrochemdissolution of 100mm of aluminum over 40 years producestotal current of approximately 150 nA/cm2. The magneticfield from such corrosion activity could be as large as 7 pTthe surface of the metal, but may be orders of magnitsmaller due to corrosion currents flowing over very smspatial scales that do not contribute significantly to the mnetic field outside the sample.4 While scanning SQUID magnetometers are capable of imaging these weak fields,weakness of the magnetic field from slow corrosion andfact that the field strength varies only slowly with time prsents particular challenges, particularly because of thecrease of both SQUID and environmental noise with decreing frequency.

Because the experimenter cannot readily modulatelevel of activity of the corrosion process, common lock-amplifier techniques cannot be used to upconvert the vlow frequency corrosion activity into a narrow bandwidthhigher frequencies, where the effects of SQUID and envirmental noise are less significant. Because the sample cascanned relative to the SQUID, the next obvious technifor eliminating the effects of these two noise sources ishave each scan extend sufficiently far beyond the samplethe magnetometer is no longer affected by the samplethat distant reference point, ideally the sole contributionsthe magnetometer output are the magnetic field withinshield and any offset, e.g., drift, that has appeared onmagnetometer output since the last time the magnetom

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was at the reference point.~Because the nonmagnetic sampis scanned while the SQUID is held stationary, any gradiein the magnetic field within the shield do not affect the images.! The magnetometer output at the end of such a scanthen be subtracted from all data points elsewhere alongscan, thereby correcting for drift in the environmental manetic field and the magnetometer output. This process isspatial equivalent of the classical technique of using temral chopping in a dc-coupled measurement. As we will slater in this section, the implementation of this approach wscanning SQUID magnetometers presents its own set officulties.

If the sample were perfectly nonmagnetic and isothmal, the corrosion activity would be the only source of manetic field, and the measurement of the time dependenccorrosion over the course of days or weeks wouldstraightforward: the instantaneous magnetic field woulddetermined solely by the instantaneous corrosion activHowever, even nonferrous materials such as aluminumcraft components can exhibit remnant magnetization frferromagnetic contamination or inclusions that are ordersmagnitude larger than the magnetic field due to corrosion.long as the remanent magnetic field is stable in time, andongoing corrosion activity can be temporarily halted~for ex-ample, starting with a dry sample or by dehydrating an owet one through vacuum baking!, the fields due to remanenmagnetization can be measured independently to providreference image that can be subtracted from subsequenages that are recorded when corrosion is occurring. Subttion of images recorded days or weeks apart places newstraints on system stability. If the remanent magnetizationot stable in time, for example, because of thermal relaxaor corrosion of the magnetized material, it may be difficultdelineate these field sources from corrosion. The obvisolutions are to avoid ferromagnetic contamination ofsamples and to use ac demagnetization in a low ambmagnetic field to minimize the remanent magnetization.

Given the weakness of the corrosion magnetic field,SQUID must be operated either in a high sensitivity moi.e., with a high gain within the flux-locked loop, or withhigh gain after the flux-locked loop. The presence of dc osets from instrument drift, the environmental field, or remnent magnetization in the sample can limit the total gain t

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4647Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

can be used. If the magnetometer and the data acquissystem are both dc coupled, then any substantial driftsoffsets will require a large dynamic range in both the flulocked loop and the analog-to-digital converter~ADC!. Sincethe corrosion signals can be small relative to the drifts aoffsets, a 16-bit or higher resolution ADC may be requiredavoid the addition of quantization noise to the corrosion snal.

2. Removal of drift and offset

a. Electronic offset subtraction. At the beginning or endof each scan, it is possible to remove offsets on the SQUoutput prior to a high gain amplifier and the ADC by usingsample-and-hold circuit at the inverting input of a differetial amplifier. We constructed an offset reset control~ORC! which contained a sample-and-hold circuit with a sficiently low drift capacitor to hold a reference voltage witout significant drift for the length of time required to complete a typical scan line. The scanning software was modito position the sample under the magnetometer at a particreference point on each scan line, away from the corrossite, and to trigger the ORC to store the reference voltprior to the start of data acquisition for each scan line. Tsample was then scanned under the magnetometer inusual stop-and-go fashion and the SQUID output was stracted electronically from the reference voltage stored inORC. This procedure was repeated until the desired areabeen scanned. This technique can reduce the offsetsoftware-controlled manner, restricted by changes in offsduring a single scan. For our measurements, we found thdrifting offset limited the use of the ORC to relatively smascan areas and short-term studies. Because the ORC hbe placed before the high-gain amplifier, it contributed noto the low-level signals from weak corrosion.

b. Offset removal by filtering. A lower noise and techni-cally simpler solution for removing drifts and offsets priorhigh-resolution digitization was to ac couple the SQUID oput to the ADC by means of high-pass filter in the SQUcontroller ~3 dB at 0.3 Hz!. While corrosion is a quasi-dcprocess, our scanning approach and our restricted sasize allow us to filter out the very lowest frequencies.

In the continuous raster scan mode, the spatial frequcies in the magnetic field distribution are manifest as temral frequencies scaled by the speed of the scan. A temphigh-pass filter applied to the SQUID output attenuatestemporal frequencies below the high-pass cutoff freque( f hc50.3 Hz). To convert this value to spatial frequency,units of mm21, we divided by the scanning speedv mea-sured in mm/s

khc52p f hc/v. ~12!

The scanning speeds used by the system range from 10mm/s. As a worst case scenario, for the minimum scannspeed of 10 mm/s, the application of the 0.3 Hz tempohigh-pass filter only attenuates spatial frequencies lower t0.02 mm21. This spatial frequency suggests that, for thspeed, the high-pass filter will attenuate spatial data cosponding to source separations of order of 33 mm and abIn practice, the source separations for our samples are m

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smaller than the limit set by the high-pass filter, in fact, fall scanning speeds within the above-mentioned range,coupled data acquisition results in no significant loss of dand allows the system to operate with a larger analog gthan would otherwise be possible. The major disadvantagthis approach is that it does not remove drift at the inputthe SQUID so that occasionally the SQUID will exceed tdynamic range of the flux-locked loop and will automaticareset. The resulting jump in the output will be high-pafiltered and will produce a long tail with an exponential timconstant equal to that of the high-pass filter. This transican then be removed by signal processing with only miloss of data. A possible alternative would be to couple tprocess with a digital reset of the SQUID at the beginningeach scan.

While filtering is an affective solution to the drift angain problems, the Ac-coupled magnetic field waveforB8(t) differ from the true, dc-coupled magnetic fieldB(t) bya term proportional to the integral of the observed sigdivided by the effective time constantt of the system20,21

B~ t !5B8~ t !11/tE B8~ t8!dt8. ~13!

The time constantt of the system was experimentally mesured to be 0.5360.04 s. Equation~13! can, for our measurements, be converted to a discrete summation over the spasampling positionsxi :

B~xi !5B8~xi !1Dx

vt (xi

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where xi5 iDx, for i 51,2,...,i max, and i max corresponds tothe total number of sampling sites along thex axis and wehave replaceddt with Dx/v.

This expression reveals the velocity dependence ofobserved signals. We can use Eq.~14! to recover the originalsignal up to an additive constant that is equivalent toarbitrary dc offset. Figure 8 demonstrates how the abtransformation recovers the original signalB(x) from theobserved signalB8(t), measured at five different scanninspeeds, above a 2-cm-diameter loop of wire carrying 0mA of current.

Since the conversion of the observed signal to the acmagnetic field includes a line-by-line spatial integrationeach raster scan, the scan area should be selectedenough to contain essentially all of the magnetic field ofcorroding region. Since the dc baseline for each scan lindetermined by the value of the first data point in that linvariations in this value between lines will change the dc lefor that line; if the variation is large enough, there will beline-by-line dc shift, which could either be a true contribtion from the sample or due to system drift. Although moof these shifts can be removed from the image by postpcessing, the appropriate preventative technique, carried othe time of the scan, is to enlarge the scan area to inclample margins around the corroding area where the magnfield does not contain large lateral~line-to-line! gradients.This reduces the possibility of artifacts and minimizes ttime required for postprocessing computations. A refinemof this approach is to make one or more scans along the

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4648 Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Abedi et al.

FIG. 8. Converting the ac-coupled magnetic field waveformsB8(x) to the true, dc-coupled, waveformsB(x). ~a! The output of the magnetometer in the amode,B8(x), for five different scanning speeds. The source of magnetic field is a 2-cm-diameter coil carrying a dc current of 0.5 mA.~b! The correction termfor each speed~i.e., the term containing the summation in Eq.~14!. ~c! The comparison of the recovered magnetic field@B(x) in Eq. ~14!#, with the actualoutput of magnetometer in the dc mode~lower curve!. In the above data, the actual magnetic field is recovered, with the exception of the dc baseline, tothan 3%.

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of reference positions or even around the entire perimetethe scanned area to determine the field distribution arothe edges, and to use these values, rather than an asszero field at the reference points, as the constraint inrestoration.

IV. NOISE SOURCES AND REDUCTION

Typically, magnetic fields due to corrosion are no largthan a nano-Tesla, so that the system noise can be antremely important limiting factor in measurements of weakcorroding samples. We previously discussed how the proselection of sampling rate and both analog and digital filting are required to optimize the signal-to-noise ratio ofimages. Even more important is to address system nfrom ground loops and electromagnetic interference fromto rf. The major sources of noise for our system are describelow.

A. Ground loops

Careful attention was paid to ground loops which wouotherwise result from the interconnection of a large numof different electronic instruments. To remove this problethe building earth ground was connected to the SQUID etronics and the Faraday cage that enclosed them, and hto the data acquisition card via the cable shield. The cthereby provides the ground to the computer chassis. Sboth the motor electronics~via the motor controller card!,and the computer monitor~via the VGA cable!, were con-nected to the computer, the computer and monitor were pered through an isolation transformer~Stancor, GIS-500!,and the motor control electronics~AT6400, and zeta drives!were powered through another isolation transformer~Stan-cor, GIS-1000!.

B. Stepper motor electronics noise

Stepper motors and their drive amplifiers generated sstantial electromagnetic noise which required significanttention to shielding and elimination of ground loops; newdesigns of motors and amplifiers, or dc motors, may redthis problem. We addressed this problem by placingmotor-control electronics in a metal chassis, by routingmotor cables through braided shields, and by locating

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stage and its motors away from the magnetometer. Also,reduced the remaining high frequency contribution from mtor drive electronics by low-pass filtering of the magnetomter output prior to data acquisition.

C. rf shield

Since our SQUID system did not include an integcryogenic rf shield, it proved to be sensitive to rf radiatioTo minimize this problem, SQUID flux-locked loop electronics, and the control electronics were placed in a pairaluminum rf shields connected by rigid copper pipe. Powfor the SQUID controller was provided by rf feedthroughThe entire rf shielding assembly was grounded via a loresistance conductive path to the main ground. The electrcables between the FLL and the iMAG were threadthrough toroidal filter cores~Part No. 5977003801, FairwriteProducts Corp., Wallkill, NY!.

D. SQUID jumps

Possibly because of the lack of a rf shield, or as a reof the design of the Conductus SQUID sensors, the SQUoccasionally exhibited excess noise or flux jumps in all chnels, mostly triggered either by they-axis channel itself, orby noise preferentially detected by that channel. For mastudies, we utilize only thez-axis channel and achievgreater system stability.

V. ADDITIONAL ISSUES

A. Heaters

Due to high humidity in the lab, and the 5 liter per daboil off of the Dewar with the closely spaced tail, we ecountered condensation on the connectors betweenSQUID sensors and the flux-locked loop. This problem wsolved by installing 30V, coaxial resistance heaters on eaconnector, connected to a 10 V dc-power supply~HewlettPackard, E610A!.

B. System calibration, tilt/rotation adjustment, andcentering

We devised a sample holder equipped with coils awires for calibration, rotation, tilt adjustment, and centeri

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4649Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

of the SQUID magnetometer with respect to the scanncoordinates. We used two wires forming a cross hair, ctered about the sample holder, to determine the relativesition of the pickup coils with respect to scanning coornates. A 2-cm-diameter loop, also centered about the samholder, allowed us to determine the orientation of thex andy-pickup coils with respect to scanning coordinates andlevel the pickup coils with respect to the scanning table.used two 30 cm long, straight wire segments for calibratof the magnetometer by comparing the measured imagthe magnetic field due to a known current flowing throueach wire with its predicted value.

VI. PRELIMINARY DATA

A. Alignment of the pickup-coil axes with thescanning system

Figure 9 shows the simultaneously measured comnents of the magnetic field above a 2-cm-diameter loopwire carrying a current of 0.5 mA. The image was obtain

FIG. 9. A simple technique for determination of the position, orientatiand tilt of the SQUID pickup coils with respect to the scanning coordinaImages~a!, ~b!, and ~c! represent the simultaneously measuredz, y, andxcomponents of the magnetic field above a 2-mm-diameter loop of wcarrying a current of 0.5 mA. The axis of symmetry in~b! and ~c! suggestthat a clockwise rotation of the SQUID Dewar by 21 degrees is necessaalignment of thex- andy-component coil axes. The difference in the manitude of the positive and negative peaks in bothx- andy-coordinate imagesprovides the necessary information for adjustment of the dewar tilt to athe axis of thez-pickup coil to be perpendicular the surface of the scanntable.

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for the subsequent alignment of the coil axes with the scning coordinates. The orientation of the symmetry axis ofimages ofx andy components of magnetic field determinthe rotation angle necessary to align the coil axes withscanning coordinates. The difference in magnitude ofpositive and negative peaks in bothx- andy-coordinate im-ages provides the information necessary for us to tiltdewar to align the axis of thez-pickup coil perpendicular tothe surface of the scanning table.

B. Aluminum corrosion

The bottom surface of a 7 cm diameter, 1.2 mm thickdisk of 7075-T6 aluminum was exposed to a 0.5 M NaOsolution at room temperature for a period of 33 h. The iages shown in Fig. 10 present the change in thez componentof the magnetic field above the corroding sample for the fi18 h of this experiment. All data are subtracted from the fi~dry sample! image. Clearly, the change in magnetic fieldlocalized to the area of the sample and displays compspatial and temporal structures at spatial scales of sevmillimeters or larger.

C. Detection of slow corrosion

The bottom ~hidden! surface of a 2024-T3 aluminumplate, with dimensions of 7537531.2 mm, was exposed aroom temperature to a slow-corrosion cocktail typical of thfound in old aircraft lap joints.22 Figure 11 represents thphotograph of the corroded surface of the plate and themulative magnetic activity of the sample recorded over 19of exposure. This experiment demonstrates that the systesufficiently sensitive to detect corrosion activity at nonaccerated, realistic, corrosion rates.

VII. DISCUSSION

The SQUID magnetometer system reported in thisticle was designed for noninvasive measurements of the

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FIG. 10. Spatiotemporal variation in magnetic field of an aluminum sample undergoing hidden corrosion. The bottom surface of a 7 cm diameter, 1.2 mmthick, disk of 7075-T6 aluminum was exposed to a 0.5 M NaOH solution for 33 h. The above images present the change in thez component of the magneticfield due to electrochemical corrosion for the first 18 h of the experiment. The magnetic activity is localized to the area of the sample and exhibitslexspatial and temporal structure.

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4650 Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Abedi et al.

of hidden corrosion in aircraft aluminum alloys with planageometries; however, its use can be extended to all nonmnetic metals. The kinematic design and automation capabties incorporated in the system allows for long-term studi~months!, as well as repeatable measurements of the corsion magnetic field of multiple samples. This featurcoupled with the magnetic and rf shielding, makes the stem ideal for laboratory investigation of hidden corrosion fovarious metal-solution combinations covering a large spetrum in corrosivity. Furthermore, the system has the sensitity to detect~in real time! the magnetic field due to extremelylow corrosion rates typical of aircraft lap joints; at these ratit often takes years before the corrosion-related thickneloss of the aircraft fuselage can be measured by other ninvasive techniques. This provides a unique advantage ining the SQUID magnetometers for hidden corrosion studi

We are in the process of utilizing this instrument inpair of studies of corrosion in aircraft aluminum. The firstdesigned to determine the quantitative relationship betwecorrosion activity and magnetic field, and utilizes samplwith a carefully controlled geometry.23,24 The second in-volves nondestructive measurements of corrosion injoints removed from aging KC-135 and Boeing-70aircraft.25 Other applications under consideration include thmagnetic measurement of filiform corrosion under paint, efoliation corrosion within thick aircraft wing planks, and theffectiveness of corrosion prevention compounds in preveing hidden corrosion.

Because properly prepared and treated aircraft docorrode rapidly, the magnetic fields associated with corsion in aircraft aluminum are weak relative to the geomanetic field, environmental magnetic noise, the magnetic fiefrom ferromagnetic fasteners, and the magnetic fields resing, from thermoelectric currents associated with tempeture gradients and galvanic fields associated with contacttween dissimilar metals. Each of these other field sourcesbe controlled in a laboratory environment either througmagnetic shielding, the use of the stationary magnetomeor gradiometer, or proper sample preparation and degaustechniques. There will be, of course, certain types

FIG. 11. Noninvasive detection of slow, hidden corrosion.~a! Photomicro-graph of the lower~hidden! surface of a 3-in. square sample of 2024-Taluminum that was exposed to a corrosive solution typical of an aircraftjoint. The dark gray area in the upper center of the image correspondnoncorroded aluminum.~b! The cumulative magnetic activity of the sampleshowing the more active regions in white and the less active ones in dgray.

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samples, such as ones with large ferromagnetic fastenerswhich it may be difficult to separate the corrosion signfrom that due to other sources. However, at present it seunlikely that this technique can be extended to measuremof corrosion signals in intact aircraft on the flight corrosioline. Even so, there is ample research that can be conduwith a laboratory SQUID instrument that is not possible wany other measurement technique.

The SQUID magnetometer system we describe shoprove to be a valuable laboratory tool for understandingprinciples underlying the generation of the corrosion manetic field and for developing appropriate models that relathe spatiotemporal variations in corrosion magnetic fieldcorrosion rate, spatial distribution, and perhaps the typehidden corrosion. The preliminary data clearly show coplex spatiotemporal variations in corrosion magnetic fiewhich suggest that a subset of corrosion information canmeasured noninvasively with this instrument. This informtion may be invaluable for better understanding the dynamof hidden corrosion, and for developing realistic models tcan predict the long-term behavior and rate of corrosionoccluded regions.

ACKNOWLEDGMENTS

The authors would like to thank Anthony P. Ewing fohis editorial suggestions and Carlos Hall for his valuacomments regarding spatial aliasing. This work was sported in part by NCI Information Systems, Inc. through AForce Contract No. F09603-97-D-0550, Task Order 91002, and by AFOSR Grant No. F49620-93-0268.

1J. R. Kirtley and J. P. Wikswo, Jr., Annu. Rev. Mater. Sci.29, 117~1999!.2J. G. Bellingham, M. L. A. MacVicar, M. Nisenoff, and P. C. Searson,Electrochem. Soc.133, 1753~1986!.

3J. G. Bellingham, M. L. A. MacVicar, and M. Nisenoff, IEEE TransMagn.23, 477 ~1987!.

4A. D. Hibbs, J. Electrochem. Soc.139, 2447~1992!.5B. D. Jette and M. L. A. MacVicar, IEEE Trans. Magn.27, 3025~1991!.6M. Misra, S. Lordi, and M. L. A. MacVicar, IEEE Trans. Magn.27, 3245~1991!.

7A. D. Hibbs, R. E. Saeger, D. W. Cox, T. H. Aukerman, T. A. Sage, aR. S. Landis, Rev. Sci. Instrum.63, 3652~1992!.

8D. S. Buchanan, D. B. Crum, D. Cox, and J. P. Wikswo, Jr.,Advances inBiomagnetism, edited by S. J. Williamson, G. Hoke, G. Stroink, and MKotani ~Plenum, New York, 1990!, p. 667.

9Y. P. Ma and J. P. Wikswo, Jr., Rev. Sci. Instrum.62, 2654~1991!.10D. Li, Y. P. Ma, W. F. Flanagan, B. D. Lichter, and J. P. Wikswo, J

Proceedings of the Tri-Service Conference on Corrosion Washington,~Department of Defense, 1994!, p. 335.

11D. Li, Y. P. Ma, W. F. Flanagan, B. D. Lichter, and J. P. Wikswo, Jr.,Min. Metals Mater.47, 36 ~1995!.

12D. Li, Y. P. Ma, W. F. Flanagan, B. D. Lichter, and J. P. Wikswo, JCorrosion~Houston! 52, 219 ~1996!.

13D. Li, Y. P. Ma, W. F. Flanagan, B. D. Lichter, and J. P. Wikswo, JCorrosion~Houston! 53, 93 ~1997!.

14W. G. Jenks, S. S. H. Sadeghi, and J. P. Wikswo, Jr., J. Appl. Phys30,293 ~1996!.

15B. J. Roth, N. G. Sepulveda, and J. P. Wikswo, Jr., J. Appl. Phys.65, 361~1989!.

16J. P. Wikswo, Jr., Electroencephalogr. Clin. Neurophysiol.69, 266~1987!.17S. Tan, B. J. Roth, and J. P. Wikswo, Jr., Electroencephalogr. Clin. N

rophysiol.76, 73 ~1989!.18SQUID Sensors: Fundamentals, Fabrication and Applications, edited by

J. P. Wikswo, Jr. and H. Weinstock~1996!.19B. J. Roth and J. P. Wikswo, Jr., Rev. Sci. Instrum.61, 2441~1990!.

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4651Rev. Sci. Instrum., Vol. 70, No. 12, December 1999 Hidden corrosion activity

20J. P. Wikswo, Jr., J. P. Barach, and J. A. Freeman, Science208, 53 ~1980!.21J. P. Barach, J. A. Freeman, and J. P. Wikswo, Jr., J. Appl. Phys.51, 4532

~1980!.22Provided by K. S. Lewis and R. G. Kelly at the University of Virginia

Listed as ion/ppm: Na/870; K/2335; Sr/48; Ca/53.2; Al/1914; Cu/28; M1333; Mn/159; Zn/10; Cl/10; NO2/160; SO4/483; NO3/44; F/9; HPO

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23A. Abedi and J. P. Wikswo, Jr.~unpublished!.24A. Abedi and J. P. Wikswo, Jr.~unpublished!.25R. G. Skennerton, A. Abedi, and J. P. Wikswo, Jr., J. Corr. Sci. E

~submitted for publication!.