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Volume 67, Issue 3, 01 August 1977

Brillouin scattering studies of orientationally disordered sodium cyanide and potassium cyanide single crystals
View Description Hide DescriptionBrillouin spectra of acoustic phonons in the orientationally disordered phase in KCN and NaCN have been studied. The phonon frequencies have been determined as a function of temperature. The frequency of the transverse acoustic phonon propagating along (110) and polarized along (001) corresponds well with mean field theory for the phase transition for the two cyanide crystals. The elastic constants C _{11}, C _{12},, and C _{44} have been determined as a function of temperature in the cubic disordered phase. The Cauchy relation for cubic crystals is found to be invalid in KCN and NaCN. The two types of phase transitions in KCN and NaCN are discussed in terms of the vanishing shear modulii C _{44} and (C _{11}−C _{12})/2, each of which induces lattice instability when it becomes small. The integrated intensities of the shear modes in KCN and NaCN were also measured as a function of temperature. The intensity enhancement upon approaching the phase transition temperature has been found to be due to the decrease of C _{44}. The relative values of the elasto‐optical constant P _{44} in KCN and NaCN have also been determined as a function of temperature.

Electrical conductivity and charge compensation in Nb doped TiO_{2} rutile
View Description Hide DescriptionThe electrical conductivity of rutile doped with 0.04–3 at.% niobium is reported as a function of oxygen pressure in the temperature range 1273–1623 K. The charge compensation is discussed in terms of a point defect model, under the assumption of a substitutional incorporation of niobium into the titanium rutile sublattice. Two kinds of charge compensation occur according to the temperature and the oxygen pressure, via an electronic or a lattice defect, in a Ti_{1−y }Nb_{ y }O_{2} or a Ti_{1−y }Nb_{ y }O_{2+y/2}solid solution, respectively. In the overstoichiometric range of the oxide, the data, when applied to undoped rutile, allow some conclusions about the atomic or electronic transportproperties, both in the high and low temperature regimes.

YbH and YbD molecules: ESR and optical spectroscopy in argon matrices at 4 °K
View Description Hide DescriptionYbH and YbD molecules have been prepared by the reaction of Yb and H(D) atoms during the formation of an argon matrix at 4 °K. Yb atom and YbH absorption and emission spectra were observed. The magnetic parameters of YbH were determined from the ESRspectrum of the ^{2}Σ molecules (with Yb nuclear spinI=0 and I=1/2) to be g _{∥}=1.9953(4), g _{⊥}=1.9402(2), A _{∥}(H) =226 MHz, A _{⊥}(H) =224 MHz, A _{⊥}[^{171}Yb (I=1/2)]=5266 MHz, A _{∥}[^{171}Yb (I=1/2)]=5724 MHz. The hyperfine parameters indicate that the spin density is less than 20% on the hydrogen and that the bonding is largely Yb^{+}H^{−}. By comparison of experimental parameters with calculated Yb and Yb^{+} data it is deduced that the unpaired electron occupies predominately the 6sσ orbital on Yb^{+} with smaller contributions of 6pσ (Yb^{+}) and 1sσ (H^{−}).

Orientational dependence of spin–lattice relaxation in nematic liquid crystals
View Description Hide DescriptionWe have extended the calculation of Ukleja, Pirs, and Doane on the spin–lattice relaxation in nematic liquid crystals to calculate the orientational dependence of the rotating frame relaxation rate T ^{−1} _{1ρ}. This calculation, including the effect of cutoff in the collective order modes, is compared to the experimental data for MBBA.

Noncritical interface near a critical end point
View Description Hide DescriptionThe interface between a noncritical phase and a critical or near‐critical phase is studied. Its structure and tension are deduced from the van der Waals, Cahn–Hilliard theory with a model free‐energy density. The composition profile is found to be such that the composition in the interface approaches that of the noncritical phase on the one side exponentially rapidly, but approaches that of the critical phase on the other side much more slowly, only as an inverse power of the distance. The interfacial tension is calculated along two essentially different paths through the critical end point: one of fixed composition that goes from the three‐phase to the two‐phase region with varying temperature, the other of fixed temperature but varying composition, lying entirely in the two‐phase region. It is predicted that the interfacial tension varies smoothly through the critical end point on both paths; that on the first path it is likely to increase as one goes from the three‐ to the two‐phase region; and that on the second path, as a function of the composition, it has the qualitative shape of a typical critical isotherm. The theoretical implications of these results are discussed, reference is made to the few relevant experiments that have been done, and suggestions are made for further measurements with which to test the theory.

Density gradient measurements of Cl_{2} dissociation in shock waves
View Description Hide DescriptionThe dissociation of Cl_{2} in the presence of Ar and He has been studied behind incident shock waves over the temperature range 1700–2800 K. Dissociationrate constants were determined from laser schlieren measurements where a quadrant photodiode difference amplifier system was used to record the density gradient behind the shock front. Mixtures containing 20% Cl_{2}–80% Ar, 10% Cl_{2}–90% Ar, 5% Cl_{2}–95% Ar, and 20% Cl_{2}–80% He were studied to establish the rate constant for each collision partner. The over‐all rate constant for each mixture was found to correspond closely to the Arrhenius rate constant expression. The relative efficiencies of Ar, He, and Cl_{2} as collision partners were found by assuming that the over‐all rate constant for the dissociationreaction is given by the linear or additive mixture expression involving the individual collision partner rate constants. A Marquardt’s computer fitting procedure minimizing the percent error for the fit was used to obtain the rate constants. The results for the measuredrate constants are given by k ^{Ar} _{ d }=2.65×10^{13} exp(−47 400/R T) cm^{3} mole^{−1} sec^{−1}, k ^{Cl} ^{ 2 } _{ d }=1.83×10^{14} exp(−47 400R T) cm^{3} mole^{−1} sec^{−1}, k ^{He} _{ d }?k ^{Ar} _{ d }. On a per collision basis relative to Ar, Cl_{2} was found to be 6.9 times more efficient as a collision partner, while He had a relative efficiency of 0.58.

NH^{+} _{4} ion motions in diammonium hydrogen phosphate
View Description Hide DescriptionProton second moments and relaxation times in the laboratory frame T _{1} in (NH_{4})_{2} HPO_{4} were measured over the temperature range 77–430 K. The relatively high activation energies associated with the different motions of the nonequivalent NH^{+} _{4} groups are attributed to hydrogen bonding between the NH^{+} _{4} groups and the surrounding nearest neighbor oxygens. It is suggested that angular oscillations of the NH^{+} _{4} groups result in the unrealistically short interproton distance of 1.47 Å determined by x‐ray diffraction. The second moment results above 215 K could be explained satisfactorily if the standard interproton distance of 1.68 Å is assumed. Below 215 K the lineshapes and second moments strongly suggest a doubling of the number of nonequivalent ammonium groups. Good agreement was obtained between second moment and relaxation results.

Electron paramagnetic resonance in nickel fluosilicate
View Description Hide DescriptionEPR data for NiSiF_{6}⋅6H_{2}O at K u band and K a band between 77 and 298 °K were fitted to an isotropic g value of approximately 2.25 with ‖D‖ varying from (0.166±0.005) cm^{−1} at 77 °K to (0.51±0.01) cm^{−1} at 298 °K. The values g _{∥}=2.26±0.01 and ‖D‖= (0.125±0.005) cm^{−1} were obtained from a K u band measurement at 4.2 °K. The magnitude of the temperature gradient ∂D/∂T had a broad maximum of about 1.8×10^{−3} cm^{−1}/ °K near 200 °K, decreasing to about 1.5×10^{−3} cm^{−1}/ °K near room temperature. The spin–lattice relaxation rate was determined from linewidth measurements to vary as T ^{2} above 200 °K. From an expression for the Raman process in the high temperature limit, the Debye Temperature ϑ_{ D } was deduced to be approximately 107 °K.

The scattering of He atoms from a hard corrugated surface model using the GR method. I
View Description Hide DescriptionExtensive computations on the scattering of atoms from a hard corrugated surface model (HCS) under the Rayleigh hypothesis by using the GR numerical method are presented. The computational applicability, the limits of convergence, as well as the sensitivity of the method are studied as a function of the scattering and corrugation parameters. We also calculate a set of curves, called topographic curves, of constant diffraction probabilities versus the incident angle and the corrugation parameters for a square unit cell. The effect of the strength and number of the Fourier coefficients of the corrugation function are analyzed obtaining rainbow disappearance when these coefficients increase in strength and number. A tentative analysis of the crystallography of the LiF(001) surface by using monoenergetic thermal helium beams is given in terms of the hard sphere and ’’contact’’ hard sphere model proposed here. The agreement with the experimental data on He/LiF(001) is excellent. We also discuss an empirical method for determining Debye–Waller factors by fitting the calculated peaks to the observed ones. We calculate the mean square displacement of the atoms vibrating at the surface for different directions on the He/LiF (001) system. These displacements and consequently the Debye–Waller factors are different than if the incident particles were electrons. Finally, several proposals for future experimental work are made.

High resolution ^{2}H NMR study of single crystals of ammonium hydrogen oxalate hemihydrate
View Description Hide DescriptionProton decoupled ^{2}H NMR spectra of ammonium hydrogen oxalate hemihydrate (AHOX, 5% deuterated) single crystals at room temperature have been employed to determine the electric field gradient tensors at the NH_{3}D^{+}, –OD (carboxyl), and HDO sites. In addition, the high resolution afforded by the narrow spectral lines (of the order of 10^{2} Hz) and high magnetic field employed (6.8 T) made it possible to determine the chemical shifttensors of the HDO and –OD groups. The spectra show the presence of two inequivalent NH_{3}D^{+} sites. At room temperature both are reorienting stepwise with rates in excess of 2×10^{5} Hz. The motionally averaged quadrupole coupling constants for the two sites are (e ^{2} q Q/h) =5.1 kHz, η=0.53 and (e ^{2} q Q/h) =8.0 kHz, η=0.34. The quadrupole coupling and chemical shifttensor elements of the carboxyl deuterons are found to be (e ^{2} q Q/h) =129 kHz, η=0.30 and σ_{ x x }=−18, σ_{ y y }=−14, and σ_{ z z }=6 ppm (relative to external D_{2}O), respectively. The orientation of the tensor components can be related to the O–D bond direction, whereas the magnitude of the quadrupole coupling constant gives information on the O–D⋅⋅⋅O hydrogen bond structure. The HDO spectra show the effect of 180° ’’flips’’ of the molecule around the bisector of the bond angle. Values of the quadrupole and chemical shifttensor components are (e ^{2} q Q/h) =122 kHz, η=0.91 and −12, −1, and 13 ppm, respectively.

EPR spectroscopy of delocalized and localized charge‐transfer excitons in phenanthrene–PMDA single crystals
View Description Hide DescriptionDetailed EPR investigations of delocalized and localized charge‐transferexcitons in phenanthrene–PMDA single crystals are reported. The ionicity of the excited charge‐transfer state is investigated by two different methods, by a detailed analysis of the fine structuretensor and by an analysis of the hyperfinetensors of the donor protons. The fine structure analysis is carried out on the basis of a ’’point charge’’ model calculation; it yields a degree of charge transfer of 76%±5%. This value is more reliable than the number derived from the hyperfine structure analysis due to uncertainties in available spin densities for the donor and acceptor molecule. The anisotropy of the exciton hopping rate parallel and perpendicular to the crystal stacking axis is at least 100:1 with a hopping rate parallel to the stack axis of ν_{∥}?10^{8}/sec at 130°K.

Rydberg states in condensed phases: Evidence for small ’’bubble’’ formation around NO 3sσ (A ^{2}Σ^{+}) in solid rare gases
View Description Hide DescriptionThe lowest Rydberg state of NO has been observed to fluoresce with unity quantum yield in solid Ar, Kr, and Xe hosts. The purely radiative lifetimes l e n g t h e n in the sequence vacuum, Ar, Kr, Xe, thus directly demonstrating an increasing delocalization of the Rydbergwavefunction in media with increasing dielectric coefficient. A simple, semiquantitative theory of the relative stability of bubble and Wannier Rydberg states favors bubble (∼10 Å diameter) formation around low nRydberg states in the lighter rare gas solids. Asymmetric phonon contours in absorption and fluoresence, as well as the experimental extent of delocalization compared with Wannier model predictions, both support bubble formation around NO 3sσ (A ^{2}Σ). Sequential two photon excitation spectra from 3sσ to higher Rydberg states near 7.5 eV are broad in all three hosts. The Rydberg 3sσ spectra and photophysics are compared with those of the nearly isoenergetic B ^{2}Π and a ^{4}Π states in both ^{14}NO and ^{15}NO. Rydberg–valence perturbations in the solid phase, as well as the difference between vertical and adiabatic solid phase ionization, are also discussed.

Stark hyperfine structure of hydrogen bromide
View Description Hide DescriptionThe ν=0, J=1,2 hyperfinespectra of hydrogen bromide have been measured with a molecular beam electric resonance spectrometer at electric fields of 1500–3500 V/cm. The hyperfine structure parameters were determined for H ^{79.81}Br and D ^{79.81}Br. The quadrupole interaction ratios are The distance derivative of the electric field gradient at the site of the bromine nucleus was determined to be d (q/q _{ e })/d ([R−R _{ e }]/R _{ e }) =1.556(3). The magnetic octupole interaction of the bromine nucleus was negligible ‖e wΩ‖<0.5 Hz. The electric polarizabilityanisotropy was measured to be (α_{∥}−α_{⊥}) =0.37(9) Å^{3}. The same technique was used for DCl with the result (α_{∥}−α_{⊥}) = 0.23(3) Å^{3}. Numbers in parenthesis are uncertainties in the final figures.

Nematic ordering in the lattice model with attractive isotropic interaction
View Description Hide DescriptionThe athermal lattice model in which elongated rigid molecules are simulated by rows of consecutive sites is generalized so as to include an attractive segment–segment interaction energy—ε. Thus a distinction is made between a liquidlike phase and a supercritical gas phase. The model is solved in the Bethe–di Marzio and in the quasichemical approximation. The presence of such an attractive interaction leads to a reasonable p,T diagram of state provided r=4 or 5 in three or six dimensions. For longer rods, only the phase transition from the supercritical gas with very large volume changes is obtained already for r?6.

Oblique phonons in uniaxial crystals
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The solute orientational order in a nematic binary solution by NMR
View Description Hide DescriptionThe orientational order of a solute (monofluorobenzene) dispersed in a nematogenic solvent (p,p′‐dihexyloxyazoxybenzene) is examined by NMR as functions of temperature and composition of the binary solution over the nematic phase region. The order is found to be solely characterized by the reduced temperature whereby a correspondence rule between T and mole fraction is established, and the coexistence curve of the nematic and isotropic phases is shown to serve as the minimum equiorder profile.

Rotational relaxation of HF
View Description Hide DescriptionA rotational nonequilibrium model of Hinchen’s HF rotational relaxation experiment has been used to determine the two constants in the Polanyi and Woodall rotational transition probability. Agreement between Polanyi and Woodall’s and Hinchen’s results is demonstrated.

Absolute infrared intensities of methyl bromide and all deuterium derivatives
View Description Hide DescriptionThe integrated infrared intensities of all the fundamentals of CH_{3}Br, CH_{2}DBr, CHD_{2}Br, and CD_{3}Br are experimentally determined using nitrogen broadening pressures of 37 atm. The results are interpreted in terms of dipole moment derivatives with respect to the symmetry coordinates (∂μ/∂S) and in terms of bond charge parameters. These molecular polar quantities derived from the observed intensities are compared with the corresponding values from molecular orbital calculations.

The computation of nuclear motion and mass polarization adiabatic energy corrections for several states of the hydrogen molecule
View Description Hide DescriptionThis paper reports the computation of the diagonal matrix elements of the nuclear motion and mass polarization operators (often referred to as adiabatic corrections) for several electronic states of the hydrogen molecule. It is observed that reasonably simple wavefunctions will yield accurate expectation values for the nuclear motion operators. The present calculation covers a greater range of R for the X ^{1}Σ^{+} _{ g } and B ^{1}Σ^{+} _{ u } states than is covered in the very accurate work of Kolos and Wolniewicz, and includes computations for the C ^{1}Π_{ u } and D ^{1}Π_{ u } states for which no theoretical results have been previously reported. For the latter states the present diagonal corrections have been used in conjunction with the very recent Born–Oppenheimer potential energy curves of Kolos and Rychlewski [J. Mol. Spectrosc. 62, 109 (1976)] to compute vibrational level energies for both H_{2} and D_{2}. The diagonal corrections largely remove the mass‐dependent part of the discrepancy between theory and experiment for these vibrational level energies.

Spin coupling of two identical complex ions. III. Singlet–triplet splitting
View Description Hide DescriptionThe theoretical treatment in a preceding paper is applied to the singlet–triplet splitting of the three compounds under consideration. The results of the numerical calculations are discussed and the suitableness of the theory to interpret the coupling mechanism in such type of dimeric complexes is pointed out. A comparison with preliminary experimental results shows an encouraging agreement and confirms the validity of the approximations introduced.