On the Dependence of the Electrical Conductivity of Certain Rocks and Minerals on Geological Processes and Time

V. N. Salnikov

(Presented by the scientific seminar of the Department of FPI, NII RF)

This study was carried out in order to examine the electrical conductivity of certain minerals and rocks and its change under the influence of geological processes and time. It is of interest, in our view, to assess the role of geological processes and time in changing the energy of the crystal lattice of the rock-forming minerals potassium feldspar and muscovite, which provide information on age by the method of determining their specific electrical conductivity in the temperature range from 900–1000°C, when the intrinsic ions of the crystal lattice play a role in charge transfer.

MacKenzie and Milne [3], after grinding muscovite together with salts of Ca, Al, and Si, established that the amount of aluminum and calcium in the muscovite increased, while the amount of silicon decreased. The authors of other works [4] confirmed significant absorption of calcium with simultaneous removal of alkali metals from the lattice, but the results differ from those of MacKenzie and Milne with respect to aluminum and silicon.

In studying the triclinicity of potassium feldspars (K-feldspars) for resolving questions of the genesis of pegmatites and granites, the authors [1] come to the conclusion that the presence of barium in K-feldspars exerts an inhibiting influence on the processes of ordering of the crystal lattice.

It is natural to suppose that the decay of \(K^{40}\) in the crystal lattice of potassium-bearing minerals and its replacement by \(Ca^{40}\) leads to the potential possibility of the release of \(Si^{+4}\), and at the same time also of the share of energy introduced by it into the compound at a temperature close to the melting point (900–1000°C). The amount of possible release of \(Si^{+4}\) depends on time and on the content in the mineral of potassium, aluminum, and trivalent iron, which are capable of compensating the neutrality of molecules in the compound. An empirical dependence of electrical conductivity on potassium content and the age of minerals was obtained by F. S. Zakirova [2].

To explain the mechanism of change in activation energy and the dependence of electrical resistance on geological processes and time, the author dwells on the assumption that polymorphic transformations in minerals under the action of heating can directly change the value of electrical conductivity. Therefore, the amount of energy for the formation of a symmetry stable under the given conditions will depend on the age of the mineral and the content of elements, including \(K^{40}\). Each polymorphic modification is characterized by a complex of physical properties. Pe-

the transition from one modification to another is accompanied by a stepwise change in physical properties even at constant temperature.

A sample of mica or rock was heated linearly at a rate of \(10^\circ\) per minute from 20 to \(1100^\circ\text{C}\), followed by cooling. During the initial heating (Fig. 1) to a temperature of \(1100^\circ\text{C}\), on the curve of the dependence

\[ \lg \delta = f\!\left(\frac{1}{T}\right) \]

within the temperature range \(560\text{--}850^\circ\text{C}\), the change in electrical conductivity is caused by dehydration of the mica and, correspondingly, by its polarization, with a subsequent decrease in the number of carriers.

The straight-line segment from 870 to \(970^\circ\text{C}\), with an activation energy of \(0.8\ \text{eV}\), characterizes the intrinsic conductivity of the mineral, where, in the author’s opinion, the cations \(Si^{+4}\) participate in conduction; above \(870^\circ\text{C}\) these are released from the feldspar molecule \((KAlSi_{3}O_{8})\), partly compensating the deficient aluminum in the newly formed anorthite molecule \((CaAl_{2}Si_{2}O_{8})\), or, recombining with oxygen ions, are separated in the form of quartz \((SiO_{2})\). As a result, above \(970^\circ\text{C}\) the activation energy increases and is equal to \(1.6\ \text{eV}\). On the reverse path, the characteristic bend at \(970^\circ\text{C}\) is not observed, and the activation energy remains unchanged \((1.6\ \text{eV})\), which indicates good ordering of the crystal lattice. Subsequent heating and cooling of the sample did not substantially change the activation energy. Rock samples containing quartz and tridymite, within the temperature range \(870\text{--}1000^\circ\text{C}\), give the same characteristic bends; this confirms that the carriers in this region are \(Si^{+4}\) cations and their complexes (Fig. 1).

Fig. 1. Dependence \(\delta = f\!\left(\frac{1}{T}\right)\) for muscovite (a, b, c) and quartz porphyry (d): a) muscovite (Inner Mongolia deposit), initial heating (1) to \(1100^\circ\text{C}\) and cooling (2); b) secondary heating (1) to \(1100^\circ\text{C}\) and cooling (2); c) muscovite (Yenskii deposit), heating (1) to \(1040^\circ\text{C}\) and cooling (2); d) quartz porphyry, heating (1) to \(1040^\circ\text{C}\) and cooling (2)

Obviously, it remains to be assumed that only an abrupt, but regular, change in structure and crystalline form, depending on a regular change in chemical composition, can affect the dependence of electrical conductivity on temperature. In this case, two structures of one and the same substance are compared with each other in two states corresponding to their different thermodynamic conditions.

As long as changes in conditions are small and do not pass certain limits, the substance remains isomorphous with itself in its initial state; but as soon as the boundary of permissible deformations has been passed, a polymorphic transformation occurs [5]. An example may be the isomorphism of feldspars

\[ \begin{gathered} NaAlSi_3O_8 \leftarrow CaAl_2Si_2O_8,\\ Na^+Al^{+3} \qquad Ca^{+2}Si^{+4}. \end{gathered} \]

The process of decay of \(K^{40}\) and formation in the lattice of \(Ca^{40}\) may also be regarded as a particular case of isomorphism.

\[ K^{40}AlSi_3O_8 \to Ca^{40}AlSi_3O_8 \]

(the compound is unstable). To compensate the charge, one ion \(Si^{+4}\) must be removed from the compound and one ion \(Al^{+3}\) introduced. Then the compound will acquire a stable form.

\[ \begin{gathered} K^{40}AlSi_3O_8 \to Ca^{40}AlSi_3O_8 \ \xrightarrow{\,t=900\text{—}1000^\circ C\,}\\ \to Ca[Al^{2/3}Si]Si_2O_8 + {}^{1/3}SiO_2 \ \text{or}\ \to CaAl_2Si_2O_8 + SiO_2. \end{gathered} \]

But if the system is closed and there is no introduction of \(Al^{+3}\), and one ion \(Si^{+4}\) has lost a bond in the silico-oxygen tetrahedron, then part of this bond may go to compensate the missing \(Al^{+3}\), and part of the positive charge may be compensated by oxygen with the formation of quartz.

If, after the lapse of some time, the rock containing accumulated radiogenic \(Ca^{40}\) was again subjected to melting or heating to a temperature of 900—1000°C and the system was open (there was an introduction of \(Al^{+3}\), or trivalent iron was present), the change in the chemical composition of potassium feldspar could proceed to completion, with the formation of an anorthite molecule and separation of quartz in an amount \(2/3\) greater than usual:

\[ K^{39}AlSi_3O_8 \cdot K^{40}AlSi_3O_8 \to \frac{ K^{39}AlSi_3O_8 \cdot Ca^{40}AlSi_3O_8 }{ \substack{ \text{heating to }900\text{—}1000^\circ C\text{ with an}\\ \text{excess of }Al^{+3}\text{ or its introduction}\\ \text{in the presence of }O_2 } } \]

\[ \to K^{39}AlSi_3O_8 \cdot Ca^{40}Al_2Si_2O_8 + SiO_2. \]

Similarly, the molecule of muscovite containing \(K^{40}\) changes:

\[ K^{40}Al_2[AlSi_3O_{10}][FOH]_2 \to Ca^{40}Al_2[AlSi_3Al_{10}][FOH]_2 \to \]

\[ \to Ca^{40}Al_2Si_2O_8 + SiO_2 + Al_2O_3 + H_2O + F_2 \uparrow \]

Consequently, the replacement of \(K^{40}\) by \(Ca^{40}\) as a result of \(\beta\)-decay should lead to the formation of a new molecule in the structure of the mineral, if the chemical bonds in the silico-oxygen tetrahedra of potassium feldspar \((KAlSi_3O_8)\) or muscovite \((KAl_2[AlSi_3O_{10}][FOH]_2)\) were broken. These bonds may be broken during melting of the mineral or partially weakened during heating of the compound, when the energy \((E\omega)\) required for formation and drift (directed transfer) of an intrinsic ion of the crystal lattice is imparted. In order to determine quantitatively the magnitude of the energy of formation of the crystal lattice of the mineral and its change over geological time, we have calculated the lattice energy on a model.

For an illustrative calculation let us take a model of a compound (muscovite, potassium feldspar, etc.) that must satisfy the following requirements:

1. The initial compound corresponds to the written chemical formula for K-feldspar (\(KAlSi_3O_8\)) and for muscovite (\(KAl_2[AlSi_3O_{10}]\cdot[FOH]_2\)).

2. At the present time the compound contains \(K^{40}\), \(0.0119\%\) of all potassium.

3. The compound was formed \(\tau\) million years ago.

4. Let us conventionally assume that during \(\tau\) million years, with each act of \(\beta\)-decay of \(K^{40}\) and formation of a \(Ca^{40}\) atom, a molecule of the corresponding compound is formed.

Example:

\[ 1.\ \frac{K^{40}AlSi_3O_8 \longrightarrow Ca^{40}Al_2Si_2O_8}{\text{K-feldspar}\hspace{4.2em}\text{anorthite}} \]

\[ 2.\ \frac{K^{40}Al_2[AlSi_3O_{10}]\ [FOH]_2 \longrightarrow Ca^{40}Al_2[Al_2Si_2O_{10}]\ [FOH]_2}{\text{muscovite}\hspace{6.5em}\text{calcium mica}} \]

Thus, over geological time, in the primary compound (in the first case, K-feldspar) there occurs an accumulation of \(Ca^{40}\), tending to ob—

Table 1

Accumulation of \(Ca^{40}\) over geological time in potassium feldspar and the potential possibility of release of \(Si^{+4}\), and with it part of the energy introduced by it into the compound

Table 2

Accumulation of \(Ca^{40}\) over geological time in muscovite and the potential possibility of release of \(Si^{+4}\), and with it part of the energy introduced by it into the compound

to form an anorthite molecule, with the release from the bonds of the silicon–oxygen tetrahedra of $Si^{+4}$ ions and the introduction of $Al^{+3}$ or its compensation by $2/3$ of the $Si^{+4}$ ions. The author has calculated the energy of the crystal lattice of primordial orthoclase and muscovite according to Fersman’s formula $U = 256.1 \cdot (\alpha \cdot ЭK_1 + \beta \cdot ЭK_2 \ldots)$ and its change over geological time as a result of the accumulation of $Ca^{40}$ and the formation of anorthite molecules when the sample is heated to $1000^\circ C$ at the present time. The calculated data are given in Tables 1 and 2 (see p. 81).

Thus, in the process of redistribution of bonds in the temperature range $900$–$1000^\circ C$, both the $Ca^{40}$ ions accumulated in the crystal lattice over geological time and the $Si^{+4}$ ions take part; the latter must partially compensate for the deficiency of $Al^{+3}$ and partially leave the silicon–oxygen tetrahedron.

The dependence of electrical resistivity on the time of formation of potassium-bearing rocks and minerals at temperatures of $900$–$1000^\circ C$ is caused by the release of a certain number of $Si^{+4}$ ions from the compound, while the change in activation energy is associated with the redistribution of $Si^{+4}$ and $Ca^{+2}$ ions in the crystal lattice of the mineral at the moment when its crystalline structure assumes the most favorable energy state, i.e., when a restructuring of some part of the molecule from potassium-feldspar to anorthite occurs. Upon cooling, this process proceeds

Fig. 2. Dependence $\sigma = f(\tau)$ (a) and $\dfrac{1}{E} = f(\tau)$ for K-feldspar (b) and muscovite (c):

a) experimental curve of the dependence of electrical conductivity on the age of the mineral (after F. S. Zakirova); b) potential possibility of energy release from $1\ \text{cm}^3$ of potassium feldspar when it is brought to the melting temperature; c) the same for $1\ \text{cm}^3$ of muscovite.

in the reverse order, energy is absorbed and the crystalline structure again acquires its original state, stable at normal temperatures. The process is repeated until the crystal lattice of the mineral is destroyed or the heating temperature of the sample is above the critical temperature at which the reverse transition is impossible.

Having plotted the dependence of the energy released during removal from the compound in the temperature range 900–1000° on time and comparing it with the curve of the dependence of specific electrical conductivity on time (obtained experimentally by F. S. Zakirova), one can note that the curves obey one and the same law of radioactive decay of \(K^{40}\) (Fig. 2).

From the calculations the following conclusions may be drawn:

1. As \(Ca^{40}\) accumulates in the lattice, ions \(Si^{+4}\) (vacancies) accumulate, and the system tends toward the lowest-energy state, which can be realized within the temperature range from 800 to 1000°C, when the bonds in the crystal lattice of the mineral are weakened.

2. The value of the electrical resistance at the second point of inflection of the curve in the temperature range 900–1000°C depends on the amount of silicon ions released from the compound and participating in charge transfer.

3. The accuracy of determining absolute age by the electrical-conductivity method will be affected by the metasomatic introduction of aluminum and trivalent iron, as well as by mechanical destruction of the crystal lattice, which promotes exchange of cations in silicon–oxygen tetrahedra.

4. The formation over geological time of a molecule of more basic plagioclase and the release of \(Si^{+4}\), its combination with \(O_2\) with the formation of \(SiO_2\), gives us one more mechanism for the separation of magma into acidic and basic as a result of the radioactive decay of \(K^{40}\). From this point of view, the formation of graphic structure in pegmatite veins can be explained by metamorphism and the phenomena of metamorphogenic quartzization.

LITERATURE

1. G. G. Afonina, B. N. Shmakin, DAN, 195, No. 4 (1970).

2. F. S. Zakirova, Study of Certain Physical Properties of Potassium Minerals and Rocks for the Purpose of Developing a New Method of Absolute Geochronology. Abstract of Cand. Sci. dissertation, Tomsk, 1966.

3. R. C. Mackenzie, and A. A. Milne. The effect of grinding on micas. Min. mag. 30, No. 222, 1953.

4. A. N. Tsvetkov and E. P. Valyashikhina. Materials on the thermal study of micas. AN SSSR, 1956.

5. A. E. Fersman. Geochemistry, Vols. I–IV. Selected Works. Vols. III–V. Publishing House of the Academy of Sciences of the USSR, 1955, 1958, 1959.