Accessible Published by De Gruyter November 28, 2015

What we know and still not know about oceanic salts

Wolfgang Voigt

Abstract

The term oceanic salts concerns the salts, which can be formed from solutions containing the major ions of seawater, that is the hexary system Na+, K+, Mg++, Ca++, Cl, SO4–H2O. Besides in geochemistry of evaporites and the potash extraction the solubility equilibria and properties of aqueous solutions containing these ions are of importance in many fields of science and technology in a wide range of temperature and composition. After a short introduction into the types of subsystems and the main features of their solubility diagrams the known salt phases, their properties and stability are listed and discussed with a focus on recent work and discoveries. The status of solubility data evaluation of the multi-component system is discussed from the view point of the data itself and the possibilities and limitations of applying thermodynamic modelling. This is demonstrated with the data compilation of Usdowski and Dietzel, the Pitzer models of Harvie, Möller and Weare as well as the model developed in the THEREDA project. Future work should be directed to improve accuracy of solubility data in multi-component solutions combined with modelling and to consider kinetics and mechanistic aspects in crystallization of phases like anhydrite or polyhalite.

Introduction

Oceanic salts, as the name already suggests, are salts crystallizing when evaporating seawater. The major ions and their concentration in modern seawater are given in Table 1. These ions form a six-component aqueous system, often called the hexary oceanic salt system. The salts formed from these ions under very different conditions of T, p and solution composition comprise the oceanic salts. An extended view includes also the carbonates of magnesium and calcium. For geochemistry the distribution of bromide ions and other trace elements as fluoride, strontium, barium, iron etc. play an important role in elucidating the seawater chemistry, however, there salts are not classified as oceanic salts [1].

Table 1

Oceanic system – major ions concentrations in modern seawater at a salinity Sa=35 [2].

Na+K+Mg2+Ca2+ClSO42–
4689.9853.310.454628.1mmol⋅kg–1
10 7643902129541719 3572699mg⋅kg–1

aS, Salinity in g⋅kg–1.

Understanding which salt phases can be formed from the major ions of seawater under certain conditions is of major importance in various fields of science and technology:

  • geochemistry of rock salt and potash salt deposits [2, 3]

  • potash salt extraction from evaporitic deposits [4] or salt lake brines [5]

  • design and safety assessment of underground waste storage in rock salt formations [6, 7]

  • planetary science, for instance origin and role of the enormous deposits of magnesium and calcium sulfates on Mars [8, 9]

  • lithium extraction from salt lakes, effective use of salt lake resources [10]

  • climate research [11–15],

  • processes in troposphere, salt hydrates formed in clouds [16]

  • natural stones and building materials weathering and measures for conservation [17]

  • gypsum-based building materials

  • MgO-based cements and concretes [18–20]

Questions, which have to be answered in all of these fields of science and technology are always similar:

  • Which salts crystallize under which conditions from which solution compositions?

  • Which salts can coexist in contact with a given solution?

  • Which salts will react with each other and convert to another salt phase?

  • What was the solution composition, when certain salts had been formed from solution?

  • How can one effectively separate and purify salt components?

  • Mass balances for conversion processes?

  • Which properties have the saturated and unsaturated solutions?

Most of these questions can be answered from the knowledge and appropriate presentation of the solid-liquid solubility diagrams, either of the complete hexary system or of its subsystems.

Today we can look back on more than 100 years of investigations on the oceanic salt system first of all in respect to solubility phenomena and the experimental establishment of solubility equilibria as well as the physical properties and structural characteristics of the salt phases and their aqueous solutions. In the last decades thermodynamic modelling of the equilibria became a larger topic with the aim to interpolate or extrapolate into data gaps of multicomponent systems.

To understand the chemistry of a certain salt – water system means to know the salt phases, which can be formed in general, the temperature-pressure-composition conditions for their stability and the properties of the saturated and unsaturated solution containing the ions of the particular system.

In this review at first the sub-systems are listed and the application of the phase rule for description of phase stability is shortly discussed. Then an overview about the known salts and salt minerals is presented. Headlined with the term “stability”, the present status of experimental investigation and evaluation of solubility data in the quinary system Na-K-Mg-Cl-SO4-H2O is discussed by looking back on historical mile-stones and pointing out still existing deficiencies. Finally the status of thermodynamic modelling in respect to the oceanic system is summarized and future work will be suggested.

Hexary oceanic system and its subsystems

The multi-component solubility diagram of the hexary oceanic system can be built up systematically beginning with the simple binary salt – water systems and then adding step by step one salt component. Thus, with the four cations and two anions 8 binary systems, 16 ternary, 6 quaternary systems with common anions, 6 quaternary reciprocal systems and 6 quinary systems can be formed as summarized in Table 2.

Table 2

The subsystems of the hexary oceanic system.

Isothermal

Blue points
Polythermal

Red points
Binary systems81 solid2 solids
Na+Cl
K+Cl
Mg++Cl
Ca++Cl
Na+SO4
K+SO4
Mg++SO4
Ca++SO4
Ternary systems122 salts3 salts
Na+K+Cl
Na+Mg++Cl
Na+Ca++Cl
K+Mg++Cl
K+Ca++Cl
Mg++Ca++Cl
Na+K+SO4
Na+Mg++SO4
Na+Ca++SO4
K+Mg++SO4
K+Ca++SO4
Mg++Ca++SO4
Quaternary systems123 salt4 salts
Na+K+Mg++Cl
Na+K+Ca++Cl
K+Mg++Ca++Cl
Na+K+Ca++SO4
K+Mg++Ca++SO4
Na+K+ClSO4
Na+Mg++ClSO4
K+Mg++ClSO4
Na+Ca++ClSO4
K+Ca++ClSO4
Mg++Ca++ClSO4
Quinary systems64 salts5 salts
Na+K+Mg++ClSO4
Na+K+Ca++ClSO4
Na+Mg++Ca++ClSO4
K+Mg++Ca++ClSO4
Na+K+Mg++Ca++Cl
Na+K+Mg++Ca++SO4

The region of temperature (pressure influence not considered here) and solution composition, where certain salt phases are in solubility equilibrium with the solution can be fixed by means of invariant points of the salt – water system under consideration according to the phase rule. These points can be read off from solubility diagrams. In a simple binary system the invariant points are manifested as the crossing points of the curves describing the temperature dependence of solubility of various hydrates (see right column in Table 2). The existence range for a hydrate is thus limited by a low and high temperature invariant point. In the 16 ternary systems these invariant temperature – composition points are to be fixed in a three dimensional solubility diagram with T – m1 – m2 coordinates, which is inconvenient. Therefore, isothermal m1 – m2 sections at constant temperature are used as shown in Table 2. Along an isotherm, several branches occur, representing the saturation with a certain salt phase, here simple salts AX, BX, and double salt AX⋅BX. The crossing points of these branches on an isotherm fix the composition, where two salts can coexist in contact with solution at this temperature. These points are named isothermal invariant points.

This means, in ternary systems, the isothermal invariant points are two-salt points. Connecting the two-salt points for every Ti in the projection (interrupted lines) yields the polythermal invariant points. In this example one invariant point comprises the 3 solids AX, AX⋅BX and BX. Thus, one can conclude from the diagram, that the double salt AX⋅BX can be formed from a solution only at temperature above T1. Connecting all the polythermal invariant three-salt points with straight lines yields saturation planes of the salt phases in a three-dimensional T – m1 – m2 diagram. However, this would be only a rough description of the solubility equilibria, since the planes have a more or less pronounced curvature, which is manifested in the curvature of the isothermal sections.

In the quaternary systems one composition variable more is necessary. In order to present the solubility equilibria in two-dimensional graphs under isothermal conditions the content of one of the components have to be neglected, usually the water. The isothermal phase relations for quaternary systems are graphically presented in triangle diagrams (one common ion) or quadratic squares diagrams for systems with two different cations and anions as shown in Table 2. In both diagram types along lines two salts are in equilibrium with solution and points represent isothermal non-variant equilibrium points with 3 solids saturating the solution. From a practical point of view, solubility studies in these systems mostly have been performed along solubility lines with two salts as solid phases present. Consequently, experimental results about the concentration inside the crystallization fields are scarce or missing.

The 6 quaternary systems with two different cations and two different anions are called reciprocal quaternary systems. When saturating a solution with salt components AX and BY the reciprocal cation-anion exchange reaction has to be taken into account and according to the solubility relations solid AY or BX can crystallize according to the reciprocal exchange reaction

AX+BYAY+BX

Plotting these diagrams at different temperatures and connecting the isothermal invariant three-salt points gives the polythermal invariant four-salt points. Note, that in these diagrams only the salt compositions can be read off, not the water content. Separate plots with water as a component are necessary to fix this quantity and also to see the crystallization pathway when evaporating water from the solutions. Extensive explanations and instructions how to use solubility diagrams in describing crystallization processes can be found in [4, 21–23]. Today such tools are frequently used to protocol geochemical or technological process data or to visualize computer calculation results from thermodynamic modelling.

Selecting five of the major ions gives 6 different quinary systems (Table 2). The system in bold letters (Na, K, Mg, Cl, SO4) was investigated most thoroughly in the past, since the salt deposits formed from evaporation of seawater contain these ions after the intitial precipitation of the low soluble calcium salts. NaCl is the overwhelming component in oceanic water and thus during evaporation the precipitation of potassium and magnesium salts proceeds always under the condition of simultaneous saturation with NaCl (halite). Therefore, the solubility equilibria in the five component system Na, K, Mg, Cl, SO4 were investigated thoroughly only at simultaneous saturation with NaCl. Only very few data exist for solid-liquid equilibria under conditions, where NaCl is not present as solid phase.

In the quinary systems simultaneous saturation with 4 salts provides the isothermal invariant points and with 5 salts the polythermal invariant points. Since the dimensionality is further increased the salt composition for solubility equilibria at one temperature requires a trigonal prism as shown in Table 2. Within the prism volume elements represent the composition ranges of one salt, surfaces the coexistence of two salts, lines of 3 salts and a point of 4 salts at given temperature (isothermal invariant points). Plotting the projections of the isothermal invariant points on the side planes of the prism for different temperatures will result in crossing points yielding the polythermal invariant equilibria with 5 salts (or at the lowest T with four salts and ice).

In order to visualize processes in evaporite geochemistry or potash extraction technology two-dimensional Jänecke plots in a Gibbs triangle are in use [22]. With these diagrams only solubility relations at saturation with NaCl are considered and as the coordinates K2++, Mg++ and SO4 are chosen, where the relation

K2+Mg+SO4=100

holds, units can be mass-% or mol-%. Reading and drawing conclusions about crystallization processes in this diagram type requires experience in order to avoid misinterpretations (see [3] p. 24, 90). However, for geochemists it helps to get a quick view on possible saturation states of solutions sampled in the field.

Finally in the hexary system at an isothermal invariant point 5 salts are in equilibrium with its solution and in the polythermal case 6 solid phases will be present.

Known salt phases and minerals

This review comprises all salt phases known at temperatures up to 473 K with emphasis to recent findings or discoveries (after the publication date of Gmelins Supplement of the Potassium volume [24]) as well as unresolved problems. For completeness also the well characterized phases are mentioned. Hydroxide-containing and acid salts are not included in this review.

Simple chlorides

NaCl (halite) and KCl (sylvite): Both salts are well-known and their physical properties have been determined in a wide range of temperature and pressure [25]. NaCl is the main constituent in rock salt formations. A remarkable property of NaCl concerns the visco-plastic behaviour, which caused the geological formation of salt domes and is also of importance in rock salt mining.

NaCl·2H2O (hydrohalite): This hydrate represents the only hydrated form of NaCl. According to the phase diagram NaCl-H2O [26] it crystallizes in form of hexagons below 273.3 K (0.2°C) at NaCl concentrations higher than 26.3 mass%. The crystal structure was determined at 150 K [27]. Sodium ion is coordinated octahedrally by four water molecules and two chloride ions in cis-position.

KCl·H2O: In Gmelins Handbook of Inorganic Chemistry [24] formation of a monohydrate of KCl is mentioned for temperatures near –10°C citing [28–30]. This hydrate should exist only in a very small temperature interval. However, there is no new work reported about this hydrate and [26] stated that the question of existence or no existence cannot be decided. Thus, the hydrate was not considered in the evaluation of the solubility curve in the temperature region between –10 and 0°C.

MgCl2·RH2O with R=2, 4, 6, 8 and 12 crystallize from aqueous solutions between the eutectic at 240 K and 523 K [31–33]. All MgCl2 hydrates are very hygroscopic, the hexa-hydrate will take up water at a relative air humidity above 30% at ambient temperature [34]. For the hydrates R=1–6 thermodynamic standard data at 298.15 K are listed in [35].

MgCl2·12H2O represents a cryo-hydrate, which congruently melts at (257.5±0.5) K [36]. These authors report that the crystals are swimming on a saturated solution, which is remarkable, but was not reassessed later. The crystal structure of [37] was re-determined recently confirming the atom positions, but including the hydrogen atom positions [38].

MgCl2·10H2O was very recently prepared under high pressure from amorphous MgCl2 hydrate at low temperature and crystal structure was determined from the crystal powder by means of synchrotron X-ray and neutron diffraction [39].

MgCl2·8H2O is formed from saturated MgCl2 solution below (273.3±0.3) K [36]. Van’t Hoff and Meyerhoffer observed a metastable octahydrate, which they denoted as the β-form. In their notation the α-form is stable, however, later the formation of a metastable form could not be reproduced [38, 40]. Even D’Ans [41] cites the upper formation temperatures for the α- and β-form at 269.7 K and 263.3 K, respectively.

MgCl2·6H2O (bischofite) represents the usual hydrate at ambient conditions. Experimentally determined densities vary between 1.56 and 1.59 g/cm3. The crystals melt incongruently at 389.85 K (116.7°C) [41] p. 71, the metastable congruent melting temperature is already at 390.05 K (117°C). The enthalpy of melting was determined as 41.2 cal/g (=172.4 J/g) [42]. Later determinations yielded 171 J/g [43]. Enthalpies of crystallization of the hexa-hydrate were evaluated on the basis of caloric measurements and temperature derivatives in the solubility diagram [44]. The specific heat capacity, Cp, of the crystals between 20 and 70°C is given with (0.3788±0.0070) cal⋅g–1⋅K–1 (=1.585±0.029 J⋅g–1⋅K–1) [42]. For the molten hexa-hydrate the same authors gave a value of 0.4911 cal/g (=2.055 J⋅g–1⋅K–1) in the interval from 117.6 to 129.7°C. With a background in latent heat storage applications DSC measurements have been performed and Cp as a function of temperature and heat of melting (34.6±0.5 kJ⋅mol–1) had been estimated [45].

Thermal dehydration was extensively investigated under dynamic [46, 47] and static conditions [48] with the focus on hydrolysis, when the lower hydrates are formed. Dehydration enthalpies were derived from vapour pressure measurements by [49].

MgCl2·4H2O: Crystal structure from a product formed by dehydration in solid state shows disorder [50], whereas in crystals grown from molten hexa-hydrate no disorder exists [51]. The latter gives a density of 1.65 g⋅cm–3 at 200 K.

MgCl2·2H2O: Crystal structure was solved for the powdered product from dehydration in solid state [52].

Calcium chloride forms a number of stable and metastable hydrates. Temperature ranges of crystallization from aqueous solution and density data are listed in Table 3. The crystal structure of the mono- and 1/3-hydrate is unknown.

Table 3

Densities and crystal structures for hydrates of CaCl2.

HydrateT range of crystallizationaDensityb g/cm3Referencesc
6H2O223.45–302.851.71[53, 54]
4H2O, α-302.85–318.551.84[55, 56]
   β-1.72[57]
   γ-1.55[58]
2H2O318.55–4491.86[53]
1.66 exp.[59]
1H2O449–460
1/3H2O460–503

aFrom [60]. bValues from crystal structure, except for “exp”. cCrystal structure.

A discussion on the lattice energies of the various hydrates can be found in [61]. Heat capacities and phase transition enthalpies between 270 and 400 K were determined for the hexa-, tetra- and di-hydrate [62]. Cooling down to the low-lying cryohydratic point (–55°C) generates no higher hydrate than the hexa-hydrate [63]. Cryoscopic Raman spectra of fluid inclusions do also not indicate other hydrates of CaCl2 than the hexahydrate [64, 65].

CaCl2·6H2O (antarcticite) is the stable hydrate from cryo-hydratic temperature 223.45 K (–49.7°C) to 302.85 K (29.7°C). As a mineral antarticite occurs in cold regions as in Antarctica.

According to the phase diagram CaCl2-H2O [60] the hexa-hydrate melts incongruently at 302.85 K (29.7°C) with precipitation of tetra-hydrate. Since the dystectic point at 303.85 K (30.2°C) is nearby the peritectic at 29.7°C congruent melting can be observed, when the hydrate is heated not too slowly.

It is remarkable that the most reliable data [60] of the solubility curve below 273 K (0°C) were derived from [63].

The melting and freezing behaviour was investigated extensively for the development of latent heat storage materials for room temperature applications [62, 66, 67]. Main obstacle is loss of heat storage capacity due to stratification of the tetra-hydrate and super-cooling of the molten hexa-hydrate.

The pressure dependence of the solubility up to very high pressures was investigated by [68, 69].

Enthalpy of crystallization was re-evaluated by [44] yielding 37.7±0.4 kJ/mol.

CaCl2·4H2O: Crystallizes as α- β- γ-form from aqueous solutions, where the α-form represents the stable one. The coordination of the calcium ion in these three modifications is quite different (Fig. 1).

Fig. 1: Coordination of Ca++ in the three modifications of CaCl2·4H2O; green spheres=Cl atom, red spheres=O atom, cyan=Ca.

Fig. 1:

Coordination of Ca++ in the three modifications of CaCl2·4H2O; green spheres=Cl atom, red spheres=O atom, cyan=Ca.

CaCl2·2H2O, CaCl2·H2O CaCl2·1/3H2O: Besides the equilibrium temperatures not much further characterization is reported. Di-hydrate was confirmed as mineral in Iraq named Sinjarite [70]. The 1/3-hydrate was identified relatively late by [71] in the course of calorimetric and phase equilibrium studies.

With modern Raman spectrometers the various hydrates can be identified by their Raman band patterns in the wavenumber range 2800–4000 cm–1 [65] even in small fluid inclusions.

Sodium and potassium sulfates: The known minerals and phases are listed below.

Na2SO4Thenardite
Na2SO4 ⋅10H2OMirabilite, Glaubers salt
Na2SO4⋅7H2Ometastable, not a mineral, structure [86, 82]
Na2SO4⋅8H2Ohigh pressure (0.5 GPa) (Brand 2009)
K2SO4Arcanite, solubility evaluation [189]
K2SO4⋅H2O?? T≈0°C [189],
Na2SO4·3K2SO4Glaserite, solid solution with Na2SO4 up to 1:1 ratio Na:K

Na2SO4 and K2SO4 exist as minerals thenardite and arcanite. From phase chemistry’s point of view thenardite belongs to the orthorhombic phase Na2SO4(V). When heated above 180°C it transforms reversibly to the form (III) and at 240°C into a hexagonal form (I). Re-formation of (III) from (I) on cooling occurs through another form (II) [72]. The observed transition temperatures vary within 10 K since the transformations are sluggish and the high temperature forms can exist days or weeks at room temperature when stabilized by cations as Ca++ [73], Ni2+, Sr2+, Y3+ [74, 75]. Presence of humidity accelerates these transformation processes. Na2SO4·10H2O is known as mineral mirabilite or also named Glauber’s salt. It melts incongruently with precipitation of anhydrous sodium sulfate at 305.533 K (32.383°C) accompanied by an enthalpy change of 78.04 kJ⋅mol–1 [76]. There were many attempts to use this heat of melting (360 kJ per liter molten hydrate) for heat storage applications, but due to the settling of the anhydrous salt the heat can be recovered only partly via rehydration, if settling is not avoided by technical measures [77–79]. In the crystal structure of the deca-hydrate exists some disorder due to thermally activated librational modes of sulfate ions near room temperature [80]. This was discussed as in agreement with earlier heat capacity measurements, from which a zero-point entropy in the order of R⋅ln2 was derived. The latter was interpreted as hydrogen bond disorder of the water molecules [81]. However, recently it could be shown that at low temperatures (120 K) the disorder disappears [82]. In the light of the new diffraction measurements low temperature heat capacity data and structure are not in agreement. A p-V-T equation of state was established for synthetic deuterated mirabilite for a range of 4–300 K by [83]. Na2SO4·7H2O represents a metastable hydrate, but it can be obtained easily by cooling supersaturated aqueous solutions of sodium sulfate from 40°C to about 293–295 K (20–22°C) [84] or to a little bit lower temperature of about 280 K [82]. The transition temperature to the stable deca-hydrate in an aqueous suspension was determined very accurately as (23.465±0.004)°C [84] and proposed as a secondary temperature calibration point. Interestingly, the hepta-hydrate was found also as a mineral (Pustynite) in Kasachstan in salt solution pools in the dessert [85]. Crystal structure analysis by Oswald [86] indicated disorder in one oxygen position of a water molecule at 150 K. Our re-investigation revealed no disorder at 150 K [82], but the structure had to be described in a unit cell of double size than had been used by Oswald et al.

Na2SO4·8H2O was crystallized recently at high pressure (1.5 GPa) from an 3.4 molal solution at 293 K and the structure was solved by in-situ single crystal diffraction [86].

Na2SO4·3K2SO4: This double salt is known as the mineral glaserite. However, the ratio of 1:3 for the two sulfates as given in the formula represents a limiting case. At enhanced temperatures and high Na/K ratio in the solution glaserite can uptake Na2SO4 reaching ratios up to 1:1. The latter salt is sometimes named aphtitalite. Thus, between these two ratios the phase represents a solid solution of glaserite with Na2SO4 [87], which can be understood structurally. Cations can occupy three different sites in the glaserite structure with coordination numbers 6 (1b), 10 (2d, two-fold), and 12(1a) [88]. At low temperatures Na+ resides only in 1b, at increasing T up to 50% of the two-fold 2d site can be occupied by Na+ resulting in a 1:1 ratio of Na+/K+ in the lattice. According to the chemical analyses of Foote [89] also at 25°C about 4% variation in the sodium sulfate occurs. We had studied the system Na2SO4-K2SO4-H2O up to 200°C where the Na/K ratio increased to 1.25 at the extremum [90].

Hydrates of magnesium sulfate

MgSO4 forms a number of hydrates (Table 4). Some of them were prepared or found only recently. A discussion about the mineral names to be used can be found in [85]. Details for preparation and observations on stability of the various hydrates can be found in [1, 109, 96]. Dehydration behaviour of MgSO4·RH2O (R=1, 1.25, 2, 3, 4, 5, 6, 7) was studied by thermo-analytical methods under quasi-isobaric conditions by [92]. The hydrate with R=1.25 was not considered as an individual hydrate, since the 0.25 mol water are released continuously and the powder X-ray diffraction pattern is identical with the monohydrate but the reflexes are broadened. All phases can be formed during the dehydration of the hepta.-hydrate, depending on conditions as for example evaporation rate.

Table 4

Magnesium sulfate hydrates.

R MgSO4RH2OMineralStructure character, ReferenceSGRDensity g⋅cm–3Other characterization
1KieseriteScrXRD, [91]C2/c2.58
5/4=1.25[92, 93]No distinct X-ray pattern compared to kieserite, but line broadening, 0.25 mol H2O
2SanderitePXRD, [94]P2121212.21

XRD
2.5PXRD, [95]C2/c2.11

XRD
3ScrNeut, [96, 97]PbcaSingle cryst. Neutron Diff. MgSO4·3D2O, Below 245 K phase transition to P21/c
4Leonhardtite (starkeyite)[98, 99]P21/n2.007

XRD

2.01

pykn
4’CranswickitePXRD, [100]C2/c1.917

Pykn.

1.918

XRD
5Allenite (pentahydrite)ScrXRD, [101]P1̅1.92

XRD
6Hexahydrite (sakiite)ScrXRD, [102]C2/c1.765

XRD
7Epsomite (reichardite) (bitter salt)ScrNeut, [103–105]P2121211.677

XRD,

1.676

Pykn.

[106]
11MeridianiiteScrXRD, [107, 108]P1̅1.51

Scr, Single crystal.

Renewed interest for the hydrates of MgSO4 arose from research related to the salts and hydrates on Martian surface. These hydrates can play a certain role in storage and redistribution of water on this planet. Therefore dehydration-hydration studies were performed at low temperatures (down to –10°C), low relative humidities and reaction times up to 46 months [110–112]. At these low temperatures amorphous forms of di-hydrate and even anhydrous MgSO4 were obtained [113]. Modern Raman spectrometer allow fast and reliable identification of the various hydrates on the bases of their water and sulfate anion vibration patterns [110, 111, 114]. A new low temperature (–10°C) form of the hepta-hydrate was discovered on the basis of changes in the Raman spectrum and powder X-ray diffraction pattern of samples held at cryotectic temperature for long time [112].

For interpretation of spectral data from Mars orbiter the optical constants (reflexion, absorption) in a wide wavelength range have been determined also for hydrates of MgSO4 [113]. From crystal structure analysis [107, 115] it is now sure that the water-richest hydrate contains 11 and not 12 mol water per MgSO4. Interestingly, this mineral was supposed to exist on Mars (Peterson und Wang 2006) before it was discovered as a mineral (Meridianiite) on earth in Canada in ponds containing MgSO4 solution in winter, where it crystallized at temperatures between 2°C and –4°C [108]. Determined lattice parameters of MgSO4⋅11D2O between 4 and 250 K by powder neutron diffraction and correlated thermal expansion characteristics with the hydrogen bond network in the structure. Formation of an undeca-hydrate seems to be a unique property of MgSO4 in the series of MSO4 hydrates (M=Mg, Fe, Co, Ni, Cu, Zn) [116]. Synthetic meridianiite can accommodate several percent of two-valent cations M2+ in the structure [116].

All the lower hydrates with R=2, 3, 4, 5 although assumed as metastable can crystallize from aqueous solution at temperatures below boiling point [92]. We observed the formation of tetra- and pentahydrate quite commonly when evaporating natural or synthetic solutions rich in magnesium, chloride and sulfate. However, formation of the monohydrate in its real kieserite structure needs longer times under hydrothermal conditions [93]. On the other hand Zeng et al claim from solubility investigations to have had obtained the monohydrate within five days in concentrated MgCl2-MgSO4 solutions at 323 K [117].

The hepta-hydrate, MgSO4·7H2O, is well-known as mineral epsomite. A refinement of the crystal structure in respect to the hydrogen position was performed by means of a single crystal neutron diffraction study [105]. Calleri et al. [104] determined the absolute configuration of crystals and showed the consequences in growth morphology.

Sometimes for the hepta-hydrate an α- or β-phase (or I and II phase) is mentioned in the literature, however the existence is unclear [118].

At pressures below 15 kbar epsomite undergoes several phase transitions and becomes finally amorphous [119]. A more detailed picture over the pressure phase transitions of the hepta-hydrate was accomplished recently [120].

MgSO4·6H2O, hexahydrite, has a stable crystallization range from 321 K (48°C) to 340 K (67°C) in MgSO4 solutions. However, it tends to remain as a metastable solid below and above these temperatures. A new set of crystal structure data was published by [102]. It confirms the structure given by [121]. An interesting observation on an instability of the hexa-hydrate at low temperatures between 235 and 265 K was reported by [122]. In order to explain the excess heat effects in measurements of the heat capacity the authors suggested a disproportionation of the hexa-hydrate into hepta- and mono-hydrate. Due to the low temperature the new phases formed remained micro-crystalline. A similar effect was observed earlier for ZnSO4·6H2O [123].

MgSO4·5H2O, the pentahydrite or allenite is considered as metastable in binary aqueous solutions. Metastable MgSO4·3H2O is easily crystallized as crystals of several mm in size during evaporation of [93, 124].

MgSO4·4H2O often crystallizes in solutions highly concentrated in MgCl2 before the stable phase of hexa-hydrate or mono-hydrate appears [125]. It is not sure, whether the tetra-hydrate has a small stable crystallization region [125]. Recently, for the tri- and tetra-hydrate heat capacity measurements between 5 and 300 K as well as heat of solution measurements were published [126]. With a mathematical programming analysis (MAP) these authors combined caloric data with new results from hydration –dehydration equilibria in solid-vapour equilibria [127] and derived two slightly different sets of formation data for the hydrates with R=7, 6, 4 and 1. It was concluded that the tetra-hydrate is metastable in the entire range of temperature and humidity from 200 K to 360 K and 15 to 80%, respectively.

Formation of the mono-hydrate MgSO4·H2O in solutions of MgSO4 or MgSO4+MgCl2 results all the time in very tiny crystals, even at long-lasting equilibration at temperatures between 363 and 513 K (90–140°C) [93]. According to the extensive investigations of Ziegenbalg on kieserite and 5/4 hydrate formation, the excess water of about 0.25 mol is the result of the incomplete and thus distorted crystal structure with incorporated water on interstitial sites. The author found out that pure monohydrate, which is structurally identical with the natural kieserite can be obtained by putting 5/4 hydrate into boiling water and evaporating the suspension until dryness. This procedure has the advantage, that the kieserite is free of adherent mother liquor, mostly of high concentrated MgCl2 or other hygroscopic salts. Also boiling of MgSO4 in a 50% H2SO4 should give a very fine crystalline kieserite [93].

Calcium sulfate phases

Calcium sulfate occurs as minerals anhydrite, CaSO4 , gypsum, CaSO4·2H2O and bassanite, CaSO4·0.5H2O. According to the solubility diagram CaSO4-H2O the hemi-hydrate is always metastable. Crystal structures of anhydrite and gypsum are well-known. A discussion and investigation of the morphology of gypsum (twinning, intergrowth of crystals etc.) in relation to growth conditions and crystal structure is given by [128]. Further studies on gypsum morphology and twinning were provided by [129, 130]. Estimations of the transition temperature between gypsum and anhydrite vary from 42 to 60°C due to the scatter of experimental solubility data and the obtuse angle, under which the solubility curves are crossing [131].

The structure of the hemi-hydrate itself was under discussion several decades, because of variations in water content and crystallinity. At appropriate conditions (temperature, water activity) the α-form of hemi-hydrate crystallizes from aqueous solutions. When drying gypsum in absence of solution the β-form is obtained. Both forms are characterized by a crystal structure, where the water molecules occupy sites in channels along c-axis. The β-form can be considered as a not completely ordered form of α-CaSO4·0.5H2O, although some authors argued for a specific structure of β-hemi-hydrate [132, 133]. Structural disorder is reflected in broadened X-ray diffraction patterns, larger specific surfaces, sub-micro crystal sizes and higher hydration rates to form gypsum with water. The α- and β-form can be distinguished easily by recording DTA curves and looking for the appearance and temperature of an exothermic effect. For the β-form this effect is more pronounced and occurs at much higher temperatures (320–375°C) [134]. The reason for the exothermic effect has obviously to be seen in the collapse of the anhydrous intermediate γ-form (also called “soluble anhydrite”), which has the hemi-hydrate structure preserved, but with empty channels [135]. The steps of dehydration from gypsum through hemihydrate and γ-CaSO4 were recently confirmed by means of micro-XRD inside of a DTA set-up with fast recording of reflexion patterns [136]. For α-hemihydrate the appearance of the exothermic effect depends also on the crystal morphology [134]. In literature related to building materials the anhydrous forms of CaSO4 are often denoted as AIII and AII for the γ-form and the stable anhydrite, respectively.

The controversial aspects of the α-CaSO4⋅0.5H2O concern the choice of the unit cell, effect of twinning and the water occupation (positions and amount) in the channels of the structure. The preferred symmetry is monoclinic as C2 or I2 [135, 137, 138], but trifold [139] or sixfold [140] twinning can give pseudo-trigonal or pseudo-hexagonal symmetry. Indications for the existence of CaSO4 -subhydrates with water contents between 0.5<×<0.8 were reported from gravimetric analyses and peak splitting of X-ray patterns in dependence on relative humidity [141, 142]. Weiss and Bräu [140] claimed that such sub-hydrates does not exist and single crystal diffraction patterns are only effected by many-fold twinning. However, from careful single crystal X-ray structure analysis at different humidities correlated with systematic powder X-ray diffraction and thermogravimetric investigations a reversible phase transition between a 0.5 hydrate and a 0.625 hydrate could be observed when crossing a relative humidity between 30% and 75% [143]. Whereas the structure of the hemi-hydrate possess only one type of water channels with 3 molecules water per unit translation along the channel the sub-hydrate has two types of channels, one with 3 and the other with 4 water molecules per unit translation [143]. For the analogous calcium selenate the sub-hydrate with 0.625 H2O represents the phase crystallizing when a di-hydrate suspension in water is heated in an autoclave to 190°C. It shows the same channel structure as found for the sulfate with 0.625 H2O [144].

Recently, Robertson and Bish [145] investigated the kinetics of dehydration of gypsum and rehydration of anhydrite under controlled humidity insitu in a diffractometer. At 220 K and 6% relative humidity the extrapolated kinetic curves predict the beginning of gypsum dehydration after about 500 years. Depending on humidity they also discussed besides bassanite with 0.5 H2O a sub-hydrate with 0.67 H2O as intermediate phases and its possible role on the surface of Mars. Finally, X-ray patterns sent from the Curiosity rover on Mars revealed 1.5% anhydrite in a sample from Gale crater [146], which underlines the importance of the CaSO4 phase chemistry for an understanding of the processes on this planet.

CaSO4⋅0.5H2O can take up sodium from saturated aqueous NaCl solutions at 70°C. The molar Na+/Ca++ ratio can reach values near 2/5. The sodium is partly incorporated into the water channels of the hemihydrate structure and partly substituting calcium ions. This process is reflected in a stepwise increase of dehydration temperatures, changes in Raman spectra and X-ray diffraction patterns [147, 148]. The highest ratio corresponds to the structure of the known double salt, sodium penta-hydrate, 5CaSO4⋅Na2SO4⋅3H2O [147].

Double salts – chlorides

Besides sylvite, the mineral carnallite, KCl·MgCl2·6H2O, represents the other most important potash mineral. It was the first mineral mined for potash production in Germany. An important property is the incongruent dissolution behaviour, where solid KCl is liberated and the solution enriches in MgCl2. Only at high concentration of MgCl2 carnallite dissolves without decomposition. Crystal structure is built of Mg(H2O)6 octahedra and K+ ions are situated in the holes of the chloride ion packing similar to perovskite lattice types. Potassium can be substituted by other large one-valence ions like NH4+, Rb+, Cs+ or Li(H2O)+, (H3O)+ and Cl by Br and I. These substitutions change the lattice symmetry from ortho-rhombic in original carnallite to monoclinic [149]. Contents of bromide, rubidium and caesium as trace elements provide important information for an understanding of the genesis of evaporitic deposits and solutions [150]. If not too fast heated, during drying of carnallite a di-hydrate, KCl·MgCl2·2H2O, can be obtained [151], which can also exist in equilibrium with molten MgCl2 hydrate saturated with KCl at T>160°C [152]. Carnallite melts incongruently in its own crystal water at 167°C. Thereby about 75% of the KCl is settling down as solid phase in the molten MgCl2 hydrate. When water is evaporated from this melt KCl⋅MgCl2⋅2H2O and 1.5KCl·MgCl2·2H2O will crystallize [152, 153]. In presence of an excess of MgCl2 in the hydrous melts solid solution formation between MgCl2·2H2O and KCl⋅MgCl2⋅2H2O was reported [152]. Interestingly, the chloridic double salt with calcium, the mineral tachhydrite, 2MgCl2·CaCl2·12H2O, melts also incongruently nearly at the same temperature as carnallite [151]. From the chemical composition it can be compared with carnallite, where KCl is substituted by CaCl2 and a twofold amount of MgCl2·6H2O. The coordination principle is the same in tachhydrite as in carnallite, however, crystal symmetry is changed to trigonal-rhombohedral [154, 155]. Whereas melting of tachhydrite liberates solid CaCl2 or its monohydrate [156] incongruent dissolution in water below 55°C yields solid MgCl2·6H2O, bischofite, above 55°C tachhydrite dissolves congruently, that is without decomposition. Due to the components MgCl2 and CaCl2 both carnallite and tachhydrite are very hygroscopic. Conditions for deliquescence and efflorescence of these minerals were modelled and discussed [34]. An interesting geological occurrence of tachhydrite exists in the salt formation in Teutschenthal (Germany), where crystals of tachhydrite are in intimate contact with kieserite, MgSO4⋅H2O, without any microscopically detectable calcium sulfate between the crystals [157].

At temperatures above 363 K (90°C) a double salt, 2CaCl2⋅MgCl2⋅6H2O, can be crystallized [156].

Double salts of MgCl2 or CaCl2 containing NaCl are not known. During solid-gas equilibration at enhanced temperature some incorporation of sodium was postulated by Orekhova et al. [158, 159]. However, double salts between KCl and CaCl2 are known as 2KCl⋅CaCl2⋅2H2O [160, 161] and KCl⋅CaCl2 (Bäumlerite) [162] crystallizing from very highly concentrated CaCl2 solution at enhanced temperatures.

Double salts with magnesium sulfate

With Na2SO4 the three minerals blödite (astrakanite), Na2SO4·MgSO4⋅4H2O, löweite, 6Na2SO4⋅7MgSO4⋅15H2O and vanthoffite, 3Na2SO4⋅MgSO4, are known since the time of van’t Hoff [1]. The exact composition of löweite was established not before the chemical analysis of Kühn [163], which was confirmed by crystal structure analysis later [164]. In 1982 a new mineral named konyaite, Na2SO4⋅MgSO4⋅5H2O, was found in Konya basin in Turkey [165]. Crystals of this double salt can be grown easily from equimolar Na2SO4-MgSO4 aqueous solution evaporating at temperatures around 300 K (27°C) and a humidity of 79%. Unfortunately, the solution composition from which the crystals grew was not determined, but the crystal structure was [166]. Asalt even richer in water, Na2SO4⋅MgSO4⋅10H2O, was prepared during evaporation of solutions at similar conditions [167, 168]. At low temperature from blödite at 263 K (–10°C) at a humidity buffered with ice within two weeks a Na2SO4⋅MgSO4⋅16H2O was obtained and the structure solved [169].

With K2SO4 magnesium sulfate forms the well-known minerals picromerite (schönite), K2SO4⋅MgSO4⋅6H2O, leonite, K2SO4⋅MgSO4⋅4H2O, and langbeinite, K2SO4⋅2MgSO4. Lowest possible formation temperature of langbeinite from solutions of the seawater system is 325 K (52°C) [31]. According to earlier sources it was 310 K (37°C) [170]. As a quite common mineral in salt deposits of the Zechstein period knowledge about the possibilities of langbeinite formation are quite important for an understanding of the evaporitic deposits.

Leonite and picromerite are intermediate products in processes for K2SO4 production from KCl and MgSO4 hydrates [171]. The crystal structure of leonite has some disorder at room temperature [172], which could be the reason for the reported ability to uptake some sodium sulfate [4]. However, Braitsch [3] discards the possibility of solid solution formation with arguments from a chemical analysis of large natural leonite crystals and the different crystal structures of bloedite (Na2SO4⋅MgSO4⋅4H2O) and leonite. To the best knowledge of the author, variable composition of leonite was never investigated in detail. At 100 K leonite structure becomes ordered, passing an intermediate structure between 269 and 121 K [173]. The successive structural transitions were confirmed by vibrational spectroscopy [174]. Standard formation enthalpies are known for leonite, picromerite (schönite) and langbeinite in [35].

Double salts with calcium sulfate

The most stable double salt with Na2SO4 represents glauberite, Na2SO4⋅CaSO4. Crystallization of glauberite is often retarded and thus labile phases like 2Na2SO4⋅CaSO4⋅2H2O (labile salt) [175] or the sodium penta-salt [176] crystallize from solutions.

2Na2SO4⋅CaSO4⋅2H2O was found as a mineral eugsterite [177]. A salt with composition 5Na2SO4⋅CaSO4⋅6H2O was found in the area of the Aral lake by Slusareva [178]. Hill had already investigated the metastable phase equilibria of these double salts in the systems Na2SO4-CaSO4-H2O [176]. As mentioned above, the Na-penta salt can be considered as an end member of the calcium substitution in CaSO4 hemi-hydrate [147].

K2SO4 forms two double salts with CaSO4: syngenite, K2SO4⋅CaSO4⋅H2O, and görgeyite, K2SO4⋅5CaSO4⋅H2O. The latter was discovered as mineral in year 1953 [179], however as a synthetic compound it was known since vant’ Hoff. At hydrothermal conditions near 200°C a anhydrous double salt, K2SO4⋅CaSO4, can crystallize [90].

No double salts are known between calcium and magnesium sulfate.

More complex salts

Salts containing more than three different ions are polyhalite, K2SO4⋅MgSO4⋅2CaSO4⋅2H2O, kainite, 4KCl⋅4MgSO4⋅11H2O, dansite (in Russian literature “nona salt”), 9Na2SO4⋅MgSO4⋅3NaCl and the so-called Na-polyhalite, 3Na2SO4⋅2K2SO4⋅25CaSO4⋅15H2O. Crystal structure analyses exist for kainite [180], and polyhalite [181, 182]. In old literature, but also up to now for kainite the formula KCl⋅MgSO4⋅3H2O is used, but the correct water content according to chemical analysis [183] and crystal structure is 2.75. For d’ansite only structure analyses are reported for the zinc [184] the manganese and iron [185] analogues. Kainite and polyhalite are very abundant evaporitic minerals.

Both from kainite and from polyhalite it is known that without seeding crystallization even from very supersaturated solutions can last several weeks up to months. Also the dissolution kinetics of polyhalite is very slow at ambient temperature.

Phase stability

In the previous chapter before 65 minerals or salt phases were mentioned, whereby 18 of them contain calcium. The degree of characterization and knowledge about stability and formation conditions for the various hydrates and double salts is quite different, often not sufficient for clear predictions of their existence fields in higher component systems or in certain temperature intervals. Modern sophisticated X-ray and Raman instruments enabled the discovery of new hydrates for instance with magnesium sulfate as a salt constituent. Questions about stability of salt phases at low and enhanced temperature are discussed again more intensely with the background of planetary science [9, 114, 186] and long-term waste disposal in salt geological formations [6].

Stable equilibria in the quinary oceanic system

Jacobus Henricus van’t Hoff was the first, who developed a systematic approach to build up the phase relations in the oceanic system from simple binary systems step-wise adding a component until reaching the hexary system. The papers from his 12 years work on this topic together with his pupils and colleagues are collected in the famous book [1]. Van’t Hoff used thermodynamic relationships and appropriate experimental methods. His main experimental methods were dilatometry, calorimetry, differential vapour pressure measurements and solubility determinations. In a very effective way he had combined these methods to fix invariant points and thus to establish the formation conditions for most of the various salt hydrates and double salts of the hexary oceanic system.

Starting with the binary systems, the lower and upper temperature for the stability of hydrates was determined, then in ternary systems the formation of double salts and its hydrates had to be studied. Figure 2 shows schematically temperature limits for some salt phases. With these temperature limits van’t Hoff constructed so-called paragenetic schemes (Fig. 3) to show the possible simultaneous existence of salt phases and their saturated solution in higher component systems at a chosen temperature in a compact form.

Fig. 2: Lower and upper temperature limits for some hydrates and double salts.

Fig. 2:

Lower and upper temperature limits for some hydrates and double salts.

Fig. 3: Phase paragenesis scheme after van’t Hoff [1] for the quinary system at 298 K.

Fig. 3:

Phase paragenesis scheme after van’t Hoff [1] for the quinary system at 298 K.

The isothermal invariant points were denoted with letters P, Q, R, Z (Fig. 3), which are still in use today (although in the original papers the letters denote not all the same phase equilibria).

Later this work was continued by a large number of scientists and groups as D’Ans, Autenrieth, Serowy, Kurnakov, Zdanovskii, Lepeshkov, Yanat’seva, Soloveva, Balarev, Emons, Holldorf and others, who exclusively applied the solubility method, mostly in order to improve accuracy of solubility description, to refine some invariant points or to extend the temperature range. D’Ans compiled and evaluated the work on oceanic solubility equilibria until 1933 [41].

Taking into account solubility data up to the year 1962 Braitsch [3] discussed certain solubility equilibria in the quinary and hexary system with particular importance for the genesis of evaporitic deposits. Thereby, he points out differences of certain mineral parageneses due to more new investigations since D’Ans and van’t Hoff. One of these parageneses was blödite-kainite at 35°C, which should not exist according to van’t Hoff and also not according to the polythermal 4-salt lines given in [41].

Collections of experimental data until 1972 can be found in the volumes [187]. In the Supplement volume of the “Potassium” volume Gmelins Handbook of Inorganic Chemistry [24] literature of oceanic systems is compiled until 1970.

The most recent evaluation of experimental solubility data from binary until the quinary system was performed by Usdowski and Dietzel [31]. For the multi-component systems in general it covers a temperature range from 0 to 100°C. However, for the subsystem K+, Mg++, Cl, SO4–H2O the authors stated, that the basis of experimental data did not justify to draw reliable solubility diagrams above 55°C. For the quinary system under the condition of saturation with NaCl Usdowski et al. [188] provided an extensive comparison of their invariant points with those given by D’Ans [41] and Autenrieth [170] (Table 5). The methodology for estimating these invariant points is illustrated in Fig. 4 and Fig. 5.

Table 5

Invariant points of the system Na+, K+, Mg++/Cl, SO4–H2O at saturation with halite according to [188].

No.aHalite +DANSAUTUSDNo.Halite +DANSAUTUSD
°C°C
1gs+mi+pc+sy222bl+ep+hx+le27.527.5
2ca+ep+ka+sy11118.518bl+ep+hx+ka27.5
bi+ca+ep+hx12.512.5hx+ka+ks+le31.531.5
3ep+le+pc+sy16.516bl+hx+ks+le3232
4ca+ep+ka+ks1719hx+ka+ks+lw34.5
bi+ca+hx+ks17.517.5ka+ks+le+lg3737
5ep+ka+le+sy17.91820bl+hx+ka+lw37
ca+ep+hx+ka1818bl+ks+le+lg37.537.5
ca+ka+hx+ks2323bl+ks+lg+lw4343
6gs+le+pc+sy25.525.52621bl+da+gs+th44
7ka+le+lg+sy555555bl+gs+th+vh4646
8gs+le+lg+sy60.560.558.5bl+le+lg+lw4747
9ca+ka+ks+sy72726922bl+ka+le+lw47
10ka+ks+lg+sy83837823ka+le+lg+lw52
11bl+ep+mi+pc4.54.54.524bl+da+gs+vh52
12bl+gs+mi+pc669.525bl+gs+le+lw56.556.555.5
13bl+gs+mi+th13.513.513.526bl+gs+lw+vh59.559.558.5
14ep+hx+ka+ks1827gs+le+lg+lw61.561.559
15bl+ep+le+pc202018.528ka+ks+lg+lw68
16bl+gs+le+pc26262629gs+lg+lw+vh989870
ep+hx+ka+le272730ks+lg+lw+vh108108108
17bl+ep+ka+le27

Codes: bi, Bischofite; bl, bloedite; ca, carnallite; da, dansite; ep, epsomite; gs, glaserite; hx, hexahydrite; ka, kainite; ks, kieserite; le, leonite; lg, langbeinite; lw, loeweite; mi, mirabilite; pc, picromerite; th, thenardite; vh, vanthoffite.

aNo number given=cancelled points, bold letters: new invariant point according to [188].

Fig. 4: Trigonal-prismatic composition space of the quinary system Na+, K+, Mg++/Cl–, SO4––H2O. Two polythermal 4-salt lines intersect at T1 giving a polythermal invariant 5-salt point.

Fig. 4:

Trigonal-prismatic composition space of the quinary system Na+, K+, Mg++/Cl, SO4–H2O. Two polythermal 4-salt lines intersect at T1 giving a polythermal invariant 5-salt point.

Fig. 5: Magnesium concentration of paragenesis R (halite, carnallite, kieserite, kainite) and Q (halite, carnallite, sylvite, kainite) at various temperatures. Intersection of the R and Q branch yields the polythermal invariant point No. 10 in Table 5. Symbols=experimental data, lines=equations from [31].

Fig. 5:

Magnesium concentration of paragenesis R (halite, carnallite, kieserite, kainite) and Q (halite, carnallite, sylvite, kainite) at various temperatures. Intersection of the R and Q branch yields the polythermal invariant point No. 10 in Table 5. Symbols=experimental data, lines=equations from [31].

At a given temperature the relative portions of salts in a solution of the quinary oceanic system Na+, K+, Mg++, Cl, SO4–H2O can be presented by a trigonal prism with the salt components at the corners as shown in Fig. 4. An isothermal invariant point at temperature T1 (4-salt point) is the result of crossing 3-salt lines in this point. If these salt phases exist also at another temperature T2 they will cross at another composition for T2 and so on for more temperatures. Plotting the projections of all these 4-salt points on the planes of the prism will yield lines, which then meet in a polythermal invariant 5-salt point. Thus, the experimenter has to take the analytically determined equilibrium concentrations for all the ions, to calculate the salt portions from it and to plot into diagrams consisting of the planes of the trigonal prism. Ideally all these plots should show a crossing point at the same Cl-SO4 ratio. Due to the analytical errors this will not be the case. Dependent on the available analytical techniques, the accuracy for the various ions will differ and calculations of ion ratios will magnify these uncertainties. One should mention here, that accurate determinations of ion concentrations by the commonly applied ICP or AAS technique requires considerable calibration efforts to ensure relative errors below 1.0% for each element in a salt solution. In Fig. 4 the water content is not included. To consider the water content a fourth dimension would be necessary. However, the water content will also change from point to point and so the absolute ion concentration in mol/kg H2O. Consequently, also the absolute ion concentrations must meet in a common point, when plotted the relevant equilibrium concentrations. This is usually done, because in this way magnifying effects of errors by calculation of ion ratios are avoided. Therefore, one chooses the concentration of that ion, which changes its concentration sensible enough in relation to the analytical accuracy. This is mostly the magnesium or sulfate ion. All the invariant points shown in Table 2 were determined by plotting the isothermal invariant points as a function of temperature and a suited composition variable as for instance the magnesium concentration in Fig. 5.

As shown in Table 5 quite a number of changes are proposed by Usdowski et al. [188]. These changes concern the phase assemblages as well as some temperature changes. Thus, 13 invariant points given by D’Ans were cancelled and 11 new invariant points are introduced. The most relevant changes concern the inclusion of dansite in the equilibria, the decrease of the upper stability limit for kainite from 83°C (van’t Hoff) to 78°C. The drawback of this compilation is that for the reader the procedure of arriving at these conclusions is not transparent. Also unpublished results had been involved and no accuracy statements have been given for fitting equations derived for the equilibria in subsystems.

Even if one knows all invariant and univariant equilibria of all subsystems the curvature of the bi-variant solubility planes or hyper-planes can only be roughly estimated. Such knowledge is for example important to elucidate concentration gradients (driving forces) or mass balances in geochemistry of evaporites, when evaluating diagenetic processes [3]. However, solubility experiments were performed nearly exclusively for uni- or non-variant equilibria not within the planes of the diagrams.

When assessing our present knowledge about the solubility equilibria in this quinary system we have to point out, that in the areas unsaturated of NaCl only a relatively small number of data is available and a complete evaluation of the system in a temperature range 273–373 K is absent until today.

CaSO4-containing solutions and the hexary system

The situation becomes worse when adding calcium and one has to switch to the hexary system. Until today, there exists no further detailed assessment of the hexary system of oceanic salts based on experimental data. Many years ago, an IUPAC initiative was started to systematically evaluate solubility data from simple binary up to the complete hexary system. Such a huge task could not be full-filled in an acceptable period of time on a voluntary basis. However, some volumes of data evaluations of subsystems appeared [26, 189].

Except gypsum all other CaSO4-containing phases require a quite long time (months, years) to equilibrate with its solution. This slow kinetics of equilibration causes a quite large scatter in the reported experimental results. Thus, stability limits between gypsum and anhydrite or the extension of the polyhalite field around ambient temperatures are not fixed accurately enough.

Equilibria between a pair of solids are well defined, if conditions can be realized in the experiments to approach the equilibrium from both sides. In case of the gypsum/anhydrite pair at room temperature only gypsum can nucleate within laboratory time scales, not anhydrite. So the accurate temperature-concentration conditions for the conversions are still too uncertain [131]. In water the transition temperatures are given between 42 and 58°C. Dissolved electrolytes depress the transition temperature due to decreasing the water activity. An actual question is, at which temperature the dehydration process of gypsum will set in, when the solution is saturated with NaCl. Is it above room temperature or below and how much? This problem concerns the use of CaSO4-based building materials in rock salt environments. Also a new experimental attempt [190] could not reduce the uncertainty, since the new experiments suffered from similar deficiencies as in [191] earlier as discussed by us [131].

Thermodynamic modelling

At least since the success of Pitzer’s equations [192–197] in applications to electrolyte solutions at high concentrations, thermodynamic modelling is common practice to describe phase equilibria and thermodynamic properties in salt – water systems up to high ionic strengths. The expectations in thermodynamic modelling are the following:

  • easy quantification of dissolution/crystallization processes in multi-component systems by means of computers and appropriate software as

  • simultaneous access to thermodynamic properties of the saturated and unsaturated solutions

  • hope for accurate enough interpolation in temperature – concentration space with spare experimental data

  • hope for extrapolation into experimentally not investigated T – p- composition ranges

  • help for evaluation of experimental data and selection of the most reliable one

Eugster, Harvie, Weare and Möller were the first to apply Pitzer’s equations and interaction coefficients to perform a complete modelling of the hexary system of the oceanic salts at T=298 K [199–201]. Later they added also the acidic and basic salt solutions as well as the carbonates [202]. In connection with computer programs mentioned above the model [202] became a common tool in geochemistry and environmental science for interpretation of mineral interactions with salt solutions and is often denoted as HMW84 database. However, the thermodynamic data (chemical potentials) are not independent from solubility data. Already Harvie and Weare had to tune parameters such that the accepted at that time equilibrium data of CaSO4 phases were described. Therefore small changes (chemical potentials, interaction parameters) were adopted in the database in the papers between 1980 and 1984.

Figure 6 shows a plot of the solubility equilibria in the quinary system at 25°C as calculated from the HMW84 model and of the data of the compilation from Usdowski and Dietzel. The overall agreement seems good, however, in details exist differences and presently it cannot be decided, which one reflects the truth better (see for example extension of grey areas).

Fig. 6: Jänecke diagram of the solubility equilibria in the quinary system Na+, K+, Mg++/Cl–, SO42––H2O at 298 K and saturation with NaCl; a) calculation by HMW84 data base; b) compilation from Usdowski 1998.

Fig. 6:

Jänecke diagram of the solubility equilibria in the quinary system Na+, K+, Mg++/Cl, SO42––H2O at 298 K and saturation with NaCl; a) calculation by HMW84 data base; b) compilation from Usdowski 1998.

If one compares ion concentrations for the invariant points in the quinary system on one side from HMW84 model and on other side from USD compilation the differences are mostly clearly outside the analytical errors as can be recognized from Table 6.

Table 6

Compositions at invariant points in the quinary oceanic system at 298.15 K according to compilation of [31] and calculation from HMW84 model, concentrations in mol/1000 mol H2O, differences (HMW84 – USD 98) in%.

Invariant pointNa2K2MgSO4
USD 98HMW 84USD 98HMW 84USD 98HMW 84USD 98HMW 84
M45.8246.789.3979.31019.4817.0723.6223.46
+2.1%–0.9%–12.4%–0.7%
N21.7922.7913.6214.3539.7038.614.115.09
+4.6%+5.4%–2.3%+7.0%
P11.5910.479.719.10957.261.1814.015.48
–9.7%–0.6%+7.0%+10.6%
Q4.534.3125.705.10673.175.865.035.654
–0.8%–10.4%+3.8%+12.4%
R2.4242.7281.4151.93886.6685.476.2247.106
+12.5%+37.0%–1.4%+14.2%
S45.8246.789.3979.31019.4817.0723.6223.46
+2.1%–0.9%–12.4%–0.7%
T29.0127.7111.6711.7933.436.0119.4120.42
–4.5%+1.0%+7.8%+5.1%
U26.922.5711.4210.6436.2742.9919.120.00
–16.1%–6.8%+18.5%+4.7%
V11.1112.836.3657.61762.359.4919.7120.52
+15.5%+19.7%–4.5%+4.1%
W10.5910.446.8457.62663.663.218.4918.52
–1.4%+11.4%–0.6%+0.2%
X6.986.9222.9954.52973.871.0111.2814.68
–0.8%+51.2%–3.8%+3.0%
Y3.203.5731.6272.03583.182.2111.010.66
+11.7%+25.1%–1.1%–3.1%
Z0.6870.8370.2130.193105.3103.31.0661.130
+22.0%–9.4%–1.9%+6.0%

After the availability of some sets of measured isopiestic data of simple electrolytes solutions at enhanced temperatures [203–213], they were combined with solubility data to establish Pitzer models up to 200°C (for example [214–216]. Unfortunately, these models cannot be used to calculate multiple equilibria involving all the ions within the claimed temperature ranges. These models should only be used for calculations equilibria in temperature and composition ranges, where they had been checked against experimental data.

The main reasons for that are:

  1. the Pitzer’s equations give no guidance for temperature dependence of ion interaction parameters outside the fitted range

  2. at enhanced temperatures new ion interactions as ion association become more and more important

  3. at the very high saturation concentrations of MgCl2 and CaCl2 activities cannot be described adequately with three Pitzer parameters at one temperature

  4. missing of sufficient activity data for unsaturated electrolyte solutions containing more than one salt.

There are efforts to overcome problem b) and c) by extending the Pitzer interaction formalism by ion strength dependent tripel ion interaction parameters [217–222]. But this increases the number of adjustable parameters and thus demands for even more experimental data. A renaissance of UNIQUAC models applied to electrolyte systems [223–227]; tries to overcome problem a), since the model formalism has inbuilt interaction energy parameter, which guide temperature dependence of the interactions. Until now with these models selected equilibria and thermodynamic properties had been successful described, multi-component systems at saturation had not been tested sufficiently. When comparing the number of adjustable parameters there is no difference between Pitzer-like and UNIQUAC-like (or local composition type) models.

The necessity to provide computational models for engineers and geochemists to perform process simulations with seawater systems generated an initiative in Germany to create a thermodynamic database (THEREDA – THEmodynamic REference DAtabase, www.thereda.de) with the primary purpose to describe as correct as possible the equilibria of the oceanic salt – water systems and in addition then phase and speciation equilibria of actinides and heavy metals in such solutions in combination with the seawaters major ions.

The decision was made to use the Pitzer model, because it is implemented in a number of programs and seems to be flexible enough to adopt the parameters for correct description of multi-phase solubility equilibria up to concentrated solutions in a limited temperature range. The envisaged temperature range is from 273 K to 383 K. The approach is to start with solution models of binary and ternary solutions as published for this temperature range and then step-wise adjust mixing parameters and chemical potentials of solids and some solution species as for example ion pairs to describe the experimental determined solubilities in binary, ternary, quaternary and quinary systems of the oceanic system.

We tried to keep consistency at 298 K with the widely used HMW84 database. A complete comparison of calculations of phase equilibria in the oceanic salt systems according to HMW84 and THEREDA at 298 K can be downloaded from THEREDA’s website. Whereas in most cases results from both databases coincide some important differences should be pointed out here, which are a consequence of new available data since 1984 or another evaluation of data. These are:

  • use of the correct formula for kainite as KCl⋅MgSO4⋅2.75 H2O (HMW84: KCl⋅MgSO4⋅3.0 H2O)

  • including görgeyite, K2SO4⋅5CaSO4⋅H2O, which has an existence field also at 298 K

  • water activity for gypsum/anhydrite transition is shifted to the more justified value of 0.85 (HMW84: 0.77)

  • new data and assessment for the solubility constant of polyhalite, K2SO4⋅MgSO4⋅2CaSO4⋅2H2O [228].

Particularly, the latter two modifications have large effects on the equilibria, where CaSO4 is participating.

Figure 7 presents a part of the phase diagram of the system Na+, Ca++, Cl, SO4–H2O. Since the HMW84 model predicts the transition between gypsum and anhydrite at a lower water activity, the crystallization field of anhydrite in the HMW84 model appears only near the NaCl saturation, whereas with THEREDA one calculates a much larger extension of the anhydrite field. The justification for the choice of the water activity for the gypsum/anhydrite transition can be seen in Fig. 8. The solubility curves of these two minerals cross each other at about 4 molal NaCl at 298 K and such a solution has a water activity of 0.85 and not 0.77 as was derived by HMW from a work of [191].

Fig. 7: Calculated phase boundaries according to HMW84 model (red) and THEREDA model (blue).

Fig. 7:

Calculated phase boundaries according to HMW84 model (red) and THEREDA model (blue).

Fig. 8: Solubility curves for gypsum and anhydrite in dependence on NaCl concentration; exp. data gypsum stars, anhydrite circles, black curve THEREDA model, grey curve HMW84 model, aw=water activity, arrows show transition points gypsum/anhydrite for the THEREDA model (filled) and HMW84 model (opened).

Fig. 8:

Solubility curves for gypsum and anhydrite in dependence on NaCl concentration; exp. data gypsum stars, anhydrite circles, black curve THEREDA model, grey curve HMW84 model, aw=water activity, arrows show transition points gypsum/anhydrite for the THEREDA model (filled) and HMW84 model (opened).

The development of the crystallization field of polyhalite along the history of data and models at T=298 K is presented in Fig. 9. Already the HMW84 model enlarged the field of polyhalite compared to D’Ans. According to our data [228] incorporated in the THEREDA model it should be even larger, which is also more appropriate considering the wide spread occurrence of polyhalite in nature at varying environments.

Fig. 9: Extension of the crystallization field of polyhalite in coordinates of the Jänecke diagram according to D’Ans, HMW84 model and the THEREDA model at 298 K.

Fig. 9:

Extension of the crystallization field of polyhalite in coordinates of the Jänecke diagram according to D’Ans, HMW84 model and the THEREDA model at 298 K.

Some selected examples for the THEREDA model quality at temperatures other than 298 K are given in Figs. 1013 in comparison with available experimental data. More examples can be found at www.thereda.de.

Fig. 10: Solubility isotherms in system NaCl-KCl-H2O; a=273 K, b=323 K, c=373 K lines=THEREDA model, circles=exp. Data.

Fig. 10:

Solubility isotherms in system NaCl-KCl-H2O; a=273 K, b=323 K, c=373 K lines=THEREDA model, circles=exp. Data.

Fig. 11: Solubility isotherms in system KCl-MgCl2-H2O; a=273 K, b=323 K, c=348 K, d=373 K; lines=THEREDA model, circles=exp. data.

Fig. 11:

Solubility isotherms in system KCl-MgCl2-H2O; a=273 K, b=323 K, c=348 K, d=373 K; lines=THEREDA model, circles=exp. data.

Fig. 12: Solubility isotherms in system K2SO4-MgSO4-H2O; a: grey=273 K, black=288 K, b=303 K, c=318 K, d=373 K; lines=THEREDA model, circles=exp. data.

Fig. 12:

Solubility isotherms in system K2SO4-MgSO4-H2O; a: grey=273 K, black=288 K, b=303 K, c=318 K, d=373 K; lines=THEREDA model, circles=exp. data.

Fig. 13: Crystallization fields in the reciprocal system Na+, Mg++/Cl–, SO4––H2O as calculated by means of THEREDA database, a=273 K, b=298 K, c=363 K; lines=calculated field borders, circles=exp. data.

Fig. 13:

Crystallization fields in the reciprocal system Na+, Mg++/Cl, SO4–H2O as calculated by means of THEREDA database, a=273 K, b=298 K, c=363 K; lines=calculated field borders, circles=exp. data.

Conclusions

The present knowledge about salt phases formed from the major ions of the oceanic system has been reviewed. Due to the progress particularly in Raman spectroscopy and X-ray diffraction technique new phases of hydrated sulfates of magnesium, sodium and calcium have been identified and characterized structurally. In the opinions of the author there is still room for more of such discoveries. However, the determination of their metastable or eventually stable crystallization fields in the solubility diagrams is left open. Even for the long time known magnesium sulfate hydrates the stability relations in contact with solutions could not be resolved satisfactorily for the lower hydrates. Whereas calorimetric measurements can improve the thermodynamic characterization of the solid phases and enhance the reliability of thermodynamic models, they are not sufficient to clarify subtle stability relations in solubility equilibria. This has to be done by means of equilibration experiments, which will be mostly solubility determinations. However, for difficult cases as for magnesium and calcium sulfates and their double salts kinetic and mechanistic aspects of crystallization and dissolution should be included in these investigations. For example the long-standing question of a definite answer at which temperature and water activity the gypsum/anhydrite transition occurs at ambient conditions requires kinetic and mechanistic insights. The AFM work of Pina [229] on anhydrite crystal growth gives good hints how to proceed. On the other side, it is not very useful in practice to know that a transition at a certain temperature should occur, but not how long it will need.

At temperatures below or above 298 K the accuracy of the best available data for invariant points and uni-variant solubility equilibria in the multi-component solutions (4–6 ions present) of oceanic salts is often much lower than modern experimental and analytical techniques would allow or even do not meet the practical requirements. For solutions not saturated in NaCl the solubility equilibria in the quinary system Na+, K+, Mg++/Cl, SO4–H2O are not systematically investigated at all, even not for 298 K.

Thermodynamic models, if correctly reflecting the experimental data enable fast access to solubility data, to establish mass and heat balances for dissolution and crystallization processes at composition and temperature ranges of interest. At 298 K (25°C) by means of the Pitzer’s equations the model has nearly arrived at such a status for the quinary system without calcium. However, thermodynamic modelling could not improve the accuracy problem in multi-component phase equilibria and not remove existing uncertainties in respect to phase stabilities in some ranges of composition and temperature. Major improvements could be achieved, if thermodynamic modelling would be connected with systematic solubility studies of single solid phases in the multi-component oceanic solutions. These equilibria are easier to establish and chemical analyses methods could be fine-tuned for these conditions. This way the estimation of interaction parameters becomes more reliable, since at present the modeller is often forced to extract these parameters from scattered data of solubility equilibria with several solid phases present. Of course, also additional isopiestic or suited galvanic cell voltage measurements in ternary and quaternary unsaturated solutions would contribute to higher model qualities.


Corresponding author: Wolfgang Voigt, TU Bergakademie Freiberg, Institute of Inorganic Chemistry, Leipziger Str. 29, 09596 Freiberg, Germany, e-mail:

References

[1] J. H. van’t Hoff. Untersuchungen über die Bildungsverhältnisse der ozeanischen Salzablagerungen insbesondere des Stassfurter Salzlagers, Akademische Verlagsges. mbH, Leipzig (1912). Search in Google Scholar

[2] J. K. Warren. Evaporites–Sediments, Resources and Hydrocarbons, Springer-Verlag, Berlin, Heidelberg (2006). Search in Google Scholar

[3] O. Braitsch. Entstehung und Stoffbestand der Salzlagerstätten, Springer-Verlag, Berlin, Göttingen, Heidelberg (1962). Search in Google Scholar

[4] F. Matthes, G. Wehner. Anorganisch-technische Verfahren: 5. Mineralsalze in der Kaliindustrie, VEB Deutscher Verlag für Grundstoffindustrie (1964). Search in Google Scholar

[5] D.E. Garrett. Potash–Deposits, Processing, Properties and Uses, Chapman & Hall, London, Glasgow, Weinheim, New York (1996). Search in Google Scholar

[6] R. Storck, J. Aschenbach, R. P. Hirsekorn, A. Nies, N. Stelte. PAGIS–Performance Assessment of Geological Isolation Systems for Radioactive Waste: Disposal in Salt Formations, Commission of the European Communities, München (1988). Search in Google Scholar

[7] OECD Nuclear Energy Agency, Natural Analogues for Safety Cases of Repositories in Rock Salt, Salt Club Workshop Proceedings, Braunschweig, 5–7 September 2013 – Radioactive Waste Management Committee 2014. Search in Google Scholar

[8] J. B. Adams, A. R. Gillespie, M. Jackson, D. R. Montgomery, T. P. Dooley, J.-P. Combe, B. C. Schreiber. Geology37, 691 (2009). Search in Google Scholar

[9] J. L. Bishop, M. Darby Dyar, Melissa D. Lane, Jillian F. Banfield. Int. J. Astrobiol.3, 275 (2005). Search in Google Scholar

[10] D. E. Garrett. Handbook of Lithium and Natural Calcium Chloride: Their Deposits, Processing, uses and Properties, Elesevier Academic Press, Amsterdam, Boston, Heidelberg (2004). Search in Google Scholar

[11] M. J. Herrero, J. I. Escavy, B. C. Schreiber. Clim. Past11, 1 (2015). Search in Google Scholar

[12] V. Manzi, R. Gennari, S. Lugli, M. Roveri, N. Scafetta, B.C. Schreiber. J. Sediment. Res.82, 991 (2012). Search in Google Scholar

[13] B. C. Schreiber, M. el Tabakh. Sedimentology47 (Suppl. 1), 215 (2000). Search in Google Scholar

[14] T. K. Lowenstein, J. Li, C. Brown, S. Roberts, T. -L. Ku, S. Luo, W. Yang. Geology27, 3 (1999). Search in Google Scholar

[15] F. Navarro-Hervas, M. -M. Ros-Salas, T. Rodriguez-Estrella, E. Fierro-Enrique, J. -S. Carrion, J. Garcia-Veigas, J. -A. Flores, M. A. Barcena, M. S. Garcia. The Holocene24, 489 (2014). Search in Google Scholar

[16] S. T. Martin. Chem. Rev.100, 3403 (2000). Search in Google Scholar

[17] M. Steiger. J. Cryst. Growth282, 455 (2005). Search in Google Scholar

[18] M. Altmaier, V. Metz, V. Neck, R. Müller, T. Fanghänel. Geochim. Cosmochim. Acta67, 3595 (2003). Search in Google Scholar

[19] R. E. Dinnebier, M. Oestreich, S. Bette, D. Freyer. Z. Anorg. Allg. Chem.638, 628 (2012). Search in Google Scholar

[20] R. E. Dinnebier, M. Pannach, D. Freyer. Z. Anorg. Allg. Chem.639, 1827 (2013). Search in Google Scholar

[21] A. Findlay. The Phase Rule and its Application, Longmans Green and Co., London, New York, Bombay (1911). Search in Google Scholar

[22] A. Findlay, A. N. Campbell, N.O. Smith. The Phase Rule and Its Application, Dover, New York (1951). Search in Google Scholar

[23] A. Findlay. Die Phasenregel und ihre Anwendungen, Verlag Chemie GmbH, Weinheim (1958). Search in Google Scholar

[24] E. Pietsch, A. Kotowski. Gmelins Handbuch der Anorganischen Chemie: Kalium–Anhangsband, Verlag Chemie GmbH, Weinheim (1970). Search in Google Scholar

[25] L. H. Gevantman, J. Lorenz, J. L. Haas Jr., M. A. Clynne, R. W. Potter II, C. M. Schafer, R. Tomkins, A. Shakor, H. R. Hume, J. M. Yang, R. A. Matula. Physical Properties Data for Rock Salt, Washington, D.C. (1981). Search in Google Scholar

[26] R. Cohen-Adad, J. W. Lorimer. Alkali metal and ammonium chlorides in water and heavy water, Pergamon Press, Oxford, New York (1991). Search in Google Scholar

[27] B. Klewe, B. Pedersen. Acta Cryst. B30, 2363 (1974). Search in Google Scholar

[28] Y. Fialkov, V. B. Chernogorenko. Dokl. Akad. Nauk SSSR102, 759 (1955). Search in Google Scholar

[29] M. P. Shul’gina, O. S. Kharchuk, O. K. Yanat’eva. Izv. Sektora. Fiz. Khim. Anal. Inst. Obshch. Neorg. Khim. Akad. Nauk SSSR26, 198 (1955). Search in Google Scholar

[30] A. G. Bergman, A. I. Kusnezova. Zh. Neorg. Khim.4, 194 (1959). Search in Google Scholar

[31] E. Usdowski, M. Dietzel. Atlas and Data of Solid-Solution Equilibria of Marine Evaporites, Springer-Verlag, Berlin, Heidelberg (1998). Search in Google Scholar

[32] T. Fanghaenel, H. H. Emons. Freib. Forschh.A, 15 (1989). Search in Google Scholar

[33] T. Fanghänel, K. Kravchuk, W. Voigt, H.-H. Emons. Z. Anorg. Allg. Chem.547, 21 (1987). Search in Google Scholar

[34] D. Freyer, W. Voigt, V. Böttge. Kali und Steinsalz 28 (2006). Search in Google Scholar

[35] D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, R. L. Nuttall. J. Phys. Chem. Ref. Data11, 1 (1982). Search in Google Scholar

[36] J. H. van’t Hoff, W. Meyerhoffer. Z. phys. Chem.27, 75 (1898). Search in Google Scholar

[37] K. Sasvari. Acta Cryst20, 875 (1966). Search in Google Scholar

[38] E. Hennings, H. Schmidt, W. Voigt. Acta Cryst. C69, 1292 (2013). Search in Google Scholar

[39] K. Komatsu, A. Shinozaki, S. Machida, T. Matsubayashi, M. Watanabe, H. Kagi, A. Sano-Furukawa, T. Hattori. Acta Crystallogr, B71, 74 (2015). Search in Google Scholar

[40] C. F. Prutton, O. F. Tower. J. Am. Chem. Soc.54, 3040 (1932). Search in Google Scholar

[41] J. D’Ans. Die Lösungsgleichgewichte der Systeme der Salze ozeanischer Salzablagerungen, Verlagsges. f. Ackerbau mbH, Berlin (1933). Search in Google Scholar

[42] E. H. Riesenfeld, C. Milchsack. Z. Anorg. Chem.85, 401 (1914). Search in Google Scholar

[43] J. Guion. Thermochim. Acta67, 167 (1983). Search in Google Scholar

[44] A. Chmarzynski, H. Piekarski. J. Therm. Anal.38, 2019 (1992). Search in Google Scholar

[45] R. Pilar, L. Svoboda, P. Honcova, L. Oravova. Thermochimica Acta546, 81 (2012). Search in Google Scholar

[46] R. Naumann, Emons, H. H. T. Pohl. Thermochim. Acta92, 673 (1985). Search in Google Scholar

[47] D. Petzold, R. Naumann. J. Thermal Anal.19, 25 (1980). Search in Google Scholar

[48] H. J. Abendroth, A. Peters, W. Fischer. Rev. Chim. Min. 11, 556 (1974). Search in Google Scholar

[49] R. W. Carling. J. Chem. Thermodyn13, 503 (1981). Search in Google Scholar

[50] K. Sugimoto, R. Dinnebier, J. C. Hanson, Acata Cryst. B63, 235 (2007). Search in Google Scholar

[51] H. Schmidt, E. Hennings, W. Voigt. Acta Cryst. C68, i4–6 (2012). Search in Google Scholar

[52] K. Sugimoto, R. E. Dinnebier, J. C. Hanson. Acta Cryst. B63, 235 (2007). Search in Google Scholar

[53] A. Leclaire, M. M. Borel. Acta Cryst. B33, 2938 (1977). Search in Google Scholar

[54] P. A. Agron, W. R. Busing. Acta Cryst. C42, 141 (1986). Search in Google Scholar

[55] U. Thewalt, C. E. Bugg. Acta Cryst. B29, 615 (1973). Search in Google Scholar

[56] A. Leclaire, M. M. Borel. Acta Cryst. B35, 585 (1979). Search in Google Scholar

[57] A. Leclaire, M. M. Borel. Acta Cryst. B34, 900 (1978). Search in Google Scholar

[58] A. Leclaire, M. M. Borel, J. C. Monier. Acta Cryst. B36, 2757 (1980). Search in Google Scholar

[59] J. W. Anthony, R. A. Bideaux, K. W. Bladh, M. C. Nichols. Handbook of Mineralogy, www.handbookofmineralogy.org/pdfs/sinjarite.pdf. Search in Google Scholar

[60] D. Garvin, V. B. Parker, H. J. White Jr. CODATA Thermodynamic Tables: Selections for some Compounds of Calcium and Related Mixtures, Hemisphere publishing Corporation, Washington, New York, London (1987). Search in Google Scholar

[61] H. Jenkins, B. Donald, P. Hartman. Phys. Chem. Minerals6, 313 (1980). Search in Google Scholar

[62] K. K. Meisingset, F. Grønvold. J. Chem. Thermodyn.18, 159 (1986). Search in Google Scholar

[63] H. W. B. Roozeboom. Z. phys. Chem. 4, 31 (1889). Search in Google Scholar

[64] I. M. Samson, R. T. Walker. Can Mineral38, 35 (2000). Search in Google Scholar

[65] M. Baumgartner, R. J. Bakker. Chemical Geology275, 58 (2010). Search in Google Scholar

[66] B. Carlsson. Solar Energy83, 485 (2009). Search in Google Scholar

[67] H. Kimura, J. Kai. Solar Energy33, 49 (1984). Search in Google Scholar

[68] B. R. Churagulov, A. N. Baranov. Zh. Neorg. Khim.36, 2953 (1991). Search in Google Scholar

[69] E. Günther, H. Mehling, M. Werner. J. Phys. D: Appl. Phys.40, 4636 (2007). Search in Google Scholar

[70] Z. A. Aljubouri, S. M. Aldabbagh. Mineral. Mag.43, 643 (1980). Search in Google Scholar

[71] G. C. Sinke, E. H. Mossner, J. L. Curnutt. J. Chem. Thermodyn.17, 893 (1985). Search in Google Scholar

[72] H. G. Wiedemann, W. Smykatz-Kloss, W. Eysel. J. Thermal Anal.6, 347 (1980). Search in Google Scholar

[73] D. Freyer, W. Voigt, K. Köhnke. Eur. J. Solid State Inorg. Chem.35, 595 (1998). Search in Google Scholar

[74] W. Eysel, H. H. Höfer, K. L. Keester, T. Hahn. Acta Cryst. B41, 5 (1985). Search in Google Scholar

[75] G. Dharmasena, R. Frech. J. Chem. Phys.99, 8929 (1993). Search in Google Scholar

[76] F. Gronvold, K. K. Meisingset. J. Chem. Thermodyn.15, 1083 (1982). Search in Google Scholar

[77] A. Kürklü. Renew. Energ.13, 89 (1998). Search in Google Scholar

[78] H.-H. Emons, R. Naumann, W. Voigt, W. Stocklöw, W. Ahrens. Int. J. Energy Res.10, 69 (1986). Search in Google Scholar

[79] C. Onwubiko, L. D. Russell. Solar Energy33, 465 (1984). Search in Google Scholar

[80] H. A. Levy, G. C. Lisensky. Acta Cryst. B34, 3502 (1978). Search in Google Scholar

[81] G. Brodale, W. F. Giauque. J. Am. Chem. Soc.80, 2042 (1958). Search in Google Scholar

[82] S. Kamburov, H. Schmidt, W. Voigt, C. Balarew. Acta Cryst. B70, 714 (2014). Search in Google Scholar

[83] A. D. Fortes, H. E. A. Brand, L. Vočadlo, A. Lindsay-Scott, F. Fernandez-Alonso, I. G. Wood. J Appl Crystallogr46, 448 (2013). Search in Google Scholar

[84] E. R. Washburn, W. J. Clem. J. Am. Chem. Soc.60, 754 (1938). Search in Google Scholar

[85] R. Kühn. Kali u. Steinsalz2, 331 (1959). Search in Google Scholar

[86] Iain D. H. Oswald, A. Hamilton, C. Hall, W. G. Marshall, T. J. Prior, C. R. Pulham. J. Am. Chem. Soc.130, 17795 (2008). Search in Google Scholar

[87] A. Goldberg, W. Eysel, T. Hahn. N. Jb. Miner. Mh.60, 241 (1973). Search in Google Scholar

[88] K. Okada, J. Ossaka. Acta Cryst. B36, 919 (1980). Search in Google Scholar

[89] H. W. Foote. J. Am. Chem. Soc.33, 463 (1911). Search in Google Scholar

[90] D. Freyer, W. Voigt. Geochim. Cosmochim. Acta68, 307 (2004). Search in Google Scholar

[91] F. C. Hawthorne, L. A. Groat, M. Raudsepp, T. S. Ercit. Neues Jahrbuch für Mineralogie, Abhandlungen157, 121 (1987). Search in Google Scholar

[92] H.-H. Emons, G. Ziegenbalg, R. Naumann, F. Paulik. J. Therm. Anal.36, 1265 (1990). Search in Google Scholar

[93] G. Ziegenbalg. Stabile und metastabile fest-flüssig-Phasengleichgewichte des Systems Na+, K+, Mg2+/Cl-, SO42-//H2O–unter besonderer Berücksichtigung der Bildungsbedingungen von Kieserit im Temperaturbereich von 90–140°C: Dissertation 1990. Search in Google Scholar

[94] H. W. Ma, D. L. Bish, H. W. Wang, S. J. Chipera. Am. Mineral.94, 622 (2009). Search in Google Scholar

[95] H. W. Ma, D. L. Bish, H. W. Wang, S. J. Chipera. Amer. Mineral.94, 1071 (2009). Search in Google Scholar

[96] R. von Hodenberg, R. Kuehn. Kali u. Steinsalz4, 326 (1967). Search in Google Scholar

[97] A. D. Fortes, M. H. Lemee-Cailleau, K. S. Knight, M. Jura (Eds.). Magnesium sulfate trihydrate: an elusive mineral on Earth and Mars? Int. Mineral. Assoc., 20th General Meeting, Abstract (2010). Search in Google Scholar

[98] W. H. Baur. Acta Cryst.15, 815 (1962). Search in Google Scholar

[99] W. H. Baur. Acta Cryst.17, 863 (1964). Search in Google Scholar

[100] R. C. Peterson. Amer. Mineral.96, 869 (2011). Search in Google Scholar

[101] W. H. Baur, J. L. Rolin. Acta Cryst. B28, 1448 (1972). Search in Google Scholar

[102] A. S. Batasanov. Acta Cryst. C56, e230–e231 (2000). Search in Google Scholar

[103] W. H. Baur. Acta Cryst.17, 1361 (1964). Search in Google Scholar

[104] M. Calleri, A. Gavetti, M. Rubbo. Acta Crystallogr B (Acta Crystallographica Section B Structural Science)40, 218 (1984). Search in Google Scholar

[105] G. Ferraris, D. W. Jones. J. Chem. Soc., Dalton Trans.1973, 816 (1973). Search in Google Scholar

[106] C. Viola. Z. Kristallographie58, 583 (1923). Search in Google Scholar

[107] F. E. Genceli, M. Lutz, A. L. Spek, G.-J. Witkamp. Cryst Growth Des7, 2460 (2007). Search in Google Scholar

[108] A. D. Fortes, I. G. Wood, K. S. Knight. Phys Chem Minerals35, 207 (2008). Search in Google Scholar

[109] H. L. Robson. J. Am Chem. Soc.49, 2772 (1927). Search in Google Scholar

[110] A. Wang, J. J. Freeman, B. L. Jolliff. J. Geophys. Res.114, 1 (2009). Search in Google Scholar

[111] A. Wang, J. F. Freeman, B. L. Jolliff, R. E. Arvidson. Lunar Planet. Sci.XXXVII, 2168 (2006). Search in Google Scholar

[112] A. Wang, J. J. Freeman, I.-M. Chou, B. L. Jolliff. J. Geophys. Res.116, E12006 (2011). Search in Google Scholar

[113] J. B. Dalton. J. Geophys. Res. 117, E09001 (2012). Search in Google Scholar

[114] I.-M. Chou, R. R. Seal, A. Wang. J. Asian Earth Sci.62, 734 (2013). Search in Google Scholar

[115] R. C. Peterson, W. Nelson, B. Madu, H. F. Shurvell. Am. Mineral.92, 1756 (2007). Search in Google Scholar

[116] A. D. Fortes. 43rd Lunar & Planetary Science Conf. 1024.pdf (2012). Search in Google Scholar

[117] Hongxia Li, D. Zeng, Yan Yao, Chuan Gao, Xia Yin, Haijun Han. J. Chem. Eng. Data59, 2177 (2014). Search in Google Scholar

[118] A. D. Fortes. Axis1, 1 (2005). Search in Google Scholar

[119] A. D. Fortes, I. G. Wood, L. Vocatio, H. E. A. Brand, P. M. Grinrod. Lunar Planet. Sci. XXXVII, 1029.pdf (2006). Search in Google Scholar

[120] E. L. Gromnitskaya, O. F. Yagafarov, A. G. Lyapin, V. V. Brazhkin, I. G. Wood, M. G. Tucker, A. D. Fortes. Phys Chem Minerals40, 271 (2013). Search in Google Scholar

[121] A. Zalkin, H. Ruben, D. H. Templeton. Acta Cryst.17, 235 (1964). Search in Google Scholar

[122] W. P. Cox, E. W. Hornung, W. F. Giauque. J. Am. Chem. Soc.77, 3935 (1955). Search in Google Scholar

[123] R. E. Barieau, W. Giauque. J. Am. Chem. Soc.72, 5676 (1950). Search in Google Scholar

[124] v. Hodenberg, R., R. Kühn. Kali u. Steinsalz4, 326 (1967). Search in Google Scholar

[125] C. Balarew, S. Tepavitcharova, D. Rabadjieva, W. Voigt. J. Solution Chem.30, 815 (2001). Search in Google Scholar

[126] K.-D. Grevel, J. Majzlan, A. Benisek, E. Dachs, M. Steiger, A. D. Fortes, B. Marler. Astrobiology12, 1042 (2012). Search in Google Scholar

[127] M. Steiger, K. Linnow, D. Ehrhardt, M. Rohde. Geochim. Cosmochim. Acta75, 3600 (2011). Search in Google Scholar

[128] S. Follner, A. Wolter, K. Helming, C. Silber, H. Bartels, H. Follner. Cryst. Res. Technol.37, 207 (2002). Search in Google Scholar

[129] F. R. Massaro, M. Rubbo, D. Aquilano. Cryst Growth Des10, 2870 (2010). Search in Google Scholar

[130] F. R. Massaro, M. Rubbo, D. Aquilano. Cryst Growth Des11, 1607 (2011). Search in Google Scholar

[131] D. Freyer, W. Voigt. Monatsh Chem134, 693 (2003). Search in Google Scholar

[132] A. N. Christensen, T. R. Jensen, A. Nonat. Dalton Trans39, 2044 (2010). Search in Google Scholar

[133] S. Follner, A. Wolter, A. Preusser, S. Indris, C. Silber, H. Follner. Cryst. Res. Technol.37, 1075 (2002). Search in Google Scholar

[134] D. Freyer, W. Voigt. ZKGInternational.62, 47 (2009). Search in Google Scholar

[135] C. Bezou, A. Nonat, J.-C. Mutin, A. Christensen, M. S. Lehmann. J. Solid State Chem.117, 165 (1995). Search in Google Scholar

[136] C. Berthold, V. Presser, N. Huber, K. G. Nickel. J. Therm. Anal. Calorim.103, 917 (2011). Search in Google Scholar

[137] P. Ballirano, A. Maras, S. Meloni, R. Caminiti. Eur. J. Mineral.13, 985 (2001). Search in Google Scholar

[138] W. Abriel, R. Nesper. Z. Kristallogr.205, 99 (1993). Search in Google Scholar

[139] O. W. Flörke. Neues Jahrbuch für Mineralogie84, 189 (1952). Search in Google Scholar

[140] H. Weiss, M. F. Bräu. Angew. Chem.121, 3572 (2009). Search in Google Scholar

[141] W. Abriel. Acta Cryst. C39, 959 (1983). Search in Google Scholar

[142] M. Oetzel. Untersuchungen der Phasenbeziehungen im System CaSO4–H2O: Dissertation 1999. Search in Google Scholar

[143] H. Schmidt, I. Paschke, D. Freyer, W. Voigt. Acta Crystallogr B67, 467 (2011). Search in Google Scholar

[144] S. Fritz, H. Schmidt, I. Paschke, O. V. Magdysyuk, R. E. Dinnebier, D. Freyer, W. Voigt. Acta Cryst. B67, 293 (2011). Search in Google Scholar

[145] K. Robertson, D. Bish. Icarus223, 407 (2013). Search in Google Scholar

[146] D. L. Bish, D. F. Blake, D. T. Vaniman, S. J. Chipera, R. V. Morris, D. W. Ming, A. H. Treiman, P. Sarrazin, S. M. Morrison, R. T. Downs, C. N. Achilles, A. S. Yen, T. F. Bristow, J. A. Crisp, J. M. Morookian, J. D. Farmer, E. B. Rampe, E. M. Stolper, N. Spanovich. Science341, 1238932 (2013). Search in Google Scholar

[147] D. Freyer, G. Reck, M. Bremer, W. Voigt. Monatsh. Chem.130, 1179 (1999). Search in Google Scholar

[148] D. Freyer, S. Ziske, W. Voigt. Freib. Forschh.E3, 127 (2002). Search in Google Scholar

[149] H.-H. Emons, P. Brand, T. Pohl, K. Köhnke. Z. Anorg. Allg. Chem.563, 180 (1988). Search in Google Scholar

[150] M. G. Siemann, M. Schramm. Geochim. Cosmochim. Acta64, 1681 (2000). Search in Google Scholar

[151] H. H. Emons, R. Naumann, T. Pohl, H. Voigt. J. Therm. Anal.29, 571 (1984). Search in Google Scholar

[152] T. Fanghänel, H. H. Emons, K. Köhnke. Z. Anorg. Allg. Chem.576, 99 (1989). Search in Google Scholar

[153] H.-H. Emons, T. Fanghänel. J. Thermal Anal.35, 2161 (1989). Search in Google Scholar

[154] A. Leclaire, M. M. Borel, J. C. Monier, Acta Crystall B36, 2734 (1980). Search in Google Scholar

[155] J. R. Clark, H. T. Evans, Jr, R. C. Erd. Acta Crystall B36, 2736 (1980). Search in Google Scholar

[156] G. O. Assarsson. J. Am. Chem. Soc.72, 1442 (1950). Search in Google Scholar

[157] D. Freyer, W. Voigt, R. Moßig. Report on Raman-Mapping einer Tachhydrit–Kieserit–Mineralprobe aus Teutschenthal, TU Bergakademie Freiberg, unpublished, available from authors (2004). Search in Google Scholar

[158] A. I. Orekhova, G. A. Sokolova, E. I. Savinkova. Zh. Prikl. Khim.55, 129 (1982). Search in Google Scholar

[159] A. I. Orekhova, A. D. Neuimin. Izv.Vyssh. Uchebn. Zaved., Tsvetn. Met.2, 59 (1978). Search in Google Scholar

[160] W. J. Lightfoot, C. F. Prutton. J. Am. Chem. Soc.69, 2098 (1947). Search in Google Scholar

[161] W. J. Lightfoot, C. F. Prutton. J. Am. Chem. Soc.71, 1233 (1949). Search in Google Scholar

[162] G. O. Assarsson. J. Am. Chem. Soc.72, 1437 (1950). Search in Google Scholar

[163] R. Hodenberg, R. Kühn, F. Rosskopf. Kali u. Steinsalz5, 178 (1969). Search in Google Scholar

[164] J. H. Fang, P. D. Robinson. Am. Mineral.55, 378 (1970). Search in Google Scholar

[165] J. van Doesburg, L. Vergouwen, L. Van der Plas. Amer. Mineral.67, 1035 (1982). Search in Google Scholar

[166] E. M. Leduc, R. C. Peterson, R. Wang. American Mineralogist94, 1005 (2009). Search in Google Scholar

[167] E. M. S. Leduc. Hydrated Sodium-Magnesium Sulfate Minerals Associated with Inland Saline Systems Atomic structure, hydrogen bonding and phase stability: Master Thesis, (2010). Search in Google Scholar

[168] E. M. Leduc, R. C. Peterson, R. Wang. Acta Cryst. C65, i81–4 (2009). Search in Google Scholar

[169] K. Leftwich, D. L. Bish, C. H. Chen. American Mineralogist98, 1772 (2013). Search in Google Scholar

[170] H. Autenrieth. Kali u. Steinsalz2, 18 (1955). Search in Google Scholar

[171] T. M. Letcher (Ed.). Developments and applications in solubility: W. Voigt: Chap. 24: Solubility of Inorganic Salts and their Industrial Importance. W. Voigt: Chap. 24: Solubility of Inorganic Salts and their Industrial Importance, RSC Pub., Cambridge (2007). Search in Google Scholar

[172] D. Jarosch. Z. Kristallogr.173, 75 (1985). Search in Google Scholar

[173] B. Hertweck, G. Giester, E. Libowitzky. Amer. Mineral.86, 1282 (2001). Search in Google Scholar

[174] B. Hertweck, E. Libowitzky. Eur.J. Mineral.14, 1009 (2002). Search in Google Scholar

[175] H.-H. Emons, H.-H. Seyfarth, E. Stegmann. Krist. Techn.6, 85 (1971). Search in Google Scholar

[176] A. E. Hill, J. H. Wills. J. Am. Chem. Soc.60, 1647 (1938). Search in Google Scholar

[177] L. Vergouwen. Amer. Mineral.66, 632 (1981). Search in Google Scholar

[178] D. E. Garrett. Sodium Sulfate: Handbook of Deposits, Processing, Properties, and Use, Academic Press, London (2001). Search in Google Scholar

[179] J. T. Kloprogge. Am. Mineral.89, 266 (2004). Search in Google Scholar

[180] P. D. Robinson, J. H. Fang, Y. Ohya. Am. Mineral.57, 1325 (1972). Search in Google Scholar

[181] M. Schlatti, K. Sahl, A. Zemann, J. Zemann. Naturwissenschaften56, 368 (1969). Search in Google Scholar

[182] M. Schlatti, K. Sahl, A. Zemann, J. Zemann. TMPM Tschermaks Petr. Mitt.14, 75 (1970). Search in Google Scholar

[183] R. Kühn, K.-H. Ritter. Kali und Steinsalz2, 238 (1958). Search in Google Scholar

[184] J. Lange, H. Burzlaff. Acta Crystallographica Section A51, 931 (1995). Search in Google Scholar

[185] F. Demartin, I. Campostrini, C. Castellano, C. M. Gramaccioli, M. Russo. Mineral. Mag.76, 2773 (2012). Search in Google Scholar

[186] S. J. Chipera, D. T. Vaniman. Geochim. Cosmochim. Acta71, 241 (2007). Search in Google Scholar

[187] A. D. Pel’sh. Handbook for experimental solubility data of multi-component water–salt systems (Russ.): Ternary and Quaternary systems, Leningrad (1973–1975). Search in Google Scholar

[188] E. Usdowski, I. Stahl, K. R. Wambach-Sommerhoff. N. Jb. Miner. Mh. 15 (1997). Search in Google Scholar

[189] J. Eysseltova, R. Bouaziz. J. Phys. Chem. Ref. Data41, 1 (2012). Search in Google Scholar

[190] M. Ossorio, A. van Driessche, P. Pérez, J. M. García-Ruiz. Chemical Geology386, 16 (2014). Search in Google Scholar

[191] Lawrence A. Hardie. Amer. Mineral.52, 171 (1967). Search in Google Scholar

[192] K. S. Pitzer. J. Phys. Chem.77, 268 (1973). Search in Google Scholar

[193] K. S. Pitzer, G. Mayorga. J. Phys. Chem.77, 2300 (1973). Search in Google Scholar

[194] K. S. Pitzer, G. Mayorga. J. Solution Chem.3, 39 (1974). Search in Google Scholar

[195] K. S. Pitzer. J. Solution Chem.4, 249 (1975). Search in Google Scholar

[196] K. S. Pitzer. Activity Coefficients in Electrolyte Solutions, CRC Press, Boca Raton (1991). Search in Google Scholar

[197] I. Grenthe, I. Puigdomenech, B. Allard. Modelling in aquatic chemistry, Nuclear Energy Agency, Organisation for Economic Co-operation and Development; [distributor, OECD Washington Center], Paris, [Washington, D.C.] (1997). Search in Google Scholar

[198] T. Wolery, R. L. Jarek. SOFTWARE USER’S MANUAL EQ3/6, Version 8.0 2003. Search in Google Scholar

[199] H. P. Eugster, C. E. Harvie, J. H. Weare. Geochim. Cosmochim. Acta44, 1335 (1980). Search in Google Scholar

[200] C. E. Harvie, J. H. Weare. Geochim. Cosmochim. Acta44, 981 (1980). Search in Google Scholar

[201] C. E. Harvie, H. P. Eugster, J. H. Weare. Geochim. Cosmochim. Acta46, 1603 (1982). Search in Google Scholar

[202] C. E. Harvie, N. Møller, J. H. Weare. Geochim. Cosmochim. Acta48, 723 (1984). Search in Google Scholar

[203] H. F. Holmes, C. F. Baes Jr, R. E. Mesmer. J. Chem. Thermodyn.13, 983 (1978). Search in Google Scholar

[204] H. F. Holmes, C. F. Baes, R. E. Mesmer. J. Chem. Thermodyn.11, 1035 (1979). Search in Google Scholar

[205] H. F. Holmes, C. F. Baes, R. E. Mesmer. J. Chem. Thermodyn.13, 101 (1981). Search in Google Scholar

[206] H. F. Holmes, R. H. Busey, J. M. Simonson, R. E. Mesmer. J. Chem. Thermodyn.26, 271 (1994). Search in Google Scholar

[207] H. F. Holmes, R. E. Mesmer. J. Chem. Thermodyn.13, 1035 (1981). Search in Google Scholar

[208] H. F. Holmes, R. E. Mesmer. J.Phys.Chem.87, 1242 (1983). Search in Google Scholar

[209] H. F. Holmes, R. E. Mesmer. J. Solution Chem.15, 495 (1986). Search in Google Scholar

[210] H. F. Holmes, R. E. Mesmer. J. Solution Chem.21, 713 (1992). Search in Google Scholar

[211] H. Holmes, R. E. Mesmer. J. Chem. Thermodyn.15, 709 (1983). Search in Google Scholar

[212] V. Brendler, W. Voigt. J. Solution Chem.25, 83 (1996). Search in Google Scholar

[213] M. S. Gruszkiewicz, J. M. Simonson. J. Chem. Thermodyn.37, 906 (2005). Search in Google Scholar

[214] C. Appelo. Applied Geochemistry55, 62 (2015). Search in Google Scholar

[215] C. Christov, N. Moller. Geochim. Cosmochim. Acta68, 3717 (2004). Search in Google Scholar

[216] C. Christov, N. Moller. Geochim. Cosmochim. Acta68, 1309 (2004). Search in Google Scholar

[217] Palmer, A. Donald, Rard,, A. Joseph, S. L. Clegg. J. Chem. Thermodyn.34, 63 (2002). Search in Google Scholar

[218] J. A. Rard, S. L. Clegg, D. A. Palmer. J. Solution Chem.29, 1 (2000). Search in Google Scholar

[219] J. A. Rard, S. L. Clegg, R. F. Platford. J. Chem. Thermodyn.35, 967 (2003). Search in Google Scholar

[220] S. L. Clegg, J. A. Rard, D. G. Miller. Isopiestic Determination of the Osmotic and Activity Coefficients of NaCl+SrCl2+H2O at 298.15 K, and Representation with an Extended Ion-Interaction Model 2004 (9 April 2015). Search in Google Scholar

[221] J. A. Rard, S. L. Clegg, D. A. Palmer. J Solution Chem36, 1347 (2007). Search in Google Scholar

[222] J. A. Rard, S. L. Clegg, D. A. Palmer. J Solution Chem37, 1625 (2008). Search in Google Scholar

[223] X. Lu, L. Zhang, Y. Wang, J. Shi, G. Maurer. Ind. Eng. Chem. Res.35, 1777 (1996). Search in Google Scholar

[224] A. V. García, K. Thomsen, E. H. Stenby. Geothermics34, 61 (2005). Search in Google Scholar

[225] A. V. García, K. Thomsen, E. H. Stenby. Geothermics35, 239 (2006). Search in Google Scholar

[226] M. C. Iliuta, K. Thomsen, P. Rasmussen. AIChE J48, 2664 (2002). Search in Google Scholar

[227] S. K. Bhattacharia, C.-C. Chen. Fluid Phase Equilibria387, 169 (2015). Search in Google Scholar

[228] G. Wollmann. Crystallization fields of polyhalite and its heavy metal analogues: Dissertation 2009. Search in Google Scholar

[229] C. M. Pina. Geochim. Cosmochim. Acta73, 7034 (2009). Search in Google Scholar

Received: 2015-6-24
Accepted: 2015-10-29
Published Online: 2015-11-28
Published in Print: 2015-12-1

©2015 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. For more information, please visit: http://creativecommons.org/licenses/by-nc-nd/4.0/