A Peltier cell calorimeter for the direct measurement of the isothermal entropy change in magnetic materials

Transcription

1 REVIEW OF SCIENTIFIC INSTRUMENTS 79, A Peltier cell calorimeter for the direct measurement of the isothermal entropy change in magnetic materials Vittorio Basso, a Michaela Küpferling, Carlo P. Sasso, and Laura Giudici b Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, Torino, Italy Received 21 December 2007; accepted 18 May 2008; published online 19 June 2008 We developed a calorimetric technique to measure the isothermal magnetocaloric entropy change. The method consists in the use of Peltier cells as heat flow sensor and heat pump at the same time. In this paper, we describe the setup, the constitutive equations of the Peltier cell as sensor and actuator, and the calibration procedure. The Peltier heat is used to keep the sample isothermal when magnetic field is changed. The temperature difference between the sample and the thermal reservoir is kept by a digital control within 5 mk for a magnetic field rate of 20 mt s 1. The heat flux sensitivity around 1 W. With this method, it is possible to measure the magnetocaloric effect in magnetic materials by tracing the curves of the exchanged entropy e s as a function of the magnetic field H. The method proves to be, in particular, suitable to reveal the role of the entropy production i s, which is connected with hysteresis. Measurement examples are shown for Gd, BaFe 12 O 19 ferrite, and Gd Si Ge American Institute of Physics. DOI: / I. INTRODUCTION Ferromagnetic materials are not in thermodynamic equilibrium because of the presence of hysteresis in their constitutive relationship. The entropy change S= e S+ i S is due both to the entropy exchanged with the surroundings e S and to the entropy production i S connected with the dissipation due to hysteresis effect. The thermal properties of a ferromagnetic material are then characterized by an entropy function S H,T, which is a multivalued, hysteretic function of its variables and by an entropy production term i S 0, which is a definite positive quantity and a function of the time history of the variables driving the thermodynamic transformation. 1,2 The experimental determination of the thermal quantities as a function of magnetic field is becoming more and more important for applications to magnetic refrigeration around room temperature. 3,4 The development of this cooling technology requires an accurate characterization of the magnetocaloric effect in the room temperature range and at magnetic field rates comparable to the frequencies of typical refrigeration cycles up to a few hertz. One of the open problems for the application of magnetic materials to magnetic cooling is the quantification of the role played by hysteresis and irreversibility effects. 5,6 The solution corresponds to the experimental determination of both the entropy change S and the entropy production i S as a function of magnetic field and temperature. In the literature, the techniques to characterize the magnetocaloric effect can be classified on the basis of the thermal quantity to measure: the isothermal entropy change S; 7 11 the adiabatic temperature change T; the field dependence of the specific heat c p H,T. 13 However, to a Electronic mail: basso@inrim.it. b Also at Politecnico di Torino, Dip. di Fisica, Corso duca degli Abruzzi 24, Torino, Italy. characterize materials with irreversibility, one has to measure directly the heat flux q=td e S/dt, 17,18 a physical quantity which is directly connected to the entropy rate ds/dt and to the entropy production rate d i S/dt by the expression q=td e S/dt=TdS/dt Td i S/dt. The experimental determination of ds/dt and d i S/dt is then connected to two capacities of the instrument: i to keep the temperature of the sample constant and ii to trace the curves d e S/dt as a function of magnetic field. This provides the possibility to measure the entropy production term in a closed magnetic field loop with the expression i S= d i S= d e S. In calorimeters that are able to determine the heat flux, one measures the heat current established between a sample and an isothermal reservoir isothermal calorimetry Peltier cells have been shown to be heat flux sensors particularly suited for the measurement of the magnetocaloric effect, because they are highly sensitive, little affected by the presence of magnetic field, and are available with small time constants. 9,10 However, the current methods Refs. 9 and 10 are based on use of Peltier cells as passive sensors, so they sense a heat flux when a temperature difference between the sample T s and the thermal bath T b is present. Then, the measurement can be considered isothermal only at very low magnetic field driving rates. With the motivation to expand the Peltier cells toward higher field rates, we have developed the active use of the cells. The concept consists in using a symmetric arrangement of two Peltier cells and two copper blocks thermal bath Ref. 22 and to obtain isothermal condition by the Peltier heat. Different from previous works in which the Peltier cells are used for heat compensation only, 19,20,23 25 our method consists in using the same cell both as a heat sensor through the Seebeck effect and actuator through the Peltier effect and corresponds in this respect to the new class of calorimeters foreseen in Ref. 9. The active measurement is obtained /2008/79 6 /063907/10/$ , American Institute of Physics

2 Basso et al. Rev. Sci. Instrum. 79, by digital feedback control, driving an electric current i through the cells while the magnetic field is changed in time. We realized the setup to work around room temperature and we performed its calibration in the temperature range of K 40 to +80 C. We tested the method and the instrument by performing measurements on selected magnetic samples: i Gd, ii BaFe 12 O 19, iii Gd Si Ge. The isothermal entropy change was measured on Gd and compared to independent measurements on the same sample giving excellent quantitative agreement. On hard barium ferrite of composition BaFe 12 O 19, we measured the entropy exchanged along the magnetization curves and we were able to discriminate the relative contributions of the entropy change S and entropy production i S in a closed loop. To sustain our data, we found that, as expected, the energy loss T i S provided by the calorimeter agrees with the energy loss given by the magnetic hysteresis loop area. Finally, to test the possibility of the instrument on materials of interest for magnetic refrigeration around room temperature, we measured a sample of Gd Si Ge alloy displaying the so-called giant magnetocaloric effect GMCE. We are able to plot the hysteresis curve of the exchanged entropy as a function of magnetic field. This kind of curves contains the full information on the material for its application as a refrigerant in cooling machines. II. Calorimeter A. Measurement principle The general scheme of the experiment consists of the sample, the thermal reservoir, and the Peltier cell, acting as a sensor and actuator, connecting the two. A change in time of either the magnetic field, with rate dh/dt, or the temperature, with rate dt s /dt, corresponds to an entropy change S and an entropy production i S in the sample. The corresponding heat flux is q=t s d e S/dt=T s ds/dt T s d i S/dt. For the sample, the heat current q s, positive toward the sample, is q s = T s d e S dt e S H = T s H t + T e S s T s dt s dt. The Peltier cell is, as a passive element, a thermal conductor, and, as actuator, a source of heat current. The heat flux at the cell in steady state, is governed by the following equation see Appendix for the derivation : q s = P i Ri2 K P T s T b, where the three terms on the right hand side represents: i the heat current due to the Peltier effect P is the Peltier coefficient and i is the electric current passing through the cell ; ii the Joule heating R is the electric resistance of the cell, and iii the heat conduction current due to the temperature difference across the cell K P is the total thermal conductance. The factor 1/2 in the Joule heating term appears because half of the Joule heating flows to the sample and half to the bath. The behavior of the sample is given by equating the two previous expressions 1 and 2. We obtain a differential equation for the sample temperature T s : 1 2 FIG. 1. Top Symmetric arrangement of Peltier cells in the calorimeter. Bottom Electric connection of the cells. e S dt s T s T s dt e S H + K P T s T b = T s H t + Pi Ri2. The right hand side of the equation contains the sources and sinks of heat. The three terms are the magnetocaloric heat, the Peltier heat, and the Joule heat. When i=0, the sensor is passive and represents a thermal conductor only. The temperature T s of the sample is then bound to change when the magnetocaloric heat on the right hand side of the equation is different from zero. When i 0, the sensor is active and if the current i is such that the sum of the three terms on the right hand side is zero the magnetocaloric heat is compensated by the Peltier heat P i and the Joule heat. If initially T s =T b, the temperature of the sample will not change and isothermal conditions are obtained. The heat flux toward the sample q s and the temperature difference between the cell faces T s T b are related to the electric voltage v and current i through the cell see Appendix. 2 The q s of Eq. 2 is then measurable and its time integration between starting state 0 at t=t 0 with H=H 0 and T s =T b, and any state t with H=H t and T s =T b gives t q s e S dt 4 = t 0 T s as a function of the history of the magnetic field H t at constant temperature T s =T b. B. Measurement setup The calorimetry setup implements the conditions of the measuring principle by employing a symmetric arrangement of two identical Peltier cells placed in contact with two parallel faces of the sample see the scheme of Fig. 1 a. The symmetry is chosen because, for the active use of the Peltier cells, all the heat flux exchanged by the sample has to flow through the measuring cells. The ensemble is placed in a tube which is evacuated in order to minimize heat flux losses 3

3 Peltier cell calorimeter Rev. Sci. Instrum. 79, given by the constitutive equations of the Peltier cells. The two equations are derived from the theory of thermoelectric effects see Appendix under the condition that the sample and the bath have homogeneous temperatures and the cell has negligible thermal capacity but finite thermal conductivity. The two equations are T s T b = 1 P v R P i, 5 FIG. 2. Color online Picture of the calorimeter. Top Brass tube hosting the calorimeter. Inlet and outlet are for the cooling with nitrogen gas. Center An open calorimeter: to each copper bar a Peltier cell is attached. The Gd sample is shown above the cell of the lower bar. from the sample. Both sensor calibration and measurements are performed at the same vacuum level with pressure of 0.5 Pa obtained by a rotary pump. The Peltier cells are in thermal opposition and their bath sides are attached to copper blocks thermal bath. The two blocks have been cut out from a copper rod of diameter 15 mm and length of 120 mm. The two Peltier cells are connected electrically in series circuit shown in Fig. 1 b. A picture is shown in Fig. 2. The measurement of the v t and v 0 t signals is done by an Agilent E1419A Multifunction programmable board and the current i t is given by i t = v 0 t v t /R c. A Keithley nanovoltmeter is used as high sensitivity amplifier for small v t signals. The Peltier cells are commercial cells with 60 junctions on an mm 2 surface, 0.9 mm height Thermion 1MC with a nominal electrical resistance of These cells were chosen because they have a fast response time. In the circuit of Fig. 1 b, the resistance R c =1 k, much larger than the resistance of the cells, permits one to set the needed current i t by setting directly the voltage v 0 t =R c i t +v t through the voltage output of the Agilent E1419A. The temperature of the copper blocks T b is regulated by compensating the heating effect of an electrical heater covering the external part of the blocks and the cooling effect of the flux of cold nitrogen gas vapors of the liquid in an outer chamber of the vacuum tube. The temperature of the blocks T b is measured by a thermocouple placed in the vicinity of the Peltier cells. With this method, T b can be regulated within an accuracy of 0.01 C over 100 s in the range of K 40 to +80 C. The magnetic field H is generated by an electromagnet. The whole calorimeter setup is inserted in the 20 mm gap formed by two tapered Fe Co pole faces of 60 mm diameter. The magnetic field is measured by a Hall probe placed outside the vacuum tube. The maximum magnetic field intensity is around 0 H= 2.3 T. The samples must have two flat parallel faces in order to have a good contact with the measuring cells. Thermal conducting grease is used in order to have a uniform thermal contact between samples and cells and to decrease the thermal contact resistance. C. Sensor equations and calibration The relationship between the measured electric quantities v t and i t and the thermal quantities T s T b and q s is q s = P i Ri2 1 S P v R P i, where P and P are the effective Seebeck and Peltier coefficients, respectively, R P is a parameter having the dimensions of an electrical resistance and including the true electrical resistance of the cell, S P = P /K P is the sensitivity, and K P is the total thermal conductance. All these effective coefficients take into account the finite thermal conductivity of the ceramic plates which are covering the cell, as shown in Appendix. These equations are appropriate to describe Peltier cells with fast response time since they do not describe the transient state. The hypotheses of uniform temperature in the sample depends on its thermal diffusivity and thickness d and has to be checked case by case. In order to pass from the measured voltage v and current i to T and q s, the effective parameters of the Peltier cells S P, R P, P must be calibrated. The two equations 5 and 6 can be directly applied to describe the measuring system composed of two cells of our setup because the two cells are in constant contact with the same sample and the same bath. The effective parameters refer then to a two-cell system. The calibration is performed by the following three independent experiments. Determination of S P. i The cells are operated with zero electric current passive configuration. ii A known source of heat an electric heater generating a Joule heat q 0 =R h i 2 h substitutes the sample. In this case, the heat current q s = q 0 is imposed by the heater and the Peltier cell voltage is proportional to the heat current v=s P q 0 from Eq. 6 with i=0. The sensitivity S P =v/q 0 is determined by measuring the Peltier voltage v under steady conditions. Determination of R P. i The cells are operated in active configuration i 0. ii Both sample and bath side faces of the cells are placed in contact with the thermal bath represented by the two copper blocks. If the blocks have sufficiently large heat capacity and thermal conductivity, the two faces of the cells are at the same temperature T=0. This isothermal condition is likely to be conserved even when a small electric current i=i 0 is supplied to the cells and a small heat current q s is traversing them. In Eq. 5, the temperature difference T s T b is identically zero and the parameter R P is determined from Eq. 5 as the ratio between the measured v and the imposed i 0 : R P =v/i 0. Determination of P. i The cells are operated in active configuration i 0. ii The sample is placed between the cells. If a continuous heat current is delivered from the thermal bath to the sample by supplying the cells with a 6

4 Basso et al. Rev. Sci. Instrum. 79, constant electric current i=i 0, the temperature of the sample will increase T 0. The steady condition will be reached when the heat flowing toward the sample P i 0 + 1/2 Ri 0 2, Peltier heat and Joule heat terms of Eq. 6 is compensated by the heat flowing backward to the thermal bath 1/S P v R P i 0 = K P T, thermal diffusion term of Eq. 6. This steady condition q s =0 in Eq. 6 is well verified if there is negligible heat loss. P is determined as P = 1 S P v i 0 R P 1 2 Ri 0, 7 by setting the constant current i 0, measuring the Peltier voltage v, and using the S P and R P coefficients calibrated in the previous two experiments. The effective parameters S P, R P, P of the cells depend on temperature, while the dependence on the magnetic field is negligible. The calibration of our setup has been made by performing the three calibration experiments at selected temperatures of the thermal bath in the range of K 40 to +80 C. S P is determined by using a strain gauge as electric heater, with a resistance of R h =120, placed between the cells. The voltage v is measured as a function of the i h in the range of 5 20 ma and S P is determined by linear best fit of v as a function of q 0 =R h i h 2. The error for each point of S P is less than 1%. The value of R P is determined by measuring v with i 0 in the range of 1 2 ma and making a linear best fit. Low current values were chosen not to alter the temperature of the copper blocks. The error for each point of R P is also less than 1%. By observing the transient behavior of the voltage v t after a current step, we observe an exponential approach to stationary value with a time constant =0.2 s. This time constant is the limit of the frequency harmonics that can be observed in a magnetocaloric experiment. By changing the magnetic field over a period around a hundred of seconds, the main frequency is about two decades below the frequency cut. The possible influence of the presence of a magnetic field on the Peltier cell parameters was checked by measuring the value of S P and R P at constant field of 0 H=2 T. The difference between the values at zero field is below the error of the determination of S P and R P, then the calibration coefficients S P and R P can be considered functions of temperature and are well described by the fit reported in Fig. 3. For the determination of P, we measured v under i 0 =1 2 ma and we computed P by Eq. 7. The sample used for the calibration of P is a Gd sample Sec. III A. The calibration as a function of temperature requires a particular care in the case of heating because one has to consider possible degradation of properties of the cells. The nominal maximum operation temperature for the cells is 85 C. We performed several tests for the use of the cells above room temperature and we found that when the cells heated below 80 C, the sensitivity S P do not deteriorates. For our aims, we check the time stability of the cells of the coefficient by performing the calibration at the room temperature before and after heating to the maximum operation FIG. 3. Color online Coefficients S P, R P, and P as a function of the temperature T, obtained from the calibration of the the measuring Peltier cells Thermion 1MC The curves shown are S P = T T T T T T T T 0 4, R P = T T 0, P = T T 0. With T 0 =296 K. temperature. For a maximum temperature of 85 C, the values are changing within the error. Figure 3 reports the results of calibration as a function of temperature for the cells used in the measurements shown in this paper. The room temperature T=296 K values are S P =0.103 V/W, R P =3.77, P =10.6 V, the effective Seebeck coefficient, given by P = P /T, where T is the absolute temperature, is P =35.8 mv/k. The electrical resistance of the series of the two cells is R=3.01. The total thermal conductance of the cells K P, given by K P = P /S P, results K P =0.348 W K 1. D. Heat flux measurement and T control The heat current q s and the temperature difference T s T b are computed from Eqs. 6 and 5, respectively, by using v t and i t signals and the values of the parameters determined by the calibration. The measured voltage signal v t includes constant instrument offsets and magnetic field induced voltage, which are subtracted. The sensitivity of the instrument as a heat flux sensor depends on the sensitivity of the measurement of v. At room temperature T=296 K, S P =0.103 V/W by using a nanovoltmeter, we have a resolution around q=1 W. This limit is mainly due to the electrical noise present. To decrease the noise level, the signals v 0 and v are sampled at t=1 ms and averaged over a period ranging from 10 to 100 ms. In active isothermal measurement, T=T s T b is controlled to the reference value T ref =0 by setting the appropriate current i. Its value is determined by a proportionalintegral digital feedback control: i t =k p e t + e t dt/ i where the error is e t = P T ref T = v R P i and the

5 Peltier cell calorimeter Rev. Sci. Instrum. 79, control system parameters k p and i are set to obtain a fast approach of the measured P T=v R P i to zero with a few oscillations. The control routine is realized digitally on the Agilent E1419A Multifunction programmable board. At every execution step, it computes numerically the current i to be set, then it applies the corresponding v 0 =v+r c i. The control routine runs at t= ms. For the Peltier cells used in this paper, we have determined as optimal values k p =0.8 1 and i =0.75 s. In Fig. 4 is shown a comparison of the active and passive measurements on a Gd sample at room temperature T b =296 K see next section for the details on the sample. The magnetic field is increased up to the maximum of 0 H max =1.5 T, then decreased to zero. The field rate was 0 H/ t =20 mts 1. In the passive measurement, the T is proportional to the heat flux. With the active control, T is kept very close to zero apart when the heat flux is changing in time. The peaks are below 3 mk. In the inset of Fig. 4, a detail of the e s as a function of the applied magnetic field H is shown. The specific entropy e s is given by the integral FIG. 4. Color online Comparison between active and passive measurement. T=T s T b is the difference between the temperature of the sample and that of the bath. The magnetic field is the same of Fig. 5. T=T s T b is computed by the sensor equation Eq. 5 by using the calibration coefficients and the measured v t and i t signals. Inset e s as a function of magnetic field for the two measurements. e s = 1 t mt t 0 q s t dt, where m is the sample mass and T=296 K is the temperature of the thermal bath. For the Gd sample at T=296 K, above its Curie point T C =293 K, we expect a negligible entropy production i s 0. The measurement gives directly the entropy change in the system s= e s as a single valued curve with no hysteresis. 8 FIG. 5. Isothermal entropy change measured on a Gd sample at T=293 K. H is the applied field waveform and e s is the measured entropy change. v and i are voltage and current measured at the Peltier cells. T=T s T b and q s are computed by the sensor equations Eqs. 6 and 5 using the calibration coefficients.

6 Basso et al. Rev. Sci. Instrum. 79, In the measured passive curve, we observe a hysteresis effect which is due to the time delays introduced by the fact that the sample is changing temperature. To evaluate the time delays introduced, we have to consider Eq. 3. In that equation, the time constant is s =C s /K P, where C s =T s ds/dt s is the thermal capacity of the sample. An estimate of s from the passive experiment can be obtained by the integration of Eq. 1. We get S= q s /T s dt C s /T s dt s /dt dt. If the variations of T s are small with respect to its value, we can take 1/T s outside the integrals: S = q s dt C s dt s /dtdt /T s. With constant C s and by using q s = K P T, we obtain S= q s dt+ s q s /T s. In the Gd experiments of Fig. 4, the passive curve reduces to a single valued curve by using the previous approximated formula if we use a time constant s =0.8 s. The curve performed by the active method is much closer to a single curve because the control system was able to keep the sample temperature sufficiently close to that of the bath and provides with sufficient accuracy directly the s versus H curve. The active method is therefore particularly useful in experiments in which one needs to obtain the e s versus H curve in a single experimental run. An example of all the time signals in active measurements is shown in Fig. 5. In the experiment shown, the magnetic field is changed at the constant rate 0 H/ t =20 mts 1. In the active measurement q s, given by Eq. 2, is mainly due to the Peltier effect. From the case shown in Fig. 5, it results that the Joule heat contribution is less than 0.01% and the heat conduction term is almost always equal to zero, except the T peaks where it reaches 10% of the Peltier heat flux. Positive q s means heat absorbed by the sample, negative q s means heat released by the sample as it is expected for Gd, that has a conventional magnetocaloric effect in which heat is released under an increasing field and absorbed under decreasing. III. Measurement examples A. Reversible effect: Gadolinium Gadolinium is a ferromagnet with a large spontaneous magnetization at low temperature 0 M s T=4.5 K =2.7 T Ref. 26 and a Curie temperature around T C =293 K. For this reason, it has been studied intensively as a material for magnetic refrigeration at room temperature. The sample is a mm 3 sheet with mass m = g. The sample is sufficiently thin to guarantee uniform temperature during the experiments. With a thickness d=1 mm and thermal diffusion coefficient = m 2 s 1 for Gd, we obtain a diffusion time = d/2 2 / of about 0.1 s, below the response time of the measuring cell 0.2 s. The magnetic field H is applied parallel to the long axis of the sample. The measurements are performed by i setting the temperature of the thermal bath T b to a given constant value, ii start the measurement by first increasing the magnetic field up to the maximum of 0 H max =1.5 T, then decreasing to zero. The measuring cells are operated in active configuration by controlling T s T b =0. The temperature of the thermal bath T b was changed in the range of FIG. 6. Set of curves of entropy change s vs applied magnetic field H at constant temperature T s measured on Gd K. In Fig. 6, the exchanged entropy Eq. 8 is plotted as a function of the applied magnetic field H at selected temperatures above T c. We verified that the graph e s versus H, obtained by first increasing and then decreasing the magnetic field, describes a single valued curve and the final value returns to the initial value Fig. 6. The entropy production is found to be negligible i s 0 also below the Curie point of Gd. Then, our measurement gives directly the entropy change in the system s= e s. In Fig. 7, the s is shown at the selected magnetic field 0 H=0.4, 0.9, and 1.5 T as a function of T=T b. The values were extracted from the isothermal curves s T,H. Inthe picture, our data are compared to the s measured on a sample taken from the same sheet with the calorimeter developed at the University of Zaragoza 16,27 with good agreement of the two curves. FIG. 7. Color online Isothermal entropy change in Gd. Full symbols Entropy change s vs temperature T at several applied magnetic field values measured on a Gd sample with the calorimeter developed in the present paper. Open symbols Measurement of a sample taken from same sheet, performed by the calorimeter developed at the University of Zaragoza Refs. 16 and 27.

7 Peltier cell calorimeter Rev. Sci. Instrum. 79, s PM phase H=0 H=H max FIG. 8. Curves of the integral of the exchanged heat T e s measured on isotropic BaFe 12 O 19 as a function of the applied magnetic field H. The history of the field is full line saturation loop 0, H max,+h max, H max,0; dashed lines return branches 0, H max,+h peak, H max, 0. The values are: 0 H max =1.8 T and 0 H peak =0.3,0.4 T. Inset A magnetic hysteresis loop for the same material. The measurements are at room temperature T=296 K. B. Irreversible effect: Hard ferrite Barium ferrite of composition BaFe 12 O 19 is a ferrimagnet with saturation magnetization 0 M s =0.48 T at room temperature and a Curie temperature around T C =742 K. 28 The magnetocaloric effect is then expected to be much lower than that of Gd. However, barium ferrite has a large coercive field due to its high uniaxial magnetic anisotropy anisotropy field 0 H A =2K 1 /M s =1.7 T. This material was selected in order to verify the ability of the instrument to measure the entropy production. By performing a closed hysteresis cycle, the dissipated energy corresponds to the area of the magnetic loop: T i s= 0 HdM. The sample is a cylinder with height h = 1.45 mm, base diameter d = 6.7 mm, and mass m = g of sintered isotropic barium ferrite. A hysteresis loop of the sample is shown in the inset of Fig. 8. The calorimetric experiment is realized at room temperature T=296 K by applying the magnetic field parallel to the cylinder axis. The field history consists of the following sequence: 0, H max,+h max, H max, 0 with field sweep rate 0 H/ t =24 mts 1. The voltage signal v t was amplified by a Keithley nanovoltmeter with gain G= The heat exchanged is computed by the expression T s e s = 1 t q s t dt, 9 V t 0 where V= m 3 is the sample volume and T s =296 K is the temperature of the sample. The curve is shown in Fig. 8. The qualitative interpretation of the shape of the curve of Fig. 8 is that a reversible magnetocaloric effect close to the saturation is superimposed to an upper shift of the curve that occurs each time the field traverses the range around the coercivity and is connected with the dissipation of energy. A curve with a similar shape was already seen for Ni see Ref. 1, p To sustain this interpretation, we have performed FM phase FIG. 9. Illustration of the entropy as a function of temperature for a material with a magnetic field driven phase transition. There is hysteresis in the s-t curves. The full arrows trace the temperature and field variation of the magnetocaloric experiments performed. measurements of return branches maximum positive field 0 H=0.3, 0.4 T shown as dashed lines in the picture. Only a part of the loop is traversed and the dissipation reduces accordingly, as it can be seen by the different positions of the reversible branches at high negative fields. Quantitatively, the calorimetric data give the dissipated energy in closed hysteresis loop T i s= Td i s= Td e s. For the saturation cycle, the value is T i s=0.205 MJ m 3. This value has to be compared to the area of the magnetic saturation hysteresis loop. By using the data shown in the inset of Fig. 8, the area is 0 HdM=0.209 MJ m 3. C. Irreversible effect: GMCE in Gd Si Ge Since the discovery of Gd Si Ge, 29 great attention is devoted to materials displaying the so-called GMCE in which a large entropy change is achieved by the magnetic field, because of the presence of a coupled magnetostructural phase transformation. The characterization of out-ofequilibrium properties is particularly important here because, when equilibrium thermodynamics methods are applied to GMCE materials for the determination of the entropy change, incongruent results may appear. 5,6 The compound Gd 5 Si 2 Ge 2 displays a coupled magnetostructural first order phase transformation between a low temperature ferromagnetic FM orthorhombic Gd 5 Si 4 -type structure and a high temperature paramagnetic PM monoclinic Gd 5 Si 2 Ge 2 -type structure 30 at T=288 K. The phase transformation can be induced by the application of a magnetic field and the entropy as a function of the temperature at different magnetic fields has the behavior sketched in Fig. 9. The sample analyzed in this paper is polycrystalline with nominal composition Gd 5 Si 2.09 Ge It is a piece of thickness 1.4 mm, irregular lateral sizes of about mm and mass m=0.149 g. The experiments were performed by T

8 Basso et al. Rev. Sci. Instrum. 79, FIG. 10. Exchanged entropy e s measured on polycrystalline Gd 5 Si 2.09 Ge 1.91 as a function of the temperature T at 0 H=1.5 T. starting at the temperature T 0 =273 K in which the material is fully in its FM state, then increasing the temperature of the bath up to the measuring temperature T=T b inducing partially or completely the FM to PM transformation, then performing the calorimetric experiment at constant T b. The magnetic field is applied parallel to the plane. In Fig. 10 are shown the values of e s as a function of temperature for the maximum field of 1.5 T. For this test, the magnetic field was increased up to 0 H=1.5 T PM to FM and decreased down to 0 T FM to PM. After each experiment, the temperature is decreased back to T 0 in order to start from a well defined FM initial state see Fig. 9. The Gd 5 Si x Ge 1 x 4 with x is known from the literature 30 to form two phase alloys. The primary phase is the Gd 5 Si 2 Ge 2 -type structure with GMCE effect. This secondary phase is a Si-rich phase with Gd 5 Si 4 -type structure. It is FM with a Curie point close to room temperature. The behavior of the measured sample can be interpreted as the superposition of the behavior of these two phases. In the entropy change of Fig. 10, we observe the GMCE peak at T = 288 K associated with the behavior of the primary Gd 5 Si 2 Ge 2 phase and smaller peak at T=303 K associated with the Curie point of the secondary Si-rich phase. The values obtained for the temperatures are in agreement with the phase diagram reported in Ref. 30 and the values of the entropy change are comparable with those obtained on similar samples investigated in Ref. 30. In Fig. 11 are shown the curves of e s as a function of the magnetic field for two selected temperatures. In the picture, the magnetic field was changed according to the following field history: 0, H max, H max,+h max, 0. The field sweep rate is 0 H/ t =20 mts 1. These curves reveal the superposition of two contributions: one from the entropy change associated with the latent heat of the first order phase transformation GMCE which is hysteretic and the other with the conventional magnetocaloric effect of the phases that has no hysteresis. At T=288 K, the primary phase Gd 5 Si 2 Ge 2 of the sample is already partially transformed in PM and the application of a magnetic field immediately start to transform FIG. 11. Curves of the integral of the exchanged entropy e s measured on polycrystalline Gd 5 Si 2.09 Ge 1.91 as a function of the applied magnetic field H. The history of the field is 0, +H max, H max, +H max, 0, with 0 H max =2.05 T. back to FM as it can be seen from the presence of hysteresis. When the phase is transformed back to FM around 1.5 T, the loop has a saturating shape. The lower slope ds/dh corresponds the conventional magnetocaloric effect of the FM phase. At T=296 K, the sample is fully in its PM phase. At magnetic fields below 1.5 T, we observe the conventional magnetocaloric effect of the phases. The partial hysteresis loop seen corresponds to a partial phase transformation to FM that is completely recovered back when the field is removed. The same phenomenology is observed when the magnetic field is applied in the opposite direction. A minor effect that has to be noticed is that the first time that magnetic field is increased, after the sample is heated from fully FM state, the s versus H branch is found to be slightly shifted to higher field. This may be due to the fact that the hysteretic phase transformation softens slightly after the first cycle. The entropy production is seen as a small positive shift of the e s curves. The value of e s after one-half loop 0-H max -0 does not return exactly to zero, however, the effect is only around 1% of the maximum entropy change. IV. CONCLUSIONS In this paper, we have studied and implemented a technique to measure the isothermal entropy change due to the magnetic field by employing Peltier cells in active way to compensate the magnetocaloric heat. The setup has been realized using a symmetric arrangement of two Peltier cells and the active measurement is obtained by a digital feedback control. With the active method, the curve e s traced while changing the magnetic field with time at a certain rate has a strongly reduced dynamic hysteresis with respect to the passive case. After calibration, we tested the setup by measuring the magnetocaloric effect of three different materials: Gd, BaFe 12 O 19, and Gd Si Ge. For Gd, our measurements give the curves of s H,T as a function of the applied magnetic field H. Our data agree with independent measurements. The exchanged entropy e s is measured as a function of the magnetic field history. This is the kind of measurement which is

9 Peltier cell calorimeter Rev. Sci. Instrum. 79, v sample i bath p n p n T s T js T jb T b q s q b 2. Thermoelectric equations The thermodynamic forces are the voltage at the terminals v and the temperature difference between the two junctions planes T j =T js T jb, which is taken here to be uniform on the planes. The currents of interest are the electric current i and heat current at the interface between the cell and the sample q s. From the equations of thermoelectric effects 2 applied to the geometry of the cell, one has v = Ri + T js T jb, A1 FIG. 12. Peltier cell connected with the sample and the thermal bath. The temperatures at junctions T js and T jb can be different from the temperatures at the sample T s and bath T b, respectively, when the heat fluxes q s and q b are not zero. of interest for the characterization of materials with the giant magnetocaloric effect because the effect of hysteresis on the refrigerant capacity has to be determined. The entropy production in a closed loop is measured on a sample of hard ferrite and compared to the magnetic hysteresis loop area. A measurement example is shown for Gd Si Ge, revealing the hysteresis of the entropy as a function of the magnetic field. The setup described in this paper removes the limitations of the passive method in which time delays are introduced by the heat capacity of the sample. The time constant is s =C s /K P, where C s is thermal capacity of the sample and K P is the thermal conductance of the cells. Active and passive reduce to the same at low driving speed, the active method is necessary for the cases in which both s is large or when the magnetic field driving rate cannot be too low. Both cases are of interest for the characterization of magnetic materials for magnetic cooling. With the presented active method, we are still limited by the time constants of the cells related to the ratio C P /K P, where C P is the thermal capacity of the Peltier cell. In this work, we have selected proper cells with short time constants. In future works, we will investigate how to take into account the dynamic effects in the theoretical description of the measuring cells. ACKNOWLEDGMENTS We thank for the samples: A. Kedous Lebouc for the Gd sheet, F. Fiorillo and C. Beatrice for the hard ferrite, M. Pasquale, V. Pecharsky, and K. Gschnidner for the Gd Si Ge. We thank the group of Professor Burriel University of Zaragoza for performing the entropy measurement on a Gd piece from the same sheet. APPENDIX: THERMOELECTRIC EFFECTS IN PELTIER CELLS 1. Peltier cell A Peltier cell is a thermoelectric device made of junctions of semiconductor pillars, doped p and n, with positive and negative thermoelectric power respectively Fig. 12. The pillars are connected electrically in series. For what concerns, the thermal conduction between the planes, the pillars constitute a parallel thermal circuit. q s = i Ri2 K c T js T jb, A2 where is the total Seebeck coefficient of the junctions, R is the total electric resistance of the pillars, =T is the Peltier coefficient, T is the absolute temperature, and K c is the total thermal conductance of the columns. The three terms of Eq. A2 represent i the Peltier heat, ii the Joule heat, and iii the heat flux due to thermal diffusion. The factor 1/2 in the Joule heat term appears because half of the heat is delivered to the sample side and half to the bath side. The difference between the heat currents at the sample side q s and at the bath side q b is the Joule heat: q s q b = Ri 2. A3 3. Sensor equations in stationary state When the cell is in contact with the thermal bath at temperature T b and the sample at temperature T s, we have to take into account the presence of the electrical insulating layers. These are made of a ceramic material acting also as a thermal insulator. When a heat flux is traversing the layers we have, because of the heat conduction equation q= K T, a difference between the temperatures T js T s at the sample side and T jb T b at the bath side. If we suppose that the temperature in the bath and in the sample is homogeneous and that the layers are thin enough to consider them as a body with a negligible thermal capacity, then the two heat currents q s and q b through the layers are continuous. The thermal conductivity of the layers is taken as l of area A and thickness d l /2 each and the two heat conduction equations give q s = 2K l T s T js and q b = 2K l T jb T b, where K l = l A/d l is the thermal conductance of the two layers 2K l is the conductance of each layer. T b is a constant independent of the heat flux q b. The temperature difference between the sample and the bath is the sum of the three differences T s T b = T s T js + T js T jb + T jb T b. By using the heat conduction equations for the two layers, we get T s T b = T js T jb 1 q s + q b. A4 K l 2 By substitution of Eqs. A2 and A3, we get the relation between the two temperature differences: T js T jb = K P K c T s T b + 1 K P K c i K c, where K P is the total thermal conductance: A5

10 Basso et al. Rev. Sci. Instrum. 79, K P = K ck l. K c + K l By substitution of Eq. A5 in Eq. A1, weget v = P T s T b + R P i, where P = K P, K c and R P = R + 1 K P K c K c, A6 A7 A8 A9 are the effective Seebeck coefficient and the effective resistance, respectively. By substitution of Eq. A5 in Eq. A2, weget q s = P i Ri2 K P T s T b, where we defined the effective Peltier coefficient P : P = K P K c. A10 A11 The thermal quantities as a function of the electric quantities are T s T b = 1 P v R P i, q s = P i Ri2 1 S P v R P i, where S P = P /K P = /K c is the sensitivity. A12 A13 1 R. M. Bozorth, Ferromagnetism IEEE, New York, H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. Wiley, New York, First IIF-IIR International Conference on Magnetic Refrigeration at Room Temperature, edited by W. Egolf International Institute of Refrigeration, Paris, France, 2005, Refrigeration Science and Technology Proceedings No Second IIF-IIR International Conference on Magnetic Refrigeration at Room Temperature, edited by A. Poredos and A. Sarlah International Institute of Refrigeration, Paris, France, 2007, Refrigeration Science and Technology Proceedings No V. Basso, M. L. Bue, C. Sasso, and G. Bertotti, J. Appl. Phys. 99, 08K G. J. Liu, J. R. Sun, J. Shen, B. Gao, H. W. Zhang, F. X. Hu, and B. G. Shen, Appl. Phys. Lett. 90, M. Foldeaki, R. Chahine, and T. K. Bose, J. Appl. Phys. 77, M. Foldeaki, W. Schnelle, E. Gmelin, P. Benard, B. Koszegi, A. Giguere, R. Chahine, and T. K. Bose, J. Appl. Phys. 82, T. Plackowski, Y. Wang, and A. Junod, Rev. Sci. Instrum. 73, J. Marcos, F. Casanova, X. Batlle, A. Labarta, A. Planes, and L. Manosa, Rev. Sci. Instrum. 74, A. Schilling and M. Reibelt, Rev. Sci. Instrum. 78, S. Y. Dan kov, A. M. Tishin, V. K. Pecharsky, and J. K. A. Gschneidner, Rev. Sci. Instrum. 68, V. K. Pecharsky, J. O. Moorman, and J. K. A. Gschneidner, Rev. Sci. Instrum. 68, B. R. Gopal, R. Chahine, M. Foldeaki, and T. K. Bose, Rev. Sci. Instrum. 66, B. R. Gopal, R. Chahine, and T. K. Bose, Rev. Sci. Instrum. 68, L. Tocado, E. Palacios, and R. Burriel, J. Therm Anal. Calorim. 84, T. Plackowski, Phys. Rev. B 72, F. Casanova, A. Labarta, X. Batlle, F. J. Perez-Reche, E. Vives, L. Manosa, and A. Planes, Appl. Phys. Lett. 86, A. Velazquez-Campoy, O. Lopez-Mayorga, and M. A. Cabrerizo-Vilchez, Rev. Sci. Instrum. 71, A. Velazquez-Campoy, O. Lopez-Mayorga, and M. A. Cabrerizo-Vilchez, Rev. Sci. Instrum. 71, A. Zogg, F. Stoessel, U. Fischer, and K. Hungerbuhler, Thermochim. Acta 419, M. Kuepferling, C. Sasso, V. Basso, and L. Giudici, IEEE Trans. Magn. 43, J. L. Hemmerich, L. Serio, and P. Milverton, Rev. Sci. Instrum. 65, J. L. Hemmerich, J.-C. Loos, A. Miller, and P. Milverton, Rev. Sci. Instrum. 67, J. C. Moreno and L. Giraldo, Rev. Sci. Instrum. 76, S. Y. Dankov, A. M. Tishin, V. K. Pecharsky, and K. A. Gschneidner, Phys. Rev. B 57, L. Tocado, Thermomagnetic study of materials with giant magnetocaloric effect, Ph.D. thesis, Prensas Universitaria de Zaragoza, R. Skomski and J. M. D. Coey, Permanent Magnetism, Condended Matter Physics Institute of Physics, Bristol, V. K. Pecharsky and K. A. Gschneidner, Jr., Phys. Rev. Lett. 78, A. O. Pecharsky, K. A. Gschneidner, V. K. Pecharsky, and C. E. Schindler, J. Alloys Compd. 338,