ON THE MECHANISM OF CHANGE IN THE CONDUCTIVITY OF POTASSIUM-BEARING ROCKS AND MINERALS OVER GEOLOGICAL TIME

V. N. SALNIKOV, A. F. KOROBEINIKOV

(Presented by the scientific seminar of the Research Institute of Applied Physics, Department of Physics and Technology)

The temperature dependence of the electrical conductivity of rocks from the Sorsk molybdenum deposit was investigated in order to assess the role of the accumulation of decay products of $K^{40}$ in the crystal lattice of potassium-bearing minerals, which provides information on age by the potassium-argon method and by the specific-conductivity method [1]. By modeling, in simplified form, the process of thermometamorphism under laboratory conditions, a mechanism is considered for a possible change in the chemical composition and energy of the crystal lattice of mica and potassium feldspar (K-feldspar) as a result of the release of bonds of some ions and the formation of new compounds.

The disturbance of radiogenic equilibrium in minerals and rocks is caused by many primary and secondary processes, and, depending on the nature of these processes, distortions of age information arise [2]. In the overwhelming majority of cases, rocks do not bear traces of visible change; and if changes are observed, they are insignificant. The age of rocks that have undergone superimposed geological processes reflects the time of occurrence of the metamorphic process. Therefore, discrepancies between age values and geological data, as a consequence of the “rejuvenation” of rocks that do not bear visible traces of change, are also associated with the influence of metamorphic processes [3, 4].

The influence of thermometamorphism on changes in the chemical composition of minerals over geological time can be reproduced, in simplified form, under laboratory conditions by using a vacuum furnace, while the physicochemical transformations can be recorded by measuring the values of the electrical conductivity of the compound during heating and cooling [5, 6].

A rock sample in the form of a plate $20 \times 20 \times 3$ mm was heated linearly at a rate of $10^\circ$ per minute from 20 to $1100^\circ$C, followed by cooling. During heating and cooling, the specific electrical conductivity was measured at direct current with a voltage of 20–50 V. Rock samples were measured that had been taken from various levels along the strike of the body of quartz-bearing porphyries, basic dikes, and from the enclosing hornblende skarns of the Sorsk molybdenum deposit (Fig. 1). From each sample three plates were cut, and their specific electrical conductivity was measured as a function of temperature. The value of electrical conductivity was taken as the arithmetic mean, which at $970^\circ$C in vacuum, for the same composition of rocks taken from different points of the geological body, varies by 2–15%. At atmospheric pressure and a temperature of $20^\circ$C, the electrical pro-

Table 1

Electrical conductivity of rocks of the Sorsk molybdenum deposit
\(\sigma\ \mathrm{ohm}^{-1}\mathrm{cm}^{-1}\) (at 970°C, pressure \(10^{-4}\) mm Hg,
and 20°C at atmospheric pressure)

conductivity depends on moisture content and the amount of other mechanical impurities; therefore the difference in its values from sample to sample reaches 1–2 orders of magnitude (Table 1).

In vacuum at a temperature of 970°C the electrical-conductivity values of quartz-bearing porphyries are lower than those of the hornblende schists enclosing them (Fig. 1). The electrical conductivity of granites differs little from that of their extrusive analogues, the quartz-bearing porphyries, whereas the electrical conductivity of samples taken at the contact of hornblende schists with quartz-bearing porphyries and diabase dikes (samples 19ᵃ, 49ᵃ; Fig. 1), and of samples collected at a distance of 10–15 m from the place of intrusion of the quartz-bearing porphyries (sample 18), is substantially reduced. On the basis of the obtained electrical-conductivity values, the rocks were divided into three groups: hornblende schists with an average electrical conductivity of \(1.8\cdot10^{-5}\ \mathrm{ohm}^{-1}\mathrm{cm}^{-1}\), quartz-bearing porphyries \(4.5\cdot10^{-6}\ \mathrm{ohm}^{-1}\mathrm{cm}^{-1}\), and rocks with anomalous electrical-conductivity values caused by near-contact processes (Table 1). It is obvious that the addition and removal of components at the boundary of two media as a result of contact metamorphism can substantially change the values of electrical conductivity in the region of intrinsic conductivity.

Usually, in dielectrics in this region the dependence of the specific electrical conductivity \(\sigma\) on absolute temperature \(T\) is described by the equation [7]:

\[ \sigma = A e^{-\frac{Ew}{kT}} \]

where \(A\) is a constant depending on the concentration of charge carriers and only weakly dependent on temperature;

\(Ew\) is the activation energy of the electrical-conductivity process (energy,

Fig. 1. Plan (based on materials of the Sorskaya GRE) and geological section with sampling sites and the values of their electrical conductivity at 970°C and a pressure of \(10^{-4}\) mm Hg:
1 — granites, granosyenites, hornblende syenites; 2 — diorites; 3 — pyroxene-hornblende syenites; 4 — sampling sites and their numbers; 5 — electrical conductivity of hornblende syenites; 6 — electrical conductivity of quartz-bearing porphyries and granites; 7 — quartz-bearing porphyries; 8 — diabase dikes; 9 — anomalous values of electrical conductivity of individual samples

necessary for the formation and drift of charge carriers in the direction of the field);

\[ K \text{ — Boltzmann’s constant.} \]

The graph of this function in the coordinate system \(\lg \sigma = f\left(\frac{1}{T}\right)\) has a linear character under the condition \(E_w = const\) and \(A = const\). For our objects, which are complex heterogeneous systems, the temperature dependences of electrical conductivity are rather complicated (see Fig. 2). The curves show inclined and horizontal segments caused by polymorphic transformations of minerals, and portions with maxima and minima of electrical conductivity associated with endothermic processes and polarization.

If \(E_w = const\), \(A = const\), and during polymorphic transformations \(T_1\) of the sample is also \(const\), then the number of current carriers will be constant; therefore, the change in electrical conductivity at the given moment of time should not—

Fig. 2. Temperature dependence of the electrical conductivity of muscovite and rocks of the Sorsk molybdenum deposit:
a) muscovite, Vnutrimongol’skoe deposit; b) diabase, sample 49; c) quartz-bearing porphyry, sample 46; d) hornblende syenite, sample 46a.

…may be observed. But since the heat capacity of the sample is greater than the heat capacity of the electrode on which the sample is placed, and the thermocouple does not directly measure the temperature of the sample, but measures the temperature of the electrode,

on the graph of the dependence \(\lg \sigma = f\!\left(\frac{1}{T}\right)\) a number of horizontal straight segments are obtained, characterizing the time and the initial temperature of polymorphic transformations of the minerals composing the rock.

On the curve of the dependence of the electrical conductivity of hornblende

syenite, on the forward and reverse runs (Fig. 2, г), horizontal lines are observed in the temperature interval 570—620°C (the transition of α-quartz to β-quartz) and in the interval 850—870°C (the transition of quartz to tridymite).

If the content of α-quartz in the total mass of the rock is small, then on the electrical-conductivity curves the segments obtained are not horizontal, but gently inclined (Fig. 2, curve в). After heating the sample to 1100°C, on the reverse run of the curve we observe the appearance of clearer plateaus in quartz-bearing porphyries (Fig. 2, curves б, в), while in diabases [6] a horizontal plateau appears which is absent on the forward run. Probably, after heating to a temperature of 1140°C and subsequent cooling, in the diabase sample a new phase of \(SiO_2\) (β-quartz) formed, as did an additional amount of β-quartz in the quartz-bearing porphyry. The transition of the additional amount of β-quartz into α-quartz also caused the appearance of clearer plateaus on the reverse-run curves. If \(E_w — const\), \(A — const\), and \(T_2\) of the sample decreases as a result of the endothermic effect, then under our experimental conditions, on the dependence curve \(\lg \sigma = f\left(\frac{1}{T}\right)\), we obtain a decrease in electrical conductivity with time. Thus, on the electrical-conductivity curves of mica, quartz-bearing porphyry, and hornblende syenite, in the temperature interval 600—800°C, a series of complex peaks arises, caused by dehydration of minerals, oxidation of \(Fe^{+2}\) cations to \(Fe^{+3}\), etc. The endothermic effect recorded on the electrical-conductivity curves of hornblende syenite and quartz-bearing porphyry at 870—900°C is probably due to the transition of potassium feldspar from one modification to another [8].

At a temperature of 870°C, polarization occurs in samples containing mica and K-feldspar, owing to the weakening of the primary bond of some of the \(K^{+1}\), \(Si^{+4}\), and \(O^{-2}\) ions; therefore the electrical conductivity is recorded by the instrument according to the residual current, which does not correspond to the true value. This discrepancy is caused by the influence of the electromotive force of polarization \((p)\), directed opposite to the external field. In this case the recorded value of the electrical conductivity is equal to

\[ G = \frac{I_{\text{inst}}\cdot h}{U\cdot S} = \frac{\left(\frac{U-p}{R_{\text{inst}}}\right)\cdot h}{U\cdot S} \]

At a temperature of 970—1040°C, complete liberation of \(Si^{+4}\) ions from silicon–oxygen tetrahedra occurs, and their combination with oxygen ions, which leads to the formation of quartz and an anorthite molecule in the structure of orthoclase and mica. If the temperature does not reach the value at which these transformations occur throughout the entire structure of the mineral, then the polarization phenomenon is partially observed on the reverse run of the curve, while the formation of α-quartz is recorded by horizontal and inclined plateaus (Fig. 2, curves б, в, г).

Let us consider successively one of the possible mechanisms of changes occurring in the crystal lattice of potassium feldspar and muscovite over geological time, with the subsequent action of thermometamorphism upon it.

One of the causes of changes in the chemical composition of rocks is the β-decay of \(K^{40}\) and its replacement in the crystal lattice of potassium-bearing minerals by \(Ca^{40}\), which leads to the accumulation of positive vacancies that subsequently form nodal complexes with hydroxyl ions, fluorine, or the neutrality of the crystal is preserved—

is due to the reduction of trivalent iron, which enters the crystal lattice isomorphically.

Example:

$$ \begin{aligned} \text{orthoclase } K^{40}Al_3O_8 &\xrightarrow[\beta\text{-decay}]{} Ca^{40}AlSi_3O_8 +\underset{\text{vacancy}}{W},\\ \text{muscovite } K^{40}Al_2[AlSi_3O_{10}][OH]_2 &\xrightarrow[\beta\text{-decay}]{} CaAl_2[AlSi_3O_{10}][OH]_2 +\underset{\text{vacancy}}{W}. \end{aligned} $$

Let us assume that, after the lapse of \(\tau\) million years, molecules with an uncompensated positive charge undergo hydration.

$$ [Ca^{40}AlSi_3O_8]^{+1}+OH^- \longrightarrow Ca^{40}AlSi_3O_8OH $$

$$ [Ca^{40}Al_2[AlSi_3O_{10}][OH]_2]^{+1}+OH^- \longrightarrow CaAl_2[AlSi_3O_{10}][OH]_3 $$

Hence the number of nodal vacant complexes in the lattice of minerals will depend on time and on the potassium content, while the amount of information preserved about the absolute age of the object will depend on the history of the sample.

Let us trace, on a model, the change in the chemical composition of the rock-forming minerals potassium feldspar and muscovite during heating of a rock as a result of thermometamorphism without introduction or removal of components \(\tau\) years after its formation.

1. The effect of thermometamorphism on a mineral containing a hydrated K-feldspar molecule \((Ca^{40}AlSi_3O_8OH)\). At \(700—800^\circ C\) the compound loses water of crystallization

\[ Ca^{40}AlSi_3O_8OH \rightarrow [Ca^{40}AlSi_3O_8]^{+1}, \]

and the framework cavity of composition \([AlSi_3O_8]^{-1}\) tends to assume a stable state, which can be attained by doubling the negative charge of the cavity and reconstructing it into a cavity of the form \([Al_2Si_2O_8]^{-2}\) in connection with the incorporation of \(Ca^{40}\). This leads, at a temperature of \(870—970^\circ C\), to the potential possibility of weakening the bond and partially activating \(Si^{+4}\), \(K^{+1}\), \(O^{-2}\), and at the same time to the release of part of the energy introduced by them into the compound:

\[ KAlSi_3O_8[Ca^{40}AlSi_3O_8]^+ \rightarrow Ca^{40}Al_2Si_2O_8 + 3SiO_2 + Si^{+4} + K^{+1} + 2O^{-2} \]

at \(970—1040^\circ C\). The silicon and oxygen ions, being released, form quartz and anorthite molecules in the crystal lattice of the mineral, which lead to the appearance in it of quasidefects

\[ \rightarrow Ca^{40}Al_2Si_2O_8 + 3SiO_2 + SiO_2 + K^{+1}. \]

Calculations show that when \(1\ \mathrm{cm}^3\) of K-feldspar, three billion years old, is heated to \(1040^\circ C\), the energy of the crystal lattice is lowered by \(304\) J owing to the formation of anorthite molecules.

1. The effect of metamorphism on a mineral containing a hydrated muscovite molecule \((Ca^{40}Al_2[AlSi_3O_{10}]\cdot[FOH]_2[OH])\).

At a temperature of \(700—800^\circ C\) [9] the compound loses a hydroxyl group

\[ Ca^{40}Al_2[AlSi_3O_{10}]^{+3}+F_2 \uparrow +3OH \rightarrow [Ca^{40}Al_2(AlSi_3O_{10})]^{+3}, \tag{3} \]

therefore the system, under the new physicochemical conditions, tends toward the lowest energy state, which will be attained upon formation of the hydrated mica margarite with the formula \(CaAl_2(Al_2Si_2O_{10})^{+2}\). In margarite the tetrahedral networks have the composition \((Al_2Si_2O_{10})\). The negative charge of the double silicate layers in this case is twice as large as for the original mica, which is also balanced by the incorporation between the layers of divalent calcium ions [10].

With a further increase in temperature, beginning at \(870^\circ C\), the reaction proceeds with the formation of free ions \(Si^{+4}\), \(K^{+1}\), \(O^{-2}\), and at \(970—1040^\circ C\), among the transformations theoretically possible in muscovite, orthoclase, anorthite, mullite, and corundum [9] arise according to the reactions:

At temperatures up to 800° C

\[ K^{40}Al_{2}[AlSi_{3}O_{10}][OH]_{2} \ \xrightarrow{\beta\text{-decay}}\ CaAl_{2}[AlSi_{3}O_{10}][OH]_{2} + \underset{\text{vacancy}}{W} \]

— charge compensation at the expense of \(OH^{-}\) or \(F^{-}\), or through the reduction of \(Fe^{+3}\) to \(Fe^{+2}\), etc.

At temperatures above 800° C

\[ KAl_{2}[AlSi_{3}O_{10}][OH]_{2} \cdot Ca^{40}Al_{2}[AlSi_{3}O_{10}][OH]_{3} \ \xrightarrow{\text{heating to }970\text{--}1040^\circ C}\ \]

\[ \longrightarrow \underset{\text{margarite}}{Ca^{40}Al[Al_{2}Si_{2}O_{10}]^{+2}} + \underset{\text{orthoclase}}{KAlSi_{3}O_{8}} + Al^{+3} + Si^{+4} + \underset{\text{charged volume}}{5H^{+1}+7O^{-2}} \longrightarrow \]

\[ \longrightarrow Ca^{40}Al_{2}Si_{2}O_{8}\cdot KAlSi_{3}O_{8} + Al_{2}O_{3} + SiO_{2} + 5H^{+1} + O^{+2}. \]

borrowing one \(Al^{+3}\) ion from a neighboring molecule, we obtain corundum, which, reacting with quartz, gives mullite

\[ \underset{\text{anorthite}}{Ca^{40}Al_{2}Si_{2}O_{8}} \quad \underset{\text{orthoclase}}{KAlSi_{3}O_{8}} \longrightarrow \underset{\text{mullite}}{Al_{2}SiO_{5}} + \underset{\text{corundum}}{Al_{2}O_{3}} . \]

In the temperature range 870—1040° in K-feldspar frameworks and in the double silicate layers of muscovite, a charged volume arises as a result of the release from bonds of the ions of the hydroxyl group \(H^{+1}\), \(O^{-2}\), and \(K^{+1}\), which impedes the transfer of charges by \(K^{+1}\) ions [1, 11] through the crystal lattice of the mineral when a constant electric field is applied. Subsequently \(Ca^{40}\), forming an anorthite molecule, breaks part of the \(Si^{+4}\) bonds in the tetrahedra, which increases the positive charge of the double silicate layers of the mica or of the K-feldspar framework. At 970—1040° C, \(Si^{+4}\) and \(Al^{+3}\) combine with \(O^{-2}\) to form quartz, mullite, and corundum, and the volume charge is eliminated, since the compounds formed are electrically neutral.

Consequently, replacement of \(K^{40}\) by \(Ca^{40}\) as a result of \(\beta\)-decay should have led to the formation of a new molecule in the structure of the mineral if chemical bonds in the silicon–oxygen tetrahedra of potassium feldspar or muscovite had been broken. These bonds may be broken during melting of the mineral or partially weakened during heating of the compound, when the energy \((Fw)\) required for the formation and drift of the intrinsic ion of the crystal lattice is supplied. Weakening of the bonds leads to increased migration of argon and to its loss by minerals in the zone of metamorphism, whereas partial formation of quartz and anorthite according to the proposed scheme does not lead to disruption of the information that gives the absolute-age value by the electrical-conductivity method. Therefore, the data obtained do not contradict the conclusions of F. S. Zakirova [1] concerning the more reliable age values obtained by this method.

From the foregoing, the following conclusions may be drawn:

1. Rocks can be classified by determining the temperature dependence of electrical conductivity in the temperature interval 870—1040° C, when intrinsic ions of the crystal lattice of the rock-forming minerals participate in charge transfer.

2. By modeling the process of metamorphism under laboratory conditions, it is possible to explain those slight changes in minerals and rocks that lead to a discrepancy between age values and geological data.

3. By quantitatively determining the value of polarization and of the endothermic effect in the temperature interval 870—1040° C, one can judge the intensity of metamorphism, as a result of which part of the released silicon, aluminum, and oxygen ions formed quartz and anorthite molecules, while the remaining part of the ions may be released from

with the formation of the corresponding compounds upon heating of the sample in the cell.

1. Within mobile geosynclinal zones with active magmatic and tectonic activity, the loss of argon and the formation of quartz and anorthite occur in rocks simultaneously, since both processes are caused by the weakening of bonds in the crystal lattice of minerals; however, the loss of argon leads to underestimated values in determining the absolute age by the potassium–argon method, whereas the partial formation of quartz and anorthite has no substantial effect on the age indications obtained by the electrical-conductivity method.

REFERENCES

1. F. S. Zakirova. Author’s abstract of Candidate’s dissertation, Tomsk, 1966.

2. E. K. Gerling. The Current State of the Argon Method for Determining Age and Its Application in Geology. Moscow, Publishing House of the Academy of Sciences of the USSR, 1961.

3. V. M. Klyarovskii. Author’s abstract of Doctoral dissertation, Tomsk, 1968.

4. V. T. Pokalov, E. S. Pastukhova. “Soviet Geology,” 1961, No. 7.

5. L. G. Berg. Introduction to Thermography. Moscow, “Nauka,” 1969.

6. E. K. Zavadovskaya, M. N. Treskina. “Zav. lab.”, 1961, No. 5.

7. I. S. Zheludev. Physics of Crystalline Dielectrics. Moscow, “Nauka,” 1967.

8. V. V. Gordienko. Mineralogy, Geochemistry, and Genesis of Spodumene Pegmatites. Leningrad, “Nauka,” 1970.

9. A. N. Tsvetkov, E. P. Valyashikhina. Materials on the Thermal Study of Minerals. Proceedings of the Academy of Sciences of the USSR. Moscow, 1956.

10. U. Breg, G. Klarringbull. The Crystalline Structure of Minerals. Moscow, “Mir,” 1967.

11. E. K. Zavadovskaya, V. A. Chernyshev, R. M. Gold, V. I. Podlipnev. Polarization in micas and the effect of β-radiation on it. Publishing House of Higher Educational Institutions, “Physics,” 1971, No. 1.