.92.... . . 1‘77. . . .. . . . 059...: E . _ _ . . 3 m... MN.) I £336 93 . . _ .33 and. Emu... . . _ M ......w.... huh.“ 1h." . . . . . . U ...| -.n‘buh raw 6...». ”#2.. «*u: r... I..." 3......) S _ $2. 1.2.. ‘ mix» . . _ . 2mm). «3...; a U ”dill- ...oi: . (Sufi " ”4.”. . o‘ 8. Que.“ , «.2.» S Fm“ 3233" in .L: in”! 01.9 n... 2.. 10.0%... m. a lit 1 c: .u .1901“ i. ii; “-2.55 ‘ 222222223222” ,, a,” ABSTRACT HYDROSTATIC PRESSURE EFFECTS ON SATURATION REMANENT MAGNETIZATION, SUSCEPTIBILITY AND MAGNETIC HARDNESS OF MAGNETITE By Joon Yol Kim The effects of hydrostatic pressure on saturation remanent magnetization and bulk susceptibility of single crystal magnetite and synthetic magnetite dispersion samples were studied. The crystal sample was a cylinder about 5 mm in diameter and 1.38 cm long which was cored normal to (111) faces of natural single crystal. Disper- sion samples were also cylinders about 0.795 cm in diameter and of slightly different length (syn - 2, 2.5 cm; syn - 3, 2.7 cm). The hydrostatic pressure was applied up to 3.2 kbar by pressing the kerosene and transformer oil mixture (1:1) within the nonmagnetic high pressure bomb. Saturation remanence decreases irreversibly until the pressure reaches 1 kbar (-30% at l kbar), and reversible changes occur after 1 kbar. Saturation remanence measure- ment results were similar in all samples. Susceptibility was {tuna decreased (-25% of initial susceptibility at 2.5 kbar) during the pressurization. It was reversibly recov- ered with a small loss after releasing the applied pressure. (Magnetite single crystal, PH-3). Joon Yol Kim The alternating field demagnetization curve and spectrum before and after the pressurization (3.2 kbar) show a slight increase in mean demagnetization field and notable increase in saturation remanence (8%) after the pressurization and resaturation (for syn - 3). This work is intended to assist in the interpretation of stress—induced changes observed for rocks in the litho— sphere. One application is in understanding of piezo- magnetic changes in magnetic field observed prior to earthquakes. HYDROSTATIC PRESSURE EFFECTS ON SATURATION REMANENT MAGNETIZATION, SUSCEPTIBILITY AND MAGNETIC HARDNESS OF MAGNETITE Joon Yol Kim A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1976 TABLE OF CONTENTS ACKNOWLEDGEMENT .............................. LIST OF TABLES ............................... LIST OF FIGURES .............................. I. INTRODUCTION ........................... II. THEORY ................................. A. Atomic Model ....................... B. Magnetic Behavior within Domains 1. Domain energies ................ Exchange energy ............. ... Domain wall energy .. ........... Magnetostatic energy ....... .... Magnetocrystalline energy ...... Magnetostriction energy ....... . 2. Grain size dependence in magnetic behavior of ferromagnetic materials .... .................. Magnetization of Ferrimagnetic Material ............ . .............. 1. Theoretical model .............. 2. Crystal inhomogeneity and its effect upon magnetization process .............. . ......... Magnetic Susceptibility ............ Stress Effect on Magnetic Properties of Ferrimagnetic Material .......... I. Effect on remanent magneti- zation . ................ . ....... 2. Effect on magnetic suscep- tibility ....................... ii Page l6 l9 19 2A 25 28 28 32 III. IV. APPARATUS AND MEASURING TECHNIQUE ........... A. High Pressure Microbomb ................. l. Microbomb description .... ........... 2. Calibration .. ....................... 3. Procedure ........................... B. Ballistic Magnetometer .................. C. Experimental Set Up ..................... D. A. F Demagnetization Technique and Apparatus Description ............... SAMPLE ANALYSIS, DESCRIPTIONS AND EXPERIMENTAL RESULTS ........................ A. General Characteristics of Magnetite B. Sample Description ...................... 1. Single crystal sample (PH-3) ........ 2. Synthetic magnetite dispersion samples (syn - 2 and 3) ..... . ....... C. Grain Size Distribution Determination by Hydrometer Method .... ....... .... ..... l. Principle ........................... 2. Procedure and result .......... . ..... D. Density Measurement of Powdered Magnetite E. Results ................................. l. Saturation remanent magnetization 2. Susceptibility .. ..... . .............. 3. Magnetic hardness ................... INTERPRETATION .............................. A. Discussion .............................. B. Theoretical Calculation of Hydrostatic Pressure Controlled Magnetization Behavior of Magnetite ................... 111 A6 52 52 56 56 56 57 57 6O 62 6a 614 en 69 71: 7A 77 Page 1. Hydrostatic pressure effect on magnetocrystalline potential barrier .. ................ . ....... 78 2. Hydrostatic pressure effect on magnetostriction (EAo) ........... 81 3. Temperature effect on Ek and EKG ......... ....... . ............. 83 VI. CONCLUSION ............................... 86 Appendix-—forgxei11siZe/hydrometer method 88 Bibliography ............................. 91 iv ACKNOWLEDGEMENT The author wishes to recognize and sincerely thank the following people for their help; Dr. Robert S. Carmichael for his encouragement, his advice, providing his pressure bomb and his chairmanship of the committee. Dr. Ted Vinson for his help and assistance providing laboratory facilities in the Department of Civil Engineer- ing. Dr. C. Foiles and Dr. J. Cowen in the Department of Physics for fabrication of the pressure bomb and use of auxiliary equipment. Dr. R. Vander Voo in the Department of Geology and Mineralogy, University of Michigan, for use of his analyt- ical equipment and his palomagnetism laboratory. Dr. James w. Trow and Dr. John T. Wilband for their guidance and critical reading of the manuscript and their participation on the committee. Table IV—1. IV-2. V—l. LIST OF TABLES Page Properties of Magnetite ............... 5“ Sample Description .................... 58 Calculation of AEk .................... 81 Calculation of AEAo ................... 83 vi Figure II—l. III-l. III-2. III—3. III—H. III—5. III—6. III-7. III—8. III-9. IV-1. IV-2. IV-3. IV-u. IV-5. IV-6. IV-7. IV-8. IV-9. LIST OF FIGURES Hysteresis Curve of Multidomain Material ..... ....... .................. Non-Magnetic Pressure Chamber and Ballistic Magnetometer ................ Pressure Microbomb Calibration ........ Hydraulic Pressure Force vs Internal Confining Pressure Inside Bomb ........ Null Field Configuration .............. Sense Coil Field ...................... Experiment Set Up ..... ..... ..... ...... A. F. Demagnetizer .............. ...... Spinner Magnetometer ............. ..... Size Distribution of Magnetite Powder Experimental Set Up (Hydrometer MethOd) .....OOOOOOOOOOOOOOOOOOO. ...... Pressurization of Magnetite (Sample PH-3) 000000000000 coo 00000000 coco. ooooo Pressurization of Magnetite (Sample syn-3) on.coco-coo00000000000000.0000 Magnetic Susceptibility Measurement (Sample Syn - 2) ........ .............. Pressurization of Magnetite (Sample Syn - 2 for Susceptibility Measure- ment) ....... ...... ....... ...... ...... Pressurization of Magnetite (Sample PH-3 for Susceptibility Measurement) A. F. Demagnetization (Sample Syn — 3) Coercivity Spectrum (Sample Syn - 3) vii Page 23 36 38 39 A1 an 45 A7 50 51 61 63 65 66 67 68 71 72 73 I. INTRODUCTION Physical properties of rocks and minerals are controlled not only by their inherent properties such as mineralogy, grain size, porosity, and fractures but also by the factors of pressure and temperature in the litho— sphere. Pressures which exist in the Earth's lithosphere are both lithostatic (confining) and tectonic (directed). Confining pressure increases at a rate of about 320 bars/ km, and at a depth of 30 km is about 10 kilobars. Directed stress in tectonically-active areas ranges up to perhaps 1.5 kilobars. Thus knowing the effect of confining and direct pressures on the physical properties of rock is important to studies in paleotectonics and paleostress determination, geodynamics, earthquake prediction, inter— pretation of deep-seated geophysical fields such as magnetic anomalies, and geochemical behavior. One of the important physical properties of rocks in the lithosphere is its magnetic properties. Because rocks in the lithosphere contain magnetic minerals, especially magnetite, they have magnetization. This magnetization extends down to the depth of the Curie-point isotherm of 575°C which corresponds to a depth ranging from 30 - 100 km depending on the local geothermal gradient. Effects of mechanical stress on magnetic properties of rocks and minerals have been studied experimentally and theoretically over the last twenty years. The strain dependence of magnetization is the general phenomenon of magnetostriction. This magnetostriction is the linear or volume strain caused by magnetization. The reciprocal relationship, change in magnetization by stress, is known as piezomagnetism. Applied stresses may be either directed or confining, or a combination of both. Most past experiments on piezomagnetism here centered on the effect of uniaxial compression on the magnetic prOp- erties of minerals and rocks. Several magnetic parameters of rocks and minerals have been shown to be stress- sensitive. The effects of mechanical deformation of magnetic minerals indicate structure-sensitive characteristics such as coercive force (Carmichael, 1967, Stacey and Wise, 1967, Carmichael, 1968, Shive, 1970). There are reversible and irreversible stress-induced changes on remanent magnetiza- tion and susceptibility. The reversible changes occur for "hard" remanence such as thermo—remanent magnetization (TRM) and chemical remanent magnetization (CRM) (Nagata and Kinoshita, 1965; Schmedbauer and Peterson, 1968; Nagata, 1969; Stacey and Johnston, 1972), magnetic susceptibiliyy (Kal- ashnikov and Kapitsa, 1952; Kapitsa, 1955; Kern, 1961; Stacey, 1962; Nagata, 1969, 1970, 1972; Pozzi, 1975; Kean et al., 1976) and already acquired TRM (Ohnaka and Kinoshita, 1968). Irreversible effects occur for the pressure demagnetization of saturation remanence (Carmichael, 1968, Nagata and Carleton, 1968, 1969), effect of a uniaxial compression on acquisition of isothermal remanent magnetization (Domen, 1957; Nagata and Kinoshita, 1965; Carmichael, 1968; Nagata and Carleton, 1968, 1969) and the effect of uniaxial compression on acquisition of thermo-remanent magnetization (Schmidbauer and Peterson, 1968). A theoretical model for domain wall movement in the elastic range was developed (Nagata, 1968; Stacey and Johnston, 1972). It states that any change in magneti— zation of ferromagnetics or ferrimagnetics can be attributed to movements of the 180° and 90° domain walls and/or the rotation of spontaneous magnetization within domains. The reversible effects are due to the rotation of spontaneous magnetization within individual magnetic domains affected by the compression and irreversible effects are due to irreversible displacement of the 90° domain walls (Nagata, 1969). A model including the effect of internal crystalline structure has been developed separately (Carmichael, 1968) to interpret both reversible and irreversible effects. It considers changes in the internal stress state of a crystal due to mechanical deformation, or actual physical changes in the micro—structure. This localized internal stress, which is determined primarily by the density and configu- ration of structural defects, is known to affect magnetic properties (Vicena, 1954, Kersten, 1956, Dietrich and Kneller, 1956, Oosterhout and Klomp, 1962). However, little work has yet been done concerning properties of magnetic minerals and rocks under high lithos (confi rocks been C et al. et al. (I) DPESsur: abOut 3( the d63 ‘ Chamber lithospheric pressure. Thus, the effects of lithostatic (confining) pressure on various magnetic properties of rocks and minerals are still little known. Some work has been done in recent years (Kume, 1962, 1964; Girdler, 1963; Nagata and Kinoshita, 1967; Avchyan, 1967; Shimada et al., 1968; Schult, 1968; Carmichael, 1969; Levedov et al., 1969; Shive, 1970). Since most rocks are or have been subjected to litho- static pressure, confining (hydrostatic) pressure would reflect more closely the condition of materials buried in the crust of the earth. Thus, more work should be done in this direction. The initial study involves the piezomagnetic effects of rocks and minerals under high pressures simulating lithospheric conditions. High pressure was achieved by a newly developed high-pressure chamber (Carmichael, Sawaoka and Kawai, 1968). This chamber can apply hydrostatic pressure up to 10 kbar, corresponding to depths down to about 30 km. It is also portable, non-ferromagnetic, and the desired pressure condition can be maintained in the chamber by locking. The study involved observation of changes of saturation remanent magnetization, magnetic susceptibility, and mechanical deformation associated with changes in remanence under hydrostatic pressure (up to A kbar). Future studies can be developed to expand the pressure range to the upper mantle, field observation, and its application in exploration geophysics and earthquake prediction. II. THEORY The magnetization of a rock or mineral specimen arises from discrete sources which may be considered at three 1evels--atoms, domains, and mineral grains. A. Atomic Model All atoms have a magnetic moment due to the orbital motion and spin of their electrons. An electron in its path around a nucleus creates a dipole moment referred to as the orbital magnetic moment. The electron also spins about its own axis, creating an additional magnetic moment known as spin magnetic moment. The magnetic dipole moment of an atom as a whole will be the resultant of all the orbital and spin magnetic moments of its electrons. Materials within which the magnetic induction is slightly less thanifluaapplied magnetic field, because of the tendency of net magnetization to align against the applied field (Larmor's precession), are known as dia- magnetic. Dismagnetism is an atomic—scale consequence of Lenz's law of induction. The permeability is slightly less than that of empty space, and magnetic susceptibility 6 cgs units). is negative and small (10- Paramagnetism originates from the phenomenon of a large number of atoms having magnetic moment and inter— action among them being very small. Within an external magnetic field, the net magnetic moment is zero. This is because at usual temperatures the spins are thermally agitated and take random orientations. Upon application of an external field, the average orientations of the spins are slightly changed so as to produce a weak induced mag— netization parallel to the applied magnetic field. The susceptibility of these materials ranges from 10—3 to 10-5, and is inversely proportional to the absolute temperature. Ferromagnetic materials are distinguished by the fact that individual atoms, and their inner orbital electrons are much closer together, and there are more valence electrons with unpaired electrons available to create a net moment. Thus the interaction between adjoining atoms is strong, giving rise to spontaneous magnetization. It is characterized by hysteresis which is a result of irre- versibility of magnetization. The magnetic polarization of ferromagnetic material depends upon its magnetic history and not merely upon the field to which it is exposed at a particular instant, so that it can remain magnetized after removal of the applied field. Weiss (1970) first proposed that the irreversibility had its origin in magnetic subdivision of a ferromagnetic body into domains. Magnetic moments of atoms or ions in a magnetic domain tend to be aligned parallel to one another in zero applied field, below the characteristic temperature called the Curie temperature. Complete ordering of magnetic moment is achieved only at absolute zero temper— ature. Above the Curie point, these materials become paramagnetic. Some substances are characterized by a subdivision into two sublattices. Those materials in which the magnetic moments of atoms or ions tend to assume an ordered but antiparallel arrangement of differing moment in zero applied field, are known as ferrimagnetic. In the usual case, within a magnetic domain, a substantial net magnetiza- tion results from the antiparallel alignment of neighbor- ing non-equivalent sublattices. The microscopic behavior is similar to that of ferromagnetism above the Neel point, and the materials become paramagnetic. Antiferromagnetic materials have the moments of atoms or ions tending to assume an ordered arrangement but anti— parallel with the same magnitude, such that the vector sum of moment is zero below a characteristic temperature called the Neel temperature. The susceptibility is comparable to that of paramagnetic materials. Above the Neel point, these materials also become paramagnetic. B. Magnetic Behavior within Domains The magnetization of a ferromagnetic or a ferri- magnetic material tends to break up into regions called domains separated by thin transition regions called domain walls to minimize the total magnetic energy of the parti~ cular specimen. Within the volume of a domain, the magnetization has its saturation value, and is directed along a single direction. The direction of domain magnetization is determined by crystallographic structure, but in all except very small grains the domains are mutually oriented. The magnetizations of other domains are directed along different directions in such a way that the net magnetization of the whole sample may have any value between zero and saturation. The application of an external magnetic field first causes some domains to grow by the motion of their walls. The essential features of atomic alignment in ferri- and ferromagnetism within domains are explained on the hypothesis of a mole- cular field, as first prOposed by Weiss (1907). 1. Domain energies Energies involved in magnetization of materials are as follows: Exchange Energy (Eex) Ferromagnetic interactions are spin-dependent electro- static interactions between electrons of neighboring atoms. This was first recognized by Heisenberg from the interfer— ence of the quantum mechanical wave functions representing each electron. Energy which involves this exchange-inter- action is called exchange energy (Eex). It is given as Eexij = -AAiJS2 cos ”13 (2-1) (Chikazumi, 196A) where A is the exchange integral or interaction energy of half unit spin (h/2) and S is total spin moment of each atom. In the case for the exchange integral A being posi— tive, the lowest energy is attained where two spins are 10 parallel to each other (gij=0)' Maximum exchange energy can thus be attained when two spins are anti- parallel to each other. Domain Wall Energy (Ew) The structure of transition layers between adjacent ferromagnetic domains was first investigated by Bloch (1932) and is called the magnetic domain wall (Chikazumi, 196A). The domain wall is produced because of the continuous characteristics of exchange energy (equation 2-1). The energy of this domain wall is determined by the counter- balance of the exchange energy (Eex) which tends to increase the thickness of wall (so that spin moments are as nearly parallel as possible), and the anisotropy energies which tend to diminish it. The exchange energy within this transition zone is explained as a function of angle between two adjacent atoms (0132) _ 2 2 Eexw - 2AS $13 + const (2—2) (Stacey & Banerjee, 197A) when we consider a 180° rotation through n atomic layers, then the $13 will be equal to H/n. For a simple-cubic lattice with lattice constant "a" the number of atoms per unit area of a (001) surface is 1/a2, so that the exchange energy stored per unit area of transition layer is given by Eex = 2.13111...— (2-3) an 11 Against the exchange energy, the rotation of spins in the wall out of the direction of "easy" (preferred) magnetization causes an increase in magnetocrystalline anisotropy energy. The anisotropy energy stored in the wall is given by Ekw = K na (2—u) (Chikazumi, 1964) where K is the anisotropy constant per unit volume. Thus the total energy stored in the wall in the sum of those two energies. It is given as 2 2 _ _ 258 H Ew - Eexw + Ekw - 2 + Kna a n _ EA 5 5 - HS (an) (Ka) (2—5) The value n is determined by the condition that Ew must be a minimum, dE _ 2A32H2 dn a2n2 + Ka = 0 (2-6) and since the volume per unit area of wall is na, the thickness of wall t is given as t = na - ns (2%)% (K)8 <2-7) (Stacey and Banerjee, 197A) Domain walls can be classified into 180° walls, in which spins rotate by 180° from one domain to the other, and 90° walls, in which the spins rotated by 90° or so. In iron for instance, there are six possible stable 12 orientations of magnetizations; [100], [100], [010], [010], [001], and [001]. The domain boundaries between [100] and [I00] domains form 180° walls, and those between [100] and [010] domains form 90° walls. However, in a substance with negative Kl such as magnetite, the easy directions of magnetization are directions, between which there are 180°, 71° and 109° walls. But we normally refer to 71° and 109° walls as "90° walls," because they are all distinguished from the 180° wall with respect to their stress-sensitive prOperty. Magnetostatic Energy (EH, ENJ) The magnetostatic energy is due to the Coulomb inter- action between magnetic free poles. When magnetic grains form magnetic free poles on their surface, they gives rise to the magnetostatic energy. There are two distinct contributions to the magneto- static energy of the magnetic grains. One is potential energy in an external field and the other is mutual poten- tial energy of its surfaces of magnetic polarity. The former is external field energy (EH), given by EH = -JS.H cos a <2—8) where saturation magnetization JS, makes on angle 0 with the field. The latter is called energy of self-demagneti— zation (ENJ) which arises from the shape anisotrOpy. In general, an ellipsoid uniformly magnetized with J has a magnetostatic energy per unit volume given by: S, l3 2 E = 8 NJS (2-9) NJ where N is the demagnetizing factor in the direction of magnetization. This magnetostatic energy between neighboring atoms in ferromagnetic material is smaller than their mutual exchange energy by a factor of 1,000 or more. However, the exchange forces are short-range forces, whereas magneto- static forces are effective on a macroscopic scale (Stacey and Banerjee, 197“). It is also reduced when large magnetic grains form closure domains near the external surface. Magnetocrystalline Anisotropy Energy (EK) A ferromagnetic crystal has certain crystallographic easy directions in which the spin moments of ions prefer to lie. They avoid "hard" (higher energy) directions. This phenomenon is referred to as magnetocrystalline anisotrOpy and the difference of magnetization energy between the hard and easy direction is the magnetocrystalline anisotropy energy. In cubic material, such as magnetite or iron, the energy of domain magnetization in an arbitary direction with respect to the crystallographic axes can be expressed in terms of direction cosines (a1, a2, a3,) with respect to the three axes and with two empirical anisotrOpy constants K1’ K2 at room temperature. It is given as 2 2 2 2 + a 2 E = K 3 2 “1 ) + K2 “1 “2 “3 (2-10) (Nagata, 1961) In It is known that anisotropy constants are temperature dependent, so that Ek change can occur by thermal agi- tation. For a temperature between -1H0°C easy magnetization directions and <100> hard directions. However, in the temperature range between -155°C become easy, and <111> is the hard direction. Below -155°C, magnetite converts its structure to orthorhombic and the c axis becomes the magnetic easy axis (Carmichael, 1971). At room temperature, magnetite has negative anisotropy with values of K = = —1.35 x 105 l ergs/cm3, K2 = -0.A8 x 105 ergs/cm3 (Carmichael, 1971). Both anisotropy constants (K1’ K2) are also stress- sensitive (Nagata and Kinoshita, 1965; Nagata, 1966a, b; Kinoshita and Nagata, 1967; Sawaoka and Kawai, 1967). Sawaoka and Kawai (1967) have shown that Kl decreases 0.3%/kb under hydrostatic pressure. Kinoshita and Nagata (1967) also found that K1 and K2 decrease under hydrostatic pressure. Magnetostriction Energy (E10) Magnetization of ferromagnetic material is usually accompanied by mechanical deformation, and this deformation causes anisotropy of crystals. This phenomenon is known as magnetostriction. Magnetostriction is positive when ferromagnetic material is spontaneously extended in the direction of magnetization and is also contracted in the transverse directions. Negative magnetostriction refers to a 15 contraction in the direction of magnetization. Anisotropy energy which arises from the magneto- striction is known as magnetostriction energy (EAo)' Magnetostriction energy (E10) due to saturation magneti- zation at an angle 6 to the stress, for a polycrystalline materials, is given as E)‘O = 3/2 As 0 cos2 M (2-11) where As is the saturation magnetostriction constant. The c is stress, positive for tension. This is the simplest form of the magnetostriction energy, and it applies to any material which has isotropic magnetostriction, such as a rock, in which the crystallographic axes of magnetite grains are randomly oriented. (Stacey and Banerjee, 197A). The validity of applying saturation magnetostriction for stressed igneous rocks was demonstrated by Stacey (1960). When we consider a single crystal or domain structure, bulk saturation magnetostriction is no longer adequate. It must be calculated in terms of the orientation of magneti- zation with respect to crystallographic axes. For cubic_ structure, such as magnetite, magnetostriction energy is given as E = 3/2 A o ( 2 y 2 + a y + a, y ) Ac 100 “I l 2 2 5 3 + 3 1111 o (ala27172 + a2a3y2y3 + ala3yly3) (2-12) where the y's are the direction cosines of the stress with respect to the axes. The X's are the magnetostriction 16 constants for the respective crystal directions. Inverse magnetostriction is known as piezomagnetism. It is mainly due to applied external stress, and internal stress associated with crystal inhomogeneities such as micro-cracks or crystal defects (dislocations, interstitials, etc.). 2. Grain size dependence of magnetic behavior of ferro- magnetic materials Magnetic properties of minerals and rocks depend not only upon composition but also on grain size. For small grains no domain wall can occur, and these are known as single domain grains. At some critical size the grain will subdivide into two or more domains to reduce the net mag- netization of entire grains and form multi-domain configur- ations. It is known that the magnetic behavior (coercivity, susceptibility etc.) of single domain and multidomain grains is quite different. But there is no sharp discon— tinuity in properties at any particle size. When the size of grains become small enough, it becomes energetically favorable to do away with the domain walls, so that the whole grain has single domain structure. This was first predicted theoretically by Frenkel and Dorfman (1930). Calculations for this transition size (critical size) have been carried out by Kittel (19A6, 19A9), Neel (19471 Morrish and Yu (1956), and Butler and Banerjee (1975)- Kittel (l9U9) considered the relation between the 17 magnetostatic energy of a spherical strain of diameter d and saturation magnetization JS in the single domain (E1) and two domain states (E2), which is explained as _ 2 2 - El - gNJS (1/6 Hd ) — 2132 (2-13) where N is demagnetizing factor (A/3 H for a sphere in cgs units). When the size of the grain increases, a domain wall is introduced and then the magnetostatic energy of two domain states (E2) is reduced by half. The transition between the two states arises when the decrease in magnetostatic energy exactly balances the wall energy (Ew) that is, E1 = E2 + EW (2-1A) where Ew = % Hd2w (2-15) Thus the critical diameter is _ _2 IE - do ‘ 2n - JS (2 16) Putting w=0.5 erg. cm-2, then for magnetite J cm.3 and we get (10 = 0.03u (McElhinny, 1973). S = A80 emu Kittel's model is only concerned with a spherical grain, which is the least favorable case for single domain size. Morrish and Yu (1955) have shown that the critical size depends on the shape and internal strains of the particle as well as on the material itself. Their experi- mental results indicate a cubic particle of magnetite about lu in diameter is of multi-domain structure, and one the 0 other hand, an elongated particle of Fe of about l-2u 2 3 18 in length and axial ratio 10:1 may still be single domained. From measurements of saturation remanence in samples with known size distributions, Dunlop (1973) deduced that the critical size of single domain for magnetite was between 0.035u and 0.05u. Soffel (1969) examined domain structures in titanomagnetite with a wide range of grain size and constant composition (0.65 Fe2T10u - 0.35 Fe30u) and found that the critical size of single domain was about 111. A recent effort to determine critical size of single domains was by Butler and Banerjee (1975). Calculation of the single domain grain size range was accomplished by calculating the superparamagnetic threshold size "ds" by Neel's relaxation equation and calculating the single domain threshold "do" at which single domain to two-domain transition occurs. The results have shown that for the cubic magnetite grain the single domain range is extremely narrow and occurs at every small grain size. At room temperature, ds = 0.05u and do = 0.076u.' However, the single domain range increases rapidly with particle elongation. For a length: width ratio of 5:1, single domain limits of ds = 0.05u and do : 1.Aum are calculated (Butler and Banerjee, 1975). In the region between single domain and multidomain, there is a "pseudo single domain" (PSD) range. It is very annall multidomain grains with a small number of domains. 19 The Barkhausen discreteness of the positions of the domain walls prevents them from occupying the precise positions necessary for zero net magnetic moment. The moments of these grains can thus be reversed, but they can not be demagnetized to zero magnetic moment. Such grains there- fore behave similar to single domain grains. Stacey (1963) estimates that the critical size for four-domain grains is about l7u. In his work (1967), he concludes that complete multidomain grain should have a grain size larger than 20u and rocks of interest to paleomagnetism should contain a sufficient fraction of magnetic grains less than 20u- Thus we can probably say that the single domain grain threshold (do) is about .05u, and multidomain threshold is about 20u for magnetite. C. Magnetization of Ferromagnetic Material 1. Theoretical models In ferromagnetic material, spontaneous characteristics of magnetization can be interpreted as the result of a change in the total magnetization owing to either a dis- placement of domain wa11(s) or the rotation in the direction of the magnetization of the domain toward the applied external field. In a single domain particle, change in magnetization can occur only with the rotation process of the total magnetic moment of the particle and the internal magnetiza- tion energy depends only on the orientation of the magnetic 2O moment with respect to certain axes fixed in the particle (Nagata, 1961). The theory of the magnetization of single domain particle was first established by Néel (1955), and it is well summarized by Nagata (1961). In considering Neel's simple uniaxial model with anisotropy energy K the 11’ total energy of the single-domain particle is given as E = Ku sin2 e - JS H cos (a - 60). (2-17) where 9 and 60 are angles of the magnetic moment and the direction of the applied field relative to the axis of easy magnetization. Then the equilibrium direction of the mag— netic moment must be determined as to minimize the total energy LT] 8 3 = 2Ku cos 6 sin 9 + J sin (6-60) = 0 (2—18) H CD (Nagata, 1961) From the equation, we can derive the coercive force with respect to the angles. It can be summarized as follows: 1) When H // easy axis (60=0) 2Ku HC = T COS 9 (2'19) S 2) When JS // easy axis (6=0) and H // easy axis 1) then _ ___E _ Hc — J (2 20) 21 ii) when e=180° Hc = ~33 (2-21) 3 iii) when e=9o° (JS L easy) Hc = 0 (2-22) iv) when 6=A5° Ku HC = 3— (2-23) 3 In the absence of any applied field the moment of a single domain grain takes up one of two possible axial orientations (0° or 180°) separated by a potential energy barrier Er. The orientation will not be altered if Er greatly exceeds the thermal energy (kT), k being Boltzman's constant, and T the absolute temperature. However, for sufficiently small grain sizes and suitably high temperatures, their agitation can cause the moment to switch positions. External stress on the grain can also cause the rotation of magnetic moment. In multidomain material, hysteresis (Fig. II-l) is interpreted in terms of the motion of the domain walls over potential-energy barriers and by domain rotation. The former is the general characteristic in small external fields and the latter generally takes place in larger fields than for wall movement. Wall motion occurs because there is a magnetostatic pressure on the wall which derives from the energy change brought about by the field. The motion is reversible if the demagnetization field is able 22 to drive the wall back over the barriers when the applied field is removed. If the wall does not return to its original position, then remanence results. As shown in Figure 11-1, "hard" magnetic minerals resist demagneti— zation well and have hysteresis with high coercivity. When the magnetic material is once saturated by the applied field and then the field removed, the resultant remanence is called saturation remanence (Jr,sat). Magnetic hardness of the material is a function of its coercive force (He) which is the (reversed) field at zero remanence (Figure 11-1). Theories of coercive force (He) in multidomain grain depend upon the potential energy barriers encountered by domain. The nature of the potential barriers is not yet completely understood. Kondorsky (1939) drew attention to the possible importance of inhomogeneous internal stress. Kersten (1959) considered the pinning of domain wall by nonmagnetic inclusions. Néel (19A6) placed a special emphasis upon the magnetostatic effects. More recent theories (Vicena, 1955; Seeger et al., 196A) also put the focus on the stress field interaction of walls and imper- fections. The role of thermal fluctuations on wall movements has been considered by Neel (19A2), Stacey (1960) and .Aver'yanov (1967). The effect of the fluctuations is to give magnetic viscosity, that is to say a time-dependent change in magnetization. It is known that the effect is 23 J K: d d" Jnsat J3 ..-- ---- __ Jun). Hc H C” K.:% ' dH J30 RIAL STERESIS CURVE OF MULTIDOMAIN MATE HY FIGURE ll-1 2A enhanced by an increase in temperature (Shimizu, 1969). 2. Crystal inhomogeneity and its effect upon magneti— zation process The internal stress, which is determined by the density and configuration of structural defects, is known to affect magnetization processes by creating energy barriers to wall movement and magnetization rotation (Vicena, 195A; Kersten, 1956; Dietrich and Kneller, 1956; Seeger et al., 196A; Carmichael, 1968). In low fields the magnetization processes are dominated by field-induced wall movements. Therefore, imperfections play an important role thorugh their effect upon wall motion (Fuller, 1970). Two different theoretical approaches have been developed for this problem, as summar- ized by Fuller (1970). Néel's (19A6) approach has been derived from magne- tostatic effects similar to those associated with the surface of a cavity. He showed that divergent magnetization, generated by the stress fields at imperfections, gives rise to free poles. Hence, magnetostatic energy can be reduced by maintaining walls at these sites of spin diver- gence. In contrast to these models, Vicena (1955) considered the interaction between the stress fields of domain walls and of dislocations, to obtain the changes in potential energy of the wall due to the stress fields of edge and screw dislocations. He considered a variety of orien— tations of these with respect to the wall (Fuller, 1970). 25 Vicena's suggestion has been followed by many workers (Seeger et al., 196A, Stacey and Wise, 1967). Stacey and Wise (1967) were concerned with the coercive force of magnetite. Their approach is similar to that of Seeger et al. but simpler in their definition of potential well generated by interaction of stress field of wall and the dislocation. The direct experimental demonstration of the wall-dislocation interaction has been given by Chebotkovich et a1. (1966) who showed that dislocations can be moved by a magnetic field (Fuller, 1970). Indirect demonstrations of the effect of the imperfections upon wall movement have been studied by various authors. In these experiments one observed susceptibility (Kapitsa, 1955; Kern, 1961; Stacey 1962; Nagata, 1970a, b; Stacey and Johnston, 1972) or coercive force (Dietrich and Kneller, 1956; Seeger et al., 196A; Carmichael, 1968) as a function of internal stress. D. Magnetic Susceptibility Magnetic susceptibility (x), which we observe, is defined as the ratio between magnetization of the material and applied external field (He). However, demagnetization characteristic (Fig. 11-1) of the magnetic material causes the difference between measured susceptibility and intrinsic susceptibility (xi). The empirical relation between X and x1 is developed by various workers and is known as 26 fxi X - l+Nx1 (2—2A) where f is the volume fraction of magnetic material. This intrinsic susceptibility is known to be structure-sensitive; it shows a general inverse correlation with coercivity over a very wide range of synthetic ferromagnetic material (Kittel, 19A9). Therefore, it would be a good indicator to explain magnetization behavior of the material. There are two distinguishable processes contributing to intrinsic susceptibility: rotation of magnetization within domains and domain-wall movement. Rotation of magnetization occurs when the applied field is not parallel to the magnetization. It causes the magnetization to turn against the force of magneto— crystalline anisotropy. Thus the energies which are involved in susceptibility will be the induced magnetiza- tion energy by external field (EH) and anisotropy energy EK due to deflection of magnetization away from easy axes. For a spherical grain, it is only dependent on crystal structure, and thus it is a known characteristic constant for the material. For magnetite, it is 2 JS sine JS Xi = 7’ Hi = —A/3(Kl+1/3K2) (2-25) (Stacey and Banerjee, 197A) In actuality, elongated grains are more dominant, so that shape anisotropy energy (ENJ) is stronger than magne- and E have a tocrystalline anisotropy (EK). Thus, ENJ H 27 major role in determining the susceptibility, and it is given as _ l X]. _ Nb—Na (2-26) where Nb and Na are the demagnetization factors of dimensions of grain ("a" is elongated eaxy axis). Inknfut magnetics, and particularly magnetically soft material, the low-field susceptibility is dominated by domain wall movements. When the applied field is parallel to the magnetization, it causes the movement of 180° domain walls. For this reason the susceptibility is represented by x//. Stacey (1963) considers a simple model of a sequence of energy minima and maxima of a wall of area A, by representing the energy as sinusoidal function of its position. The energy which is involved in this movement is explained as EO E = —§ [1 - cos ( 2Hx —t—,)] - 2AJSHX (2-27) where E0 is the potential barrier height and t' is wall d_E thickness. The coercive force is obtained by (dx max :0, because the field is then just strong enough to impel the wall past the barrier. This gives; E0 Hc =81t73; (2‘28) :D d‘ N ll 0, equation (2-27) can be simplified as 28 2 _ 2 x E - H EO ET? - 2AJSHX (2-29) . dB and equilibrium condition (a; = 0) At‘2JSH x = —-é-—— (2‘30) H EO Then, induced magnetization is 2 ,2 2 J. = 2AJ x = 2A t Js H (2-31) in S 2 H EO If there are n/v favorably oriented domain walls per unit volume of the magnetic material, then; 2 ,2 2 = Jin 2nA t JS H - 2 (2-32) vH EO and combining (2—28) and (2-32), we can obtain the relation <13 x// J _ n ! _§ _ X//Hc ‘ UAt n (2 33) (Stacey and Banerjee, 1974) E. Stress Effect on Magnetic Properties of Ferromagnetic Material 1. Effect on remanent magnetization The effect of external uniaxial stress on the magneti- zation of rocks and minerals has been studied by various workers (Kalashnikov and Kapitsa, 1952; Kalashnikov, 195A; Graham, 1956, 1957; Nagata and Kinoshita, 1965; Schmidbauer and Peterson, 1968; Carmichael, 1968; Nagata and Carleton, 1968, 1969a, b; Nagata, 1969; Stacey and Johnston, 1972). Graham et al. (1957) and Dowell (1960) reported that all... 1 29 rocks with different chemical composition give rise to different sensitivity of magnetization to compression. Stott and Stacey (1959) investigated the effects of com- pression upon the acquisition of remanence by magnetic minerals due to the application of stress in a magnetic field. It is now known as piezo-remanent magnetization F“ (PRM). Later, systematic studies on this problem were done by Nagata and Kinoshita (1965) for assemblages of magnetic minerals and Nagata and Carleton (1968, 1969a, b) YI- for igneous rocks. The effect of elastic deformation on I coercive force and saturation remanence (Jr,sat) was separately investigated by Carmichael (1968). On the other hand, the effect of hydrostatic pressure upon the magnetization of material is less well known. Some work has been done in this direction (Kume, 1962, 196A; Girdler, 1963; Avchyan, 1967; Carmichael, 1969; Bezuglaya et al., 1975). Kume (1962) investigated substantial reduction in the isothermal remanent magnetization (IRM) of hematite (d-Fe203) but little reduction in the IRM of maghemite (y-Fe203) and intermediate (30%) reduction on magnetite. Girdler (1963) studied the hydrostatic pressure effect on TRM in a variety of materials. His results showed that there is little change in TRM of volcanic rocks, and magnetite and hematite. Avchyan (1967) has reported the comparative stability of various types of remanent magnetizations against hydrostatic pressure. His results indicated that the TRM is most 3O stable and IRM the least. Results of Carmichael's (1969) experiment on magnetite under hydrostatic pressure showed an increase in saturation coercivity (He, sat). Summarizing various different effects of uniaxial compressions on magnetization of magnetic material described previously, the effects are classified into two different categories: a reversible effect, and an irreversible effect, with respect to a compression 0. The reversible effects include Thermo-remanent mag- netization which is hard remanence. The longitudinal effect of a uniaxial compression is a decrease in remanent magnetization whereas its transverse effect is an increase. Both types of change in magnetization are reversible with n. The change of magnetization with o of this category is due to the reversible rotation of spontaneous magnetization within magnetic domains (Nagata, 1969). It is also known that much of the domain wall motion is reversible, especi- ally in a material without many internal defects and stress concentrations (Carmichael, 1968). The effect of stress on Piezo-remanent magnetization (PRM), and the compression demagnetization effect for Isothermal remanent magnetization (IRM) are known to be irreversible. Both longitudinal and transverse compression result in a decrease of IRM in the case of compression demagnetization effect while they cause an increase of remanent magnetization in other types such as PRM. The effects depend on the magnitude of the external magnetic 31 field. The change of magnetization with o of this category is attributable to the irreversible movements of 90° domain walls (Nagata, 1969). It is also known that the change in magnetization produced by rotation-aided rearrangement of a multi-domain pattern by stress is largely irreversible (Carmichael, 1968). Theoretical interpretation of PRM was proposed by several workers (Nagata, 1966; Stacey, 196A; Carmichael, 1968). Nagata (1966) considered a dispersion of non- interacting grains or domains which are probably best regarded as single domain particles (Fuller, 1970). Carmichael (1968b) suggested a model for a broader range of applications (single to multi-domain). It is summarized as follows. Control of the direction of domain alignment can be determined by the anisotropy of the net energy. This can be calculated by an appropriate energy balancing of anisotropy of Ek and Bid with the stress required. Thus it is possible to examine the change of magnetocrystalline potential barrier which may be effectively removed, or sufficiently reduced by magnetoelastic anisotropy energy (E10)° Cubic—structure crystals of magnetite (and nickel) have preferred axes, which E minima in these k direction. The effective rotation of magnetization for stress of appropriate sign will thus be 70.5° or 109.5° to a neighboring easy axis. If such a transfer occurs, the Y 32 magnetization will be considered to be "controlled" by the external stress. For an even greater stress, the domain magnetizations will continue to be deflected towards the magnetoelastic minima and away from some exact orientations (Carmichael, 1968b). 2. Effect on susceptibility The dependence of magnetic susceptibility of rocks upon a uniaxial compression was first systematically examined by Kalashnikov and Kapitsa (1952) and Kapitsa (1955). Kapitsa studied the effect in different rock types such as basalt, diabase, syenite and granite and in magnetite and hematite. His results show that the longitudinal magnetic susceptibility, X//(d) decreases with an increase of a uniaxial compression 0, whereas the transverse magnetic susceptibility, XL(O) increases with c and approaches a finite asymptotic value for large value of a. It is generally known as anisotropy of susceptibility. Along with the development of measuring technology, experi- ments on susceptibility has been done by various workers (Kern, 1961; Stacey, 1962; Nagata and Kinoshita, 1965; Nagata, 1966, 1969, 1970, 1972; Kinoshita, 1968; Ohnaka and Kinoshita, 1968; Pozzi, 1975; Kean et al., 1976). Theoretical expression of the relation between x//(o) and a has been achieved with satisfactory results and it is empirically known as _ X0 X//(°) “ “1+Bc (2-36) 33 where x0 denotes the isotropic magnetic susceptibility for o=O and B is a material constant. In most igneous rocks, u Bis of the order of magnitude of 10' cm2/kg (Nagata, 1969). Ohnaka and Kinoshita (1968) showed that the stress sensi— tivity increases as the composition parameter x increases in the titanomagnetite series. They worked in the range F: x=0 to x=0.7 making observations at each increment of 0.1. They also found an increase in B with the increase of x. - Hi The effect of grain size on B was predicted by Nagata (1966) and later explained by Kean et al. (1976). 4 An empirical formula for XL(O) related to o is more complicated. Following Nagata's (1970) theoretical model, it can be described with two parameters 8, and 6. It is given as xo XL(0) = (2-37) l+/e2+%B202—(e+%80) 3A where B E s and E 2 A/2 K/n (2-28) NJS2+A/3 K/H NJS2A/3 K/n It has been tested with experimental results by Nagata (1970), and fairly good agreement was obtained. The effect of hydrostatic pressure on the magneto- crystalline anisotropy constants K1 and K2 of magnetite has been studied by Sawaoka and Kawai (1967), and effect on magnetostriction and magnetocrystalline anisotropy has been separately studied by Nagata and Kinoshita (1967). 3A The result obtained was that Kl decreases by -l.35%/kb (Sawaoka and Kawai, 1967) up to 10 kbar, -5%/khar (Nagata and Kinoshita, 1967) up to 2 kbar, and K2 decreases by almost the same ratio as Kl (Nagata and Kinoshita, 1967) or with almost no change (Sawaoka and Kawai, 1967). The magnetostriction constants 1111 and 1100, also decrease by the ratio of 15%/kbar up to 2 kbar (Nagata and Kinoshita, 1967). However, no measurement has been done on bulk susceptibility under hydrostatic pressure. Theoretical models for uniaxial stress effect on sus- ceptibility anisotropy have been developed by Nagata (1970) and Stacey and Johnston (1972). Their models are based on rotation of spontaneous magnetization of domains by the effect of inverse magnetostriction and it has been accepted as a major mechanism for this model (Kean et al., 1976). Recent experimental results (Kean et al., 1976) showed that these theories are not likely to yield a useful analy- sis for magnetic material with many domains which interact strongly, and whose initial response to stress and weak field susceptibility is dominated by the wall movement. They also suggested that the effects of grain shape and texture have to be considered and showed a grain size dependence for the uniaxial stress effect on magnetic susceptibility. 35 III. APPARATUS AND MEASURING TECHNIQUE The equipment is divided into two different categories: one is for high pressure which can apply high hydrostatic pressure to samples and the other is for measuring magneti- zation of samples under the pressure condition. For the former purpose, a high pressure microbomb was used and for the latter purpose a ballistic magnetometer was designed. A. High Pressure Microbomb 1. Microbomb description The pressure vessel used in experiments was developed (Carmichael, Sawaoka and Kawai, 1968) to apply pressure up to 10 kbar. Using a single source of uniaxial external force, it can apply the various models of applied pressure; simple uniaxial stress, hydrostatic pressure, and combina- tion of both. And it can also vary either pressure continuously and independently of the other, with the magnitude of each known. As shown in Figure III-l, it has two different inde- pendent piston systems. Hydrostatic pressure can be produced by pressurizing the fluid medium (Kerosene and transformer oil) in the chamber and additional directed pressure can be exerted by contact of one piston with the sample. The construction material is hardened diamagnetic Beryllium-copper alloy (1.8% Beryllium by weight) with a 36 LARGE PISTON ASSEMBLY ‘ ' ”5T0" Be-Cu WASHERS <— LEAD GASKET RUBBER GASKET ALL PIECES HAVE “— MUSHROOM CAP CIRCULAR CROSS—SECTION SMALL PISTON ASSEMBLY <- PISTON /'D Be—Cu WASHERS \Hg 84—- Pb GASKET ‘3 3‘— RUBBER GASKET <— MUSHRDOM CAP SCALE _::_::3 0 1,2" 1” PISTON ASSEMBLIES FIGURE Ill—1 37 susceptibility of -O.6 x 10“7 emu/gm at room temperature, so its effect on the measurement of magnetic properties of a contained sample is negligible. As shown in Figure III-2, it is portable and can sit in the solenoid (for control of magnetic field) and ballistic system (sense coils) for measuring magnetization of samples. It can also maintain the desired pressure for a longer-time experiment by using locking caps and is portable with pressure. A modified version (Maher, thesis in progress) has been used and calibrated. It allows a sample up to 1.2 cm in diameter and 2.5 cm in length. Several corrections of the original design were made and described by Maher. 2. Calibration Internal hydrostatic pressure within the chamber was determined by using a sample of NHuF. NHuF undergoes a structural change resulting in a decrease (30%) in volume at 3.65 kb at 25°C. A packet of NHuF crystallites sealed to exclude the fluid is pressurized in the microbomb by the fluid medium. The piston displacement was monitored by a strain gauge. Then the displacement of piston versus applied external pressure was plotted (Fig. III—3). The abrupt rise in the curve corresponds to a pressure of 3.65 kb inside the microbomb. The structural transformation is reversible and the hysteresis that results on release of pressure is due to friction of the piston packing. It is known that the half-width of the hysteresis loop of pressure cycle 38 NON— MAGNETIC PRESSURE CHAMBER AND BALLISTIC MAGNETOMETER PISTON SENSE COIL \ TROLLEY I SOLENOID _J |__ _ COIL , IJ ‘vvv / / LOCKING CAP I" r I k ‘L PISTON SUPPORT CYLINDER FIGURE III- 2 39 n I... MGDGE _ aezz 026: 20.5.3340 92805.2 383.: .3 Sex memo“. ..so 2 z 2 N. .: S m a a m _ _ _ _ _ _ 1 _ 1 s m..u>u .EN I oz.m momOu. wmwmn. O...D<¢O>I Am; oootc women. 450 9 2 3 up 2 o o v u o . a . . N (SHVBO‘IIMI BOSSBHd ONINIJNOO 'IVNUBINI Al QN an ON vi: wmswi 920m mnsz. wmawwwmn. 02.2.“.200 I_ momOh. mmmmn. O_._D.._ .m._ oootc women. .25 9 o. 8 N. o. o o v N o . 4 . . R (SHVSO'IIM) BOSSBHd ONINldNOO 'IVNHSINI Al QN NN ON vi: meGI 920m mn:wz_ mewwmmn. 02.2.“.200 I_ womOn. wwwmn. 0_._DI .mA coo—x. womo... .310 9 2 8 2 o. o o e N o . . — . . (SHVSO'IIM) BOSSHHd ONINHNOO 'IVNHBINI A2 with fluid, and the opposite side piston (large in diameter) inserted and locked. Two ways of applying the pressure are possible: both pistons may be driven by the external uniaxial pressure or one piston can be locked in place while the other piston is forced inward. The latter method was used because it is desirable for a reversible run . B. Ballistic Magnetometer The ballistic method a convenient for the purpose of measuring the magnetic susceptibility and remanent magnetization of rocks and minerals in a weak magnetic field. The principle of this method can be summarized as follows. The total current change, which is induced in a sense coil as a result of the change in magnetic flux caused by the relative movement of a magnetized specimen in the sense coil, can be measured either directly by galvanometer (Nagata, 1961) or transformed to voltage by an integrator and measured by voltmeter. The change in flux can be generated by either the movement of magnetized specimen along the axis of the sense coil or movement of the sense coil against the fixed magnetized sample. The ballistic magnetometer, which is used for this experiment, consists of a solenoid with supplementary end coils, a pair of sense coils, integrator, sensitive null voltmeter, and regulated D. C. power supply. The solenoid and supplementary end coils were designed for “3 two purposes: either null out the field or apply additional field (max 2A0 oe in the center) inside the solenoid. For this experiment, the solenoid was used to null out the geomagnetic and ambient laboratory field. A solenoid may be described as n turns of uniformly wound wires on a cylindrical former. Fields produced by a solenoid with limited length show considerable inhomogeneity along the axis; being strongest in the center, and showing sharp decrease toward the end of the solenoid. This can make it difficult to maintain a uniform null field throughout the region in which the sample is located and may cause a constant error in measuring the magnetization of the sample. Thus supplementary end coils were introduced (Fig. III-5) to extend a broader uniform field region. The actual technique was done by experiment and the result is given in Figure III-5. This method can reduce axial field inhomogeneity from :50 moe to :16 moe through the region where measuring of sample magnetization occurs. Sense coils were designed as a pair of oppositely wound coils for measurement of flux changes. The sensitivity is twice as large as that of single—sense-coil apparatus. The advantage of these sense coils is that any change in the external magnetic field is eliminated by canceling the electromotive forces induced in each coil so long as the disturbance field is uniform (Nagata, 1967). The original sense coils (Maher, thesis in progress) were modified to AA \\(\\\\{\\ SOLENOID "noun“... 0 o— - o 4- . I { "fiom 80!. now \ \ / \"'- ~ ...—cu!" Keno con. muons M“ \\J\N\\\ \\ \ LATHE / NULL FIELD CONFIGURATION (SOLENOID +END COILI FIGURE III-5 ’,’1-16mA A5 mi: wmbwi (00m) Om. ..4 04m; .200 wmzwm .20.m02<...m_o o. o o v a o «I cI ol ol o? u i L i i . 1 T .A i I. ll 1.6.- ll. LIOOI \ \ X I \ \ ...3- H \ \ \ \ IIJIJI season 0 I\ X 3.8:. 9:3 .3: \ \ X \ \ .9 11 \ \ \ \ Jr. .60 RI- Jr . 1’ ch— 1- q- AI- an. AI. O13 |:| OILSNDVN mi: wmawl 04w; .200 mmzwm .so.moz¢._.m_o A5 (00m) o o e a o «I on on o... o... p p . b p — p F — P I 1 J . . q q a q q a . ITO.- LS- \ X R \ -....- \ \ L \ I \ DI....J.I . III\ “ X 929 .3: \ \ \ 18 X x \ \ .8 ....8 P - . p F . . b u d n D d c - # ‘- III- 0'13 I:I OILSNBVN A5 ®I___ meGE (com) Om. «.< 04m... 4.00 mmzwm 50502320 2 o o v « o «I «I oi ol 3. p P . F . — . F _ p I q a . . . d a q . A . 1.6. L13- \ \ V “ \ 11:1 X \ L \ \ _ I _II celwfi 0 III\ fl \ 9:3 .3: \ G X \ .9 K \ .6. S p p p p P n p F . p . . q a q 1 I u 1 . . a (new ouansvu no increase sensitivity by increasing coil windings by 50%, and the new curve of the field produced by a 500 uA current in the sense coils is given in Figure III-6. C. Experimental Set Up The portable pressure bomb was prepared with sample and fluid medium for pressurization. Then it was placed in the center of the solenoid (Fig. III-2), which was positioned in the center of hydraulic press machine. While the uniaxial external pressure was applied by the hydraulic press, the sense coil can be moved vertically within the solenoid and the induced current in the sense coil trans- mitted to the integrator. The integrator transforms current to voltage, and voltage changes were measured by voltmeter. The apparatus is shown in Figure III-7. E. A. F. Demagnetization Technique and Apparatus Description The use of alternating-frequency demagnetization was first introduced in paleomagnetic work for examining the stability of remanent magnetization and for removing the soft component of Natural Remanent Magnetization (NRM) by Thellier and Rimbert (195A). The essential procedure of this technique is to apply to the specimen an alter- nating magnetic field which decreases gradually from a certain magnitude of peak field (Hp) to zero. Thus the magnetization of all domains with a coercive force less ’h than Hp will follow the field as it alternates. As the A7 EXPERIMENT SET UP FIGURE III-7 A8 field is reduced, domains with progressively lower coer- civities become fixed in random orientations governed by the structure of the magnetic minerals. The magnetization is then measured by magnetometer, and the process repeated using a higher value of Hp. During the demagnetization, if steady field such as that of Earth's is present, or if the variations in the alternating field are asymmetrical, an unwanted anhysteretic remanent magnetization (ARM) will be introduced in the specimen. Such effects are avoided by carrying out the demagnetization in zero field, and by filtering the current supply to the demagnetizating solenoid (As and Zijderveld, 1958) or by spinning the specimen (Creer, 1959). The results of such a stepwise demagnetization may be expressed graphically, as changes in the intensity of magnetization. These results can give us information about stabilities of various remanent magnetizations of speciment and also represent the distri- bution of coercivity of a specimen indirectly. Since coercivity of magnetic material is known to be a structure- sensitive characteristic (Carmichael, 1970), the demagneti- zation curve can be used as a indicator of mechanical change of a sample. For this experiment, the sample was always saturated by a strong A. C. magnet (maximum field; 10 kilogauss) before demagnetization was measured by a spinner magnetom- eter (Schonstedt Model SSM-l at the University of Michigan). A9 Demagnetization was done by A. F. Demagnetizer (Schonstedt Model GSD-l at the University of Michigan) with stepwise procedure. The magnetization of the sample was measured at each step. The spinner type magnetometer is a small dynamo in which the alternative electro—motive force (e.m.f.) is induced in a fixed pick-up coil system by a rotating magnetic sample. A cylindrical sample was rotated at high speed on the axis of a multi-turned circular coil. Thus the component of magnetization perpendicular to the axis of rotation produces a rotating magnetic field, including an alternating e.m.f. in the coil. The e.m.f. is then amplified electronically. Equipment is shown in Figures III-8 and 111-9. 5O A.F DEMAGNETIZER FIGURE III- 8 51 SPINNER MAGNETOMETER FIGURE Ill- 9- 52 IV. SAMPLE, ANALYSIS, DESCRIPTIONS AND EXPERIMENTAL RESULTS Outline Two different types of magnetite samples were prepared for the experiment: a natural single crystal cored perpen- dicular to a (111) face, and dispersed synthetic magnetite powder in epoxy cement with 1.7% volume fraction of magne- tite. The density of the magnetite powder was determined by pyncnometer method and grain size distribution of magnetite powder was determined by Hydrometer method. A. General Characteristics of Magnetite Magnetite is a common mineral found disseminated as an accessory through most igneous rocks. Sometimes, through magnetic segregation it becomes one of the chief constitu- ents, and may thus form large iron ore bodies. It is commonly associated with crystalline metamorphic rocks, and also frequently in rocks that are rich in ferromagnesian minerals, such as diorite, gabbro, and peridotite. It also occurs in immense beds and lenses, and is sometimes found in black sands of the sea shore. The crystalline variety with strong magnetic characteristics, is known as lodestone. As a member of the titanomagnetite solid solution series 2+ A+ 2+ X Fe T 3+ 2 1 Fe ) on: Ou-(l-X)Fe3+ (Fe 53 it has chemical formula Fe30u with Fe2+ (2A.l), Fe3+ (A8.3), 02' (27.6) percent by weight. The crystallographic struc- ture is cubic spinel of the inverse type with hexagonal close-packed oxygen planes along the direction. The cations are located in two lattices A and B, the A sites in four-fold co-ordination with oxygen ions and the B sites in six-fold co-ordination. There are two B cations for each A cation so that the two interacting sublattice moments are unequal giving rise to the observed ferri- magnetism. Iron atoms occupy layers between two adjacent planes; successive layers having iron atoms either in octahedral sites B between individual oxygens, or one— third in octahedral sites B and two-third in tetrahedral sites A. The structure converts to orthorhombic below about -155°C. The transition is abrupt for synthetic crystals, but can be spread over about 10° for natural crystals, and the presence of impurities lowers the transition temperature (Carmichael, 1971). With saturation magnetization of A80 emu cm—3 (McEl- hinny, 1973), magnetite has Curie Point at 575°C and has cubic cell dimension a = 8.39°A. Complete solid solution of titanomagnetite series exists at temperatures in excess of 600°C (Basta, 1960). Critical grain size for single domains is between 0.035 um and 0.05 um (DunlOp, 1973) and for pseudo—single domain is about 17 um (Stacey, 1963). Other known crystallographic and physical 5A TABLE IV-l PROPERTIES OF MAGNETITE cell dimensions (cubic phase) 0 a = 8.39A A 0 distance between (111) oxygen planes m 2.9 A distance between Fe and 0 octahedral site: tetrahedral site: angle between O-Fe-O octahedral site: 90°, 91.9° tetrahedral site: Mineral characteristics: 0 2.06 A 1.87 K 88.1°, 109.5O crystals are generally octahedral form (111), but may occur as cubic (100) or dodecahedral (110) twinning and parting on (111) hardness about 6 3 density = 5.2 gm/cm Magnetic properties: ferrimagnetic at room temperature JS m 98 cgs/gm at 0°K m 92 cgs/gm at room temperature (A80 cgs/cm critical single domain size about 0.11 micron magnetic anisotropy 3) magnetocrystalline transition at Tk = -1A0°C T < T k 0 hard axis <100>} K1 negative -155° < T < T easy axis <100> "c" axis k hard axis <1ll>} Kl positive T < -155°: 5 eaxy axis — orthorhombic Kl N -1.35 x 10 ergs/cm3 K2 m -0.A8 x 105 ergs/cm3 transition suppressed if grain size too small-— less than about O-lu -6 1100 N20 x 10 cm/cm A -6 110 N60 x 10 cm/cm 55 1111 ~78 x 10"6 cm/cm AS MAO x 10.6 cm/cm To = 575°C 0 domain (Bloch) wall: thickness m 500—1500 A energy m l erg/cm2 Mechanical properties: 6 G N 0.5 x 106 kg/cm E m 1.6 x 10 kg/cm2 (Young's modulus) 2 (shear modulus) K m 0.6 x 106 kg/cm2 (bulk modulus) Poisson's o m 0.3 slip plane {111}, slip direction <110> 2 ultimate compressive strength (crystal) w 1000 kg/cm electrical resistivity p «:10-3 —102 ohm—meter (Carmichael, 1971) 56 parameters are given in Table IV-l. B. Sample Description 1. Single crystal sample (PH-3) Single crystal sample (PH—3) was cored perpendicular to the (111) face of a natural single crystal of magnetite. It was coated with epoxy to prevent fluid from entering any small cracks and causing the sample to disintegrate under pressure. It also has experienced pressure by prior experiment (Maher, thesis in progress). It has a nearly cylindrical shape with 1.33 cm length, 1.7081 gm weight. Chemical and x-ray analysis shows 1.06% of T102 and small amount of Ni, Sn, Cu, CaO, and K20 (Table IV-2). 2. Synthetic magnetite dispersion samples (Syn-2 and Syn-3) The synthetic magnetite samples were prepared by dis- persing synthetic magnetite powder in epoxy cement (1.7% volume fraction of magnetite powder). The synthetic mag— netite powder was derived from an aniline chemical process. It had been previously roasted at 90°C to remove water, then it was ground and sieved to under 100 mesh (grains greater than 1A9 u in diameter were removed). Then the density of the magnetite powder was measured by pyncnometer method (Sect. D) and has a value of A.92l g/cm3 which is a little less than for average magnetite (A.9 - 5.2 g/cm3)l/. 1/Handbook of Physics and Chemistry. The grain size distribution of sieved magnetite powder was determined by hydrometer method (Sect. C). It shows size range about 2 to 100 microns with average diameter of 8 microns (Fig. IV-l). However, it is assumed that it also consists of grain more than 100 microns in diameter. Because the coarsest grains sink too fast in suspension, the hydrometer method could not detect it. Thus the grain size of magnetite powder ranges from single domain to multidomain with mainly the intermediate pseudo—single domain. Other description on samples Syn-2 and 3 is given in Table IV-2. C. Grain Size Distribution Determination by Hydrometer Method l. Principle The principle of this method is based on Stoke's law which shows the relationship between the velocity of fall, and the density of a spherical particle. It is expressed as 2 Y ' Yf D 2 I = — —— — A—l v 9 n (2) ( ) where: v = velocity of fall of the particle (cm/sec) y = density of the particle (g/cm3) yf = density of the fluid (g/cm3) n = absolute viscosity of the fluid (dyne-sec/cm2) D = diameter of the spherical particle (cm) Solving equation A-l for D by using the density of water for yf we can obtain 58 TABLE IV-2 SAMPLE DESCRIPTION Sample PH-3 Magnetite (Fe30u), [111] rod from Port Henry (Essex Country), N.Y. Length 1.33 cm Weight 1.70808 gms Trace analysis; T1 02 = 1.06% (T1 = .636%) Ni = A00 ppm Sn = 160 ppm Cu = 150 ppm Ca0 = 280 ppm K20 = 60 ppm Magnetite powder x-ray analysis of material showed only magnetite structure (has small amounts of Si, Al, S and organic material). Measured density value is A.92 gm/cm3. Synthetic sample Dispersed magnetite powder with epoxy (volume fraction l.7A% of magnetite) Sample syn—2 shape cylinder height 2.5 cm diameter 0.7950 cm Sample syn-3 shape cylinder height 2.71 cm diameter 0.7952 cm 59 D = nV (A-2) s-Yw Approximately, the range of grain diameter D for this equation to be valid is 0.2 u i D i 0.2 mm. Larger grains cause excessive fluid turbulence and very small grains are subject to Brownian motion. To solve equation (A-2), we need to obtain the velocity term v, know the correct values of Ys and Yw’ have access to a table of viscosity of water (see Appendix). Since the unit weight of water and its viscosity vary with temperature, it is evident that this variable must also be reckoned with. Thus the calculated tables (Appendix) were used for the purpose. For computational purposes, equation (A-2) is usually rewritten using L in centimeters and t in minutes to obtain D in millimeters as follows: D = 30h (A-3) L 980 (PS-9W7? mm To obtain the velocity of fall of the particles, the hydrometer is used. The hydrometer was a type 152H (ASTM designation) and is calibrated to read grams of grains of a value of specific gravity (Gs) = 2.65 in 1000 cm3 of suspension as long as no more than 60 gm of grain involved. Since the hydrometer is used, the smaller the hydrometer reading R regardless of the amount of material in sus- pension, corrections must be applied to the actual reading to obtain a hydrometer reading which accurately measures 60 the material in suspension to make a percent-finer com— putation. The corrected hydrometer reading is, therefore, computed as Rc = Ractual The temperature correction factor Ct is calculated in the - Zero correction + Ct (A-A) Appendix. After a corrected hydrometer reading has been obtained, correction for the solid particle which is Gs : 2.65 is needed. It can be obtained using the following formula: a 1 Gs/(Gs-l) ‘ 2.65/(2.65-1) Solving for a, one obtains, = Gs(l.65) ° (Gs-1) 2.65 The calculated value a for magnetite powder (p=A.928/cm3) was 0.769. Then the percent-finer is computed as Percent-finer = 5%: x 100 percent (A-5) where Ws is weight of original magnetite powder in suspen- sion (50 g). Value of L (effective depth) for use in Stoke's formula for diameters of particles for ASTM soil LHydrometer 152H is given in the Appendix. Thus with Ineasured values of Ract., time interval t, the Appendix, and equations (A-3, A-5), we can obtain the distribution curve (Fig. IV-l). 2. Procedure and result 50 g of magnetite powder was prepared, then it was 61 FI>_ MEDOE .mZOIOZZ. wN_w w..0_...mOzw30wmu. fl m2340> 62 demagnetized to eliminate the possible error caused by its magnetization which may raise the critical size of Brownian motion. After demagnetization, it was mixed with 125 cm3 of AZ sodium metaphosphate solution.(NaP03). This is often used as dispersal agent to neutralize the soil- particle charges. Then the mixture was transferred to the malt—mixture cup and tap water added and mixed for 10 minutes. After mixing, all the materials in the cup were transferred to the 1000 cm3 capacity sedimentation cylinder and the cylinder capped. It was then carefully agitated for at least 1 minute. The jar was set down, the cap removed, the hydrometer inserted, and the hydrometer read then at elapsed time of l, 2, 3, ..., sec. Beside that from the control jar, the temperature reading and meniscus reading of hydrometer were taken. Apparatus is shown in Figure IV-2, and the result is given in Figure IV-l. D. Density Measurement of Powdered Magnetite Specific gravity or density of a powder or aggregate of mineral fragments can be accurately obtained by means of a pycnometer. The pycnometer is a small bottle fitted with a ground-glass stopper through which a capillary Opening has been drilled. In making a density determination, the dry bottle with stOpper is frist weighed empty (P). The powdered magnetite is then introduced into the bottle and a second weighing (M) 63 EXPERIMENT SET UP HYDROMETER METHOD FIGURE IV - 2 6A is made. The bottle is partially filled with distilled water and the added water volume (V1) is measured. The bottle is boiled for a few minutes to drive off air bubbles in pore spaces between grains. Then it is cooled. While cooling, the bottle is attached to weak suction pump to drive off air bubbles. After cooling, the 5 ml pycnometer is filled with distilled water and again the added volume of water is measured (V2). Then the density of powder can be determined: ° = 5 - v1 - v2 (g/Cm The measured density value of synthetic magnetite powder is given in Table IV—2. E. Results Through the experiments, all samples were pressurized in the high pressure microbomb. l. Saturation remanent magnetization (Jr,sat) This was examined in the null field created by the solenoid and the results are presented in Figure IV-3 and Figure IV—A. Results show an abrupt change in Jr,sat up to l kbar and an irreversivle loss of initial satura- tion remanence (Jr, 0) of 30%, and a reversible change over the range up to 3.2 kb. 2. Susceptibility Susceptibility has been determined from the lepe of the small change in Jr,sat with an applied small external ml). wanOT... :3: 3.33:: 0.33.0.3; o « P B 4 D an! Ia moa2_ mm.3mv_m mcawmmca U.h1 n N .. n b D d ‘| ‘ .mlxa maa2_ mmDGE .mx.mc:mmmca 0:350:03. N p I 4 q- 8-z>m 3.51..“ 5950.: miszwazz ”.0 zo_.... wm30_n. . my. . mznmmmca U.h: o N n P u d ‘. . «I 22.. mthw20<2 ".0 m4u3......_m_._.n.m0w:w 69 field (i 100 moe) forming a small hysteresis (Fig. IV—5). Then the slopes of these hysteresis curves are analysed by statistical calculation. Results show a decrease in susceptibility parallel to the applied pressure (Fig. IV—6, 7). There is a decrease in susceptibility over the pressure range up to l kbar (-20% of initial susceptibility) and a total decrease of -25% in susceptibility was obtained at 2.5 kbar for synthetic sample Syn-2 (Fig. IV-6). For single crystal sample, there is a similar decrease in susceptibility in the first pressurizing cycle. However, the reverse cycle (releasing the pressure) shows a small change in susceptibility: susceptibility at zero pressure shows a loss of about 5% (Fig. IV—7). 3. Magnetic hardness Mechanical deformation of smaples and consequent change in magnetic hardness has been indirectly tested by using the Alternating Frequency demagnetization method. Coercive force is known to be a structure-sensitive property of the material, and also gives coercivity distribution indirectly. Samples are A. F. demagnetized before and after the pressurization by 3.2 kb. Results for a synthetic sample (Syn-3) are presented in Figure IV-8 and coercivity spectra are also obtained and plotted (Fig. IV—9). Before pressurization, the curve shows a mean demag— netization field (MDF) about 100 oe and coercivities range up to about A00+ oe. After pressurization, the curve 70 indicates that the saturation remanence has been increased by 8%, and MDF increases slightly. 71 NI>_ mmDOT. A ox . wmsmmmca O....<...wO¢O>... qL JI- Deanna... 023:1... .0. IIIII 20:32:23.... ... . .2523 3025 .slxa maaz.:4_m:.n.m0m3m 72 w|>_ mm30_u Amara .n..< x Stacey and Banerjee (1974) developed the above formula by the relation of magnetocrystalline constants Kl’ K2, magnetostriction constants A111, A100, and magnetostatic anisotropy for cubic structure magnetite. It is given as fJ 2 s . x(c) 2 (6’2) -u/3(k1+1/3k2) + o(%AlOO+5/2Alll) + NJs X = __2_ 1+Bo where 1/2A +5/2A B = 100 111 2 (6-3) —u/3(Kl+1/3K2)+NJS 77 Measured values of K1, K2 and A100, A111 by Nagata and Kinoshita (1969) showed that K and K decrease (—5%/kb) l 2 and A100, A111 increase (15%/kbar) with pressure. Thus the qualitative interpretation of hydrostatic pressure effect on susceptibility can be obtained as follows. 8 will increase by a decrease in K1’ K2, and A increase in A 100. Therefore, x(o) will be decreased 111’ with pressure applied by the relation presented in equation 6—1. It gives fairly good agreement with our result qualitatively. Similar results have been reported by applying uniaxial pressure on magnetic susceptibility (Nagata and Kinoshita, 1965; Ohnaka and Kinoshita, 1968; Nagata, 1970). 8. Theoretical Calculation of Hydrostatic Pressure- Controlled Magnetization Behavior of Magnetite Outline The orientation of magnetic domains is determined by the magnetocrystalline energy (Ek) when there are no other energies introducing an anisotropy. The direction of spontaneous magnetization (Js) is a preferred direction determined by the symmetry of the crystal. The appli- cation of stress gives rise to a bulk magnetoelastic energy (EAo). This energy favors directions that depend on the orientation of the principal stresses, and the nature of the material's magnetostriction. 78 When external stress is applied, domain wall motion can begin with a lowering of the magnetocrystalline potential barrier or by increase in directional magneto— striction energy anisotropy. Then the changes of orien— tation are guided by influence of the bulk energy balance of both Ek and EAo. Carmichael (1968) developed a technique to calculate appropriate energy balancing of the two energies (Ek, EAo) for magnetite and nickel single crystals with measured values of magnetocrystalline anisotropy constants (K1, K2) and magnetostriction constants (1111, A100) under uniaxial pressure. This technique can be used for calculating the hydro- static pressure effect on Ek and EAo by using the different values of K1’ K2, A111 and A100 (Nagata and Kinoshita, 1967; Sawaoka and Kawai, 1967) for magnetite under hydrostatic pressure. The temperature effect on Ek and EAo can also be calculated with known measured values of K1’ K2, A111 and A (Syono, 196U). 100 Thus, combination of the effects of temperature and hydrostatic pressure on Ek and EAo will give us an idea of the magnetization behavior of magnetic minerals or rocks at depths beneath the earth's surface. 1. Hydrostatic pressure effect on magnetocrystalline potential barrier For a cubic structure such as magnetite, magneto— 79 crystalline anisotropy energy is Ek = Ek - E0 where _ 2 2 2 2 2 2 Ek - KO + Kl (al a2 + a2 a3 + a3 a1 ) + 2 2 2 K2 (a1 a2 a3 ) + ————— In the case of magnetite, there are magnetocrystalline anisotropy energy barriers between two axes over the intermediate [110] axis. Thus, the potential barrier is AEk = Ek,(llO) - Ek,(lll) The K's are the magnetocrystalline energy constants, and a's are the direction cosines of Js with respect to the cubic axes. The direction cosines of magnetite are l l l l 1 (/§, /§’ /§ ) for (111) axes and (;§: jij 0) for (110) axes, and measured values (Syono, 1965) of K1 and K2 for 4 and -4.4 x 10h erg/cm3 magnetite are —l3.6 x 10 respectively. Therefore, calculation for magnetocrystalline potential barrier of magnetite at atmospheric pressure can be performed as Ahk = AEk’ (110) u ’ AEk’ (111) —3.H X 10 - (-4.69 X 10“) 1.29 x 10“ (erg/cm3) 80 where r .l_ 2 1 2 1 2 1 2 ? = _ J _ ___.. __ __ ALk) (111) 1036 X 10 [(/3 ) (J3 ) + (J? ) (/§ ) + _l_ 2 _l_ 2 '5 1 1 1 (f3) ((3') J-OJU-l :10 (3- g ’ '3') = -l.36 [ § ] - o.uu [ 27 ] = -0.u69 x 105 12k, (110) = -1.36 x 105[% + o + o 1 — o.uu x 105[ o J = -l.36 x 105 [ E = —o.3u x 105 Hydrostatic pressure effects on K1 and K2 have been studied by Sawaoka and Kawai (1967), and Nagata and Kinoshita (1967). The former's results showed that Kl decreases -l.35 x 10"2 erg/cm3/kbar. The change in K2 was too small to be evaluated. Nagata and Kinoshita's (1967) result indicates Kl of magnetite single crystal decreases ~l2% by 2.1 kbar of hydrostatic pressure. Thus the quantitative evaluation of hydrostatic pressure effect on potential varrier can be performed. Result of the calculation is given in Table V—l. The calculated results for AEk without considering K2 indicate the potential barrier is reduced ~23% (Nagata and Kinoshita's) or ~15% (Sawaoka and Kawai's) by 2 kilobars of hydrostatic pressure. Thus the domain walls became easier to move by any applied pressure. 81 TABLE V—l Pressure K's A Ek (kbar) (erg/cm3) x 105 (ergs/cm3) x 105 0.001 -1.361 (a) -O.uu (b) 0.129 0.“ -1.35 (c) -0.113 0.8 -l.3l (C) -O.109 1 -l.3u (d) -.112 1.2 -1.27 (C) -0.106 1.6 —l.22 (C) -O.102 2.0 -1.21 (c) -l.32 (d) -0.101 -0.110 (a) (b) Syono's (196”) value for K1 and K2 (c) magata and Kinoshita's value for Kl(1967) (d) Sawaoka and Kawai's (1968) value for K1 2. Hydrostatic pressure effect on magnetostriction (EAo) Magnetostriction (or magnetoelastic) energy for cubic structure single crystal is known as _ 2 E10 - -3/2 A1000 (a1 Y1 + “1 0‘3 Y1 Y3) '3 ' A1110 (“1 “2 Y1 Y2 + “2 Y3 0‘2 Y3 where the y's are the direction cosines of the stress with respect to the axes and the A's are the magnetostriction constants for the respective crystal directions. For a magnetite single crystal with the stress 1 parallel to axes, y's are known as Y1 = 7?‘, 82 1 l = 7§—, Y3 = 7%“ and measured values of A and A Y2 111 100 are 78 x 10.6 and -20 x 10"6 cm/cm respectively (Syono, 196“). Therefore, magnetostriction anisotropy between the two directions and <110> is determined by; AEAo = EAo - EAo (110) (111) 6 6 o - (68 X 10- 3 —29 x 10' o) 39 x 10"6 o erg/cm The hydrostatic pressure effect on magnetostriction coefficients A111, A100 has been measured by Nagata and Kinoshita (1967) for single crystal magnetite. Their result shows that both A111, A100 increases w15%/kbar of hydrostatic pressure. By using their result on A's hydrostatic pressure effect on magnetostriction anisotrOpy for directional (uniaxial) stress which is assumed to be produced because of local accumulation of stress can be calculated. Calculated results are given in Table V-2. As a result of 2 kilobars of hydrostatic pressure, magnetostriction anisotropy increases ~28% with unknown uniaxial pressure which would be produced by applied hydrostatic pressure. Thus the unknown uniaxial stress 0 which produces equivalent effect of 2 kilobars of hydrostatic pressure which reduces potential barrier around 15% (0.019 x 105 erg/cm3) can be obtained by 49.72 x 10‘6 o 5 0.019 x 10 - 3.8 x 107 (dyne/cmz) Q I I! 40 bar 83 TABLE V-2 Pressure A110 A100 AEAc (kbar) (X10-6) (XlO-6)o ergs/cm3 0.001 78 (a) —20 (a) 39.0 0.“ 80.7 (b) —22.2 (b) “0.0 0.8 86.6 (b) -23.2 (b) u3.3 1.2 89.5 (b) -2“.3 (b) ““.8 1.57 96.7 (b) -2“.9 (b) “8.“ 2.0 99.5 (b) -25.u (b) M9.7 (a) values from Syono (196“) (b) values from Nagata (1967) 3. Temperature effect on Ek and EAo Temperature effect on K's and (A111, A100) for titano- magnetite series have been measured by Syono (196“). At a depth of around 6 km (equivalent temperature of 160°C), magnetite (x=o, in titanomagnetite series) has values of Kl=-0.6 x 105 erg/cm3, K =0.l x 105 erg/cm3 and A 10'6, A 6. =7 2 111 '1 X =-l2 x 10- Thus, the temperature (160°C) 100 effect on AEk and AEAo can be obtained by Carmichael's calculation method and it is as follows. For magnetite (x=o). AEk at T=160°C is AEk, = 0.0“6 x 105 (erg/cm3) (110) — (111) AEAo at T=160°C is _ -6 3 AEAo, (110) _ (111) - 35.5 x 10 o (erg/cm ) 8“ The above result shows that a temperature of 160°C reduces the magnetocrystalline potential barrier around 65% (0.083 x 105 erg/cm3) with reduction of ~9% of magnetostriction anisotrOpy energy. The equivalent uniaxial stress for this result can be obtained as 0.083 X 105 35.5 X 106 o 2.3 x 108 (dyne/cmz) O R 230 bar Thus the combined effect of pressure and temperature on Ek and EAo will be characterized as follows. 1. Crystalline potential barrier (AEk) is reduced around 80% whereas AEAo increases around 19% by a temperature of 160°C and 2 kbar of hydro- static pressure. This reduction of AEk should enable freer domain wall movement. This will appear as reduction of a saturation remanent magnetization of rocks and minerals. The effect of 2 kbar of hydrostatic pressure on AEk is equivalent to around “0 bar of uniaxial stress and the effect of temperature (160°C) on AEk is equivalent to about 230 bars of uniaxial stress. 85 Thus the depth of N6 km in the earth's crust (ml60°C and 2 kbar) will have an effect on AEk the same as 270 bar of uniaxial pressure on AEk at atmospheric conditions. However, rocks and minerals in the Earth's lithosphere are not isothermally saturated. Therefore the effect of hydrostatic pressure on remanent magnetization of rocks and minerals in the lithosphere is less pronounced than for saturation isothermal remanence (Jr,sat). The effect of hydrostatic pressure on hard remanence (i.e., TRM) is even less pronounced. 86 VI. CONCLUSION Hydrostatic pressure was applied to magnetite samples up to 2.3 kbar, which corresponds to a depth of N7 km in the Earth's crust. A notable reduction of isothermal remanent magnetization has been observed along with reduction of magnetic susceptibility of the samples. Thus, the effect of pressure on magnetic properties can be an important factor in considering the behavior of rocks in situ in the crust. Along with the effect of increased temperature,a theoretical magnetic model of Earth's crustal behavior should be possible. This will help interpret deformation-induced anisotropy of mechanical properties of rocks (Karp and Donath, 1966) or magnetic properties (Graham, 1966) to determine the orientation and magnitude of stresses acting in the geologic past. It is also known that the effect of hydrostatic pressure varies with depth. Thus it influences the piezom- agnetic response of rock to tectonic (non—hydrostatic) stress at depth. Therefore we need to know this hydro- static effect to interpret observed geopiezomagnetic changes for earthquake focal regions at a given depth and with a given stress buildup prior to earthquake release. Theoretical interpretation of piezomagnetic behavior of magnetic rocks and minerals has been attempted with 87 empirical, quantitative data from other authors (Sawaoka and Kawai, 1967; Nagata and Kinoshita, 1967). The results show the possible influence of pressure on magnetocrys— talline potential energy barriers and make it possible to compare the effects of hydrostatic pressure, uniaxial stress and temperature on magnetic properties. Therefore, further studies should be developed on temperature and pressure combined in experiment, improv- ing accuracy of quantitative measurement, and tectonomag— netic modeling of the Earth's crust for studies in paleotectonics, geodynamics, geochemical behavior, and earthquake prediction. APPENDIX 89 APPENDIX Properties of Distilled Water Correction Factors for a Unit Weight of Solids Unit weight Viscosity Unit weight of Temp of water of water grain solids Correction 0 ( C) (g/cm3) (poises) (g/cm3) factor “ 1.00000 0.01567 2.85 0.96 2.80 0.97 16 0.99897 0.01111 2.75 0.98 17 0.99880 0.01083 2.70 0.99 18 0.99862 0.01056 2.65 1.00 19 0.998““ 0.01030 2.60 1.01 20 0.99823 0.01005 2.55 1.02 2.50 1.0“ 21 0.99882 0'0098é 22 0.997 0 0.0095 g _ 33 g-gggg; g-ggggg n2§i§21?§ei X?$38g$/§3§>mi§ 25 0.99708 0.0089“ 0.769 from equation Gs (1.65 26 0.99682 0.0087“ Gs- . 5 27 0.99655 0.00855 28 0.99627 0.00837 29 0.99598 0.00818 30 0.99568 0.00801 Temperature Correction Factor Cy T 133? C' (58? CY 15 -l.10 25 +1.30 16 —0.90 26 +1.65 17 -0.70 27 +2.00 18 -0.50 28 +2.50 19 -0.30 29 +3.05 20 0.00 30 +3.80 21 +0.20 22 +0.“0 23 +0.70 2“ +1.00 9O m.m H: e.ma . om ~.m o: m.ma ma m.m ow m.m mm m.mH ma 0.0 mm H.0H mm m.mH NH m.m mm m.oa pm w.mH ma 0.5 pm :.OH mm m.mH ma H.> mm m.oa mm 0.:H :H m.~ mm >.oa am m.:H ma a.» :m m.oa mm m.:a NH w.» mm H.HH mm m.:a HH m.» mm m.HH Hm 5.:H OH m.» Hm z.HH om m.=H m H.@ om m.HH mm e.ma m m.w m: ~.HH mm «.ma w :.m w: m.HH pm m.ma o m.m w: e.mH mm m.mH m m.m w: m.ma mm m.mH : m.w m: :.ma am m.mH m H.m z: m.ma mm e.ma m m.m m: ~.ma mm H.mH H :.m m: m.mH Hm m.mH o Amaco moomficoe AmHQo mzomfisoe Ahaco mSochoE AEov pom Uopomhhoov AEov Low Umpooppoov AEov mom Umpomnpoov A 59006 mafiommp A 39006 wcfiowmn A Spamo mcfiomom 0>Hpommmm popoEopomn 0>Hpowmmm nmmeopozn 0>Hpoommm nopmsomomn Hmcawfiho Hmsawfimo Hmcawfino mmmfi abmeOEUAm Hfiom same no mbaofipbmm do whopoemfim pom Mademom .mmepm Ca mom: ho“ Aspamm m>Huomwmmv 4 mo mosam> 91 BIBLIOGRAPHY Avchyan, Gé N., Effect of hydrostatic pressure up to 8000 kg/cm on various types of remanent magnetization of rocks, Izv. 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