Fluid Inﬁltration and Mass Transfer along a Lamprophyre Dyke–Marble Contact: An Example from the South-Western Korean Peninsula

: In this contribution, we report the metasomatic characteristics of a lamprophyre dyke–marble contact zone from the Hongseong–Imjingang belt along the western Gyeonggi Massif, South Korea. The lamprophyre dyke intruded into the dolomitic marble, forming a serpentinized contact zone. The zone consists of olivine, serpentine, calcite, dolomite, biotite, spinel, and hematite. Minor F and Cl contents in the serpentine and biotite indicate the composition of the inﬁltrating H 2 O-CO 2 ﬂuid. SiO 2 (12.42 wt %), FeO (1.83 wt %), K 2 O (0.03 wt %), Sr (89 ppm), U (0.7 ppm), Th (1.44 ppm), and rare earth elements (REEs) are highly mobile, while Zr, Cr, and Ba are moderately mobile in the ﬂuid. Phase equilibria modelling suggests that the olivine, spinel, biotite, and calcite assemblage might be formed by the dissolution of dolomite at ~700 ◦ C, 130 MPa. Such modelling requires stable diopside in the observed conditions in the presence of silica-saturated ﬂuid. The lack of diopside in the metasomatized region is due to the high K activity of the ﬂuid. Our log activity K 2 O (a K2O )–temperature pseudosection shows that at a K2O ~ − 40, the olivine, spinel, biotite, and calcite assemblage is stable without diopside. Subsequently, at ~450 ◦ C, 130 MPa, serpentine is formed due to the inﬁltration of H 2 O during the cooling of the lamprophyre dyke. This suggests that hot H 2 O-CO 2 ﬂuids with dissolved major and trace elements inﬁltrated through fractures, grain boundaries, and micron-scale porosity, which dissolved dolomite in the marble and precipitated the observed olivine-bearing peak metasomatic assemblage. During cooling, exsolved CO 2 could increase the water activity to stabilize the serpentine. Our example implies that dissolution-reprecipitation is an important process, locally and regionally, that could impart important textural and geochemical variations in metasomatized rocks. of apatite range from 2.04 to 3.71 and 0.13, respectively. The chondrite normalized REE values in apatite show a slight enrichment in the HREE.


Introduction
Metasomatism is the alteration of rocks by hot, chemically active fluids that infiltrate or diffuse through the rocks, causing recrystallization and compositional change [1]. Heat and fluids released by the crystallizing magma could pervasively interact with the rocks regionally or locally, generating metasomatized zones/aureoles [2,3]. On a regional scale, infiltration by H 2 O-CO 2 brines causes metasomatic alterations in the lower crust and the mantle [4][5][6]. During metasomatic alteration, metal concentrations in fluids can lead to the genesis of ore deposits that are economically important [7].
Significant changes in mineralogy, geochemistry, and rheology evolved through fluid-rock interactions are important in evaluating geodynamic processes over time [8]. Metasomatic changes through the introduction of fluid from an external source adds and removes materials in solution by infiltration metasomatism [9,10]. The chemical potential of perfectly mobile components depends not only on their concentration but also on the influence of inert (immobile) components in the system during the infiltration metasomatism, where the chemical potentials of perfectly mobile components differ from those in the external medium in contrast to diffusion processes [9]. Our understanding of such processes is limited because of the lack of fluid properties under high pressure (P) and temperature (T) conditions, and the absence of fluid phase preserved in these samples. Important advances are made by the constraining of our understanding of fluid properties [11]. Further textural and geochemical studies of metasomatic zones are very useful in understanding metasomatism and the dissolution-precipitation process, and can deliver more information about the chemical composition of fluids and mobility of different components in it with respect to the external conditions [12].
Our understanding about metasomatism in natural systems comes from outcrop-scale observations of such phenomena due to magmatism in rocks [13][14][15][16][17]. The metasomatism of marble attracted wide attention because of sharp changes in mineralogy between metasomatized and unmetasomatized sections compared to metasomatized igneous or other metamorphic rocks [13][14][15]. A simple chemical system includes the formation of metasomatic products and their well-defined thermodynamic properties [13]. Such metasomatized zones in marble are commonly characterized by the replacement of dolomite by olivine. The formation of the infiltration-driven olivine-bearing metasomatic zone by the silicification of dolomite could be represented by the following Reaction [13]: Dolomite + SiO 2 (aq) = Forsterite + 2Calcite + 2CO 2 . (1) Nevertheless, the Equation (1) requires an aqueous fluid with an activity of SiO 2 of less than one in order to form forsterite at the observed pressure (P) and temperature (T) conditions [14][15][16][17][18][19][20]. In silica-saturated fluids, forsterite cannot be formed by a direct reaction between dolomite and silica-saturated fluid [13]. If fluid is silica-saturated, forsterite can be formed by Equation (2), where the initial silica activity is reduced by the formation of diopside [21][22][23][24][25][26].
Diopside + 3Dolomite = 2Forsterite + 4Calcite + 2CO 2 . (2) Several other possibilities have been proposed for the formation of forsterite during the contact metamorphism of carbonate rocks, suggesting that metasomatic olivine in dolomitic marble could be a source of silica other than diopside if the reaction occurred far from equilibrium/disequilibrium [25][26][27][28]. Here, we investigate an infiltration metasomatic zone developed on a dolomitic marble by lamprophyre dyke intrusion. The formation of an olivine-bearing serpentinized metasomatic zone developed on dolomitic marble is examined through textural study, geochemical information, and phase equilibria modelling. We also provide geochemical variation in elements, which might be an important factor in characterizing the mobility of different elements during such an infiltration process. Thus, the main objective of this study is to expand our understanding of geochemical variations during infiltration metasomatism by taking an example of metasomatism caused by a lamprophyre dyke-marble contact zone from the southwestern Korean Peninsula.

Geological Setting and Sampling
In the southwestern Korean Peninsula, the Hongseong-Imjingang belt (Figure 1), which is also called the Gyeonggi marginal belt [29], along the western Gyeonggi Massif has been considered as part of the most plausible collisional belt in the Korean Peninsula. The belt is correlated to the Qinling-Dabie-Sulu belt between the North and South China cratons in terms of collisional tectonics [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Our samples are from a lamprophyre dyke-marble contact zone exposed in the southern part of the Hongseong-Imjingang belt. Such dykes (predominantly quartz porphyry, lamprophyre, andesite, and felsite) in the study area are reported to have formed mostly in the Jurassic times [44]. Lamprophyre dykes are considered as a tectonic marker of late orogenic transtension [45].
Minerals 2020, 10, x FOR PEER REVIEW 3 of 19 and felsite) in the study area are reported to have formed mostly in the Jurassic times [44]. Lamprophyre dykes are considered as a tectonic marker of late orogenic transtension [45].  [30] and references therein).
The medium-grained dark-colored ~1 m-width lamprophyre dyke intruded the dolomitic marble of ~10 m exposure. The dyke consists of dark to brown biotite and amphibole crystals of ~2 to 5 mm in size, indicating a relatively slow cooling during their crystallization because of insulation by the surrounding marble. The light-greenish ~70 cm-width metasomatic area is formed within the marble along the dyke-marble contact (Figure 2a). This area displays well-defined mineralogical zones with a light greenish to dark-colored highly serpentinized area and light brownish-colored partially serpentinized olivine-bearing portions (Figure 2b). The serpentinized area is relatively finegrained (<1 mm) compared to the medium-grained (2-3 mm) olivine-bearing portions. As   The medium-grained dark-colored~1 m-width lamprophyre dyke intruded the dolomitic marble of~10 m exposure. The dyke consists of dark to brown biotite and amphibole crystals of~2 to 5 mm in size, indicating a relatively slow cooling during their crystallization because of insulation by the surrounding marble. The light-greenish~70 cm-width metasomatic area is formed within the marble along the dyke-marble contact (Figure 2a). This area displays well-defined mineralogical zones with a light greenish to dark-colored highly serpentinized area and light brownish-colored partially serpentinized olivine-bearing portions (Figure 2b). The serpentinized area is relatively fine-grained (<1 mm) compared to the medium-grained (2-3 mm) olivine-bearing portions. As we move further Minerals 2020, 10, 828 4 of 18 towards the unmetasomatized marble region, there are alternating mm-scale thin layers of olivine and calcite that could have been formed by the self-organization of minerals driven by grain growth (Figure 2b) [46]. olivine and calcite that could have been formed by the self-organization of minerals driven by grain growth (Figure 2b) [46]. A total of nine samples were systematically collected from a road-cut outcrop, exposing a metasomatized zone comprising a lamprophyre dyke ~1 m in width ( Figure 3). Three samples of lamprophyre dyke were collected from this dyke at distances 0.5 m apart (Figure 3a). We avoided sampling close to the contact zone in order to obtain the original composition of the lamprophyre dyke. Three olivine-bearing samples (0.5 m apart from one another) were also collected from the partially serpentinized, olivine-enriched area ( Figure 3b). Again, three marble samples were collected, 0.5 m apart, ~1 m away from the metasomatized region ( Figure 3c). From these samples, petrographic observation was carried out on thin sections to investigate the changes in mineralogy and bulk rock chemistry during the metasomatic processes. Because of the consistency in the mineral assemblage of each group, one sample from each group is considered representative for the further investigation using both the electron microprobe and bulk rock chemistry to assess the variations in mineral chemistry as well as the major, trace, and rare earth element (REE) abundances, respectively. A total of nine samples were systematically collected from a road-cut outcrop, exposing a metasomatized zone comprising a lamprophyre dyke~1 m in width ( Figure 3). Three samples of lamprophyre dyke were collected from this dyke at distances 0.5 m apart (Figure 3a). We avoided sampling close to the contact zone in order to obtain the original composition of the lamprophyre dyke. Three olivine-bearing samples (0.5 m apart from one another) were also collected from the partially serpentinized, olivine-enriched area ( Figure 3b). Again, three marble samples were collected, 0.5 m apart,~1 m away from the metasomatized region ( Figure 3c). From these samples, petrographic observation was carried out on thin sections to investigate the changes in mineralogy and bulk rock chemistry during the metasomatic processes. Because of the consistency in the mineral assemblage of each group, one sample from each group is considered representative for the further investigation using both the electron microprobe and bulk rock chemistry to assess the variations in mineral chemistry as well as the major, trace, and rare earth element (REE) abundances, respectively. olivine and calcite that could have been formed by the self-organization of minerals driven by grain growth (Figure 2b) [46]. A total of nine samples were systematically collected from a road-cut outcrop, exposing a metasomatized zone comprising a lamprophyre dyke ~1 m in width ( Figure 3). Three samples of lamprophyre dyke were collected from this dyke at distances 0.5 m apart (Figure 3a). We avoided sampling close to the contact zone in order to obtain the original composition of the lamprophyre dyke. Three olivine-bearing samples (0.5 m apart from one another) were also collected from the partially serpentinized, olivine-enriched area ( Figure 3b). Again, three marble samples were collected, 0.5 m apart, ~1 m away from the metasomatized region ( Figure 3c). From these samples, petrographic observation was carried out on thin sections to investigate the changes in mineralogy and bulk rock chemistry during the metasomatic processes. Because of the consistency in the mineral assemblage of each group, one sample from each group is considered representative for the further investigation using both the electron microprobe and bulk rock chemistry to assess the variations in mineral chemistry as well as the major, trace, and rare earth element (REE) abundances, respectively.

Lamprophyre
All the three lamprophyre samples are mineralogically similar and show minor grain size variations. The lamprophyre sample consists mainly of amphibole, biotite, and plagioclase (Figure 3a,d and Figure 4). Biotite and amphibole are present in similar amounts and constitute most of the sample (Figure 4a). Plagioclase covers~20% of the sample. A minor amount (1-2%) of quartz is present occasionally. Biotite appears as mm-size, elongated laths, and is mainly present as a group of three to four laths. The amphibole shape is wider and bigger compared to biotite. It also exists as a group of grains in the plagioclase matrix. Few amphiboles have apatite inclusions (Figure 4b) that are not observed in the matrix. Plagioclase forms subhedral grains that are mostly interconnected. The major opaque mineral is ilmenite, and it is present dispersed in the matrix, as inclusions, and as discrete grains on the grain boundaries of amphibole and biotite. given for panel c is same for all panels. (d-f) Thin section photographs of lamprophyre dyke, metasomatized marble, and dolomitic marble, respectively. Bt-Biotite; Ilm-Ilmenite; Pl-Plagioclase; Amph-Amphibole; Atg-Antigorite; Ol-Olivine; Cal-Calcite; Dol-Dolomite.

Lamprophyre
All the three lamprophyre samples are mineralogically similar and show minor grain size variations. The lamprophyre sample consists mainly of amphibole, biotite, and plagioclase (Figures 3a,d  and 4). Biotite and amphibole are present in similar amounts and constitute most of the sample (Figure 4a). Plagioclase covers ~20% of the sample. A minor amount (1-2%) of quartz is present occasionally. Biotite appears as mm-size, elongated laths, and is mainly present as a group of three to four laths. The amphibole shape is wider and bigger compared to biotite. It also exists as a group of grains in the plagioclase matrix. Few amphiboles have apatite inclusions (Figure 4b) that are not observed in the matrix. Plagioclase forms subhedral grains that are mostly interconnected. The major opaque mineral is ilmenite, and it is present dispersed in the matrix, as inclusions, and as discrete grains on the grain boundaries of amphibole and biotite.

Metasomatized Intermediate Marble
Three intermediate metasomatized partially serpentinized marble samples consist of dolomite, calcite, olivine, serpentine (antigorite), biotite, spinel, and hematite (Figures 3b,e and 5). Most of the dolomite has a resorbed texture with an irregular boundary. They are mostly replaced by calcite and serpentine in a large area in the metasomatized thin section (Figure 5a). Serpentinization appears as large pods in association with calcite and minorly resorbed dolomite. Few olivine grains are preserved within the serpentinized pods with resorbed olivine in them ( Figure 5b). They might be former olivine grains that were replaced during a later hydration event. Only two biotite grains are observed in the entire thin section (Figure 5c). They appear along the contact between the calcite and serpentinized pods. Biotite has a thick blade-like texture compared to the elongated ones in the lamprophyre. Minor euhedral spinel is present along the dolomite-calcite contact ( Figure 5d). The major oxide mineral is hematite, and Ti is absent. It is easily distinguished by their polished surface compared to the rough surface that is commonly observed in magnetite. Hematite forms as micrometer-sized grains dispersed along the grain boundaries of serpentinized pods (Figure 5e). They appear like the oxidation texture formed on earlier olivine grains. They are also present as veins and

Metasomatized Intermediate Marble
Three intermediate metasomatized partially serpentinized marble samples consist of dolomite, calcite, olivine, serpentine (antigorite), biotite, spinel, and hematite (Figure 3b,e and Figure 5). Most of the dolomite has a resorbed texture with an irregular boundary. They are mostly replaced by calcite and serpentine in a large area in the metasomatized thin section (Figure 5a). Serpentinization appears as large pods in association with calcite and minorly resorbed dolomite. Few olivine grains are preserved within the serpentinized pods with resorbed olivine in them ( Figure 5b). They might be former olivine grains that were replaced during a later hydration event. Only two biotite grains are observed in the entire thin section (Figure 5c). They appear along the contact between the calcite and serpentinized pods. Biotite has a thick blade-like texture compared to the elongated ones in the lamprophyre. Minor euhedral spinel is present along the dolomite-calcite contact ( Figure 5d). The major oxide mineral is hematite, and Ti is absent. It is easily distinguished by their polished surface compared to the rough surface that is commonly observed in magnetite. Hematite forms as micro-meter-sized grains dispersed along the grain boundaries of serpentinized pods (Figure 5e). They appear like the oxidation texture formed on earlier olivine grains. They are also present as veins and discrete grains, well-dispersed in the calcite dolomite matrix. Replacement calcite precipitation also occurs along the cleavage planes of dolomite grains (Figure 5f). discrete grains, well-dispersed in the calcite dolomite matrix. Replacement calcite precipitation also occurs along the cleavage planes of dolomite grains (Figure 5f).

Marble
All the three marble samples consist mostly of dolomite (Figures 3c,f and 6). Near the contact zone, where metasomatism occurred, veins of serpentine and calcite were formed in the dolomitic marble ( Figure 6). Here, both a serpentine vein with precipitated calcite (Figure 6a) and a calcite vein with precipitated serpentine (Figure 6b) occur simultaneously, in all three samples. There are no calcite grains observed in the marble sample other than those created in the vein filling fractures.  100µm 100µm  discrete grains, well-dispersed in the calcite dolomite matrix. Replacement calcite precipitation also occurs along the cleavage planes of dolomite grains (Figure 5f).

Marble
All the three marble samples consist mostly of dolomite (Figures 3c,f and 6). Near the contact zone, where metasomatism occurred, veins of serpentine and calcite were formed in the dolomitic marble ( Figure 6). Here, both a serpentine vein with precipitated calcite (Figure 6a) and a calcite vein with precipitated serpentine (Figure 6b) occur simultaneously, in all three samples. There are no calcite grains observed in the marble sample other than those created in the vein filling fractures.

Electron Probe Micro Analyzer (EPMA)
The mineral compositions of three representative samples of the lamprophyre dyke, the intermediate metasomatized zone, and the dolomitic marble were analyzed using a JEOL JXA-8100 Superprobe, Electron Probe Micro Analyzer (EPMA), housed at the Earth System Sciences, Yonsei University, Seoul, Korea. Analyses were performed using an accelerating voltage of 20 kV, beam current of 20 nA, and counting time of 10 s. Care has been taken to analyze mineral core compositions in order to obtain compositions that might be present during peak crystallization/metasomatic conditions. An electron beam spot size of 5 µm is used for the analysis of biotite, amphibole, ilmenite, olivine, serpentine, calcite, dolomite, spinel, and hematite and 15 µm for plagioclase. Natural and synthetic silicates and oxides supplied by JEOL and ASTIMEX standards Ltd. (Saint-Hubert, QC, Canada), were used for calibration. The data were reduced using the ZAF correction procedures supplied by JEOL. Apatite standardization and offline interference corrections have been carried out based on suggestions from [47]. An electron beam spot size of 15 µm is used for the apatite analysis. The standards for apatite and REEs are generously provided by Dr. Daniel Harlov, GFZ, Postdam, Germany.

Bulk Chemistry
A whole-rock analysis of three representative samples of the lamprophyre, the intermediate metasomatized zone, and the dolomitic marble were carried out for the major, trace, and rare earth element (REE) abundances at Activation Laboratories, Ltd., Ancaster, ON, Canada. The lithium metaborate/tetraborate fusion ICP method was used for the major and trace elements. Samples were run for major oxides and selected trace elements on a combination simultaneous/sequential Thermo Jarrell-Ash ENVIRO II ICP or a Varian Vista 735 ICP. Calibration was performed using 14 prepared USGS and CANMET-certified reference materials. One of the 14 standards was used during the analysis for every group of 10 samples. Totals should be between 98.5% and 101%. If the results came out lower, the samples were scanned for base metals. Low reported totals may indicate sulphate being present or other elements such as Li, which would not normally be scanned for. Samples with low totals, however, were automatically re-fused and reanalyzed. Option 4B1 was used for accurate levels of the base metals Cu, Pb, Zn, Ni, and Ag. In-lab standards (traceable to certified reference materials) or certified reference materials were used for quality control. Samples were analyzed using a Varian Vista 735 ICP. Option 4B-INAA (Instrumental Neutron Activation Analysis) for the As, Sb, high W > 100 ppm, Cr > 1000 ppm, and Sn > 50 ppm (for details, please visit https://actlabs.com/geochemistry/lithogeochemistry-and-whole rock analysis/).

Marble
Serpentine, calcite, and dolomite are analyzed in the marble sample (Supplementary Materials  Table S3). Serpentine has X Mg = 0.99, with a very small content of FeO (~0.97 wt %) compared to that in the metasomatized zone. In the serpentine, the F and Cl values are~0.3 wt % and~0.01 wt %, respectively. Calcite has~52 wt % CaO, with a small amount of MgO (~1.38 wt %) and FeO (~0.04 wt %) compared to the metasomatized zone. Dolomite consists of~20 wt % MgO and~30 wt % CaO with minor FeO~0.15 wt %.

Bulk Chemistry
The  Table S4).

Bulk Chemistry
The  Table S4).    Table S4). Zr, V, Cr, Y, Ba, LREE, Sr, U, and Th are enriched in the metasomatized marble compared to the marble (Figure 7d; Figure 8a-c). Among the elements, Zr, V, Cr, Y, and Ba are moderately enriched, and have values less than that of the lamprophyre dyke (Figure 7d). The primitive mantle normalized REE values [48] show that they are high in the lamprophyre dyke compared to the marble (Figure 8a). The REE pattern shows that LREEs are comparatively depleted compared to HREEs in the dyke sample (Figure 8a). LREEs in the marble are slightly enriched compared to HREEs (Figure 8a). In the metasomatized marble, LREEs are highly enriched, and HREEs show a flat pattern comparable to the marble (Figure 8a). Trace element composition of the representative samples are divided into three groups based on their enrichment in the metasomatized marble compared to the marble (Supplementary Materials  Table S4). Zr, V, Cr, Y, Ba, LREE, Sr, U, and Th are enriched in the metasomatized marble compared to the marble (Figure 7d; Figure 8a-c). Among the elements, Zr, V, Cr, Y, and Ba are moderately enriched, and have values less than that of the lamprophyre dyke (Figure 7d). The primitive mantle normalized REE values [48] show that they are high in the lamprophyre dyke compared to the marble (Figure 8a). The REE pattern shows that LREEs are comparatively depleted compared to HREEs in the dyke sample (Figure 8a). LREEs in the marble are slightly enriched compared to HREEs ( Figure  8a). In the metasomatized marble, LREEs are highly enriched, and HREEs show a flat pattern comparable to the marble (Figure 8a).  The Sr, U, and Th in the metasomatized marble are very high compared to both the lamprophyre dyke and the marble (Figure 8b). There are no other elements except these three elements that show such a high enrichment compared to the other two samples. Among the elements, Sr shows the highest enrichment of~600 ppm, and U and Th are moderately enriched. Most of the other analyzed elements such as Be, Rb, Ni, Cu, Zn, Ag, Nb, Ta, W, Pb, Ge, Sc, Co, Ga, Cs, and Hf have high contents in the lamprophyre dyke. These elements are not particularly enriched in the metasomatized marble. All these elements have comparatively similar values in both the metasomatized and the un-metasomatized portions of the marble.

Phase Equilibria Modelling
The petrologic pseudo-sections were computed using PERPLE_X 6.7.9 version available at http://www.perplex.ethz.ch [49][50][51] using the hp02ver.dat database [52]. An H 2 O-CO 2 fluid equation of state [53] is used to model these phase diagrams. The bulk chemistry data of the intermediate metasomatized marble (Supplementary Materials Table S4) is used for the modelling. The P 2 O 5 , Na 2 O, and TiO 2 concentrations were not considered due to their low contents (<0.5 wt %). The total loss on ignition (LOI) in this sample is 32.88. The H 2 O content is assumed to be 0.1% of this total LOI. The value of CO 2 is 30.25 wt % and of H 2 O is 2.5 wt %. The solid solution models used for the modelling are olivine (O(HP)) [52], serpentine (Atg; ideal), calcite (Cc(AE)) [54], dolomite (Do(HP)) [52], biotite (Bio(TCC)) [55], and spinel (Sp(HP)) [52].
In the first calculation, we attempted to vary the pressure (P) between 30 and 200 MPa and temperature (T) between 300 and 800 • C. The result shows that olivine, diopside, dolomite, calcite, and CO 2 are stable in this window, where the dolomite to calcite transition occurs above 500 to 650 • C (Figure 9a). We have not observed any diopside in our sample. In addition, we have not observed stable biotite or serpentine in the phase diagram at the first attempt. The Sr, U, and Th in the metasomatized marble are very high compared to both the lamprophyre dyke and the marble (Figure 8b). There are no other elements except these three elements that show such a high enrichment compared to the other two samples. Among the elements, Sr shows the highest enrichment of ~600 ppm, and U and Th are moderately enriched. Most of the other analyzed elements such as Be, Rb, Ni, Cu, Zn, Ag, Nb, Ta, W, Pb, Ge, Sc, Co, Ga, Cs, and Hf have high contents in the lamprophyre dyke. These elements are not particularly enriched in the metasomatized marble. All these elements have comparatively similar values in both the metasomatized and the unmetasomatized portions of the marble.
In the first calculation, we attempted to vary the pressure (P) between 30 and 200 MPa and temperature (T) between 300 and 800 °C. The result shows that olivine, diopside, dolomite, calcite, and CO2 are stable in this window, where the dolomite to calcite transition occurs above 500 to 650 °C (Figure 9a). We have not observed any diopside in our sample. In addition, we have not observed stable biotite or serpentine in the phase diagram at the first attempt. Because of the hematite that is present as oxidation rims on the serpentine pods, vein-filled fractures, and discrete grains, we assumed an oxygen fugacity of ~log fO2 = −14 with a magnetite to hematite transition at 600-800 °C [56] in the second run. This result is more comparable to our Because of the hematite that is present as oxidation rims on the serpentine pods, vein-filled fractures, and discrete grains, we assumed an oxygen fugacity of~log fO 2 = −14 with a magnetite to hematite transition at 600-800 • C [56] in the second run. This result is more comparable to our petrologic observation except for the stability of diopside (Figure 9b). The second run successfully generated olivine, serpentine, biotite, spinel, calcite, dolomite, and hematite. Here, olivine, biotite, and calcite are stable everywhere in the phase diagram. The mineral composition of olivine shows X Mg = 0.94. We have computed the isopleths for the X Mg variation in olivine in the phase diagram. Our isopleth calculation shows that the olivine X Mg is increasing towards the lower temperature portion in the phase diagram. An X Mg of 0.94 is present towards~750 • C. Since we observed spinel in the sample, we have computed the isopleths for X Mg variation in spinel as well in the phase diagram. Spinel in our sample has an X Mg of 0.86. This composition is also present near~750 • C. Above~130 MPa, spinel is absent and anorthite is stable. Therefore, the phase diagram result suggests a maximum pressure of~130 MPa. Serpentine and hematite are stable towards the low-temperature portion at~450 • C. Now, the major question is why we could not get any diopside in our sample. Our phase diagram calculations suggest that diopside is stable in the pressure-temperature conditions considered for these calculations.
Since we neither have observed any diopside inclusions in olivine nor have seen any possibility of low silica activity at out-of-equilibrium conditions, the K 2 O activity has changed during the third run. The absence of diopside at high concentration of K is shown by the experimental results on granodioritic samples [57,58]. Furthermore, we have observed stable biotite in our sample, which makes it possible to consider varying K 2 O activity during the phase diagram modelling. We have varied the log activity of K 2 O from −80 to −30, and the temperature from 300 to 800 • C, with a pressure of 130 MPa. The result shows that with a high K 2 O activity and at~750 • C, olivine, spinel, biotite, and calcite are stable without diopside (Figure 10). Diopside will present only below a log a K2O > −40, and above this condition all the phases observed in the metasomatized zone are stable.
Minerals 2020, 10, x FOR PEER REVIEW 12 of 19 Figure 10. Log activity K2O-temperature pseudosection calculated at a pressure of 130MPa. Bulk chemistry used for the calculation is given above the diagram.

Isocon Method
To evaluate the percentage of addition or subtraction of mobile elements during metasomatism, we have applied the isocon method [59,60]. The density of metasomatized and un-metasomatized marble is measured, using conventional methods by measuring the mass and volume of the samples. The density of the unmetasomatized and metasomatized samples is 2.75 g/cm 3 and 2.74 g/cm 3 , respectively. This defines an isocon for the elements, as shown in the formula of Equation (3) below: Figure 10. Log activity K 2 O-temperature pseudosection calculated at a pressure of 130MPa. Bulk chemistry used for the calculation is given above the diagram.

Isocon Method
To evaluate the percentage of addition or subtraction of mobile elements during metasomatism, we have applied the isocon method [59,60]. The density of metasomatized and un-metasomatized marble is measured, using conventional methods by measuring the mass and volume of the samples. The density of the unmetasomatized and metasomatized samples is 2.75 g/cm 3 and 2.74 g/cm 3 , respectively. This defines an isocon for the elements, as shown in the formula of Equation (3) below: where C MM is the concentration of oxide or element in the metasomatized sample and C M is the concentration of oxide or element in the unmetasomatized sample. The percentage difference in the mobile elements or oxides from this isocon can be calculated using Equation (4): These values are given in the Supplementary Materials Table S5. The deviation of each oxide or element from the isocon is represented in Figure 11. In the major elements, SiO 2 (552%), FeO (610%), and TiO 2 (487%) show maximum enrichments (Figure 11a). Al 2 O 3 , MnO, and K 2 O are moderately enriched (~200-300%). CaO, MgO, and Na 2 O are the least mobile or depleted (−33-4%) (Figure 11b). All the REEs are highly enriched in the metasomatized marble sample (>400%) (Figure 11c,d). Trace elements such as Th (576%), Cs (400%), Y (361%), U (304%), V (220%), Sr (167%), Zr (125%), Ba, and Nb (100%), and Cr (50%) also show a high enrichment compared to the unaltered sample (Figure 11c,d).

Discussion
The intrusion of hot magma into country rocks is a common phenomenon, and is important in understanding the process of the exchange of heat and fluids between cooling magma and cold country rocks [16,17,[61][62][63]. Fluid infiltration and heating around the boundaries of a hot magmatic intrusion cause chemical and mineralogical alterations to nearby rocks [15][16][17]27]. Such altered rocks are typically called skarn [61][62][63][64][65][66]. Different types of rocks such as limestone, dolostone, marble, granite, basalt, conglomerate, tuff, and shale can be transformed into skarn by metasomatism [64][65][66]. Skarns can form on both sides of a contact between a magma body and its surrounding rock [64][65][66]. Those formed on igneous side of the contact are known as endoskarns, while those formed on the country-rock side of the contact are known as exoskarns [64][65][66]. In this study, we provide the characteristics of formation of such a metasomatized zone (exoskarn) developed at the contact between the intruded lamprophyre dyke and the dolomitic marble. We have not observed any effect

Discussion
The intrusion of hot magma into country rocks is a common phenomenon, and is important in understanding the process of the exchange of heat and fluids between cooling magma and cold country rocks [16,17,[61][62][63]. Fluid infiltration and heating around the boundaries of a hot magmatic intrusion cause chemical and mineralogical alterations to nearby rocks [15][16][17]27]. Such altered rocks are typically called skarn [61][62][63][64][65][66]. Different types of rocks such as limestone, dolostone, marble, granite, basalt, conglomerate, tuff, and shale can be transformed into skarn by metasomatism [64][65][66]. Skarns can form on both sides of a contact between a magma body and its surrounding rock [64][65][66].
Those formed on igneous side of the contact are known as endoskarns, while those formed on the country-rock side of the contact are known as exoskarns [64][65][66]. In this study, we provide the characteristics of formation of such a metasomatized zone (exoskarn) developed at the contact between the intruded lamprophyre dyke and the dolomitic marble. We have not observed any effect of a reverse process in the outcrop, with the fluids entering the hot lamprophyre dyke and metasomatizing it. Our petrographic observation shows that most of the biotite and amphibole have not undergone any alterations/dehydration due to inflow of CO 2 from the country rocks to dyke. The Ca and Mg (main elements in the marble) bearing CO 2 expulsion towards the dyke could have generated dry minerals by dehydration of amphibole/biotite in the dyke because of the high volume of CO 2 in the marble. However, such alterations are not observed in the lamprophyre dyke.
In our example, the lamprophyre dyke intruded the marble producing the development of the metasomatized marble zone characterized by olivine, serpentine, biotite, spinel, calcite, dolomite, and hematite. As the intruding magma cools down, it releases heat and fluid. Fluid expelled from the magma acts like a solvent that might have ability to dissolve and re-precipitate new minerals in the neighboring rocks [67,68]. Fluid released from the crystallizing intrusion infiltrates through interconnected fracture networks, pores, and along mineral grain boundaries [15,16,[61][62][63][64]68]. Equation (1) shows that the olivine and calcite-bearing metasomatized marble region could be formed by the infiltration of silica-saturated fluid that dissolved existing dolomite in the marble. Our phase diagram result, in the first run, suggests that olivine, diopside, dolomite, calcite, and CO 2 are stable in the bulk chemistry of the metasomatized marble, where the dolomite to calcite transition occurs above 500 to 650 • C (Figure 9a). However, this result could not generate all the minerals observed in the metasomatized marble, such as biotite, spinel, and hematite.
Our detailed observations revealed that hematite acts as a major oxide mineral in the metasomatized marble. Serpentine pods bearing resorbed olivine have an oxidation rim of hematite around them. This rim could have formed initially on olivine grain boundaries before serpentinization occurred. The formation of the rim could be represented by the following reaction: 2 Fe 2 SiO 4 (olivine) + O 2 = 2 Fe 2 O 3 (hematite) + 2 SiO 2 .
We have not observed any graphite in the metasomatized marble, where the presence of graphite would represent reduced conditions. For these reasons, we calculated the new pseudosection at an oxygen fugacity of~log fO 2 = −14 (magnetite to hematite transition at 600-800 • C) [56] in the second run. Our new calculations show that biotite and spinel is stable at a high temperature with a high oxygen fugacity (Figure 9b). The comparison of the mineral chemistry data of the olivine and spinel with that of the isopleths for them in the P-T conditions indicates that the olivine, biotite, calcite, spinel and diopside assemblage could be formed at~750 • C and 130 MPa. Spinel is absent, and anorthite is stable beyond this pressure. Serpentine is stable towards the low temperature side (Figure 9b). Serpentine formation can be explained by the increase in water activity due to the escape of exsolved CO 2 at low temperature or the influx of a second round of water from the cooling dyke.
If the dolomite was dissolved by the infiltration of silica saturated fluid, diopside should have formed prior to olivine (Figure 9). Previous studies on the variation in SiO 2 vs. CO 2 activity have expected the formation of diopside + calcite by Equation (2) earlier than olivine + calcite forms by Equation (1) [13]. They also predict approximately 10 times more diopside-bearing rock than the current assemblage. Their model fluid flow also suggests that olivine + calcite forms only if the silica in the initial fluid has been removed after formation of diopside by Equation (2) upstream. Our sample has stable biotite formed along with the olivine, spinel and calcite assemblage. The effect of the K concentration on the stability of clinopyroxene is observed in the experiments on granodioritic rocks [57,58]. Therefore, we considered the effect of K activity on the stability of minerals in our third pseudosection calculation. In this attempt, K 2 O is considered as an independent mobile component in the system. Our result suggests that at~750 • C and 130 MPa, the biotite-bearing olivine, spinel, and calcite assemblage is stable above log a K2O~4 0 ( Figure 10). The diopside-bearing assemblage is stable below this activity. The result suggests that K 2 O activity instead of SiO 2 has a major role in destabilizing diopside in the silica-saturated infiltrating fluid.
Our geochemical data and Gresens analysis using the isocon method show that major elements such as SiO 2 , FeO, and a minor amount of K 2 O are mostly infiltrated from the fluid expelled from the lamprophyre dyke (Figures 7 and 11). No/minor addition of CaO or MgO occurred in the metasomatized marble compared to the normal marble. The presence of hematite and biotite shows that infiltrating fluid was relatively oxidizing. LREEs, U, Th, and Sr are the main trace elements highly dissolved in the infiltrating fluid (Figures 8 and 11). HREEs show enrichment and a flat pattern comparable to the dolomitic marble. Most of the other trace elements show no particular enrichment in the metasomatized marble. However, Zr, V, Cr, Y, and Ba show a slight enrichment ( Figure 11). Our example shows that Si, Fe, K, Sr, U, Th, and REEs are highly mobile during the infiltration metasomatic event (Figures 8 and 11).
In the metasomatized marble, fluid infiltration occurs along mineral grain boundaries, through fracture networks in the dolomite, and by generating nano-scale porosity in the dolomite. Depending on the existing pressure-temperature conditions, dissolved chemical components in the fluid eventually get saturated and precipitate new minerals [68]. This process would last until an equilibrium established between minerals and fluid composition [68]. This study is an example of geochemical and thermodynamic changes that might happen during metasomatic processes at a local scale. Many such studies explain how the breakdown or dissolution of carbonate assemblages occurs in skarn deposits, calcareous sandstones, and many hydrothermally altered rocks [15][16][17][61][62][63][64]68]. In this study, we have shown the importance of K activity in the infiltrating fluid, which could control the mineralogy of the metasomatized marble. Experimental studies show that CO 2 solubility is highly dependent on various cations, such as Ca, Na, and K, in the fluid/melt [69][70][71]. Although much is understood about fluid occurrence in the absence of high P-T constraints [70,71], we mainly extrapolate fluid properties at more familiar low-pressure conditions to study the implications of such process in a regional-scale (lower crust/mantle) metasomatism [71,72]. In a regional scale, fluid-rock interactions play an important role in the evolution and properties of the crust/mantle [3][4][5][6]. A high abundance of C-bearing phases in mantle is obvious from studies of mantle xenoliths, carbonatites, nephelinites, and melilitites [72][73][74][75]. Our study is important in further expanding our knowledge about the capacity of solute-bearing H 2 O-CO 2 fluids to change the geochemistry and mineralogy of the rocks that they are in contact with. Our example shows that Si, Fe, K, Y, V, Sr, Nb, U, Th, and REEs are highly mobile in such fluids. Most of these elements are main components of exploring geochemical evolution of rocks in crust/mantle. The middle crust is composed of rocks at amphibolite facies P-T conditions with a granodioritic bulk composition containing significant amounts of K, Th, and U [8]. The results from this study will help us to understand the possible regional effects of such fluid interactions during crustal/mantle interactions.

Conclusions
(1) The intrusion of the hot lamprophyre dyke into the dolomitic marble generated the metasomatized marble zone containing an olivine, serpentine, biotite, spinel, dolomite, calcite. and hematite assemblage. (2) Fluid infiltration is the main cause of metasomatic alteration in the dolomitic marble at~750 • C/ 130 MPa. (3) The fluid composition was mainly CO 2 , with minor H 2 O, Cl, and F during the initial stage. As the dyke cooled and crystallized, water released from the dyke serpentinized the assemblages that were formed during the initial stage.    Table S5: Isocon method using bulk-chemisty data and density of metasomatized and unmetasomatized samples.

Conflicts of Interest:
The authors declare no conflict of interest. The sponsors had no role in the design, execution, interpretation, or writing of the study.