- Email: [email protected]
Variations of the mean susceptibility of rocks under hydrostatic and non-hydrostatic pressure
Physics of the Earth and Planetary Interiors, 63 (1990) 78—84 Elsevier Science Publishers B.V., Amsterdam
78
Variations of the mean susceptibility of rocks under hydrostatic and non-hydrostatic pressure A1e~Kapiëka Geophysical Institute, Czechoslovak Academy of Sciences, 141 31 Prague 4, Boc~n1II(Czechoslovakia) (Accepted for publication 1 February 1990)
ABSTRACT Kapi~ka,A., 1990. Variations of the mean susceptibility of rocks under hydrostatic and non-hydrostatic pressure. Phys. Earth Planet. Inter., 63: 78—84. The variations of the mean susceptibility of basaltic rocks and polycrystalline magnetite, measured in a weak magnetic field, under external non-hydrostatic (uniaxial) and hydrostatic pressure, are studied. A decrease of the mean susceptibility with increasing pressure was observed in both cases, the changes under uniaxial stress being systematically much larger than those under hydrostatic pressure. These changes are reversible with respect to the application of the external stress. The decrease of mean susceptibility under uniaxial stress is related to the qualitatively different behaviour of the changes of directional susceptibilities of orientations different with respect to the applied stress. The magnitude of the decrease of the actual rocks depends on the ratio of the stress sensitivity constants of the various directional susceptibilities. Small changes of the mean susceptibility under external hydrostatic pressure may be the result of the inhomogeneity of internal stresses acting on ferrimagnetic minerals as a result of the anisotropy of the transmitting properties of the non-magnetic matrix.
1. Introduction Magnetic susceptibility in a weak magnetic field is one of the most frequently studied parameters under pressure. Laboratory measurements of pressure changes of susceptibility may, on the one hand, be applied directly to solving geophysical problems related e.g. to explaining magnetic anomalies; on the other hand, they serve to verify various theoretical physical models describing the magnetic parameters of rocks and minerals as functions of external stress. In experimental modelling one uses either hydrostatic pressure or uniaxial stress. Most published papers concentrate on studying susceptibility under uniaxial stress up to 100—200 MPa. Changes of the directional susceptibilities have been measured and the corresponding results are in qualitative and, to a large extent, quantitative agreement with theoretical models. A review of the experimental and theoretical results is given, e.g. in the review papers by Nagata (1970a), Kean 0031-9201/90/$03.50
© 1990
-
Elsevier Science Publishers B.V.
et al. (1976) and Davis (1983). Much less attention has as yet been devoted to magnetic susceptibility under external omnidirectional pressures. The reaSons for this are the generally smaller hydrostatic effects (compared with uniaxial stress), the more complicated hydrostatic experiments, and also the more difficult interpretation of the results. Only a few experimental results related to measurements of susceptibility under hydrostatic pressures up to 200 MPa have been published (Kim, 1976; Nullman et al., 1978; Martin, 1980). The disadvantage of all these experiments is that they only monitor the changes of the directional susceptibility. As regards uniaxial stress, the susceptibilities are measured parallel or perpendicular to the stress and only exceptionally in some other directions (Kean et al., 1976). However, since additional anisotropy of the rock susceptibility is generated under external stresses (Nagata, 1970b), directional susceptibility alone is evidently not a representative parameter. The susceptibility tensor has to be employed to achieve a complex
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
79
description of rock susceptibility in a weak magnetic field. However, to determine this tensor (a symmetric tensor of the second order is involved) the directional susceptibility has to be measured in at least six independent directions in the specimen (Jelinek, 1973). Consequently, in designing the experiments we concentrated not only on measuring directional susceptibility under various pressure conditions, but also on measuring the whole complex set of anisotropy parameters. We therefore constructed a uniaxial chamber (Kapi&a et a!., 1985) and a hydrostatic chamber (Kapi~ka, 1987) both of which could be placed inside the pick-up coils of a sensitive bridge for measuring susceptibility anisotropy. In other words, the pick-up coils are outside the pressure vessels and are not subject to pressure effects. The results of measuring the
2. SpecImens and method of measurement used The measurements were carried out on specimens of polycrystalline magnetite and of several basaltic rocks from the Bohemian Massif. The specimens were selected from a more numerous set used previously to study reversible and irreversible changes of susceptibility anisotropy under umaxial stress (Kapi~ka,1983, 1988). The selection was made with a view to the different stabilities of the directional susceptibility relative to uniaxial stress. The stress sensitivity constant fi” of these specimens varied between L9 x i0~ MPa1 (specimen 220) and 8.3 x i0~ MPa1 (specimen 219) (Kapi~ka,1988). The ferrimagnetic fraction of the basalts consists of non-stoichiometric titanomagnetites with varying proportions of ulvospinel x (x Fe 2TiO4(1 x)Fe304) as well as varying degrees of oxidation z. The detailed chemical composition of these specimens can be found in Kropá~ekand Kapi~ka(1979). The values of x and z, of the concentration of the ferrimagnetic fraction, the grain size, mean susceptibility, degree of anisotropy and Young’s modulus of elasticity of the specimens are given in Table 1. Identical cylindrical specimens, 8 mm in diameter and 10 mm in height, whose front surface hadbeen ground plane-parallel, were used in the hydrostatic and uniaxial experiments. The stress applied to the specimens in the uniaxial chamber was generated by a hydraulic press. The value of the effective stress applied to the specimen was determined from the tensometrically measured deformation and known Young’s mod—
changes of the principal parameters of anisotropy (the degree of anisotropy, orientation of the major axes of the susceptibility ellipsoid, etc.) under uniaxial stress have been published (Kapi~ka, 1988). One of the characteristic parameters of rock magnetism is the mean suceptibility which is defined as the mean value of all directional susceptibilities. Since the changes of the various directional susceptibilities under external pressure exerted on the rock vary not only quantitatively but also qualitatively, we are faced with the problem as to the degree to which their mean susceptibility also changes. This paper is devoted to reporting the measurements and discussing these changes under uniaxial stress and hydrostatic pressure.
TABLE 1 Mean susceptibility (k), degree of anisotropy (Pa), concentration of the magnetic fraction (c), grain size (4,), content of ulvospinel in titanomagnetite (x), degree of oxidation (z) and Young’s modulus of elasticity (E) for samples of basalt and magnetite
Specimen
~a
(102 SI) 207 219
220 231 259 Magnetite
14.4 12.0 8.4
13.1 6.2 269.8
1.02 1.04 1.03 1.04 1.03 1.37
4, (mm)
X
Z
(vol.%)
E (10~MPa)
13.4 12.2 11.7
0.06—0.2 0.07—0.2 0.03—0.15
0.58 0.67 0.14
11.3
0.01—0.07
0.63
9.1
0.01—0.05
0.67
0.42 0.51 0.85 0.43 0.15
35 34 36 32 39
—
—
—
—
79
C
80 A. KAPI(~KA
I
ulus of elasticity. The pressure in the hydrostatic pressure medium was mineral oil. The effective pressure within the chamber (after the source had chamber was generated by a hydraulic pump. The been disconnected) was measured by the changes of resistance of a manganirie sensor. Chambers with fixed uniaxial stress and hydrostatic pressure acting on the specimen were placed inside the measuring coils of the bridge at defmed positions. In the hydrostatic experiments this set-up completely eliminates the effect of the pressure medium on the measuring coils. Undesirable changes of temperature, related to the rapid increase or decrease of pressure in the hydrostatic chamber, were minimized by adopting a very slow pattern of pressure variations. Since both the chambers for measuring the susceptibility had to be made of non-metallic material with a low diamagnetic shielding effect, the maximum achievable uniaxial stress and hydrostatic pressure were 60 and 30 MPa, respectively. Monitoring the susceptibility variations under hydrostatic pressure, when only relatively small effects can be expected, calls for a high accuracy of measurement. Consequently, we used a highly sensitive digital bridge, a KLY-2 Kappabridge with an accuracy of 0.5% (Jelinek, 1973), in our pressure experiments. Since the pressure measurements are made in a single measuring range of the bridge, the accuracy in this particular case is even higher. The bridge is equipped with automatic compensation for the temperature drift so that it is zeroed before the next measurement of directional susceptibility in each case. The reproducibility of measurements over a longer time interval and the calibration of the bridge were tested by repeated measurements of a standard specimen provided by the manufacturer. The susceptibility was measured in an A.C. magnetic field whose intensity was 300 A m The specimen was measured under constant pressure and 15 various orientations of the chamber. The resulting directional susceptibilities were used to calculate the susceptibility tensor and the principal parameters of the susceptibility ellipsoid using the Aniso program (Jeinek, 1973). The mean susceptibility k was determined from the principal susceptibilities: k = ~(k1 + k2 + k3) where k1 is the maximum, k2 ~.
kIS I]
0.1
0.12
~
011
0 231 219
__________________________
30 60 t [MPO] Fig. 1. Mean susceptibility ~ of basalts as a function of uniaxial stress r. 0 and 0 are the susceptibility values after unloading from 60 MPa. the intermediate and k3 the minimum susceptibility. The degree of anisotropy of the specimens in the undeformed condition was determined using the well-known relation ~a = k1/k3. ~ Expeiimental results and discussion Figure 1 shows the changes of the mean susceptibilities of basalts k under a uniaxial stress of 60 MPa. All the basalts and magnetite specimens investigated displayed a similar decrease of the mean susceptibility with increasing uniaxial stress. These changes are reversible with regard to pressure; after unloading, the value of the mean susceptibility increases to approximately its original value. Table 2 gives the relative changes of the mean susceptibility of the investigated basalts and magnetite for stresses of 30 and 60 MPa. Under 60
TABLE 2 Relative changes of the mean susceptibility under uniaxial stresses of 30 and 60 MPa S~~en
(%)
(%)
207
95
89
219 220 231 259 Magnetite
93 96 92 94 95
88 93 87 90 93
81
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
MPa, the decrease amounts to 7—13% of the origi-
12.3-i
i~[io~Si] 0
nalOur value. experimental results clearly indicate that the mean susceptibility of basalts and magnetite, subjected to uniaxial stress, is lower than under unloaded conditions. This result is closely related to the magnitude of changes of the directional susceptibilities with different orientations relative to the uniaxial stress. The theoretical model describing the susceptibility of ferrimagnetic minerals under uniaxial stress, based on the mechanism of rotation of spontaneous magnetization within domains (e.g. Nagata, 1970b), gives a qualitative explanation of the behaviour of directional susceptibilities determined experimentally: in fernmagnetic minerals with a positive magnetostrictive constant the parallel susceptibility k” decreases and the perpendicular susceptibility k increases with increasing pressure. However, the ratio of the observed stress sensitivity constants, $ ‘/$“, for real rock specimens is considerably lower than the theoretical values. For example, the ratio of these coefficients for the basalts and magnetite we studied is between 0.1 and 0.31 (Kapi&a, 1988). Quantitative agreement with theory was not achieved even in the case of single-domain grains, and this difference has not been explained in full so far (Davis, 1983). As regards pseudo-single-domain and multidomain grains the deviations are larger because processes of domain wall nucleation are involved even under small stresses (Boyd et al., 1984), as well as the mechanism of displacement of domain walls (Kean et a!., 1976). However, it remains a fact that, from a macroscopic point of view, the decrease of parallel susceptibility with increasing uniaxial stress in rocks containing titanomagnetite is dominant. The decrease of the mean susceptibility k (which can be determined from any three mutually perpendicular directional susceptibilities) agrees with this conclusion. The magnitude of constants $ depends mainly on the size of titanomagnetite grains, decreases with increasing degree of oxidation (Kean et al., 1976) and increases with the content of ulvöspinel (Ohnaka and Kinoshita, 1968). The analysis of these results from this point of view was not the purpose of this study because the specimens in question contained titanomagnetites
0
122
p =0
12.1 219 2b 3b p [MPa] Fig. 2. Mean susceptibility k of a basalt specimen as a function of hydrostatic pressure p. The encircled values indicate an unloaded sample. with different ulvospinel contents, as well as with different degrees of oxidation. Nevertheless, one can see that the mean susceptibility is the most stable in specimen 220 which contains titanomagnetite with the lowest percentage of ulvospinel and a high degree of oxidation (Table 1). However, measurements of specimens with selected chemical compositions, grain size and defined matrix properties are necessary for systematic studies of the stress sensitivity of nonstoichiometric titanomagnetites. Figure 2 shows the mean susceptibility of a basalt specimen as a function of hydrostatic pressure up to 30 MPa. The actual behaviours of the separate basalts and magnetite differ, but at least a small decrease of mean susceptibility with increasing pressure was observed in all cases. In comparison with the external uniaxial stress, however, the overall changes of k are much smaller. This can be seen in Table 3 which gives the relative decrease of the mean susceptibility for
TABLE 3 Relative changes of the mean susceptibility under hydrostatic pressures of 20 and 30 MPa
Specimen
k20/k0
(%) 207
219 220 231 Magnetite
(%) 98
99 100 98 99
97 99 97 99
82
A. KAPIt~KA
hydrostatic pressures of 20 and 30 MPa. The maximum change at 30 MPa is 3% of the original value, and the differences between the separate specimens are minimal. These results do not contradict those of earlier hydrostatic experiments (Nullman et al., 1978; Ma±tin,1980) in which relative changes of the directional susceptibilities of various rocks were found to be a few per cent, The causes of these changes, however, are not completely clear. From a theoretical point of view, the changes of susceptibility under purely hydrostatic pressure are related to the change of the magnetocrystalline anisotropy. Regardless of the mechanism of magnetization, the initial susceptibility k of a cubic ferrimagnetic mineral depends on the saturation magnetization f~and on the constant of magnetocrystalline anisotropy K1
k
—
J
/
K
s/
1
‘ /
The change of the constant of magnetocrystalline anisotropy under hydrostatic pressure was determined experimentally for monocrystals of magnetite (Nagata and Kinoshita, 1967). It was found that, at pressures up to 200 MPa, K1 decreases uniformly as aK /ap = 5% per 100 MPa (2) —
hydrostatic pressure, the mean susceptibility k should also grow. This conclusion is, however, in qualitative contradiction with our experimental results (Table 3). The reversible changes of mean susceptibility in real rocks cannot, therefore, be explained in terms of the mechanism described above. The reason is that the condition of pure hydrostatic pressure on the ferrimagnetic mineral is not satisfied. In real rocks the ferrimagnetic grains are dispersed in a non-magnetic matrix. This is formed by various minerals whose grains are separated by grain boundaries, microcracks, pores, etc. On the scale of laboratory specimens, therefore, rocks cannot be considered to be an elastic continuum and the nature of internal stresses does not in general correspond to the external stress field (Jaeger and Cook, 1971). The internal stresses were calculated theoretically for simplified models, e.g. of two isolated rigid inclusions located in an elastic solid matter (Shelley and Yi-Yuan, 1966). If an elastic solid is in an external hydrostatic stress field, the stress field at their boundary does not have a hydrostatic nature owing to the interaction of both inclusions. In some directions the stress increases, in others it decreases. The actual stress field in which the ferrimagnetic grains are
located under hydrostatic pressure on the rock is
1
As regards the initial susceptibility of fernmagnetic minerals under hydrostatic pressure, it follows that k (p) = k (0) (1 + C1 p) (3) where C1 is a constant. In rocks in which the ferrimagnetic minerals with susceptibility k. are dispersed in a non-magnetic matrix, their apparent susceptibility ka is given by the relation, e.g. (Janãk, 1977) k ~i ‘1 P Nk 1 (4\ ka IL ~ ~‘ ‘J “ ~‘ —
‘~
—
—~
—
where P is the concentration of the ferrimagnetic mineral and N the demagnetization factor. A relation analogous to (3) then holds for the pressure dependence of the rock susceptibility ka( p): ( ~ ( ~( —
a
where C2 = constant
thus considerably inhomogeneous, and the stress components in the various directions may differ considerably. In this respect, the moderate decrease of mean susceptibility under hydrostatic pressure, determined experimentally, can be explained in very much the same way as in the model experiments with external uniaxial stress. At the same time, it is evident that the changes of susceptibility due to stress deviations under external hydrostatic pressure will be relatively small. The inhomogeneity of internal stresses is also evidenced by the changes of various directional susceptibilities under hydrostatic pressure (Fig. 3). Three mutually perpendicular directional susceptibilities were selected from the nine independent directions in the specimen and the measurements were made accordingly. The selected directions are indicated schematically in Fig. 3. As m the case of the external umaxial pressure (Kapi~ka, 1988), their behaviour is not uniform, but a moderate
83
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
12.51
k [i02S I] —
—
123
— —
—
These changes may be caused by local concentration of stress at the boundaries of ferrimagnetic grains owing to the inhomogeneous transfer of stress across the non-magnetic matrix. In the hy-
~.
—+—
.— —
-i--
k 2
drostatic experiments, therefore, apart from the stress sensitivity of ferrimagnetic minerals, the
30 p [MPo]
mechanical properties of the actual matrix (configminerals, concentration of microcracks, etc.) are uration and contact of grains, elastic properties of also of considerable significance. The general relationship between the macroscopic fabric of rocks and the concentration of internal stresses on a microscopic scale is not unique (Jaeger and Cook, 1971). However, measurements of magnetic antsotropy under hydrostatic pressure could be used to determine the basic components of internal stress in particular types of rock.
12.1 119
k2 k1~
219
ib
20
~
Fig. 3. Changes of three mutually perpendicular directional susceptibilities of a basalt specimen as a function of hydrostatic pressure. The orientation of the directional susceptibilities relative to the specimen is shown schematically.
increase as well as decrease of the directional susceptibilities can be observed. The degree of anisotropy increased in this example from 2% at zero pressure to 6.5% at 30 MPa. In the case of external uniaxial stresses the problem of transmitting stress to fernimagnetic minerals in rocks is not of principal importance. However, it was discussed in connection with artificial specimens with ferrimagnetic minerals displaying different elastic properties in their matrixes (Kean et al., 1976). However, this factor must be considered when explaining the changes of the magnetic parameters under hydrostatic
References Boyd, I.R., Fuller, M. and Halgedahl, S., 1984. Domain wall nucleation as a controlling factor in the behaviour of fine magnetic particles in rocks. Geophys. Res. Lets., 11 (3): 193-196. Davis, P.M., 1983. Tectonomagnetism. Rev. Geophys. Space Phys., 21: 685—693. Jaeger, J.C. and Cook, N.G.W., 1971. Fundamentals of Rock Mechanics. Chapman and Hall, London, pp. 5-47.
pressure.
Janâk, F., 1977. The determination of the content of fernmagnetic minerals in rock samples. Sb. Geol. Ved, Uzita Geofyz., 153—162. Jelinek, V., 17: 1973. Precision A.C. bridge set for measuring magnetic susceptibility and its anisotropy. Stud. Geophys.
4. Conclusion
Geod., 17: 36—45. Kapi&a, A., 1983. Irreversible changes of anisotropy of magnetic susceptibility of rocks due to uniaxial pressure. J.
The mean susceptibility is a parameter which can be characterized relatively easily by the susceptibility of anisotropic rocks. Since external stress is one of the causes of anisotropy, it is useful to investigate the changes of the mean susceptibility under model pressure conditions. Our experimental results indicate that the mean susceptibility of basalts and polycrystalline magnetite decreases under umaxial stress. This agrees with the theoretical model of pressure changes of directional susceptibilities. A moderatedecrease of the mean susceptibility in the specimens was also observed under external hydrostatic pressure.
Geophys., 53: 144—148. Kapi~ka,A., 1987. Nova metoda m~enimagnetické anizotropie hornin ph hydrostatickém tiaku. In: A. Fojtek and A. Kapi~ka(Editors), Fyzikâlni vlastnosti hornin a jejich vyuiitl v geofyzice a geologii II. J(~SMF,Praha, pp. 72-75 (in Czech). Kapi~ka,A., 1988. Anisotropy of magnetic susceptibility in a weak magnetic field induced by stress. Phys. Earth Planet. Inter., 51: 349—354. ~ A., P~o~ovâ, Z. and ~tërba, 0., 1985. Pribor dlya izmereniya anizotropii vosprijmchivosti gornykh pored pni odnoosnom davlenii. Trans. Symp. High-pressure TechnolO~, Geophys. Inst. Czech. Acad. Sci., pp. 96—108 (in Russian). Kean, W.F., Day, R., Fuller, M. and Schmidt, V.A., 1976. The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain size and composition of their
84
A. KAPIOtA
constituent titanomagnetites. J. Geophys. Res., 81(5): 861— 872. Kim, J., 1976. Hydrostatic pressure effects on saturation remanent magnetization, susceptibility and magnetic hardness of magnetite. Ph.D. Thesis, Michigan State University. Kropa~ek,V. and Kapi~ka,A., 1979. Changes of stability of remanent magnetization with the concentration of vacancies in titanomagnetites. Stud. Geophys. Geod., 23: 168— 173. Martin HI, RJ., 1980. Is piezomagnetism influenced by microcracks during cyclic loading? J. Geomagn. Geoelectr., 32: 741—755. Nagata, T., 1970a. Basic magnetic properties of rocks under the effects of mechanical stresses. Tectonophysics, 9: 167— 195. Nagata, T., 1970b. Anisotropy magnetic susceptibility of rocks under mechanical stresses. Pure Appl. Geophys., 78: 110—
122.
Nagata, T. and Kinoshita, H., 1967. Effect of hydrostatic pressure on magnetostriction and magnetocrystalline anisotropy of magnetite. Phys. Earth Planet. Inter., 1: 44—48. Nuilman, A.A., Shapiro, V.A., Maksimovski, S.I., Ivanov, N.A., Kim, J. and Carmichael, R.S., 1978. Magnetic susceptibility of magnetite under hydrostatic pressure, and implications for tectonomagnetism. J. Geomagn. Geoelectr., 30: 585— 592. Ohnaka, M. and Kinoshita, H., 1968. Effect of axial stress upon initial susceptibility of an assemblage of fine grains of Fe 2TiO4—Fe304 solid solution series. J. Geomagn. Geoelectr., 20: 107—109. Shelley, I.F. and Yi-Yuan Yu, 1966. The effect of two rigid spherical inclusions on the stress in an infinite elastic solid. J. Appl. Mech., 33: 68—74.
78
Variations of the mean susceptibility of rocks under hydrostatic and non-hydrostatic pressure A1e~Kapiëka Geophysical Institute, Czechoslovak Academy of Sciences, 141 31 Prague 4, Boc~n1II(Czechoslovakia) (Accepted for publication 1 February 1990)
ABSTRACT Kapi~ka,A., 1990. Variations of the mean susceptibility of rocks under hydrostatic and non-hydrostatic pressure. Phys. Earth Planet. Inter., 63: 78—84. The variations of the mean susceptibility of basaltic rocks and polycrystalline magnetite, measured in a weak magnetic field, under external non-hydrostatic (uniaxial) and hydrostatic pressure, are studied. A decrease of the mean susceptibility with increasing pressure was observed in both cases, the changes under uniaxial stress being systematically much larger than those under hydrostatic pressure. These changes are reversible with respect to the application of the external stress. The decrease of mean susceptibility under uniaxial stress is related to the qualitatively different behaviour of the changes of directional susceptibilities of orientations different with respect to the applied stress. The magnitude of the decrease of the actual rocks depends on the ratio of the stress sensitivity constants of the various directional susceptibilities. Small changes of the mean susceptibility under external hydrostatic pressure may be the result of the inhomogeneity of internal stresses acting on ferrimagnetic minerals as a result of the anisotropy of the transmitting properties of the non-magnetic matrix.
1. Introduction Magnetic susceptibility in a weak magnetic field is one of the most frequently studied parameters under pressure. Laboratory measurements of pressure changes of susceptibility may, on the one hand, be applied directly to solving geophysical problems related e.g. to explaining magnetic anomalies; on the other hand, they serve to verify various theoretical physical models describing the magnetic parameters of rocks and minerals as functions of external stress. In experimental modelling one uses either hydrostatic pressure or uniaxial stress. Most published papers concentrate on studying susceptibility under uniaxial stress up to 100—200 MPa. Changes of the directional susceptibilities have been measured and the corresponding results are in qualitative and, to a large extent, quantitative agreement with theoretical models. A review of the experimental and theoretical results is given, e.g. in the review papers by Nagata (1970a), Kean 0031-9201/90/$03.50
© 1990
-
Elsevier Science Publishers B.V.
et al. (1976) and Davis (1983). Much less attention has as yet been devoted to magnetic susceptibility under external omnidirectional pressures. The reaSons for this are the generally smaller hydrostatic effects (compared with uniaxial stress), the more complicated hydrostatic experiments, and also the more difficult interpretation of the results. Only a few experimental results related to measurements of susceptibility under hydrostatic pressures up to 200 MPa have been published (Kim, 1976; Nullman et al., 1978; Martin, 1980). The disadvantage of all these experiments is that they only monitor the changes of the directional susceptibility. As regards uniaxial stress, the susceptibilities are measured parallel or perpendicular to the stress and only exceptionally in some other directions (Kean et al., 1976). However, since additional anisotropy of the rock susceptibility is generated under external stresses (Nagata, 1970b), directional susceptibility alone is evidently not a representative parameter. The susceptibility tensor has to be employed to achieve a complex
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
79
description of rock susceptibility in a weak magnetic field. However, to determine this tensor (a symmetric tensor of the second order is involved) the directional susceptibility has to be measured in at least six independent directions in the specimen (Jelinek, 1973). Consequently, in designing the experiments we concentrated not only on measuring directional susceptibility under various pressure conditions, but also on measuring the whole complex set of anisotropy parameters. We therefore constructed a uniaxial chamber (Kapi&a et a!., 1985) and a hydrostatic chamber (Kapi~ka, 1987) both of which could be placed inside the pick-up coils of a sensitive bridge for measuring susceptibility anisotropy. In other words, the pick-up coils are outside the pressure vessels and are not subject to pressure effects. The results of measuring the
2. SpecImens and method of measurement used The measurements were carried out on specimens of polycrystalline magnetite and of several basaltic rocks from the Bohemian Massif. The specimens were selected from a more numerous set used previously to study reversible and irreversible changes of susceptibility anisotropy under umaxial stress (Kapi~ka,1983, 1988). The selection was made with a view to the different stabilities of the directional susceptibility relative to uniaxial stress. The stress sensitivity constant fi” of these specimens varied between L9 x i0~ MPa1 (specimen 220) and 8.3 x i0~ MPa1 (specimen 219) (Kapi~ka,1988). The ferrimagnetic fraction of the basalts consists of non-stoichiometric titanomagnetites with varying proportions of ulvospinel x (x Fe 2TiO4(1 x)Fe304) as well as varying degrees of oxidation z. The detailed chemical composition of these specimens can be found in Kropá~ekand Kapi~ka(1979). The values of x and z, of the concentration of the ferrimagnetic fraction, the grain size, mean susceptibility, degree of anisotropy and Young’s modulus of elasticity of the specimens are given in Table 1. Identical cylindrical specimens, 8 mm in diameter and 10 mm in height, whose front surface hadbeen ground plane-parallel, were used in the hydrostatic and uniaxial experiments. The stress applied to the specimens in the uniaxial chamber was generated by a hydraulic press. The value of the effective stress applied to the specimen was determined from the tensometrically measured deformation and known Young’s mod—
changes of the principal parameters of anisotropy (the degree of anisotropy, orientation of the major axes of the susceptibility ellipsoid, etc.) under uniaxial stress have been published (Kapi~ka, 1988). One of the characteristic parameters of rock magnetism is the mean suceptibility which is defined as the mean value of all directional susceptibilities. Since the changes of the various directional susceptibilities under external pressure exerted on the rock vary not only quantitatively but also qualitatively, we are faced with the problem as to the degree to which their mean susceptibility also changes. This paper is devoted to reporting the measurements and discussing these changes under uniaxial stress and hydrostatic pressure.
TABLE 1 Mean susceptibility (k), degree of anisotropy (Pa), concentration of the magnetic fraction (c), grain size (4,), content of ulvospinel in titanomagnetite (x), degree of oxidation (z) and Young’s modulus of elasticity (E) for samples of basalt and magnetite
Specimen
~a
(102 SI) 207 219
220 231 259 Magnetite
14.4 12.0 8.4
13.1 6.2 269.8
1.02 1.04 1.03 1.04 1.03 1.37
4, (mm)
X
Z
(vol.%)
E (10~MPa)
13.4 12.2 11.7
0.06—0.2 0.07—0.2 0.03—0.15
0.58 0.67 0.14
11.3
0.01—0.07
0.63
9.1
0.01—0.05
0.67
0.42 0.51 0.85 0.43 0.15
35 34 36 32 39
—
—
—
—
79
C
80 A. KAPI(~KA
I
ulus of elasticity. The pressure in the hydrostatic pressure medium was mineral oil. The effective pressure within the chamber (after the source had chamber was generated by a hydraulic pump. The been disconnected) was measured by the changes of resistance of a manganirie sensor. Chambers with fixed uniaxial stress and hydrostatic pressure acting on the specimen were placed inside the measuring coils of the bridge at defmed positions. In the hydrostatic experiments this set-up completely eliminates the effect of the pressure medium on the measuring coils. Undesirable changes of temperature, related to the rapid increase or decrease of pressure in the hydrostatic chamber, were minimized by adopting a very slow pattern of pressure variations. Since both the chambers for measuring the susceptibility had to be made of non-metallic material with a low diamagnetic shielding effect, the maximum achievable uniaxial stress and hydrostatic pressure were 60 and 30 MPa, respectively. Monitoring the susceptibility variations under hydrostatic pressure, when only relatively small effects can be expected, calls for a high accuracy of measurement. Consequently, we used a highly sensitive digital bridge, a KLY-2 Kappabridge with an accuracy of 0.5% (Jelinek, 1973), in our pressure experiments. Since the pressure measurements are made in a single measuring range of the bridge, the accuracy in this particular case is even higher. The bridge is equipped with automatic compensation for the temperature drift so that it is zeroed before the next measurement of directional susceptibility in each case. The reproducibility of measurements over a longer time interval and the calibration of the bridge were tested by repeated measurements of a standard specimen provided by the manufacturer. The susceptibility was measured in an A.C. magnetic field whose intensity was 300 A m The specimen was measured under constant pressure and 15 various orientations of the chamber. The resulting directional susceptibilities were used to calculate the susceptibility tensor and the principal parameters of the susceptibility ellipsoid using the Aniso program (Jeinek, 1973). The mean susceptibility k was determined from the principal susceptibilities: k = ~(k1 + k2 + k3) where k1 is the maximum, k2 ~.
kIS I]
0.1
0.12
~
011
0 231 219
__________________________
30 60 t [MPO] Fig. 1. Mean susceptibility ~ of basalts as a function of uniaxial stress r. 0 and 0 are the susceptibility values after unloading from 60 MPa. the intermediate and k3 the minimum susceptibility. The degree of anisotropy of the specimens in the undeformed condition was determined using the well-known relation ~a = k1/k3. ~ Expeiimental results and discussion Figure 1 shows the changes of the mean susceptibilities of basalts k under a uniaxial stress of 60 MPa. All the basalts and magnetite specimens investigated displayed a similar decrease of the mean susceptibility with increasing uniaxial stress. These changes are reversible with regard to pressure; after unloading, the value of the mean susceptibility increases to approximately its original value. Table 2 gives the relative changes of the mean susceptibility of the investigated basalts and magnetite for stresses of 30 and 60 MPa. Under 60
TABLE 2 Relative changes of the mean susceptibility under uniaxial stresses of 30 and 60 MPa S~~en
(%)
(%)
207
95
89
219 220 231 259 Magnetite
93 96 92 94 95
88 93 87 90 93
81
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
MPa, the decrease amounts to 7—13% of the origi-
12.3-i
i~[io~Si] 0
nalOur value. experimental results clearly indicate that the mean susceptibility of basalts and magnetite, subjected to uniaxial stress, is lower than under unloaded conditions. This result is closely related to the magnitude of changes of the directional susceptibilities with different orientations relative to the uniaxial stress. The theoretical model describing the susceptibility of ferrimagnetic minerals under uniaxial stress, based on the mechanism of rotation of spontaneous magnetization within domains (e.g. Nagata, 1970b), gives a qualitative explanation of the behaviour of directional susceptibilities determined experimentally: in fernmagnetic minerals with a positive magnetostrictive constant the parallel susceptibility k” decreases and the perpendicular susceptibility k increases with increasing pressure. However, the ratio of the observed stress sensitivity constants, $ ‘/$“, for real rock specimens is considerably lower than the theoretical values. For example, the ratio of these coefficients for the basalts and magnetite we studied is between 0.1 and 0.31 (Kapi&a, 1988). Quantitative agreement with theory was not achieved even in the case of single-domain grains, and this difference has not been explained in full so far (Davis, 1983). As regards pseudo-single-domain and multidomain grains the deviations are larger because processes of domain wall nucleation are involved even under small stresses (Boyd et al., 1984), as well as the mechanism of displacement of domain walls (Kean et a!., 1976). However, it remains a fact that, from a macroscopic point of view, the decrease of parallel susceptibility with increasing uniaxial stress in rocks containing titanomagnetite is dominant. The decrease of the mean susceptibility k (which can be determined from any three mutually perpendicular directional susceptibilities) agrees with this conclusion. The magnitude of constants $ depends mainly on the size of titanomagnetite grains, decreases with increasing degree of oxidation (Kean et al., 1976) and increases with the content of ulvöspinel (Ohnaka and Kinoshita, 1968). The analysis of these results from this point of view was not the purpose of this study because the specimens in question contained titanomagnetites
0
122
p =0
12.1 219 2b 3b p [MPa] Fig. 2. Mean susceptibility k of a basalt specimen as a function of hydrostatic pressure p. The encircled values indicate an unloaded sample. with different ulvospinel contents, as well as with different degrees of oxidation. Nevertheless, one can see that the mean susceptibility is the most stable in specimen 220 which contains titanomagnetite with the lowest percentage of ulvospinel and a high degree of oxidation (Table 1). However, measurements of specimens with selected chemical compositions, grain size and defined matrix properties are necessary for systematic studies of the stress sensitivity of nonstoichiometric titanomagnetites. Figure 2 shows the mean susceptibility of a basalt specimen as a function of hydrostatic pressure up to 30 MPa. The actual behaviours of the separate basalts and magnetite differ, but at least a small decrease of mean susceptibility with increasing pressure was observed in all cases. In comparison with the external uniaxial stress, however, the overall changes of k are much smaller. This can be seen in Table 3 which gives the relative decrease of the mean susceptibility for
TABLE 3 Relative changes of the mean susceptibility under hydrostatic pressures of 20 and 30 MPa
Specimen
k20/k0
(%) 207
219 220 231 Magnetite
(%) 98
99 100 98 99
97 99 97 99
82
A. KAPIt~KA
hydrostatic pressures of 20 and 30 MPa. The maximum change at 30 MPa is 3% of the original value, and the differences between the separate specimens are minimal. These results do not contradict those of earlier hydrostatic experiments (Nullman et al., 1978; Ma±tin,1980) in which relative changes of the directional susceptibilities of various rocks were found to be a few per cent, The causes of these changes, however, are not completely clear. From a theoretical point of view, the changes of susceptibility under purely hydrostatic pressure are related to the change of the magnetocrystalline anisotropy. Regardless of the mechanism of magnetization, the initial susceptibility k of a cubic ferrimagnetic mineral depends on the saturation magnetization f~and on the constant of magnetocrystalline anisotropy K1
k
—
J
/
K
s/
1
‘ /
The change of the constant of magnetocrystalline anisotropy under hydrostatic pressure was determined experimentally for monocrystals of magnetite (Nagata and Kinoshita, 1967). It was found that, at pressures up to 200 MPa, K1 decreases uniformly as aK /ap = 5% per 100 MPa (2) —
hydrostatic pressure, the mean susceptibility k should also grow. This conclusion is, however, in qualitative contradiction with our experimental results (Table 3). The reversible changes of mean susceptibility in real rocks cannot, therefore, be explained in terms of the mechanism described above. The reason is that the condition of pure hydrostatic pressure on the ferrimagnetic mineral is not satisfied. In real rocks the ferrimagnetic grains are dispersed in a non-magnetic matrix. This is formed by various minerals whose grains are separated by grain boundaries, microcracks, pores, etc. On the scale of laboratory specimens, therefore, rocks cannot be considered to be an elastic continuum and the nature of internal stresses does not in general correspond to the external stress field (Jaeger and Cook, 1971). The internal stresses were calculated theoretically for simplified models, e.g. of two isolated rigid inclusions located in an elastic solid matter (Shelley and Yi-Yuan, 1966). If an elastic solid is in an external hydrostatic stress field, the stress field at their boundary does not have a hydrostatic nature owing to the interaction of both inclusions. In some directions the stress increases, in others it decreases. The actual stress field in which the ferrimagnetic grains are
located under hydrostatic pressure on the rock is
1
As regards the initial susceptibility of fernmagnetic minerals under hydrostatic pressure, it follows that k (p) = k (0) (1 + C1 p) (3) where C1 is a constant. In rocks in which the ferrimagnetic minerals with susceptibility k. are dispersed in a non-magnetic matrix, their apparent susceptibility ka is given by the relation, e.g. (Janãk, 1977) k ~i ‘1 P Nk 1 (4\ ka IL ~ ~‘ ‘J “ ~‘ —
‘~
—
—~
—
where P is the concentration of the ferrimagnetic mineral and N the demagnetization factor. A relation analogous to (3) then holds for the pressure dependence of the rock susceptibility ka( p): ( ~ ( ~( —
a
where C2 = constant
thus considerably inhomogeneous, and the stress components in the various directions may differ considerably. In this respect, the moderate decrease of mean susceptibility under hydrostatic pressure, determined experimentally, can be explained in very much the same way as in the model experiments with external uniaxial stress. At the same time, it is evident that the changes of susceptibility due to stress deviations under external hydrostatic pressure will be relatively small. The inhomogeneity of internal stresses is also evidenced by the changes of various directional susceptibilities under hydrostatic pressure (Fig. 3). Three mutually perpendicular directional susceptibilities were selected from the nine independent directions in the specimen and the measurements were made accordingly. The selected directions are indicated schematically in Fig. 3. As m the case of the external umaxial pressure (Kapi~ka, 1988), their behaviour is not uniform, but a moderate
83
VARIATIONS OF MEAN SUSCEPTIBILITY OF ROCKS
12.51
k [i02S I] —
—
123
— —
—
These changes may be caused by local concentration of stress at the boundaries of ferrimagnetic grains owing to the inhomogeneous transfer of stress across the non-magnetic matrix. In the hy-
~.
—+—
.— —
-i--
k 2
drostatic experiments, therefore, apart from the stress sensitivity of ferrimagnetic minerals, the
30 p [MPo]
mechanical properties of the actual matrix (configminerals, concentration of microcracks, etc.) are uration and contact of grains, elastic properties of also of considerable significance. The general relationship between the macroscopic fabric of rocks and the concentration of internal stresses on a microscopic scale is not unique (Jaeger and Cook, 1971). However, measurements of magnetic antsotropy under hydrostatic pressure could be used to determine the basic components of internal stress in particular types of rock.
12.1 119
k2 k1~
219
ib
20
~
Fig. 3. Changes of three mutually perpendicular directional susceptibilities of a basalt specimen as a function of hydrostatic pressure. The orientation of the directional susceptibilities relative to the specimen is shown schematically.
increase as well as decrease of the directional susceptibilities can be observed. The degree of anisotropy increased in this example from 2% at zero pressure to 6.5% at 30 MPa. In the case of external uniaxial stresses the problem of transmitting stress to fernimagnetic minerals in rocks is not of principal importance. However, it was discussed in connection with artificial specimens with ferrimagnetic minerals displaying different elastic properties in their matrixes (Kean et al., 1976). However, this factor must be considered when explaining the changes of the magnetic parameters under hydrostatic
References Boyd, I.R., Fuller, M. and Halgedahl, S., 1984. Domain wall nucleation as a controlling factor in the behaviour of fine magnetic particles in rocks. Geophys. Res. Lets., 11 (3): 193-196. Davis, P.M., 1983. Tectonomagnetism. Rev. Geophys. Space Phys., 21: 685—693. Jaeger, J.C. and Cook, N.G.W., 1971. Fundamentals of Rock Mechanics. Chapman and Hall, London, pp. 5-47.
pressure.
Janâk, F., 1977. The determination of the content of fernmagnetic minerals in rock samples. Sb. Geol. Ved, Uzita Geofyz., 153—162. Jelinek, V., 17: 1973. Precision A.C. bridge set for measuring magnetic susceptibility and its anisotropy. Stud. Geophys.
4. Conclusion
Geod., 17: 36—45. Kapi&a, A., 1983. Irreversible changes of anisotropy of magnetic susceptibility of rocks due to uniaxial pressure. J.
The mean susceptibility is a parameter which can be characterized relatively easily by the susceptibility of anisotropic rocks. Since external stress is one of the causes of anisotropy, it is useful to investigate the changes of the mean susceptibility under model pressure conditions. Our experimental results indicate that the mean susceptibility of basalts and polycrystalline magnetite decreases under umaxial stress. This agrees with the theoretical model of pressure changes of directional susceptibilities. A moderatedecrease of the mean susceptibility in the specimens was also observed under external hydrostatic pressure.
Geophys., 53: 144—148. Kapi~ka,A., 1987. Nova metoda m~enimagnetické anizotropie hornin ph hydrostatickém tiaku. In: A. Fojtek and A. Kapi~ka(Editors), Fyzikâlni vlastnosti hornin a jejich vyuiitl v geofyzice a geologii II. J(~SMF,Praha, pp. 72-75 (in Czech). Kapi~ka,A., 1988. Anisotropy of magnetic susceptibility in a weak magnetic field induced by stress. Phys. Earth Planet. Inter., 51: 349—354. ~ A., P~o~ovâ, Z. and ~tërba, 0., 1985. Pribor dlya izmereniya anizotropii vosprijmchivosti gornykh pored pni odnoosnom davlenii. Trans. Symp. High-pressure TechnolO~, Geophys. Inst. Czech. Acad. Sci., pp. 96—108 (in Russian). Kean, W.F., Day, R., Fuller, M. and Schmidt, V.A., 1976. The effect of uniaxial compression on the initial susceptibility of rocks as a function of grain size and composition of their
84
A. KAPIOtA
constituent titanomagnetites. J. Geophys. Res., 81(5): 861— 872. Kim, J., 1976. Hydrostatic pressure effects on saturation remanent magnetization, susceptibility and magnetic hardness of magnetite. Ph.D. Thesis, Michigan State University. Kropa~ek,V. and Kapi~ka,A., 1979. Changes of stability of remanent magnetization with the concentration of vacancies in titanomagnetites. Stud. Geophys. Geod., 23: 168— 173. Martin HI, RJ., 1980. Is piezomagnetism influenced by microcracks during cyclic loading? J. Geomagn. Geoelectr., 32: 741—755. Nagata, T., 1970a. Basic magnetic properties of rocks under the effects of mechanical stresses. Tectonophysics, 9: 167— 195. Nagata, T., 1970b. Anisotropy magnetic susceptibility of rocks under mechanical stresses. Pure Appl. Geophys., 78: 110—
122.
Nagata, T. and Kinoshita, H., 1967. Effect of hydrostatic pressure on magnetostriction and magnetocrystalline anisotropy of magnetite. Phys. Earth Planet. Inter., 1: 44—48. Nuilman, A.A., Shapiro, V.A., Maksimovski, S.I., Ivanov, N.A., Kim, J. and Carmichael, R.S., 1978. Magnetic susceptibility of magnetite under hydrostatic pressure, and implications for tectonomagnetism. J. Geomagn. Geoelectr., 30: 585— 592. Ohnaka, M. and Kinoshita, H., 1968. Effect of axial stress upon initial susceptibility of an assemblage of fine grains of Fe 2TiO4—Fe304 solid solution series. J. Geomagn. Geoelectr., 20: 107—109. Shelley, I.F. and Yi-Yuan Yu, 1966. The effect of two rigid spherical inclusions on the stress in an infinite elastic solid. J. Appl. Mech., 33: 68—74.