Average Ln Research Articles

General Synthesis and Structural Evolution of a Layered Family of Ln8(OH)20Cl4·nH2O (Ln = Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Y)

The synthesis process and crystal structure evolution for a family of stoichiometric layered rare-earth hydroxides with general formula Ln(8)(OH)(20)Cl(4) x nH(2)O (Ln = Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Y; n approximately 6-7) are described. Synthesis was accomplished through homogeneous precipitation of LnCl(3) x xH(2)O with hexamethylenetetramine to yield a single-phase product for Sm-Er and Y. Some minor coexisting phases were observed for Nd(3+) and Tm(3+), indicating a size limit for this layered series. Light lanthanides (Nd, Sm, Eu) crystallized into rectangular platelets, whereas platelets of heavy lanthanides from Gd tended to be of quasi-hexagonal morphology. Rietveld profile analysis revealed that all phases were isostructural in an orthorhombic layered structure featuring a positively charged layer, [Ln(8)(OH)(20)(H(2)O)(n)](4+), and interlayer charge-balancing Cl(-) ions. In-plane lattice parameters a and b decreased nearly linearly with a decrease in the rare-earth cation size. The interlamellar distance, c, was almost constant (approximately 8.70 A) for rare-earth elements Nd(3+), Sm(3+), and Eu(3+), but it suddenly decreased to approximately 8.45 A for Tb(3+), Dy(3+), Ho(3+), and Er(3+), which can be ascribed to two different degrees of hydration. Nd(3+) typically adopted a phase with high hydration, whereas a low-hydration phase was preferred for Tb(3+), Dy(3+), Ho(3+), Er(3+), and Tm(3+). Sm(3+), Eu(3+), and Gd(3+) samples were sensitive to humidity conditions because high- and low-hydration phases were interconvertible at a critical humidity of 10%, 20%, and 50%, respectively, as supported by both X-ray diffraction and gravimetry as a function of the relative humidity. In the phase conversion process, interlayer expansion or contraction of approximately 0.2 A also occurred as a possible consequence of absorption/desorption of H(2)O molecules. The hydration difference was also evidenced by refinement results. The number of coordinated water molecules per formula weight, n, changed from 6.6 for the high-hydration Gd sample to 6.0 for the low-hydration Gd sample. Also, the hydration number usually decreased with increasing atomic number; e.g., n = 7.4, 6.3, 7.2, and 6.6 for high-hydration Nd, Sm, Eu, and Gd, and n = 6.0, 5.8, 5.6, 5.4, and 4.9 for low-hydration Gd, Tb, Dy, Ho, and Er. The variation in the average Ln-O bond length with decreasing size of the lanthanide ions is also discussed. This family of layered lanthanide compounds highlights a novel chemistry of interplay between crystal structure stability and coordination geometry with water molecules.

1D‐Polyoxometalate‐Based Composite Compounds − Design, Synthesis, Crystal Structures, and Properties of [{Ln(NMP)6}(PMo12O40)]n (Ln = La, Ce, Pr; NMP = N‐methyl‐2‐pyrrolidone)

AbstractThe structures of three 1:1 composite compounds prepared with the polyoxometalate (POM) [PMo12O40]3− and the cations [Ln(NMP)6]3+ [Ln = La (1), Ce (3), Pr (2); NMP = N‐methyl‐2‐pyrrolidone] exhibit two types of zig‐zag chains with alternating cations and anions through Mo−Ot−Ln−Ot−Mo links in the crystal. The compounds were characterized by IR, UV, and ESR spectroscopy, single‐crystal X‐ray structural analysis, and by a study of their thermal properties. In all the compounds, the La3+, Pr3+, and Ce3+ centers are eight‐coordinate with the oxygen atoms in bicapped trigonal‐prismatic geometries. The variation of the average Ln−O separations along the La, Ce, and Pr series is consistent with the effects of the lanthanide contraction. The results of the single‐crystal X‐ray diffraction analyses and the IR spectroscopic studies are in agreement and both show the metal cation units are coordinatively bonded to the Keggin clusters. The UV spectra of the title compounds suggest that their structures are entirely disrupted in dilute solution. Low‐temperature ESR spectra indicate that thermal electron delocalization occurs among the Mo atoms in the three compounds. The results of cyclic voltammetry (CV) show that compounds 1, 2, and 3 all undergo five two‐electron reversible reductions and that the [PMo12O40]3− anions are the active centers for electrochemical redox reactions in solution, while the corresponding cations have only a small effect on the electrochemical properties. Studies of magnetic properties show that 1 is diamagnetic, while 2and 3 exhibit antiferromagnetic Pr−Pr or Ce−Ce exchange interactions. In addition to the results of CV, the average bond lengths and the magnetic properties of compound 3 indicate that the oxidation state of cerium is III in the compound of formula [{Ce(NMP)6}(PMo12O40)]n. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2004)

Crystal Structures and Magnetic Properties of Ordered Perovskites Ba2LnNbO6 (Ln=Lanthanide Elements)

A series of double-perovskite oxides Ba2LnNbO6 (Ln=lanthanide elements) were synthesized. Their powder X-ray diffraction measurements and Rietveld analysis show that they are monoclinic with space group P21/n and that Ln3+ and Nb5+ ions are structurally ordered. Although the average Ln–O bond length increases with the ionic radius of Ln3+, the average Nb–O bond length is nearly constant for all the Ba2LnNbO6. Magnetic susceptibility measurements show that they are paramagnetic down to 2 K. The 151Eu Mössbauer spectrum for Ba2EuNbO6 indicates that the Eu ion is in the trivalent state and a quadrupole interaction exists in this compound. Both the magnetic susceptibility and the electron paramagnetic resonance (EPR) spectrum measurements show that the Gd3+ ion is in the 8S7/2 state. In addition, the anisotropic EPR spectrum indicates that the six oxygen coordination around the Gd3+ ion has no longer a perfect octahedral symmetry.

Syntheses, characterization and crystal structures of 5,14-dihydro-6,8,15,17-tetramethyldibenzo[b,i][1,4,8,11]tetraazacyclotetradecine rare earth(III) complexes

Rare earth(III) complexes of tmtaa, Ln(tmtaa)(Htmtaa)·0.6CH2Cl2 (Ln = Pr 1, Nd 2, Sm 3, Gd 4, Tb 5, Er 6 and Yb 7; H2tmtaa = 5,14-dihydro-6,8,15,17-tetramethyldibenzo[b,i][1,4,8,11]tetraazacyclotetradecine) were prepared by reaction of Li2tmtaa with LnCl3(THF)3 in tetrahydrofuran (THF). The complexes were characterized by infrared, mass and electronic spectra as well as DSC measurement. The crystal structures of Ln(tmtaa)(Htmtaa)·0.6CH2Cl2 (Ln = Sm 3, Tb 5, Er 6 and Yb 7) were determined by X-ray crystal diffraction. The complexes are isomorphous and the crystals belong to a monoclinic crystal system with the space group of C2/m. The rare earth(III) ions in the complexes are coordinated by eight nitrogen atoms from tmtaa and Htmtaa to form eight-coordinate sandwich complexes. The average Ln–N bond lengths for tmtaa and Htmtaa are 2.463(7) and 2.543(7) A for 3, 2.438(7) and 2.540(7) A for 5, 2.406(9) and 2.474(9) A for 6 and 2.388(8) and 2.495(8) A for 7, respectively. The tmtaa and Htmtaa in the complexes adopt markedly saddle conformations and coordinate to the rare earth(III) ions as delocalized conjugated π-electron systems. The acidic hydrogen in the complexes does not bind strongly to any of the nitrogen atoms of tmtaa or Htmtaa, but may belong to the four nitrogen atoms of Htmtaa. The influences of sandwich structures on the dihedral angles of the ligands were studied.

Crystallization of LnCu2O4 (Ln = La, Nd, Sm, Eu, Gd, Dy, Ho, Y, Er) from Hydroxide Melts: Synthesis and Structure

The synthesis and structure of LnCu2O4 with Ln = La, Nd, Sm, Eu, Gd, Dy, Ho, Y, and Er are reported. These cuprates were synthesized by precipitation from NaOH/KOH at 350−400 °C under ambient conditions. The effects of changing the relative amounts of NaOH and KOH, the quantities of the starting reagents, the reaction temperature, and the time at which the reagents were added on the yield, purity, and crystallinity of LnCu2O4 are described. Generally, the formation of LnCu2O4 is favored in dry, highly oxidizing melts with large quantities of dissolved reactants. Powder X-ray diffraction data were used to refine the structure of the various analogues using Rietveld profile analysis. The lattice parameters and average Ln−O distances decrease with decreasing size of the lanthanide ion. The average Cu−O bond distances, on the other hand, do not significantly change with the size of the lanthanide ion.

749-2 Autonomic Imbalance in Patients with Inappropriate Sinus Tachycardia

Mechanisms responsible for inappropriate sinus tachycardia (IST) may include an intrinsic defect in the sinus node, autonomic imbalances, or both. To disclose the existence of spontaneous autonomic abnormalities, we analyzed heart rate variability (HRV) in 24-hour ECG recordings in 6 ambulatory adult pts with IST (defined as 24-hr average heart rate ≥ 95 bpm) and in 6 ageand sex-matched normal controls. All subjects were free of heart disease, diabetes, and autonomic disfunction. Mean average HR was 98 ± 2.6 bpm in pts with IST and 69.6 ± 7 bpm in controls. Percent of difference between adjacent RR intervals greater than 50 msec (pNN50) was 2.63 in pts and 23.9 in controls (p < 0.001). Standard deviation of RR intervals (SDNN), root mean square of successive differences (RMSSD), and standard deviation of 5-minute RR intervals (SDANN)forthe 24 hour period were significantly lower in pts than in controls for both day- and night-times (table). SDNN RMSSD SDANN Day Night Day Night Day Night Patients 47.59 51.22 19.04 23.4 62.3 30.7 Controls 98.1 97.78 41.9 58.55 50.55 29.9 P value < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 0.01 Hourly variation for RMSDDs is plotted in the figure. Low and high frequency (freq) power were estimated at 10-min intervals throughout the 24 hour-period. Average Ln of low freq power was 10.26 in pts with IST and 11.27 in controls (p = 0.09). Average Ln of high freq power was 9.81 in pts and 11.31 in controls (p = 0.002). 1) HRV is markedly decreased in pts with IST; 2) This seems to be related to an abnormally low parasympathetic tone; 3) The long-term prognosis of pts with IST deserves further investigation.

Dehydrogenation of organolanthanide alkoxides and X-ray crystal structures of the reaction product [{(C 5H 5) 2Ln(μ-O(Me)CCHCH 3)} 2] (Ln  Dy Yb)

Reaction Of Cp 3Ln (CpC 5H 5; Ln  Dy, Yb) with 2-butanol in THF (THF = tetrahydrofuran) at room temperature yielded the complexes [Cp 2Ln(μ-OCH(Me)CH 2CH 3)] 2 [Ln  Dy ( 1, Yb ( 2)], which have been characterized by elemental analysis, IR and MS spectra. The complexes 1 and 2 have been dehydrogenated to give the new enolate complexes [Cp 2Ln(μ-O(Me)CCHCH 3)] 2 [Ln  Dy ( 3), Yb ( 4)] upon refluxing in THF solution. The new complexes 3 and 4 have been structurally characterized by single-crystal diffraction studies. Complexes 3 and 4 crystallize from THF solution as isomorphous crystals of space group Pnnm with the following unit cell parameters: 3[ 4]; a = 9.910(5X9.853 (3)], b = 10.940(2)[10.917(3)] c = 12.258(2) [12.151(3)] Å, V= 1329(1)1307(1)] Å 3, Z = 2, Dc = 1.82[1.90] g cm −3, R = 0.025[0.042], R w = 0.036[0.0491. The molecules are oxygen-bridged dimers. The bridging unit Ln 2O 2 is completely planar. The metal atom is coordinated by two η 5-Cp groups and two oxygen atoms of enolate ligands to form a pseudotetrahedral geometry. The average LnC bond lengths for 3 and 4 are 2.668(6) and 2.629(9) Å, respectively. The LnC distances of 3 and 4 are 2.256(4) and 2.210(2) Å, respectively. Complex 4 has been hydrolysed to give the organic compound CH 3COCH 2CH 3, which has been confirmed by NMR spectra.

NUMERICAL STUDIES OF RESISTANCE AND CONDUCTANCE FLUCTUATIONS IN CHAINS WITH CONTINUOUS DISORDERED POTENTIALS

We have studied the behaviour of resistance and conductance vfluctuation in disordered chains, using the invariant embedding approach. Length dependence of the average ln (1 + ρ), where ρ is the resistance of the sample, is linear for all values of ρ. We have shown that in the mesoscopic regime the conductance fluctuation in this model is almost constant with length and takes a value about 0.26 independent of the degree of disorder. These fluctuations die down at large lengths beyond mesoscopic region. This is entirely because of coherent backscattering due to disorder and has nothing to do with inelastic scattering which is absent in our model.

Multidimensional diffusion in random potentials.

It is shown that, in the long-time limit, d-dimensional diffusion in a Gaussian random potential has the logarithm of the average population ln 〈P〉 growing as ${t}^{(2\mathrm{\ensuremath{-}}d/2)}$. The dimension d=4 is critical. For d\ensuremath{\ge}4, 〈P〉 only grows as a power of t. Numerical simulations have confirmed this result.

Some average performance measures for the B-tree

Several average performance measures are presented for large B-trees formed from insertions, where large refers to the number of keys. Formulas are first derived for the expected number of nodes of each size on the bottom level of the tree, where the size of a node is the number of keys currently contained in the node. This is followed by formulas for the probability of making an insertion into a node of a given size, the probability of a split during an insertion into a node, and the expected number of splits during an insertion into the tree. It is shown that for large trees of high order m, the expected number of splits per insertion is approximately 1/((ln 2) m). A formula is presented for the average storage utilization, and it is shown that this average approaches ln 2 as m approaches infinity. A simpler formula is derived for the average storage utilization at the bottom level of the tree, and it is shown that this formula is an increasing function of m ranging from 2/3 to ln 2. It is shown that the expected tree height and the expected search path length are approximately logarithmic to the base (ln 2) m. Simulation results are presented to corroborate the theoretical analysis.

Crystal and molecular structures of [AsPh4][Ln(S2PMe2)4](Ln = Ce or Tm) and their comparison with results obtained from paramagnetic nuclear magnetic resonance data in solution

The crystal structures of the title compounds have been determined from diffractometer data. The crystals of the cerium compound are tetragonal, space group P4222 with four molecules in the unit cell of dimensions a= 11.461(2), c= 33.479(6)A(R= 0.060). The thulium analogue is orthorhombic, space group Pca21 with four molecules in the unit cell of dimensions a= 19.899(3), b= 11.451(2), c= 19.051(2)A(R= 0.037). In both compounds the lanthanide ion is co-ordinated to eight sulphur atoms with average Ln–S distances of 2.991 A(Ce) and 2.870 A(Tm). The co-ordination polyhedra are D2d, dodecahedra (mmmm isomer) distorted towards the D2 square antiprism, the cerium compound having two independent molecules in the unit cell, both with 222 crystallographic symmetry. Despite the difference in crystallography between the Ce and Tm compounds, the molecular structures are quite similar in the solid state. However, in solution this is not the case as shown by paramagnetic n.m.r. data. The 31P dipolar shifts are shown to be in accord with a change from dodecahedral to square-antiprismatic geometry when Ln = Dy.

ChemInform Abstract: CRYSTAL AND MOLECULAR STRUCTURES OF (ASPH4)(LN(S2P(OET)2)4) (LN = LA OR ER) AND THEIR COMPARISON WITH RESULTS OBTAINED IN SOLUTION FROM PARAMAGNETIC NUCLEAR MAGNETIC RESONANCE DATA

The crystal structures of the title compounds have been determined from diffractometer data. The crystals of both compounds are monoclinic, space group P21/c, and have four molecules in unit cells of dimensions: Ln = La, a= 20.053(7), b= 15.207(3), c= 20.389(4)A, β= 112.02(2)°(R= 0.071); Ln = Er, a= 19.972(3), b= 15.148(2), c= 20.244(3)A, β= 112.27(1)°(R= 0.059). In both cases the lanthanide ion is co-ordinated to eight sulphur atoms, the average Ln–S distances being 2.989 (La) and 2.858 A(Er). The co-ordination polyhedra are both almost perfect D2d dodecahedra (mmmm isomer). Although the compounds have similar structures in the solid state, in solution they are quite different as demonstrated by paramagnetic n.m.r. data. The change in the observed 31P dipolar shift is shown to be in accord with a change from dodecahedral to square antiprismatic geometry for such compounds when Ln = holmium.

Crystal and molecular structures of [AsPh4][Ln{S2P(OEt)2}4](Ln = La or Er) and their comparison with results obtained in solution from paramagnetic nuclear magnetic resonance data

The crystal structures of the title compounds have been determined from diffractometer data. The crystals of both compounds are monoclinic, space group P21/c, and have four molecules in unit cells of dimensions: Ln = La, a= 20.053(7), b= 15.207(3), c= 20.389(4)A, β= 112.02(2)°(R= 0.071); Ln = Er, a= 19.972(3), b= 15.148(2), c= 20.244(3)A, β= 112.27(1)°(R= 0.059). In both cases the lanthanide ion is co-ordinated to eight sulphur atoms, the average Ln–S distances being 2.989 (La) and 2.858 A(Er). The co-ordination polyhedra are both almost perfect D2d dodecahedra (mmmm isomer). Although the compounds have similar structures in the solid state, in solution they are quite different as demonstrated by paramagnetic n.m.r. data. The change in the observed 31P dipolar shift is shown to be in accord with a change from dodecahedral to square antiprismatic geometry for such compounds when Ln = holmium.

Ground-state entropy of the infinite-range model of a spin glass

It is proved that, for the infinite-range spin glass proposed by Sherrington and Kirkpatrick (1972), the logarithmic average of the ground state degeneracy (lng0((J)))J is given by the logarithm of the average ln(g0((J)))J, so that the zero temperature entropy S0 is given by S0/kb=ln(g0((J)))J=0.19923 N from the known value of (g0((J)))J.

Comments on amplitude dependent damping in zirconium

Data and arguments are presented to show that the analytical results by Fernandez and Povolo [Phil. Mag., 31: 1081 (1975)] on damping versus strain amplitude spikes in Zr containing small quantities of H at 77$sup 0$K are incorrect. It is noted that for this analysis to yield reasonable values of Ln/ Lc where Lc is the average loop length and Ln is the constant network lengths, the temperature, T, must be very small implying that very few dislocations take part in the breakaway process. This is the case if fresh dislocations associated with the hydride particles are responsible for the spikes. This invalidates the analysis by Fernandez and Povolo. (JRD)