The K 2 CO 3 –CaCO 3 –MgCO 3 System at 6 GPa: Implications for Diamond Forming Carbonatitic Melts

: Carbonate micro inclusions with abnormally high K 2 O appear in diamonds worldwide. However, the precise determination of their chemical and phase compositions is complicated due to their sub-micron size. The K 2 CO 3 –CaCO 3 –MgCO 3 is the simplest system that can be used as a basis for the reconstruction of the phase composition and P–T conditions of the origin of the K-rich carbonatitic inclusions in diamonds. In this regard, this paper is concerned with the subsolidus and melting phase relations in the K 2 CO 3 –CaCO 3 –MgCO 3 system established in Kawai-type multianvil experiments at 6 GPa and 900–1300 ◦ C. At 900 ◦ C, the system has three intermediate compounds K 2 Ca 3 (CO 3 ) 4 (Ca# ≥ 97), 1100 ◦ C; (2) its remelting during transport by hot kimberlite magma, and (3) repeated crystallization in inclusion that retained mantle pressure during kimberlite magma emplacement. The obtained results indicate that the K–Ca–Mg carbonate melts containing 20–40 mol% K 2 CO 3 is stable under P–T conditions of 6 GPa and 1100–1200 ◦ C corresponding to the base of the continental lithospheric mantle. It must be emphasized that the high alkali content in the carbonate melt is a necessary condition for its existence under geothermal conditions of the continental lithosphere, otherwise, it will simply freeze.

A number of studies of 'fibrous' diamonds (diamonds with high dislocation density) from kimberlites worldwide revealed the presence of K-rich carbonatitic melt inclusions coexisting with both peridotitic and eclogitic minerals [18][19][20][21][22][23][24][25]. The inclusions retain high internal pressure suggesting the mantle origin of the entrapped melt [26]. Recently this melt was also found as micro inclusions in the central part of a gem-quality diamond crystal [27] and along the twinning plane in ancient diamonds [28]. This suggests that alkali-rich carbonate melts have been introduced into the reduced lithospheric mantle since the Archaean and that these melts could be responsible for the formation of most lithospheric diamonds [28].
It was shown experimentally that the upper mantle K-rich carbonate melts could be formed by partial melting of carbonated pelites [29][30][31] at pressures of 5-8 GPa. However, precise determination of the compositions of these melts and subsolidus phases controlling melting reactions in the complex natural-like systems with realistic bulk compositions involving small proportions of CO 2 is problematic due to their trace amounts and the lack of stability of quenched products during polishing and electron probe microanalysis [32]. It is also difficult to determine the true position of the solidus lines in the P-T space.
In contrast, the study of pure carbonate systems allows careful determination of subsolidus carbonate phases, minimum melting temperatures, and the composition of incipient melt, which facilitate the interpretation of the natural-like carbonate-bearing silicate systems.
The study of the K 2 CO 3 -CaCO 3 -MgCO 3 system at 6 GPa was initiated by Shatskiy, et al. [33], who examined a binary K 2 CO 3 -Ca 0.5 Mg 0.5 -(CO 3 ) 2 join. In the present work, we carried out a full study of the K 2 CO 3 -CaCO 3 -MgCO 3 phase diagram involving an incomparably larger number of experimental points collected at 6 GPa in the range of 900-1300 • C (Tables S1-S9).

Materials and Methods
Experiments were performed in a 'Discoverer-1500' DIA-type multianvil apparatus at IGM SB RAS in Novosibirsk, Russia. The inner stage of anvils consisted of eight 26 mm tungsten carbide cubes, "Fujilloy N-05", with 12 mm truncations. ZrO 2 pressure media (OZ-8C, MinoYogyo Co., Ltd [34]) was shaped as a 20.5 mm octahedron with ground edges and corners. A multi-charge assembly allowed simultaneous loading of up to 16 samples [35]. The temperature was measured by a W 97 Re 3 -W 75 Re 25 thermocouple and controlled automatically within 2.0 • C of the target value. The thermocouple junction was located at the heater center in the high-temperature (HT) zone. Maximum thermal gradient across the sample charge did not exceed 5-8 • C/mm at 900-1300 • C [35,36]. Uncertainty in the temperature and pressure estimates are less than 20 • C and 0.5 GPa, respectively. The cell assembly design, pressure calibration, and temperature distribution across sample charge are given in [35,36]. Since the studied system includes highly hygroscopic K 2 CO 3 , special care was taken to avoid the contamination of the samples by water before the experiment and to prevent damage of the post-experimental samples by atmospheric humidity during polishing. K 2 CO 3 -bearing samples easily absorb water from the atmospheric air. Placing the sample in a vacuum for carbon coating results in water evaporation and precipitation of needle crystals of K-phase, presumably KHCO 3 , on the sample surface. This prevents the chemical analysis of the obtained phases. Examples of BSE images of well-polished samples and the same samples damaged by atmospheric humidity are shown in Figure S1. The procedures of the sample preparation and polishing are described in [31,37].
Recovered samples were studied using a MIRA 3 LMU scanning electron microscope (Tescan Orsay Holding, Brno, Czech) coupled with an INCA energy-dispersive X-ray microanalysis system 450 equipped with the liquid nitrogen-free Large area EDS X-Max-80 Silicon Drift Detector (Oxford Instruments Nanoanalysis Ltd, Oxford, UK) at IGM SB RAS (see [37] for details).

Experimental Results
The results of the experiments in the system K 2 CO 3 −CaCO 3 − MgCO 3 including phase  compositions of recovered samples and chemical compositions of obtained carbonate phases are  summarized in Tables S1-S9. Backscattered electron (BSE) images of experimental samples are shown in Figures 1-4. The isothermal sections of the T-X ternary diagram are shown in Figure 5. A list of abbreviations is given in the Nomenclature section.

Experimental Results
The results of the experiments in the system K2CO3−CaCO3−MgCO3 including phase compositions of recovered samples and chemical compositions of obtained carbonate phases are summarized in Tables S1-S9. Backscattered electron (BSE) images of experimental samples are shown in Figures 1-4. The isothermal sections of the T-X ternary diagram are shown in Figure 5. A list of abbreviations is given in the Nomenclature section. At 900 °C (run D075, 48 h) and 1000 °C (run D077, 24 h), the run products are represented by subsolidus phase assemblages (Figure 5a,b). Typically, the limiting reagents have been consumed At 900 • C (run D075, 48 h) and 1000 • C (run D077, 24 h), the run products are represented by subsolidus phase assemblages (Figure 5a,b). Typically, the limiting reagents have been consumed completely. However, in some runs, the relicts of Mgs were observed among the run products (Figure 1c,d,g). At these temperatures, three intermediate compounds, K 2 Mg, K 2 Ca, and K 2 Ca 3 , were found. Their stoichiometries resemble those in the corresponding binary systems [36,38]. The K 2 Ca 3 and K 2 Ca compounds dissolve up to 7 and 30-40 mol% of Mg components, respectively, whereas K 2 Mg dissolves up to 17 mol% of Ca component (Tables S1 and S2). The compositions of these compounds can be approximated as follows: K 2 (Ca ≥0.93 Mg ≤0.07 ) 3 (CO 3 ) 4 (Tables S1 and S2). Although a mutual solubility of K 2 Mg and K 2 Ca compounds is noticeable, a miscibility gap between these phases was observed (Figures 1i and 5a,b, and Tables S1 and S2). It was previously shown that at 6 GPa, K 2 Ca(CO 3 ) 2 bütschliite decomposes between 950 and 1000 • C according to the reaction [38,39]: Our results suggest that the partial substitution of Ca with Mg extends its stability to 1000 • C ( Figure 5b). K 2 CO 3 dissolves up to 2 mol% CaCO 3 and minor amounts of MgCO 3 (Figure 5a,b, Tables S1 and S2).
Some samples recovered from the 1100 • C experiments contain subsolidus assemblages at their low-temperature (LT) side. Given the thermal gradient across the sample charge, 6-7 • C/mm at 1100 • C, and the longest distance from the thermocouple junction to the sample end, 2.5-3.0 mm, the temperature at the LT side was about 1080 • C in the runs at 1100 • C. Phase relations inferred from the LT samples sides are shown in Figure 5c. The results suggest that temperature increase from 1000 to 1080 • C, the Arg + K 2 Mg assemblage becomes prohibited owing to the following subsolidus reaction: Reaction (2) changes subsolidus assemblages in the join Mgs-Arg-K 2 Ca 3 -K 2 Mg and yields an appearance of the following three-phase fields: K 2 Mg + Mgs + K 2 Ca 3 (Figure 2c,d), Mgs + Dol + K 2 Ca 3 (Figure 2a), and Ca-Dol + Arg + K 2 Ca 3 (Figures 2b and 5c). Considering subsolidus phase relations at~1080 • C ( Figure 5c) and melting phase relations at 1100 • C (Figure 5e), the system has two eutectics controlled by the following four-phase reactions ( Figure 5d and Table S10).     Regardless of the temperature and the composition of the starting mixture, the maximum CaCO3 and MgCO3 contents established in potassium carbonate are less than 3 and 1 mol%, respectively ( Figure 5 and Tables S1-S9). The K2CO3 content in alkaline earth carbonates (aragonite, calcite, calcitedolomite solid solutions, and magnesite) varies within the uncertainty of our EDS measurements (i.e., <0.5 mol%) (Tables S1-S9).
Liquidus phase relations in the K2CO3-CaCO3-MgCO3 system are illustrated in Figure 6. There are eight primary solidification phase fields characterized by the initial crystallization of Mgs (Figures  3i and   With a further increase in temperature, the melt region continues to expand, while the number of two-phase and three-phase fields decreases (Figure 5g,h). At 1250 • C (run D169, 4h), the K 8 Ca 3 + L and Mgs + K 2 Mg fields disappear. The isothermal section includes seven two-phase fields: Mgs + L, Dol + L, Arg + L, Arg + K 2 Ca 3 , K 2 Ca 3 + L, K 2 + L, K 2 Mg + L and four three-phase fields: K 2 Mg + Mgs + L (Figure 4e Regardless of the temperature and the composition of the starting mixture, the maximum CaCO 3 and MgCO 3 contents established in potassium carbonate are less than 3 and 1 mol%, respectively ( Figure 5 and Tables S1-S9). The K 2 CO 3 content in alkaline earth carbonates (aragonite, calcite, calcite-dolomite solid solutions, and magnesite) varies within the uncertainty of our EDS measurements (i.e., <0.5 mol%) (Tables S1-S9).

Comparison with the Previous Study
Shatskiy et al. [33] determined the phase relations along the K2CO3-Ca0.5Mg0.5CO3 join at 6 GPa using an experimental and analytical technique similar to the present study. Although a number of experimental points in their study were very limited, they succeeded to infer a few phase fields, Arg + K2Mg, K2Mg + K2, Mgs + K2Mg, and Arg + K2Mg + Mgs at 900 °C (Figure 3a in their study) like those established in the present study ( Figure 5a). They also observed two distinct compositions of the K2(Mg, Ca)(CO3)2 compound with Ca# of ~10 and 50-58 and interpreted them as solid solution series, i.e., as a single phase (Figure 3a in their study). Yet, based on the present results these compounds are immiscible under the specified P-T conditions (Figure 5a).
They also found two minima on the liquidus surface (Figure 3a in their study), whose compositions resemble those established in the present study, and succeeded to establish the Mgs + L, K2Mg + Mgs + L, and K2Mg + L fields (Figure 3b in their study) (Figure 5b). Given the temperature step of 100 °C in both studies, slightly lower minimum melting temperatures, 1000 °C instead of 1080 °C in the present study, is not surprising.
The experimental points obtained by Shatskiy et al. [33] at 1100 and 1200 °C (Figure 3c,d in their study) are in reasonable agreement with those obtained in the present study (Figure 5e,f). The difference in some details of their interpretation is rather associated with an insufficient number of experimental points in their study [33] than with the inconsistency in the experimental data. For instance, Shatskiy, et al. [33] have interpreted the first melt [36K2CO3•64(Ca0.65Mg0.35)CO3], found in coexistence with Mgs and K2Mg at 1000 °C as a eutectics. However, according to present results, the melt with such composition and coexisting phases is generated by peritectic reaction 5 (P 1 in Figure 6).

Effect of Pressure
Under mantle pressures and temperatures, the K2CO3-CaCO3-MgCO3 system (KCM) forms several intermediate compounds represented by alkali-alkaline earth double carbonates. At 3 GPa and 750 °C, these carbonates are represented by the low-pressure phases including K2Mg(CO3)2,

Comparison with the Previous Study
Shatskiy et al. [33] determined the phase relations along the K 2 CO 3 -Ca 0.5 Mg 0.5 CO 3 join at 6 GPa using an experimental and analytical technique similar to the present study. Although a number of experimental points in their study were very limited, they succeeded to infer a few phase fields, Arg + K 2 Mg, K 2 Mg + K 2 , Mgs + K 2 Mg, and Arg + K 2 Mg + Mgs at 900 • C (Figure 3a in their study) like those established in the present study (Figure 5a). They also observed two distinct compositions of the K 2 (Mg, Ca)(CO 3 ) 2 compound with Ca# of~10 and 50-58 and interpreted them as solid solution series, i.e., as a single phase (Figure 3a in their study). Yet, based on the present results these compounds are immiscible under the specified P-T conditions (Figure 5a).
They also found two minima on the liquidus surface (Figure 3a in their study), whose compositions resemble those established in the present study, and succeeded to establish the Mgs + L, K 2 Mg + Mgs + L, and K 2 Mg + L fields (Figure 3b in their study) (Figure 5b). Given the temperature step of 100 • C in both studies, slightly lower minimum melting temperatures, 1000 • C instead of 1080 • C in the present study, is not surprising.
The experimental points obtained by Shatskiy et al. [33] at 1100 and 1200 • C (Figure 3c,d in their study) are in reasonable agreement with those obtained in the present study (Figure 5e,f). The difference in some details of their interpretation is rather associated with an insufficient number of experimental points in their study [33] than with the inconsistency in the experimental data. For instance, Shatskiy, et al. [33] have interpreted the first melt [36K 2 CO 3 ·64(Ca 0.65 Mg 0.35 )CO 3 ], found in coexistence with Mgs and K 2 Mg at 1000 • C as a eutectics. However, according to present results, the melt with such composition and coexisting phases is generated by peritectic reaction 5 (P 1 in Figure 6).
The melting along the CaCO 3 -MgCO 3 join extends from 1660 • C (CaCO 3 ) to 1780 • C (MgCO 3 ) through a minimum at 1400 • C and 62 mol% CaCO 3 [35] (Figure 6). Consequently, monomineralic inclusions of MgCO 3 , CaCO 3 , and CaMg(CO 3 ) 2 in diamonds must be entrapped as minerals, because their melting points exceed the growth temperatures of most lithospheric diamonds (Figure 9). The melting along the CaCO3-MgCO3 join extends from 1660 °C (CaCO3) to 1780 °C (MgCO3) through a minimum at 1400 °C and 62 mol% CaCO3 [35] (Figure 6). Consequently, monomineralic inclusions of MgCO3, CaCO3, and CaMg(CO3)2 in diamonds must be entrapped as minerals, because their melting points exceed the growth temperatures of most lithospheric diamonds (Figure 9).  [35] compared with mantle adiabat [64] and P-T range of diamond growth in the lithospheric mantle [56]. Gr/Dia-the equilibrium boundary between diamond and graphite [65]. Jablon and Navon [28] discovered K-rich carbonate inclusions of a few hundred nanometers in size entrapped along the twining plane of macles formed by clear octahedral diamond crystals. The electron probe micro-analyzer (EPMA) revealed that some of these inclusions resemble K2(Mg, Ca)(CO3)2 with Ca# = 20-43. Our results suggest that these inclusions could be formed in the diamond stability field because at lower pressure, the K2Ca(CO3)2 solubility in the K2(Mg, Ca)(CO3)2 decreases [37]. The temperature of the entrapment has to be restricted by 1100 °C because at 100 °C higher and lower temperatures the K2Ca(CO3)2 content decreases below 10-20 mol% (Figure 5b,f and Tables S2,  S6, and S7). Thus, the Ca# of about 40 of the K2(Mg, Ca)(CO3)2 compound found as single-phase inclusions in diamond implies that its crystallization under the P-T conditions of 6 GPa and 1100 °C, corresponding to the base of the continental lithospheric mantle. However, the further entrapment of diamond by the hot kimberlite magma (1400-1500 °C) [66,67] implies the remelting of the K2(Mg, Ca)(CO3)2 compound and its repeated crystallization during kimberlite magma emplacement.
Logvinova et al. [27] identified K2Ca(CO3)2 bütschliite within 30 µ m carbonate inclusion in a gem-quality octahedral diamond crystal from Sytykanskaya kimberlite pipe (Yakutia). Bütschliite was found in coexistence with dolomite and Na2Mg(CO3)2 eitelite. The present results on KCM (Figure 5a,b) and data on NCM [44,45] indicate that neither bütschliite nor eitelite can coexist with dolomite under the P-T conditions of diamond crystallization in the lithospheric mantle ( Figure 5). This led to the conclusion that at the time of entrapment, the inclusion material was an alkali-bearing dolomitic melt and that bütschliite is a daughter phase [27].
Although high-pressure carbonates, K8Ca3(CO3)7 and K2Ca3(CO3) 4 have not yet been found in diamonds, their high melting points, >1200 and >1300 °C, respectively, do not exclude the possibility of their со-crystallization with diamond and their entrapment as mono-and polymineral inclusions ( Figure 6).  [35] compared with mantle adiabat [64] and P-T range of diamond growth in the lithospheric mantle [56]. Gr/Dia-the equilibrium boundary between diamond and graphite [65]. Jablon and Navon [28] discovered K-rich carbonate inclusions of a few hundred nanometers in size entrapped along the twining plane of macles formed by clear octahedral diamond crystals. The electron probe micro-analyzer (EPMA) revealed that some of these inclusions resemble K 2 (Mg, Ca)(CO 3 ) 2 with Ca# = 20-43. Our results suggest that these inclusions could be formed in the diamond stability field because at lower pressure, the K 2 Ca(CO 3 ) 2 solubility in the K 2 (Mg, Ca)(CO 3 ) 2 decreases [37]. The temperature of the entrapment has to be restricted by 1100 • C because at 100 • C higher and lower temperatures the K 2 Ca(CO 3 ) 2 content decreases below 10-20 mol% (Figure 5b,f and Tables S2, S6 and  S7). Thus, the Ca# of about 40 of the K 2 (Mg, Ca)(CO 3 ) 2 compound found as single-phase inclusions in diamond implies that its crystallization under the P-T conditions of 6 GPa and 1100 • C, corresponding to the base of the continental lithospheric mantle. However, the further entrapment of diamond by the hot kimberlite magma (1400-1500 • C) [66,67] implies the remelting of the K 2 (Mg, Ca)(CO 3 ) 2 compound and its repeated crystallization during kimberlite magma emplacement.

Thermal Stability of Carbonatitic Melts vs. Alkalinity
Logvinova et al. [27] identified K 2 Ca(CO 3 ) 2 bütschliite within 30 µm carbonate inclusion in a gem-quality octahedral diamond crystal from Sytykanskaya kimberlite pipe (Yakutia). Bütschliite was found in coexistence with dolomite and Na 2 Mg(CO 3 ) 2 eitelite. The present results on KCM (Figure 5a,b) and data on NCM [44,45] indicate that neither bütschliite nor eitelite can coexist with dolomite under the P-T conditions of diamond crystallization in the lithospheric mantle ( Figure 5). This led to the conclusion that at the time of entrapment, the inclusion material was an alkali-bearing dolomitic melt and that bütschliite is a daughter phase [27].
Although high-pressure carbonates, K 8 Ca 3 (CO 3 ) 7 and K 2 Ca 3 (CO 3 ) 4 have not yet been found in diamonds, their high melting points, >1200 and >1300 • C, respectively, do not exclude the possibility of their co-crystallization with diamond and their entrapment as mono-and polymineral inclusions ( Figure 6).
In contrast to alkali-rich carbonates, alkali-poor carbonates do not experience a full melting under the P-T conditions of the continental geotherm. The melting of Ca-Mg-Fe carbonates [35,78,79] is possible under the temperatures of the convective mantle in asthenosphere, 1450-1500 • C at a depth of 200 km [64], or at the base of lithospheric mantle under 'kinked' geotherm (≥1350 • C) developed presumably due to mantle plume activity [80][81][82][83]. There is direct evidence of the formation of such melts, namely, kimberlite-associated diamondiferous magnesiocarbonatites [84].

Daughter Carbonate Minerals, Which Can Be Expected in Diamond Inclusions
Most of the carbonatitic inclusions in diamonds fall into the primary crystallization field of Mgs. Slow cooling of these inclusions, which could occur in hypabyssal conditions, should cause crystallization of Mgs. This shifts the residual melt composition toward the K-rich eutectic one (E 1 ) and yields precipitation of K 2 Mg + K 2 Ca 3 + K 8 Ca 3 at the final stage of crystallization (Figure 7d). If we consider a possible pressure drop upon cooling, the daughter phases may also include K 2 Ca 2 , K 2 Ca, and K 2 (Figure 7a,b).
Explosive eruption of kimberlite magma implies a rapid cooling of diamonds and micro inclusions therein. In this case, the following assemblages of carbonate phases can be formed: Mgs + Arg + K 2 Mg, Arg + K 2 Ca 3 + K 2 Mg, K 2 Mg + K 2 Ca + K 2 Ca 3 , and K 2 + K 2 Mg + K 2 Ca (Figure 7c). A pressure drop upon cooling can also yield an appearance of the following assemblages Mgs + K 2 Ca + K 2 Mg, Mgs + K 2 Ca + K 2 Ca 2 , and Mgs + K 2 Ca 2 + Dol (Figure 7a).

Comparison with Carbonated Pelite-Derived Melts
Neither peridotites nor eclogites with the natural abundance of K 2 O can yield formation of K-rich melts [85][86][87]. On the other hand, partial melting of carbonated pelites at 5-8 GPa and 1000-1100 • C yields K-rich dolomitic melts [29][30][31], which resemble a minimum on the K 2 CO 3 -CaCO 3 -MgCO 3 liquidus established in the present study (Figure 10a). This suggests that the melting behavior of the KAlSi 3 O 8 -CaMg(CO 3 ) 2 system, controlling carbonated pelite solidus, is essentially the same as that established here in the K 2 CO 3 -CaCO 3 -MgCO 3 system at 6 GPa.
The high alkali content in the carbonate melt is a necessary condition for its existence under geothermal conditions of the continental lithosphere. The obtained results indicate that at 6 GPa and 1100-1200 • C corresponding to the base of the continental lithospheric mantle, the K-Ca-Mg carbonate melts must contain 20-40 mol% K 2 CO 3 , otherwise, it will simply freeze.