Continuous Series Of Solid Solutions Research Articles

Stability of the solid–liquid interface under constitutional undercooling in the crystal growth of TlCl–TlBr and TlBr–TlI solid solutions

Using phase diagram data for the TlCl–TlBr and TlBr–TlI systems, we have calculated the stability functions of the solid–liquid interface under constitutional undercooling for solid solutions of these systems. The curves thus obtained are typical of systems containing continuous series of solid solutions and having minima in their liquidus and solidus curves. The curves can be used to evaluate technologically important process parameters necessary for the growth of crystals of high optical quality.

Partitioning triangles KCl-KBr-Li2WO4 and KCl-KBr-LiKWO4 of the quaternary reciprocal system Li,K‖Cl,Br,WO4

The quaternary reciprocal system Li,K‖Cl,Br,WO4 was partitioned into simplexes using graph theory by writing an adjacency matrix and solving a logical expression. A tree of phases of the system was constructed. The tree of phases has a linear structure and consists of two stable tetrahedra and a stable pentatope, which are divided by two partitioning triangles. In the quaternary reciprocal system Li,K‖Cl,Br,WO4, based on the constructed tree of phases, crystallizing phases were predicted. The partitioning triangles KCl-KBr-Li2WO4 and KCl-KBr-LiKWO4 were experimentally studied by differential thermal analysis. There are no invariant equilibrium points in the triangles. Continuous series of solid solutions are stable and do not decompose.

Thermodynamic study of Tl5Te3 − x Br x solid solutions by EMF measurements

The Tl5Te3-Tl5Te2Br system has been studied in the temperature range 300–430 K using emf measurements on thallium concentration cells. We have identified a continuous series of solid solutions in the system and determined their partial and standard integral thermodynamic functions.

Structure and ion-exchange properties of crystalline tungstoantimonic acid

We have studied the effect of Li+, Na+, K+, and Ag+ for proton ion exchange on the structural characteristics of crystalline tungstoantimonic acid with the composition H3OWSbO6 · nH2O. The metal ion substitutions for protons have been shown to result in the formation of a continuous series of solid solutions existing in a limited composition range. The dependence of the unit-cell parameter on the ionic radius of the substituents has been analyzed.

Pure iron and other magnetic minerals in meteorites

The results of thermomagnetic and microprobe analyses of 37 samples from 25 different types of meteorite are analyzed with the focus on the presence of pure (nickel-free) iron in them. It is established that the metallic particles in the studied meteorites cluster in three isolated groups: (1) pure iron, (2) kamacite with mode 3–6% Ni, and (3) taenite with mode ∼50% Ni. The hiatuses in the Fe-Ni alloy compositions between these groups of magnetic grains contradict the Fe-Ni phase diagram, which predicts a continuous series of solid solutions in this system. This isolated distribution of the compositions of the metallic particles in the meteorites is reasonably accounted for by the specific properties of the melt (melts) and the processes of their crystallization and decomposition in space. It is suggested that pure iron in the meteorites could have been formed by either of two scenarios. According to the “primary,” pure iron crystallizes from the melt, and according to the “secondary” scenario, it is produced by the decomposition of the solid solution.

Phase equilibria in the quaternary systems Li‖F,Cl,Br,CrO4 and Li‖F,Cl,Br,WO4

Phase equilibria in the quaternary systems Li‖F,Cl,Br,CrO4 and Li‖F,Cl,Br,WO4 were studied by differential thermal analysis. In these systems, the stability of continuous series of solid solutions based on lithium chloride and bromide is preserved. The number and compositions of crystallizing phases in the systems Li‖F,Cl,Br,CrO4 and Li‖F,Cl,Br,WO4 were confirmed by X-ray powder diffraction analysis.

Sol-gel synthesis and structure of MZr2(AsO4)3 arsenates and MZr2(AsO4) x (PO4)3 − x arsenate phosphates (M = K, Rb, Cs)

MZr2(AsO4)3 arsenates and MZr2(AsO4) x (PO4)3 − x arsenate phosphates (M = K, Rb, Cs) have been obtained by sol-gel synthesis followed by heat treatment and have been characterized by X-ray diffraction, electron probe microanalysis, and IR spectroscopy. Continuous series of substitutional solid solutions form in the MZr2(AsO4) x (PO4)3 − x systems (0 ≤ x ≤ 3). The solid solutions have a kosnarite structure (KZr2(PO4)3, space group $R\bar 3c$ ). The crystal structures of MZr2(AsO4)3 and MZr2(AsO4)1.5(PO4)1.5 have been refined by full-profile analysis. The structural frameworks of these phases are built from ZrO6 octahedra and AsO4 tetrahedra or (As,P)O4 tetrahedra statistically populated by arsenic and phosphorus atoms. The alkali metal atoms occupy extraframework sites. The effect of the crystal chemical properties of alkali metals on the formation of the structures of MZr2(AsO4)3 arsenates (M = Li-Cs) and MZr2(AsO4) x (PO4)3 − x solid solutions is discussed.

Structure and properties of (1 − x)BiFeO3 · xPbFe2/3W1/3O3 (0 ≤ x ≤ 1) solid solutions

(1 − x)BiFeO3 · xPbFe2/3W1/3O3 ((1 − x)BFO · xPFWO) samples with 0 ≤ x ≤ 1 have been prepared by a standard ceramic processing technique and characterized by X-ray diffraction, dielectric measurements, and Mossbauer spectroscopy. The system has been shown to contain a continuous series of perovskite solid solutions. The solid solutions in the range 0 ≤ x < 0.32 have a rhombohedral structure and those with 0.32 ≤ x ≤ 1 have a cubic structure. Increasing the BFO content from 0 to 40% leads to rapid degradation of the dielectric permittivity peak that occurs at 180 K in PFWO and is due to the relaxor behavior of this component. At higher BFO concentrations, the electrical conductivity of the solid solutions increases by about two orders of magnitude. The temperature dependences of permittivity for the samples containing ∼80% BFO have prominent maxima around 430 and 520 K, whose position is frequency-independent. The solid solutions exhibited no piezoelectric or pyroelectric effect, probably because they were insufficiently poled in a field of 10 kV/cm at 300 K. At higher electric field intensities, the samples experienced breakdown.

Phase equilibria in the pseudoternary system Ag2Se-Ag8GeSe6-Ag8SnSe6

Phase equilibria in the Ag2Se-Ag8GeSe6-Ag8SnSe6 system have been studied by differential thermal analysis, X-ray diffraction, scanning electron microscopy, and emf measurements on concentration cells with Ag4RbI5 as a solid electrolyte. We have mapped out the T-x phase diagram of the constituent binary system Ag8GeSe6-Ag8SnSe6, those of two mutually perpendicular sections, and the liquidus projection. The two crystalline phases of the constituent selenides Ag8GeSe6 and Ag8SnSe6 have been shown to form a continuous series of solid solutions. The Ag2Se-Ag8GeSe6-Ag8SnSe6 system is a pseudoternary section through the quaternary system Ag-Ge-Sn-Se, and its phase diagram has a univariant eutectic.

Phase relationship of Dy-Fe-Mn system at 773 K

Rare-earth intermetallic compounds formed in many R-Fe-Mn (R=rare-earth element) systems exhibit excellent properties. In order to understand the existence and stability of the compounds in the system and further search for the potential application of R-Fe-Mn alloys in various aspects, it is necessary to investigate the phase relations of the Dy-Fe-Mn ternary system. A total of 96 samples of the Dy-Fe-Mn alloys were prepared by arc-melting and examined by metallographic analysis, X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques. The phase relationship of the Dy-Fe-Mn system at 773 K was determined. It was found that the isothermal section was characterized by intermediate solid solutions based on the substitutions of Fe/Mn atoms and the large extensions of the binaries into the ternary domains. The solid solubilities of the third element in the binary compounds and the phase boundaries were also determined by XRD technique using the phase disappearing method combined with the lattice parameter method and SEM/EDS technique. Two pairs of corresponding binary compounds in the Dy-Fe and Dy-Mn systems (DyFe2 and DyMn2, Dy6Fe23 and Dy6Mn23) formed a continuous series of solid solution at 773 K, respectively.

The phase equilibria in the Ag2S–Ag8GeS6–Ag8SnS6 system

The phase equilibria in the Ag2S–Ag8GeS6–Ag8SnS6 system were investigated experimentally by means of differential thermal analysis (DTA), X-ray diffraction (XRD) techniques, scanning electron microscopy (SEM) and electromotive force (EMF) measurements of the concentration chains with Ag4RbI5 solid electrolyte. The phase diagram of the boundary Ag8GeS6–Ag8SnS6 system, two isopleth sections as well as liquidus surface projection of the Ag2S–Ag8GeS6–Ag8SnS6 system was plotted. The continuous solid solution series between low and high temperature modifications of both initial compounds were found along the boundary Ag8GeS6–Ag8SnS6 system. It was found that the Ag2S–Ag8GeS6–Ag8SnS6 system is quasi-ternary plane of the quaternary system and relates to monovariant eutectic type. The partial molar thermodynamic functions (ΔG‾,ΔH‾,ΔS¯) of silver were calculated for the LTM-Ag8Ge1−xSnxS6 (for x=0.2; 0.4; 0.6; 0.8) solid solution based on the results of the EMF measurements.

Study of the YbTe–SnTe–Sb2Te3 quasi-ternary system

The phase equilibria in the YbTe–SnTe–Sb2Te3 system were investigated by using differential thermal analysis (DTA), X-ray diffraction (XRD) and scanning electron microscopy (SEM-EDS) techniques. Isothermal sections of the phase diagram at 300, 700, 900 and 1000K, the liquidus surface projection as well as some isopleth sections were experimentally constructed. The primary crystallization fields of phases, the type and coordinates of invariant and monovariant equilibria were determined. The boundary YbTe–SnTe system restudied and existence of the ternary compound YbSnTe2 reported earlier was not confirmed. Moreover, the continuous solid solution series with the NaCl type cubic structure system was revealed in this system and it was also found that a spinodal-type phase decomposition of this solid solution occurs below ∼950K.

X-ray diffraction study of the crystallographic characteristics of TlInS x Se2 − x solid solutions

Crystallographic parameters of TlInSxSe2 − x solid solutions have been measured by X-ray diffraction. Dependences of the unit-cell parameters on the composition are determined. It is established that the values of parameters a, b, and c and the angle β decrease with an increase in x. It is shown that the TlInSxSe2 − x system includes a continuous series of solid solutions based on the TlInSe2 compound with tetragonal symmetry at x values ≤ 0.4, while at x ≥ 0.6 solid solutions based on the TlInS2 compound with a monoclinic structure are formed.

Synthesis and properties of LiZr2(AsO4)3 and LiZr2(AsO4) x (PO4)3 − x

The LiZr2(AsO4)3 arsenate and LiZr2(AsO4)x(PO4)3 − x solid solutions have been prepared through precipitation followed by heat treatment, and characterized by X-ray diffraction, X-ray structure analysis, IR spectroscopy, and impedance spectroscopy. We have established conditions for the crystallization of the arsenate and a continuous series of arsenate phosphate solid solutions (0 ≤ x ≤ 3), which have been obtained as two polymorphs: monoclinic and hexagonal. Using the Rietveld method, we have refined the crystal structures of the polymorphs of LiZr2(AsO4)3 (sp. gr. P21/n, a = 9.1064(2), b = 9.1906(2), c = 12.7269(3) A, β = 90.844(2)°, V =1065.03(5) A3, Z = 4; sp. gr. R\(\bar 3\)c, a = 9.1600(4), c = 22.9059(13) A, V = 1664.44(14) A, Z = 6) and LiZr2(AsO4)1.5(PO4)1.5. Their structural frameworks are built up of AsO4 tetrahedra—or (As,P)O4 tetrahedra occupied by arsenic and phosphorus atoms at random—and ZrO6 octahedra, with the lithium atoms in between. The ionic conductivity of the materials has been measured. The cation conductivity of monoclinic LiZr2(AsO4)x(PO4)3 − x with 0 ≤ x ≤ 1 has been shown to exceed the conductivity of lithium zirconium phosphate.

Perboeite-(Ce) and alnaperboeite-(Ce), two new members of the epidote-tornebohmite polysomatic series: Chemistry, structure, dehydrogenation, and clue for a sodian epidote end-member

In yttrian fluorite from pegmatites of the Tysfjord granite, Norway, grayish-green to very pale green gatelite-like crystals occur along with millimeter-size aggregates of Y-silicates as a late primary phase; they are associated with allanite-(Ce), bastnasite-(Ce), and intimately inter- or overgrown by tornebohmite-(Ce). Sub- to euhedral crystals, up to 400 μm in size, are chemically zoned between two near-end-member compositions that imply the existence of two new members of the polysomatic gatelite group, in which ET polysomes are composed of E modules with epidote-type structure alternating with T modules of tornebohmite-type structure. The two new minerals form a continuous solid-solution series, along which two crystals of intermediate compositions served for species definition. Their electron-microprobe analyses yield the empirical formulas (Ca 1.00 Mn 0.03 Na 0.08 La 0.51 Ce 1.30 Pr 0.16 Nd 0.62 Sm 0.10 Gd 0.06 Dy 0.03 Er 0.01 Y 0.06 Th 0.01 ) ∑3.97 (Al 3.21 Fe 2+ 0.79 ) ∑4.00 Si 5.01 O 20 (OH) 2 for perboeite-(Ce) [IMA 2011-55] and (Ca 1.10 Mn 0.03 Na 0.20 La 0.42 Ce 1.14 Pr 0.16 Nd 0.60 Sm 0.13 Gd 0.07 Dy 0.03 Er 0.01 Yb 0.01 Y 0.12 Th 0.02 ) ∑4.04 (Al 3.54 Fe 2+ 0.40 Mg 0.02 ) ∑3.96 Si 4.99 O 20 (OH) 2 for alnaperboeite-(Ce) [IMA 2012-54]. The respective end-member formulas are A (Ce 3 Ca) M (Al 3 Fe 2+ )Si 2 O 7 (SiO 4 ) 3 O(OH) 2 , which requires Ce 2 O 3 45.10, CaO 5.14, FeO 6.58, Al 2 O 3 14.01, SiO 2 27.52, H 2 O 1.65, total 100.00 wt%; and A (Ce 2.5 CaNa 0.5 ) M (Al 4 )Si 2 O 7 (SiO 4 ) 3 O(OH) 2 , which requires Ce 2 O 3 40.86, CaO 5.58, Na 2 O 1.54, Al 2 O 3 20.31, SiO 2 29.92, H 2 O 1.79, total 100.00 wt%. Cell parameters of perboeite-(Ce) and alnaperboeite-(Ce) for these crystals are a = 8.9277(6) and 8.9110(4), b = 5.6548(6) and 5.6866(2), c = 17.587(1) and 17.5252(7) A, β = 116.475(8) and 116.300(5)°, V = 794.8(1) and 796.13(7) A 3 , respectively. Members of the perboeite-(Ce)–alnaperboeite-(Ce) solid solution are topologically identical to the minerals gatelite-(Ce) and vastmanlandite-(Ce). Structural data (space group P 2 1 / m ) were obtained for the holotype crystals and for several crystals with intermediate composition. Structural refinements of a crystal annealed step-wise in air confirm that most of Fe in M3 is divalent before heating and show that oxidation/dehydrogenation takes place mostly in the E module (M3 and H1). Perboeite-(Ce) derives from gatelite-(Ce) by the homovalent substitution [ M3 Fe 2+ → M3 Mg]. Alnaperboeite-(Ce) derives from perboeite-(Ce) or gatelite-(Ce) by the coupled heterovalent substitutions [ A Na + + 2 M3 Al 3+ → A REE + 2 M3 (Fe 2+ or Mg)]. Tornebohmite-(Ce) associated with alnaperboeite-(Ce) is Na-free, whereas coexisting allanite is Na-bearing and shows the same coupled substitution between A and M sites as the one relating perboeite-(Ce) and alnaperboeite-(Ce) (Na 0.5 Al ↔ REE 0.5 Fe 2+ ). This could suggest, although crystallographic evidence is inconclusive, that Na incorporation in the ET polysome occurs in the E module alone (A2 or A1 sites), leading to the sodian E end-member A (CaREE 0.5 Na 0.5 ) M (Al 3 )Si 2 O 7 (SiO 4 )O(OH). In any event, this new epidote end-member is needed to account for up to ca. 10 mol% of the composition of allanite-group minerals, in which Na 2 O contents may reach 0.3 wt%. Sodium must be analyzed in epidote-supergroup and gatelite-group minerals.

Phase diagrams of the Ln2S3-EuS (Ln = La-Gd) systems

The phase diagrams of the Ln2S3-EuS (Ln = La-Gd) systems were studied. In these systems, continuous series of solid solutions form between γ-Ln2S3 and EuLn2S4 (Th3P4 structural type), and also eutectics between EuLa2S4 and a solid solution based on EuS form at the following coordinates: 71.5 mol % EuS, 2280 K; 66.5 mol % EuS, 2240 K; and 63.5 mol % EuS, 2100 K. The characteristics of the forming compounds are the following: EuLa2S4: a = 0.8759 nm, T melt = 2420 K, and H = 2380 MPa; EuNd2S4: a = 0.8615 nm, T melt = 2380 K, and H = 2530 MPa; and EuGd2S4: a = 0.8507 nm, T melt = 2300 K, and H = 2670 MPa.

Solubility in the NdCl3-LnCl3-HCl-H2O systems (Ln = Sm, Gd) at 25°C

The solubility at 25°C in the NdCl3-SmCl3-HCl-H2O and NdCl3-GdCl3-HCl-H2O quaternary water-salt systems has been studied in 40% hydrochloric acid sections. The NdCl3-SmCl3-HCl-H2O system represents a continuous series of solid solutions (type I solid solutions). The NdCl3-GdCl3-HCl-H2O system is a system with peritonic discontinuity (type V solid solutions). The discontinuity point of the peritonic solution has the following composition (wt %): NdCl3 · 6H2O, 1.13; GdCl3 · 6H2O, 0.11; HCl, 39.5; H2O, 59.26.

Formation of continuous solid solutions near the minimum point of a phase diagram

A model of structure ordering in alloys of the compositions corresponding to the minimum points of phase diagrams with continuous series of solid solutions was proposed based on calculating the concentration dependence of the energy of mixing and the results of X-ray powder diffraction study of solid solutions in the systems Sb-As, Sb2Se3-Bi2S3, and Cu-Mn.

Polythermal section Sn4P3-Sn4As3

The T-x diagram of the polythermal section Sn4P3-Sn4As3 of the Sn-P-As system was constructed using the results of X-ray powder diffraction and differential thermal analyses. A continuous series of solid solutions (Sn4P3) x (Sn4As3)1 − x was found to exist. The section is not quasi-binary; in a Sn4As3-rich region, this section intersects the peritectic part of the three-phase volume (L + SnAs + α) of the ternary diagram.

Interaction between lead bromide and barium bromide

The phase diagram of the PbBr2-BaBr2 system over the entire concentration range is studied for the first time by differential thermal analysis and X-ray powder diffraction analysis. No new compounds are formed in the system. The phase diagram is represented by a continuous series of solid solutions (type I by Rooseboom’s classification). The unit cell parameters change as a linear function of composition.