Melting Curve of Potassium Carbonate K₂CO₃ at High Pressures

Abstract

Melting of carbonated rocks in the mantle influences the Earth’s deep carbon cycle and the long-term evolution of the atmosphere. Previous studies of the high-pressure melting curve of K₂CO₃ have yielded inconsistent results, with discrepancies of nearly 200 °C at 3 GPa and more than 400 °C at 12 GPa. Here, we report constraints on the melting curve of K₂CO₃ at pressures up to 20 GPa from in situ ionic conduction experiments and Pt sphere experiments. To help resolve the large discrepancies, we tested the ionic conduction method against the well-established differential thermal analysis (DTA) method and conventional Pt sphere method at the ambient pressure of 1 bar. Furthermore, ionic conduction experiments were conducted on sodium chloride (NaCl) to reduce uncertainties in pressure calibration of the multi-anvil press. We also modified the configuration of the in situ ionic conduction experiments to minimize the influence of thermal gradient on melting point determination. Finally, we inspected the effect of water by varying the initial sample state and container wall thickness in the Pt sphere experiments and applied X-ray radiography as a reliable and efficient method to examine the products. Compared with the results from the ionic conduction experiments, the melting point of K₂CO₃ from the Pt sphere experiments was found to be 200~400 °C lower, likely due to a small amount of water trapped by hygroscopic K₂CO₃ in closed platinum (Pt) capsules. We find that anhydrous K₂CO₃ remains more refractory than Na₂CO₃ at elevated pressures.

1. Introduction

The Earth’s carbon cycle is directly linked to global climate change. Recent research has shed light on the significance of the deep carbon cycle involving more than three-quarters of our planet’s carbon stored in the Earth’s interior (e.g., [1,2,3,4]). When hydrothermally altered oceanic lithosphere undergoes subduction, carbonates are transported into the Earth’s interior (e.g., [5]). Eventually, CO₂ is released from the mantle through volcanic activity, completing the cycle. The study of alkali carbonate melts is of significant interest due to their unique chemical properties and their role in various geological processes. For instance, the presence of a small amount of carbonate melts may be responsible for the high electric conductivity of the oceanic low-velocity zone (LVZ) [6,7,8]. Furthermore, chemically reactive and highly mobile alkali carbonate melts can facilitate the growth of diamonds [9,10,11]. Evidence of alkali-rich carbonatite melts in nature is found in the eruption of natrocarbonate magma from Oldoinyo Lengai volcano in east Africa, with phenocrysts of nyerereite (Na,K)₂Ca(CO₃)₂ and gregoryite (Na,Ca,K)₂CO₃ [12,13]. Therefore, it is important to investigate alkali carbonate melts under mantle conditions.

The first step in assessing the role of carbonate melts in mantle structure and processes is determining their melting curves at relevant pressures. The high-pressure melting behaviors of alkaline earth carbonates (MgCO₃ and CaCO₃) [14,15,16,17] and alkali carbonates (Na₂CO₃, K₂CO₃) [16,18,19,20,21], including binary and ternary systems [5,14,15,17,22], have been studied extensively. The melting curve of potassium carbonate (K₂CO₃), however, remains poorly constrained. Various research groups have reported inconsistent melting points for K₂CO₃ under high pressures, particularly at 3 to 12 GPa. Experimental results from the ionic conduction method [18] yielded melting temperatures of K₂CO₃ that were at least 150 °C higher than those using the Pt sphere method to bracket the melting point at 3 GPa [20]. At higher pressure, the discrepancy becomes even larger and reaches 400 °C at 12 GPa [21]. Other studies found that the melting point of K₂CO₃ increases with increasing pressure [14,15], which supports the trend of ionic conduction experiment data and disagrees with the relatively flat melting curve obtained from the Pt sphere experiments [20,21]. The large discrepancies beyond the experimental uncertainties remained unexplained for more than a decade. Considering the importance of the K₂CO₃ high-pressure melting curve, the significant discrepancies among existing studies of the Pt sphere method and ionic conduction method must be resolved.

Possible explanations for the discrepancies include (1) uncertainties in pressure calibration; (2) uncertainties in temperature measurements; (3) uncertainties in the melting detection criteria of the ionic conduction method; and (4) trapped water in the sample lowering the melting points of hygroscopic K₂CO₃ in Pt sphere experiments. In this study, we conduct ionic conduction experiments on sodium chloride (NaCl) to reduce uncertainties in the pressure calibration of the multi-anvil press. A single-sided experimental design is implemented to reduce temperature uncertainties in ionic conduction experiments on K₂CO₃. To test the validity of the ionic conduction method for determining the melting point of K₂CO₃, we perform concurrent measurements using the well-established differential thermal analysis (DTA) method and conventional Pt sphere method at 1 bar. Finally, a series of Pt sphere experiments are conducted to test the effect of water on melting point determination of K₂CO₃ at high pressures.

2. Materials and Methods

The starting materials for the experiments were high-purity K₂CO₃ (Alfa Aesar 10839, 99.999%, Haverhill, MA, USA) or NaCl (Alfa Aesar 10862, 99.999%).

2.1. Concurrent DTA and Ionic Conduction Experiments at Ambient Pressure (1 Bar)

Differential thermal analysis (DTA) is a conventional technique extensively used in chemistry and material sciences since the 20th century [23]. In the DTA method, the temperature difference is measured between a sample and a reference material as a function of temperature under the same controlled heating program. During heating, the temperature difference peaks at the sample’s melting point as its temperature plateaus due to latent heat absorption, while the reference temperature continues to increase. The ionic conduction (IC) method detects the melting of an ionic compound such as K₂CO₃ based on a sharp large rise in ionic current at a constant excitation voltage, due to its transition from an insulating solid to a conductive liquid during heating.

To test the validity of the IC method on K₂CO₃, we conducted concurrent DTA and IC experiments [24] at ambient pressure (1 bar) using a Petit box furnace (Figure S1). Powder of K₂CO₃ was packed into a 10 mL platinum crucible. For DTA, we used two pairs of type S (Pt-Rh) thermocouples (TCs) with welded junctions. One thermocouple inserted in a 2-bore alumina tube was positioned near the K₂CO₃ sample surface to measure the reference environment temperature (T_Ref), while the other TC in a 4-bore alumina tube for sample temperature (T) and two platinum electrodes for ionic current measurements of the IC method were embedded within the sample. Given a constant excitation voltage in the circuit (Figure S2), current through the sample was monitored and a current surge was used as an indicator of melting. Temperatures were recorded by a multi-channel DataQ device. The circuit was powered by 0.1 VAC and 60 Hz excitation voltage. A FLUKE 289 ammeter (Fluke Corporation, Everett, WA, USA) was used to detect ionic current through the sample, and a Mastech variac was used to adjust the excitation voltage. To further test and monitor the existence of melting, a platinum (Pt) sphere (~800 µm in diameter) was placed on the top of the K₂CO₃ sample without touching the Pt crucible, Pt electrodes or thermocouples. The heating and cooling cycles were repeated multiple times in most experiments, with a heating rate of 0.2 to 1 °C/s. The existence of melting was detected by a latent heat ledge in DTA, a rapid current increase in the IC method and the sinking of the Pt sphere. The verification of the ionic conduction (IC) method is based on the consistency between the measured melting points of K₂CO₃ at 1 bar by both the DTA and IC methods, with the bottom position of the Pt sphere being further evidence of melting.

2.2. Ionic Conduction Experiments at High Pressures

In situ ionic conduction experiments were conducted using a 1000-ton Walker-type multi-anvil press at the University of Michigan (Ann Arbor, MI, USA). High pressures were generated using Toshiba-Tungaloy F-grade tungsten carbide cubes with an 8 mm truncation edge length (TEL). Pressure calibration experiments (see details in Appendix A) were performed based on a well-established NaCl melting curve [25] to provide accurate and precise pressure determination [26]. Same as the 1 bar experiments, the temperature was monitored using a type-S thermocouple (TC). An ionic current circuit (Figure S2) through the sample was provided.

A single-sided configuration was used for the IC experiments [24,26] in order to reduce temperature uncertainty in prior studies using a double-sided design [16,18,25,27]. In this configuration (Figure 1a), the Pt electrode wires and thermocouple wires were inserted into a four-bore alumina tubing, which was then positioned axially into the cylindrical rhenium (Re) heater from the top. The electrode tips and thermocouple junction were seated at the heater’s equator (the mid-plane in Figure 1a) and were in direct contact with the sample. By design, the temperature and current readings were from the same region in direct touch with the sample. MgO was used as the confining media instead of the alumina employed in a prior study [26]. Zirconia-based castable Aremco compound 646 octahedra with precast fins were used as the pressure media. Two pairs of grooves were cut in the gasket fins to hold thermocouple wires (corner grooves) and Pt electrodes (side grooves) on the top triangle face of the 646 octahedra.

To remove water and porosity, a recrystallization process (Appendix B and Figure A1) was employed for the K₂CO₃ and NaCl samples before assembling the Pt sample capsule into an octahedra. Furthermore, the final assembly including the loaded sample capsule was kept at 110 °C in a vacuum oven for more than 24 h before being placed into the multi-anvil press.

During each experiment, we aimed to measure the melting points of samples at several pressures by detecting ionic current surging. The external circuit setup was the same as the 1 bar experiments (Figure S1). At each pressure, the current passing through the sample was recorded over at least two heating and cooling cycles before proceeding to the next target pressure. The heating rate was 0.2~1 °C/s. After heating at all pressures, the sample was rapidly quenched by powering off the system. A Zeiss petrographic microscope and a Leica microscope (Wetzlar, Germany) were employed to examine the experimental products.

2.3. Pt Sphere Experiments on K₂CO₃ at High Pressures and X-Ray Radiography

To cross-examine the results of ionic conduction experiments on K₂CO₃, we conducted platinum (Pt) sphere experiments from 3 GPa to 10 GPa using the multi-anvil press. Tungsten carbide cubic anvils (8 mm TEL) and the 646 octahedra assemblies were used to generate high pressures. The configuration for Pt sphere experiments (Figure 1b) was adjusted from the ionic conduction method (Figure 1a), while closed sample capsules were used in the Pt sphere method. Temperature was monitored by a type C (W-Re) thermocouple. At target pressure, the sample was heated to the target temperature and held for 5~20 min before quenching. Before heating to the target temperature, two Pt spheres (200~300 μm) were positioned at the upper and lower part of the sample capsule, respectively, separated by the solid K₂CO₃. The two spheres were used to eliminate ambiguity in sample orientation. When K₂CO₃ melts at high pressures, the upper Pt sphere falls to the lower half of the capsule due to the density difference in Pt and K₂CO₃ liquid. The movement or stationary positions of Pt spheres in the recovered experimental products indicate whether the sample melted at the target temperatures.

To reduce the effect of sample deformation, partial recrystallization (Figure A1b and Appendix A) was performed during sample loading in most of the Pt sphere experiments, providing two recrystallized K₂CO₃ spacers between the Pt spheres and sample capsules. The rest of the sample in the capsule was simply packed with K₂CO₃ powder. To achieve various degrees of dehydration, simple packing of K₂CO₃ powder without recrystallization and two sample capsule thicknesses (thin: 25.4 μm; thick: 76.2 μm) were also used in the Pt sphere experiments for comparison. All capsules were baked in a vacuum oven at 110 °C for at least 24 h before and after final assembly.

X-ray radiography was collected to non-destructively visualize the internal structure to examine the eventual positions of the Pt spheres. The experimental products (compressed octahedra) were first ground to remove the hard 646 pressure media as much as possible without exposing the sample in order to avoid the effect of moisture on hygroscopic K₂CO₃. X-ray radiography on the products was scanned in the computed tomography at the Earth and Environmental Sciences (CTEES) facility at the University of Michigan using a Nikon XT H 225ST industrial μCT system (Nikon, Tokyo, Japan) with a Perkin Elmer 1620 X-ray detector panel (Perkin Elmer, Waltham, MA, USA) and a tungsten reflection target. Scan conditions were set at 60~110 kV and 100~142 μA.

3. Results

3.1. Concurrent DTA and Ionic Conduction Experiment on K₂CO₃ at 1 Bar

The DTA yielded a melting point of 890 °C, where a latent heat ledge was observed upon heating (Figure 2c) and the difference between T_Ref and T reached the maximum value. From the ionic conduction experiments, the melting point was determined as 891 °C at the peak of dI/dT curve. The current (I) remained below 100 μA along the heating path until the sample temperature (T) reached 840 °C. The current then increased gradually, reaching a local maximum of approximately 500 μA at 885 °C. After the current decreased and stabilized at around 250 μA, it surged to over 900 μA at 891 °C, which is the peak of the dI/dT curve (Figure 2b). With further heating, the current plateaued again. After turning off the furnace at 910 °C, the Pt sphere was found at the bottom of the recovered sample in the 10 mL Pt crucible, indicating the occurrence of melting below 910 °C.

The agreement between the results from the IC method and the well-established DTA method at 1 bar confirms that the ionic conduction method is applicable to K₂CO₃ and that the peak in the dI/dT curve corresponds to the melting temperature.

3.2. Pressure Calibration Using NaCl Melting Curve

The melting points of NaCl were determined using the ionic conduction method at 30 to 100 bar oil pressure load (Figure S3, Table S1). At each oil pressure, we observed a sharp increase in ionic current through the sample associated with melting (Figure 3). Initially, as the samples were heated from room temperature, the current maintained a low level, varying from a few to several tens of microamps. At approximately 100 °C below the point of steepest current increase, the current began to accelerate, reaching around 400 to 600 μA at the peak. The current–temperature pattern was consistent in all calibration experiments across all pressure points. The temperature of the maximum dI/dT was identified as the melting point at each pressure. Subsequent heating resulted in either a plateau or a small decrease in the current. The maximum current decreases with increasing pressure. The current–temperature relations were reproduced in multiple heating and cooling cycles at each pressure.

The pressure calibration of this study using MgO media (Figure S3, Tables S1 and S2) agrees with the previous NaCl calibration using alumina within ±20 °C [26], indicating a negligible effect of confining media in sample assembly on pressure calibration.

3.3. Ionic Conduction Experiments on K₂CO₃ at High Pressures

Constraints on the high-pressure melting points of K₂CO₃ by the single-sided and double-sided IC methods are reported (

Table 1. High-pressure melting points of K₂CO₃ determined by ionic conduction experiments.

Exp. ID	Pressure 1 (GPa)	Melting Temperature 2 (°C)
		Measurement	Average
8 mm TEL single-sided configuration
M100623_8	2.5	1328	1330 ± 2
		1331
M110623_8	3.0	1385	1380 ± 7
		1375
M100624_8	5.0	1475 ± 20	1475
M061624_8	10.0	1641 ± 14	1641
5 mm TEL double-sided configuration [18]
M081814_5	3.0	1337	1353 ± 14
		1364
		1359
	4.5	1455	1456 ± 1
		1457
	6.0	1524	1520 ± 6
		1516
	9.0	1623	1621 ± 3
		1619
	12.0	1785	1788 ± 3
		1790
	15.0	1936	1933 ± 4
		1930
	18.0	2050	2045 ± 7
		2040
	20.0	2110	2108 ± 2
		2107
M090214_5	3.0	1343	1348 ± 7
		1353
	4.5	1475	1476 ± 1
		1476
	6.0	1558	1557 ± 1
		1555
	9.0	1688	1688 ± 1
		1687
	10.0	1751	1750 ± 1
		1749
	12.0	1875	1876 ± 1
		1876
	16.0	2048	2046 ± 3
		2043
	20.0	2209	2208 ± 2
		2206

¹ The pressure uncertainties were estimated at 7%, including calibration uncertainty and pressure drift during heating. ² Uncertainties in melting temperature measurements were estimated from a combination of the thermocouple uncertainties and full width at half maximum (FWHM) of dI/dT, and are within ±5 °C unless noted in the table. Uncertainty shown in the average is calculated from one standard deviation. For 5 mm TEL double-sided experiments, total temperature uncertainties are estimated as 5% on the basis of a combination of type C thermocouple uncertainties, reproducibility within a single experiment, and variations among duplicate experiments due to sample geometry deformation under compression [18].

and Figure 3). In each heating cycle of every experiment, in a similar pattern to the 1 bar experiments, the current gradually increased from a few μAs to approximately 200–400 μA and stopped increasing at a current plateau before soaring to several hundred μAs. Melting points were again determined as the peak positions of dI/dT. With a single-sided configuration, we determined the melting point of K₂CO₃ to rise from 1330 ± 5 °C at 2.5 GPa to 1641 ± 14 °C at 10 GPa. With a double-sided configuration, the melting point was found to increase from 1350 ± 68 °C at 3 GPa to 2158 ± 108 °C at 20 GPa.

3.4. Pt Sphere Experiments on K₂CO₃ at High Pressures

The results of the Pt sphere experiments provide other constraints on the melting curve of K₂CO₃ at high pressure (

Table 2. Results from Pt sphere experiments on K₂CO₃ at high pressures.

Exp. ID	Pressure 1 (GPa)	Thermocouple Temperature (°C)	Upper Sphere Position	Upper Sphere Movement 2	Melting Temperature (°C)
M011624	4.0	1300	Top	No sink	>1380
M011924	5.0	1352	Top	No sink	>1422
M020424 3	3.0	~1500	Bottom	Sink	<1500
M022024	3.0	1300	Middle	Partial sink	1368
M030324 4	3.0	1200	Bottom	Sink	<1200
M030824	6.0	1400	Middle	Partial sink	1480
M031024	7.0	1450	Middle	Partial sink	1510
M062224	7.0	1300	Top	No sink	>1394
M092924	10.0	1600	Middle	Partial sink	1670

¹ The pressure uncertainties are estimated as 7% based on the pressure drift during heating, calibration uncertainty, and other system uncertainties. ² No sink: the upper sphere did not sink and no melting was detected; partial sink: the upper sphere sank to the middle but did not reach the bottom of the capsule, indicating part of the sample was melted; sink: the upper sphere sank to the bottom of the capsule and the entire sample melted. ³ Power curve was used to estimate the temperature of M020424. ⁴ All Pt sphere experiments used a thin Pt sample capsule of 0.001 inch (25.4 μm), except for M030324, which used a thicker Pt capsule of 0.003 inches (76.2 μm).

and Figure 4). X-ray radiography of the experimental products (Figure 4 and Figure S4) reveals the eventual positions of the spheres, indicating whether the sample melted during heating. Three outcomes were identified based on the upper sphere positions: (1) No sink (“top” position): the upper Pt sphere remained in the upper part of the sample capsule when the compressed K₂CO₃ did not melt during heating (Figure 4a). Therefore, melting temperatures are higher than thermocouple readings in these cases. (2) Partial sink (“middle” position): the upper sphere sank to a middle position, signifying only part of the sample melted due to the thermal gradient within the sample region (Figure 4b). (3) Sink (“bottom” position): both the upper and lower spheres sank to the bottom of the sample capsule, indicating that melting of K₂CO₃ existed throughout the entire capsule (Figure 4c).

3.5. Melting Curve of K₂CO₃ at High Pressures

The melting curve of K₂CO₃ from 1 bar to 10 GPa was fitted to the Simon melting equation [29] from the results of the single-sided ionic conduction experiment in this study. The empirical Simon melting equation is commonly used to fit pressure-dependent melting temperature in the form of (T/T₀)^c = (P − P₀)/A + 1, where A and c are constants, and T₀ is the melting point of a solid at ambient pressure P₀ (1 bar). The Simon melting equation is notable for its simplicity and does not require knowledge of the solid phase’s equation of state (EoS), even though the fitting parameters A and c lack clear physical meanings and are not independent. Taking T₀ = 1164.15 K from the 1 bar ionic conduction experiment in this study and the reference pressure P₀ = 0.0001 GPa, our fitting yields A = 0.25(4) and c = 7.5(3) (Figure 5). The Simon equation is supposed to fit the melting curve of a solid with a given structure. A previous study [30] reported several phase transitions in K₂CO₃ between 1 bar and 10 GPa. We found that within experimental error, a single Simon equation adequately fit our data, suggesting negligible effects of phase transitions within this pressure range.

4. Discussion

4.1. Concurrent Ionic Conduction Method and DTA at 1 Bar

The perfect match between the results of the well-established DTA method and the ionic conduction method demonstrates that the ionic conduction change is a reliable criterion for melting temperature determination of K₂CO₃. The criterion of identifying the melting point by selecting the peak of the dI/dT curve has been confirmed as well in this cross-examination benchmark experiment at 1 bar. Additionally, our results from both the DTA and IC methods are consistent with the melting points reported by previous studies (e.g., 898 °C [20] and 896 °C [31]) and most chemical companies (e.g., 891 °C by Alfa Aesar and J.T. Baker, etc.). Therefore, the 1 bar experiments established the criterion for melting detection in IC experiments by selecting the temperature corresponding to the peak rise in current as the melting point. This criterion serves as the basis for applying the IC method to calibrate pressure using the melting curve of NaCl and determine the melting points of K₂CO₃ at high pressures in this study.

4.2. Ionic Conduction Experiments on K₂CO₃ at High Pressures

Accurate pressure determination and temperature measurements in high-pressure experiments are crucial and heavily influenced by the assembly configuration. This study introduces a methodological enhancement by employing a single-sided assembly, which addresses limitations observed in the double-sided assembly used in prior studies on the ionic conduction method, including Li (2015) [18] and subsequent studies [16,24,27]. In double-sided setup, the thermocouple and electrodes were symmetrically placed on opposite sides of the sample chamber under the assumption that they were at the identical temperature due to their equal distance from the hottest mid-plane of the sample, where temperature gradient is expected to be minimized. However, relatively large uncertainties (±85 °C) were reported for the double-sided design due to unpredictable variations in sample geometry and assembly deformation under compression. Improved from the prior double-sided arrangement, a single-sided configuration was used in this study, in which both the thermocouple and electrodes were inserted from the same side onto the sample surface, allowing direct measurements of current and temperature at the same region of the sample. Theoretically, the single-sided design minimizes the temperature gradient between the thermocouple and electrodes to near zero. Temperature uncertainties inevitably arise from melting point selection, as a significant current increase occurred over a 10~40 °C range, and the FWHM of dI/dT peaks was used to quantify uncertainty. Additional melting temperature uncertainties were from fluctuations among multiple heating cycles and duplicated experimental runs.

The rise in ionic current upon melting seems to occur over larger temperature intervals in the single-sided experiments than in the double-sided experiments, likely due to the placements of the electrode tips with respect to thermal gradient. In single-sided experiments, the electrode tips are placed at the hottest part of the assembly and detect melting progressing from the hotter region toward the colder region of the sample during heating; in double-sided experiments [18], the electrode tips are placed at the coldest part and detect melting only when the last portion of the sample melts. While double-sided experiments provide sharper melting signals and allow the use of stronger type C thermocouples, they rely on symmetrical placements of the thermocouple junction and the electrode tips, which can introduce relatively large uncertainties in temperature measurements (e.g., ±85 °C at 10 GPa). Single-sided experiments, with the electrode tips and thermocouple junction placed at the same position, reduce uncertainties in temperature (e.g., ±20 °C at 10 GPa), even though the melting signal is sharper and the type S thermocouple wires are more vulnerable to mechanical failure.

Our pressure calibration against the NaCl melting curve improved pressure constraints using an identical experimental setup under a comparable temperature range to the K₂CO₃ melting range instead of using the conventional solid-phase transition calibrations [32,33,34,35,36] at lower temperatures employed in prior studies on the ionic conduction method [16,18,24,25,26,27]. This calibration eliminated uncertainties in pressure as the cause of the large discrepancies among studies on melting curves of K₂CO₃ [14,15,18,20,21]. The pressure uncertainty was estimated at 7%, including calibration errors, pressure drift during heating, and other system-related uncertainties.

One interesting phenomenon found in the ionic current measurements of K₂CO₃ was the current plateau before the rapid climbing at melting point, which has not been reported in ionic conduction experiments of other carbonates. The current–temperature curves of BaCO₃ [27], CaCO₃ [16], and Na₂CO₃ [16] are similar to the trend of NaCl [25]. The cause of the plateau in ionic current is unclear. A possible explanation is solid-state phase transition, such as the transformation of the low-temperature γ-K₂CO₃ to the high-temperature II-K₂CO₃ at 3 GPa. However, the current plateau of K₂CO₃ is consistently observed near 900 °C at all pressures from 2.5 GPa to 10 GPa, which cannot be explained by a small number of phase transitions within this pressure range (Figure 5).

We were unable to recover the samples for texture or chemical analysis because K₂CO₃ turned into goo upon air exposure. Furthermore, during oil polishing, samples easily chipped and showed no recognizable texture. Despite this limitation, several observations support the robustness of our results: (1) multiple heating and cooling cycles in ionic conduction experiments showed consistent peak ionic currents and melting temperatures, indicating negligible sample leakage or contamination; (2) radiographs of the Pt sphere experiments revealed no visible damage to sample capsules (Figure 4 and Figure S4); and (3) the results from our Pt sphere experiments with partially recrystallized K₂CO₃ in closed capsules agree with that of our ionic conduction experiments.

4.3. Pt Sphere Experiments on K₂CO₃ at High Pressures

The combination of the Pt sphere method and X-ray radiography provides a non-destructive and efficient technique for the examination of the eventual positions of Pt spheres covered in hard zirconia-based pressure media after high-pressure experiments. It avoids the complexity and mess of conventional oil/dry polishing and eliminates the possibility of losing samples or Pt spheres during sample recovery or polishing, which helped us make the most effective use of the precious high-pressure experimental products. Notably, the upper sphere sinking to the “middle” position not only indicated melting existed in part of the sample but also visualized the solid–liquid phase boundary of K₂CO₃, allowing direct estimation of the actual melting point of K₂CO₃ by considering the thermal gradient in compressed samples. Compared to the conventional bracketing method that requires a series of Pt sphere experiments at different target temperatures under identical pressure conditions, this approach maximized the information obtained from a single experiment, significantly enhancing the efficiency of Pt sphere experiments. However, a key challenge of this method is to select an appropriate target heating temperature to ensure the unknown melting point is covered by the temperature distribution within the sample. The accuracy of estimation depends on good constraints of thermal gradient within the sample assembly.

4.4. Discrepancies Among Melting Points of K₂CO₃ and Effect of Water

The significant effect of water on lowering the melting point of K₂CO₃ explains long-standing discrepancies between the results from the Pt sphere and ionic conduction (IC) methods. This study measured K₂CO₃ melting points from 2.5 to 10 GPa using the single-sided IC method, which closely matched values reported by the double-sided IC method [18] but were significantly higher than those from existing Pt sphere studies [14,15,20,21]. For instance, at around 3 GPa, the melting point recorded in this study was 180 °C higher than that in L07 [20] and over 100 °C higher than A18 [14], which cannot be fully explained by the reported uncertainties.

The effect of water was hypothesized to contribute to these discrepancies [14] but lacks extensive investigation. K₂CO₃ easily absorbs moisture and we even observed that K₂CO₃ powder became gooey after about 15–20 min of exposure to air with 47% humidity. While prior studies baked samples at 400 °C for hours to remove water, either residual moisture could have persisted, or K₂CO₃ might have reabsorbed water during assembly or compression for hours due to its hygroscopic nature. The recrystallization process of the starting materials used in this study (Appendix B) ensured minimal water content in samples for both the ionic conduction and Pt sphere methods. With less water trapped in K₂CO₃, this study measured higher melting temperatures than prior Pt sphere experiments, as expected. In this study, the results of a series of Pt sphere experiments (Figure 6) with various experimental setups and degrees of sample dehydration provide evidence of the significant effect of water on lowering melting point. All Pt sphere experiments used sealed Pt capsules, potentially trapping water if the dehydration was not thorough and lowering the melting point of K₂CO₃, while the ionic conduction experiments used open capsules, allowing water to escape during multiple heating cycles. For example, at 3 GPa, the single-sided ionic conduction method with complete dehydration (open capsule and recrystallized sample) yielded a melting point of 1380 °C; Pt sphere experiments with a lower dehydration degree (thin capsules and partially recrystallized samples) showed no melting below 1300 °C; however, melting was detected in experiments with the lowest dehydration degree (thick capsules and packed powder sample) at 1200 °C, consistent with L07 [20]. These results confirm that even a small amount of trapped water caused by experimental setups and incomplete dehydration or subsequent rehydration can significantly lower the melting temperature of K₂CO₃ under high pressures.

4.5. Implications for Diamond Formation

Compared with the melting curves of other carbonates (in Figure 7), the anhydrous melting curve of K₂CO₃ is slightly higher than Na₂CO₃, but both alkali carbonates (K₂CO₃ and Na₂CO₃) are lower than the alkali earth carbonates (MgCO₃ and CaCO₃).

The fluid-bearing (alkali-enriched H₂O-CO₂ fluids) alkali carbonate melts provide a possible media for natural diamond formation, which happens mostly in the sub-continental lithospheric mantle at depths of 140~220 km [9,10,11,37,38]. However, anhydrous K₂CO₃ melts do not naturally exist in diamond formation conditions based on the phase diagram (Figure 7). According to this study, the presence of water could allow the melting curve of nominally anhydrous K₂CO₃ to fall into the diamond formation zone. Therefore, it is possible that K₂CO₃ melts exist under hydrous mantle conditions, which sets the foundation of this hypothesis for diamond formation.

5. Conclusions

Through concurrent differential thermal analysis (DTA) and Pt sphere experiments at 1 bar, we have validated the melting point determination of K₂CO₃ using the ionic conduction (IC) method. The melting point of K₂CO₃ at 1 bar determined from the IC measurements is 891 ± 3 °C, which agrees with the DTA result of 890 ± 2 °C.

We have conducted ionic conduction and Pt sphere experiments with various degrees of dehydration to examine the effect of water on the melting points of K₂CO₃ from 3 GPa to 10 GPa. A comparison between the results of the IC and Pt sphere experiments revealed a significant effect of water on lowering the melting points of K₂CO₃ at high pressures. Due to the hygroscopic nature of K₂CO₃, prior Pt sphere experiments may have reported the melting curve of nominally anhydrous K₂CO₃ with a small amount of water unintendedly trapped in closed sample capsules; thus, the large discrepancies between the results of the IC and Pt sphere experiments may be explained by the effect of water. Our findings suggest that the Pt sphere method may underestimate the melting point of hygroscopic materials at high pressure and must be used with caution.

Applying the IC method with a single-sided configuration, we determined that the melting point of K₂CO₃ rises from 1330 ± 5 °C at 2.5 GPa to 1641 ± 14 °C at 10 GPa. With a double-sided configuration, the melting point is found to increase from 1350 ± 68 °C at 3 GPa to 2158 ± 108 °C at 20 GPa. Our results show that K₂CO₃ melts at 100~200 °C lower than alkaline earth carbonates but is more refractory than sodium carbonate under upper mantle conditions. The established melting curve of K₂CO₃ at 2.5 to 20 GPa provides a valuable basis for systematic thermodynamic modeling of carbonate melting in the mantle.