Determination of the quantitative relationship between crystallographic texture and magnetic properties in advanced permanent magnets may be hampered by complex microstructures, which complicate methods that rely on diffraction, or by interparticulate interactions, which adversely affect methods based on magnetic remanence measurements. To this end, new techniques in the determination of texture of bulk permanent magnets are being explored to overcome these inherent experimental difficulties. The analysis of inverse paramagnetic susceptibility measurements constitutes a new method to investigate crystallographic texture. Such measurements also provide Curie temperature data, which is sensitive to chemical changes that may have occurred in the magnetic phase during processing. The mathematical formalism underlying the analysis of inverse susceptibility measurements is outlined, and is used to evaluate magnetic measurements taken from a series of Nd{sub 2}Fe{sub 14}B magnets that have been processed by different means, and thus contain different degrees of texture. While this method does provide qualitative information concerning the relative crystallographic alignment of magnet samples, it needs calibration to obtain an explicit value for a texture order parameter

Lewis, L.H.

Welch, D.O.

UNT Digital Library

I V BNL-6 3 4 16 Form 2075 Crystallogrphic texture determinations from inverse susceptibility measurements L. H. Lewis and D. 0. Welch Department of Applied Science Brookhaven National Laboratory Upton, NY 11973-5000 Presented at 41st Annual Conf. on Magnetism and Magnetic Materials Atlanta, Georgia NOV. 12-15,1996 Proceedings to be published in Journal of Applied Physics This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation. or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency therwf. _ _  This research was performed under the auspices of the U.S. Department of Energy, Division of Materials Sciences, Office of Basic Energy Sciences under Contract No. DE-AC02-76CH00016. By acceptance of this article, the publisher and/or recipient acknowledges the US. Government's right to retain a nonexclusive, royalty-free license in and to any copyright covering this paper. DlSTRIBUT1ON OF THIS DOCWENT IS UNLIMITED. 3 FE-13 CRYSTALLOGRAPHIC l?XlTJRE DETERMINATIONS FROM INVERSE SUSCE~IBILITY MEASUREMENTS L. H. Lewis and D. 0. Welch Department of Applied Science, Brookhaven National Laboratory, Upton, New York, 11973-5000 Abstract: Determination of the quantitative relationship between crystallographic texture and magnetic proper ties in advanced permanent magnets may be hampered by complex mi- crostructures, which complicate methods that rely on diffrac- tion,. or by interpar ticulate interactions, which adversely af- fect methods based on magnetic remanence measurements. To this end, new techniques in the determination of texture of bulk permanent magnets are being explored to overcome these inherent experimental difficulties. The analysis of in- verse paramagnetic susceptibility measurements constitutes a new method to investigate crystallographic texture. Such measurements also provide Curie temperature data, which is sensitive to chemical changes that may have 'occurred in the magnetic phase during processing. The mathematical formalism underlying the analysis of inverse susceptibility measurements is outlined, and is used to evaluate magnetic measurements taken from a series of Nd2Fe14B magnets that have been processed by different means, and thus contain different degrees of texture. While -1- , this method dqes provide qualitative information concern- ing the relative crystallographic alignment of magnet sam- ples, it needs calibration to obtain an explicit value for a tex- ture order parameter. -2- DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. . 6 Introduction: I Improvements in processing to approach an ideal degree of crystallographic texture are desired for the engineering of increasingly higher (BH),,, magnets. Unfortunately, the de- gree of crystallographic alignment in bulk magnets is some- times difficult to determine. A number of methods based on a variety of techniques, such as magnetic measurements, x- ray diffraction and microscopy methods egst to evaluate tex- ture, but there are limitations to the application of each technique. By way of example, the anticipated debut of two- phase anisotropic "exchange-spring" magnets consisting of a magnetically soft phase intimately mixed with an aligned hard phase (I) presents significant challenges in the deter- mination of the degree of orientation of the ensemble of crystallites. In this case the exchange interactions amongst the constituent phases nullify the use of techniques that uti- lize measurements of the remanence Br, such as the angular dependence of Br (2) or the remanence ratio &/M, (3). The analysis of the temperature dependence of the in- verse paramagnetic susceptibility l/xp provides an alterna- tive method to obtain information concerning crystallo- graphic texture. Because the material is probed while it is in a paramagnetic state there are no interphase or intergranular interactions to affect the data. This method also allows an examination of the samples' paramagnetic Curie tempera- tures, allowing one to easily monitor any chemical changes that may have occurred in the paramagnetic phase during I -3- processing. We present here the mathematical formalism used to examine the inverse susceptibility, and then apply the results to a series of Nd2Fe14B magnets that have been fabricated by different processes. Theoretical Framework: The paramagnetic susceptibility x of a material of uniax- ial symmetry is a second-rank tensor with two distinct ele- ments: the susceptibilities for magnetic field parallel and perpendicular to the symmetry axis (4). Thus, in principle, if one has a suitable single crystal with which to establish these two tensor elements, it is possible to use a measurement of the susceptibility of a textured polycrystal to estimate the de- gree of texture present. This work will address only the case of measurements made at temperatures high enough such that a Curie-Weiss-type temperature dependence is observed. Practically speaking, the data must be taken at elevated temperatures that are at least 50 K above the Curie temperature of the phase of interest. In such cases the distinct elements of the susceptibility tensor of each crystallite have the form: where i denotes either the basal (ab) or the axial (c) compo- nent. In principle, both the Curie constant Ci and the para- magnetic Curie temperature Si depend on the direction of -4- the magnetic field with respect to the crystallite axis. Bowden et al. (5) have considered the case of anisotropy in the paramagnetic Curie temperature f3i that arises from crys- tal field effects, while Niira and Oguchi (6 )  have discussed the anisotropy of the Curie constant Ci which can arise from anisotropic g-factors. Anisotropy of Ci can also arise from anisotropic exchange. If it is assumed that both 9i and Ci are anisotropic, then the transformation properties of second rank tensors (4) show that the paramagnetic susceptibility of an ensemble of independent crystallites, a good approxima- tion to a polycrystal in the Curie-Weiss regime of paramag- netism, even for exchange-coupled two-phase materials, is given by: where (n2) is an ensemble average of the square of the cosine ni of the angle between the symmetry axis of each crystallite and the applied field. The texture dependence of (n2) is the key to using the paramagnetic susceptibility as a measure of crystallographic texture: for a random polycrystal 1 (n2)=- while for a perfectly axially-textured polycrystal ("')>=I. It is convenient to introduce a texture order parameter S which lies in the range 0 S S S 1 for these cases as a measure of the axial texture: 3' ( n 2 ) - i  1 1-- 3 z =  (3) Thus I: is valid in the range -1/2 5 I: S 1, where C=1/2 de- scribes the isotropic &o-dimensional case with all symmetry axes in a plane, Z=O describes the random alignment case, and Z=l is the uniaxially-aligned case. In terms of the tex- ture order parameter Z, the susceptibility of the polycrystal is If the single crystal parameters Cab, Cc, and Bc are known, then a measurement of the polycrystalline suscepti- bility yields the texture order parameter I; for the polycrystal. This, however, is not always the case, since processing may alter the values of Ci and Oi as well as the texture. Thus it is of value to simplify and approximate Eq. (4). The experi- mental data of Burzo ef al, (8) and Liu et al. (9) show that the deviation of the paramagnetic Curie temperature 0~ from the thermodynamic Curie temperature TC is small compared with Tc for both polycrystals (8) and single crystals (9). Furthermore, these data plus o w  own work show that the anisotropy of 0p (6c-eab)  , is also small. To first order in T C  this anisotropy and in the anisotropy of the Curie constant, (" cab) ,  Eq. (4) becomes: CC where and Tc are the paramagnetic and thermodynamic Curie temperatures, respectively, of the polycrystal and AC E Cc-Cab, A O =  &-6ab. In the derivation of Eq. (5) it was as- sumed that the deviation of ep from Tc arises from crystal field effects only, and that, following the use of experimental crystal field coefficients of Boltich and Wallace (7) in the the- ory of Bowden et a2 (51, eC>&b.. From Eq. (5) we see that a plot of the inverse susceptibil- ity %j1 versus the scaled temperature - yields a straight T e P  line with a slope !2 that varies linearly with the texture order parameter Z. The condition that this slope increases with decreasing texture, as is observed experimentally and discussed in  the next section, is simply that '' -'Ob > - ' O b ,  i.e., that the fractional anisotropy of the Curie constant be dominant over the fractional anisotropy of cc Tc  the paramagnetic Curie temperature. Experimental Procedures and Results: Magnetic measurements were made on a series of sam- ples with nominally the same composition but processed in different manners. The nominal compositions and process- ing details of the samples are listed in Table I. The samples were cut with a slow-speed wire saw to the appropriate di- mensions to fit inside quartz capillary tubes. The tubes were -7- evacuated to a base pressure of 5.6 x 10-5 torr and sealed with Zr turnings to avoid oxidation during measurement (10). Prior to each high-temperature hysteresis loop measurement the magnets were brought to temperature and then saturated in an applied field of +5.0 T. The resultant hysteresis loops were adjusted for demagnetization with a geometric correc- tion. In every case the magnets were confirmed to consist mainly of Nd2Fe14B with a small amount, on the order of 0.1 vol%, of an unknown ferromagnetic phase that has a Curie temperature Tcin the vicinity of 950 "C (11). Additionally, room-tempera ture saturation magnetization measurements indicate that the sintered sample contains only 86% of the Nd2Fe14B phase, the remainder presumably being the 1-44 phase; the slope of the paramagnetic signal was adjusted for this deficiency. The paramagnetic signal from the 2-14-1 ma- trix phase and the ferromagnetic signal of the unknown phase were separated from one another (11). Fig. 1 shows the inverse of the susceptibility of the paramagnetic portion of the signal graphed as a function of reduced temperature, TIOp, where 6p was determined experimentally to be the linear extrapolation of the inverse susceptibility to the tem- perature axis. The paramagnetic Curie temperatures 0p for each sample are included in the legend of Fig. 1. Fig. 1 also displays the susceptibilities taken from the literature of isotropic single-phase Nd2Fe14B powder (8) and a Nd2Fe14B single crystal (9), measured along the easy-axis c-direction. It -8- 4 should be noted that Liu et al. (9) determined the single crys- I tal to possess a Curie temperature of 574 K, approximately 20 ' degrees lower than the accepted literature values of 595 K - 600 K. In accordance with the formalism outlined above, the experimental inverse susceptibilities DS. reduced tempera- ture curves exhibit slopes that increase with decreasing sam- ple alignment. The inverse susceptibility slopes increase from the single crystal and MQ-3 sample to the sintered sample and are highest for the powder and hot-pressed sam- ples. It is reassuring that the two isotropic samples, the pow- der and the hot-pressed samples, both exhibit very similar slopes. However, it is not expected that the single crystal and the MQ-3 sample would have exactly the same slope; it ap- pears that the slope of the inverse susceptibility curve is not sensitive to small misorientation angles. This empirical ob- servation may be understood by way of the analysis of the construction of a simple "box distribution" to describe the distribution of misorientation angles between the symmetry axes of the constituent crystals and the overall deformation direction. For the box distribution the population of crystal. axes is uniform over a solid angle for misorientation angles less than @, whereas there are no crystals with such misori- entation for angles greater than @. If the "box distribution" is chosen so as to match its variance with that of the true dis- tribution, the cutoff parameter Q, is approximately 2.7 times the half-width at half-maximum (HWHM) of the rocking -9- curve. The texture order parameter C of Eq. 5 may be related to the box-distribution cut-off angle as: cos<Psinz a 2 ' [l -cos@] C r  This expression is graphed in Fig. 2. Note that for good tex- tures, with only small deviations from uniaxial alignment, the texture order parameter may be approximated as Z = [1 -($)I, This result means that small misorientation deviations from ideal alignment do not significantly affect the paramagnetic susceptibility because of the quadratic vari- ation in a; this situation appears verified experimentally, as noted above. Summary : The methodology and underlying rationale for a new technique that may be used to probe the crystallographic tex- ture distribution in a polycrystalline magnetic material have been presented. The use of paramagnetic susceptibility mea- surements, while preliminary, may prove to be useful in cir- cumstances that preclude the use of the more standard de- terminations of magnetic remanence, Br, such as in the case of novel exchange-spring magnets. The trend of the inverse paramagnetic susceptibility vs. temperature data collected from a selection of Nd~Fel4B-based magnetic materials fabri- cated by different methods agrees with that predicted from a -io- simple linearization of the Curie-Weiss law for textured polycrystals that has been rewritten to' take into account both anisotropic paramagnetic Curie temperatures and anisotropic Curie constants. While this method does pro- vide qualitative : information concerning the relative crystal- lographic alignment of magnet samples, it needs calibration to obtain an explicit value for the texture order parameter. Acknowledgments The authors would like to thank F. Pourarian of the Carnegie Mellon Research Institute and Carl Fuerst of General Motors Research for supplying samples. This re- searc.h was performed under the auspices of the U.S. Department of Energy, Division of Materials Sciences, Office of Basic Energy Sciences under Contract No. DE-AC02- 76CH00016. -11- . . . .- I -  t , '  , .- References: 1. R. Skomski, J. Appl. Phys. 76 (10) (1994) 7059. 2. K. Elk, L Hahn and R. Scholl, 1. Map. Map. Mater. 72 (1988) 335. 3. E. C. Stoner and E. P. Wohlfarth, Philos. Trans. Roy. SOC. London A 240 599, (1948). 4. J. F. Nye, Phvsical Prouerties of Crvstals (Oxford, Clarendon Press, London, 1957). 5. G. J. Bowden, D. St. P. Bunbury and M. A. H. McCausland, J. Phys. C: Solid St. Phys. 4 (1971) 1840. 6. K. Niira and T. Oguchi, Prog. Theo. Phys. 11 (1954) 425. 7. E. B. Boltich and W. E. Wallace, Solid State Commun. 55 (1985) 529. 8. E. Burzo, E. Oswald, M . 4 .  Huang, E. Boltich and W. E. Wallace, J. Appl. Phys. 57 (1) (1985) 4109. 9. Y. Liu, L. Mei, H. Chen and F. Chen, Chinese Phys. Lett. 4 (11) (1987) 513. 10. L. H. Lewis and Konrad Bussmann, Rm. Sci. Instrum., in press. 11. L. H. Lewis, D. 0. Welch and E Pourarian, J. Appl. Phys., 79 (8) (1996) 5513. -1 2- I , Table I: Descriptions I of Nd2Fel4B-based samples: Processing Bulk Composition Die-upset (MQ-3) Nd 13.75Fe80.25B6 Sintered -13- Figure Captions: 1: Inverse susceptibilities of Nd2Fel4B magnetic materials processed in vari- ous manners. 2. The order parameter X, based on the "box distribution" as defined in the text, as a function of crystallite misorientation angle. -14- sintered: 8p=600.1 K -e- hot-pressed 8 ~ 5 9 9 . 6  K - -8- die-upset: 8 ~ 5 9 9 . 6  K - -n- single crystal: 8 ~ 3 7 4 . 4  K - + powder: 6 ~ 5 9 9 . 9  Kl ' " ' " ' ' ' ~ " ' ' ~ ' '  1 1.1 1.2 1.3 1.4 L. H. Lewis, et al., FE-13, MMM'96 Fig. 1 , . -. w 0 20 40 60 80 Distribution misorientation angle CP (degrees) L. H. Lewis, et al., FE-13, MMM'96 Fig. 2 I ,  , .- 

Crystallographic texture determinations from inverse susceptibility measurements

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Crystallographic texture determinations from inverse susceptibility measurements

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