Infrared absorption spectra of some lanthanide acetylacetonate complexes

The infrared absorption spectra of 12 lanthanide acetylacetonate complexes were measured in the region 400–2000 cm^?1 and discussed. Assignments of the bands especially those due to metal-oxygen (M—O), C=O and C=C stretching vibration is given. It is found that the band at 530 ± 5 cm^?1 is due mainly to Ln—O stretching vibration. In the carbonyl region, it is confirmed that the band at lower frequency is a C=C stretching vibration while that at higher frequency is due to C=O stretching vibration. Integral intensities for the M—O, C=O and C=C stretching vibrations were calculated in KB₁ and CHCl₃ solutions. The variation of the intensities of the M—O bands witn complexed cation were discussed in terms of crystal field stabilization energy (CFSE).     

Optical absorption of Co2+ doped NH4Cl: Phase transformation studies

The absorption spectrum of Co²⁺ doped NH₄Cl has been studied from the room temperature to the liquid nitrogen temperature. A sudden change in the spectrum is observed between 243° K and 233° K which is attributed to the phase transition in the crystal. From the observed spectrum it is suggested that Co²⁺ goes in interstitially as well as substitutionally. Both the types of centers exist at room temperature, but with decrease in temperature substitutional ions migrate to interstitial sites, the process being stimulated at the phase transformation point so that the 77° K spectrum seems to be mostly due to the interstitial centers. The 77° K spectrum is analyzed in the approximation of octahedral symmetry for interstitial ions and the band positions are fitted fairly well with B = 870 cm.^?1 Dq = 850 cm.^?1 and C = 4·4 B. A blue shift of about 100 cm.^?1 is observed for⁴T₁ (P) band at the phase transition which is attributed to the increase in Dq value with the anomalous lattice contraction at the phase transition. The decrease in the lattice parameter calculated from this blue shift is around 0·4% which is in good agreement with the results of X-ray measurements. Two possible models for the interstitial complex are examined and the one with fourfold chlorine coordination associated with two neutral water molecules at the first neighbour (NH₄)⁺ site lying along < 100> direction is suggested to be more probable.     

The near ultraviolet absorption spectrum of tetrahydro-naphthalene

The near ultraviolet absorption spectrum of tetrahydronaphthalene commonly known as tetralin consists of sharp bands in the region from 2800 to 2500 Å. The spectrum consists of about sixty bands. The maximum number of bands is obtained by using a path length of 200 cm. at room temperature which was nearly 30° C. Several of these very sharp bands have to be assigned tov-v transitions. The 0, 0 band is chosen to be at 36790 cm^?1. Vibrational frequencies in the excited state have values 1185, 951 and 682 and combinations and overtones of these are present. Assignments of the different frequencies are discussed.     

Forbidden hyperfine transitions in electron spin resonance of Mn2+ in NaCl single crystal

Forbidden hyperfine transitions are observed in the electron spin resonance spectrum of divalent Mn⁵⁵ ion in NaCl single crystal for a particular associated pair. From the measurements of the M = + 1/2 → ?1/2, Δm = ± 1 transitions the parametersQ′ and Q″ of the nuclear electric quadrupole part of the spin-Hamiltonian H_o = Q′ [I_z ² ? 1/3 I (I + 1)] + Q″ (I_x ²?I_y ²) are found to be + 1.70 × 10^?4 cm.^?1 and +0.16 × 10^?4 cm.^?1 respectively.     

Infrared spectrum of ferroelectric lithium hydrazinium sulphate [Li (N2H5) SO4]

Dielectric observations on lithium hydrazinium sulphate have shown earlier that it is ferroelectric over a range of temperatures from below ?15° C. to above 80° C. and a new type of hydrogen bond rearrangement which would allow the protons to migrate along the chain has also been suggested by others. The infrared spectrum of LiH _z S in the form of mull and as single crystal sections parallel and perpendicular to the ‘C’ axis exhibit about 21 well-defined absorption maxima. The position and the width of the maxima agree with the known structure of the crystal according to which the hydrazine group exists in the form of the hydrazinium ion, NH₂·NH ₃ ⁺ and the observed N⁺-H frequencies agree better with the new correlation curve given by R. S. Krishnan and K. Krishnan (1964). However it has been pointed out that from a comparative study of the new infrared spectra of hydrazonium sulphate and lithium ammonium sulphate that the absorption band at 969 cm.^?1 is due to N-N stretching vibration and that the fairly intense band between 2050–2170 cm.^?1 is due to the bending vibrations of the NH ₃ ⁺ group.     

The near ultraviolet absorption spectra ofortho- andmeta-thiocresols

The absorption spectra ofortho- andmeta-thiocresols have been studied in the present investigation. The ortho-thiocresol spectrum consists of about forty-five bands of rather a diffuse nature and in general low intensity in the region from 2873 Å to 2600 Å. The maximum number of bands is obtained by using a path length of 330 cm. for absorption, the temperature of the bulb being maintained at 14°C. Several of these bands are assigned as due tov-v-transitions. The (0, 0) band is chosen at 35386 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 729, 957 and 1159 and combinations and overtones of these are present. Themeta-thiocresol spectrum consists of about forty bands of rather a diffuse nature and very weak intensities in the region from 2900 Å to 2590 Å. The maximum number of bands is obtained by using a path length 200 cm. for absorption and by keeping the temperature of the bulb at 20° C. The (0, 0) band is chosen to be that at 34793 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 492, 611, 720, 845, 965, 1016 and 1155 cm.^?1 and combinations and overtones of these are present.     

The near ultraviolet absorption spectrum ofpara-thio-cresol

The absorption spectrum ofpara-thio-cresol consists of about ten bands in the region 2922 to 2600 Å. The bands are quite intense but broad and fail to show any structure such as is observed in the case ofpara-cresol bands. The maximum number of bands about ten is obtained by using an absorption path length of 100 cm. The (0, 0) band is chosen to be that at 34222 cm.^?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 353, 752 and 1114 and combinations and overtones of these are found to be present.     

The1I6 state of Pr3+ in LaCl3 at 77°K

A single crystal of 5% Pr³⁺ in LaCl₃ was grown by Stockbarger’s method and its absorption spectrum at 77° K. recorded in the region 4200–5400 Å on a grating spectrograph having a dispersion of 5 Å/mm. in the first order. Polarization of the absorption lines has also been obtained. In the group of lines arising from¹I₆ ←³H₄ transition, six more lines in addition to the four previously known have been observed. Satisfactory analysis of all these ten lines is given. One additional Stark level in¹I₆ is established at 21407 cm.^?1 withμ=1. For a few lines the polarization results obtained here do not agree with those of previous workers but fit in satisfactorily in the analysis.     

Dinuclear copper (II) and nickel (II) systems with planar M2N2O2 bridge

The tridentate ligand systemb (abbreviated as inkR₂) readily yield copper (II) and nickel (II) species of the formula M₂ (inkR₂)₂(CLO₄)₂. 2xH₂O (x=0–1). Dinuclear formulation is based on variable temperature magnetic susceptibility and conductivity data and on the known structure of some related systems. The Cu₂ (inkR₂) ₂ ²⁺ species are strongly antiferromagnetic (?2J=600–800 cm^?1) while the Ni₂(inkR₂) ₂ ²⁺ species are diamagnetic. The major coordination sphere is planar around each metal (II). The metal ions in a dimer are linked by planar M₂N₂O₂ bridge. The copper (II) and nickel (II) species freely form solid solutions. In these statistical scrambling of copper and nickel occur among the metal ion sites of the dimeric structure. Powder epr spectra of such mixed crystals are indicative of axial geometry around copper (II) ion.     

The diamond: Its structure and properties

A critical study of the crystal forms of diamond from various sources demonstrates that the symmetry of the structure may be either that of Class 32 or Class 31, in other words that the structure may be either centrosymmetric or non-centrosymmetric. Diamonds belonging to Class 31 may however exhibit a pseudo-octahedral symmetry of external form by reason of the interpenetration of oppositely directed structures having the lower symmetry. The existence of diamond with two differing structures provides an insight into the many remarkable properties of this material,viz., the striking differences observed in the infra-red absorption spectra, differences in transparency to ultra-violet rays, the differences in the intensity of their X-ray reflections and the variations in the intensity and colour of the luminescence exhibited by them. The modes of atomic vibration in diamond can be completely described and their frequencies evaluated by very simple procedures. The vibration frequencies can be determined experimentally by observations of the frequency shifts in the scattering of light or by infra-red spectroscopy, the results by the two methods being fully in agreement. The heat capacity of diamond may then be computed, giving results in highly satisfactory concordance with the observational data. The principal mode of atomic vibration having a frequency of 1332 cm.^?1 is triply degenerate. These vibrations can be excited in the lattice planes of diamond by the incidence of monochromatic X-rays if it belongs to crystal Class 31. The three-fold degeneracy of the vibration reveals itself as the three distinct spots in the resulting dynamic X-ray reflection by the octahedral lattice planes. The complete electronic frequency spectrum of diamond has been evaluated by a very simple procedure. The results are highly successful in explaining the known optical and spectroscopic properties of diamond.     

Phase transitions of the Moran process and algorithmic consequences

The Moran process is a random process that models the spread of genetic mutations through graphs. On connected graphs, the process eventually reaches “fixation,” where all vertices are mutants, or “extinction,” where none are. Our main result is an almost‐tight upper bound on expected absorption time. For all ?>0, we show that the expected absorption time on an n‐vertex graph is o(n^3+?). Specifically, it is at most , and there is a family of graphs where it is Ω(n³). In proving this, we establish a phase transition in the probability of fixation, depending on the mutants' fitness r. We show that no similar phase transition occurs for digraphs, where it is already known that the expected absorption time can be exponential. Finally, we give an improved fully polynomial randomized approximation scheme (FPRAS) for approximating the probability of fixation. On degree‐bounded graphs where some basic properties are given, its running time is independent of the number of vertices.     

The crystal and molecular structure of 3, 4-dihydroxy L-phenyl-alanine

The molecule crystallizes in spacegroup P2₁ with two molecules per unit cell. The unit cell dimensions area = 6.044 Å,b = 13.607 Å,c = 5.311 Å,γ = 97.55°. The density was calculated to be 1.512 g.ml.^?1 and found to be 1.51 g.ml.^?1 The major atoms were located by the reliable image method and the hydrogen atoms were located from a difference electron density map. Full-matrix least squares refinement of the parameters yielded an unweighted residual indexR of 0.088. The bond lengths and angles of the amino acid grouping are consistent with values in other amino acids. The structural parameters of the aromatic system are very similar to those of noradrenaline and dopamine hydrochlorides. The crystal structure is dominated by a three-dimensional intermolecular hydrogen bonding system. The molecular conformation is different from that displayed by any other aromatic amino acid or peptide whose crystal structure is known.     

On regular polyhedra with hidden symmetries

We consider polyhedral realizations of oriented regular maps with or without self-intersections in E³ whose symmetry group is a subsgroup of small index in their. automorphism group. The four classical kepler-poinsot polyhedra are the only ones of index 1. There are exactly five of Index 2, all with icosahedral symmetry group [W2] as the Kepler-poinsot polyhedra. In this paper we show that there are no such polyhedral realizations with octahedral (tetrahedral) symmetry group and index 2 or 3 (2,3,4,5), which is best possible in the octahedral case.     

Mixed complexes of iron (III)—thiocyanate with some nitrogen and oxygen donors and their analytical applications

Methods for the determination of iron (III) as thiocyanate complex in the presence of neutral donors like isoquinoline and antipyrine have been developed. The two methods are of equal sensitivity (ε=18,000±100 lit. mole^?1 cm^?1) but operate at widely different hydrogen ion concentrations ranging from 10^?5 N(pH 5·0) to 7N. The interference of various foreign substances has been studied in the two methods. The application of these methods in the analysis of alloys and commercial HCl for iron has been explored and the composition of the extracting species established.     

Role of chloride ions in relation to copper corrosion and inhibition

Corrosion rates of copper single crystal faces are determined in stirred 0·1N sulphuric acid with various chloride ion concentrations. A mechanism is proposed to explain the variation of corrosion rate with Cl^? ion concentration. Up to 7·5 × 10^?3 M Cl^? ions, the stabilities of the crystal faces are in the order (111)>(100)>(110) but this order is changed to (110)>(100)>(111) in presence of 10^?2 M Cl^? ions. The corrosion potentials of the crystal faces are less noble at all concentrations of Cl^? ions and Cl^? ion acts as a cathodic inhibitor. There is no significant orientation effect on the kinetics of dissolution of copper.     

Scattering and local absorption for the Schrödinger operator

We investigate the problem of local absorption for the Schrödinger operator H = ?Δ + V with potential V singular on a compact set ∑ of measure zero but sufficiently regular outside. In dimension n = 3 and for V?L² + L^∞ outside of ∑, Pearson proved that the subspace of absolute continuity of H can be decomposed as the direct sum of the subspace of scattering states and of the subspace of states locally absorbed on ∑. We extend this result to arbitrary dimension and to potentials that are only locally semibounded with respect to Δ in a suitable sense away from ∑ (in particular they may be strongly oscillating away from ∑ and have arbitrary behavior at infinity). As a by-product, we prove that certain types of local singularities do not interfere with the question of asymptotic completeness, thereby generalizing previous results by Deift and Simon.     

Emission spectrum of bismuth monochloride

Bismuth chloride has been excited in flowing condition with an uncondensed transformer discharge. About 390 bands are observed in the present experiments of which only 140 were recorded by earlier workers. The vibrational constants obtained are the same as those obtained by Morgan from obsorption experiments except for the addition of a cubic term for the upper state. It appears quite likely that the upper state of the system dissociates into Bi (⁴S_3/2) + Cl (²P_1/2) while the lower state, which is probably the ground state, dissociates into Bi (⁴S_3/2) + Cl (²P_3/2). The rough values of the dissociation energies obtained by extrapolations are D₀′=3750 cm.^?1 and D₀″=24614 cm.^?1     

Asymptotic behavior of number fields with prescribed ℓ-class numbers

Let K be a cyclic Galois extension of the rational numbers Q of degree ?, where ? is a prime number. Let h_? denote the order of the Sylow ?-subgroup of the ideal class group of K. If h_? = ?^s(s ≥ 0), it is known that the number of (finite) primes that ramify in K/Q is at most s + 1 (or s + 2 if K is real quadratic). This paper shows that “most” of these fields K with h_? = ?^s have exactly s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic). Furthermore the Sylow ?-subgroup of the ideal class group is elementary abelian when h_? = ?^s and there are s + 1 ramified primes (or s + 2 ramified primes if K is real quadratic).     

Electron spin resonance studies of the ligand exchange in cupric complexes with diethyldithiocarbamate and diethyldithiophosphate as ligands

The kinetics of ligand substitutions in the cupric complexes where a diethyldithiocarbamate (dtc^?) is replaced by a diethyldithiophosphate (dtp^?) has been studied with chloroform as solvent. The relative concentrations of the paramagnetic species produced in the reactions have been determined using electron spin resonance. The reaction studies suggest the presence of the short time equilibria: Cu (dtc)₂ + dtpH ? Cu (dtc) (dtp) + dtcH Cu (dtc) (dtp) + dtpH ? Cu (dtp)₂ + dtcH where the equilibrium constants have the value, 0.0625 and 0.00143 respectively. The equilibria are disturbed by the reaction: dtcH + dtpH → (C₂ H₅)₂ NH₂ ⁺ dtp^? + CS₂ with a rate constantk = 0.07 1. mole^?1 sec.^?1 at 26°C. Analysis of the thermodynamic parameters determined from the study of the kinetics of the reactions at various temperatures shows that dtp^? group favours more solvent and excess ligand coordination than dtc^?. This is consistent with the study of “Long time equilibrium” which indicates that Cu (dtp)₂ exists with further two weakly bonded dtpH groups in the axial positions in chloroform solutions.     

An infinite family of type (m,n) sets in PG(2,q2), q a square

A k-set of type (m,n), with k=(q+√q+1)(q²?q+1), m= 1+√q, n=q+√q+1, is proved to exist in a Galois plane PG(2,q²), q a square, and its construction is given. Thus, its complement, i.e. a ((q?√q)(q+√q+1)(q²?q+1); √q(q√q?√q?1),√q(q √q?1))-set, exists too. The special case q=16 is considered and the points of a (91;3,7)-set in PG(2,16) are exhibited. A generalization is given.