Phase transition of potassium sulfate,K2SO4 (III); thermodynamical and phenomenological study

The orthorhombic-hexagonal phase transition of K₂SO₄ has been investigated by measurements of the temperature dependencies of the specific heat, expansion, and X-ray intensity of superstructure reflections, correlated with the structural point of view. The values of the net enthalpy and entropy changes are ΔH=4.28 KJ/mol and ΔS=4.98 J/mol·K at the phase transition temperature (587°C), respectively. The thermal expansion along the c axis shows strong anisotropic character above about 300°C and exhibits a very large discontinuous increase at 587°C, whereas those along the a and b axes increase linearly and exhibit small discontinuous decreases at 587°C. The X-ray intensity of superstructure reflections in the low-temperature form gradually decrease with increasing temperature, and come to extinction at 587°C, exhibiting a discontinuity. The observed entropy change and pressure dependence of the phase transition temperature were explained successfully by the use of results of the structural analysis and measured physical properties. The temperature dependencies of the spontaneous strain, X-ray intensity of superstructure reflection, and birefringence were consistently described by introducing a transition parameter on the basis of an instability at the M point in the Brillouin zone of the hexagonal phase.     

Thermal phase transition of potassium sulfate,K2SO4

The thermal phase transition of K₂SO₄ has been investigated by high temperature polarized light microscopy. K₂SO₄ undergoes a first-order transition at 587° C where the orthorhombic low temperature form (Pmcn) transforms into a hexagonal high temperature modification (P6₃/mmc). Prior to the beginning of the phase transition, K₂SO₄ shows an anomalous optical behavior. The crystal apparently becomes optically uniaxial twice at 338° and 425° C, respectively, and truly optically uniaxial at 587° C. The phase transition propagates through an intermediate temperature form, which is sandwiched between the low and the high temperature forms and moves in a definite direction, 〈130〉 (orthorhombic indices), in the vicinity of the phase transition. Passing through the phase transition point on cooling, dark belts crossing each other are observed which are a result of the transformation twins parallel to {110} and {130}.     

Phase transition in K2Cd2(SO4)3: Order parameter and microscopic distortions

The transition from P2₁3(T ⁴) to P2₁2₁2₁(D ₂ ⁴ ) in the langbeinite K₂Cd₂(SO₄)₃ has been analyzed using group theoretical methods and previously published structural data above and below the transition. We find that because the transition is strongly first-order, the primary-order parameter has relatively large values at the transition temperature, and higher order terms which involve the order parameter, the strain, and the coupling of the two must be included in the Landau expansion for the free energy. Complex displacements occur at the transition for all atoms of the unit cell, but these displacements can be resolved into contributions which can be shown from symmetry considerations to transform as the _{2 3} irrep of P2 ₁ 3(T ⁴) as well as contributions from symmetry-preserving displacements which transform under the irrep ₁. Therefore, the transition is not a simple one and involves sulfate rotations and cadmium and potassium ion displacements.     

Phase transitions in langbeinites II: Raman spectroscopic investigations of K2Cd2(SO4)3

Polarized single crystal Raman spectra of the langbeinite K₂Cd₂(SO₄)₃ were recorded for different polarisations. With a view to understanding the phase transition mechanism, the lattice vibrational spectra (0–300 cm^?1), as well as the SO₄ symmetric stretching mode v ₁ (1,022 cm^?1), were recorded at different temperatures. No soft modes were observed. From the study of the temperature variation of the integrated intensity I ₀ and band width Γ of the hard mode (1,022 cm^?1), both SO₄ libration and SO₄ order/disorder models were ruled out as possible phase transition models. On the other hand, the model of Speer and Salje (paper I), involving the distortion of the polyhedra around Cd and K ions, explains the observed temperature behaviour of the Raman spectra very well. The consequences of a possible hypothetical high-temperature phase are discussed.     

Heat capacity studies of phase transitions in langbeinites II. K2Mg2(SO4)3

Heat capacity measurements have been made on a synthetic sample of langbeinite, K₂Mg₂(SO₄)₃, from 13 to 342 K in an adiabatic calorimeter. Three phase transitions, at 51.0, 54.9 and 63.8 K, have been observed in this material. Our study is the first to report the existence of such phase transitions in K₂Mg₂(S0₄)₃ and disputes predictions that none would take place below 77 K. Two models which have been proposed to explain the transition in potassium langbeinites are discussed in light of these results.     

Thermodynamic Calculation of Solubility of Na2SO4/K2SO4 in Hydrothermal Fluids

Sulfate fluids are common fluids in nature, and their salinity studies can provide important information for the evolution of ore-forming fluids, migration and enrichment of ore-forming elements, and the classification of deposit types. Considerable research has been carried out to investigate the solubility of Na₂SO₄ and K₂SO₄ in hydrothermal fluids, however most of the literature reported experimental data were under saturated vapor pressure or the water supercritical region. A few data have been reported for the low temperature hydrothermal mineralization region. Thermodynamic model is a useful method to study the properties of hydrothermal geofluids, especially for mineral solubility. Pitzer interaction model is one of the most widely used model to calculate the thermodynamic properties of hydrothermal fluids, but few work have ever been carried out to calculate the solubility of sulfate at high temperature and pressure. With Pitzer specific interaction model, using the literature reported density data of Na₂SO₄ and K₂SO₄ solutions at high temperature and pressure, the pressure effect on Pitzer activity coefficient of sulfate and the standard partial molar volume change during sulfate dissolution process were evaluated and related parameters were obtained. The standard partial molar volumes of Na₂SO₄ and K₂SO₄ calculated with these parameters agreed well with those reported in the literature. Combined with the relevant parameters in the literature under saturated vapor pressure, a thermodynamic model for Na₂SO₄ and K₂SO₄ solubility calculation with temperature up to 250 ℃ and pressure up to 40 MPa was developed. The model gave very good agreement with the experimental solubility data. With this model, Na₂SO₄ and K₂SO₄ solubility was calculated at high temperature and pressure. The calculation results showed that pressure had a positive effect on both the average activity coefficient and solubility product of Na₂SO₄ and K₂SO₄, but the solubility of Na₂SO₄ and K₂SO₄ decreased with pressure due to the larger change of the average activity coefficient with pressure. And as the temperature increased, the degree of such reduction became larger. The results herein can provide instructions for the compositional analysis of sulfate fluid inclusions.     

The magnetic structure of the langbeinite K2Mn2 (SO4)3

K₂Mn₂(SO₄)₃ orders magnetically at T_N= 1.75 K. One of the orthorhombic cell edges of the low temperature Langbeinite structure becomes doubled in the magnetically ordered state. The antiferromagnetic spin structure found is characterized by weak or vanishing molecular fields due to nearest neighbours. There are no indications of magnetic order down to 1.45 K in the isomorphic compound K₂Co₂ (SO₄)₃.     

Structural investigations,high temperature behavior and phase transition of Na6Ca4(SO4)6F2

Polycrystalline material of a sulfate apatite with chemical composition Na₆Ca₄(SO₄)₆F₂ or (Na₂Ca₄)Na₄(SO₄)₆F₂ has been synthesized by solid state reactions. Basic crystallographic data are as follows: hexagonal symmetry, a?=?9.3976(1) Å, c?=?6.8956(1) Å, V?=?527.39(1) ų, Z?=?1, space group P6₃/m. For structural investigations the Rietveld method was employed. Thermal expansion has been studied between 25 and 600 °C. High temperature (HT) powder diffraction data as well as thermal analysis indicate that the apatite-type compound undergoes a reconstructive phase transition in the range between 610 and 630 °C. Single-crystals of the HT-polymorph were directly grown from the melt. Structural investigations based on single-crystal diffraction data of the quenched crystals performed at ?100 °C showed orthorhombic symmetry (space group Pna2₁) with a?=?12.7560(8) Å, b?=?8.6930(4) Å, c?=?9.8980(5) Å, V?=?1097.57(10) ų and Z?=?2. Unit cell parameters for a quenched polycrystalline sample of the HT-form obtained at ambient conditions from a LeBail-fit are as follows: a?=?12.7875(1) Å, b?=?8.7255(1) Å, c?=?9.9261(1) Å, V?=?1107.53(2) ų. The lattice parameters of both modifications are related by the following approximate relationships: a _HT?≈?2c _RT, b _HT?≈?-(½a _RT?+?b _RT), c _HT?≈?a _RT. The HT-modification is isotypic with the corresponding potassium compound K₆Ca₄(SO₄)₆F₂. The pronounced disorder of the sulphate group even at low temperatures has been studied by maximum entropy calculations. Despite the first-order character of the transformation clusters of sulfate groups surrounding the fluorine anions can be identified in both polymorphs. Each of the three next neighbor SO₄-tetrahedra within a cluster is in turn surrounded by 8–9 M-cations (M: Na,Ca) defining cage-like units. However, in the apatite structure the corresponding three tricapped trigonal prisms are symmetry equivalent. Furthermore, the central fluorine atom of each cluster is coordinated by three next M-neighbors (FM₃-triangles), whereas in the HT-polymorph a four-fold coordination is observed (FM₄-tetrahedra).     

氯化钠和硫酸钾晶体生长动力学研究

研究了不同添加剂对晶体生长的影响,对NaCl和K2SO4晶体在流化床中的动态生长行为及单个晶体在溶液中的静态生长行为进行了研究.实验中还考虑了晶体表面的完整程度对晶体生长的影响,并对上述晶体的生长机理进行了分析.此外,对存在添加剂及纯溶液中NaCl和K2SO4晶体的溶解过程进行了研究.结果表明,本实验所选用的添加剂在低浓度下即能有效抑制NaCl和K2SO4晶体生长.     

交互四元体系Li+,Mg2+//SO2-4,B4O2-7-H2O 288 K时相平衡研究

采用等温溶解平衡法研究了288K时Li+, Mg2+//SO2-4, B4O2-7- H2O四元体系的固液相平衡关系,测定了该四元体系在288K时平衡液相的溶解度和密度.依据实验测定的平衡溶解度数据及对应的平衡固相,绘制了该四元体系的平衡相图及密度组成图.研究结果表明:交互四元体系Li+, Mg2+//SO2-4, B4O2-7- H2O 288K时平衡相图中有2个共饱点,5条单变量曲线,4个结晶区对应的平衡固相分别为Li2B4O7·3H2O,Li2SO4·H2O,MgB4O7·9H2O和MgSO4·7H2O.     

Die Kristallstruktur des Polyhalits,K2Ca2Mg[SO4]4.2H2O

Zusammenfassung Die Kristallstruktur des triklin-pinakoidalen Polyhalits, K₂Ca₂Mg[SO₄]₄. 2H₂O wurde aus photographischen Daten mit Hilfe der 3-dimensionalen Patterson-Funktion ermittelt. Die Verfeinerung mit der Methode der kleinsten Quadrate führte mit individuellen, isotropen Temperaturfaktoren für die beobachteten Reflexe auf R=0,09.In der Atomanordnung sind Sulfatgruppen durch oktaedrisch koordinierte Mg²⁺, 8-koordinierte Ca²⁺ und 11-koordinierte K⁺ miteinander verknüpft. Die H₂O-Moleküle sind jeweils an ein Mg²⁺ und ein K⁺ koordiniert. Die wahrscheinliche Lage der H-Atome wird aus den interatomaren Abständen erschlossen.

---

The crystal structure of polyhalite, K₂Ca₂Mg[SO₄]₄.2H₂O

Summary The crystal structure of the triclinic-pinacoidal mineral polyhalite, K₂Ca₂Mg[SO₄].2H₂O, is derived from photographic data by means of the 3-dimensional Patterson-function. The least squares-refinement resulted for the observed reflections and individual, isotropic temperature factors in R=0.09.In the atomic arrangement the sulfate groups are linked by octahedrally coordinated Mg²⁺, 8-coordinated Ca²⁺, and 11-coordinated K⁺. Each H₂O-molecule is coordinated to one Mg²⁺ and one K⁺. The probable positions of the H-atoms are derived from the interatomic distances.

---

---

Mit 2 Abbildungen     

Effects of composition and high pressures on the electrical conductivity of Fe-rich (Mg,Fe)2SiO4 olivines and spinels

Synthetic olivines, with composition Fa₅₀, Fa₇₅ and Fa₁₀₀, have been transformed into spinel in a laser-heated diamond-cell at pressures from 70 to 200 kbar and at a luminance temperature of about 1,200° C. The electrical conductivity σ was measured, at room temperature and up to 200 kbar, on olivine (Lacam 1982; 1983) and spinel (present study). The data obtained permit the following conclusions:

1. Sample nature effect: under the same conditions (composition, pressure), the σ of spinel is more than three orders of magnitude of the σ of olivine.
2. Composition effect: there are more than three orders of magnitude between the values of σ for spinels derived from initial compositions of Fa₅₀ and Fa₁₀₀, respectively.
3. Pressure effect: The P-effect on σ is greater for olivines than for spinels.

Besides, as in the case of olivine, in spinel the σ obeys an empirical Boltzmann relation: $$\log {\text{ }}\sigma = n \times x + S \times P + const$$ where the first and second term are the composition and pressure contributions, respectively; x the ratio Fa/Fo in mole percent. In spinel, the activation volume, in direct connection with S, was found to be in the order of 0.3 cm³/mol, about one half of that for olivine.     

Phase transitions in langbeinites I: Crystal chemistry and structures of K-double sulfates of the langbeinite type M 2 + + K2(SO4)3, M + +=Mg,Ni, Co,Zn, Ca

The crystal structures of the langbeinite type M ₂ ^{+ +} K₂(SO₄)₃ with M ^{+ +}=Mg, Ni, Co, Zn, Ca in their cubic phase (P 2 ₁ 3) and Ca₂K₂(SO₄)₃ in its orthorhombic phase (P 2 ₁ 2 ₁ 2 ₁) are determined. Whereas the SO₄-tetrahedra in these compounds are almost undistorted, the two symmetry-independent coordination polyhedra of M ^{+ +} are highly distorted octahedra with trigonal site symmetry in P 2 ₁ 3. The deformation of the oxygen octahedra and the off-centering of M ^{+ +} along the trigonal axis show systematic dependences on the ionic radii and the electronegativities of the M ^{+ +}-ions. The correlations are remarkably different for the two symmetry-independent M ^{+ +}-ions indicating different M ^{+ +} — O bonding. The octahedral deformations show also linear correlations with the phase transition temperatures (P 2 ₁ 3 — P 2 ₁ 2 ₁ 2 ₁) of the different compounds. This observation leads to a new model for the phase transition mechanism which is based on thermal instabilities of the M ^{+ +} — O and K — O polyhedral distortions. The cubic high temperature phase is characterized by high symmetric oxygen coordinations around M ^{+ +} which distort with decreasing temperature. At T _c the trigonal site symmetry is broken in such a way that the K — O coordination becomes denser at the expense of a wider and less symmetric M ^{+ +} — O coordination.     

硫酸侵蚀下水泥土的电阻率特性研究

通过室内试验模拟了水泥土试块受不同浓度硫酸（H2SO4）溶液侵蚀的过程,采用电阻率法研究了电阻率与各参数、无侧限抗压强度之间的关系。结果表明,受H2SO4侵蚀后,水泥土电阻率、孔隙水电阻率、水泥土抗压强度均随着溶液浓度的增加而减小,而水泥土的结构因子和重度均随着溶液浓度的增加而增加,水泥土抗压强度与水泥土电阻率成正比。在试验的基础上,考虑侵蚀因素对水泥土电阻率的影响,通过对Archie法则进行修正,得到了H2SO4侵蚀下水泥土电阻率模型。通过对无侧限抗压强度试验结果的分析,并结合试块表观变化,提出了利用电阻率来评价侵蚀程度的方法。     

Phase transition(s) in titanite CaTiSiO5: An infrared spectroscopic,dielectric response and heat capacity study

The structural phase transition in titanite near 500 K (averaged symmetries A2/aP2 ₁/a) and a second anomaly around 900 K have been studied using infrared spectroscopy on single crystals aqnd powder samples, measurements of the dielectric properties and the specific heat. The same synthetic single crystal was used in all experiments.The phase transition near 500 K is associated with a break in the temperature evolution of phonon frequencies and absorption intensities. Some phonon signals decrease rapidly under further heating and their extrapolated intensities disappear at ca. 850 K. The most dominant temperature effect relates to Ti-O phonons with amplitudes along the crystallographic a axis. These phonons show large LO-To splitting and continue to soften under heating even at temperatures above the transitions point (ca. 500 K).     

Structure of cobalt doped K2Cd2(SO4)3 langbeinite at three temperatures above the P213-P212121 phase transition,and a new trigger mechanism for the ferroelastic transformation

X-ray structure determinations of Langbeinite type K₂(Cd_1-xCo_x)₂(SO₄)₃, x≅0.02 at three temperatures (440, 540 and 640 K) above the P2 ₁3-P2 ₁2₁2₁ transition temperature (434 K) reveal that the M ²⁺ (M ²⁺=Cd) ion is displaced from the centre of the octahedron at all temperatures in the cubic phase. Simultaneously the distortion of the oxygen framework decreases with increasing temperature. The structural phase transition occurs when the bond lengths of the six bonds in each of the M ²⁺ octahedra are all equal, and it is proposed that this equalisation of bond lengths acts as the trigger for the phase transition. The structural deformation of the oxygen sublattice is such that rather regular octahedra around Cd occur at very high temperatures with Cd displaced from the centre. With decreasing temperature the octahedra distort under conservation of the triad, such that the differences between the various bond lengths Cd-O decrease. The phase transition occurs when all bond lengths around the Cd position become equal. The behaviour of the oxygen framework and the offcentring of the Cd/Co atom combine to produce an increasing distortion with increasing temperature as viewed by the central atom. Thus the interpretation of Optical Spectra, in which an increase in line splitting with temperature was observed, as being due to the off-centring of the Co, is confirmed.     

Phase Equilibrium and Phase Diagram of the Ternary System(MgCl_2 + MgB_2O_4 + H_2O) at 288 and 298 K

正1 Introduction The brines with high concentrations of magnesium and boron resources are widely distributed in the Qaidam Basin of the Qinghai-Tibet plateau,China(ZhengTang,1988).Although some works on the ternary system     

Optical absorption spectroscopy of the P213-P212121 transformation in K2Co2(SO4)3 langbeinite

Crystal field spectra have been obtained from K₂Co₂(SO₄)₃ at a number of temperatures from 20 K to room temperature. The transition to the ⁴ T _1g(P) excited state is found to be split at all temperatures owing to the trigonal distortion of the Co site. Below the P2₁3-P2₁2₁2₁ phase transition temperature an excess splitting is observed owing to the additional distortion of the site in the orthorhombic phase. This excess distortion is found to be a linear function of temperature with no first order step at T _c. Thus on a local scale the transition appears to be second order. The trigonal splitting increases with increasing temperature above T_c; this is not expected from the Speer-Salje model of the transition mechanism, which predicted decreasing distortion of the oxygen octahedra with increasing temperature. We propose that the apparent increase of asymmetry is due to the off centring of the Co atom in the high temperature phase in a more regular environment.     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000