Volume 55, Issue 9-10

The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the 'k calculus' which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle's position are Gaussian and Poisson, respectively.

The pure rotational b -type spectrum of the van der Waals complex Ne-CO has been measured using a pulsed jet, intracavity millimeter wave spectrometer. The millimeter wave generation is based on the OROTRON principle. The high sensitivity of the spectrometer allowed measurements of R(J), K = 1 ← 0 transitions between 108 and 150 GHz of the Ne isotopomers 20 Ne-CO and 22 Ne-CO. This new millimeter wave data set together with the microwave data in the literature, i.e. a-type microwave transitions, yield in a fit to an asymmetric rotor a reliable set of ground state constants. These are for 20 Ne-CO: A = 107127.021(14) MHz, B = 3479.6597(95) MHz, and C = 3039.5387(93) MHz. For both 20 Ne-CO and 22 Ne-CO, a global fit to a near-symmetric rotor was performed, taking into account the infrared and microwave transition frequencies from the literature and the millimeter wave measurements of the present work.

DSC measurements performed at 95 -290 K have shown that [Mn(H 2 O) 6 ](CIO 4 ) 2 possesses, besides a high-temperature phase, existing above 323 K, four low-temperature solid phases. The inelastic incoherent neutron scattering (IINS) spectra and neutron powder diffraction (NPD) pat-terns registered at 20 -290 K have supported the DSC results and provided evidence that the investigated substance possesses even more than five solid phases. The IINS spectra have shown that in the room-temperature phase, water molecules perform fast stochastic reorientation at the picosecond scale. The orientational disorder characteristic for the room-temperature phase can be easily overcooled and frozen. Even by relatively slow cooling at ca. 40 K/hour a metastable, orientational (protonic) glass phase is formed below ca. 160 K. Below ca. 100 K, a structural phase transition was observed by the NPD, however the IINS spectra indicate existence of the pure ordered low-temperature phase only after annealing the sample for a few hours at 100 K. On heating, a structural phase transition takes place at ca. 120 K, and at ca. 225 K water molecules begin fast reorientation.

The crystal structure of (CH 3 ) 3 NHBF 4 was studied in three solid phases by X-ray diffraction techniques. The structures of the ionic plastic phase (Phase I) stable above 453 K and Phase II between 384 and 453 K are CsCl-type cubic ( a = 5.772(4) Å) and tetragonal ( a = 9.815(5) and c = 6.895(5) Å), respectively. The room temperature phase (Phase III) forms a monoclinic lattice (space group P2 1 /m, a = 5.7017(8), b = 8.5724(9), c = 7.444(1) Å, and ß = 102.76(1)°). BF 4 − ions in this phase were shown to be disordered in four orientations.

Molecular orbital calculations were performed for the six saturated alkylamines (CH 3 NH 2 , (CH 3 ) 2 NH, (CH 3 ) 3 N, CH 3 CH 2 NH 2 , (CH 3 ) 2 CHNH 2 , (CH 3 ) 3 CNH 2 ), their protonated cations (CH 3 NH 3 + , (CH 3 ) 2 NH 2 + , (CH 3 ) 3 NH + , CH 3 CH 2 NH 3 + , (CH 3 ) 2 CHNH 3 + , (CH 3 ) 3 CNH 3 +), and (CH 3 ) 4 N + using the Hartree-Fock, second-order M0ller-Plesset, and density functional theory methods with the 6-311+G(d,p) basis set. Protonation lengthens the C-N bonds of the amines by 0.05 -0.08 Å and shortens the C-C bonds of CH 3 CH 2 NH 2 , (CH 3 ) 2 CHNH 2 , and (CH 3 ) 3 CNH 2 by ca. 0.01 Å.

We study within an ionic model the structure and energetics of neutral and charged molecular clusters which may be relevant to molten ThCl 4 and to its liquid mixtures with alkali chlorides, with reference to Raman scattering experiments by Photiadis and Papatheodorou. As stressed by these authors, the most striking facts for ThCl 4 in comparison to other tetrachloride compounds (and in particular to ZrCl 4 ) are the appreciable ionic conductivity of the pure melt and the continuous structural changes which occur in the melt mixtures with varying composition. After adjusting our model to data on the isolated ThCl 4 tetrahedral molecule, we evaluate (i) the Th 2 Cl 8 dimer and the singly charged species obtained from it by chlorine-ion transfer between two such neutral dimers; (ii) the ThCl 6 and ThCl 7 clusters both as charged anions and as alkali-compensated species; and (iii) various oligomers carrying positive or negative double charges. Our study shows that the characteristic structural properties of the ThCl 4 compound and of the alkali-Th chloride systems are the consequence of the relatively high ionic character of the binding, which is already evident in the isolated ThCl 4 monomer.

The effect of side chain and ring substitutions on the crystal structures of N-(2,4,6-substitutedpheny)- chloroacetamides of the type, 2,4,6-X 3 C 6 H 2 -NHCO-CH 3 _ y Cl y (X = CH 3 or Cl and 1 ⩽ y ⩽ 3), has been studied by determining the crystal structures of N-(2,4,6-trimethylphenyl)- 2-chloroacetamide, 2,4,6-(CH 3 ) 3 C 6 H 2 -NHCO-CH 2 Cl (TMPMCA); N-(2,4,6-trichlorophenyl)-2- chloroacetamide, 2,4,6-Cl 3 C 6 H 2 -NHCO-CH 2 Cl (TCPMCA); N-(2,4,6-trichlorophenyl)-2,2-dichloroacetamide, 2,4,6-Cl 3 C 6 H 2 -NHCO-CHCl 2 (TCPDCA) and N-(2,4,6-trichlorophenyl)-2,2,2- trichloroacetamide, 2,4,6-Cl 3 C 6 H 2 -NHCO-CCl 3 (TCPTCA). The crystal type, space group, formula units and lattice constants in A are: (TMiPMCA); monoclinic, P2 1 ,/n, Z = 8, a = 9.029(5), b = 15.688(2), c = 16.150(3), ß = 96.77(2)°; (TCPMCA): orthorhombic, Pna2 1 , Z = 8, a = 30.708(4), b = 4.685(1), c = 14.506(2); (TCPDCA) orthorhombic, P2 1 2 1 2 1 Z = 4, a = 16.459(3), b = 15.240(3), c = 4.640(1) and (TCPTCA): triclinic, P Ī , Z = 4, a = 9.828(2), b = 11.953(2), c = 12.278(2), a = 71,05( 1)°, ß = 75.26(2)°, g = 83.29( 1)°. The results have been analysed along with the structures of the ring unsubstituted N-phenylacetamide (PA), N-phenyl-2,2,2-trichloro-acetamide, side chain unsubstituted N-(2,4,6-trichlorophenyl)-acetamide, 2,4,6-Cl 3 C 6 H 2 -NHCO-CH 3 (TCPA) and the corresponding di-substituted phenyl acetamides and chloroacetamides. The compounds TMPMCA, TCPMCA and TCPTCA have 2 molecules each in their asymmetric units. This is in agreement with the multiple lines observed in the 35 CI NQR spectra of TCPTCA. Further, this compound shows disorder as indicated by the multiplicity of the C(side chain) - Cl bonds. The compound TCPMCA does not show 35 C1 NQR spectra, while the compound TMPMCA shows a single frequency which fades out above 200 K, indicating that it may undergo a phase transition well below room temperature. Conversion of 2,4,6-trichloroaniline into 2,4,6-trichlorophenyl acetamide and gradual replacement of H-atoms in the side chain of the latter decreases slightly the mean ring distances of the compounds, while the replacement of the 3 Cl by 3 CH 3 groups in the ring increases it's mean distance. Changes in the mean ring distances are smaller as the effect has to be transmitted through the peptide linkage. The molecules in compounds TCPDCA and TCPTCA are linked in chains by -NH-O- hydrogen bonds (about 3 Å) between the amide groups of the molecules.

The effect of side chain substitution on the 35 CI NQR and crystal structure of amides of the type N-(2,6-dichlorophenyl)-amides, 2,6-Cl 2 C 6 H 3 -NHCO-R (R = H or CH 3_y X y where X = CH 3 or CI and y = 0, 1, 2 or 3), has been studied by measuring the 35C1 NQR spectra and determining the crystal structures of the compounds N-(2,6-dichlorophenyl)-formamide, 2,6-Cl 2 C 6 H 3- NHCO-H (DCPFA); N-(2,6-dichlorophenyl)-2-methylacetamide(propionamide), 2,6-Cl 2 C 6 H 3- NHCO-CH 2 CH 3 (DCPMA); N-(2,6-dichlorophenyl)-2,2-dimethylacetamide(isobutyramide), 2,6- Cl 2 C 6 H 3- NHCO-CH(CH 3 ) 2 (DCPDMA) and N-(2,6-dichlorophenyl)-2,2,2-trimethylacetamide (neopentylamide), 2,6-Cl 2 C 6 H 3- NHCO-C(CH 3 ) 3 (DCPTMA), and by analysing the present data along with the 35 CI NQR spectra and / or crystal structures of the compounds, 2,6-dichloroaniline, 2,6-Cl 2 C 6 H 3 -NH 2 (DCA), N-(2,6-dichlorophenyl)-acetamide, 2,6-Cl 2 C 6 H 3 --NHCO-CH 3 (DCPA), N-(2,6-dichlorophenyl)-2-chloroacetamide, 2,6-Cl 2 C 6 H 3 -NHCO-CH 2 Cl (DCPCA), N- (2,6-dichlorophenyl)-2,2-dichloroacetamide, 2,6-Cl 2 C 6 H 3 -NHCO-CHCl 2 (DCPDCA) and N- (2,6-dichlorophenyl)-2,2,2-trichloroacetamide, 2,6-Cl 2 C 6 H 3 -NHCO-CCl 3 (DCPTCA). The crystal type, space group, formula units and lattice constants in A of the new structures are;DCPFA: orthorhombic, Pbca, Z = 8, a = 8.593(3), b = 12.728(4), c = 14.376(4); DCPMA: orthorhombic, P2 1 2 1 2 1 , Z = 4, a = 4.774(2), b = 10.961(5), c = 19.562(8); DCPDMA: monoclinic, P2 1 /c, Z = 4, a = 9.901(4), b = 13.785(5), c = 9.060(3), ß = 103.58(2)° and DCPTMA: monoclinic, P2 1 /n, Z = 8, a = 16.047(5), b = 9.882(3), c = 16.270(5) ß = 102.12(1)°. The compound, DCPTMA shows two molecules in its asymmetric unit. This is in agreement with the multiple lines observed in the 35 CI NQR spectra of the compound. The conversion of DCA (monoclinic) into it's various acid amides DCPFA, DCPA, DCPMA, DCPDMA, DCPTMA, DCPCA and DCPTCA affects it's crystal symmetry. The replacement of the side chain CH 3 in DCPA by the H atom or substitution of either a CH 3 group or a CI atom for one of the H atoms in the side chain CH 3 or replacement of the two ring CI atoms by the H atoms changes it's crystal symmetry from monoclinic to orthorhombic, while the substitution of 2 or all the 3 H atoms in the CH 3 group of DCPA by 2 or 3 CH 3 groups or CI atoms restores it's crystal symmetry back to the monoclinic type. The bond lengths and bond angles are normal except for some deviations.

The phase sequence of (Et 4 N) 2 ZnBr 4 has been determined based on thermal analysis. Below the decomposition point (572 K) four phases are distinguished. The structures of three of the phases have been determined from 4-circle diffraction data at 240 (neu-trons), 299 and 373 K (X-rays), respectively. The multiply twinned low-temperature phase (at 240 K) is characterized by a pseudo-orthorhombic lattice (monoclinic, Plal, a = 17.6120(9] Å, b = 8.8195(4) Å, c = 16.1062(6) Å and ß=89.94(2)°), whereas the room-temperature phase (299 K:P42 1 c, a = 8.9874(6)Åand c = 15.9774 Å) and the first high-temperature phase (373 K: P4 2 /nmc, a= 9.145(4) Å and c = 15.835(8) Å) belong to the tetragonal crystal system. The transitions between the three phases are essen-tially connected with a stepwise ordering of the Et 4 N + ions, whereas the positions of the heavy atoms change only slightly. Three 81 Br NQR lines are observed between 77 and 204 K.

On the basis of the temperature dependence of the static principal permittivities, £y and e x , measured for the nematic phase of «-hexylcyanobiphenyl (C 6 H 13 -Ph-Ph-C=N, 6CB), a value of the angle ß between the long molecular axis and the direction of the dipole moment /µ of 6CB, as well as the order parameter S(T), were obtained by use of the Maier-Meier equations. From the dielectric relaxation and viscosity data, the contribution of the nematic potential to the molecular dynamics was estimated. In the isotropic phase the dielectric and viscosity data allow one, in the framework of the Debye model, to estimate the effective length of 6CB molecule.

The electric dipole moments in the ground /µg and excited state of the fluorescent probe LAUR-DAN are determined from solvatochromic and thermochromic shifts to be /µg = 3.46 D, µe = 10.6 D and /µg = 3.76 D, /µe = 10.24 D, respectively. These values concern the free LAURDAN molecule. The val-ues of the dipole moments of LAURDAN (= 6-decanoyl-2-dimethylamine-naphthalene) exceed dis-tinctly those of PRODAN (= 6-propionyl-2-dimethylamine-naphthalene).

P, V m , T data have been measured for the nematic and isotropic phases of 3-cyanobenzyl 2,5-bis (4-n-octyloxybenzoyloxy)benzoate between 273 and 423 K and up to 250 MPa. The volume changes accompanying the crystal -nematic and nematic -isotropic transitions have been determined. The cor-responding enthalpy changes have been calculated using the Clausius-Clapeyron equation. The p, V m , T data enable also to estimate the volume entropy for the nematic-isotropic transition. It is found that the configurational part of the transition entropy amounts to 80%, this portion being distinctly larger than found in previous studies for conventional rod-like liquid crystals.

In this paper we establish the formulas of EPR g||, g⟂, for 3d 7 ions in trigonal octahedral crystals from a cluster approach. In these formulas, the contributions from configuration interaction-and covalency-effects are considered. The parameters related to both effects can be determined from the optical spectra and the structural parameters of the studied crystal. With these formulas, the defect structure of a Co 2+ center in α-LiIO 3 crystal is studied. It is found that, to reach good fits between the calculated and observed g||, g⟂ , the O 2_ ions between Co 2+ and Li + vacancy (V Li ) should shift away from the V Li by about 0.49 Å. The displacement direction is consistent with those obtained for Cr 3+ , Fe 3+ , and Mn 2+ centers in α-LiIO 3 crystals as well as with the expectation based on the electrostatic interaction model.

The paper reports on the photochemical trans-cis isomerization of some new polymerizable triazine-stilbene fluorescent brighteners and their copolymers with styrene in aqueous and ethanol solutions. A dependence of trans-cis isomers in solution equilibrium and in solid polymeric films on the nature of the substituent in the triazine ring has been found.

The nonlinear Rayleigh-Taylor stability of a cylindrical interface between vapor and the liquid phases of a fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple time scale expansion is used for the investigation. A simple nondimensional parameter is found to characterize the stability of the system. Using this parameter, the region of stability is displayed graphically.

Mean amplitudes of vibration of the pseudo-trigonal bipyra-midal PF 4 − anion have been calculated from vibrational spectroscopic data in the temperature range between 0 and 1000 K. The results are briefly discussed in relation to the structural peculiarities of the anion and some comparisons with related species are made.

In a recent paper [1] S. Golden is trying an interpretation of Einstein's theory of special relativity solely based on the propagation of light-pulses which aims at circumventing the problems scientists sometimes do have with the "twin paradox", i.e. with the physical reality of the kinematical dilation-of-time. However it is well known that propagation of light does not cover the whole structure of relativistic spacetime because of the conformal invariance of the Maxwell equations. Thus the paper [1] is fundamentally incomplete in its applied physical tools. In my comment it will be shown that the title of the paper is a misconception and that another aspect in the paper is false too. If S. Golden would have treated in the paper not only light-pulses but also decaying systems the shortcomings would not have occurred. The sole tool of the author for relating inertial systems is the exchange of light-pulses (including reflections) between two inertial systems, called A-system and B-system, with time coordinates t and r, respectively. The light-pulses are propagating either into the direction of the inertial-systems relative velocity or into the opposite direction. No doubt, the ratio At/AT of the time-intervals between fixed-position (origins of the systems) passage-times of the same two light-pulses in the A-system and in the B-system is given by, combine the Eqs. (6) and (12) in the paper in question,

In his comment G. Schäfer [1] points out that S. Golden's [2] time-dilation equations (12) and (13) are of kinematic type and that the title of Golden's paper is therefore a misconception. He also states that Golden's treatment of the time-dilation problem is incomplete, since Golden has not considered particle decay in his paper. I should like to present my comment on these two points raised by G. Schäfer. Although Golden describes his equation (13) as "spatially dependent," he says at the beginning of Sect. 4 of his paper that his equations (12) and (13) can be regarded as "either velocity dependent or spatially dependent." But this is not at all the essence of his paper. The essence of his paper is that the two time-dilation equations that he has derived do not imply "any actual dilation-of-time in clocks that may be stationed in the systems." Hence he concludes that Einstein's time-dilation relation is merely a transformation relation and that the motion of the systems does not affect "the intrinsic time-rates of any clocks stationed within them." In order to judge the significance of Golden's paper, it is important to remember that Einstein arrived at the ideas of kinematic time-dilation and length contraction in moving systems not as a result of a rigorous deduction from any mathematical, physical or logical relations, but simply by interpreting in his own way the physical significance of transformation equations for space and time (Lorentz transformation equations) [3]. Ever since the publication of his 1905 article, Einstein's ideas of kinematic length contraction and time dilation