Phase composition and phase equilibrium diagrams as the Evidence of the Colloidal State of melts

. One of the most extensively studied silicate systems with complete miscibility in the solid and liquid state – albite (Ab)-anorthite (An) system – has been analyzed in detail. It has been established that the commonly accepted system and interpretation rules for these diagrams do not match their graphic representation. Calculations have proved the colloidal state of the “solid” phase on the solidus. Actual data support the colloidal (liquid) state of the solidus phase below the solidus and eutectic point. Crystallization in multicomponent systems, at least in silicate melts, has been shown to be based on the sol coagulation mechanism. Thus, silicate solid phases, even those of fixed composition, have no particular melting point. They consolidate and melt within a temperature band. The bandwidth is subject to the system composition that predetermines the micelle structure and directly affects coagulation and peptization processes.


Introduction
One of the main questions of modern sciences dealing with the formation and evolution of the planet Earth is ingress to its surface of various chemical elements as silicate melts and volcanic activity products that form volcanic rock solids and bodies. Melts cannot be studied directly due to the energy of volcanism processes and high temperature of effusive liquids. Obtaining actual material to study the conditions of generation and evolution of melts at their origin sites that occur at the depths inaccessible to research is even a bigger challenge. The only source of actual data on the conditions of formation and evolution trends of silicate melts in subsurface conditions is experiments with melting and crystallizing various silicate systems in a broad temperature and pressure range.
In experimental petrology, N.L. Bowen may be recognized as the initiator of experiments and, in fact, creator of a new schoolexperimental petrology [1][2][3][4][5]. The second half of the 20th century saw publication of a vast number of experimental data and phase diagrams that enabled elaboration of numerous generic models of crystallization of minerals and evolution of silicate melts in the Earth crust and upper mantle that covers the depths from the first ones to several hundred kilometers, in particular [6][7][8]. Primary experimental research data, phase diagrams constructed and interpretation rules elaborated for them grew into axiomatic statements and made their way to all petrology textbooks, in particular [14][15].
The entire tremendous scope of experimental data obtained is used as basic parameters to interpret the course of evolution of, in the first place, crystallization systems, and their thermodynamic parameter analysis. This ignores a number of fundamentally important factors. First of all: 1. Diagrams are designed or data is acquired experimentally based on, accordingly, equilibrium thermodynamics mathematical tools or experiments conducted in equilibrium conditions, i.e. constant values of evolution factors. No equilibrium processes may occur in cooling (crystallizing) natural magmatic and man-made systems. 2. Silicate system crystallization and melting experiments normally use test portions of substances with as simplified chemical composition as possible (so-called model compounds), whereas calculations and conclusions are made without regard to the structural condition of coexisting phases.
3. There is no proof that the solidus phase is in the solid state at the solidus with an experiment temperature.
All this gives rise to doubt not only as to the possibility to interpolate data acquired to natural systems but also as to the methodological framework of silicate system phase state diagram interpretation. This may be shown by the example of one of the most extensively studied diagramsplagioclase fusion diagram in the albite-anorthite (Ab-An) system.

Methodological Framework
Let us consider the classical experiment and diagram data interpretation method. Plagioclases make up an isomorphous series in the albite (Ab) (chemical formula -NaAlSi3O8)anorthite (An) (chemical formula -CaAl2Si2O8) system. Plagioclase is a system with complete miscibility in the solid and liquid states of isomorphous series extremes. Plagioclase composition may be rendered in Ab or An molecular percent, but the numbering matching anorthite molecule weight percent is commonly used [9]. Difference between plagioclase composition values in molecular and weight percent may not exceed a maximum of 6.1% even between isomorphous series extremes. Further on, we will discuss the phase compositions, in which this difference does not exceed 0.5-0.6%. This is why the content of albite and anorthite molecules in the text is given in molecular percent based on the figure 1 diagram for convenience and better visualization of calculations. Plagioclases are classified as framework alumosilicates, the 3D crystal structure in which is the result of polymerization of the radicals [SiO4]-4 and [AlO4]-5 that are referred to as "tetrahedrons" in special literature [10]. Sodium and calcium atoms are positioned in a free space between aluminosilicate tetrahedrons and are coordinated solely by oxygen atoms, just like aluminum and silicium.
Chemically, plagioclases are cross-linked (interlaced) polymers with mostly anionic type of 3D generation structure of isomorphous series minerals in the albiteanorthite system.
Minor difference in terms "framework silicate" (geology) and "cross-linked polymer" (chemistry) is major when analyzing thermodynamic parameters of plagioclase crystallization/melting [11][12]. The geological classificatory term may ignore a medium dispersion degree as far as mineral crystal size is concerned. So, thermodynamic characteristics are calculated or observed per mol of substance, i.e. for the plagioclase chemical formula ignoring structural condition and crystal surface energy. In terms of polymer structure, each crystal is a macromolecule; so, molecules of various sizes have different crystallization/melting thermodynamic parameters. It should be remembered when analyzing the evolution of natural silicate systems that often contain several generations of silicate minerals that vary in size.
Modern petrological studies of silicate magma origin, melting and crystallization in subsurface conditions may only be based on the thermodynamic calculations, baseline parameters for which are obtained from experimental works, for example [11][12][13]. As an example, let us consider the fusion diagram of a two-component system with complete miscibility in the solid and liquid statesplagioclasesthat has made it to all basic petrology textbooks ( fig. 1). The figure and diagram interpretation are based on literary sources [14][15].
Let us remind you the experiment and diagram construction method. Silicate glass that matches stoichiometric coefficients of a term of the Ab -An isomorphous series in terms of its chemical composition is melted at a temperature exceeding the liquidus temperature.  [14]).
Next, the temperature goes down and the melt is kept in this temperature section for long. It is said to be needed for the system to reach the solid-liquid equilibrium. Once the experiment in this temperature section is over, the melt is tempered. Microcrystal composition of the solidus phase is determined. The liquidus point is recorded based on the experiment, the products of which revealed the solidus phase for the first time ( fig. 1, point 2L). For experiments of isothermal sections Тх at Т2>Тх>Т4, the liquidus point is located by the lever rule ( fig. 1, points 3L, 3, 3S). Original melt composition in this temperature range is identical to that of point 1, i.e. the melt of this composition is simply cooled down to the required subliquidus area temperature and the course of the experiment is equal to that for Т2.
When the temperature goes down and An40 melt reaches temperature Т2, its crystallization starts at point 2L. ~An40 melt and scarce plagioclase ~An82 microcrystals are located at this point. Crystallization of the melt set by point 1 will be over at Т4, in which the solidus phase is represented by An40. Crystal phase composition change is recorded by solidus 2S(~An82)→4S(An40) and that of silicate meltby liquidus 2L(~An40)→4L(An7) [14].
All study materials underline expressly that the crystal phase of point 4S(An40) melts in reverse order.
Let us analyze the diagram under study irrespective of any hypotheses, theories, and opinions based on the rules and requirements elaborated for diagrams.

Results
Let us analyze the course of crystallization of the Ab -An system ( fig. 1). An40 melt at point 4S only crystallizes into the solid phase of the corresponding composition. All other stages result in a calcium-rich mineral, up to ~An82. With a uniform temperature decrease, the average composition of the solidus phase will match ~An61. Thus, commonly accepted diagram interpretation rules argue that if the temperature decreases to the solidus, the (Na0.6,Ca0.4)Al1.4Si2.6O8 melt will fully and entirely convert into the solid phase with the average composition of (Na0.39,Ca0.61)Al1.61Si2.39O8, which is in absolute conflict with the mass conservation law. At the same time, even an approximate estimate of calcium distribution between the liquidus and solidus phases during crystallization proves unambiguously that at least An40 solidus phase with the composition of (Na0.6,Ca0.4)Al1.4Si2.6O8 will crystallize from the melt without a single calcium atom. Thus, the diagram's graphic form and its interpretation rules are generally in absolute conflict with inorganic chemistry laws.
Fusion analysis of An40 homogeneous (azonal) crystal at point 4S also reveals a number of inconsistencies between the diagram and fundamental chemical and physical laws. The most obvious and unambiguous ones in the context hereof are as follows: 1. No isomorphous series term, other than pure anorthites (An100, CaAl2Si2O8) and albites (Ab100, NaAlSi3O8) has a fusing point but melts in a temperature range. For example, An40 ( fig. 1) melts in the Т4-Т2 temperature range, which is about 200 о C. The recorded fact is in absolute conflict with both experimental plagioclase melting data and fundamental laws of physics.
2. In the Т4-Т2 temperature range in any isothermal section, the composition of the melting plagioclase does not match chemistry of the coexisting liquid phase. This is typical incongruent melting. Thus, solidus is a peritectic line. Overall, the system may not be classified as "condensed systems with complete miscibility in the solid and liquid states" and the diagram type may not be designated as Roseboom type I [15].
3. According to experimental observations [14][15], isothermal section Т2 will feature the equilibrium of An40 liquid and ~An82 solidus phase crystals (in the original text [14] -An76). However, according to common diagram analysis rules, no azonal crystals or any crystals at all may be in equilibrium with a melt at the liquidus. Solid phase mass cannot increase in equilibrium, i.e. crystals cannot grow. Besides, only a surface crystal layer may be in equilibrium with liquid. Their inner parts have to be formed in non-equilibrium conditions and, according to the diagram, crystallization of its central part has to start at a higher temperaturein the subliquidus area.
At the same time, each and every experimental diagram study stresses the azonal character of the solidus phase. Its azonal structure with homogenous chemistry may also occur in two instances: 1. Average composition of microcrystals is determined using instrumental analysis methods.
2. The composition of microcrystals equalizes as a result of thermal diffusion during system's prolonged subjection to isothermal conditions. Based on peculiarities of numerous and various analytical methods that experimentalists use to determine solidus phase chemistry and analyze the kinetics of diffusion processes and energy balance of coexistence of solid and liquid phases in isothermal and isobaric conditions, it is safe to say that none of the above instances is implemented experimentally. For detailed analysis of these processes, see [16].

Discussions
It is clear from the above results of analysis not confirmed by existing ideas that only one fact is indisputable in the current database. It is stated by experimentalists: in isothermal and isobaric conditions of experiments, liquid and solid (?) phases homogenous in terms of chemistry are in equilibrium at the solidus.
Points that mark off the solidus are located by the appearance of the first microcrystal extractions in a homogeneous system following many hours of melt subjection to isothermal and isobaric conditions. The presence of solidus phase micro extractions is recorded using optical or X-ray microanalysis methods. However, in normal conditions (Т~19-21 о C, Р=1 atm), there are two solid phases present in tempered preparationscontinuous and dispersed. Both phases match a certain mineral by their chemical composition, for example, An40 and An82 ( fig. 1). There is no proof of the solid crystal state of the dispersed phase (An82) at the experiment temperature. This means that the experimentalists were only guided by the phase chemical composition when they decided that, at the experiment temperature, one of themcontinuous phasewas in the liquid state and the dispersed onein the solid crystal state and its appearance recorded both the crystallizing point and the solidus. Both phases are in equilibrium, which, according to the experimentalists, is evidenced by the azonal nature of solidus phase crystals that could not crystallize in equilibrium conditions in principle.
First, the left part of the equation ignores liquid's structural conditionits components are in elementary form. Evidently, the melt contains some primary complexes, atom structure or combination of which is close to that of plagioclases. Paradoxically, the less is the difference between the chemical composition of solid and liquid phases, the less probable is their state of equilibrium (stoichiometric coefficients go up). However, with total chemical composition correspondence, equation's stoichiometry becomes normal.
Second, in the right part of the equation, formula (Na18,Ca82)Al182Si218O800 does not represent a molecule of the substance. Instead, it represents the total number of atoms and their proportions on the surface of one particle of the solidus phase, i.e. the ones available for exchange with the liquid. This assumption helps estimate the surface area per An82 plagioclase particle, which is in equilibrium with An40 liquid. Subject to very close packing of atoms in the crystal structure, the surface area of a particle will be equal to the sum of areas occupied by atoms and space between atoms. Same-radius atoms occupy 78.5% of the area and the space between them accounts for 21.5% (atom positions like in NaCl crystal structure). Atomic radii (Å): Na -1.89, Ca -1.97, Al -1.43, Si -1.34 [16]. Intermolecular radius or van der Waals oxygen radius -1.40Å [10]. Let us calculate the atom area on the surface of one particle of {(Na18,Ca82)Al182Si218O800}s solidus phase The atom space area is 2334.164012 Å 2 . The total surface area of a particle of the solidus phase is 10856.5768 Å 2 . Let us calculate the radius of a ball-shaped particle with the same surface area. The ball surface area is Sb=πD 2 , thus D=√ / =√10856.5768/3.14 ~ 58.8006 Å or about 5.88 nm. Despite a number of serious assumptions that enabled these calculations, it is obvious that even if the particle diameter is increased by sixteen times (256-fold increase in the surface area of a particle) or decreased by five times (25-fold decrease in the surface area of a particle), the solidus phase particle will remain in the dispersion range from 1 to 100 nm. Thus, the solidus phase, which is in equilibrium with a silicate melt, may in no case be in the solid state. Its dispersion degree in the broad range of particle radii matches the colloidal state (sol), i.e. the solidus phase has to be either in the liquid or plastic (bordering liquid) state. Based on the analysis and calculations made it is safe to say that the solidus is marked off by the appearance of the liquid phase represented by the dispersed phase coacervate instead of the solid phase.
The crystallizing point of optically transparent minerals of a particular composition, which comes closest to the actual one, is obtained in the course of fluid inclusion studies that determine the homogenizing temperature of primary inclusions of various composition, for example [18][19][20]. According to thermometric data, crystallization of the overwhelming majority of rock-forming minerals [20][21][22] occurs at a temperature much lower than the fusing point given for these minerals in reference literature [17], the values of which are used for calculations, charting or are obtained from experimental data. A similar regularity has been recorded for the titanium-aluminum system [23].
A fragment of the plagioclase fusion diagram from figure 2 comprises authors' data on homogenization of inclusions in plagioclase porphyritic insets from the basic rock of the Siberian platform [24]. There is an evident temperature gap between the diagram solidus and thermobaric geochemistry solidus (∆Т). This gap becomes even wider when a solid solution is enriched with the phase that has a lower fusing point. fig. 1 with the thermobaric geochemistry solidus.

Fig. 2. Fragment of diagram from
The same regularity is observed in all minerals that are solid solutions with varying degrees of ideality [17,20]. Absolute maximum of the gap between crystallizing/fusing point and inclusion homogenizing temperature was recorded for hydrothermal quartz -Тfs.=1,413±5 о C, Тhm.~169-400 о C [17,20]. Absurdly, crystallizing/fusing point is determined experimentally on lumps of practically ideal rhinestone (quartz) crystals that naturally crystallize at about 200 о C.
It should be remembered in this regard that in physical and chemical petrology, diagrams of phase (mineral) composition versus temperature are built by calculating the molar free energy potential of the isothermal and isobaric system, while diagrams are the graphic representation of this potential [14]. The fact that the crystallizing point equals the fusing point is also practically assured.
Analysis of the plagioclase fusion diagram ( fig. 1) based on the data interpretation regulations, rules and requirements elaborated for this type of diagrams has revealed a number of inconsistencies between the diagram's graphic form, its interpretation rules and fundamental chemical and physical laws. Let us single out the most fundamental inconsistencies: the liquidus may not have the trajectory shown on the diagram; chemical composition of the solid phase may not form depending on the solidus position; the system may not reach the equilibrium between solid and liquid phases in isothermal and isobaric conditions; solidus phase has to be zoned; solidus does not record the appearance of the solid crystal phase. Thus, only results of numerous experiments remain incontestablein isothermal and isobaric conditions, there are two phases coexisting in the system that are homogenous at the level of instrumental analysis methods. One of these phases is dispersed and the other one is continuous.
Nearly all the recorded inconsistencies, other than the liquidus position, may be explained if the An-Ab system melt is viewed as a colloid with the sol structure. In this respect, "crystallization" or silicate melt evolution occurs as follows. With the "liquidus" temperature, the system is structurally heterogeneous, which is expressed in the appearance of the dispersed phase, the composition and structure of which are different from those of the continuous phase. Heterogeneity of silicate melts is confirmed by mathematic simulation [25]. Considering the diameter of dispersed phase particles (about 10 nm), they are micelle nuclei that have an adsorption and, perhaps, a diffuse layer. The availability and thickness of the diffuse layer completely depend, in the first instance, on the magma composition and presence of the components that are outside of the silicate melt structure, such as water, hydrogen, nitrogen, helium, chlorine, fluorine, sulfur, phosphorus, their ions, and simplest compounds.
Chemically, the dispersed phase is also a high-molecular substance dissolved in the parent phase and subjected to coacervation. The dispersed phase forms liquid drops rich in the dissolved matter. Each isothermal and isobaric section (condition of a specific experiment) matches an azonal coacervate of the particular composition. Accordingly, it is safe to say that the "solidus" line records the composition of the coacervate formed at this temperature in the liquid form, but not structured as a colloid. Temperature decrease will cause sol's gradual coagulation from the center of the drop towards its edges. Subject to coagulation dynamics, micelle structure and diffusion of elements in the coacervate's liquid phase, both zoned and azonal minerals may eventually develop at the thermobaric geochemistry solidus. However, all the minerals that crystallize following the sol's coagulation mechanism must, firstly, have a fusing "range" instead of the fusing "point" on fusion diagrams and, secondly, consolidate into a completely solid phase at the thermobaric geochemistry solidus, i.e. at the temperature below the eutectic point. Presence of the fusing/crystallization range of minerals of constant composition is confirmed by data of all known diagrams of phase composition and phase equilibrium versus temperature [14]. For example, on the diopside-anorthite diagram, minerals have crystallization range of, accordingly, 1,390-1,274 о С and 1,553-1,274 о С; on the Na2SiO3 -SiO2 diagram: christobalite -1,713-1,470 о С, tridymite -1,470-867 о С, quartz -867-789 о С; on the leucitesilica diagram: christobalite -1,713-1,470 о С, tridymite -1,470-990 о С, leucite -1,685-1,150 о С, orthoclase -1,150-990 о С. In the last diagram, orthoclase and tridymite crystallize below the eutectic point (990 о С) to about 870 о С, and below itorthoclase and quartz. These subeutectic or, rather, subsolidus changes in phase composition are also seen in anorthite-albite, plagioclase-alkali feldspars and nepheline-kalsilite systems [15]. Besides, systems with recorded long-term, most probably liquid evolution in the subsolidus area, were assigned their own types -IV and V according to Roseboom [14]. Today, there is the proof that no diffusion may occur in the crystal lattice of silicate minerals [16] with prevailing covalent binding and, accordingly, no subsolidus structures of breakdown of solid solutions may develop at the solidus and, the more so, in the subsolidus area in natural systems.
Thus, "solidus" lines on any diagram of the phase composition and phase equilibrium versus temperature record the temperature of expression of liquid coacervate of particular composition and there are no lines and points that match crystal phases. Thus, the evolution of silicate melts, the formation of the mineral composition of originating rocks and rock structure are the results of system development in the liquid state based on the coacervation mechanism.
The proposed hypothesis of the colloid state of silicate systems over virtually the entire temperature range of their evolution enables somewhat different interpretation of diagrams of the phase composition versus temperature for condensed systems [14]. Let us take a look at some innovations: -Liquidus curve ( fig. 1) starts at point 2 L and ends at point 4 S . Its linearity versus 2 L -3 -4 S (position on the diagram) depends on the molar quantity of the substance isolated in the coacervate, composition of which is recorded by the solidus.
-Difference in the solidus exponential curve on fusion diagrams of systems with solid phases of constant composition and Roseboom diagrams of types I-V is due to the fact that, in the former case, it records isolation of the continuous phase coacervate and, in the latter instanceisolation of the dispersed phase coacervate.
-Peritectic points and lines on diagrams record inversion of the colloid's structural condition when the continuous and disperse phases change places. In natural systems, the inversion zone free of any silicate eruptive rocks is within the range of magma bridging polymerization values ~ 35.9-47.2% [28].

Conclusion
To sum up the results of the analysis conducted, one has to mention incorrectness of commonly accepted interpretation rules of phase composition and phase equilibrium diagrams in the first place. They were elaborated almost hundred years ago to solve, most likely, some private theoretical equilibrium thermodynamics problems that have nothing to do with actual processes. Most of the identified fundamental inconsistencies between diagram interpretation rules, their graphic representation, physical and chemical laws are removed if a silicate melt is viewed as a colloid system (sol). Anyhow, the colloid degree of dispersion for any isothermal section (provided that it has "solidus" and "liquidus" phases) is quite easy to calculate using the equilibrium equation for these phases. This degree of dispersion, corresponding structural condition, and properties of the system bring about a number of quite unexpected conclusions. Let us consider only some of them.
First. "Solidus" does not record the appearance of the solid crystal phase; instead, it records the source region of colloid's liquid dispersed phase drops that develop following the coacervation mechanism.
Second. In the "subsolidus" area of diagrams of Roseboom types IV-V, the field of breakdown of solid solutions transforms into the colloid's liquid evolution area following the coacervation mechanism.
Third. Commonly accepted terms "phase crystallizing point" and "phase fusing point" are replaced with, correspondingly, "coagulation temperature range" and "peptization temperature range".
Fourth. The coagulation and peptization temperature range and its energy state depend on the presence in the system of the components, chemical elements or their ions capable of forming the diffuse layer of micelle structured nuclei.
Fifth. All natural and man-made system evolution calculations based on analysis or data obtained from diagrams of the phase composition and phase equilibrium versus extensive and intensive parameters for condensed systems must be adjusted.
The evidence of going through the colloidal state may always be found for any systems that have gone through the colloidal stage of dispersion in the course of evolution, in crystals or segregations of specific solid phases. Fresh chips of these phases have to reveal submicroscopic structures of the "soapsuds surface" type where each "bubble" is either an individual micelle or a coacervate drop.

Recommendations
The colloidal evolution model proposed herein may be primarily targeted at the specialists dealing with the Earth's evolution, formation, and crystallization of silicate melts and development of ore deposits. At the same time, considering that all conclusions of the work are based on analysis of standard diagrams, it may be of interest to any researcher who deals with condensed systems. Special attention of the scientific community should be brought to the possibility to use the colloidal system as the basis for the development of the new energysaving technology of metal peptization (melting) and coagulation (crystallization) to derive ultrapure products with preset structural properties.