System KF Research Articles

Vapor–Liquid Equilibrium and Solid Phase in the Ternary System KF–NaF–H2O at Different Temperatures

The vapor–liquid equilibria and solid phase of the mixed aqueous solutions of sodium and potassium fluorides were studied at different temperatures from 298.15 to 353.15 K. The water activities of ...

TRUTHS, INDUCTIVE DEFINITIONS, AND KRIPKE-PLATEK SYSTEMS OVER SET THEORY

AbstractIn this article we study the systems KF and VF of truth over set theory as well as related systems and compare them with the corresponding systems over arithmetic.

On the Costs of Nonclassical Logic

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: (a variant) of the system KF of Feferman (The Journal of Symbolic Logic, 56, 1–49, 1991) formulated in classical logic, and (a variant of) the system PKF of Halbach and Horsten (The Journal of Symbolic Logic, 71, 677–712, 2006), formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true.

Phase equilibria in the ternary systems KF–K2CrO4–K2MoO4 and KI–K2CrO4–K2MoO4

The ternary systems KF–K2CrO4–K2MoO4 and KI–K2CrO4–K2MoO4 were studied by differential thermal analysis. Continuous series of solid solutions are formed in these ternary systems.

Contextual-Hierarchical Reconstructions of the Strengthened Liar Problem

In this paper we shall introduce two types of contextual-hierarchical (from now on abbreviated by ‘ch’) approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates Trn and Trn+1 of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the Trn+1-schema should hold for all sentences of \(\mathcal {L}^{n}\). In contrast, the alternative ch-reconstruction, for which we shall argue in section four, is motivated by the idea that Trn and Trn+1 are coherent in the sense that the same sentences of \(\mathcal {L}^{n}\) should be true according to Trn and Trn+1. We show that instances of the standard ch-reconstruction can be obtained by iterating Kripke’s strong Kleene jump operator. Furthermore, we will demonstrate how instances of the alternative ch-reconstruction can be obtained by a slight modification of the iterated axiom system KF and of the iterated strong Kleene jump operator.

Fluorides containing lanthanides and yttrium at extreme conditions

We are interested in crystal structures and stabilities of fluoride materials containing lanthanides and yttrium that are related to the CaF2 structure. These compounds are laser hosts and luminescent materials, oxygen sensors as well as components of solar cells. They exhibit various schemes of (dis)ordering of cations and anions in fluorite superstructures and anion-excess fluorites. In the last few years, we have performed a series of studies on the bulk AMF4 and MF3 materials (A = Li, Na, K; M = Y, lanthanide) at different pressure-temperature conditions. Among them, ordered LiYF4 is a commercial host for solid state lasers, while partially ordered NaYF4 doped with lanthanides is the most efficient material for green and blue up-conversion known to date. In the system KF–YF3, we have studied not only KYF4 [1] but also KY3F10, which is an anion-excess 2×2×2 superstructure of fluorite at atmospheric conditions. At high temperatures and high pressures, it converts to another fluorite superstructure with disordered fluorine atoms. The pressure-induced LaF3 post-tysonite structure is another example of the anion-excess fluorite [2]. Our work on the fluorite-related materials at extreme conditions provides information on their structural instabilities that could further be used to better understand and control their materials properties. For instance, we demonstrated that the NaMF4 up-converters are unstable and that the ordering of the cations and vacancies in their structure is a slow process [3]. Consequently, the order–disorder transformations have a profound influence over the luminescent properties of these materials when doped.

AXIOMS FOR GROUNDED TRUTH

AbstractWe axiomatize Leitgeb’s (2005) theory of truth and show that this theory proves all arithmetical sentences of the system of ramified analysis up to ε0. We also give alternative axiomatizations of Kripke’s (1975) theory of truth (Strong Kleene and supervaluational version) and show that they are at least as strong as the Kripke-Feferman system KF and Cantini’s VF, respectively.

ChemInform Abstract: High Pressure Synthesis and Properties of Ternary Titanium(III) Fluorides in the System KF—TiF3 Containing Regular Pentagonal Bipyramids [TiF7

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Solvent-free and time-efficient Suzuki–Miyaura reaction in a ball mill: the solid reagent system KF–Al2O3under inspection

Although a plethora of synthetic procedures mediated by KF-loaded aluminas is available in the literature, there is almost no data concerning the influence of parameters such as alumina modification or KF-loading on experimental results. Hence, the Pd-catalyzed, solvent-free Suzuki–Miyaura reaction was chosen as model reaction to investigate the effect of the above mentioned parameters on the results of coupling reactions. The results from ball milling experiments led to the conclusion that self-prepared and commercially available KF–Al2O3 differ in water content. The higher the residual water content, the higher are the product yields.

High pressure synthesis and properties of ternary titanium (III) fluorides in the system KF–TiF 3 containing regular pentagonal bipyramids [TiF 7

Titanium trifluoride TiF 3 has the distorted ReO 3 structure composed of corner sharing TiF 6 octahedra linked with Ti–F–Ti bridges. Potassium fluoride KF was inserted into the bridges using high-pressure and high-temperature conditions (5 GPa, 1000–1200 °C). When the molar ratio KF/TiF 3≥1, a few low dimensional compounds were obtained forming non-bridged F ions. At the composition KF/TiF 3=1/2, a new compound KTi 2F 7 was formed, which crystallizes with the space group Cmmm and the lattice parameters of a=6.371(3), b=10.448(6), c=3.958(2) Å, consisting of edge-sharing pentagonal bipyramids [TiF 7] forming ribbons running along the a axis. The ribbons are linked by corners to construct a three-dimensional framework without forming non-bridged F ions. The compound is antiferromagnetic with the Néel temperature T N =75 K, and the optical band gap was 6.4 eV. A new fluoride K 2TiF 5 (KF/TiF 3=2) with the space group Pbcn and the lattice parameters of a=7.4626(2), b=12.9544(4) and c=20.6906(7) Å was also obtained by the high pressure and high temperature treatment (5 GPa at 1000 °C) of a molar mixture of 2 KF+TiF 3. The compound contains one-dimensional chains of corner-sharing TiF 6 octahedra.

Calorimetric study of melts in the system KF - K2TaF7

Abstract Enthalpy increment measurements on melts in the system KF-K2TaF7 were carried out by drop calorimetry at temperatures between 298 K and 1063, 1103 and 1143 K for selected compositions. Heat capacities of the melted mixtures and enthalpies of mixing have been determined. Careful calorimetric experiments showed small but distinct non-ideality of the melt. The molar heat capacity of melt exhibits small positive divergence from additivity. The molar enthalpy of mixing shows negative deviation from ideality which decreases with increasing temperature. The thermal effect at mixing was assigned predominantly to association reactions producing more complex fluorotantalate anions. The formation of complex anions with lower coordination number of Ta may not be excluded.

Calorimetric study of melts in the System KF - K2NbF7

Abstract The relative enthalpies of melts in the system KF - K2NbF7 were measured by drop-calorimetry at the temperatures 1058, 1140 and 1208 K as a function of composition. Heat capacities of melted mixtures and enthalpies of mixing were determined using the experimental data. The molar heat capacity of melts diverges slightly from additivity. The molar enthalpy of mixing of melts shows small negative deviation from ideality which decreases with decreasing temperature. The thermal effect at mixing was assigned predominantly to association reactions producing more complex fluoroniobate anions.

Density and Surface Tension of the System KF–K2TaF7–Ta2O5

The density of the system KF–K2TaF7–Ta2O5 was measured by the Archimedean method and the surface tension by the maximum bubble pressure method in the composition range up to 20 mol% Ta2O5. The density in the system KF–K2TaF7–Ta2O5 increases from KF through K2TaF7 to Ta2O5 and the surface tension increases from K2TaF7 through KF to Ta2O5. Based on the measured density values, the molar volumes of the binary and ternary melts at 860 °C, 900 °C and 950 °C were calculated as well as the partial molar volumes of particular components in different binaries. The small negative deviation from ideal behaviour in the binary system KF–K2TaF7 was identified by the calculation of the molar excess volume. The formation of complex anions [TaF8]3− is expected in this binary system. The surface tension decreases monotonically from KF to K2TaF7 in the binary system KF–K2TaF7. In the next two binaries KF–Ta2O5 and K2TaF7–Ta2O5 decrease of the surface tension was observed with the initial addition of Ta2O5 followed by the increase of the surface tension by further addition of Ta2O5. Based on measured data it was concluded that in binaries KF–Ta2O5 and K2TaF7–Ta2O5 the surface active component is Ta2O5 and in the binary KF–K2TaF7 the surface active component is K2TaF7. Mathematical description of the concentration dependence of the molar volume and surface tension of the measured ternary system was done by the polynomial function at 860°C, 900°C, and at 950°C.

Surface Tension of Melts of the System KF + K2NbF7 + Nb2O5

The surface tension of the molten system KF(1) + K2NbF7(2) + Nb2O5(3) up to x3 = 0.2 has been investigated using the maximum bubble pressure method over the temperature range from 1133 K to 1233 K. The uncertainty of the surface tension measurement was estimated to be ±1.5%. On the basis of the data presented, the composition dependence of the surface tension and the surface tension excess were calculated.

Viscosity of the System KF–K2NbF7–Nb2O5

Abstract The viscosity of melts of the system KF–K2NbF7–Nb2O5 has been measured using computerized torsion pendulum method. An equation describing the dependency of the viscosity in logarithm values on composition at 1173 K was calculated by multiple linear regression analysis. The sum of viscosities of pure components in logarithm values multiplied by their mole fraction was used as an “additive” behaviour. In the concept of modified Redlich–Kister's type equation binary interactions of the particular components were found.

Density of the System KF + K2NbF7 + Nb2O5

The density of melts of the system KF(1) + K2NbF7(2) + Nb2O5(3) up to 20 mol % Nb2O5 has been measured using the Archimedean method. On the basis of the measured density values, the molar volumes of the melts and partial molar volumes of Nb2O5 in different binaries were calculated. The density in the system KF(1) + K2NbF7(2) + Nb2O5(3) increases from KF through K2NbF7 to Nb2O5. In all three binary systems, some interactions have been determined.

Low-Melting Electrolyte for Aluminum Smelting

A tube-type cell was used to determine the electrical conductivity of low-melting electrolytes (AlF3-rich) by applying ACtechniques with a sine wave signal with small amplitude in the high-frequency range. The tested melt contained 55 mol % KF and 45 mol % AlF3 (molar ratio KF/AlF3 = 1.22) with and without the addition of 2 mass % alumina in the temperature range from 660 °C to 750 °C. The electrical conductivity κ in this system can be described by the equation κ/(Ω1-·cm-1) = 6.458 exp(−1858.91/T/K) − 0.01876(w(Al2O3)), where w(Al2O3) is the alumina concentration in the melt (mass %). Phase diagrams of the systems KF + AlF3 and KF + AlF3 + Al2O3 up to 10 mol % Al2O3 for molar ratios KF/AlF3 = 2.35, 2.2, 1.85, and 1.22 (30, 31, 35, 45 mol % AlF3) were measured. In the melt with composition 55 mol % KF and 45 mol % AlF3, the solubility of alumina was aproximately 4 mol % (2.8 mass %) at 540 °C.

Structural and thermodynamic aspects in the molybdenum melts of the system KF–K2MoO4–SiO2

The complex physico-chemical analysis of the system KF–K 2 MoO 4 –SiO 2 , based on the phase diagram, density, surface tension and viscosity measurements, was performed. The phase diagrams of the binary systems as well as that of the ternary system in the range up to 50% SiO 2 were measured using the thermal analysis method. The results proved the presence of the congruently melting compound K 3 FMoO 4 at 751 °C in the binary melt KF–K 2 MoO 4 . The strong positive deviation from ideal behaviour of the ternary system KF–K 2 MoO 4 –SiO 2 was ascribed to the formation of heteropolyanions [SiMo 12 O 40 ] 4− in the melt. In the investigated concentration range of the ternary system, no eutectic point has been found. It lies most probably beyond the investigated part of the system. The probable inaccuracy in the calculated ternary phase diagram is 5.9 °C. The density of the melts of the system KF–K 2 MoO 4 –SiO 2 was measured using the Archimedean method. Based on the obtained density data the molar volume, partial molar volume and excess molar volume of the melts were calculated in order to consider the possible chemical interactions of components. The degree of thermal dissociation of the additive compound K 3 FMoO 4 was calculated based on both the thermodynamic analysis of the phase diagram and the volume properties of the investigated system. It was found that the degree of the thermal dissociation of K 3 FMoO 4 at the melting point attains the value α o =0.81. The dissociation enthalpy, calculated on the basis of the density values is Δ H (dis, K 3 FMoO 4 )=18.8 kJ mol −1 . The surface tension of the molten system KF–K 2 MoO 4 –SiO 2 has been determined using the maximum bubble pressure method. Based on the obtained data the concentration dependence of the surface tension and of the surface tension excess of the investigated system was calculated. The viscosity of melts of the system KF–K 2 MoO 4 –SiO 2 has been measured using the computerised torsional pendulum method. The sum of viscosities of pure components in logarithm values multiplied by their mole fraction was used as an ‘additive’ behaviour. A multiple linear regression analysis was performed to obtain coefficients of the modified Redlich–Kister's type equation. Binary and ternary interactions of the particular components were found. X-ray powder diffraction patterns and IR spectra of the certain quenched powdered samples of both binary and ternary mixtures were recorded. By both techniques the presence of starting compounds and the presence of another compounds, as well, was detected. Some of these compounds were recognized based on the known data. The remaining data were attributed to the possible expected compounds.

Structural and thermodynamic aspects in the molybdenum melts of the system KF–K 2MoO 4–SiO 2

The complex physico-chemical analysis of the system KF–K 2MoO 4–SiO 2, based on the phase diagram, density, surface tension and viscosity measurements, was performed. The phase diagrams of the binary systems as well as that of the ternary system in the range up to 50% SiO 2 were measured using the thermal analysis method. The results proved the presence of the congruently melting compound K 3FMoO 4 at 751 °C in the binary melt KF–K 2MoO 4. The strong positive deviation from ideal behaviour of the ternary system KF–K 2MoO 4–SiO 2 was ascribed to the formation of heteropolyanions [SiMo 12O 40] 4− in the melt. In the investigated concentration range of the ternary system, no eutectic point has been found. It lies most probably beyond the investigated part of the system. The probable inaccuracy in the calculated ternary phase diagram is 5.9 °C. The density of the melts of the system KF–K 2MoO 4–SiO 2 was measured using the Archimedean method. Based on the obtained density data the molar volume, partial molar volume and excess molar volume of the melts were calculated in order to consider the possible chemical interactions of components. The degree of thermal dissociation of the additive compound K 3FMoO 4 was calculated based on both the thermodynamic analysis of the phase diagram and the volume properties of the investigated system. It was found that the degree of the thermal dissociation of K 3FMoO 4 at the melting point attains the value α o=0.81. The dissociation enthalpy, calculated on the basis of the density values is Δ H(dis, K 3FMoO 4)=18.8 kJ mol −1. The surface tension of the molten system KF–K 2MoO 4–SiO 2 has been determined using the maximum bubble pressure method. Based on the obtained data the concentration dependence of the surface tension and of the surface tension excess of the investigated system was calculated. The viscosity of melts of the system KF–K 2MoO 4–SiO 2 has been measured using the computerised torsional pendulum method. The sum of viscosities of pure components in logarithm values multiplied by their mole fraction was used as an ‘additive’ behaviour. A multiple linear regression analysis was performed to obtain coefficients of the modified Redlich–Kister's type equation. Binary and ternary interactions of the particular components were found. X-ray powder diffraction patterns and IR spectra of the certain quenched powdered samples of both binary and ternary mixtures were recorded. By both techniques the presence of starting compounds and the presence of another compounds, as well, was detected. Some of these compounds were recognized based on the known data. The remaining data were attributed to the possible expected compounds.

Coordination chemistry of tin: Part III. The crystal structure and thermal behavior of dipotassium dimethyl-tetrafluoro-stannate dihydrate, K 2[(CH 3) 2SnF 4]·2H 2O

Reaction of (CH 3) 2SnF 2 with two equivalents of KF in aqueous medium leads to the formation of the complex salt K 2[(CH 3) 2SnF 4]·2H 2O ( 1). Its crystal structure was determined by single-crystal X-ray diffraction. Complex 1 crystallizes in the monoclinic space group C2 (No. 5) with the lattice parameters a=9.265(1), b=7.556(1), c=7.076(1) Å; β=98.21(1)° and Z=2. The structure is characterized by the anion [(CH 3) 2SnF 4] 2− in which the tin atom adopts a slightly distorted octahedral coordination, with the methyl groups in trans position. The potassium cations are pentacoordinated from three fluorine atoms and the oxygen atoms of two water molecules in the form of a distorted square pyramid. In addition, the thermal behavior of the compound was studied with the aid of TG/DSC-measurements coupled with MS, revealing that the dehydration of 1 takes place at 75 °C, with an enthalpy of 57.79 kJ mol −1, and that it decomposes without melting in two further endothermic steps to undetermined phases in the system KF–SnF 2–SnF 4 and free carbon (∼0.1%).