Curie point, susceptibility, and temperature measurements of rapidly heatedferromagnetic wiresMuhammad Sabieh Anwar and Wasif Zia Citation: Review of Scientific Instruments 81, 124904 (2010); doi: 10.1063/1.3525797 View online: http://dx.doi.org/10.1063/1.3525797 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/81/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Determining Curie temperatures in dilute ferromagnetic semiconductors: High Curie temperature (Ga,Mn)As Appl. Phys. Lett. 104, 132406 (2014); 10.1063/1.4870521 Spatially resolved measurements of the ferromagnetic phase transition by ac-susceptibility investigations with x-ray photoelectron emission microscope Appl. Phys. Lett. 96, 122501 (2010); 10.1063/1.3360205 Distinguishing local moment versus itinerant ferromagnets: Dynamic magnetic susceptibility J. Appl. Phys. 103, 07D302 (2008); 10.1063/1.2832349 Dependence of the high-field grain-boundary magnetoresistance of ferromagnetic manganites on Curietemperature J. Appl. Phys. 99, 053904 (2006); 10.1063/1.2177929 Limits on the Curie temperature of (III,Mn)V ferromagnetic semiconductors Appl. Phys. Lett. 78, 1550 (2001); 10.1063/1.1355300

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REVIEW OF SCIENTIFIC INSTRUMENTS 81, 124904 (2010)

Curie point, susceptibility, and temperature measurements of rapidlyheated ferromagnetic wires

Muhammad Sabieh Anwara) and Wasif ZiaLUMS School of Science and Engineering, Lahore University of Management Sciences (LUMS),Opposite Sector U, DHA, Lahore 54792, Pakistan

(Received 3 September 2010; accepted 18 November 2010; published online 30 December 2010)

This article describes a technique to measure the temperature of a resistively heated ferromagneticwire. The wire’s temperature rapidly increases, a scenario in which a thermocouple or thermistor’sthermal inertia prevents it from keeping up with the rapid temperature variation. The temperatureis derived from electrical measurands (voltage and current) and time, as well as thermophysical datasuch as heat losses and emissivity, and is based on a dynamical thermal–electrical energy conservationprinciple. We go on to use our technique for the quantitative determination of the Curie point aswell as the magnetic susceptibility at elevated temperatures. The results are in good agreement withaccepted values. © 2010 American Institute of Physics. [doi:10.1063/1.3525797]

I. INTRODUCTION

Magnetic phase transitions and temperature-dependentmagnetic properties are routinely investigated for the char-acterization and optimization of new magnetic materials.1, 2

Such materials are used in a wide range of applications, suchas magnetoresistive sensors, nanomagnetic particles, colos-sal magnetoresistance materials, diluted magnetic semicon-ductors, and spintronics. The two most important magneticreordering temperatures are the Curie and Nèel tempera-tures, indicating, respectively, the transition from ferromag-netism or antiferromagnetism to paramagnetism. The Curiepoint can be determined by a change in some physical prop-erty near the critical point. Commonly investigated propertiesinclude the temperature derivative of the resistivity,3 mechan-ical yield strength,4 volume magnetostriction,5 and differen-tial scanning calorimetry.6 In the present work, we determinethe Curie point of a ferromagnetic resistive heating elementfrom its temperature-dependent interaction with a permanentmagnet.

Ferromagnetic heaters are an important class of mate-rials. They are characterized by their small temperature co-efficient of resistivity and enjoy widespread use in heatingapplications. The emblematic material is nichrome which,dependent on the exact composition (Ni/Cr/Fe), can be fer-romagnetic or nonmagnetic. As these materials heat up withthe passage of electric current, their magnetic properties shift.The magnetic susceptibility changes and eventually at theCurie point, the phase transition to the paramagnetic statetakes place. The present work aims at finding the Curie pointof these materials using an analytical expression based on theelectrical energy input and energy internalized or lost by thematerial, the basic idea being derived from the pedagogicalwork.7 We show that with a knowledge of the sample’s geo-metrical and thermophysical properties such as the emissivityand coefficient of heat loss, one can use a stop watch as a ther-mometer, meaning that the time duration of heating, voltage,and current determines the instantaneous temperature. Here,

a)Electronic mail: sabieh@lums.edu.pk.

we report the major improvements and generalizations to theinsightful experiment performed by Kizowski and co-workersand also show that in these rapid heating processes, temper-ature measurements with a thermocouple will be inaccuratedue to the effects of thermal inertia and the damped thermo-couple response.8–10

II. THE EXPERIMENT

A. Setup and basic idea

The experimental setup is shown in Fig. 1. The idea isto electrically heat the ferromagnetic wire until it reachesthe Curie temperature, marked by the wire snapping awayfrom an array of disk-shaped permanent magnets placed in thevicinity of the wire. A variac supplies ac current to the wireand is controlled by a custom circuit equipped with a mag-netic contactor, emergency stop button, circuit breaker, andon–off push-buttons. Figure 2 shows the internal schematicof the control circuit. For the direct measurement of the wiretemperature using a thermocouple, a data acquisition card(National Instruments PCI 6221) and a signal routing module(SCC-68) were used while all data acquisition and processingprograms were written in MATLAB and LABVIEW.

We describe experiments measuring temperature, theCurie point, and susceptibility performed on the elementalwires iron and nickel (purity 99%) as well as a commonlyused resistive heating element called Kanthal-D. The latter isa mixture of C (0.08%), Si (0.7%), Mn (0.5%), Cr (0.23%,max), Al (4.8%, nominal), and Fe in the balance.11 The nickeland iron wire are 1m in length, spiralled into the form of aspring and connected to the circuit through ceramic connec-tors affixed onto a metallic pole. The wire is attracted by thepermanent magnets, and carefully filed disks of alumina sili-cate ensure electrical and thermal insulation between the wireand the magnet. For Kanthal, five wires of length 29.5 cm arecrimped together and connected with the circuit using spadeconnectors. In this way, we have a multistranded wire of fer-romagnetic Kanthal.

0034-6748/2010/81(12)/124904/5/$30.00 © 2010 American Institute of Physics81, 124904-1

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124904-2 M. S. Anwar and W. Zia Rev. Sci. Instrum. 81, 124904 (2010)

CeramicInsulators

AluminaSilicate disc

(b)

TC

PC, DAQsystem

Operated by control circuit

magnets

FIG. 1. (Color online) (a) The thermocouple bead snugly cuddled inside mica leaves and placed in between the wires. The wire is being attracted to thepermanent disc magnets. (b) A schematic of the setup used to measure the Curie temperature of the ferromagnetic alloy.

B. The energy balance equation

The experiment requires one to note down the voltage V ,current I , and measure time t , using a stopwatch, from theinitiation of the current to the wire’s departure from the insu-lated disk magnets. The product of the mentioned quantitiesgives the electrical energy supplied which is equated with thesum of the internal energy gained by the ferromagnet and theenergy dissipated in convection and radiation processes. Con-sider an infinitesimally small time interval dτ . Energy preser-vation during dτ yields

V I dτ = mc[T (τ + dτ ) − T (τ )]

+ Sh[T (τ + dτ ) − Tr ] dτ

+ Sσε[T 4(τ + dτ ) − T 4

r

]dτ. (1)

The second and third terms on the right hand side representthe convective and radiative modes of heat transfer and in-volve temperature differences with the room temperature Tr .Integrating over successive time intervals starting from an

FIG. 2. The schematic of the circuit used for controlling the heating mecha-nism. When the ON button is momentarily depressed, a current energizes thesolenoid and all “open” switches make contact. Once the push button is re-leased, the current stops flowing through the ON push button wire and takesthe contactor route to keep the circuit on. At the same time, current is flow-ing through the ac mains to the variac and the heating element. We depressthe OFF push button momentarily stopping the current through the solenoid,opening all contacts. The solenoid and contacts are housed inside the mag-netic contactor.

initial time 0 to a final time t , one obtains

V I t = mc[T (t) − Tr ]

+ Sh∫ t

0[T (τ ) − Tr ] dτ

+ Sσε

∫ t

0

[T 4(τ ) − T 4

r

]dτ. (2)

Here, m, c, and S are the mass, specific heat, and the sur-face area of the wire, σ is the Stefan–Boltzmann constant5.67 × 10−8 W/(m2 K4), ε is the emissivity, and h is the co-efficient of heat loss that is directly measured with a ther-mocouple during a cooling curve. Details follow shortly. Thevalues of ε for partially oxidized iron, fresh polished nickel,and Kanthal are 0.6, 0.05, and 0.7, respectively.11, 12 The spe-cific heat capacities of iron and nickel are also temperature-dependent, steeply rising near the phase transition. Thisnecessitates the use of temperature-dependent heat capacitiesc[T (t)]. For iron and nickel, we use the data provided in thethe foundational experiments.13, 14 Figure 3 shows the exper-imental data along with the spline fits. In the determination ofthe instantaneous temperatures, we use the instantaneous heatcapacities read off from these spline interpolants.

An iterative solution to the dynamical equation (2) yieldsthe temperature T (t) at any time t along the heating curve.In effect, one is measuring the temperature using a voltmeter,ammeter, stopwatch, and a computer program for numericallyintegrating over successive time intervals. Clearly, one alsorequires thermophysical and geometric data, namely, c(T ), h,ε, and S. The coefficient h is measured using a thermocouple,with either of these methods: placing the thermocouple beadin between two mica leaves and snuggled between the Kanthalwires or by thermally cementing the thermocouple to the ironand nickel wires.

C. Determining the coefficient of heat loss h

To solve Eq. (2), one needs to determine h. This is alumped parameter primarily composing convection but also

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124904-3 M. S. Anwar and W. Zia Rev. Sci. Instrum. 81, 124904 (2010)

FIG. 3. (Color online) Temperature-dependent specific heat capacities of (a)iron and (b) nickel. The squares (�) and the circles (•) are experimental datapoints (Refs. 13 and 14) and the solid lines are spline interpolation curves.

including conductive losses to the thermocouple wires. (Weestimate from the heat conductivity data that conductionthrough the alumina silicate and porcelain connectors ac-counts for less than 0.1% of the total energy transfer mech-anisms.) The coefficient h is measured by electrically heatingthe wire to some finite temperature T1 and tracing the cool-ing curve. Since T1 − Tr is small, the radiative losses are neg-ligible (owing to the small value of σ ). The heat losses aremodeled by Newton’s cooling15, 16

T = T1 exp (−hSt/mc). (3)

A complete temperature profile from one such experi-ment is shown in Fig. 4(a). The current starts to flow at pointa, t = 0. In the region a → b, we see the rise in temperature atan ever decreasing rate which is the consequence of increasedradiative and convective losses. The region between 40 and140 s (b → c) is the region where the delivered and dissi-pated energies are equal, before the current is switched off atc. However, there is a slight decrease in temperature just be-fore the switch-off, at about 100 s, which is due to the forcedconvective currents that are established around the heatingelement. Finally, c → d is the natural cooling curve. Fig-ure 4(b) shows a typical cooling curve under ambient condi-tions and an exponential fit which shows nearly perfect agree-

0 50 100 150 200 250 300 350 400 450200

300

400

500

600

700

800

900

1000

Time (s)

Tem

pera

ture

(K

)

(a)

a

bc

d

0 20 40 60 80 100 120 140 160 1800

50

100

150

200

250

300

350

400

450

500

Time (s)

Tem

pera

ture

(K

)

(b)

FIG. 4. (Color online) (a) A typical experiment illustrating the complete tem-perature profile and (b) a representative cooling curve experienced in our ex-periments. This curve is explicable by Newton’s law of cooling, validated bythe almost perfect solid-line fit. These data are for the Kanthal wire and thecoefficient h is measured as 230 W m−2 K−1.

ment with the experimental points. The fit yields an estimatefor h = 230 W m−2 K−1 for this particular sample. The heattransfer coefficient h depends on several parameters such asthe geometry, aspect ratio of the wire, the atmospheric con-ditions, and mean air velocity. Considerable variation in thecoefficient can result from these parameters.17 In such con-ditions, the best approach is to experimentally measure thiscoefficient.

The excellent fit with Eq. (3) indicates that compared toradiation, convection is the dominant mode of heat transfer.Surprisingly, the convection term was altogether neglected inRef. 7, but we know that if the heating is fast, the radiativecontribution will be small. For example, in a 10 s heating in-terval for the Kanthal sample, the total energy lost by radia-tion Sσε

∫ t0 [T 4(τ ) − T 4

r ] dτ is only 8% of the energy lost byconvection Sh

∫ t0 [T (τ ) − Tr ] dτ . The fast heating undermines

the radiative losses, which is advantageous, because estimat-ing the emissivity is prone to difficulties,18 it often requiresa reference material for calibration, depends on the texture,

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124904-4 M. S. Anwar and W. Zia Rev. Sci. Instrum. 81, 124904 (2010)

FIG. 5. (Color online) Representative heating curves for a iron and b nickel.The parameters used for these experiments are (iron followed by nickel): dia-meter = (0.92, 0.5) mm, ε = (0.6, 0.05), h = (230, 135) W m−2K−1, length= (1) m each, Tr = (25, 32) ◦C, V = (32.3, 12.3) V, and I = (19.2, 5.9) A.The arrows indicate the Curie temperatures.

composition, and surface color of the heating element, and allof this may well vary during multiple thermal cycles.

III. RESULTS AND DISCUSSION

A. Determining the instantaneous temperatureand the Curie point

Typical heating curves for iron and nickel are shown inFig. 5 and for Kanthal in Fig. 6. These temperature curvesare numerical solutions of the dynamical equation (2). (TheMATLAB solver codes can be obtained from the authors.) Theresults are highly reproducible. For example, in 15 differentexperiments on the iron sample, we obtain a mean Curie tem-perature of 1047 K with a standard error of ±2 K, resulting ina 95% confidence level estimate of (1047 ± 4) K. Similarly,from six different experiments performed on nickel, the Curiepoint at the 95% confidence level is (622 ± 6) K. These val-ues are in good agreement with published19, 20 critical temper-atures of 1043 and 627 K. The uncertainties mentioned hereare of the type A,21 the random scatter from repeated mea-

FIG. 6. (Color online) Heating curves for Kanthal. Curve a represents Eq.(2) without the convection term while curve b is a complete representation ofEq. (2), and curve c is the data acquired using the thermocouple. The resis-tive heating is performed at V = 10.0 V and I = 34 A, while ε = 0.7 andh = 230 W m−2K−1.

surements. The systematic errors, i.e., the type-B uncertain-ties are mainly due to the imprecision in the knowledge of ε

and the timing inaccuracy. These uncertainties are larger. Inprinciple, the timing uncertainty can be reduced through theuse of a proximity or magnetic sensor that is attached to theferromagnetic wire and is capable of sensing the detachmentfrom the permanent magnet.

The results for Kanthal are shown in Fig. 6. Herein b rep-resents the temperature, the numerical solution of Eq. (2). TheCurie point is determined as (725 ± 4) K, where ±4 K is therandom scatter at the 95% confidence level. This value con-trasts with the value of ≈ 973 K presented in the data sheet aswell as in Ref. 7, which ignored the convective losses, effec-tively dropping out the second term in the right side of Eq. (2).Indeed, when we performed a similar erroneous calculation,we reproduced their Curie temperature, and the results areshown in the curve labeled as a. As far as an independentverification of our Curie point of the alloy is concerned, wehave not found any reference besides the manufacturer’s datasheet. However, looking at page 104 of the CRC Handbook ofPhysics and Chemistry,20 we can find a listing of three Fe–Alcompositions. (Kanthal is an Fe–Al alloy.) The listed percent-age compositions of (Fe–Al) are 84–16, 87–13, and 96.5–3.5.The Curie points of the former two alloys are 723 and 673 K,respectively. Our Curie point is approximately 725 K. Unfor-tunately, the Curie temperature of the 96.5–3.5 compositionthat is the closest match is not provided, but our values seemplausible. In any case, the precise measurements on elemen-tal iron and nickel and their concordance with accepted datais evident.

Finally, the bottom curve c in Fig. 6 shows the exper-imentally determined temperatures from the thermocouple.There is disagreement between the thermocouple data andthe predicted temperature. The origin of this discrepancy isthe thermal inertia of the thermocouple bead. The inertia be-comes significant in thermally dynamic environments,22, 23 es-pecially when the temperature rise is extremely rapid. This isan applicable scenario in our case too. We observe that thethermocouple response c catches up with the real temperatureb in the latter parts of the heating curve, when the heat lossesbecome large due to the large temperature gradient T − Tr ,and consequently, the heating rate slows down.

B. Determining high temperature susceptibilities

By a straightforward extension, it is possible to measureother high temperature magnetic properties of ferromagneticmaterials such as the magnetic susceptibility. Introducing aferromagnetic material in the vicinity or inside the core ofan inductor changes its impedance, notably its inductance L .This translates into a change in the resonant frequency ω

∼ 1/(LC)1/2. A measurement of the frequency shift revealsthe magnetic and electrical properties of the ferromagnet suchas the susceptibility χ and resistivity ρ.

Different techniques have been employed to measure thesusceptibility. The underlying component is a resonant tankcircuit that is driven by an oscillator circuit such as the Col-pitts oscillator or a tunnel diode biased in the negative con-ductance region.24 Several low temperature measurements of

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124904-5 M. S. Anwar and W. Zia Rev. Sci. Instrum. 81, 124904 (2010)

FIG. 7. (Color online) The susceptibility and temperature plot of Kanthalalloy. The standard error in the χ measurement is approximately ±130.

susceptibilities and resistivities of various kinds of techno-logically promising materials have been reported.25, 26 In thepresent article, we show the possibility of determining thehigh temperature susceptibilities of ferromagnetic materialsusing the dynamical equation (2). In the present experiment,the wire-shaped alloy forms the core of a hand-wound induc-tor whose inductance is directly measured with a precisionLC R meter (Quadtech 1920).

The setup for the susceptibility measurement is essen-tially the same as shown in Fig. 1 with minor modifications:the wire is coaxially placed inside and magnetically cou-pled to an inductor, which is electrically connected to theLC R meter. The inductor was hand-wound around borosil-icate glass tubes, with nominal inductances ranging from25 μH to 1.5 mH. The inductance and the time since the ini-tiation of the electrical current were recorded by the data ac-quisition system. Finally, the temperature-dependent suscep-tibility is measured from L using the relationship27

L = L0(1 + αχ ), (4)

where L0 is the inductance without the ferromagnetic sampleand α is a product of the filling factor and the demagnetizationcoefficient.28 The filling factor is the ratio of the volumes ofthe coil and wire, and in our case, the factor was determined tobe 0.023 while the demagnetization coefficient for the cylin-drical geometry was 0.004, resulting in α ≈ 9.2 × 10−5.

Figure 7 shows a typical χ versus temperature plot forKanthal, and χ drops from ∼ 9000 to zero at the Curie tem-perature, which is around 720 K, corroborating the value fromthe previous section. The length of the experiment was keptshort in order to keep the coil from changing its resistancewhile heating. Typically, the experiment lasted for about 10 s.Fortuitously, fast heating ensures that the monitor coil doesnot significantly heat up to change its resistance during themeasurement.

IV. SUMMARY

In summary, we started out by measuring the Curie tem-perature of a ferromagnetic alloy reckoning all modes of heattransfer and established the challenges in direct temperature

measurement using thermocouples in rapidly increasing tem-perature environments, a scenario applicable to resistivelyheated elements. We present details of a technique in whichthe temperature is directly deducible from electrical and ther-mal measurands and employs a simple energy-balance equa-tion. For the complete thermophysical data, however, we re-quire the use of a thermocouple in a slow cooling curve tomeasure the heat losses. We also present the magnetic sus-ceptibility versus temperature plot for a ferromagnetic wireby registering its magnetic coupling to an inductor whoseimpedance shifts with temperature. The experiment is verysimilar in spirit to hot-wire anemometry wherein a wire isheated and the resistance change measures the temperaturechange, from which the air velocity can be extracted. Interest-ingly, our experiment covers a much larger temperature rangethan what is commonplace in the anemometry literature.29

The authors like to thank Moeez Hassan for help in measure-ments and Abdul Mannan for help in building some of thehardware.

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