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An Anomalously Large Value of the Ratio of Remanence Coercive Force (Hrc)To Coercive Force (Hc) (I.E

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An Anomalously Large Value of the Ratio of Remanence Coercive Force (Hrc)To Coercive Force (Hc) (I.E J. Geomag. Geoelectr., 39, 441-461,1987 Magnetic Remanence Coercivity of Rocks Takesi NAGATAand Barbara J. CARLETON National Institute of Polar Research,ltabashi-ku, Tokyo, Japan (ReceivedFebruary 24,1987; Revised May 15. 1987) An anomalously large value of the ratio of remanence coercive force (HRc)to coercive force (Hc) (i.e. HRc/Hc) which is much beyond a range of HRc/Hc for a single phase magnetic mineral, is often found in natural rocks, particularly in extraterrestrial rocks. The observedlarge values of HRc/He are interpreted as mostly due to the coexistence of a high coercivity component (a) and a low coercivity component (b). In a binary system of high and low coercivity components, HRc is largely controlled by the high coercivity component and He largely by the low coercivity component in accordance with definitions of HRc and Hc, respectively. A simple model of such a magnetic binary systemfor purposes of estimatingthe magnetic coercivitiesof both components from the observedbulk values of HRc, He and IR/ Is is proposed, whereIR and Is respectivelydenote saturation remanenceand saturation magnetization. It is shown that the proposed model well approximates experimental data with an uncertainty of less than a factor of 2. 1. Introduction The magnetic remanence coercive force (HRc) of magnetic (i.e. ferromagnetic and ferrimagnetic) materials is defined by ID(HRc)=0, where ID(H) denotes the DC demagnetization remanence acquired after saturation in one direction and the subsequent application of DC field of intensity H in the opposite direction. For a randomly oriented assemble of non-interacting uniaxial magnetic particles , the ratio of HRc to the coercive force (Hc) is theoretically given (WOHLFARTH, 1958, 1963) by (1) As summarized by WOHLFARTH(1958, 1963), however, experimentally observed values of HRc/Hc of assemblies of single-domain (SD) particles dispersed in a non-magnetic matrix is always larger than 1.1, in the range of 1.3-2.0. The observed discrepancy of HRc/ Hc from the theoretical value is attributable partially to the magnetic interaction among magnetic particles and partially to the effect of considerably wide distribution of the anisotropy constant for individual particles. Hc and HRc of rock-forming minerals have been studied by WASILEWSKI (1973), DAY et al. (1977), DUNLOP(1981) and others. Their experimental results show that 1.1<HRC/ Hc<2.4 for SD particles and HRc/ Hc=4-5 for multi-domain (MD) particles. For magnetic minerals having grain-sizes between SD particles and MD 447 448 T. NAGATA and B. 1. CARLETON particles, HRc/ Hc takes values intermediate between those of SD and MD particles, so that HRc/ Hc values for assemblies of magnetic grains of approximately the same composition and the same grain size diluted in non-magnetic matrix ranges between 1.1 and about 5 in general. However, observed values of HRc/ Hc for terrestrial and lunar rocks, as well as meteorites, which is a summary of magnetic hysteresis measurements of natural rocks obtained in the writers' laboratory, range widely from 1.3 to 102, as shown by the histograms of HRc/ Hc in Fig. 1, where HRc/ Hc>8 for 23% of terrestrial igneous rocks, while HRc/ Hc>8 for 76% of lunar rocks and 71% of chondritic meteorites. In some lunar rocks and chondrites, HRc/ He values exceed 30, amounting to more than 100 in extreme cases (e.g. NAGATA,1979). Fig. 1. Histograms of HRc/ Hc of terrestrial igneous rocks (Top), lunar rocks (Middle) and chondrites (Bottom). (HRc/ Hc values in logarithmic scale). N: number of measured rock samples. Magnetic Remanence Coercivity of Rocks 449 Special examples of anomalously large values of HRc/ Hc for some lunar rocks, in which ferromagnetic Fe-Ni metallic grains are mixed with superparamagnetically fine metallic grains, have already been qualitatively discussed (NAGATAet al., 1972; WASILEWSKI, 1973). It was noted in these studies that a superposition of the superparamagnetic magnetization on the ferromagnetization results in a much larger reduction of the He value than that of the HRc value. An experimental demonstration that a mixture of a high magnetic coercivity component and a low coercivity component can have an anomalously large value of HRC/He has been reported by DAY et al. (1977). Since it has been microscopically and magnetically confirmed that a number of natural rocks, having a large HRc value and a relatively small Hc value consist of both magnetically high coercive and low coercive components, it seems most likely that an observed large HRc/ Hc value for a rock indicates the co-existence of both high and low coercivity components together in the single rock piece. In the present study, the problem of magnetic coercivity of binary systems consisting of magnetically high and low coercivity components is more quantitatively examined. 2. Coercive Force (Hc) of a Binary System An example of experimental results for He and HRc measurements of a mixture of high coercivity SD particles and low coercivity MD particles of titanomagnetite obtained by DAY et al. (1977) is reproduced in Fig. 2(a). As shown in the figure, the SD particles are characterized by He=Hc(a)=1580 Oe and HRc=HRc(a)=2130 Oe so that HRc/ Hc=1.34, while the MD particles are characterized by Hc=Hc(b) =39 Oe and HRc-HRc(b)=148 Oe so that HRc(b)/Hc(b)=3.79. The mixing rate of SD particles within the total titanomagnetite is given by m, where all titanomagnetite grains are uniformly diluted in non-magnetic KBr powder to 1%. The Hc vs. m curve is an upward concave curve, in which He values are only several times as large as Hc(b)for m<0.5. The HRc vs. m curve is an upward convex curve, in which HRc values are nearly the same as HRc(a)for m?0.5 and larger than HRC(a)/3 for m>0.1. Thus, HRc/ Hc takes its maximum value (i.e. HRc/ Hc=30) around m=0.25. An approximate representation of He for a binary system consisting of high and low coercivity components has been discussed with respect to lunar rocks (NAGATAet al., 1972) and meteorites (NAGATAand FUNAKI,1982). In these previous works, the magnetization curve, I(H), in the course of magnetization from 0 to H after saturation magnetization in the opposite direction, is roughly approximated by (2) where IR denotes saturation remanence after saturated magnetization by H→+∞.IR and He for a binary system consisting of a high coercivity component (a), characterized by IR(a)and Hc(a), and a low coercivity component (b), characterized by 450 T. NAGATA and B. J. CARLETON Fig. 2. Hc(m) and HRc(m) of mixtures of high coercivity SD particles and low coercivity MD particles of titanomagnetite, 60Fe2TiO4"40Fe3O4.m: mixing rate of high coercivity component. (a) Experimental results, (DAY et al., 1977). (b) Theoretical results derived by the present model. Hc(1) for the case of I(H)' IR (1-H/Hc). Hc(2)for the case of I(H)=IR{1-(HcH+H2)/2(Hc)2}. IR(b)and Hc(b),in a mutual mixing rate m(a):m(b)=m:(1-m) are then given by (3) (4) where (5) The extreme case represented by (5) corresponds to a binary system composed of ferromagnetic particles (a) and superparamagnetic particles (b). Putting IR(a)/IR(b)=Y and Hc(a)/Hc(b)≡ η,、Hc/Hc(a)≡ ζis derived from(2),(3)and(4)as (b) Sinceη=40.5 and Y=11.0 in the case of example shown in Fig.2(a),the Hc vs. m curve in the present model is obtained from (6) and shown by curve Hc(1) in Fig. 2(b). Magnetic Remanence Coercivity of Rocks 451 As can be seen the general characteristics of the Hc vs. m curve given by (6) are in approximate agreement with the observed results. Since, however, in all magnetic hysteresis curves of terrestrial rocks, lunar rocks and meteorites measured in the writers' laboratory, it has been experimentally confirmed that (2*) is a better approximation than(2)for the measured l(H). Then,ζis derived from(2*) and(3)as (6*) Solving(6*)for a positive value ofζgives Hc/Hc(a)as a function of m,ηand Y. The Hc vs. m relation given by (6*) for the example shown in Fig. 2(a) is illustrated by Hc(2) curve in Fig. 2(b). The general characteristics of the Hc(2) vs. m curve based on the revised model are in reasonably good agreement with the observed results. Other experimental results of the He vs. m relation of a binary system (DAY et al., 1977) are reasonably well interpreted with the present revised model. 3. Remanence Coercive Force (HRC) According to the definition of HRc, HRc values for a high coercivity component (a) and a low coercivity component (b) are expressed in terms of the static remanent magnetization, Ir(H), which is acquired after magnetizing up to Hin a static magnetic field, as (7) respectively, where HRc(a)>HRc(b). HRc for a binary system of a mixture of (a) and (b) components with a mixing ratio of m to (1-m) is given by (8) 452 T. NAGATA and B. J. CARLETON Then, (7) and (8) lead to a relation, (9) For the purpose of evaluating HRc/ HRc(a)on the basis of (9), it is necessary to know functional forms of Ir(a)(H) and Ir(b)(H). Although exact functional forms of Ir(H) for individual magnetic grains are somewhat different from one another, their general characteristics must satisfy the following 3 conditions, i.e., A possible simple empirical formula of Ir(H) which can satisfy the three conditions and reasonably well fit the experimental data are (10) The empirical formula of Ir(H) can approximately represent the observed Ir(H) vs.
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