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Article

Studying the Stability of the K/Ar Isotopic System of Phlogopites in Conditions of High T, P: 40Ar/39Ar Dating, Laboratory Experiment, Numerical Simulation

by
Denis Yudin
1,
Nikolay Murzintsev
1,
Alexey Travin
1,2,*,
Taisiya Alifirova
1,3,
Egor Zhimulev
1 and
Sofya Novikova
1
1
V.S. Sobolev Institute of Geology and Mineralogy, Siberian Branch of the Russian Academyof Sciences, 3 Academician Koptyug ave., 630090 Novosibirsk, Russia
2
Faculty of Geology and Geography, National Research Tomsk State University, 634050 Tomsk, Russia
3
Department of Lithospheric Research, University of Vienna, Althanstraße 14/UZA2, 1090 Vienna, Austria
*
Author to whom correspondence should be addressed.
Minerals 2021, 11(2), 192; https://doi.org/10.3390/min11020192
Submission received: 24 October 2020 / Revised: 19 January 2021 / Accepted: 8 February 2021 / Published: 12 February 2021
(This article belongs to the Special Issue Isotope Dating Methods and Numerical Modeling in Reconstructions of Geological and Geodynamic Processes)
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Abstract

:
Typically, 40Ar/39Ar dating of phlogopites from deep-seated xenoliths of kimberlite pipes produces estimates that suggest much older ages than those when these pipes were intruded. High-pressure (3 GPa) laboratory experiments enabled the authors to explore the behaviour of argon in the phlogopite structure under the conditions that correspond to the mantle, at the temperatures (from 700 to 1000 °С), far exceeding closure temperature of the K/Ar isotopic system. “Volume diffusion” remains foremost for describing the mobility of argon in phlogopite at high pressures. The mantle material age can be estimated through the dating of the phlogopites from deep-seated xenoliths of kimberlites, employing the 40Ar/39Ar method, subject to correction for a partial loss of radiogenic 40Ar when xenolith moves upwards to the Earth’s surface. The obtained data served as the basis for proposing the behaviour model of the K/Ar isotopic system of minerals in conditions of great depths (lower crust, mantle), and when transporting xenoliths in the kimberlite melt.

1. Introduction

The mantle is the Earth’s shell, which is the most extensive in volume. However, we know little about it since the information is not readily accessible. Kimberlite melts, which entrap the material of the lithospheric mantle and ancient cratons while rising to the surface, remain a principal source of information on the Mantle structure and evolution. Currently, kimberlite bodies are found on all continents, where ancient platforms are known. They constitute a heterogeneous mixture of restitic, protomagmatic, xenogenic, and late-magmatic mineral parageneses. Determining the age of intrusion of kimberlites and the age of formation of entrapped by them deep-seated xenoliths is of great importance for tracing the evolution of the kimberlite melt from its origination to the ascent to the Earth’s surface. The economic value of some kimberlite pipes, as motherlodes of diamonds, also increases the importance of age data, allowing diamond prospecting problems to be formulated more clearly.
Dating of kimberlites can be performed based on the U/Pb method for determining age by perovskite, and based on the 40Ar/39Ar and Rb/Sr method for determining age by phlogopite. 40Ar/39Ar dating method is also the most readily available method for acquiring information about the mantle material age. Dating of xenoliths entrapped by kimberlites, can be performed using the 40Ar/39Ar method for determining age by phlogopite, because of phlogopite is quite common in the upper mantle rocks. As compared to the Rb/Sr isochronal method, the 40Ar/39Ar method, according to which only one Potassium-containing mineral phase is required, offers an advantage since it employs the spectrum of ages that makes it possible to reconstruct the thermal history of rocks formed in a complex manner. Reliability of data, obtained using the 40Ar/39Ar method, is usually defined by internal criteria of the method accuracy (isochronal regression, presence of plateaux in the spectrum, etc.) and external: by comparing with geological data, dating results obtained using other isotopic methods. To date, there are numerous works devoted to 40Ar/39Ar dating of phlogopites from kimberlites [1,2,3,4,5,6,7,8,9,10] and others.
In the interpretation of isotopic dating results, the concepts of stability in isotopic systems are of fundamental importance. Research studies of the mechanisms of argon diffusion with an evaluation of kinetic parameters of mobility (activation energy, frequency factor) are based on the experiments on stepped annealing in a vacuum [11,12,13,14,15,16], experiments, where laser heating is used [17,18,19], laboratory hydrothermal experiments.
Conditions for conducting laboratory hydrothermal experiments are selected to be as close to natural ones as possible, ensuring stability in the crystal structure of a mineral. Hodges presents one of the most complete overviews of the results of laboratory experiments on frequently used mineral-geochronometers, including phlogopite [20]. Lee and Aldama [21] offered a model of argon mobility, where both volume diffusion migration through lattice, and short path migration (through linear defects in the mineral structure) are presumed. At temperatures above 800 °С, a volume diffusion mechanism therewith predominates, below 500 °С a short path migration prevails.
It is worthy of note that if in crustal conditions, the effect of pressure on argon mobility, which implies that the P*Va term (P—pressure, Va—activation volume) is added to activation energy Ea, is minor, in conditions of considerable (mantle) depths, it may become significant. Thus, Harrison and co-authors had carried out hydrothermal experiments at high pressure (14 kbar) with biotite [22], muscovite (10 kbar) [23], based on which 14 cm3/mol estimates of activation volume were obtained. This value should lead to substantial changes in argon mobility in the mantle conditions [24].
Closure temperature of the K/Ar isotopic system in phlogopite is known to be about 400 °C [20], while the estimated mantle temperature at around 100 km, at 30 kbar pressure, is ~1000 °C [25,26,27,28], what, at first glance, would seem a problem for potential accumulation of radiogenic 40Ar in the phlogopite structure. However, 40Ar/39Ar examination of phlogopites from deep-seated xenoliths of kimberlites often produces complex age spectra with the values substantially exceeding the age of intrusion of kimberlite pipes [7,9,10,29], which is difficult to explain by the mere effect of pressure on argon mobility at depth. It is common to explain such data by contamination of a mineral-geochronometer with “excess” 40Ar [29,30,31,32].
The problem of retaining argon in the structure of phlogopites at depth and at the temperatures, exceeding closure temperature of the K/Ar isotopic system in phlogopite, was considered in the work of Foland [33]. It has been known that Ar is more soluble in micas as compared to other mantle minerals [33,34,35,36]. Hence, with no other “sinks”, argon will enter the phlogopite structure, rather than a denser lattice of olivine, garnet, pyroxenes. The situation can be considered in terms of the model, suggested by the example of high-pressure metamorphic complexes [37]. Exchange of radiogenic argon between phlogopite and environment occurs through the inter-grain space, characterised by a relatively increased mobility of argon and limited capacity. Argon migrates towards the nearest potential “sinks”. In the mantle, only adjacent phlogopite grains represent such “sinks”. In this case, radiogenic argon is efficiently accumulated in phlogopite grains, which provides a way of acquiring geologically significant 40Ar/39Ar dating results for phlogopites from xenoliths of kimberlites [38]. Radiogenic argon therewith is accumulated in phlogopite in line with the radioactive decay equation minus the percentage of argon, remaining within the inter-grain space. Taking the above-said into account, migration of radiogenic 40Ar from phlogopite is defined by the ratio between the inter-grain space volume and the phlogopite volume.
Our article attempts to comprehend the phlogopite capability for accumulating radiogenic 40Ar at great (mantle) depths in conditions of high T-P, utilizing two approaches: (a) 40Ar/39Ar examination of phlogopites of mantle origin from diamond-containing kimberlite pipes; (b) high-pressure laboratory experiments, conducted to identify the mechanisms controlling the mobility of argon isotopes at high T-P; (c) numerical simulation of migration of argon isotopes at high T-P based on the regularities, established in laboratory experiments, and the above-suggested model; comparison between the obtained results and 40Ar/39Ar dating of phlogopites from deep-seated xenoliths.

2. Laboratory Experiment

Morphology, composition, and structural features of phlogopites from xenoliths of kimberlites, and phlogopites prior to and after high-pressure experiments were examined in the Centre of shared use of research equipment for multi-component and isotope studies of the Siberian Branch of the Russian Academy of Sciences (SB RAS MIS RE CSU) with the use of scanning electronic microscopy (electronic microscope MIRA3 with the system of microanalysis, TESCAN, Brno, the Czech Republic), electron probe microanalysis with electron probe (microanalyzer JXA-8100, JEOL, Tokyo, Japan), infrared spectroscopy (Fourier-spectrometer VERTEX 70 FT IR of the Bruker corporation, Karlsruhe, Germany) and X-ray structure analysis (X-ray diffractometer DRON-4, Joint Stock Company «Bourevestnik», Sankt-Petersberg, Russia).
Isotopic composition of argon of phlogopites from xenoliths of kimberlites, and phlogopites prior to and after high-pressure laboratory experiments was measured in SB RAS MIS RE CSU. Weighed amount of phlogopites together with weighed amount of biotite MSA-11 (DSS No.129-88), used as a monitor, were wrapped in the aluminium foil, placed into a quartz vessel and were sealed up after pumping air therefrom. Biotite MSA-11, prepared by the All-Russian scientific-research institute of mineral resources named after N.M. Fedorovsky in 1988 as a standard K/Ar specimen, was certified as the 40Ar/39Ar monitor using international standard specimens of muscovite Bern 4m, biotite LP-6 [39]. The mean value of calibration results, amounting to 311.0 ± 1.5 Ma, is assumed to be the integral age of biotite MSA-11. The procedure is noteworthy for the exposure of quartz vessels with specimens to radiation in a water-cooled channel of the research reactor facility at the Tomsk State Polytechnic University (Tomsk). With exposure to radiation in such conditions, vessels with specimens are heated to not more than 100 °C. Gradient of neutron current did not surpass 0.5% in the specimen size. Stepped heating experiments were conducted in a quartz reactor with external heat-up furnace. 40Ar blank run (10min at 1200 °С) provided results not exceeding 5 × 10−10 cm3 STP. ZrAl SAES-getters were employed to clean argon. Isotopic composition of argon was measured by multi-collector mass-spectrometer Argus of the GV-Instruments company (England).
The high-pressure experiments were performed using a multi-anvil apparatus of “split sphere” type (BARS) at V.S. Sobolev Institute of Geology and Mineralogy of the Siberian Branch of Russian Academy of Sciences. The studies employed high-pressure cell (HPC) made of the mixture of refractory oxides ZrO2 and СаО [40]. HPC is a prism 23 mm high, 20.5 mm wide with truncated edges. Parallel to the 4th order axis, there is an opening, into which a heater is inserted. HPC heating system is comprised of a cylinder-shaped thin-walled graphite heater, graphite covers installed along heater edges, Мo- disks, Мo- current leads. A bushing made of MgO with the examined specimen was mounted immediately in the graphite heater. Reaction volume was assembled as follows: cut bands of two phlogopites at different ages were placed into the platinum capsule (capsule sizes: outside/inside diameter 6/5 mm, height 10 mm), then the capsule was closed with a platinum cover and mounted in the MgO bushing. The bushing faces were closed with pellets, fabricated from MgO as well. Accuracy of measuring temperature in the experiments amounted to ±25 °С, pressure-±0.2 GPa. Specimens were cooled by quenching, namely, cutting-off the heater current with no pressure release. Quenching time was 2–3 s. Pressure was determined by calibration curve, constructed at the room temperature according to transitions between phases in PbSe and Bi standard substances. Temperature was estimated by calibration curve, expressing the dependence of the heater current power on PtRh 30/6 thermocouple readings. Further details of the experimental procedures are described in [41,42].

3. Results

3.1. Results of 40Ar/39Ar Dating of Phlogopite of the Mantle Xenoliths

Four mantle xenoliths of pyroxenites from diamond-bearing kimberlite Mir and Udachnaya–Vostochnaya pipes were selected for examination. The estimated age of pipes intrusion is 360−382 Ma [29,43,44]. Phlogopite therein is represented by large plates (M4/01—1−1.5 mm; M5/01—up to 3 mm; M31/01—up to 1 mm; UV300/09—up to 6 mm), fills micro-cracks up to 1mm thick and exists in the form of fine grains (50−200 µm) in reaction garnet rims (Figure 1). According to [45], large plates of phlogopite in xenoliths of pyroxenites are in a structural equilibrium condition with respect to other minerals of these rocks. Chemical composition of such phlogopites is in compliance with primarily metasomatic origin. They are considered to be associated with the processes of ancient enrichment of the continental lithosphere [46]. Within the Siberian craton, several stages of mantle metasomatism [47,48] are evident. One of the earliest stages had developed in the slowly cooled Archaean lithosphere due to ingress of metasomatic potassium-, REE- and phosphorus-rich fluids. Among minerals, there are phlogopite, sulphides, Cr-spinel, apatite, graphite. One of late-stage metasomatic events is considered as a treatment of the continental lithospheric mantle with oxidized astenospheric fluids, prior to developing kimberlite seats in the upper mantle. Reaction rims around pyroxenes and garnet seem to appear at this stage.
For 40Ar/39Ar dating, there had been selected large plates of a uniformly composed phlogopite, that correspond to the early metasomatic stage (Figure 1). There had been obtained age spectra (Table 1, Figure 2), in which, after moving upwards in the low-temperature section, either mini-plateau of two stages (specimens M-04/01, UV-300/09), or individual stages are seen with extremely high age values, which for specimens M4/01, M5/01 and UV300/09 amounted to 2568 ± 18, 2430 ± 17 and 2336 ± 16 Ma, respectively (Figure 2). The age spectrum of phlogopite М31/01 in a high-temperature section has a prominent mini-plateau aged 2288 ± 16 Ma. These age estimates correspond to the estimates of time, when the material from the mantle entered the crust of superposed fold belts of microcontinents (2.5−2.3 billion years) [49], that subsequently became the parts of the Siberian craton; they are in line with reformation processes in the mantle, and are likely to indicate the time of a major metasomatic event.
Thus, it can be inferred that despite being in the high-temperature mantle conditions for a long time, and being transported later to the surface in the kimberlite melt, the K/Ar isotopic system of phlogopite from xenoliths of pyroxenites retained all accumulated radiogenic (or excess) 40Ar corrected for 40Ar released due to volume diffusion.
When selecting the conditions for experimental modelling of phlogopite’s staying in the mantle conditions, to identify the mechanisms that regulate mobility of argon isotopes, the authors were guided by the estimates of PT parameters of forming deep-seated xenoliths, from which the examined phlogopite was chosen (Table 2). Laboratory experiments were carried out, utilising two types of phlogopite—aged 8.5 Ma from the Kuhi-Lal field (Tajikistan, SW Pamir) rocks and aged 1872 Ma from magnesial skarns of the Aldanian shield. Bands of variously aged phlogopites were packed together so as not only to study the losses of radiogenic argon in the mineral lattice, but also to verify the potential for its migration from one mineral to another. There were four conducted experiments (T = 800, 850, 900 and 1000 °C) at 3 GPa pressure and 2 h long, and four laboratory experiments (T = 700, 800, 900 and 1000 °C) at 3 GPa pressure, 72 h long.

3.2. Morphology, Composition, and Structural Features of Phlogopites Prior to and after Laboratory Experiments

Phlogopites from magnesial skarns of the Aldanian shield and Kuhi-Lal field (Tajikistan, SW Pamir) have a homogeneous chemical composition and contain no inclusions (Table 3, Figure 3). Phlogopite from the Aldanian shield skarns contains (% wt): FeO~6, Na2O~0.3, MnO~0.1, TiO2~0.6, BaO~0.6, F—1.2−1.5, Cl~0.2. Phlogopite from skarns of the Kuhi-Lal field contains almost no FeO (<0.06% wt) and is characterised by the presence of the following admixtures (% wt): Na2O~1.3, TiO2~0.7, BaO~0.1; the content of F and Cl therein is ~1.3 and ~0.05% wt, respectively (Table 3).
According to the results of SEM-observations, no changes in the morphology of phlogopites heat-treated at high pressures were detected, particularly, no signs of recrystallisation, solid-phase transformations, or melting were noticed (Figure 3). No significant differences in amounts of components in compositions of original and heat-treated phlogopites were identified that would indirectly indicate that a mineral had lost water while being heat-treated. No other significant differences in compositions of original and heated phlogopites were found (Table 3) as well.
The parameters of cells of phlogopites, heat-treated at high pressures, in general, alter slightly as compared to those of the original mica (except for specimens, heat-treated at 700 °С) (Table 4). This indicates that high-pressure heating led to no meaningful transformations in the structure of phlogopites (deformities and rotations of tetrahedral and octahedral polyhedrons, reduction of interlayer space [52,53,54,55]).
To assess the degree of dihydroxylation in phlogopites from the first series of laboratory experiments (2 h long each), the Raman spectroscopy method was employed. A 3600−3780 cm−1 area of the Raman spectra of original phlogopites and all phlogopites, heat-treated at high pressures and temperatures, contains lines, conforming to vibrations in OH-groups. The intensities of these lines in the Raman spectra of original and heat-treated phlogopites are similar (Figure 4A,B). It can be inferred from these data that, at high-pressure 2 h long heating, dihydroxylation in phlogopites was minor.
To assess the degree of dihydroxylation in phlogopites from the second series of experiments (72 h), an infrared-spectroscopy method was used. IR-spectra of heat-treated specimens are similar to the spectra of original phlogopite specimens. IR-spectra of original micas within~3630−3780 cm−1 spectral range have two peaks of various intensity, that correspond to vibrations of hydroxyl ion, coordinated with di- and trivalent cations. IR-spectra of heat-treated phlogopites within this range have changes in the form and intensity of bands, that correspond to vibrations of MgFe2+R3+MgOH links. More intense transformations—dihydroxylation (perhaps, due to Fe2+ oxidation)—are seen in the phlogopite from skarns of the Aldanian shield (Figure 4D). Phlogopite from Kuhi-Lal field (Tajikistan), almost without iron, underwent smaller changes (Figure 4C).
The results of 40Ar/39Ar dating of phlogopite specimens prior to and after laboratory experiments are given in Table 5, in Figure 5. If standard plateaux with respective age values are seen in the spectra of original phlogopites, then as the intensity of influence increases, on one hand, measured values in the “Tadjik” phlogopite spectra raise, on the other hand, rejuvenation in the “Aldanian” phlogopite spectra takes place (Figure 5). Hence, it can be concluded that even in “close-to-real” laboratory conditions, there is an efficient mechanism of introducing radiogenic argon, released from the ancient phlogopite lattice, into the structure of younger phlogopite. It supports the assumption we have previously made that a mechanism exists for the effective exchange of radiogenic argon between phlogopite grains in the mantle conditions. On the other hand, due to a substantially higher concentration of radiogenic argon in the ancient phlogopite, the measured kinetics of its releasing can be utilised to estimate the parameters of argon diffusion in the mineral lattice.
Figure 6 presents the Arrhenius diagram, obtained from the results of laboratory experiments. Resultant experimental points correspond well with the theoretical line for argon diffusion at 30 kbar pressure.
Our experimental data: Green—laboratory experiment duration 2 h and pressure 3 GPa; Red—laboratory experiment: duration 72 h and pressure 3 GPa; the dotted line is designed for a pressure of 30 kbar taking into account the known kinetic parameters of the phlogopite [23] and is characterized by DO = 0.75 cm2/sec and Ea = 284,672 J/mol for 3 GPa (activation volume—14 cm3/mol [23]).

4. Numerical Simulation

Numerical simulation of the K/Ar isotopic system behaviour in phlogopite was based on argon mobility, described by the law of “volume thermally activated diffusion”. Kinetic parameters of argon mobility in phlogopite: activation energy—242672 J/mol, pre-exponential factor—7.5e−5 m2/sec, diffusion domain size—150 µm, activation volume—14 cm3/mol [22,56,57,58,59].
When modelling the K/Ar isotopic system behaviour, a change in the content of radiogenic argon in the mineral lattice is considered, defined by the superposition of two factors: accumulation of 40Ar due to radioactive 40K decay and argon diffusion as per the second Fick’s law. The general form of the obtained diffusion equation is as follows:
d C A r ( r → , t ) d t = ∇ ⋅ ( D ( r , P , T ( t ) ) ∇ C A r ( r → , t ) ) − d C K ( t ) d t
where C A r ( r → , t ) —distribution of radiogenic argon isotope distribution, D—diffusion coefficient, CK(t)—distribution of potassium concentration in mineral grains, defined by the law of radioactive decay: C K ( t ) = C K 0 e − λ t .
Diffusion coefficient depends on both temperature, and pressure according to the Arrhenius law: D ( P , T ) = D 0 e − E a + P V a R T ,
where D0—pre-exponential factor, Ea—activation energy, P—ambient pressure, Va—activation volume, R—universal gas constant, T—temperature.
Since phlogopite has a cylindrical symmetry, it seems logical to convert the equation to cylindrical coordinate system. At the grain–inter-grain space interface, there is a jump in the diffusion coefficient from D in the grain to some effective value of diffusion coefficient Deff in the inter-grain space. As Deff >> D, argon rapidly propagates throughout the inter-grain space. Equation (1) will take the form:
d C A r ( r , t ) d t = D ( r , P , T ( t ) ) ( d 2 C A r ( r , t ) d r 2 + 1 r d C A r ( r , t ) d r ) + d D ( r , P , T ( t ) ) d r d C A r ( r , t ) d r + λ C K 0 e − λ t
When diffusion coefficient changes stepwise, term d D ( r , P , T ( t ) ) d r d C A r ( r , t ) d r is a boundary condition of the 3rd type for the grain–inter-grain space interface, i.e., this condition will be taken into account automatically when solving differential Equation (2), and it need not be further introduced.
To construct a numerical algorithm for solving Equation (2), Euler’s method was employed. The algorithm was implemented using a package of MatLab mathematical programs (MATLAB 7).
We used Equation (2), with specifying respective initial and boundary conditions, both in numerical simulation of the evolution of the K/Ar isotopic system of phlogopite in conditions of a high-pressure laboratory experiment, and in numerical calculations of the model, describing the evolution of the K/Ar isotopic system of phlogopite from its origination at depth to transporting to the earth’s surface by the kimberlite melt.
Work [60] presents the MacArgon software programme for Apple Macintosh to model the effect of P-T-t history on the diffusion of argon in minerals.

5. Discussion

The results of numerical simulation of the behaviour observed in the K/Ar isotopic system of phlogopite in various conditions of the laboratory experiment are given in Figure 7. Comparing them with the experimental data of 40Ar/39Ar dating of phlogopites prior to and after high-pressure laboratory heating (Table 5, Figure 7b,c) provides a good fit within the limits of error for all experiments, except for one—3 GPa, 1000 °С, 72 h. In the last experiment, 340 Ma rejuvenation of the K/Ar isotopic system of phlogopite was achieved, which is markedly higher than the numeric estimate of the loss. Conceivably, this is because of a large degree of dihydroxylation in phlogopite in the course of this laboratory experiment, which is also proved by the IR-spectroscopy data (Figure 4D). Reconciliation of the numerical simulation data with the laboratory experiment data enables the conclusion to the drawn that the mechanism of the mobility of radiogenic argon in phlogopite lattice—volume diffusion, incorporated into the numerical simulation, is justified.
It can be seen that even considering the addition to the energy of argon diffusion activation, associated with pressure at depth, several hours of heating suffice for a considerable loss of radiogenic argon at temperatures exceeding 850 °С. This is in conflict with the fact that the K/Ar isotopic system of phlogopite from deep-seated xenoliths М-31/01 (formation temperature ~890 °С, Table 2), UV-300/09 (formation temperature ~895 °С, Table 2), despite their long (at least 2 billion years) exposure in the mantle conditions, retained the memory of their formation age. Apparently, this phenomenon is explained by constrained sinks for radiogenic argon from phlogopite in the mantle conditions.
In view of the above-said, when describing the evolution of the K/Ar isotopic system of phlogopite, from its origination at depth in the mantle conditions to transporting it to the Earth’s surface in the kimberlite melt, applying numerical simulation, we considered three stages and assumed boundary conditions, according to the phlogopite position:
Stage 1. The grain is a part of a deep-seated block of rocks. The value of temperature and pressure is assumed to be in line with estimates, obtained for each examined xenolith (Table 2). It is supposed that the grain exchanges argon with other grains through the inter-grain space, which leads to the accumulation of some amount of radiogenic argon in the inter-grain space. Hence, suppose that, around the grain, some area in the space exists, where the total flow of argon from adjacent grains becomes equal to the counter flow from the grain itself, i.e., a boundary is formed, at which the total flow of argon is zero. Then, based on the first Fick’s law: q = − D ∇ → C (the flow rate is directly proportional to the diffusion coefficient and negative gradient)—we obtain that the concentration gradient of radiogenic argon at the interface of computation area is zero.
Stage 2. Xenolith with phlogopite is in the kimberlite melt (due to the small sizes of xenolith with respect to the original rock). We have a zero boundary condition to retain argon at the interface of phlogopite grain, computation area therewith reduces the diffusion domain sizes. The kimberlite melt temperature is assumed to be 1000 °C [26]. Pressure changes linearly, from the value obtained by mineral geobarometer for each examined xenolith, to 0.0001 GPa in the Earth’s surface.
Stage 3. After the kimberlite body had been formed on the surface, the phlogopite temperature is lower than the closure temperature of its K/Ar isotopic system. Radiogenic 40Ar is accumulated due to 40K radioactive decay.
Comparison between numerical simulation results and results of 40Ar/39Ar dating for phlogopites from deep-seated xenoliths
Phlogopite loses 40Ar in the considered model only at the 2nd stage, namely, during the xenolith ascent in the kimberlite melt to the surface. At the 1st and 3rd stages, the mere accumulation of radiogenic 40Ar takes place according to the law of radioactive decay.
A typical shape in the 40Ar/39Ar age spectrum in the form of an “up staircase” is an indicator of the partial loss of radiogenic 40Ar for specimens of phlogopites from deep-seated xenoliths (Table 1, Figure 2). In terms of quantity, the degree of 40Ar loss is estimated based on the difference in Ma between the age value of the highest temperature step in the age spectrum (the closest to the initial age) and integral age. For instance, for specimen M05/01 this difference is 75.9 Ma, for UV300/09—215 Ma. It can be noted that this value correlates well with PT-estimates for the analysed xenoliths (Table 2). The greater the depth, from which xenolith with phlogopite came, the greater the loss of radiogenic argon.
Figure 8 presents a model dependence of the calculated degree of radiogenic 40Ar loss by phlogopite on the ascent rate of xenolith in the kimberlite melt. For each xenolith, ascent had started from the depth of its formation, depending on the estimate of pressure in a state of the last equilibrium (Table 2). An option of rising at a constant rate was considered. The slower the rate, the longer the time for rock heating at the melt temperature (~1000 °С) and, respectively, the greater the loss of radiogenic 40Ar. An optimum ascent rate (Figure 8) was estimated from the intersection of the model value and the value, calculated according to the age 40Ar/39Ar spectrum of phlogopite, of the loss for each specimen. It can be seen that the obtained estimates of the kimberlite melt ascent rate (Figure 9) agree with one another for the two deep-seated xenoliths of the Mir pipe, and xenolith of the Udachnaya–Vostochnaya pipe. For xenolith M-05/01 of the Mir pipe from the depth of 66 km, a minimum loss of radiogenic 40Ar was observed. This is quite likely to be the reason for a greater error in computing the ascent rate. On the other hand, a relatively inflated estimate for a xenolith from the shallowest depth can be associated with an increase in the melt ascent rate in the upper part of the continental crust, when overburden pressure falls. The weighted average of the rate of the kimberlite melt ascent for all the examined xenoliths is 16 ± 3 km/h.

6. Conclusions

Based on 40Ar/39Ar dating of phlogopite of mantle xenoliths of pyroxenites from diamond-bearing kimberlite Mir and Udachnaya–Vostochnaya pipes, we obtained the estimates of age within 2568-2288 Ma, corresponding to the stage of early mantle metasomatism within the Siberian craton.
Laboratory experiments using phlogopite from magnesial skarns of the Aldanian shield (1872 Ma age) and Kuhi-Lal (Tajikistan, SW Pamir, 8.5 Ma age) and numerical simulation show that in conditions of increased P-T, the mobility of argon in the phlogopite lattice is in line with the concept of volume diffusion, and that, even in dry conditions, there is an efficient mechanism of exchange of radiogenic argon, released from the lattice of ancient phlogopite, with the structure of younger phlogopite. Thus, the survival of the mantle phlogopite isotopic system of metasomatic origin can be related to a limited volume of sinks for radiogenic 40Ar, existing at depth.
The losses of radiogenic argon in phlogopite, when xenoliths of Mir, Udachnaya–Vostochnaya pipes rise to the surface in the kimberlite melt (temperature ~1000 °С), obtained through numeric simulation, and estimates of melting rate correlate with one another; the mean rate is 16 ± 3 km/h.

Author Contributions

D.Y. organized and coordinated experimental, 40Ar/39Ar studies, participated in the interpretation of the results and preparation of the article. N.M. conducted numerical simulations and participated in 40Ar/39Ar Dating. T.A. conducted selection, preparation, and research of a collection of deep xenoliths from kimberlite pipes. A.T. participated in 40Ar/39Ar Dating, interpretation of results, and preparation of the article. E.Z. conducted laboratory experiments with phlogopite under high P-T conditions. S.N. participated in the study of phlogopite samples before and after laboratory experiments. All authors have read and agreed to the published version of the manuscript.

Funding

The study was carried out within the framework of a State Assignment of Sobolev Institute of Geology and Mineralogy, Siberian Branch, Russian Academy of Sciences, Novosibirsk, under support of the Ministry of Science and Education of the Russian Federation, project no. 14.Y26.31.0012, and supported by the Russian Foundation for Basic Research no. 18-05-00211.

Acknowledgments

The authors are grateful to Alexey Ivanov for providing the Aldan phlogopite for laboratory research, and to Tatyana Smirnova for providing the phlogopite from the rocks of the Kuhi-Lal Deposit. Authors express sincere appreciation to Ludmila Pokhilenko for providing xenolith samples from Mir kimberlite, for her valuable comments and for a joint work on the earlier stages of this study.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Morphology of the phlogopite from the studied xenoliths. Cpx—clinopyroxene, Grt—garnet, Ol—olivine, Phl—phlogopite.
Figure 1. Morphology of the phlogopite from the studied xenoliths. Cpx—clinopyroxene, Grt—garnet, Ol—olivine, Phl—phlogopite.
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Figure 2. 40Ar/39Ar age spectra obtained for phlogopites from deep xenoliths of the Mir (Samples M4/01, M5/01, M31/01) and Udachnaya–Vostochnaya (Sample UV300/09) kimberlite pipes.
Figure 2. 40Ar/39Ar age spectra obtained for phlogopites from deep xenoliths of the Mir (Samples M4/01, M5/01, M31/01) and Udachnaya–Vostochnaya (Sample UV300/09) kimberlite pipes.
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Figure 3. Morphology of original and heat-treated at high temperatures and pressures phlogopites (3 GPa) (BSE-photo, polished compounds). T—phlogopite from Tajikistan skarns, A—phlogopite from skarns of the Aldanian shield; (a,b)original specimens; (c–i)heat-treated specimens. Sp. 4-30-18—specimen, heat-treated at the temperature of 1000 °С during 72 h; sp. 4-35-18—specimen, heat-treated at the temperature of 800 °С during 72 h; sp. 4-33-18—specimen, heat-treated at the temperature of 900ºС during 72 h; sp. 2-10-15—specimen, heat-treated at the temperature of 850 °С during 2 h; sp. 2-7-15—specimen, heat-treated at the temperature of 1000 °С during 2 h.
Figure 3. Morphology of original and heat-treated at high temperatures and pressures phlogopites (3 GPa) (BSE-photo, polished compounds). T—phlogopite from Tajikistan skarns, A—phlogopite from skarns of the Aldanian shield; (a,b)original specimens; (c–i)heat-treated specimens. Sp. 4-30-18—specimen, heat-treated at the temperature of 1000 °С during 72 h; sp. 4-35-18—specimen, heat-treated at the temperature of 800 °С during 72 h; sp. 4-33-18—specimen, heat-treated at the temperature of 900ºС during 72 h; sp. 2-10-15—specimen, heat-treated at the temperature of 850 °С during 2 h; sp. 2-7-15—specimen, heat-treated at the temperature of 1000 °С during 2 h.
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Figure 4. Raman spectra (R) and IR-spectra (A) Raman spectra of original and heat-treated at high temperatures and pressure of 3 GPa phlogopites in the area of stretching vibrations of OH-groups (phlogopite from the Aldanian shield rocks): 1—original specimen; 2—specimen, heat-treated at Т = 850 °С, 2 h; 3—specimen, heat-treated at Т = 1000 °С, 2 h.(B). Raman spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of OH-groups (phlogopite from the Kuhi-Lal field rocks (Tajikistan)): 1—original specimen; 2—specimen, heat-treated at Т = 850 °С, 2 h; 3—specimen, heat-treated at Т = 1000 °С, 2 h.(C). Fragments of IR-spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of ОН groups (phlogopite from the Kuhi-Lal field rocks (Tajikistan, SW Pamir)): 1—original specimen; 2—specimen, heat-treated at Т = 700 °С, 72 h; 3—specimen, heat-treated at Т = 800 °С, 72 h; 4—specimen, heat-treated at Т = 900 °С, 72 h; 5—specimen, heat-treated at Т = 1000 °С, 72 h.(D). Fragments of IR-spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of ОН groups (phlogopite from magnesial skarns of the Aldanian shield): 1—original specimen; 2—specimen, heat-treated at Т = 800 °С, 72 h; 3—specimen, heat-treated at Т = 900 °С, 72 h; 4—specimen, heat-treated at Т = 1000 °С, 72 h.
Figure 4. Raman spectra (R) and IR-spectra (A) Raman spectra of original and heat-treated at high temperatures and pressure of 3 GPa phlogopites in the area of stretching vibrations of OH-groups (phlogopite from the Aldanian shield rocks): 1—original specimen; 2—specimen, heat-treated at Т = 850 °С, 2 h; 3—specimen, heat-treated at Т = 1000 °С, 2 h.(B). Raman spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of OH-groups (phlogopite from the Kuhi-Lal field rocks (Tajikistan)): 1—original specimen; 2—specimen, heat-treated at Т = 850 °С, 2 h; 3—specimen, heat-treated at Т = 1000 °С, 2 h.(C). Fragments of IR-spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of ОН groups (phlogopite from the Kuhi-Lal field rocks (Tajikistan, SW Pamir)): 1—original specimen; 2—specimen, heat-treated at Т = 700 °С, 72 h; 3—specimen, heat-treated at Т = 800 °С, 72 h; 4—specimen, heat-treated at Т = 900 °С, 72 h; 5—specimen, heat-treated at Т = 1000 °С, 72 h.(D). Fragments of IR-spectra of original and heat-treated at high temperatures and pressure 3 GPa phlogopites in the area of stretching vibrations of ОН groups (phlogopite from magnesial skarns of the Aldanian shield): 1—original specimen; 2—specimen, heat-treated at Т = 800 °С, 72 h; 3—specimen, heat-treated at Т = 900 °С, 72 h; 4—specimen, heat-treated at Т = 1000 °С, 72 h.
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Figure 5. 40Ar/39Ar age spectra obtained by phlogopite (a) from the Aldanian shield rocks, (b) from the Kuhi-Lal field (Tajikistan) original and heat-treated at high temperatures and 3 GPa pressure. Parameters of the experiment and the values of integral age (TFA) are written in the figure. OS—original specimen.
Figure 5. 40Ar/39Ar age spectra obtained by phlogopite (a) from the Aldanian shield rocks, (b) from the Kuhi-Lal field (Tajikistan) original and heat-treated at high temperatures and 3 GPa pressure. Parameters of the experiment and the values of integral age (TFA) are written in the figure. OS—original specimen.
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Figure 6. Arrhenius plot for radiogenic argon diffusion in phlogopite mica. Open circles and line are for data reported in [56] where all data are for 2 kbar water pressure except at 900 °C where they are for 1 kbar. Line has DO = 0.75 cm2/s and Ea = 242,672 J/mol. The two squares at 900 °C and 1080 °C are for runs at 15 kbar water pressure. The solid triangle at 550 °C was for a 1 bar water pressure run.
Figure 6. Arrhenius plot for radiogenic argon diffusion in phlogopite mica. Open circles and line are for data reported in [56] where all data are for 2 kbar water pressure except at 900 °C where they are for 1 kbar. Line has DO = 0.75 cm2/s and Ea = 242,672 J/mol. The two squares at 900 °C and 1080 °C are for runs at 15 kbar water pressure. The solid triangle at 550 °C was for a 1 bar water pressure run.
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Figure 7. (a) Result of numerical modelling of evolution of the K/Ar isotopic system of phlogopite from magnesial skarns of the Aldanian shield (with 1902 Ma initial age) depending on conditions of the laboratory experiment (temperature and duration) at 3 GPa pressure. Rejuvenation degree of the isotopic system of phlogopite corresponds to the value in million years, by which its integral age decreased in the course of the experiment. Comparison between the results of laboratory experiments 2 h (b) and 72 h (c) long and the numerical simulation results.
Figure 7. (a) Result of numerical modelling of evolution of the K/Ar isotopic system of phlogopite from magnesial skarns of the Aldanian shield (with 1902 Ma initial age) depending on conditions of the laboratory experiment (temperature and duration) at 3 GPa pressure. Rejuvenation degree of the isotopic system of phlogopite corresponds to the value in million years, by which its integral age decreased in the course of the experiment. Comparison between the results of laboratory experiments 2 h (b) and 72 h (c) long and the numerical simulation results.
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Figure 8. Result of numerical modelling of evolution of the K/Ar isotopic system of phlogopites from deep-seated xenoliths of kimberlite Mir (a) М5/01, (b) М4/01, (c) М31/01 and Udachnaya–Vostochnaya (d) UV300/09 pipes when rising to the Earth’s surface.
Figure 8. Result of numerical modelling of evolution of the K/Ar isotopic system of phlogopites from deep-seated xenoliths of kimberlite Mir (a) М5/01, (b) М4/01, (c) М31/01 and Udachnaya–Vostochnaya (d) UV300/09 pipes when rising to the Earth’s surface.
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Figure 9. Estimate of the ascent rate of xenoliths in the kimberlite melt, based on the degree of radiogenic 40Ar loss by phlogopite. Red colour—Mir pipe, blue colour—Udachnaya–Vostochnaya pipe.
Figure 9. Estimate of the ascent rate of xenoliths in the kimberlite melt, based on the degree of radiogenic 40Ar loss by phlogopite. Red colour—Mir pipe, blue colour—Udachnaya–Vostochnaya pipe.
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Table
Table 1. Results of 40Ar/39Ar dating of phlogopite samples from deep xenoliths of the Mir (Samples M4/01, M5/01, M31/01) and the Udachnaya–Vostochnaya (Sample UV300/09) kimberlite pipes.
Table 1. Results of 40Ar/39Ar dating of phlogopite samples from deep xenoliths of the Mir (Samples M4/01, M5/01, M31/01) and the Udachnaya–Vostochnaya (Sample UV300/09) kimberlite pipes.
T0Ct (min)40Ar, 10−9 cm3 STP40Ar/39Ar±1σ38Ar/39Ar±1σ37Ar/39Ar±1σ36Ar/39Ar±1σCa/K∑39Ar
(%)		Age, Ma±1σ
М4/01 phlogopite (0.89 mg), J = 0.00465 ± 0.000057; Total Fusion Age (TFA) = 2404 ± 17 Ma
500103.56257.2633.760.00610.04990.5000.66060.67200.11881.7981.0435.4163.3
7501047.03351.063.460.07290.00860.1860.10200.19830.00890.66911.11549.118.7
90010123.05590.642.840.03300.00590.0800.05590.03840.00460.28626.82357.317.6
100010135.97627.211.910.01080.00210.1080.02160.04530.00370.38943.12434.117.0
107010127.95657.523.850.04750.00690.07010.03420.09620.008670.25257.72467.019.1
110010270.49692.552.760.01940.00390.04340.01760.03490.002020.15687.12577.117.7
11306117.06682.018.240.04980.00590.00120.04560.03970.00630.00431002553.023.8
М5/01 phlogopite (0.74 mg), J = 0.00463 ± 0.000056; TFA = 2354 ± 17 Ma
6501015.80406.6913.000.08160.01700.4500.22230.10600.03231.6205.11817.148.7
8001061.34567.224.480.00180.01220.0910.05770.03200.01500.32619.32302.121.4
9001075.90592.184.020.02820.01010.2090.05520.09810.00510.75336.22314.718.4
10001067.17608.567.210.04840.01360.0820.08380.10390.01210.29650.72348.423.6
11306240.21639.592.360.040.00280.1150.02650.08490.00290.4131002429.817.0
М31/01 phlogopite (12.84 mg), J = 0.004611 ± 0.000056; TFA = 2099 ± 15 Ma
500109.65232.229.020.17780.02980.8160.06410.48490.03982.9360.2619.964.7
6001019.83349.9412.300.18360.02332.4770.11710.58460.02828.9170.51077.339.9
7001047.46298.511.590.06010.00890.4050.02220.14280.00831.4591.31407.516.0
80010207.15338.190.920.03660.00360.0260.01630.08190.00150.0924.51615.013.4
90010653.33341.990.420.02950.000940.00820.00420.05540.001080.029614.31654.113.3
95010725.87387.250.390.02820.000860.01970.00450.05640.000810.07123.91797.713.9
98010851.55484.190.430.03110.00140.00490.00370.060.001050.017833.02070.515.0
100010766.97518.620.460.03170.000810.00910.00250.07710.000680.032840.62146.415.3
102010681.26539.220.460.02770.000280.01440.00660.07430.000770.051947.12199.915.5
1040101195.4543.760.820.03260.000590.00320.00400.08140.00110.011458.42205.915.6
1050102196.2564.540.830.0380.000730.00790.00450.12010.001290.028578.42228.615.7
105010349.27572.961.660.03180.00340.0170.01240.07880.003340.061281.52277.816.3
106010925.45576.190.570.03360.000580.00060.00360.07290.001030.002389.82289.515.8
107010762.07582.610.780.03360.00140.01130.00450.08490.001590.040696.52296.215.9
108010304.65556.591.320.03370.0030.04370.01110.09810.001720.157499.32225.115.9
11001069.209518.247.0380.05090.00820.05230.02190.09350.006880.18831002133.223.3
УВ300/09 phlogopite (1.19 mg), J = 0.004571 ± 0.000055; TFA = 2122 ± 15 Ma
500105.77359.817.370.23940.05360.2670.87660.53480.09220.9610.91179.0117.9
7001020.14138.781.700.01770.01050.1650.04870.01930.00810.5929.1857.317.0
8501038.93231.021.710.03460.00450.0950.06800.04490.00820.34418.71246.316.2
97510120.08477.961.580.04330.00720.0570.03820.05490.00440.20732.92047.315.7
105010142.64586.773.280.04130.00720.0350.03110.04430.00230.12546.72322.017.4
11306558.17593.081.0020.02330.001290.0210.00880.02650.000980.0751002348.216.0
Table
Table 2. Types of rocks and estimates of temperatures and pressures of the last equilibrium for phlogopite-containing xenoliths from kimberlite Mir (М4/01, М5/01, М31/01) and Udachnaya–Vostochnaya (UV300/09) pipes.
Table 2. Types of rocks and estimates of temperatures and pressures of the last equilibrium for phlogopite-containing xenoliths from kimberlite Mir (М4/01, М5/01, М31/01) and Udachnaya–Vostochnaya (UV300/09) pipes.
SampleRockT, °CP, GPa
M4/01spinel-garnet olivine websterite560 *2.8 *
M5/01garnet websterite690 **2.0 **
M31/01garnet olivine websterite890 **4.3 **
УВ300/09garnet-olivine clinopyroxenite895 *3.7 *
Note: PT-parameters are computed according to [50] (*), [51] (**).
Table
Table 3. Representative microprobe analyses (wt %) of phlogopites from magnesian skarns of the Aldan shield (A) and Kuhi-Lal field (Tajikistan, SW Pamir, T), original and heat-treated at 3 GPa pressure.
Table 3. Representative microprobe analyses (wt %) of phlogopites from magnesian skarns of the Aldan shield (A) and Kuhi-Lal field (Tajikistan, SW Pamir, T), original and heat-treated at 3 GPa pressure.
No. of SpecimenА 800 °С, 2 hА 850 °С, 2 hА 1000 °С, 2 hАА 700 °С, 72 hА 800 °С, 72 hА 900 °С, 72 hА 1000 °С, 72 h
SiO237.7437.9738.0338.3137.8438.3937.9638.12
TiO20.620.600.610.590.590.630.620.60
Cr2O3bdlbdlbdlbdlbdlbdlbdlbdl
Al2O316.7116.6217.1416.4816.6316.8016.7216.50
FeO6.106.016.075.966.106.306.056.22
MnO0.060.070.070.050.060.060.070.07
MgO22.5022.3722.7622.8822.8023.1222.8922.62
CaO0.030.06bdlbdlbdlbdlbdlbdl
BaO0.590.630.470.620.720.550.660.68
Na2O0.280.330.290.340.310.360.330.33
K2O9.9410.0610.139.589.899.889.929.70
RbO0.03bdlbdlbdlbdlbdlbdlbdl
F1.351.341.381.191.481.391.401.38
Cl0.190.220.200.220.190.170.200.20
Total95.5395.6796.5295.8396.0697.0796.2895.91
Si2.7422.7552.7302.7722.7372.7422.7362.764
IVAl1.2581.2451.2701.2281.2631.2581.2641.236
Ti0.0340.0330.0330.0320.0320.0340.0340.033
Fe2+0.3710.3650.3640.3610.3690.3760.3650.377
VIAl0.1730.1780.1810.1770.1550.1570.1570.174
Mn0.0040.0040.0040.0030.0040.0040.0050.004
Mg2.4362.4202.4352.4672.4582.4612.4592.444
Ʃoct3.0183.0003.0183.0403.0193.0333.0203.031
Ca0.0020.0050.000bdlbdlbdlbdlbdl
Ba0.0170.0180.0130.0180.0200.0150.0190.019
Na0.0400.0470.0410.0480.0430.0500.0470.046
K0.9210.9310.9280.8840.9130.9010.9120.897
Ʃ K0.9821.0000.9820.9600.9810.9670.9800.969
F0.3100.3080.3130.2730.3390.3150.3180.316
Cl0.0230.0270.0240.0270.0230.0210.0250.024
No. of SpecimenТТ 700 °С, 72 hТ 800 °С, 72 hТ 900 °С, 72 hТ 1000 °С, 72 h
SiO240.1940.1440.2439.9740.73
TiO20.720.740.560.640.79
Cr2O30.050.040.04<0.010.05
Al2O315.9815.4716.6816.3115.36
FeO0.040.050.050.060.03
MgO26.5827.1227.0027.0026.98
BaO0.070.130.100.200.10
Na2O1.080.881.241.080.81
K2O8.839.328.799.019.34
Rb2O<0.04<0.040.06<0.04<0.04
F1.291.561.251.261.76
Cl0.040.050.040.080.07
Total94.3594.9295.5395.1095.32
Si2.8542.8382.8152.8132.877
IVAl1.1461.1621.1851.1871.123
Ti0.0380.0390.0290.0340.042
Fe2+0.0020.0030.0030.0030.002
VIAl0.1920.1270.1910.1660.156
Mg2.8132.8582.8162.8322.840
Ʃoct3.0493.0303.0423.0373.043
Ba0.0020.0040.0030.0050.003
Na0.1490.1200.1690.1480.111
K0.8000.8410.7840.8090.841
ƩK0.9510.9700.9580.9630.957
F0.2900.3480.2760.2810.394
Cl0.0050.0060.0050.0090.008
Note: bdl = below the detection limit; A—phlogopite from skarns of the Aldan shield; Cr2O3 and CaO content on average <0.01% wt, Rb2O content on average <0.04% wt; IVAl, VIAl—tetrahedral and octahedral Al. Т—phlogopite from Tajikistan skarns; MnO content <0.01% wt, CaO content on average <0.01% wt; IVAl, VIAl—tetrahedral and octahedral Al.
Table
Table 4. Parameters of the unit cell of the initial and heated at high temperatures and pressures (3 GPa) phlogopites.
Table 4. Parameters of the unit cell of the initial and heated at high temperatures and pressures (3 GPa) phlogopites.
№ А (Initial)А 700 °С, 72 hА 800 °С, 72 hА 900 °С, 72 hА 1000 °С, 72 hТ (Initial)Т 700 °С, 72 hТ 800 °С, 72 hТ 900 °С, 72 hТ 1000 °С, 72 h
a, Å5.3301 ± 0.00035.3322 ± 0.00055.3422 ± 0.00035.3373 ± 0.00055.3199 ± 0.00045.3229 ± 0.00085.3836 ± 0.00245.3188 ± 0.00105.3366 ± 0.00195.3186 ± 0.0017
b, Å9.2322 ± 0.00049.1994 ± 0.00259.2448 ± 0.00039.2203 ± 0.00149.2184 ± 0.00109.1876 ± 0.00479.2182 ± 0.00089.2114 ± 0.00159.2034 ± 0.00409.2112 ± 0.0057
c, Å10.2424 ± 0.000410.2549 ± 0.000810.2481 ± 0.000310.2639 ± 0.000710.2499 ± 0.000510.2593 ± 0.001710.2442 ± 0.000610.2421 ± 0.001310.2488 ± 0.000910.2538 ± 0.0014
β, °100.0944 ± 0.0065100.4084 ± 0.0156100.1893 ± 0.0050100.3785 ± 0.014699.8768 ± 0.0079100.6716 ± 0.0265100.4040 ± 0.0197100.3047 ± 0.0334100.2990 ± 0.0375100.3638 ± 0.0457
V, Å3496.2102 ± 0.0306494.7522 ± 0.1319498.1426 ± 0.0317496.8366 ± 0.0885495.2188 ± 0.0550493.0516 ± 0.2382500.0320 ± 0.2071493.7001 ± 0.1113495.2574 ± 0.3390494.1426 ± 0.3101
Note: A—phlogopite from skarns of the Aldan shield; T—phlogopyte from the Kuhi-Lal ore field (Tajikistan, South Pamir).
Table
Table 5. Results of 40Ar/39Ar Dating of phlogopite samples from magnesian skarns of the Aldan shield (A) and the Kuhi-Lal Deposit (Tajikistan, South Pamir, T) before and after laboratory experiments.
Table 5. Results of 40Ar/39Ar Dating of phlogopite samples from magnesian skarns of the Aldan shield (A) and the Kuhi-Lal Deposit (Tajikistan, South Pamir, T) before and after laboratory experiments.
T °Ct m40Ar, 10−9 cm3 STP40Ar/39Ar±1σ38Ar/39Ar±1σ37Ar/39Ar±1σ36Ar/39Ar±1σCa/K∑39Ar
(%)		Age, Ma±1σ
Original phlogopite from magnesial skarns of the Aldanian shield, crystal edge, specimen А phlogopite (10.26 mg)
J = 0.003832 ± 0.000038; TFA = 1902 ± 21 Ma
50010177.2302.90.5850.0890.00199——0.2790.0019—0.21665.319.7
60010717.6288.40.2900.0300.00077——0.0680.0010—1.01887.421.0
700101774.5279.00.1270.0230.00021——0.0260.0004—3.21900.221.0
800103598.8276.00.0660.0200.00015——0.0190.0002—7.51896.421.0
850106761.3280.60.0670.0210.00008——0.0280.0002—15.61905.121.0
8751010748.5276.00.0580.0190.00008——0.0140.0002—28.71902.321.0
9001011469.8273.40.0470.0170.00007——0.0070.0001—42.81900.821.0
925105093.1273.50.0610.0170.00007——0.0060.0002—49.01902.721.0
950107743.3273.90.0580.0170.00006——0.0060.0001—58.51904.521.0
975105243.9274.90.0810.0170.00009——0.0080.0003—64.91905.921.0
1000104304.6275.80.0800.0180.00013——0.0130.0002—70.21903.921.0
1025104698.4277.90.0880.0190.00010——0.0200.0003—75.91903.921.0
1050102474.2280.50.0740.0220.00023——0.0290.0002—78.81902.721.0
1090105907.2278.80.0730.0210.00008——0.0260.0002—85.91899.621.0
11301011577.2276.50.0540.0190.00012——0.0160.0002—100.01902.721.0
Original phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) specimen T phlogopite (6.58 mg)
J = 0.00974 ± 0.000245; TFA = 8.3 ± 0.5 Ma
8001031.75.10.0040.0160.00030.03440.00630.0170.00050.1241.92.22.6
90010132.93.30.0010.0160.00010.00040.00080.0090.00020.00114.58.61.0
1000107.51.80.0030.0140.00050.01440.00570.0050.00070.05215.96.83.5
105010182.81.30.0010.0150.000020.000010.0000020.0030.00020.0000360.98.00.8
10751069.50.90.0010.0150.000050.000010.000010.0020.00020.0000483.68.21.0
11301059.51.10.0010.0150.000030.00060.00080.0020.00020.002100.09.71.1
Original phlogopite from magnesial skarns of the Aldanian shield, crystal edge, specimen А phlogopite (0.16 mg)
J = 0.004134 ± 0.000045; TFA = 1876 ± 13 Ma
1130103159.4452.50.1640.0230.00040.0010.0050.0340.00030.005100.01876.012.7
Original phlogopite from magnesial skarns of the Aldanian shield, crystal centre, specimen А phlogopite (0.32 mg)
J = 0.004125 ± 0.000045; TFA = 1875 ± 13 Ma
1130105375.3448.00.0590.0190.00020.0080.0020.0170.00010.027100.01874.612.7
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 2 h 3 GPa 800 °C, specimen 2-34-15 A phlogopite (0.13 mg)
J = 0.004421 ± 0.000051; TFA = 1872 ± 13 Ma
1130102483.4421.50.2050.0220.00031.0500.4400.0310.00033.778100.01872.413.5
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 2 h 3 GPa 900 °C, specimen 2-35-15 A phlogopite (0.18 mg)
J = 0.004417 ± 0.000051; TFA = 1869 ± 13 Ma
1130102838.5425.50.2280.0260.00011.4810.2730.0470.00055.331100.01869.413.5
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 2 h 3 GPa 850 °C, specimen 2-10-15 A phlogopite (4.46 mg)
J = 0.004168 ± 0.000046; TFA = 1896 ± 13 Ma
11301069801.7469.40.0680.0310.00010.9440.1400.0780.00013.40100.01896.013.0
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment 2 h 3 GPa 850 °C, specimen 2-10-15 T phlogopite (5.8 mg)
J = 0.004149 ± 0.000045; TFA = 10.0 ± 0.2 Ma
50010153.3329.61.3210.2250.00330.0130.0451.0850.00590.050.267.18.6
80010484.543.40.0100.0420.00010.0170.0030.1410.00020.065.713.60.5
90010588.312.90.0020.0230.000050.3050.0850.0390.00011.1027.810.40.3
97510399.810.10.0020.0210.00000.5470.1510.0300.00011.9747.09.30.2
105010418.58.50.0020.0200.00010.3590.1120.0240.00011.2970.89.90.2
113010404.96.70.0010.0190.000020.00010.00060.0190.00010.0003100.09.40.2
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 2 h 3 GPa 1000 °C, specimen 2-7-15 A phlogopite (2.53 mg)
J = 0.004158 ± 0.000045; TFA = 1872 ± 13 Ma
11301032022.3449.60.0780.0230.00010.9900.1380.0380.00013.56100.01871.712.6
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment 2 h 3 GPa 1000 °C, specimen 2-7-15 T phlogopite (1.98 mg)
J = 0.004141 ± 0.000045; TFA = 10.6 ± 0.2 Ma
50010129.7522.86.0120.3910.009124.97710.2971.7600.021989.920.420.518.2
70010399.5271.90.4680.1930.00117.4041.6590.9140.002026.662.812.82.5
1000101334.834.90.0030.0370.000030.0010.00040.1130.00010.00466.011.70.2
113010367.217.90.0040.0260.00010.2370.1280.0570.00020.85100.08.50.4
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 72 h 3 GPa 700 °C, specimen 4-36-18 А (5.28 mg)
J = 0.006802 ± 0.000120; TFA = 1874 ± 21 Ma
50010159.6532.02.5170.3030.004913.0070.6481.17830.007310.8240.21463.419.8
60010461.7324.00.2000.0660.000950.7040.0850.25630.00062.5361.41784.320.0
70010866.3293.90.2560.0440.000450.1280.1010.11190.00090.4603.91840.820.4
800101587.0281.00.0860.0280.000190.2790.0450.05000.00031.0038.61864.520.5
900108037.0275.90.0640.0210.000100.0130.0100.02230.00020.04532.81877.820.6
950106254.9272.30.0510.0180.000090.0280.0130.01130.00010.10051.81876.620.6
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 72 h 3 GPa 800 °C, specimen 4-35-18 А (6.95 mg)
J = 0.006864 ± 0.000123; TFA = 1857 ± 21 Ma
50010273.8538.32.0370.2630.003383.8830.7081.25700.006013.9780.41377.218.7
60010618.7306.20.2900.0710.000740.3510.1270.27350.00101.2632.01686.519.7
70010966.0298.30.1460.0470.000590.8580.1310.17240.00053.0904.61790.420.4
800101568.1285.60.0870.0330.000200.0010.0000.09480.00030.0059.01837.020.7
900105805.9278.40.0530.0260.000060.0920.0090.05480.00010.33125.71857.320.8
950105159.0271.50.0750.0210.000090.0650.0200.02630.00020.23241.01864.320.8
975106338.4270.60.0380.0190.000050.00030.00010.02090.00010.00159.81867.320.8
1000101107.4269.90.1310.0230.000360.4190.0650.02450.00051.50863.11859.420.8
1050104853.9271.10.0570.0200.000090.0100.0140.02270.00020.03577.41867.020.8
1075102012.1271.00.0730.0190.000240.04100.06500.02420.00020.147583.41864.820.8
1130105602.6270.00.0680.0190.000070.04710.01640.01920.00020.170100.01866.720.8
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 72 h 3 GPa 900 °C, specimen 4-33-18 А (4.02 mg)
J = 0.006876 ± 0.000123; TFA = 1876±21 Ma
5001084.2430.01.7960.2340.006461.6841.4170.98160.01206.0610.31216.126.6
60010553.4283.20.2290.0680.000740.2670.1050.24060.00090.9623.21622.819.2
70010665.9293.00.2100.0470.001011.0830.0980.15250.00143.8996.51795.120.4
800101043.2285.40.1840.0330.000450.2290.0850.08990.00080.82611.91844.520.7
900103589.8280.10.0640.0250.000170.0840.0190.04140.00020.30330.81884.320.9
950103285.9277.00.0650.0210.000200.0370.0300.02710.00010.13448.41889.320.9
1000103560.2278.20.0430.0210.000110.0290.0220.02820.00020.10367.21892.821.0
1050102251.4279.30.0620.0200.000160.0040.0340.03330.00030.01479.11891.421.0
1130103925.3277.90.0950.0200.000070.0430.0160.02530.00010.156100.01895.221.0
Phlogopite from magnesial skarns of the Aldanian shield after laboratory experiment 72 h 3 GPa 1000 °C, specimen 4-30-18 А (10.07 mg)
J = 0.006855 ± 0.000122; TFA = 1537 ± 18 Ma
50010506.1621.00.8120.2070.002451.3780.3700.93930.00174.9610.72183.522.6
60010762.5144.80.0660.0370.000330.3200.0530.09570.00041.1515.31059.314.3
70010703.8145.90.0760.0360.000450.0170.0750.09830.00050.0639.61061.514.3
80010540.3142.20.0660.0350.000600.1350.0600.09390.00040.48512.91044.914.1
85010423.0185.60.1420.0360.000830.6000.0970.10930.00082.15914.91295.816.5
90010913.8232.40.1090.0440.000520.0010.0010.13630.00050.00218.41516.018.3
950101973.5232.50.0540.0370.000190.0970.0350.10890.00020.35025.81559.318.6
1000103700.5213.60.0520.0280.000120.0310.0190.06650.00020.11041.11525.618.3
1050105167.6217.50.0530.0260.000070.0270.0080.05050.00020.09761.91570.918.7
1130109887.9228.30.0820.0220.000030.00010.00010.03510.00010.0002100.01648.819.2
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment 72 h 3 GPa 700 °C, specimen 4-36-18 Т (6.35 mg)
J = 0.006785 ± 0.000120; TFA = 9.4±0.2 Ma
95010677.08.70.0020.0200.000020.0580.0120.02690.000030.20758.59.50.2
102510162.34.20.0020.0170.000040.00050.0000.01190.00010.00287.49.00.3
113010109.66.50.0030.0190.000070.1960.0190.01940.00010.707100.09.90.4
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment 72 h 3 GPa 800 °C, specimen 4-35-18 Т (15.53 mg)
J = 0.006832 ± 0.000121; TFA = 7.3 ± 0.2 Ma
900101284.136.20.0070.0380.000060.0130.0040.12170.00010.04513.42.50.2
1000102913.837.30.0100.0390.000020.0140.0050.12460.00010.05042.86.10.2
1130101312.38.60.0020.0210.000010.0170.0020.02670.000010.062100.09.10.2
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment 72 h 3 GPa 900 °C, specimen 4-33-18 Т (12.11 mg)
J = 0.006881 ± 0.000123; TFA = 14.7 ± 0.4 Ma
700101294.5499.20.2650.3430.000860.7020.1281.68940.00102.5271.10.11.9
800101050.6207.90.0850.1510.000420.3050.0780.69840.00051.0983.218.51.4
900101688.733.80.0040.0360.000040.0050.0050.11190.00010.01723.88.80.3
1000102688.040.20.0060.0400.000030.0140.0030.13230.00010.04951.513.90.5
1130101896.516.20.0040.0250.000020.0240.0020.04980.00010.087100.017.80.5
Phlogopite from Kuhi-Lal field (Tajikistan, SW Pamir) after laboratory experiment: 72 h 3 GPa 1000 °C, specimen 4-30-18 Т (20.3 mg)
J = 0.006844 ± 0.000122; TFA = 55.9 ± 1.0 Ma
50010122.9150.70.2710.1060.002030.0240.3750.45680.00190.0850.2184.56.5
60010472.064.40.0190.0500.000070.1370.0340.17820.00030.4932.5139.72.6
70010422.767.00.0250.0530.000130.0790.0390.18710.00040.2834.4139.12.7
80010223.869.70.0450.0560.000790.0590.1120.20300.00060.2115.4115.82.9
90010771.868.10.0200.0530.000170.0320.0190.19660.00020.1168.8119.52.2
1000101225.231.30.0050.0320.000030.0460.0060.08880.00010.16420.761.81.1
1130105612.721.60.0040.0270.000010.0230.0010.06010.00010.083100.046.50.9
“—“—not determined.
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MDPI and ACS Style

Yudin, D.; Murzintsev, N.; Travin, A.; Alifirova, T.; Zhimulev, E.; Novikova, S. Studying the Stability of the K/Ar Isotopic System of Phlogopites in Conditions of High T, P: 40Ar/39Ar Dating, Laboratory Experiment, Numerical Simulation. Minerals 2021, 11, 192. https://doi.org/10.3390/min11020192

AMA Style

Yudin D, Murzintsev N, Travin A, Alifirova T, Zhimulev E, Novikova S. Studying the Stability of the K/Ar Isotopic System of Phlogopites in Conditions of High T, P: 40Ar/39Ar Dating, Laboratory Experiment, Numerical Simulation. Minerals. 2021; 11(2):192. https://doi.org/10.3390/min11020192

Chicago/Turabian Style

Yudin, Denis, Nikolay Murzintsev, Alexey Travin, Taisiya Alifirova, Egor Zhimulev, and Sofya Novikova. 2021. "Studying the Stability of the K/Ar Isotopic System of Phlogopites in Conditions of High T, P: 40Ar/39Ar Dating, Laboratory Experiment, Numerical Simulation" Minerals 11, no. 2: 192. https://doi.org/10.3390/min11020192

APA Style

Yudin, D., Murzintsev, N., Travin, A., Alifirova, T., Zhimulev, E., & Novikova, S. (2021). Studying the Stability of the K/Ar Isotopic System of Phlogopites in Conditions of High T, P: 40Ar/39Ar Dating, Laboratory Experiment, Numerical Simulation. Minerals, 11(2), 192. https://doi.org/10.3390/min11020192

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