The Precipitation of Sparingly-Soluble Alkaline-Earth Metal and Lead Salts with Slow Development of Supersaturation (Slow Anion and Hydroxyl Ion Addition): Kinetics of Nucleation and Induction Periods

Barium and lead sulphate and chromate precipitations were studied at 20° to 95°C at precipitation rates varying from 10⁻³ to 10⁻⁷ ion l⁻¹ sec⁻¹: the supersaturation was developed by slow direct addition of anion to metal nitrate solution and by neutralisation of equivalent metal salt in excess acid solution. Slow heterogeneous nucleation occurred onto particles dispersed within the aqueous solution. The nucleation rate at any time was Where k_n is the rate constant for heterogeneous nucleation, N_∞ is the maximum number of potential nuclei, n_t is the number of nuclei after time t, I. P_t is the ionic product (C_mt)(C_mt) and 2π is the number of metal salt ions in the critical nucleus, generally eight. Crystal growth started after induction periods (t̄) at times just after the times for maximum rate of formation of nuclei. The induction periods (t̄) for precipitations from solutions of initial cation concentration ^cM₀ varied with precipitation rate (R) according to the relation, where γ = π/(π + 1) and k₁ (the unit reciprocal induction period) = . Nucleation rate constants for different precipitations were estimated from the k₁ values and are tabulated. For slow precipitations by direct anion addition, the rate constants were lower for precipitation from solution of the salt of greater solubility. The rate constants for slow precipitation of metal chromates from acid solution were far lower than those for slow precipitation by direct chromate addition. Rate constants decreased somewhat with rise in precipitation temperature.     

The precipitation of barium chromate from aqueous solution (with rapid mixing): Kinetics of the crystal growth

The kinetics of precipitation of barium chromate from well-stirred aqueous solutions of initial solute concentrations C₀ = 0.0001 to 0.0010 M (supersaturations 8 to 80) was studied at 25 °C by conductivity measurements and chemical analysis. Nucleation occurred during induction periods and regular crystal growth then took place onto the crystallites formed during the induction periods. The crystal growth was rate-controlled, in this range, by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate, at any time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation, the growth rate expressed in terms of degree of crystallisation was then The rate constant (K_α) for the crystallisation of barium chromate at 25 °C was 1.5 10⁶ sec⁻¹ M⁻².     

The Precipitation of Barium Chromate with Slow Development of Supersaturation. Kinetics of the Crystal Growth

Slow barium chromate precipitation was studied in well-stirred solutions — final concentration 0.002 mole 1⁻¹ — at 20°C at mixing rates varying from 0.2 to 2 · 10⁶ mole 1⁻¹ sec⁻¹; the kinetics of the crystal growth process were studied by chemical analysis and by optical microscopy. The crystal growth started after induction periods; regular growth then took place on the nuclei formed during these periods. For the main growth, up to about seventy percent precipitation time, growth rates at any time depended on the (residual excess solute concentrations in solution)². Immediately after the induction periods, crystal lengths varied with growth time according to the relation, for the main growth, crystal lengths varied with growth time according to a more complex relation, where k_l is the rate constant for surface growth, R_c is the rate of development of metal salt concentration and K is a constant that depends on the number of precipitate crystals. After some growth time τ = τ^*, when l_τ = l_τ*, all fresh solute added to the solution was utilised immediately and was deposited onto the growing crystals; then, for the final thirty percent precipitation, crystal lengths varied with growth time according to the relation, .     

The Precipitation of Strontium and Lead Sulphates from Aqueous Solution. Kinetics of the Crystal Growth

The precipitation of strontium and lead sulphates from well-stirred supersaturated aqueous solutions, of initial solute concentrations C₀ = 0.001 to 0.020 M and C₀ = 0.0002 to 0.003 M respectively, was studied at 20° and 40°C by chemical analysis and optical microscopy. Nucleation occurred during induction periods and continuous regular growth then took place onto the nuclei formed during these periods. Crystallisation was complete after 4 to 48 hr. The crystal growth was rate-controlled by the rate of deposition of metal salt ions onto the growing crystal surfaces. This rate (dC/dt), at any growth time, then depended on both the overall surface area (A_t) and on the residual excess solute concentration (ΔC_t) in solution according to the relation while the growth rate (dα/dt), expressed in terms of degree of crystallisation, was . The rate constants (k_α) for the crystal growth of strontium and lead sulphates at 20°C were 22 and 4200 sec⁻¹ M⁻² respectively — that is, greatest for the salt with least cation hydration –; these constants increased 4 to 6 times for 20°C temperature rise. The rate-determining process for the metal salt deposition was probably the ion dehydration.     

Rheological behaviour of lamellar eutectic Al?Al2?Cu elaborated by induction heating

This paper presents solutions to the experimental problems encountered in the elaboration of lamellar Al Al₂Cu or fibrous Al Al₃Ni eutectic samples using the Bridgman technique. The objective is to prepare samples for use in mechanical tests. The investigation of the elaborated structures of Al Al₂Cu (orientation, grain selection, shape of the solid-liquid (S.L.) interface, interlamellar spacing λ…) can then be used to confirm the predicted behavior. Creep tests under constant applied stress σ (from 2 to 5 · 10⁷ N/m²) at temperatures from 300 to 450 °C show:

• – that a stationary state exists (with constant strain rate )
• – the influence of an imperfect orientation
• – the existence of a Bailey-Norton creep law = kσⁿ. This law leads to the possiblity of finding a constitutive equation for high temperatures tests.

     

The precipitation of calcium carbonate powders from aqueous solution with slow development of supersaturation. Induction periods,crystal numbers and final sizes

The precipitation of calcium carbonate was studied by slow addition of anion solution to excess cation solution and by slow mixing of equivalent cation land anion solutions at 20 °C: the final solute concentrations (C_fin were varied from 0.01 to 0.75 mole 1⁻¹ while the rates (R) of addition of ions were varied from 0.06 to 6 · 10⁻³ ion 1⁻¹ sec⁻¹. At first, mainly heterogeneous nuclei formed continuously during induction periods; then, as the metal salt concentration in solution increased, some more heterogeneous nuclei formed but homogeneous nucleation soon predominated. The second nucleation process probably attained its maximum rate when the metal salt concentratio in solution reached its maximum value (C_max) and then probably terminated quite rapidly. Some further nuclei also formed during the growth process when crystal growth was prolonged. The final nucleus numbers (N) (and thence the crystal numbers) for slow precipitations from dilute solutions were then rather higher than the optimum number N∞ (het) of heterogeneous nuclei in the solution; nucleus numbers then increased with increasing maxing rate according to the relations . These numbers were similar to those noted for rapid precipitation – onto homogeneous nuclei – from calcium carbonate solutions of concentrations somewhat lower than the C_max values. The final average crystal lengths of any precipitate then generally varied with mixing rate according to the relations, . where l₁ values increased with (C_fln)^0.33.     

The precipitation of barium sulphate and chromate powders from aqueous solution with slow development of supersaturation. Crystal numbers and final crystal sizes

The precipitations of barium sulphate and chromate were studied by slow addition of anion to metal cation solution at 20°C, to give final equivalent metal salt solutions; the final solute concentrations (C_fin) were varied from 0.002 to 0.30 mol l⁻¹ while the rates (R) of addition of anion were varied from 10⁻⁴ to 10⁻² ion l⁻¹. At first, mainly heterogeneous nuclei formed continuously during induction periods; then, as the metal salt concentration in solution increased, homogeneous nucleation soon predominated. This second nucleation process probably attained its maximum rate when the metal salt concentration in solution reached its maximum value (C_max) and then probably terminated quite rapidly. Some further nuclei also formed during the growth process when crystal growth was prolonged. The final nucleus numbers (N), and thence the crystal numbers for slow precipitations from very dilute solutions were then rather higher than the number N ∞ (het) of heterogeneous nuclei in solution: nucleus numbers then increased with increasing mixing rate according to the relation, (where β = 0.7–0.9) (where β = 0.7–0.9). The final average crystal lengths of any precipitate were then 2 to 40 times the sizes noted for rapid precipitation from equivalent solutions of the same concentration: generally, final lengths varied with mixing rate according to the relation, .     

Mathematical Description of Strongly Nonlinear Pressure Dependence of Phase Transition Temperatures

In order to describe mathematically the pressure dependence of phase transition temperatures we have derived an equation using the following assumption: i. The transition enthalpy Δ_tH = const. ii. The transition volume Δ_tV depends on the pressure p according to: The modified Simon-Glatzel-equation T = T₀(1 + p/b)^a exp (cp) allows to calculate the transition temperatures T also in cases of strongly non-linear relations.     

The precipitation of alkaline-earth metal and transition metal ‘oxinate’ powders from aqueous solution. Crystal numbers and final sizes

The precipitation of barium strontium, calcium, magnesium, zinc, cadmium and lead, manganese, cobalt, nickel and copper 8-quinolinolates (‘oxinates’) was studied from equivalent solutions, at pHs from 4.5 to 10, by optical microscopy: the metal cation and overall ‘oxinate’ with ‘oxine’ concentrations were varied from 0.0002 to 0.020 M (while the mean metal oxinate concentrations varied from 10⁻⁷ to 0.001 M). Crystal growth started after induction periods; the precipitations were heterogeneously nucleated at low supersaturations and homogeneously nucleated at medium to high supersaturations. The final precipitate crystal numbers depended on the number of nuclei formed during the induction periods. Crystal numbers at medium to high supersaturations increased with increasing initial metal oxinate concentration according to the relation, The final crystal lengths in this supersaturation range then decreased (from maximum values) with increasing initial mean metal oxinate concentration according to the relation, For precipitation from solutions of any concentration at any pH, smaller crystals were generally obtained in the precipitates from solutions of the metal oxinate of lower solubility.     

The crystallisation of alkaline-earth metal molybdates and tungstates from lithium chloride melts by continuous cooling. Nucleation mechanism and kinetics and induction periods

Calcium, strontium and barium molybdate (and tungstate) solutions in lithium chloride melts were crystallised in alumina and in platinum crucibles; saturated solutions were cooled from initial temperatures 700° to 800°C down to room temperature at cooling rates 40° to 200°C hr⁻¹. The nucleation and early crystal growth were investigated by chemical and differential thermal analysis and by optical microscopy studies. Crystallisation occurred through heterogeneous nucleation at low supersaturations. Heterogeneous nuclei formed slowly onto metal aluminate (and platinate) particles within the solution during induction periods from < 0.2 to 14 hr. The main growth surge then started and few new nuclei were formed. The nucleation probably terminated at times just after the times for maximum rate of formation of nuclei. Then, at any temperature, the induction periods (t ) varied inversely with cooling rate and with the rate (R_c) of development of excess solute concentration according to the relation, The parameters k₁ were related to the rate constants (k_n) for the heterogeneous nucleation. These constants in turn probably dependend on the free energy for formation of critical heterogeneous nuclei and thence on some nucleator vs solute surface energy ‘wetting’ function. The k₁ and k_n values at any temperature decreased in the order : they increased from 2 to 4 times for 100°C rise in temperature.     

Synthesis and crystal chemical characteristics of the structure of <Emphasis Type="Italic">M</Emphasis><Subscript>0.5</Subscript>Zr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> phosphates

Double phosphates of zirconium and metals with an oxidation degree of +2 of the composition M_0.5Zr₂(PO₄)₃ (M = Mg, Ca, Mn, Co, Ni, Cu, Zn, Sr, Cd, and Ba) are synthesized and characterized by X-ray diffraction methods and IR spectroscopy. The crystal structures of all the compounds are based on three-dimensional frameworks of corner-sharing PO₄-tetrahedra and ZrO₆-octahedra. Phosphates with large Cd²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ cations octahedrally coordinated with oxygen atoms form rhombohedral structures (space group R3), whereas phosphates with small tetrahedrally coordinated Mg²⁺, Ni²⁺, Cu²⁺, Co²⁺, Zn ²⁺, and Mn²⁺-cations are monoclinic (space group P2₁/n). The effect of various structure-forming factors on the M_0.5Zr₂(PO₄)₃ compounds with a common structural motif but different symmetries are discussed.     

Electric conductivity and lattice disorder of PbMoO4 crystals

From differential thermal analysis (DTA), thermal etching, perfectly reversable redox treatments and electric conductivity it is concluded that the Pb/Mo ratio of the PbMoO₄ crystals is always 1 and that phase transitions do not occur. Pb³⁺ ions detectable by an absorption band at 435 nm cause a p-conductivity due to the reaction Pb³⁺ ⇌ Pb⁺⁺ + e⁺. At elevated temperatures the p-conductivity increases with increasing oxygen partial pressure of the surrounding atmosphere. The influence of foreign ions on the concentration of ionic and electronic defects in PbMoO₄, CaMoO₄, PbO, and PbTiO₃ can be explained by an anti-Frenkel disorder of the oxygen ion sublattice. For PbMoO₄ crystals the mobility O⁻ ion vacancies and the free formation enthalpy of anti-Frenkel defects are found to be v_v = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop - \limits_T^{9160} $\end{document} exp (−1.15 eV/kT) cm² K/Vs and g_AF = 3.6kT −2.2 eV, respectively.     

Synthesis and crystal structure of a phthalate-bridged copper(II) complex {[Cu(L)(Phen)(H<Subscript>2</Subscript>O)]⋅H<Subscript>2</Subscript>O}<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

A phthalate-bridged copper(II) complex {[Cu(phth)(Phen)(H₂O)] H₂O}_n (H₂phth: phthalic acid, Phen: 1,10-phenanthroline) has been synthesized by the reaction of CuCl₂ and phthalic acid in the presence of 1,10-phenanthroline in aqueous solution. The crystal structure of the complex has been determined by X-ray diffraction analysis to be orthorhombic, with the centrosymmetric space group Pbcm, where a = 11.6652(3) Å, b = 11.1709(3) Å, c = 14.0532(4) Å, V = 1831.28(9) ų, Z = 4. The L^2– (the acid radical of H₂phth) ion is coordinated to the Cu²⁺ ion as a monodentate ligand. Each L^2– ion bridges two adjacent Cu²⁺ ions with its two oxygen atoms from two carboxylic groups to form a one-dimensional zigzag chain. The coordination water and uncoordinated carboxylic oxygen atoms from neighboring chains are linked through hydrogen bonds to form a two-dimensional structure. There is a weak interaction between the coordination water molecule and the Cu²⁺ ion in the neighboring chain.     

Synthesis and structure of a terephthalato-bridged nickel complex [Ni(tpt)(imi)<Subscript>3</Subscript>(H<Subscript>2</Subscript>O)]<Emphasis Type="Italic">n</Emphasis>

At room temperature, a new coordination polymer [Ni(tpt)(imi)₃(H₂O)]n was synthesized by the reaction of NiCl₂?6H₂O, terephthalic acid, and imidazole in aqueous solution. The structure was determined by X-ray crystallography. It crystallizes in monoclinicP2₁/n space group with the crystal cell parameters ofa = 9.8626(4) Å,b = 15.2498(3) Å, andc = 12.7681(3)Å, β = 90.309(2)^°,V = 1920.33(10) ų, andZ = 4. The crystal X-ray analysis shows that each nickel atom is coordinated by three imidazole ligands, two terephthalate ions, and one water molecule. Each terephthalate ion bridges two nickel atoms to form a zigzag chain. The chains are further linked together via hydrogen bonds to a three-dimensional network.     

Zum Reflexionsvermögen und Polarisationsverhältnis bei der Röntgenstrahlbeugung am Realkristall (I) Experimentelle Ergebnisse und Vergleich mit der Theorie

Experimental data, a lack of satisfactory theoretical discussion, and some practical problems (application of crystal monochromators, analysis of real structure) as well demand an improvement of the theory of integrated reflectivity, R_i, and of polarization ratio, p, in case of X-ray diffraction in thick real crystals (symmetrical Bragg case). Relatively simple expressions have been obtained concerning the diffraction process in a layer model containing dynamically diffracting mosaic blocks. They fit experimental results, especially the maximum of p at average crystal quality. The theory yields for that maximum p = \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {|\cos 2\Theta |} $\end{document} in case of strong primary and secondary extinction. This is, obviously, in better agreement with experimental work using ordinary monochromator crystals than expressions of the type p = cos² 2 Θ or | cos 2 Θ| or averages of them.     

The precipitation of alkaline-earth metal and transition metal oxalates from aqueous solution. Induction periods and nucleation rates

The precipitation of magnesium, calcium, strontium and barium oxalates and of manganous, ferrous, cobalt, nickel and copper oxalates was studied from equivalent aqueous solutions at 22°C: the initial overall concentrations (C) generally varied from 0.001 to 0.2 M and the saturation ratios (S_mox) varied from <10 to >3000. The induction periods before the main growth surge were measured and nucleation rates were determined from final crystal numbers and induction periods. Precipitation occurred through homogenous nucleation: the critical nuclei in supersaturated alkaline-earth metal oxalate solutions were formed by aggregation of 6–8 M⁺⁺Ox⁻ ion-pairs while the critical nuclei in supersaturated transition metal oxalate solutions were formed by aggregation of 6–8 MOx complexes (to units of 3–4 M⁺⁺MOx₂⁻ ion-pairs). Over the range studied, the nucleation rates then varied with saturation ratios according to the relation, Nucleation rates at any saturation ratio decreased in the order Mg > Sr, Ba > Ca and Fe > Mn > Co, Cu > Ni; that is, generally in the order of increasing M⁺⁺–Ox⁻ and M⁺⁺–MOx₂⁻ bond strengths and increasing surface energies of the metal oxalate crystals. Induction periods decreased with increasing-concentration and saturation ratio; over The factors t _C1 and t _S1 depended in turn on the ‘rate constants’ for nucleation and growth during the induction periods and on metal oxalate solubilities.     

Structure of (2,2′-bipyridine)lead(II) saccharinate monohydrate

The structure of (2,2-bipyridine)lead(II) saccharinate monohydrate has been investigated by X-ray diffraction. The compound crystallizes in the monoclinic space group P2 ₁/n with a = 22.903(7), b = 12.608(3), c = 8.682(2) Å, = 96.76(3)°, and Z = 4. The structure consists of Pb²⁺ cations, 2,2-bipyridine ligands, saccharinato anions and water molecules. The Pb²⁺ cation is surrounded by two O atoms and four N atoms. The two saccharinato ions are nonequivalent. The water molecule forms hydrogen bonds of O_W···O_CO [2.810(16) Å] and O_W···O_SO2 [2.893(16) Å] type.     

Increase in the Fluorine-Ion Conductivity of Single Crystals of Tysonite-type CeF<Subscript>3</Subscript> Superionic Conductor by Substituting Polarized Cd<Superscript>2+</Superscript> Ions for Ce<Superscript>3+</Superscript> Ions

The fluorine-ion conductivity of single crystals with a tysonite (LaF₃) structure with heterovalent isomorphic substitutions of highly polarizable Cd²⁺ cations with a 18-electron shell for rare earth ions Ce³⁺ have been studied for the first time. Ce_0.995Cd_0.005F_2.995 single crystals have been grown from melt by the Bridgman technique in a fluorinating atmosphere. The fluorine-ion conductivity of single crystal is measured by impedance spectroscopy in the temperature range from 153 to 1073 K, where it increases by a factor of 10⁹, approaching the value σ_dc = 5 × 10^–2 S/cm at 1073 K. At T₀ = 450 ± 20 K, the dependence σ_dc(T) is split into two portions with the ion-transport activation enthalpy ΔH_σ = 0.39 ± 0.01 eV (T < T₀) and ΔH_σ = 0.23 ± 0.02 eV (T > T0). It is found that at T = 293 K the conductivity σ_dc = 3 × 10^–5 S/cm of Ce_0.995Cd_0.005F_2.995 crystal is higher by a factor of 10 than the conductivity of the tysonite matrix CeF₃ and close to the σ_dc value for Ce_0.995Sr_0.005F_2.995 crystal. This finding indicates a significant effect of the substitutions of Cd²⁺ ions for Ce³⁺ on the σdc value and the advantage of Cd²⁺ ions over Ca²⁺ and Ba²⁺ from the viewpoint of increasing σ_dc.     

Synthesis and molecular structure of the organometallic zwitterion (η5-C5H3MeBCl3)Fe(CO)3: evidence for alternative sites of nucleophilicity within the [(η5-C5R5)Fe(CO)2 − anion

The organometallic zwitterion (⁵-C₅H₃MeBCl₃)Fe(CO)₃ (2) is isolated as a minor product from the reaction between the sodium salt of the anion [(⁵-C₅H₄Me)Fe(CO)₂]^– and boron trichloride. The crystal structure of 2 [P2₁/n, a = 7.3927(5) Å, b = 13.8027(9) Å, c = 12.2759(9) Å, = = 90°, = 92.517(3)°] features discrete molecules in which the coordination sphere of the iron center comprises three carbonyls and a novel ( ⁵-C₅H₃MeBCl₃) ligand, derived from attack of BCl₃ on the ( ⁵-C₅H₄Me) moiety of the parent compound. The isolation of 2 confirms that the nucleophilic properties of organometallic anions of the type [( ⁵-C₅R₅)M(CO) _n ]^– (M = Fe, Ru, n = 2; M = Mo, W, n = 3) are not confined to the metal center, or to the carbonyl oxygens (examples of which have previously been reported) but also encompass the cyclopentadienyl ligand.     

Tetra-n-butylammonium bromide-thiourea (1/2), a layer-type inclusion compound

The inclusion compound built of tetra-n-butylammonium bromide-thiourea (1/2), [(n-C₄H₉)₄N⁺Br^– 2(NH₂)₂CS], has been prepared and characterized by X-ray crystallography. The compound crystalline in orthorhombic space group Pbca, with a = 16.872(6) Å, b = 17.214(6) Å, c = 18.561(6) Å, V = 5390(3) ų, Z = 8. The compound features a sandwich-like crystal structure built up from planar layers. In the crystal structure, zigzag hydrogen-bonded thiourea ribbons are linked by bromide anions to generate puckered layers matching the (100) planes, and the (n-C₄H₉)₄N⁺ cations occupy the intervening space.