5.1. Disagreements between the WDS and the XRPD results
It is indicative that there are a few determined discrepancies between the WDS and the XRPD results (Tables 1-4). Namely, accounting the different variation trends between the samples, samples 3 and 5 have changed the place with the sample 2 (5<3<2<1<4 vs. 2<3<5<1<4; Tables 2 and 4), whereas sample 1 have changed own position just in a few places, belonging the sample 4 {5<2<3<4<1 (apfu contents of Sr) and 5<3<2<4<1 [ratios Σ(Pb+Ba)/Σ(Ca+X)] vs. 2<3<5<1<4; Tables 1 and 4}. Thus, there is a poor correlation C(3) of the ionic radiuses (Table 2) variations by the a0, b0, c0 and V0 unit-cell parameters (Table 4) of 0.731; 0.366; 0.620 and 0.593, respectively (Figure S11 in the ESM). Optionally, the interpretation of these disagreements could be reached by assessing the likely structural or/and compositional circumstances, such as: (i) inadequate structural model, leading to the poorly calculated unit-cell parameters; or/and (ii) a wrong apfu’s basis, leading to the miscalculation of the crystal-chemical formulas, and the corresponding ionic radiuses; or/and (iii) the presence of other previously undetected mineral phases, leading also to the miscalculation of the crystal-chemical formulas, and the corresponding ionic radiuses; or/and (iv) the incomplete calculation of the ionic radiuses; or/and (v) that the palette of the structural variations within the samples could take place. Despite seemingly perplexing or even (in)significant, we believe that the listing of these possible reasons could be of highest importance, as a step towards avoiding any eventual misleading. Hence, neither of these disagreements will be apriori rejected, and disagreements will be further investigated in a great detail.
(i) The study emphasizes the Le Bail (1988) method, because of the extensive experiments previously applied for the barite-group of minerals (Kuang et al. 2017; Li et al. 2018; Girard et al. 2019; Ye et al. 2019). Very good profile parameters and relatively low reliability factors characterized by this method (Table S2 in the ESM), satisfactory level of quality of the obtained difference plots [Figures S3 (column II) and S5 in the ESM], and a very high positive correlations C(1) and C(2) among the unit-cell parameters (Figures S6 and S7 in the ESM), corroborate that the studied samples are suitable to celestines and its structural model. A lower quality result of the samples 3 and 5, are most probably influenced by their higher preferred orientations, in comparison with the samples 1, 2 and 4 (see Table S1 and Figure S4 in the ESM). In addition, a considerably lower esd’s (Table 4), which are mostly better even than the reference standards used, provide the validation that the unit-cell parameters were well-calculated and refined. Therefore, these facts allow us to reject this as a possible reason for the aforementioned disagreements.
(ii) In this study, we calculated the apfu’s by using the 4 oxygen anions (Table 1), what led to the calculated theoretical ionic radiuses of the M cations (Table 2). Another choice is that the apfu’s could be also calculated at the 2 (ΣM+S) ions basis. For example, Antao (2012) for therein studied celestine derived (Sr0.966Fe0.001Ba0.001)0.968(SO4)1.027 chemical formula, which is adequate to the herein calculated (Sr0.953Fe0.001Ba0.001)0.955S1.016O4 (F and Cl apfu's in both cases remained the same, i.e. 0.002 and 0.004, respectively; Table S4 in the ESM). As expected, there are no significant differences for the samples 1 and 4; whereas the samples 2, 3 and 5, show a slightly higher content of Sr, S and O ions. The results show that the samples are mutually similar, fitting into the celestine near-end members having only 1.6-3.5 at. % of Sr2+ content (ΔSr=1.9 at. %), substituted by the same contents of Pb2+ (0.7-0.9 at. %), Ba2+ (0.5-0.7 at. %) and Ca2+ (0.2-0.8 at. %). The variations of the apfu content of the Sr and Σ(Pb+Ba)/Σ(Ca+X) ratios remained identical, i.e., 5<2<3<4<1 and 5<3<2<4<1, respectively. The only difference is a slightly lower content of the X component (0.7-1.3 at. %; ΔX=0.3-0.6 at. %) which, in turn, lead to a slightly higher calculated ionic radiuses for the aforementioned three samples, and their 5<3<2<4<1 variation (Table S5 in the ESM). However, the resulting correlations C(4), among these ionic radiuses variations by the a0, b0, c0 and V0 parameters (Table 4) having 0.611; 0.254; 0.501 and 0.467, respectively (Figure S12 in the ESM), are significantly less-correlative than the previous one [i.e. C(3); Figure S11 in the ESM]. Such a low correlativity allows rejecting of this possibility as well.
(iii) Although the observed chemical composition is rather simple (Table 1), the X component could hypothetically indicate to the presence of other mineral phases, such as gypsum (CaSO4×2H2O), anhydrite (CaSO4), native sulfur (S) and calcite (CaCO3). It is well known that these mineral phases have often been occurring in the paragenesis with celestine (Palache et al. 1951; Deer et al. 2013). In addition, there is a possibility of the presence of numerous other minerals, such as anglesite, barite, strontianite (SrCO3), aragonite (CaCO3), cerussite (PbCO3), hydrocerussite [Pb3(CO3)2(OH)2], witherite (BaCO3), SrSO4×1/2H2O phase (Takahashi et al., 1993) etc., making the interpretation even more complex. In order to check an eventual presence of anhydrite (samples 1 and 4) and gypsum, including other minerals with the X component (samples 2, 3 and 5), we implemented the additional recalculations of the WDS analyses (Table S6 in the ESM). These recalculations are based on the CaO component, the apfu’s deficit of the M cations; including the sulfur excess (Table 1).
According to the results, it could be speculated that there is a tentative minor content of: a) anhydrite in the samples 1 (0.17 mol. %) and 4 (0.58 mol. %); b) gypsum in the samples 2 (0.49 mol. %), 3 (0.46 mol. %), and 5 (0.68 mol. %); and c) other minerals with the X component in the samples 2 (0.10 mol. %), 3 (0.30 mol. %), and 5 (0.60 mol. %). If these contents are taken into the account, it appears quite logical and understandable that these minerals couldn't be detected by the XRPD method, because of their quantity that is below the detection limit of about 1-2 mol. This includes a close inspection of the 2θ angle regions, which are fitting into the strongest reflections for these phases, as well. In addition, the WDS method could fail to separate these from the celestine, mainly because of the similarities in the chemical composition, and its limitations of detecting some elements (already mentioned before). The apfu's calculation of 12-coordinated M2+ cations (Table S6 in the ESM) was moreover recalculated by applying the theoretical ionic radiuses of these cations (Table S7 in the ESM). The new correlations C(5) of such ionic radiuses by the a0, b0, c0 and V0 parameters of 0.927; 0.620; 0.850 and 0.832, respectively (Figure S13 in the ESM) have a considerably better fit than the C(3) (Figure S11 in the ESM). Consequently, a minor content of anhydrite and/or gypsum could be present together with the investigated celestines. In contrast, the presence of other minerals with the X component in the paragenesis with celestine (although with the desired 2<3<5<1<4 variations) should be rejected, accounting their lower correlativity [C(6)] of 0.653; 0.325; 0.526 and 0.516, respectively (Figure S14 in the ESM) in comparison with the previously considered two options [i.e. C(3) and C(5); Figures S11 and S13 in the ESM].
The results show that the majority of the samples are represented with celestine, having a neglected anhydrite or gypsum content (0.17-0.68 mol. %). The investigated celestines have the form of solid solutions, with a low quantity of anglesite and barite. The presence of the vacancies (hereinafter Z), and the excessive sulfur content in the samples 2, 3 and 5 are also documented. Therefore, exclusively 1.4-3.2 at. % of the Sr2+ content (ΔSr=1.8 at. %) was substituted by the Pb2+ (0.7-0.9 at. %), Ba2+ (0.5-0.7 at. %), including Z (0.8-1.7 at. %; in three samples). Thus, the new, recalculated crystal-chemical formulas are: (Sr0.986Pb0.009Ba0.005)SO4 (sample 1), (Sr0.977Z0.008Pb0.008Ba0.007)S1.002O4 (sample 2), (Sr0.979Z0.009Pb0.007Ba0.005)S1.003O4 (sample 3), (Sr0.985Pb0.008Ba0.007)SO4 (sample 4) and (Sr0.968Z0.017Pb0.008Ba0.007)S1.006O4 (sample 5). The apfu content of the Sr in all of the samples remain the same as for those exhibited in Table 1, i.e., they increase as 5<2<3<4<1.
Finally, the recalculated occupancies (calc1,2; Table S7 in the ESM) of the twelve-coordination site have very similar values, corroborating the similarities among the samples (Δocc=1.70 at. %), moreover, having the increase in the same order (5<3<2<1<4; Table 2). However, despite this option of the dominant celestines with the presence of a lower amount of gypsum and anhydrite fits better than that of the monomineral celestines (and because of that it could be eventually accepted), its correlation is quite far from the ideal case. Therefore, this option does not provide a complete explanation of the previously discussed discrepancies and their link with the XRPD results, thus being of tentative character.
(iv) According to the apfu’s deficit of the M cations in the samples 2, 3 and 5 (Table 1), it could be speculated that the theoretical ionic radiuses need another recalculation, this time by adding the appropriate sulfur excess of 0.3, 0.3, including 0.6 at. % of the S6+ taken from the tetrahedral site (0.12 Å in coordination IV; Shannon, 1976), respectively. The two options are chosen (Table S8 in the ESM) as the (1) monomineral celestines (Table 2) and the (2) major celestines, barely having any anhydrite or gypsum (Table S7 in the ESM). A similar correlation of these ionic radiuses by the a0, b0, c0 and V0 parameters of 0.733; 0.368; 0.622 and 0.595, respectively [C(7); Figure S15 in the ESM]; including these of 0.669; 0.300; 0.558 and 0.525, respectively [C(8); Figure S16 in the ESM] is observed in these two cases. However, neither the first, nor the second option do not reach any improvement, in regards to those from the C(3) (Figure S11 in the ESM). Hence, this correlation should also be rejected as a possible reason for the aforementioned disagreements. At last, a single remaining solution should be taken into consideration.
(v) Although the crystal structure refinements are beyond the scope of this paper, our previous studies of various mineral species, and solid-solutions, have demonstrated that the different unit-cell parameters, various polyhedral distortions, site occupancy factors, bond lengths, bond angles, valence units, etc., could be induced either by (a) the different inserted cations into the mineral structure; or/and by (b) the different conditions of their formation, in particular, the temperature and pressure (Tančić 2017, 2018; Tančić and Kremenović 2022; Tančić et al. 2012, 2020).
(a) Whilst considering the influenced variations of the unit-cell parameters accounting the different inserted cations into the mineral structure, we initiated the process, by introducing the calculations of their presumed values by the multiplication of the Sr, Ca, Pb and Ba apfu's with the corresponding unit-cell parameters of celestine, anhydrite, anglesite and barite reference standards (ICDD-PDF's: 89-0953, 37-1496, 36-1461 and 24-1035, respectively). For the selected apfu's, we have chosen the two previously discussed options: (1) the celestines as the monomineral phases (Table 1); and (2) the option of the celestines without Ca, which hypothetically belongs to the minor amounts of gypsum and anhydrite phases (Table S6 in the ESM). The results (presented at Table S9 in the ESM) indicate that the largest differences (Δ) between these presumed values and those of the XRPD method (Table 4) are, valid for both options, occurring in the samples 2, 3 and 5. Such correlativity is expected and suites to the already emphasized vacancies, and the here used calculations. Accordingly, the ratios increased by ca. 1, 1 and 2 %, respectively. In both cases, we observe an excellent correlations of the calculated ionic radiuses (Table 2 and Table S7 in the ESM) by the a0, b0, c0 and V0 parameters: (1) 1.000; 1.000; 1.000 and 0.995, respectively [C(9); Figure S17 in the ESM]; and (2) 0.997; 0.998; 0.997 and 0.977, respectively [C(10); Figure S18 in the ESM]. Because both options are almost identical, this couldn’t be used as a reliable parameter for distinguished factors among them. On the other hand, these results further indicate that the presumed unit-cell parameters should be theoretically near the realistic chemical composition. However, as discussed earlier, such scenario is obviously not the case. Namely, the presumed unit-cell volumes of the samples 2, 3 and 5 have no fitting in no case, because they have significantly lower values, even by comparing with the anhydrite (ICDD-PDF: 37-1496; V=305.60 Å3) reference standard. Consequently, we observe a very poor correlation between the presumed (Table S9 in the ESM) and determined (Table 4) a0, b0, c0 and V0 unit-cell parameters of 0.397; 0.388; 0.403 and 0.348, respectively [C(11); Figure S19 in the ESM].
Thus, we further reconsider the impact of the existing vacancies in the celestine structure on their unit-cell parameters. Namely, the available reference data (Table S10 in the ESM) show that there is an example having a significant content of the vacancy of 3 at. % [Antao 2012; already discussed within part (ii)]. This celestine example has more-less similar [ICDD-PDF's: 05-0593 and 89-0953; Table 4; Miyake et al. (1978)], or even larger unit-cell parameters, relative to those without any vacancy [Hawthorne and Ferguson (1975); Jacobsen et al. (1998); Ye et al. (2019)]. Furthermore, three selected samples showing the identical average <M-O> distances of 2.827(1)Å (Hawthorne and Ferguson 1975; Jacobsen et al. 1998; Antao 2012). Accordingly, it seems that the existing vacancies in the celestine structure do not have any significant impact on their unit-cell parameters. The reasons for such behavior could be the geometrical changes of the SO4 and MO12 polyhedral, i.e., a decrease of the average <M-O> distance, the charge on the O ions that have lower values, including the average <S-O> distance that is longer in this case; or vice versa (Antao 2012). In addition, the tetrahedral distortions are a function of the geometry of the structure, rather than the chemistry of the twelve-coordinated site (Hawthorne and Ferguson 1975; Brigatti et al. 1997). In order to check the afore described option, another two variances discussed earlier (ii-iv) yet without the existing vacancies (included for the samples 2, 3 and 5) are taken into the consideration: (1) celestines as monomineral phases, with previously characterized apfu's (Table 1), including the theoretical ionic radiuses of the M cations with occupancies of the twelve-coordination site (Table 2) that are further recalculated (Tables S11 and S12 in the ESM), and (2) as the major celestines with the neglected gypsum or anhydrite phases (including the previously determined apfu's; Table S6 in the ESM). The recalculation includes the theoretical ionic radiuses of the M cations and occupancies of the twelve-coordination site (Table S7 in the ESM), which are presented at Tables S13 and S14 in the ESM. The correlations of the recalculated ionic radiuses (Tables S12 and S14 in the ESM) by the a0, b0, c0 and V0 parameters are: (1) 0.884; 0.957; 0.955 and 0.927, respectively [C(12); Figure S20 in the ESM], including (2) 0.126; 0.102; 0.113 and 0.098, respectively [C(13); Figure S21 in the ESM]. Therefore, the first option [C(12)] shows the best fit of all of the available correlations associated with the problem of the ionic radiuses by unit-cell parameters variations [i.e. C(3)-C(8)]. On the contrary, the second option [C(13)] shows the lowest correlativity of all of these correlations.
Finally, the newly calculated unit-cell parameters are characterized on the basis of the apfu's (Table S11 in the ESM) and are presented in Table S15 in the ESM. The correlations between these a0, b0, c0 and V0 values, with those of the XRPD method (Table 4) having 0.884; 0.955; 0.959 and 0.936, respectively [C(14); Figure S22 in the ESM] have, in this case, a considerably good and significantly better correlation, than the previous one associated with this problematic [i.e. C(11); Table S9 and Figure S19 in the ESM]. These observations corroborate that the existing vacancies in the structures of the samples 2, 3 and 5 [C(9) and C(10); Figures S17 and S18 in the ESM] do not have any significant impact on their unit-cell parameters. Such a good correlativity further leads to the final conclusion that entire set of 1-5 samples should be interpreted exclusively as a monomineral celestine near-end members, in the agreement with the SEM-WDS, XRPD and IR results. Therefore, the correlativity allows definitively rejecting the option (iii) as a possible cause for the previously discussed disagreements. In addition, in a such manner, it is possible to provide explanation for the slightly better correlation in the cases of the higher similarity for any purpose of their previous comparison, i.e. C(7) vs. C(8) and C(9) vs. C(10) (Figures S15, S16, S17 and S18 in the ESM).
(b) The results in the Tables S9 and S15, show that there is a slightly different ratio between various crystallographic axes, such as c0<a0<b0 (samples 1 and 4), a0<c0<b0 (samples 2 and 3) and a0=c0<b0 (sample 5). Such different ratios indicates the presence of the axial anisotropy, which was previously observed and studied for the synthetic and natural end members of the barite group of minerals (see for examples: Kuang et al. 2017; Li et al. 2018; Girard et al. 2019; Ye et al. 2019; and references therein). This phenomenon appears in the conditions recording an increase of the temperature environment (axial expansion anisotropy) and elevated formation pressure (axial compression anisotropy) conditions. To the best of our knowledge, there is a lack of similar experiments hitherto dealing with the solid-solutions between minerals within the barite group. Accordingly, we further recalculated the variations of the temperature dependence by the unit-cell parameters for the Clt98Ang02, Clt96Ang04 and Clt94Ang06 celestine-anglesite (Table S16 in the ESM), and for the Clt99Brt01, Clt98Brt02 and Clt97Brt03 celestine-barite (Table S17 in the ESM) solid-solution series [mineral name symbols such as Ang, Brt and Clt refer to anglesite, barite, and celestine, respectively (Warr, 2021)]. These recalculations use the combination of the initial experimental data at the ambient pressure for anglesite (Li et al. 2018), and celestine and barite (Ye et al. 2019); according to the suitable cell transformation from the Pbnm (II) to the Pnma (I) space group, constrained as follows: a0I=b0II, b0I=c0II, and c0I=a0II. The resulting data (Tables S16 and S17 in the ESM) are further used for the construction of Fig. 4. In addition, we also calculated expansion degree of the unit-cell parameters (i.e., their ratio) of celestine, anglesite and barite between 320K and 520K (Table S18 in the ESM).
By using the recalculated theoretical ionic radiuses of the M cations (Table S12 in the ESM), the excesses of the Sr2+, Ca2+ and Ba2+ apfu's, reaching over 1.44 Å, are converted as the total Pb2+, i.e. as the anglesite 1.40-3.10 mol. % content in celestine. Similarly, the excesses of Sr2+, Ca2+ and Pb2+ apfu's over 1.44 Å are converted as the total Ba2+, i.e. as the barite 0.41-0.91 mol. % content in celestine (Table 7). Subsequently, the Ang and Brt values (Table 7, plotted at Fig. 4) further allowed the estimation of the formation temperatures for the investigated 1-5 celestine samples by using their determined unit-cell parameters (Table 4). The results show that a set of very similar temperatures are characterizing both, the celestine-anglesite and the celestine-barite solid-solution series. In that manner, we have the confirmation that the recalculated Ang and Brt values are valid. The results clearly exhibit that the sample 2 underwent lowest temperatures reaching as low as ~368K, whereas the sample 4 was under the exposure to higher most temperature range reaching ~430K. The samples 1, 3 and 5 were formed at very similar average temperatures of ~387K, ~384K and ~387K, respectively. Therefore, the sampled celestines were formed at the ~368-430K (~95-157 oC) temperature range, at the ambient pressure conditions. Different correlations between the crystallographic axes are b0<a0<c0 (samples 1 and 4) and a0<b0<c0 (samples 2, 3 and 5).
At last, we provide the explanation of the discussed discrepancies between the WDS and the XRPD results. Namely, Figure S23 in the ESM contains five possible variations (plotted from Fig. 4h; should be taken into account only as an example, because of its validity for each of the other a0, b0 and c0 unit-cell axes, including the Ang contents): 1. volume increase by temperature increase, including the Brt contents increase; 2. volume increase by constant temperature, including the Brt contents increase; 3. volume increase by temperature decrease, including the Brt contents increase; 4. constant volume by temperature increase, including the Brt contents decrease; and 5. volume increase by temperature increase, having a constant Brt content. We underline that each of these possible interpretations could be also vice versa. In our favorable case, we concluded that the investigated celestine 1-5 samples, are mostly with the first variation type, having partially the fifth variation type, i.e., that their unit-cell parameters increased mainly accounting a temperature increase, whereas the Ang and the Brt contents are reaching almost the constant (i.e., having a small content difference of ΔAng=1.70 mol. %, and ΔBrt=0.50 mol. %; Table 7) following the increase status. Because the samples 3 and 5 were exposed to higher temperatures than the sample 2, whereas the sample 4 was formed at a higher temperature than the sample 1, the former has larger thermal expansions of the unit-cell parameters than the latter. This is the main reason for the average 2<3<1~5<4 and 2<3~1=5<4 variation behaviors (Tables 4 and 7, respectively). In addition, the samples 3 and 5 have larger expansion of the b0 axis, reaching values over even the sample 1; other possible interpretation is that the sample 1 was formed at a higher pressure by comparing to the samples 3 and 5, because this axis is the most compressible (Kuang et al. 2017; Ye et al. 2019). Accordingly, we strongly believe that this argument is sufficient evidence, supporting the interpretation that the formation temperature is the primary cause, whereas different inserted cations into the structure should be interpreted as a secondary factor for the unit-cell parameters variations of celestine. To underline these observations in a more simplified manner, there is almost a perfect correlativity C(15) of the average temperature dependence (Table 7) by the a0, b0, c0 and V0 unit-cell parameters (Table 4) of 0.965; 0.951; 0.991 and 0.997, respectively (Figure S24 in the ESM). The correlation is superior comparing to the C(12) correlation of the celestine composition (Figure S20 in the ESM).
By using the extrapolated data (Tables S16 and S17 in the ESM; Table 7 and Fig. 4) we, moreover, estimate the unit-cell parameters of the studied samples formed at a near-room temperature (23 oC), under the ambient pressure conditions (Table S19 in the ESM). The resulting data are used exclusively for the characterization of the relative unit-cell parameters (Table 8). In this case, a wide range of the correlations between the crystallographic axes are observed: b0<c0<a0 (samples 1 and 4), a0<b0<c0 (sample 2), a0<c0<b0 (sample 3), and c0<b0<a0 (sample 5).
The results have almost a perfect correlation C(16) of the average temperature dependence (Table 7), by the a0, b0, c0 and V0 ratios (Table 8) of 0.979; 0.926; 0.988 and 0.998, respectively (Figure S25 in the ESM). These are, as expected, very similar to the C(15) correlations, relative to the temperature by the unit-cell parameters variations (Figure S24 in the ESM). In addition, the linear and the polynomial variations have almost the same values in these two cases.
The synthesis of data (Tables 7 and 8; Figure S25 in the ESM), allowed us to additionally construct the variation diagram of the relative a0, b0, c0 and V0 unit-cell parameters (i.e., their ratios) by the temperature dependence of the studied samples at the ambient pressure conditions (Fig. 5). Importantly, the resulting variation diagram has the fits (i.e. for all of the five samples together) adequate to the celestine c0<b0<a0 crystal growth expansive behavior (see Figs. 11b and 12b at Ye et al. 2019; and Table S18 in the ESM). Taking into account solemnly the crystal expansion caused by temperature (Table 7), the samples 1 and 4 are showing the variations that are similar to that of barite, whereas the samples 2, 3 and 5 show the variations similar to that of celestine (Ye et al. 2019; and Table S18 in the ESM). By interpreting the structural aspect (Antao 2012), the first group of samples are less distorted, in comparison with the second, being in the agreement with the geometry change of the SO4 and MO12 polyhedral, which were influenced mainly by the vacancies present for the latter ones (already discussed before). On the other hand, taking into account solemnly the crystal compression by pressure (Table 8), it appears that the sample 4 was also formed at a considerably higher pressure (similarly to sample 1) relative to the samples 2, 3 and 5 because of their identical axes variations.
5.2. Consideration about the celestine minerogenesis and other possible formation conditions
In this part, we take into the consideration other celestine formation conditions, in particular, typifying shallow crustal and marine environments (Hanor 2000). The results indicate that the celestines were formed at ~368-430K (~95-157 oC) temperature range, at the ambient pressure conditions (Table 7). Consequently, we take into the consideration the following options for the celestine minerogenesis: 1. temperature remains constant by a pressure increase; 2. temperature increase by a pressure increase; and 3. temperature increase by a pressure decrease (Figure S26a in the ESM). Following the experimental data (Kuang et al. 2017; Li et al. 2018; Girard et al. 2019; Ye et al. 2019), we believe that if the subsurface pressure increases, temperatures should also follow a pressure increase. The latter phenomenon occurs accounting the axial compression, which should be simultaneously compensated by the axial expansion, so that the unit-cell parameters remain unchanged (i.e. as already previously characterized; Table 4). Accordingly, we have chosen the second option, because the other two options led exclusively to the smaller unit-cell parameters. This scenario is graphically outlined by the yellow full lines at Figure S26a in the ESM. The increasing slope is approximated, accounting the lacking of the appropriate experimental data for the formation pressure. The increase of the formation pressure allowed us to put constraints, evaluating the probable subsurface conditions under which the investigated crystals could have been formed. For example, if we presume that the pressure was 250 bars, accordingly, the temperature range becomes a slightly higher, ca. 372-434K (~99-161 oC) fitting into the volcanic areas.
On the other hand, subsidence and deposition within sedimentary basins yields higher pressures than that observed within the investigated volcanic areas. By presuming a pressure increase, reaching up to 500, 750, 1000 and 1250 bars, the temperature range may increase reaching ~382-444K (~109-171 oC), ~391-453K (~118-180 oC), ~429-482K (~147-209 oC), and ~452-514K (~179-241 oC), respectively (Figure S26a in the ESM). By combining the data, we additionally constructed a wider range, allowing further narrowing of the celestine formation area/depth. As a result, the celestine minerogenesis could originate from the following subsurface conditions:
- from ~382K (~109 oC; sample 2), over ~417K (~144 oC; sample 1), to ~482K (~209 oC; sample 4), at 500, 750 and 1000 bars, respectively (Figure S26b in the ESM); or
- from ~372K (~99 oC; sample 2), over ~412K (~139 oC; sample 1), to ~453K (~180 oC; sample 4), at 250, 500 and 750 bars, respectively (Figure S26c in the ESM).
We underline that these values have rather a speculative character, because constrained on reasonable temperature and pressure ranges reaching 373-473K (~100-200 oC), formed at a range from 250 to 1000 bars.
Contributing further to the higher-pressure conditions, result fits additionally into a different compression behavior of the unit-cell axes. According to Kuang et al. (2017), the study proposes that the b0 axis is the most compressible, whereas the a0 axis is the most incompressible for celestine. The authors explained this in the following manner: “Although the b0 axis is the shortest crystallographic axis in celestine, the largest bond distance of Sr-O is also parallel to the b0 axis in celestine structure. Therefore, the bonding force between Sr-O in this direction is the weakest and thus results in the b0 axis being the most compressible axis”. Such behavior is clearly visible in the samples 1 and 4 (already mentioned earlier in the text, Table 8), explaining a lowermost b0 by a0 correlativity among the unit-cell parameters (Figures S7d and S8a in the ESM).
There are additional facts contributing the final conclusions are as follows:
- The celestines collected from the Al Gata member (formation Wadi Thámat) occurring as a larger accumulation in the clayey, slightly carbonate sedimentary rocks;
- These sedimentary formations carrying the investigated celestine are top-sealed by the younger basalt outflows;
- The celestines are originated from druses or clusters exposed at the surface outcrop scale;
- In addition, rare occurrences of fibrous celestine are observed too, representing the resulting pseudomorphosis of fibrous gypsum;
- Other minerals identified in a close vicinity of celestine are quartz, gypsum, anhydrite, calcite and aragonite (Rundić and Daloub 2007; Vasić and Sheriff 2007; Rundić et al. 2012);
- The investigated celestine is a mineral that usually precipitates when Sr-bearing fluids, reach contact with sulphate-rich solutions (or rocks in various sedimentary settings), probably developed over a large temperature range (25–200 °C; Hanor 2000, 2004); and
- Forjanes et al. (2020) reported that the gypsum-to-celestite transformation rapidly advances, once interacting with a Sr-bearing solution. During the process of interacting with a Ba-bearing solution, gypsum barely transforms into barite, regardless of the length of the interaction.
Finally, we conclude that the Jabal Eghei celestines were formed as the secondary minerals in the position over a gypsum and/or anhydrite layer (as a source of S and Ca). The celestine formation have occurred after the interaction with a hydrothermal (Sr, Pb and Ba)-bearing solution, most probably sourced from the basalt extrusion-related activity (Radivojević et al. 2015). These elements (Ba, Sr, Pb) are dominantly sourced by the 1st and 2nd volcanic extrusion stage, in particular the Pb (Radivojević et al. 2015). The temperatures are over ~368K (~95 oC), and at pressures over 250 bars. Considering that the first basalt extrusion phase occurred during the Middle to Late Miocene time (basalts show a K/Ar age range from 16.1 ± 2.9 Ma to 7.9 ± 2.3 Ma), and the second phase is of Late Miocene to Pliocene age (7.19 ± 0.36 Ma and 4.32 ± 0.35 Ma; Radivojević et al. 2015), the emplacement of the celestine-bearing brine could have occurred prior the phase 3 or the 3rd volcanic extrusion stage. By comparing the hypothetical pressure condition (Figure S26b,c in the ESM, green color), we argue that the tentative age of the celestine formation, is after the deposition and exposure to the successor erosional stage of the Wadi Thámat formation. Considering that the age of the weather crust (location of the celestine druses) is after the 1st volcanic stage, the age should be similar to the oldest basalts.