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The transformation of γ Fe2O3 to α Fe2O3: thermal activation and the effect of elevated pressure
Physics of the Earth and Planetary Interiors 110 Ž1999. 43–50
The transformation of g Fe 2 O 3 to a Fe 2 O 3: thermal activation and the effect of elevated pressure J. Adnan 1, W. O’Reilly
)
Department of Physics, UniÕersity of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK Received 27 January 1998; revised 27 July 1998; accepted 3 September 1998
Abstract The transformation of acicular g Fe 2 O 3 particles to a Fe 2 O 3 has been monitored using magnetic properties as a proxy for g Fe 2 O 3 concentration during the inversion process. The transformation is thermally activated, the height of the barrier opposing inversion being 3.7 eV at atmospheric pressure and 0.5 eV at a pressure of about 100 MPa. The barrier arises from the combination of a term representing the reduction in lattice energy in an inverted region, and the strain energy associated with the interface between the inverted and non-inverted phases. The sensitivity of the inversion process to pressure can be understood in terms of the dependence of these energy terms, and the energy barrier, on interatomic spacing. Extrapolation of these laboratory data to the conditions of the submarine crust at Site 504B of the Deep Sea Drilling Project is consistent with the inferred magnetic mineralogy of the recovered material. q 1999 Elsevier Science B.V. All rights reserved. Keywords: g Fe 2 O 3 ; a Fe 2 O 3 ; Thermal activation; Submarine crust
1. Inversion—a thermally activated process The inversion of maghemite, g Fe 2 O 3 , with cation deficient spinel structure, to haematite, a Fe 2 O 3 , with corundum structure has been a subject of interest from early work in the 1930s up to the present ¨ decade Že.g., Ozdemir, 1990.. The transformation takes place without change in bulk chemical composition but can be monitored by the measurement of structure sensitive physical properties, notably magnetism. The progress of inversion can be studied by
)
Corresponding author. Tel.: q44-191226000; Fax: q441912227361. 1 On leave from Universiti Teknologi Malaysia.
X-ray diffractograms or Mossbauer effect spectra ¨ ŽMorrish and Sawatzky, 1971.. The transformation is exothermic and can be monitored by differential thermal analysis ŽLodding and Hammell, 1960.. Of particular interest, in the context of maghemite and haematite as magnetic materials, is the loss or acquisition of magnetic remanence which might accompany inversion in the presence of a magnetic field ¨ ŽOzdemir and Dunlop, 1988.. In the palaeomagnetic context, inversion may be a significant process in the older and deeper parts of the submarine crust ŽFacey et al., 1985.. In this case the mineral involved is titanomaghemite and the inversion product is an intergrowth of phases ŽReadman and O’Reilly, 1971.. The temperature at which inversion is observed to take place on a laboratory timescale is referred to as
0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 Ž 9 8 . 0 0 1 2 8 - 9
44
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
the ‘inversion temperature’ with reported values ranging from 350–6508C at atmospheric pressure. Elevated pressure assists inversion, 150 MPa lowering the inversion temperature to 08C ŽKushiro, 1960.. However it seems likely that inversion is a thermally activated process ŽMorrish and Sawatzky, 1971; Ozima and Ozima, 1972; Housden et al., 1988. so that the value of the inversion temperature depends on
the time scale over which inversion is allowed to take place, millions of years in nature. Thermal activation implies an energy barrier to the process of inversion. This may arise from the interplay of two energy terms. A spherical zone of inverted ferric oxide existing within an uninverted crystal has a reduced lattice energy. The reduction in energy is proportional to the volume of the inclusion. The lattice mismatch, and consequent strain energy, at the surface of the inclusion increases the energy of the crystal by an amount proportional to the surface area. The combination of the two terms, one negative and proportional to R 3 Žwhere R is the radius of the a Fe 2 O 3 inclusion., and one positive and proportional to R 2 , provides an energy barrier to the growth of the inverted inclusion ŽFig. 1.. Once the inclusion grows beyond R crit ŽFig. 1. the whole particle may rapidly transform to the a form. The purpose of the present work is to observe the thermal activation of the g to a transformation using magnetic properties to monitor the process. The effect of hydrostatic pressure, which is of physical interest and geophysical importance, is also to be studied.
2. Observation of inversion at atmospheric pressure
Fig. 1. The energy of a spherical inclusion of a Fe 2 O 3 of radius R in a crystal of g Fe 2 O 3 . The reduction in electrostatic energy is proportional to R 3 and the added surface strain energy proportional to R 2 . The combined terms produce an energy barrier to the transformation of the crystal from the g to a form.
The maghemite used in the present study was manufactured by BASF, product code FT26. The average length of the acicular magnetic tape particles is 0.5 mm with a length–width ratio of 6:1. A small quantity was heated at a rate of 208C miny1 up to about 5708C, in air, in a field of 0.8 MA my1 , in the magnetic balance described by Housden et al. Ž1988.. The more rapid fall in magnetization above about 5108C ŽFig. 2. suggests that above this temperature, and at this heating rate, inversion to essentially non-magnetic a Fe 2 O 3 is dominating the magnetization–temperature fall. The lack of recovery of magnetization on cooling, and X-ray analysis of the final, cooled, material confirm the essentially complete and irreversible transformation to a Fe 2 O 3 when heating at 208C miny1 . In a further series of thermomagnetic runs, fresh samples of g Fe 2 O 3 , were heated at 208C miny1 to one of a number of isotherms between 4008C and
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
45
Fig. 4. Logarithm of the inversion rates, deduced from the data of Fig. 2, plotted against the reciprocal temperature. The slope yields the activation energy of the inversion process.
Fig. 2. Thermomagnetic curve of BASF g Fe 2 O 3 heated at 208C miny1 up to 5708C in a field of 0.8 MA my1 . Inversion is evident above 5108C.
4808C and magnetization monitored for a time up to 4 h. Fig. 3 shows the time dependencies of magnetization normalized to the starting value on arrival at each of the respective isotherms. At 4008C no fall indicating inversion is detectable after 4 h. At 4808C inversion approaches completion after about 1 h.
A precise analysis of the reaction kinetics is complicated by the fact that inversion will have started before the isotherm is reached and the sample at t s 0 is already a gra mixture. However, because the magnetization of the end product is so weak, this may have a negligible effect when magnetization is used as the proxy for g Fe 2 O 3 concentration. Another source of uncertainty arises because the reaction is exothermic, and the observations may only be approximately isothermal. We suppose that the transformation is described by an equation of the form d mrdt s ymrt , where m is the magnetization at time t, normalised to t s 0, and t is a time constant. t is related to temperature by the Arrhenius equation for a thermally activated process 1rt s Ž1rt 0 .expŽyE brkT ., where E b is the activation energy. t is estimated in the present case by taking the initial part of the m–t curves of Fig. 3 as being linear and having slope y1rt . The inferred values of lnŽ1rt . are plotted against 1rT in Fig. 4, the slope of the line yielding an activation energy of 3.7 eV, and a frequency factor, 1rt 0 , of 10 22 sy1 .
3. Inversion observed at elevated pressure Fig. 3. Variation of the magnetization of g Fe 2 O 3 with time at several isotherms. The fall in magnetization indicates transformation to essentially non-magnetic a Fe 2 O 3 .
Inversion of g Fe 2 O 3 at elevated pressure was studied using the apparatus described by Adnan et al. Ž1992., in which magnetic susceptibility can be mea-
46
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
sured as a function of temperature and pressure. Samples were made up from a powder mixture of 30% g Fe 2 O 3 dispersed in Al 2 0 3 . The powder was compacted under a pressure of 160 MPa into a cylindrical form of length 1.5 cm and diameter 1 cm. The magnetic susceptibility of the compressed sample Ž2.3 dimensionless MKS units. is consistent with a random array of monodomain needle-shaped particles. The samples were heated at a rate of 58C miny1 to a series of isotherms between about 2508C and 4508C. At each isotherm the pressure was raised to 140 MPa in about 2 min and then released, during which time the susceptibility fell irreversibly, by about 2% at 2578C and by about 20% at 4418C. Microstructure dependent magnetic susceptibility is a less perfect measure of g Fe 2 O 3 concentration than saturation magnetization. It is acceptable as such provided magnetic particle size does not change during inversion. This will be the case if the a Fe 2 O 3 nuclei, with size up to R crit , have a negligible effect on the magnetic susceptibility, and if, once the size of the a Fe 2 O 3 inclusion exceeds R crit , the whole particle rapidly transforms to a Fe 2 O 3 . If a particle is made of ‘nanocrystals’, the travelling boundary between the g and a phases may come to
Fig. 6. Logarithm of the inversion rates at constant temperature as a function of the pressure. The relationship is approximately linear.
a halt on meeting the surface of the nanocrystal. A particle may then consist of stable zones of g and a phases. In that case, susceptibility may provide an acceptable proxy for the g Fe 2 O 3 concentration if the microstructural element controlling susceptibility of the uninverted particles is the nanocrystal boundary rather than the particle boundary. As before, we assume d xrdt s yxrt , where x is the susceptibility, normalised to t s 0, and take the fall in x during the 2 min during which the pressure is applied as the near-linear initial part of the x y t fall. This gives values of 1rt which are plotted against 1rT in Fig. 5. The activation energy is 0.5 eV and the frequency factor 0.5 sy1 . In a further experiment a sample of g Fe 2 O 3 was held at an isotherm Ž2658C. and subjected to pressures of 55, 95 and 130 MPa, each pressure being held for 30 min. The fall in susceptibility during each application of pressure was approximately linear with time. This gives values of 1rt as a function of pressure at the isotherm. The variation of lnŽ1rt . with pressure is approximately linear ŽFig. 6..
4. Discussion 4.1. The actiÕation energies Fig. 5. Logarithm of the inversion rates at elevated pressure against the reciprocal of the temperature. The slope yields the activation energy.
Morrish and Sawatzky Ž1971. express the thermal activation of the inversion of maghemite in terms of activation temperature, TA , which is the activation
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
energy divided by Boltzmann’s constant. They obtain values of 37,000 K Žacicular particles., 43,000 K Žspherical., 54,000 K Ž1.5% Co-doped. and 59,000 K Ž3% Co-doped.. The activation energy at atmospheric pressure obtained for acicular particles in the present investigation, equivalent to a TA of 43,000 K is the same as that of the spherical undoped sample of Morrish and Sawatzky Ž1971.. Morrish and Sawatzky Ž1971. determined degree of inversion from room temperature Mossbauer spectra of materials ¨ which had been heated for periods at elevated temperature, whereas in the present study the inversion process is monitored continuously at elevated temperature. This may account for the difference in TA , but it is more likely that variation in inversion behaviour in nominally similar materials is expected; ¨ for example the acicular maghemite of Ozdemir Ž1990. inverted in the laboratory timescale only after being heated to about 7508C, such behaviour presumably corresponding to a high activation energy. Whether the nature of the external envelope of the particle Žshape and size. is a major influence on the activation of inversion is not at all clear. It would seem more likely that variation in concentration and type of internal defects which resulted from different methods of preparation would play a more important role than the surface of the particle. The frequency factor at atmospheric pressure is comparable to Morrish and Sawatzky’s acicular particles Ž10 23 sy1 . but significantly lower than the frequency factors for the rest of their suite, which ascend along with the activation temperatures through 10 26 sy1 , 10 31 sy1 and 10 32 sy1 . Morrish and Sawatzky speculate that the ‘large’ frequency factor may imply that inversion, once started, goes on to completion in the particle. This would be broadly consistent with the model of Fig. 1. Essentially the activation energy would be associated with the nucleation of a stable region of the a phase, and the frequency factor associated with the subsequent growth of the a phase region i.e., the velocity of the arg boundary. The kinetics of nucleation and growth are apparently connected. A particle with a high barrier to inversion may be more difficult to invert but, once the process has started, the particle more rapidly transforms to the a phase. A particle with low barrier inverts easily but the phase boundary progresses slowly. The presence of defects in general
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results in a raised lattice energy so that the reduction in energy on inversion is potentially greater if the inversion product is less defective, that is, if the process of inversion also ‘refines’ the crystal structure. This would increase the coefficient of the R 3 term and lower the activation energy. On the other hand the presence of defects may reduce the mobility of the phase boundary in the same way that defects ‘pin’ and reduce the mobility of a domain wall. Thus a low activation energy and high frequency factor may correspond to a high concentration of crystal defects. 4.2. The effect of pressure High pressure results in a lowered barrier and hence lowered activation temperature, 5800 K in the present study. However, unlike the material of Kushiro Ž1960., 140 MPa is not enough to invert the BASF g Fe 2 O 3 at room temperature, which would need 9 years at pressure of the order of 100 MPa. It seems intuitively correct that elevated pressure should promote inversion, but how is E b lowered by increased pressure? The effect of pressure is to reduce interatomic distance and this must lead to the pressure sensitivity of E b . If the energy of the inclusion, Einc , of Fig. 1 is expressed as Einc s bR 2 y cR 3 where b and c are constant at constant temperature and pressure, it can be seen that the barrier height E b s Ž4r27. b 3rc 2 and R crit s 2 br3c. The coefficient c is related to the difference in lattice energy of the 2 phases. The lattice energy per ion pair of a crystal is y
Mz1 z 2 e 2 4p´ 0 r 0
Ž 1 y rrr 0 .
where M is the Madelung constant, z 1 and z 2 the valence number of the anions and cations, e the electronic charge, r 0 the nearest neighbour anion– cation distance and ´ 0 and r are constants. The transformation from an ideal cubic close packed array of rigid spheres Žthe oxygen ions of g Fe 2 O 3 . to an ideal hexagonal close packed array of rigid spheres Žthe anions of a Fe 2 O 3 . involves no change of volume. However, the cations in the interstices do not have negligible volume and the anion structures also suffer deformation from the ideal array. A calcu-
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J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
lation of the ‘X-ray densities’ based on the dimensions and contents of the unit cell shows that, on inversion, there is a volume contraction of about 8% and therefore a linear contraction of about 3%. The above expression for lattice energy is rather approximate for compounds such as those of the present study which have some degree of covalent bonding and contain different numbers of anions and cations. However it does not seem necessary to develop the detail of the model to plausibly show the origin of the strong sensitivity of the inversion transformation on pressure. We may suppose that the lattice energies per ion pair of the g and a phases can be expressed in the form yK grrg and yK arra where K is a constant and r is the interionic distance as before. Two possibilities that can be envisaged are: in determining the reduction in lattice energy, the change in the structure related parameter K dominates over the change in interionic distance, r 0 , in which case the reduction in lattice energy due to the transformation can be written D Krr0 ; or, the change in interionic distance from rg to ra dominates over the change in the structural factor, leading to a reduction in lattice energy of KDŽ1rr 0 . or KD r 0rr 02 . The spherical inclusion contains of the order of R 3rr 03 ion pairs so the reduction in energy due to the inclusion is either yŽ D Krr 04 . R 3 or yŽ KD r 0r r 05 . R 3. The bracketed coefficients of R 3 are the parameter c of our model. If the interface between the 2 phases is crystallographically coherent, the lattice on either side of the interface would be strained by the order of D r 0rr 0 , that is, a few percent, far in excess of the strain corresponding to the maximum elastic strength of ceramic materials. The two phases may therefore be bridged by a plastic semi-amorphous zone rich in crystal defects. This will result in strains only a fraction of D r0rr0 , but still possibly proportional to D r 0rr 0 . If so the strain energy per unit volume of the bridging zone will be proportional to Ž D r 0rr 0 . 2 . Thus the coefficient to the r 2 function of Fig. 1, b, is proportional to Ž D r 0rr 0 . 2 . We now substitute for b and c to find the dependence of E b and R crit on the interionic distance r 0 . Thus E b A Ž D r 0rr 0 . 6 r 08 or Ž D r 0rr 0 . 4 r08 and R crit A Ž D r 0rr 0 . 2 r 04 or Ž D r 0rr 0 . r 04 . The bulk moduli of the two ceramic phases are about the same, so the value of Ž D r 0rr 0 . will not change much as pressure
is applied, so the strain term, which resists inversion, is approximately pressure independent. On the other hand, the lattice term, which drives inversion, is sensitive to pressure. In either formulation of the lattice term the sensitivity of E b to pressure will arise predominantly through the r 08 dependence, hence the strong fall in E b with pressure. R crit will similarly depend on pressure as r 04 in either formulation of the lattice term. 4.3. Estimation of R cr i t It is possible to make an estimate of R crit by using the empirical value of E b and a typical value of the lattice energy of a close-packed metal oxide. The problematic parameter b related to the strain energy of the region bridging the two phases can be eliminated between the expressions for E b and R crit to obtain R crit s Ž2 E brc .1r3. Verwey et al. Ž1948. show that the electrostatic lattice energy of a spinel oxide is of the order of 3 = 10y2 6ra Joules per spinel formula unit, where a is the cell edge. The precise evaluation depends on the charge distribution between the cation sublattices, the distortion of the anion framework and degree of ordering of the cations. Contributions to the lattice energy also come from the repulsive forces between the constituents of the assembled lattice and the individual site preferences of cations due to the formation of covalent bonds ŽBlasse, 1964.. For the present estimate we simply take the lattice energy as the electrostatic energy of the lattice. We choose the case in which the energy fall on inversion is due to the contraction in interionic distance and express this as a change in a. Thus the energy change is Ž3 = 10y2 6 . D ara2 Joules per formula unit. In the spinel structure there are 8 formula units in the unit cell of volume a3 , so the reduction in lattice energy in an inverted inclusion of radius R is Ž3 = 10y2 6D ara2 .Ž8ra3 . Ž4p R 3r3. Joules. Taking Ž D ara. as the linear contraction on inversion of 3% and a as typically 1 nm, the inclusion represents a reduction in energy of 3 = 10 10 R 3 Joules. Thus the parameter c is of the order of 3 = 10 10 J my3 . Substituting for c and E b in the expression for R crit yields R crit ; 5 = 10y1 0 m so the spherical inclusion of critical volume would contain about 5 unit cells of a Fe 2 O 3 , a plausible result.
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
4.4. Implications for the submarine crust The data of Figs. 4–6 provide a starting point in the construction of a diagram in P–T space showing contours of constant t . Although the data are few, the linearity of the relationships between lnŽ1rt . and 1rT and lnŽ1rt . and P suggests that a diagram with 1rT as one coordinate and P as the other will have linear contours of constant lnŽ1rt .. Inserting values for the activation energies and frequency factors of the present investigation yields the equation in Ž1rT . y P space for a contour of lnŽ1rt .. 10 6 T
ž
s y 1.1 ln
1
t
/
q 9.4 P y 23 ln
1
t
q 1.2 = 10 3
where P is in MPa. The equation can be inverted to provide the value of t for given P and T. In newly formed submarine crust, the near surface temperatures are high and fall with progressive age. A model T Ž t . could be used together with the inferred t ŽT, P . relation to calculate the cumulative degree of inversion of the cooling material at a particular horizon in the submarine crust. The time available for inversion is not the same as the age of the material as, initially, time must be spent developing significant cation deficiency Žthe ‘maghemitization’ of submarine weathering. before inversion can begin. In the present context the potential usefulness of the laboratory data is examined by considering the state of the magnetic minerals studied in cores recovered from Hole 504B of the Deep Sea Drilling Project located in the eastern equatorial Pacific ŽAnderson et al., 1982.. The presence of maghemitized and therefore, at most, only partially inverted titanomagnetite was inferred from magnetic properties of basalt recovered from the uppermost 214 metres of the basement ŽO’Donovan and O’Reilly, 1983. but material at deeper levels revealed no maghemitization ŽFacey et al., 1985.. The temperature rises with depth from about 608C to 858C in the upper 214 metres of the basement which is overlain by 275 metres of sediment ŽAnderson et al., 1982.. The pressure may be estimated as rising from 41 Mbar to 46 Mbar. The time constants for these ŽT, P . conditions are 8 Myr for the top of the section and 0.07 Myr for the bottom. The age of Site 504 is estimated at 6.2 Myr so the survival of maghemitized
49
titanomagnetite in the upper horizons seems consistent with the laboratory data, as does the absence of maghemitized material at deeper levels.
5. Conclusions The transformation of g Fe 2 O 3 to a Fe 2 O 3 is thermally activated. In the case of the acicular tape particles of the present study the activation energy, or energy barrier opposing the process, is 3.7 eV at atmospheric pressure, and 0.5 eV at a pressure of about 100 MPa. The energy barrier can be understood as resulting from the combination of two energy terms, one representing the reduction in lattice energy of an inverted inclusion and the other the strain energy of the interface between the 2 phases, which are probably bridged by a plastic semi-amorphous zone. The reduction in lattice energy, due to the presence of the inverted inclusion, depends on ry4 0 , where r 0 is the typical interionic distance in the two phases; and the barrier to inversion depends on r 08. The barrier height is therefore sensitive to pressure. Extrapolation of the laboratory data to the temperatures and pressures of the submarine crust at Site 504B of the Deep Sea Drilling Project in the eastern Pacific is consistent with the survival of maghemitized uninverted material in the upper part of the core recovered from Hole 504B, as inferred by magnetic studies.
Acknowledgements One of the authors ŽJA. has received support from the Universiti Teknologi Malaysia and the Government of Malaysia. We thank Dr R.J. Veitch of BASF for supplying the g Fe 2 O 3 particles.
References Adnan, J., de Sa, A., O’Reilly, W., 1992. Simultaneous measurement of the variations in magnetic susceptibility and remanence of materials in the temperature range 108C–7008C and
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elevated pressure Ž16 MPa–160 MPa.. Meas. Sci. Technol. 3, 289–295. Anderson, R.N., Honnorez, J., Becker, K., Adamson, A.C., Alt, J.C., Emmermann, R., Kempton, P.D., Kinoshita, H., Laverne, C., Mottl, M.J., Nemark, R.L., 1982. DSDP Hole 504B, the first reference section over 1 km through Layer 2 of the oceanic crust. Nature 300, 589–594. Blasse, G., 1964. Crystal chemistry and some magnetic properties of mixed metal oxides with spinel structure. Philips Res. Repts. Suppl. 3, 139. Facey, D., Housden, J., O’Reilly, W., 1985. A magnetopetrological study of rocks from Leg 83, Hole 504B, Deep Sea Drilling Project. In: Anderson, R.N., Honnorez, J., Becker, R., et al., ŽEds.., Init. Repts of the Deep Sea Drilling Project, LXXXIII. US Govt. Printing Office, Washington, pp. 339–346. Housden, J., de Sa, A., O’Reilly, W., 1988. The magnetic balance of its application to studying the magnetic mineralogy of igneous rocks. J. Geomagn. Geoelectr. 40, 63–75. Kushiro, I., 1960. g – a transition in Fe 2 O 3 with pressure. J. Geomagn. Geoelectr. 11, 148–151. Lodding, W., Hammell, L., 1960. DTA of hydroxides in a reducing atmosphere. Anal. Chem. 32, 657–662.
Morrish, A.H., Sawatzky, G.A., Mossbauer study of the gamma to alpha transformation in pure and cobalt-doped ferric oxide, pp. 144–147, FERRITES: proceedings of the International Conference, University of Tokyo Press, 1971. O’Donovan, J.B., O’Reilly, W., 1983. Magnetic properties of basalts from Hole 504B, Deep Sea Drilling Project Leg69, Init. Reports of the Deep Sea Drilling Project, LXIX, Ed Cann, J.R., Langseth, M.G., Honnorez, J., et al., Washington ŽU.S. Govt. Printing Office., 721–726. ¨ Ozdemir, O., 1990. High temperature hysteresis and thermoremanence of single domain maghemite. Phys. Earth Planet. Inter. 65, 125–136. ¨ ¨ Dunlop, D.J., 1988. Crystallization remanent magneOzdemir, O., tization during the transformation of maghemite to hematite. J. Geophys. Res. 93, 6530–6544. Ozima, M., Ozima, M., 1972. Activation energy of unimixing of titanomaghemite. Phys. Earth Planet. Inter. 5, 87–89. Readman, P.W., O’Reilly, W., 1971. The synthesis and inversion of non-stoichiometric titanomagnetites. Phys. Earth Planet. Inter. 4, 121–128. Verwey, E.J.W., de Boer, F., Santen, J.H., 1948. Cation arrangement in spinels. J. Chem. Phys. 16, 1091–1092.
The transformation of g Fe 2 O 3 to a Fe 2 O 3: thermal activation and the effect of elevated pressure J. Adnan 1, W. O’Reilly
)
Department of Physics, UniÕersity of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK Received 27 January 1998; revised 27 July 1998; accepted 3 September 1998
Abstract The transformation of acicular g Fe 2 O 3 particles to a Fe 2 O 3 has been monitored using magnetic properties as a proxy for g Fe 2 O 3 concentration during the inversion process. The transformation is thermally activated, the height of the barrier opposing inversion being 3.7 eV at atmospheric pressure and 0.5 eV at a pressure of about 100 MPa. The barrier arises from the combination of a term representing the reduction in lattice energy in an inverted region, and the strain energy associated with the interface between the inverted and non-inverted phases. The sensitivity of the inversion process to pressure can be understood in terms of the dependence of these energy terms, and the energy barrier, on interatomic spacing. Extrapolation of these laboratory data to the conditions of the submarine crust at Site 504B of the Deep Sea Drilling Project is consistent with the inferred magnetic mineralogy of the recovered material. q 1999 Elsevier Science B.V. All rights reserved. Keywords: g Fe 2 O 3 ; a Fe 2 O 3 ; Thermal activation; Submarine crust
1. Inversion—a thermally activated process The inversion of maghemite, g Fe 2 O 3 , with cation deficient spinel structure, to haematite, a Fe 2 O 3 , with corundum structure has been a subject of interest from early work in the 1930s up to the present ¨ decade Že.g., Ozdemir, 1990.. The transformation takes place without change in bulk chemical composition but can be monitored by the measurement of structure sensitive physical properties, notably magnetism. The progress of inversion can be studied by
)
Corresponding author. Tel.: q44-191226000; Fax: q441912227361. 1 On leave from Universiti Teknologi Malaysia.
X-ray diffractograms or Mossbauer effect spectra ¨ ŽMorrish and Sawatzky, 1971.. The transformation is exothermic and can be monitored by differential thermal analysis ŽLodding and Hammell, 1960.. Of particular interest, in the context of maghemite and haematite as magnetic materials, is the loss or acquisition of magnetic remanence which might accompany inversion in the presence of a magnetic field ¨ ŽOzdemir and Dunlop, 1988.. In the palaeomagnetic context, inversion may be a significant process in the older and deeper parts of the submarine crust ŽFacey et al., 1985.. In this case the mineral involved is titanomaghemite and the inversion product is an intergrowth of phases ŽReadman and O’Reilly, 1971.. The temperature at which inversion is observed to take place on a laboratory timescale is referred to as
0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 Ž 9 8 . 0 0 1 2 8 - 9
44
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
the ‘inversion temperature’ with reported values ranging from 350–6508C at atmospheric pressure. Elevated pressure assists inversion, 150 MPa lowering the inversion temperature to 08C ŽKushiro, 1960.. However it seems likely that inversion is a thermally activated process ŽMorrish and Sawatzky, 1971; Ozima and Ozima, 1972; Housden et al., 1988. so that the value of the inversion temperature depends on
the time scale over which inversion is allowed to take place, millions of years in nature. Thermal activation implies an energy barrier to the process of inversion. This may arise from the interplay of two energy terms. A spherical zone of inverted ferric oxide existing within an uninverted crystal has a reduced lattice energy. The reduction in energy is proportional to the volume of the inclusion. The lattice mismatch, and consequent strain energy, at the surface of the inclusion increases the energy of the crystal by an amount proportional to the surface area. The combination of the two terms, one negative and proportional to R 3 Žwhere R is the radius of the a Fe 2 O 3 inclusion., and one positive and proportional to R 2 , provides an energy barrier to the growth of the inverted inclusion ŽFig. 1.. Once the inclusion grows beyond R crit ŽFig. 1. the whole particle may rapidly transform to the a form. The purpose of the present work is to observe the thermal activation of the g to a transformation using magnetic properties to monitor the process. The effect of hydrostatic pressure, which is of physical interest and geophysical importance, is also to be studied.
2. Observation of inversion at atmospheric pressure
Fig. 1. The energy of a spherical inclusion of a Fe 2 O 3 of radius R in a crystal of g Fe 2 O 3 . The reduction in electrostatic energy is proportional to R 3 and the added surface strain energy proportional to R 2 . The combined terms produce an energy barrier to the transformation of the crystal from the g to a form.
The maghemite used in the present study was manufactured by BASF, product code FT26. The average length of the acicular magnetic tape particles is 0.5 mm with a length–width ratio of 6:1. A small quantity was heated at a rate of 208C miny1 up to about 5708C, in air, in a field of 0.8 MA my1 , in the magnetic balance described by Housden et al. Ž1988.. The more rapid fall in magnetization above about 5108C ŽFig. 2. suggests that above this temperature, and at this heating rate, inversion to essentially non-magnetic a Fe 2 O 3 is dominating the magnetization–temperature fall. The lack of recovery of magnetization on cooling, and X-ray analysis of the final, cooled, material confirm the essentially complete and irreversible transformation to a Fe 2 O 3 when heating at 208C miny1 . In a further series of thermomagnetic runs, fresh samples of g Fe 2 O 3 , were heated at 208C miny1 to one of a number of isotherms between 4008C and
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
45
Fig. 4. Logarithm of the inversion rates, deduced from the data of Fig. 2, plotted against the reciprocal temperature. The slope yields the activation energy of the inversion process.
Fig. 2. Thermomagnetic curve of BASF g Fe 2 O 3 heated at 208C miny1 up to 5708C in a field of 0.8 MA my1 . Inversion is evident above 5108C.
4808C and magnetization monitored for a time up to 4 h. Fig. 3 shows the time dependencies of magnetization normalized to the starting value on arrival at each of the respective isotherms. At 4008C no fall indicating inversion is detectable after 4 h. At 4808C inversion approaches completion after about 1 h.
A precise analysis of the reaction kinetics is complicated by the fact that inversion will have started before the isotherm is reached and the sample at t s 0 is already a gra mixture. However, because the magnetization of the end product is so weak, this may have a negligible effect when magnetization is used as the proxy for g Fe 2 O 3 concentration. Another source of uncertainty arises because the reaction is exothermic, and the observations may only be approximately isothermal. We suppose that the transformation is described by an equation of the form d mrdt s ymrt , where m is the magnetization at time t, normalised to t s 0, and t is a time constant. t is related to temperature by the Arrhenius equation for a thermally activated process 1rt s Ž1rt 0 .expŽyE brkT ., where E b is the activation energy. t is estimated in the present case by taking the initial part of the m–t curves of Fig. 3 as being linear and having slope y1rt . The inferred values of lnŽ1rt . are plotted against 1rT in Fig. 4, the slope of the line yielding an activation energy of 3.7 eV, and a frequency factor, 1rt 0 , of 10 22 sy1 .
3. Inversion observed at elevated pressure Fig. 3. Variation of the magnetization of g Fe 2 O 3 with time at several isotherms. The fall in magnetization indicates transformation to essentially non-magnetic a Fe 2 O 3 .
Inversion of g Fe 2 O 3 at elevated pressure was studied using the apparatus described by Adnan et al. Ž1992., in which magnetic susceptibility can be mea-
46
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
sured as a function of temperature and pressure. Samples were made up from a powder mixture of 30% g Fe 2 O 3 dispersed in Al 2 0 3 . The powder was compacted under a pressure of 160 MPa into a cylindrical form of length 1.5 cm and diameter 1 cm. The magnetic susceptibility of the compressed sample Ž2.3 dimensionless MKS units. is consistent with a random array of monodomain needle-shaped particles. The samples were heated at a rate of 58C miny1 to a series of isotherms between about 2508C and 4508C. At each isotherm the pressure was raised to 140 MPa in about 2 min and then released, during which time the susceptibility fell irreversibly, by about 2% at 2578C and by about 20% at 4418C. Microstructure dependent magnetic susceptibility is a less perfect measure of g Fe 2 O 3 concentration than saturation magnetization. It is acceptable as such provided magnetic particle size does not change during inversion. This will be the case if the a Fe 2 O 3 nuclei, with size up to R crit , have a negligible effect on the magnetic susceptibility, and if, once the size of the a Fe 2 O 3 inclusion exceeds R crit , the whole particle rapidly transforms to a Fe 2 O 3 . If a particle is made of ‘nanocrystals’, the travelling boundary between the g and a phases may come to
Fig. 6. Logarithm of the inversion rates at constant temperature as a function of the pressure. The relationship is approximately linear.
a halt on meeting the surface of the nanocrystal. A particle may then consist of stable zones of g and a phases. In that case, susceptibility may provide an acceptable proxy for the g Fe 2 O 3 concentration if the microstructural element controlling susceptibility of the uninverted particles is the nanocrystal boundary rather than the particle boundary. As before, we assume d xrdt s yxrt , where x is the susceptibility, normalised to t s 0, and take the fall in x during the 2 min during which the pressure is applied as the near-linear initial part of the x y t fall. This gives values of 1rt which are plotted against 1rT in Fig. 5. The activation energy is 0.5 eV and the frequency factor 0.5 sy1 . In a further experiment a sample of g Fe 2 O 3 was held at an isotherm Ž2658C. and subjected to pressures of 55, 95 and 130 MPa, each pressure being held for 30 min. The fall in susceptibility during each application of pressure was approximately linear with time. This gives values of 1rt as a function of pressure at the isotherm. The variation of lnŽ1rt . with pressure is approximately linear ŽFig. 6..
4. Discussion 4.1. The actiÕation energies Fig. 5. Logarithm of the inversion rates at elevated pressure against the reciprocal of the temperature. The slope yields the activation energy.
Morrish and Sawatzky Ž1971. express the thermal activation of the inversion of maghemite in terms of activation temperature, TA , which is the activation
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
energy divided by Boltzmann’s constant. They obtain values of 37,000 K Žacicular particles., 43,000 K Žspherical., 54,000 K Ž1.5% Co-doped. and 59,000 K Ž3% Co-doped.. The activation energy at atmospheric pressure obtained for acicular particles in the present investigation, equivalent to a TA of 43,000 K is the same as that of the spherical undoped sample of Morrish and Sawatzky Ž1971.. Morrish and Sawatzky Ž1971. determined degree of inversion from room temperature Mossbauer spectra of materials ¨ which had been heated for periods at elevated temperature, whereas in the present study the inversion process is monitored continuously at elevated temperature. This may account for the difference in TA , but it is more likely that variation in inversion behaviour in nominally similar materials is expected; ¨ for example the acicular maghemite of Ozdemir Ž1990. inverted in the laboratory timescale only after being heated to about 7508C, such behaviour presumably corresponding to a high activation energy. Whether the nature of the external envelope of the particle Žshape and size. is a major influence on the activation of inversion is not at all clear. It would seem more likely that variation in concentration and type of internal defects which resulted from different methods of preparation would play a more important role than the surface of the particle. The frequency factor at atmospheric pressure is comparable to Morrish and Sawatzky’s acicular particles Ž10 23 sy1 . but significantly lower than the frequency factors for the rest of their suite, which ascend along with the activation temperatures through 10 26 sy1 , 10 31 sy1 and 10 32 sy1 . Morrish and Sawatzky speculate that the ‘large’ frequency factor may imply that inversion, once started, goes on to completion in the particle. This would be broadly consistent with the model of Fig. 1. Essentially the activation energy would be associated with the nucleation of a stable region of the a phase, and the frequency factor associated with the subsequent growth of the a phase region i.e., the velocity of the arg boundary. The kinetics of nucleation and growth are apparently connected. A particle with a high barrier to inversion may be more difficult to invert but, once the process has started, the particle more rapidly transforms to the a phase. A particle with low barrier inverts easily but the phase boundary progresses slowly. The presence of defects in general
47
results in a raised lattice energy so that the reduction in energy on inversion is potentially greater if the inversion product is less defective, that is, if the process of inversion also ‘refines’ the crystal structure. This would increase the coefficient of the R 3 term and lower the activation energy. On the other hand the presence of defects may reduce the mobility of the phase boundary in the same way that defects ‘pin’ and reduce the mobility of a domain wall. Thus a low activation energy and high frequency factor may correspond to a high concentration of crystal defects. 4.2. The effect of pressure High pressure results in a lowered barrier and hence lowered activation temperature, 5800 K in the present study. However, unlike the material of Kushiro Ž1960., 140 MPa is not enough to invert the BASF g Fe 2 O 3 at room temperature, which would need 9 years at pressure of the order of 100 MPa. It seems intuitively correct that elevated pressure should promote inversion, but how is E b lowered by increased pressure? The effect of pressure is to reduce interatomic distance and this must lead to the pressure sensitivity of E b . If the energy of the inclusion, Einc , of Fig. 1 is expressed as Einc s bR 2 y cR 3 where b and c are constant at constant temperature and pressure, it can be seen that the barrier height E b s Ž4r27. b 3rc 2 and R crit s 2 br3c. The coefficient c is related to the difference in lattice energy of the 2 phases. The lattice energy per ion pair of a crystal is y
Mz1 z 2 e 2 4p´ 0 r 0
Ž 1 y rrr 0 .
where M is the Madelung constant, z 1 and z 2 the valence number of the anions and cations, e the electronic charge, r 0 the nearest neighbour anion– cation distance and ´ 0 and r are constants. The transformation from an ideal cubic close packed array of rigid spheres Žthe oxygen ions of g Fe 2 O 3 . to an ideal hexagonal close packed array of rigid spheres Žthe anions of a Fe 2 O 3 . involves no change of volume. However, the cations in the interstices do not have negligible volume and the anion structures also suffer deformation from the ideal array. A calcu-
48
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
lation of the ‘X-ray densities’ based on the dimensions and contents of the unit cell shows that, on inversion, there is a volume contraction of about 8% and therefore a linear contraction of about 3%. The above expression for lattice energy is rather approximate for compounds such as those of the present study which have some degree of covalent bonding and contain different numbers of anions and cations. However it does not seem necessary to develop the detail of the model to plausibly show the origin of the strong sensitivity of the inversion transformation on pressure. We may suppose that the lattice energies per ion pair of the g and a phases can be expressed in the form yK grrg and yK arra where K is a constant and r is the interionic distance as before. Two possibilities that can be envisaged are: in determining the reduction in lattice energy, the change in the structure related parameter K dominates over the change in interionic distance, r 0 , in which case the reduction in lattice energy due to the transformation can be written D Krr0 ; or, the change in interionic distance from rg to ra dominates over the change in the structural factor, leading to a reduction in lattice energy of KDŽ1rr 0 . or KD r 0rr 02 . The spherical inclusion contains of the order of R 3rr 03 ion pairs so the reduction in energy due to the inclusion is either yŽ D Krr 04 . R 3 or yŽ KD r 0r r 05 . R 3. The bracketed coefficients of R 3 are the parameter c of our model. If the interface between the 2 phases is crystallographically coherent, the lattice on either side of the interface would be strained by the order of D r 0rr 0 , that is, a few percent, far in excess of the strain corresponding to the maximum elastic strength of ceramic materials. The two phases may therefore be bridged by a plastic semi-amorphous zone rich in crystal defects. This will result in strains only a fraction of D r0rr0 , but still possibly proportional to D r 0rr 0 . If so the strain energy per unit volume of the bridging zone will be proportional to Ž D r 0rr 0 . 2 . Thus the coefficient to the r 2 function of Fig. 1, b, is proportional to Ž D r 0rr 0 . 2 . We now substitute for b and c to find the dependence of E b and R crit on the interionic distance r 0 . Thus E b A Ž D r 0rr 0 . 6 r 08 or Ž D r 0rr 0 . 4 r08 and R crit A Ž D r 0rr 0 . 2 r 04 or Ž D r 0rr 0 . r 04 . The bulk moduli of the two ceramic phases are about the same, so the value of Ž D r 0rr 0 . will not change much as pressure
is applied, so the strain term, which resists inversion, is approximately pressure independent. On the other hand, the lattice term, which drives inversion, is sensitive to pressure. In either formulation of the lattice term the sensitivity of E b to pressure will arise predominantly through the r 08 dependence, hence the strong fall in E b with pressure. R crit will similarly depend on pressure as r 04 in either formulation of the lattice term. 4.3. Estimation of R cr i t It is possible to make an estimate of R crit by using the empirical value of E b and a typical value of the lattice energy of a close-packed metal oxide. The problematic parameter b related to the strain energy of the region bridging the two phases can be eliminated between the expressions for E b and R crit to obtain R crit s Ž2 E brc .1r3. Verwey et al. Ž1948. show that the electrostatic lattice energy of a spinel oxide is of the order of 3 = 10y2 6ra Joules per spinel formula unit, where a is the cell edge. The precise evaluation depends on the charge distribution between the cation sublattices, the distortion of the anion framework and degree of ordering of the cations. Contributions to the lattice energy also come from the repulsive forces between the constituents of the assembled lattice and the individual site preferences of cations due to the formation of covalent bonds ŽBlasse, 1964.. For the present estimate we simply take the lattice energy as the electrostatic energy of the lattice. We choose the case in which the energy fall on inversion is due to the contraction in interionic distance and express this as a change in a. Thus the energy change is Ž3 = 10y2 6 . D ara2 Joules per formula unit. In the spinel structure there are 8 formula units in the unit cell of volume a3 , so the reduction in lattice energy in an inverted inclusion of radius R is Ž3 = 10y2 6D ara2 .Ž8ra3 . Ž4p R 3r3. Joules. Taking Ž D ara. as the linear contraction on inversion of 3% and a as typically 1 nm, the inclusion represents a reduction in energy of 3 = 10 10 R 3 Joules. Thus the parameter c is of the order of 3 = 10 10 J my3 . Substituting for c and E b in the expression for R crit yields R crit ; 5 = 10y1 0 m so the spherical inclusion of critical volume would contain about 5 unit cells of a Fe 2 O 3 , a plausible result.
J. Adnan, W. O’Reillyr Physics of the Earth and Planetary Interiors 110 (1999) 43–50
4.4. Implications for the submarine crust The data of Figs. 4–6 provide a starting point in the construction of a diagram in P–T space showing contours of constant t . Although the data are few, the linearity of the relationships between lnŽ1rt . and 1rT and lnŽ1rt . and P suggests that a diagram with 1rT as one coordinate and P as the other will have linear contours of constant lnŽ1rt .. Inserting values for the activation energies and frequency factors of the present investigation yields the equation in Ž1rT . y P space for a contour of lnŽ1rt .. 10 6 T
ž
s y 1.1 ln
1
t
/
q 9.4 P y 23 ln
1
t
q 1.2 = 10 3
where P is in MPa. The equation can be inverted to provide the value of t for given P and T. In newly formed submarine crust, the near surface temperatures are high and fall with progressive age. A model T Ž t . could be used together with the inferred t ŽT, P . relation to calculate the cumulative degree of inversion of the cooling material at a particular horizon in the submarine crust. The time available for inversion is not the same as the age of the material as, initially, time must be spent developing significant cation deficiency Žthe ‘maghemitization’ of submarine weathering. before inversion can begin. In the present context the potential usefulness of the laboratory data is examined by considering the state of the magnetic minerals studied in cores recovered from Hole 504B of the Deep Sea Drilling Project located in the eastern equatorial Pacific ŽAnderson et al., 1982.. The presence of maghemitized and therefore, at most, only partially inverted titanomagnetite was inferred from magnetic properties of basalt recovered from the uppermost 214 metres of the basement ŽO’Donovan and O’Reilly, 1983. but material at deeper levels revealed no maghemitization ŽFacey et al., 1985.. The temperature rises with depth from about 608C to 858C in the upper 214 metres of the basement which is overlain by 275 metres of sediment ŽAnderson et al., 1982.. The pressure may be estimated as rising from 41 Mbar to 46 Mbar. The time constants for these ŽT, P . conditions are 8 Myr for the top of the section and 0.07 Myr for the bottom. The age of Site 504 is estimated at 6.2 Myr so the survival of maghemitized
49
titanomagnetite in the upper horizons seems consistent with the laboratory data, as does the absence of maghemitized material at deeper levels.
5. Conclusions The transformation of g Fe 2 O 3 to a Fe 2 O 3 is thermally activated. In the case of the acicular tape particles of the present study the activation energy, or energy barrier opposing the process, is 3.7 eV at atmospheric pressure, and 0.5 eV at a pressure of about 100 MPa. The energy barrier can be understood as resulting from the combination of two energy terms, one representing the reduction in lattice energy of an inverted inclusion and the other the strain energy of the interface between the 2 phases, which are probably bridged by a plastic semi-amorphous zone. The reduction in lattice energy, due to the presence of the inverted inclusion, depends on ry4 0 , where r 0 is the typical interionic distance in the two phases; and the barrier to inversion depends on r 08. The barrier height is therefore sensitive to pressure. Extrapolation of the laboratory data to the temperatures and pressures of the submarine crust at Site 504B of the Deep Sea Drilling Project in the eastern Pacific is consistent with the survival of maghemitized uninverted material in the upper part of the core recovered from Hole 504B, as inferred by magnetic studies.
Acknowledgements One of the authors ŽJA. has received support from the Universiti Teknologi Malaysia and the Government of Malaysia. We thank Dr R.J. Veitch of BASF for supplying the g Fe 2 O 3 particles.
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elevated pressure Ž16 MPa–160 MPa.. Meas. Sci. Technol. 3, 289–295. Anderson, R.N., Honnorez, J., Becker, K., Adamson, A.C., Alt, J.C., Emmermann, R., Kempton, P.D., Kinoshita, H., Laverne, C., Mottl, M.J., Nemark, R.L., 1982. DSDP Hole 504B, the first reference section over 1 km through Layer 2 of the oceanic crust. Nature 300, 589–594. Blasse, G., 1964. Crystal chemistry and some magnetic properties of mixed metal oxides with spinel structure. Philips Res. Repts. Suppl. 3, 139. Facey, D., Housden, J., O’Reilly, W., 1985. A magnetopetrological study of rocks from Leg 83, Hole 504B, Deep Sea Drilling Project. In: Anderson, R.N., Honnorez, J., Becker, R., et al., ŽEds.., Init. Repts of the Deep Sea Drilling Project, LXXXIII. US Govt. Printing Office, Washington, pp. 339–346. Housden, J., de Sa, A., O’Reilly, W., 1988. The magnetic balance of its application to studying the magnetic mineralogy of igneous rocks. J. Geomagn. Geoelectr. 40, 63–75. Kushiro, I., 1960. g – a transition in Fe 2 O 3 with pressure. J. Geomagn. Geoelectr. 11, 148–151. Lodding, W., Hammell, L., 1960. DTA of hydroxides in a reducing atmosphere. Anal. Chem. 32, 657–662.
Morrish, A.H., Sawatzky, G.A., Mossbauer study of the gamma to alpha transformation in pure and cobalt-doped ferric oxide, pp. 144–147, FERRITES: proceedings of the International Conference, University of Tokyo Press, 1971. O’Donovan, J.B., O’Reilly, W., 1983. Magnetic properties of basalts from Hole 504B, Deep Sea Drilling Project Leg69, Init. Reports of the Deep Sea Drilling Project, LXIX, Ed Cann, J.R., Langseth, M.G., Honnorez, J., et al., Washington ŽU.S. Govt. Printing Office., 721–726. ¨ Ozdemir, O., 1990. High temperature hysteresis and thermoremanence of single domain maghemite. Phys. Earth Planet. Inter. 65, 125–136. ¨ ¨ Dunlop, D.J., 1988. Crystallization remanent magneOzdemir, O., tization during the transformation of maghemite to hematite. J. Geophys. Res. 93, 6530–6544. Ozima, M., Ozima, M., 1972. Activation energy of unimixing of titanomaghemite. Phys. Earth Planet. Inter. 5, 87–89. Readman, P.W., O’Reilly, W., 1971. The synthesis and inversion of non-stoichiometric titanomagnetites. Phys. Earth Planet. Inter. 4, 121–128. Verwey, E.J.W., de Boer, F., Santen, J.H., 1948. Cation arrangement in spinels. J. Chem. Phys. 16, 1091–1092.