Influence of the starting temperature of calorimetric measurements on the accuracy of determined magnetocaloric effect

Influence of the starting temperature of calorimetric measurements on the accuracy of determined magnetocaloric effect L.M. Moreno-Ramírez a, V. Franco a, A. Conde a, H. Neves Bezb, Y. Mudrykb, V.K. Pecharskyb,c a Dpto. Física de la Materia Condensada, ICMSE-CSIC, Universidad de Sevilla, P.O. Box 1065, 41080-Sevilla, Spain. b Ames Laboratory, Iowa State University, Ames, IA, 50011, USA. c Department of Materials Science and Engineering, Iowa State University, Ames, IA, 50011, USA. Journal of Magnetism and Magnetic Materials Volume 457, 1 July 2018, Pages 64-69 https://doi.org/10.1016/j.jmmm.2018.02.083 Abstract Availability of a restricted heat capacity data range has a clear influence on the accuracy of calculated magnetocaloric effect, as confirmed by both numerical simulations and experimental measurements. Simulations using the Bean-Rodbell model show that, in general, the approximated magnetocaloric effect curves calculated using a linear extrapolation of the data starting from a selected temperature point down to zero kelvin deviate in a non-monotonic way from those correctly calculated by fully integrating the data from near zero temperatures. However, we discovered that a particular temperature range exists where the approximated magnetocaloric calculation provides the same result as the fully integrated one. These specific truncated intervals exist for both first and second order phase transitions and are the same for the adiabatic temperature change and magnetic entropy change curves. The effect of this truncated integration in real samples was confirmed using heat capacity data of Gd metal and Gd5Si2Ge2 compound measured from near zero temperatures. 1. Introduction The magnetocaloric (MC) effect [1,2], a change of materials temperature and/or entropy with a change in external magnetic field, underpins a new generation of room temperature solid state refrigeration devices: magnetic refrigerators [3,4,5]. The goal is for such devices to replace traditional vapor-compression refrigerators because magnetic refrigeration supports higher energy efficiency and is, therefore, environmentally friendlier. Nominally, the MC effect is the temperature change produced by the application/removal of magnetic field under adiabatic conditions, ∆𝑇𝑎𝑑 [6,7]. This phenomenon is ascribed to the coupling of the crystallographic and magnetic sub-lattices: in an adiabatic process the entropy variations of the magnetic sub-lattice have to be balanced by the corresponding entropy changes of the crystallographic sub-lattice to conserve total entropy, leading to a temperature change of the material. Consequently, other quantity used to describe the MC effect is the magnetic entropy change, ∆𝑆𝑀, produced by the application/removal of a magnetic field under isothermal conditions. This effect is always present in any magnetic material although it is only relevant for significant magnetic entropy variations. For near room temperature magnetic refrigeration, such variation occurs in the region close to a phase transition which implies magnetization changes of either first (FOPT) or second (SOPT) order type [8]. Typically, SOPT materials present lower MC response than FOPT materials, despite covering a broader temperature range and having a reversible character (FOPT materials often show thermal and magnetic hysteresis) [9,10]. The MC magnitudes can be determined indirectly, using magnetization, 𝑀, and/or heat capacity measurements, 𝐶 (specific heat capacity is denoted by 𝑐) [11]. To determine indirectly the adiabatic temperature change, heat capacity data are needed (alone, by collecting data in applied magnetic field, or combined with magnetization data), while the magnetic entropy change can be determined indirectly exclusively using magnetization or heat capacity data/isothermal calorimetric measurements. To determine both MC magnitudes using heat capacity measurements only, first of all, the total entropy of the system (𝑆) has to be calculated [12]: 𝑆𝐻(𝑇)=𝑆0,𝐻 +∫ 𝐶𝐻(𝑇) 𝑇 𝑇 0 K d𝑇, (1) where the subscript 𝐻 indicates constant magnetic field, 𝑇 is the temperature and 𝑆0,𝐻 is the zero kelvin entropy term. From the total entropy, the magnetic entropy change and the adiabatic temperature change are calculated according to: ∆𝑆𝑀(𝑇,∆𝐻=𝐻𝐹−𝐻𝐼)=𝑆𝐻𝐹(𝑇)−𝑆𝐻𝐼(𝑇) (2) ∆𝑇𝑎𝑑(𝑇,∆𝐻=𝐻𝐹−𝐻𝐼)=𝑇𝐻𝐹(𝑆)−𝑇𝐻𝐼(𝑆)=𝑇𝐻𝐹(𝑆=𝑆𝐻𝐼(𝑇)) − 𝑇 , (3) where HI and HF are the initial and final magnetic fields, respectively. According to equation (1), 𝑆0,𝐻 must be known down to temperatures close to zero kelvin for accurate integration. With respect to 𝑆0,𝐻, if it is assumed to be field independent (as it is typical for a condensed system [13]), than it has no influence on the resulting ∆𝑆𝑀 and ∆𝑇𝑎𝑑 values. However, when temperatures close to 0 K cannot be reached in the heat capacity measurement, the calculations will be affected by a systematic error. In this case, a linear behavior of the integrand (𝐶𝐻/𝑇) vs T can be assumed for the missing low temperature range (taking 𝐶𝐻/𝑇(0 K)=0), and the total entropy under this approximation is [11]: 𝑆𝐻 𝑎𝑝(𝑇)=1 2𝐶𝐻(𝑇𝑖𝑛𝑖)+∫ 𝐶𝐻(𝑇) 𝑇 𝑇 𝑇𝑖𝑛𝑖 d𝑇, (4) where 𝑇𝑖𝑛𝑖 is the initial temperature of the measurement and the index ap denotes the approximated entropy. Using this obtained 𝑆𝐻 𝑎𝑝(𝑇) dependence, the estimated MC values can be calculated using equations (2) and (3). The effect of this approximation was studied previously for second order phase transitions [14]. In that work, numerical calculations were performed for SOPT materials using the Brillouin function, Debye model and Fermi electron statistics. It was shown that at certain initial temperatures the approximated MC curves are the same (for the whole temperature range starting from 𝑇𝑖𝑛𝑖) as the curves for which the integration started from very close to zero kelvin. The value of the optimal initial temperature was the same for ∆𝑆𝑀 and ∆𝑇𝑎𝑑 and was slightly field dependent. Consequently, a method was proposed to calculate the MC magnitudes from heat capacity data measured in a restricted temperature range. The procedure was successfully applied to a set of heat capacity data of a single phase GdZn alloy [15] obtained using a relaxation calorimeter. However, the possible generalization to first order phase transition materials remained an open issue. As, nowadays, many magnetocaloric materials used in magnetic refrigerator prototypes are FOPT materials [16], the generalization of this method can be helpful to increase the throughput of characterization of these technologically important materials. In this work, we extend the previous analysis to materials with a first order phase transition by using the Bean-Rodbell model [17]. It has previously been shown that this model can be applied to describe the MC response of different materials with a FOPT [18,19]. Specifically, the modification of a parameter (𝜂) can simulate magnetic phase transitions of either first or second order type. In order to corroborate theoretical predictions of the influence of the truncated temperature range, the result of the approximation was checked experimentally using heat capacity data measured from 4 K in a heat-pulse calorimeter for two prototypical MC materials with phase transitions of different order: Gd metal (SOPT) and Gd5Si2Ge2 compound (FOPT). 2. Models and experimental techniques As a general feature, magnetic mean field theory approximates the exchange interactions of the surroundings of a magnetic moment by an effective magnetic field (molecular field), 𝐻𝑚𝑜𝑙 [20]: 𝐻𝑚𝑜𝑙 =𝜆𝑀, (5) where 𝜆 is a coefficient related to the exchange integral and 𝑀 is the magnetization of the material. Based on that, Bean and Rodbell assume that magnetic interactions and deformations of the lattice are related. They propose that the effect on the magnetic interactions produced by deformation can be written as [17]: 𝜆=𝜆0(1+𝛽𝑉−𝑉0 𝑉0), (6) where 𝜆0 is the molecular field coefficient in the absence of deformation, 𝛽 is an introduced parameter, 𝑉 is the volume and 𝑉0 is the volume of the system at 0 K without interactions. Defining 𝜔=(𝑉−𝑉0)/𝑉0, the Gibbs free energy per unit volume of a magnetic material in which there are also deformation effects can be expressed as: 𝑔=−𝜆𝑀2+1 2𝐾𝜔2+𝑝𝜔−𝑇𝑠−𝐻𝑀, (7) where the first term corresponds to the exchange and the second and third terms correspond to the distortion of the lattice, 𝐾 being the compressibility of the material, 𝑝 the external pressure and 𝑇 the temperature. As a first approximation, 𝑠 can be considered the magnetic entropy, 𝑠𝑀 (neglecting the lattice entropy term). By minimizing 𝑔 with respect to 𝜔 and magnetization it can be found that, for 𝑝=0, the value of magnetization that minimizes 𝑔 is: 𝑚=𝐵𝐽(𝑥),with 𝑥=𝑔𝜇𝐵𝐽 𝑘𝐵𝑇𝐻+3𝑇𝐶 𝑇(𝐽 𝐽+1)𝑚+9 5((2𝐽+1)4−1 (2(𝐽+1))4)𝑇𝐶𝜂𝑚3, (8) where 𝑚 is the normalized magnetization (𝑚=𝑀/𝑛𝑔𝜇𝐵𝐽), 𝑛 is the density of magnetic atoms, 𝑇𝐶 is the Curie temperature in the absence of deformation, 𝑔 is the spectroscopic splitting factor, 𝜇𝐵 is the Bohr magneton and 𝐽 is the total quantum angular momentum. The magnetic heat capacity can be determined from: 𝑐𝑀=𝑛𝐾𝐵𝑇(𝜕[𝑙𝑛(sinh (2𝐽+1 2𝐽 𝑥) sinh ( 1 2𝐽𝑥) )−𝑥𝐵𝐽(𝑥)] 𝜕𝑇⁄ )𝐻, (9) using the 𝑥 values previously obtained in (8). The parameter 𝜂 controls the order of a transition: 𝜂=5 2((2𝐽+1)4−1 (2(𝐽+1))4)𝑁𝑘𝐵𝐾𝑇𝐶𝛽2. (10) Namely, a transition is of first order type (discontinuous changes of 𝑀) if 𝜂>1. The heat capacity of the system can be considered as the sum of the magnetic, lattice and electronic contributions. For the lattice (𝐶𝑙) and electronic (𝐶𝑒) contributions, the models of Debye and Fermi [21] have been used, respectively: 𝐶𝑙=9𝑁𝑘𝐵(𝑇 𝜃𝐷)3∫𝑥4𝑒𝑥 (𝑒𝑥−1)2 𝜃𝐷 𝑇 0d𝑥 (11) 𝐶𝑒=𝛾𝑇, (12) where 𝑘𝐵 is the Boltzmann constant, 𝜃𝐷 is the Debye temperature and 𝛾 is the electronic specific heat constant that depends on the density of states at the Fermi level. The parameters used for the simulations in this work are those for Gadolinum (𝐽=7/2, 𝑇𝐶=293 K, 𝜃𝐷=163 K, 𝛾=6.4 mJ mol-1 K-2 and 𝐾=2.64∙10−11 Pa-1). The heat capacity for applied magnetic fields 0, 2, 5, 7.5, and 10 T was measured from 4 to 350 K by using a heat-pulse calorimeter which has been described elsewhere [22]. The uncertainties of the heat capacity data were 1% from 4 to 20 K, and less than 0.5% in the temperature range from 20 to 350 K. 3. Results and discussion 3.1 Numerical calculations Figure 1 shows the temperature dependence of the heat capacity data at several applied magnetic fields simulated using Gd parameters (𝑇𝐶=293 K) with 𝜂=0 (a SOPT; upper panel) and 1.5 (a FOPT; lower panel) . The Debye contribution is plotted separately. The Fermi (electronic) contribution to the heat capacity is not plotted due to its relatively low values. The graphs show that by using the models described in Eqs. (5) – (12), the main features of heat capacities of materials with both SOPT and FOPT - specifically a sharper peak near the transition as the parameter 𝜂 increases - are qualitatively reproduced. These heat capacity data are used to calculate the total entropy according to (4). To study the effect of the approximation (extrapolation of the heat capacity data from the initial temperature down to zero kelvin), the data are truncated at different temperatures (𝑇𝑖𝑛𝑖). With the obtained approximated entropy curves, the MC magnitudes (∆𝑠𝑀 𝑎𝑝 and ∆𝑇𝑎𝑑 𝑎𝑝) are calculated according to (2) and (3). Figure 2 shows the temperature dependence of the approximated MC curves (∆𝑠𝑀 𝑎𝑝 and ∆𝑇𝑎𝑑 𝑎𝑝, upper and lower panels, respectively) for different initial temperatures (𝑇𝑖𝑛𝑖) at magnetic field change of 5 T simulated using 𝜂=1.5. The insets of figure 2 show the differences of each approximated curve with respect to the one obtained by integration from 0 K (these differences are denoted by 𝛿): for ∆𝑠𝑀 𝑎𝑝 (upper panel), the differences are temperature independent, while for ∆𝑇𝑎𝑑 𝑎𝑝 (lower panel) 𝛿 is temperature dependent. These features, that were previously observed for SOPT simulated using the Brillouin model, remain valid for the Bean-Rodbell model regardless of the value of the parameter 𝜂. For the ∆𝑇𝑎𝑑 𝑎𝑝 curves, 𝛿 shows a sharp peak in the region close to the transition. Figure 3 shows the 𝛿 curve of the peak vs. the initial temperature (𝑇𝑖𝑛𝑖) for different 𝜂 and a magnetic field change of 5 T. Independently of the 𝜂 values, all curves exhibit a similar behavior: when 𝑇𝑖𝑛𝑖 is low, the differences are practically equal to zero, but as 𝑇𝑖𝑛𝑖 increases, the difference shows one minimum and one maximum (the maximum has a larger absolute value), followed by a change of sign of the differences below 𝑇𝐶. Therefore, we can observe two temperatures (denoted as optimal initial temperatures, 𝑇𝑖𝑛𝑖 𝑜𝑝𝑡) for which the approximated values are coincident with those obtained when integration starts from 0 K (the value is the same for both ∆𝑠𝑀 𝑎𝑝 and ∆𝑇𝑎𝑑 𝑎𝑝 data). A general feature, as follows from Fig. 3, is that as 𝜂 increases, the maximum values of 𝛿 decrease, and the effect of the approximation becomes less significant for FOPT materials when compared with SOPT. This should be related to the different height and width of the heat capacity peak for FOPT and SOPT, that makes the low temperature part of the curve relatively less important for FOPT. To further discuss the previous results we now consider the relationship between the total entropy, 𝑠𝐻 (equation (1), starting the integration from 0 K), and the approximated entropy, 𝑠𝐻 𝑎𝑝 (equation (4)), ignoring the zero entropy term: 𝑠𝐻(𝑇)=∫ 𝑐𝐻 𝑇d𝑇 𝑇 0=𝑠𝐻 𝑎𝑝(𝑇)−1 2𝑐𝐻(𝑇ini)+∫ 𝑐𝐻 𝑇d𝑇=𝑠𝐻 𝑎𝑝(𝑇)+ξ𝐻(𝑇𝑖𝑛𝑖) 𝑇ini 0 (13) where the error parameter ξ𝐻 depends on both 𝐻 and 𝑇𝑖𝑛𝑖. The relationship between the true and approximated magnetic entropy change for any initial temperature 𝑇∗ is: ∆𝑠𝑀(𝑇∗)=𝑠𝐻(𝑇∗)−𝑠0(𝑇∗)=𝑠𝐻 𝑎𝑝(𝑇∗)+ξ𝐻−(𝑠0 𝑎𝑝(𝑇∗)+ξ0) =∆𝑠𝑀 𝑎𝑝(𝑇∗)+(ξ𝐻−ξ0), (14) and ∆𝑠𝑀(𝑇∗)=∆𝑠𝑀 𝑎𝑝(𝑇∗) only when: ξ𝐻=ξ0, (15) i.e. the approximation provides the correct value only if the shift in the total entropy is the same for both magnetic fields. Simulations show that there are two optimal initial temperatures, 𝑇𝑖𝑛𝑖 𝑜𝑝𝑡, that fulfill condition (15) and that, for other initial temperatures, the differences of the approximated magnetic entropy changes compared to the true values that can be obtained starting the integration from T = 0 remain constant across the whole temperature range. The analysis of the truncation effect on the resultant adiabatic temperature can be performed in a similar way. The definitions of both ΔTad and ΔTadap for a temperature 𝑇∗ are ∆𝑇𝑎𝑑(𝑇∗)=𝑇𝐻(𝑠∗)−𝑇0(𝑠∗) ( 16) ∆𝑇𝑎𝑑 𝑎𝑝(𝑇∗)=𝑇𝐻 𝑎𝑝(𝑠𝑎𝑝∗)−𝑇0𝑎𝑝(𝑠𝑎𝑝∗), ( 17) where the selected temperature 𝑇∗ gives the values of the corresponding entropy parameters 𝑠∗=𝑠0(𝑇∗) and 𝑠𝑎𝑝∗=𝑠0 𝑎𝑝(𝑇∗), defined for 𝐻=0 because it is the initial state of the system. The relation between both values, according to equation (13), in the case of zero applied field is 𝑠𝑎𝑝∗=𝑠∗−ξ0. ( 18) Figure 2. Approximated magnetic entropy change, ∆𝑠𝑀 𝑎𝑝, (upper panel) and adiabatic temperature change, ∆𝑇𝑎𝑑 𝑎𝑝, (lower panel) vs. temperature curves at 5 T simulated using 𝜂=1.5. Insets show the differences of each approximated curve with respect to the curve integrated from 0 K (𝛿). Figure 3. Differences at 𝑇𝑝𝑒𝑎𝑘 of the approximated magnetic entropy change curves (∆𝑠𝑀 𝑎𝑝,𝑝𝑒𝑎𝑘) with respect to those integrated from 0 K (∆𝑠𝑀 𝑝𝑒𝑎𝑘) vs. the initial temperature (𝑇𝑖𝑛𝑖) simulated using different 𝜂 values. For this simulation, 𝑇𝐶=293 K. Figure 4. Experimental specific heat (𝑐𝐻) vs. temperature (𝑇) curves measured at different magnetic fields for pure Gd and Gd5Si2Ge2. Figure 5. Approximated magnetic entropy change, ∆𝑠𝑀 𝑎𝑝, (upper panel) and adiabatic temperature change, ∆𝑇𝑎𝑑 𝑎𝑝, (lower panel) vs. temperature curves at 7.5 T for different initial temperatures (𝑇𝑖𝑛𝑖) for pure Gd. The insets show the temperature dependence of the difference of each approximated curve with respect to the curve integrated from 4 K (𝛿). Figure 6. Approximated magnetic entropy change, ∆𝑠𝑀 𝑎𝑝, (upper panel) and adiabatic temperature change, ∆𝑇𝑎𝑑 𝑎𝑝, (lower panel) vs. temperature curves at 7.5 T for different initial temperatures (𝑇𝑖𝑛𝑖) for Gd5Si2Ge2. The insets show the temperature dependence of the difference of each approximated curve with respect to the curve integrated from 4 K (𝛿). Figure 7. Differences at 𝑇𝑝𝑒𝑎𝑘 of the approximated magnetic entropy change curves (∆𝑠𝑀 𝑎𝑝,𝑝𝑒𝑎𝑘) from those determined using 𝑇𝑖𝑛𝑖 = 4 K (∆𝑠𝑀 𝑝𝑒𝑎𝑘) vs. the initial temperature (𝑇𝑖𝑛𝑖) for different applied magnetic field changes for pure Gd (upper panel) and Gd5Si2Ge2 (lower panel). Thicker lines are guides to the eye. For Gd5Si2Ge2, the curve corresponding to 2T has a poor signal to noise ratio due to the relative lower importance of the approximation for FOPT and it is therefore not plotted. [1] P. Weiss, A. Piccard, “Sur un nouveau phénoène magnétocalorique” Comptes Rendus 166, 352-354, 1918. [2] W.F. Giauque, D.P. MacDougall, Phys. Rev. 43 (1933) 768. [3] O. Gutfleisch, M.A. Willard, E. Bruck, C.H. Chen, S.G. Sankar, J.P. Liu, “Magnetic materials and devices for the 21st century: stronger, lighter, and more energy efficient”, Advanced Materials 23, 821-842, 2011. [4] E. Brück, “Developments in magnetocaloric refrigeration”, J. Phys. D: Appl. Phys. 38, R381–R391, 2005. [5] C. Zimm, A. Jastrab, A. Sternberg, V. Pecharsky, K. Gschneidner Jr., M. Osborne, I. Anderson, “Description and Performance of a Near-Room Temperature Magnetic Refrigerator”, Advances in Cryogenic Engineering 43, 1759-1766, 1998. [6] K.A. Gschneidner, V.K. Pecharsky, “Magnetocaloric Materials”, Annu. Rev. Mater. Sci. 30, 387–429, 2000. [7] V. Franco, J.S. Blázquez, B. Ingale, A. Conde, “The Magnetocaloric Effect and Magnetic Refrigeration Near Room Temperature: Materials and Models”, Annu. Rev. Mater. Sci. 42, 305–342, 2012. [8] P. Ehrenfest, “Phasenumwandlungen im ueblichen und erweiterten Sinn, classifiziert nach dem entsprechenden Singularitaeten des thermodynamischen Potentiales.” Communications from the Physical Laboratory of the University of Leiden 36, 153– 157,1933 [9] V. Franco and J.S. Blázquez and J.J. Ipus and J.Y. Law and L.M. Moreno-Ramírez and A. Conde, “Magnetocaloric effect: From materials research to refrigeration devices”, Progress in Materials Science 93, 112-232, 2018. [10] O. Gutfleisch, T. Gottschall, M. Fries, D. Benke, I. Radulov, K. P. Skokov, H. Wende, M. Gruner, M. Acet, P. Entel, M. Farle, “Mastering hysteresis in magnetocaloric materials”, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 274, 2074, 2016. [11] V.K. Pecharsky, K.A. Gschneidner, “Magnetocaloric effect from indirect measurements: Magnetization and heat capacity”, J. Appl. Phys. 86, 565-575, 1999. [12] A.M. Tishin, Y.I. Spichkin, “The magnetocaloric effect and its applications”, Institute of Physics Publishing, 2003. [13] M. W. Zemansky, “Heat and Thermodynamics”, 5th ed. McGraw-Hill, 1968. [14] L.M. Moreno-Ramírez, J.S. Blázquez, J.Y. Law, V. Franco and A. Conde , “Optimal temperature range for determining magnetocaloric magnitudes from heat capacity”, J. Phys. D: Appl. Phys. 49, 495001, 2016. [15] J.Y. Law, L.M. Moreno-Ramírez, J.S. Blázquez, V. Franco, A. Conde, “Gd plus GdZn biphasic magnetic composites synthesized in a single preparation step: Increasing refrigerant capacity without decreasing magnetic entropy change”, J. All. Compd. 675, 244–247, 2016. [16] BASF, Premiere of cutting-edge cooling appliance at CES (2015). Available at https://www.basf.com/cn/en/company/news-and-media/news-releases/2015/01/p-15- 100.html. [17] C. P. Bean, D. S. Rodbell, “Magnetic Disorder as a First-Order Phase Transformation”, Phys. Rev 126, 104-115, 1962 [18] M. Oumezzine, J. S. Amaral, F. J Mompean, M. G. Hernandez, M. Oumezzine, “Structural, magnetic, magneto-transport properties and Bean-Rodbell model simulation of disorder effects in Cr3+ substituted La0.67Ba0.33MnO3 nanocrystalline synthesized by modified Pechini method”, RSC Advances 6, 32193-32201, 2016 [19] P.J. von Ranke, N.A. de Oliveira, S. Gama, “Understanding the influence of the firstorder magnetic phase transition on the magnetocaloric effect: application to Gd5(SixGe1−x)4”, J. Magn. Magn. Mater. 277, 78-83, 2004. [20] P. Weiss, “L’hypothése du champ moléculaire et la propriété ferromagnétique” J.Phys. (Paris) 6, 661-690, 1907. [21] C. Kittel, “Introduction to Solid State Physics”, ISBN 978-0471415268 [22] V.K. Pecharsky, J.O. Moorman, K.A. Gschneidner Jr., “A 3–350 K fast automatic small sample calorimeter”, Rev. Sci. Instrum. 68, 4196-4207, 1997. [23] S. Yu. Dankov, A. M. Tishin, V. K. Pecharsky, K. A. Gschneidner Jr., “Magnetic phase transitions and the magne-tothermal properties of gadolinium”, Phys. Rev. B 57, 3478-3490, 1998. [24] V.K. Pecharsky, K.A. Gschneidner Jr., “Giant Magnetocaloric Effect in Gd5Si2Ge2”, Phys. Rev. Letters 78, 4494-4497, 1997.