Heat capacity and entropy of rutile (TiO<Subscript>2</Subscript>) and nepheline (NaAlSiO<Subscript>4</Subscript>)

 From heat capacities measured adiabatically at low temperatures, the standard entropies at 298.15 K of synthetic rutile (TiO₂) and nepheline (NaAlSiO₄) have been determined to be 50.0 ± 0.1 and 122.8 ± 0.3 J mol⁻¹ K, respectively. These values agree with previous measurements and in particular confirm the higher entropy of nepheline with respect to that of the less dense NaAlSiO₄ polymorph carnegieite. Received: 23 July 2001 / Accepted: 12 October 2001     

Zinclipscombite,ZnFe<Stack><Subscript>2</Subscript><Superscript>3+</Superscript></Stack>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>2</Subscript>, a new mineral species

Zinclipscombite, a new mineral species, has been found together with apophyllite, quartz, barite, jarosite, plumbojarosite, turquoise, and calcite at the Silver Coin mine, Edna Mountains, Valmy, Humboldt County, Nevada, United States. The new mineral forms spheroidal, fibrous segregations; the thickness of the fibers, which extend along the c axis, reaches 20 μm, and the diameter of spherulites is up to 2.5 mm. The color is dark green to brown with a light green to beige streak and a vitreous luster. The mineral is translucent. The Mohs hardness is 5. Zinclipscombite is brittle; cleavage is not observed; fracture is uneven. The density is 3.65(4) g/cm³ measured by hydrostatic weighing and 3.727 g/cm³ calculated from X-ray powder data. The frequencies of absorption bands in the infrared spectrum of zinclipscombite are (cm^?1; the frequencies of the strongest bands are underlined; sh, shoulder; w, weak band) 3535, 3330sh, 3260, 1625w, 1530w, 1068, 1047, 1022, 970sh, 768w, 684w, 609, 502, and 460. The Mössbauer spectrum of zinclipscombite contains only a doublet corresponding to Fe³⁺ with sixfold coordination and a quadrupole splitting of 0.562 mm/s; Fe²⁺ is absent. The mineral is optically uniaxial and positive, ω = 1.755(5), ? = 1.795(5). Zinclipscombite is pleochroic, from bright green to blue-green on X and light greenish brown on Z (X > Z). Chemical composition (electron microprobe, average of five point analyses, wt %): CaO 0.30, ZnO 15.90, Al₂O₃ 4.77, Fe₂O₃ 35.14, P₂O₅ 33.86, As₂O₅ 4.05, H₂O (determined by the Penfield method) 4.94, total 98.96. The empirical formula calculated on the basis of (PO₄,AsO₄)₂ is (Zn_0.76Ca_0.02)_Σ0.78(Fe _1.72 ³⁺ Al_0.36)_Σ2.08[(PO₄)_1.86(AsO₄)_0.14]_Σ2.00(OH)_{1. 80} · 0.17H₂O. The simplified formula is ZnFe ₂ ³⁺ (PO₄)₂(OH)₂. Zinclipscombite is tetragonal, space group P4₃2₁2 or P4₁2₁2; a = 7.242(2) Å, c = 13.125(5) Å, V = 688.4(5) ų, Z = 4. The strongest reflections in the X-ray powder diffraction pattern (d, (I, %) ((hkl)) are 4.79(80)(111), 3.32(100)(113), 3.21(60)(210), 2.602(45)(213), 2.299(40)(214), 2.049(40)(106), 1.663(45)(226), 1.605(50)(421, 108). Zinclipscombite is an analogue of lipscombite, Fe²⁺Fe ₂ ³⁺ (PO₄)₂(OH)₂ (tetragonal), with Zn instead of Fe²⁺. The mineral is named for its chemical composition, the Zn-dominant analogue of lipscombite. The type material of zinclipscombite is deposited in the Mineralogical Collection of the Technische Universität Bergakademie Freiberg, Germany.     

Peierls dislocation modelling in perovskite (CaTiO<Subscript>3</Subscript>): comparison with tausonite (SrTiO<Subscript>3</Subscript>) and MgSiO<Subscript>3</Subscript> perovskite

We present here a numerical modelling study of dislocations in perovskite CaTiO₃. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSF are determined from first-principles calculations using the VASP code. The dislocation properties such as collinear, planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [010](100), [010](001), [001](100), [001](010), and All dislocations exhibit lattice friction, but glide appears to be easier for [100](010) and [010](100). [001](010) and [001](100) exhibit collinear dissociation. Comparing Peierls stresses among tausonite (SrTiO₃), perovskite (CaTiO₃) and MgSiO₃ perovskite demonstrates the strong influence of orthorhombic distortions on lattice friction. However, and despite some quantitative differences, CaTiO₃ appears to be a satisfactory analogue material for MgSiO₃ perovskite as far as dislocation glide is concerned.     

Thermodynamic properties,low-temperature heat-capacity anomalies,and single-crystal X-ray refinement of hydronium jarosite, (H<Subscript>3</Subscript>O)Fe<Subscript>3</Subscript>(SO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>6</Subscript>

Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)–SO₄ solutions. Single-crystal XRD refinement with R₁=0.0232 for the unique observed reflections (|F_o| > 4_F) and wR₂=0.0451 for all data gave a=7.3559(8) Å, c=17.019(3) Å, V^o=160.11(4) cm³, and fractional positions for all atoms except the H in the H₃O groups. The chemical composition of this sample is described by the formula (H₃O)_0.91Fe_2.91(SO₄)₂[(OH)_5.64(H₂O)_0.18]. The enthalpy of formation (H^o_f) is –3694.5 ± 4.6 kJ mol^–1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, -FeOOH, MgO, H₂O, and -MgSO₄. The entropy at standard temperature and pressure (S^o) is 438.9±0.7 J mol^–1 K^–1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (C_p) data between 273 and 400 K were fitted to a Maier-Kelley polynomial C_p(T in K)=280.6 + 0.6149T–3199700T^–2. The Gibbs free energy of formation is –3162.2 ± 4.6 kJ mol^–1. Speciation and activity calculations for Fe(III)–SO₄ solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the C_p data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in C_p, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H₃O)Fe₃(SO₄)₂(OH)₆ was estimated: G^o_f= –3226.4 ± 4.6 kJ mol^–1, H^o_f=–3770.2 ± 4.6 kJ mol^–1, S^o=448.2 ± 0.7 J mol^–1 K^–1, C_p (T in K)=287.2 + 0.6281T–3286000T^–2 (between 273 and 400 K).     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

The crystal structure of alumoklyuchevskite,K<Subscript>3</Subscript>Cu<Subscript>3</Subscript>AlO<Subscript>2</Subscript>(SO<Subscript>4</Subscript>)<Subscript>4</Subscript>

The crystal structure of the unstable mineral alumoklyuchevskite K₃Cu₃AlO₂(SO₄)₄ [monoclinic, I2, a = 18.772(7), b = 4.967(2), c = 18.468(7) Å, β = 101.66(1)°, V = 1686(1) Å] was refined to R ₁ = 0.131 for 2450 unique reflections with F ≥ 4σF _hkl. The structure is based on oxocentered tetrahedrons (OAlCu ₃ ⁷⁺ ) linked into chains via edges. Each chain is surrounded by SO₄ tetrahedrons forming a structural complex. Each complex is elongated along the b axis. This type of crystal structure was also found in other fumarole minerals of the Great Tolbachik Fissure Eruption (GTFE, Kamchatka Peninsula, Russia, 1975–1976), klyuchevskite, K₃Cu₃Fe³⁺O₂(SO₄)₄; and piypite, K₂Cu₂O(SO₄)₂.     

Shock-induced formation of kyanite (Al<Subscript>2</Subscript>SiO<Subscript>5</Subscript>) from sillimanite within a dense metamorphic rock from the Ries crater (Germany)

A dense (~3.34 g cm^–3) garnet–sillimanite-rich metamorphic rock from the suevite breccia of the Ries impact crater was studied by scanning-electron microscopy and Raman microprobe spectroscopy. In the strongly shocked rock clast kyanite was formed from sillimanite under momentary high pressures of natural shock waves. Kyanite aggregates were found as thin (~0.3–2.0 m) seams along grain boundaries between, and fractures within, sillimanite grains. Within these seams kyanite c-axes are oriented perpendicular to original grain boundaries and fractures. In addition, larger (up to 10 m) isolated kyanite grains were rarely found within host sillimanite. Filamentary kyanite aggregates and isolated crystals typically show shrinkage cracks due to volume decrease (~10%). Locally, broad interstices between sillimanite crystals are filled with aluminosilicate glass containing a high volume fraction of sub-micrometer-sized euhedral crystals. The silica-rich glass suggests incongruent melting of sillimanite at local post-shock temperatures significantly higher than 1,300°C. The edges of adjacent sillimanite grains are thermally and chemically altered. The local generation of temperature spikes is attributed to strong shock wave interactions due to very high shock impedance contrasts.     

Thermal expansion of new arsenate minerals,bradaczekite, NaCu<Subscript>4</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>, and urusovite,Cu(AsAlO<Subscript>5</Subscript>)

Thermal behavior of two new exhalation copper-bearing minerals, bradaczekite and urusovite, from the Great Tolbachik Fissure Eruption (1975–1976, Kamchatka Peninsula, Russia) has been studied by X-ray thermal analysis within the range 20–700°C in air. The following major values of the thermal expansion tensor have been calculated for urusovite: α₁₁ = 10, α₂₂ = α_b = 7, α₃₃ = 4, α_V = 21 × 10⁻⁶°C⁻¹, μ = c∧α₃₃ = 49° and bradaczekite: α_11aver = 23, α₂₂ = 8, α_33aver = 6 × 10⁻⁶°C⁻¹, μ(c∧α₃₃) = 73°. The sharp anisotropy of thermal deformations of these minerals, absences of phase transitions, and stability of the minerals in the selected temperature range corresponding to conditions of their formation and alteration during the posteruption period of the volcanic activity are established.     

In situ high-temperature X-ray and neutron powder diffraction study of cation partitioning in synthetic Mg(Fe<Subscript>0.5</Subscript>Al<Subscript>0.5</Subscript>)<Subscript>2</Subscript>O<Subscript>4</Subscript> spinel

The intra-crystalline cation partitioning over T- and M-sites in a synthetic Mg(Fe,Al)₂O₄ spinel sample has been determined as a function of temperature by Rietveld structure refinements from powder diffraction data, combining in situ high-temperature neutron powder diffraction (NPD; POLARIS diffractometer, at ISIS, Rutherford Appleton Laboratory, UK), to determine the Mg and Al occupancy factors, with in situ high-temperature X-ray powder diffraction, to fix the Fe³⁺ distribution. The results obtained agree with a two-stage reaction, in which an initial exchange between Fe³⁺ and Mg, the former leaving and the latter entering tetrahedral sites, is successively followed by a rearrangement involving also Al. The measured cation distribution has then been compared and discussed with that calculated by the Maximum Configuration Entropy principle, for which only NPD patterns have been used. The cation partitioning has finally been interpreted in the light of the configuration model of O’Neill and Navrotsky.     

Temperature-jump induced cation exchange kinetics in (Co<Subscript>0.1</Subscript>Mg<Subscript>0.9</Subscript>)<Subscript>2</Subscript>SiO<Subscript>4</Subscript> olivine: an in situ optical spectroscopic study

In the olivine crystal structure, cations are distributed over two inequivalent octahedral sites, M1 and M2. Kinetics of cation exchange between the two octahedral sites in (Co_0.1Mg_0.9)₂SiO₄ single crystal have been studied in the temperature range from 600 to 800°C by monitoring the time evolution of the absorbance of Co²⁺ ions in M1 or M2 sites using optical spectroscopy after rapid temperature jumps. It was found from such temperature-jump induced relaxation experiments that with increasing temperature the absorbance of Co²⁺ ions in the M1 site decreases while that in the M2 site increases. This indicates a tendency of Co²⁺ cations to populate the M2 site with increasing temperatures and vice versa. The experimental relaxation data can be modeled using a triple exponential equation based on theoretical analysis. Activation energies of 221 ± 4 and 213 ± 10 kJ/mol were derived from relaxation experiments on the M2 site and M1 site, respectively, for the cation exchange processes in (Co_0.1Mg_0.9)₂SiO₄ olivine. Implications for cation diffusion at low temperatures are discussed.     

Elastic behavior of vanadinite,Pb<Subscript>10</Subscript>(VO<Subscript>4</Subscript>)<Subscript>6</Subscript>Cl<Subscript>2</Subscript>, a microporous non-zeolitic mineral

The high-pressure behavior of a vanadinite (Pb₁₀(VO₄)₆Cl₂, a = b = 10.3254(5), c = 7.3450(4) Å, space group P6₃/m), a natural microporous mineral, has been investigated using in-situ HP-synchrotron X-ray powder diffraction up to 7.67 GPa with a diamond anvil cell under hydrostatic conditions. No phase transition has been observed within the pressure range investigated. Axial and volume isothermal Equations of State (EoS) of vanadinite were determined. Fitting the P–V data with a third-order Birch-Murnaghan (BM) EoS, using the data weighted by the uncertainties in P and V, we obtained: V ₀ = 681(1) Å³, K ₀ = 41(5) GPa, and K′ = 12.5(2.5). The evolution of the lattice constants with P shows a strong anisotropic compression pattern. The axial bulk moduli were calculated with a third-order “linearized” BM-EoS. The EoS parameters are: a ₀ = 10.3302(2) Å, K ₀(a) = 35(2) GPa and K′(a) = 10(1) for the a-axis; c ₀ = 7.3520(3) Å, K ₀(c) = 98(4) GPa, and K′(c) = 9(2) for the c-axis (K ₀(a):K ₀(c) = 1:2.80). Axial and volume Eulerian-finite strain (fe) at different normalized stress (Fe) were calculated. The weighted linear regression through the data points yields the following intercept values: Fe _a (0) = 35(2) GPa for the a-axis, Fe _c (0) = 98(4) GPa for the c-axis and Fe _V (0) = 45(2) GPa for the unit-cell volume. The slope of the regression lines gives rise to K′ values of 10(1) for the a-axis, 9(2) for the c-axis and 11(1) for the unit cell-volume. A comparison between the HP-elastic response of vanadinite and the iso-structural apatite is carried out. The possible reasons of the elastic anisotropy are discussed.     

Atomistic model of diopside-K-jadeite (CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>-KAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution

Atomistic model was proposed to describe the thermodynamics of mixing in the diopside-K-jadeite solid solution (CaMgSi₂O6-KAlSi₂O₆). The simulations were based on minimization of the lattice energies of 800 structures within a 2 × 2 × 4 supercell of C2/c diopside with the compositions between CaMgSi₂O₆ and KAlSi₂O₆ and with variable degrees of order/disorder in the arrangement of Ca/K cations in M2 site and Mg/Al in Ml site. The energy minimization was performed with the help of a force-field model. The results of the calculations were used to define a generalized Ising model, which included 37 pair interaction parameters. Isotherms of the enthalpy of mixing within the range of 273–2023 K were calculated with a Monte Carlo algorithm, while the Gibbs free energies of mixing were obtained by thermodynamic integration of the enthalpies of mixing. The calculated T-X diagram for the system CaMgSi₂O₆-KAlSi₂O₆ at temperatures below 1000 K shows several miscibility gaps, which are separated by intervals of stability of intermediate ordered compounds. At temperatures above 1000 K a homogeneous solid solution is formed. The standard thermodynamic properties of K-jadeite (KAlSi₂O₆) evaluated from quantum mechanical calculations were used to determine location of several mineral reactions with the participation of the diopside-K-jadeite solid solution. The results of the simulations suggest that the low content of KalSi₂O₆ in natural clinopyroxenes is not related to crystal chemical factors preventing isomorphism, but is determined by relatively high standard enthalpy of this end member.     

Crystal chemistry of selenates with mineral-like structures. III. Heteropolyhedral chains in the crystal structure of [Mg(H<Subscript>2</Subscript>O)<Subscript>4</Subscript>(SeO<Subscript>4</Subscript>)]<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)

The crystal structure of a new compound [Mg(H₂O)₄(SeO₄)]₂(H₂O) (monoclinic, P2 ₁/a, a = 7.2549(12), b = 20.059(5), c = 10.3934(17) Å, β = 101.989(13), V = 1479.5(5) ų) has been solved by direct methods and refined to R ₁ = 0.059 for 2577 observed reflections with |F _hkl | ≥ 4σ|F _hkl |. The structure consists of [Mg(H₂O)₄(SeO₄)]⁰ chains formed by alternating corner-sharing Mg octahedrons and (SeO₄)^2? tetrahedrons. O atoms of Mg octahedrons that are shared with selenate tetrahedrons are in a trans orientation. The heteropoly-hedral octahedral-tetrahedral chains are parallel to the c axis and undulate within the (010) plane. The adjacent chains are linked by hydrogen bonds involving H₂O molecules not bound with M²⁺ cations.     

Fahlore thermochemistry: Gaps inside the (Cu,Ag)<Subscript>10</Subscript>(Fe,Zn)<Subscript>2</Subscript>(Sb,As)<Subscript>4</Subscript>S<Subscript>13</Subscript> cube

Possible topologies of miscibility gaps in arsenian (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores are examined. These topologies are based on a thermodynamic model for fahlores whose calibration has been verified for (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ fahlores, and conform with experimental constraints on the incompatibility between As and Ag in (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores, and with experimental and natural constraints on the incompatibility between As and Zn and the nonideality of the As for Sb substitution in Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores. It is inferred that miscibility gaps in (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores have critical temperatures several °C below those established for their Sb counterparts (170 to 185°C). Depending on the structural role of Ag in arsenian fahlores, critical temperatures for (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlores may vary from comparable to those inferred for (Cu,Ag)₁₀(Fe,Zn)₂As₄S₁₃ fahlores, if the As for Sb substitution stabilizes Ag in tetrahedral metal sites, to temperatures approaching 370°C, if the As for Sb substitution results in an increase in the site preference of Ag for trigonal-planar metal sites. The latter topology is more likely based on comparison of calculated miscibility gaps with compositions of fahlores from nature exhibiting the greatest departure from the Cu₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ and (Cu,Ag)₁₀(Fe,Zn)₂Sb₄S₁₃ planes of the (Cu,Ag)₁₀(Fe,Zn)₂(Sb,As)₄S₁₃ fahlore cube.     

Low-temperature heat capacities of MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> and spinels of the MgCr<Subscript>2</Subscript>O<Subscript>4</Subscript>–MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> solid solution

We present results from low-temperature heat capacity measurements of spinels along the solid solution between MgAl₂O₄ and MgCr₂O₄. The data also include new low-temperature heat capacity measurements for MgAl₂O₄ spinel. Heat capacities were measured between 1.5 and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed for MgAl₂O₄ spinel; however, we observe a low-temperature heat capacity anomaly for Cr-bearing spinels at temperatures below 15 K. From our data we calculate standard entropies (298.15 K) for Mg(Cr,Al)₂O₄ spinels. We suggest a standard entropy for MgAl₂O₄ of 80.9 ± 0.6 J mol⁻¹ K⁻¹. For the solid solution between MgAl₂O₄ and MgCr₂O₄, we observe a linear increase of the standard entropies from 80.9 J mol⁻¹ K⁻¹ for MgAl₂O₄ to 118.3 J mol⁻¹ K⁻¹ for MgCr₂O₄.     

Structure and chemistry of (111) twin boundaries in MgAl<Subscript>2</Subscript>O<Subscript>4</Subscript> spinel crystals from Mogok

The atomic scale structure and chemistry of (111) twins in MgAl₂O₄ spinel crystals from the Pinpyit locality near Mogok (Myanmar, formerly Burma) were analysed using complementary methods of transmission electron microscopy (TEM). To obtain a three-dimensional information on the atomic structure, the twin boundaries were investigated in crystallographic projections and Using conventional electron diffraction and high-resolution TEM (HRTEM) analysis we have shown that (111) twins in spinel can be crystallographically described by 180° rotation of the oxygen sublattice normal to the twin composition plane. This operation generates a local hcp stacking in otherwise ccp lattice and maintains a regular sequence of kagome and mixed layers. In addition to rotation, no other translations are present in (111) twins in these spinel crystals. Chemical analysis of the twin boundary was performed by energy-dispersive X-ray spectroscopy (EDS) using a variable beam diameter (VBD) technique, which is perfectly suited for analysing chemical composition of twin boundaries on a sub-nm scale. The VBD/EDS measurements indicated that (111) twin boundary in spinel is Mg-deficient. Quantitative analyses of HRTEM (phase contrast) and HAADF-STEM (Z-contrast) images of (111) twin boundary have confirmed that Mg²⁺ ions are replaced with Be²⁺ ions in boundary tetrahedral sites. The Be-rich twin boundary structure is closely related to BeAl₂O₄ (chrysoberyl) and BeMg₃Al₈O₁₆ (taaffeite) group of intermediate polysomatic minerals. Based on these results, we conclude that the formation of (111) twins in spinel is a preparatory stage of polytype/polysome formation (taaffeite) and is a result of thermodynamically favourable formation of hcp stacking due to Be incorporation on the {111} planes of the spinel structure in the nucleation stage of crystal growth. The twin structure grows as long as the surrounding geochemical conditions allow its formation. The incorporation of Be induces a 2D-anisotropy and exaggerated growth of the crystal along the (111) twin boundary.     

Cocrystallization of isomorphic components in solutions and crystal zoning: An example of the (Ba,Pb)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> series

The phase equilibrium and growth of mixed (Ba,Pb)(NO₃)₂ crystals in aqueous solutions were investigated. The microcrystallization method was adapted to systems with isomorphic components, where crystal composition deviates from the thermodynamic equilibrium even at a low supercooling. The solid phase is characterized by continuous miscibility of the components within the analyzed ranges of temperature and solution composition. The diagram is characterized by substantial nonlinearity of the solubility isotherms and nonuniformity of the solid isocomposite location. Quasiequilibrium paths change their slope depending on solution enrichment in Ba(NO₃)₂ and depletion in Pb(NO₃)₂. The area of curvature of quasiequilibrium paths is coordinated with the area of the changing isotherm slope, i.e., the area of “remarkable” points, where the behavior of the system changes drastically. Examples of theoretical zoning of a crystal approximated to a sphere were calculated for paths at a temperature decreasing from 50 to 15°C. The content of the Ba component decreases toward the periphery with the consecutive overgrowing of zones. Each zone corresponds to one gram of (Ba,Pb)(NO₃)₂. Crystals grown from different initial solutions consist of different numbers of zones owing to the nonlinearity of solubility isotherms. Specific features of mixed crystal formation should be taken into account in genetic interpretation of natural minerals of mixed composition.