Sum Of Radii Research Articles

The local geometry of chalcogen atoms on Pd(100): the low coverage phases of O and S

The local geometrical structures of the p(2 × 2) and c(2 × 2) phases of S Pd(100) as well as of the p(2 × 2) structure of atomic oxygen on the same surface were determined by LEED- IV analysis using the energy range between 35 and 350 eV. The total energy range available for analysis varied between 2900 eV for the p(2 × 2) structures and 1750 eV for the c(2 × 2) structure. Pendry R-factors between 0.15 and 0.19 were obtained for the best fit geometries. In all cases the adsorbate atoms were found to stay above the first substrate layer and to occupy the fourfold coordinated hollow site. Bond lengths to the first substrate neighbors are close to the sum of covalent radii for both S structures, but significantly longer (by 0.10 Å) for oxygen. Whereas lateral shifts and rotations of groups of atoms in the substrate layers turn out to be below the detection limits, significant buckling of the second substrate layer was found for all three systems, being largest for oxygen (0.12 Å). The unusually extended first to second layer distance found already for the clean Pd(100) surface remains virtually unchanged in all structures and is not compensated by a contraction between the second and third layers.

A General Survey of Quartz and Quartz-like Materials: Packing Distortions, Temperature, and Pressure Effects

A general survey of quartz and quartz-like structures (SiO2, GeO2, andMXO4withM= Al, Ga, Fe andX= P, As) has been undertaken to ascertain the effects of pressure and temperature on the quartz framework. All the quartz isotype crystal structures and their variations with respect to pressure and temperature can be expressed in terms ofM–X(the nonbonded radius sum) andM–O–X(the corresponding angle). Thus, crystal packing can be described by the geometrical characteristics ofMX4(orXM4) tetrahedral units, such asM–X–Mangle distortions,M–Xlengths, andc/aratios.MO4andXO4tetrahedral distortions can be closely related to theM–O–Xangle. Crystal structure distortions expressed by theM–O—Xangle lead to different physical properties. Density, piezoelectric coupling coefficient of AT cut, and dielectric constant anisotropy are linearly related to theM–O–Xvalue. Thus, the knowledge of theM–O–Xvalue allows prediction of the physical properties of quartz-like crystals that have not been synthesized. In conclusion, all the crystal structures and the physical properties of the quartz-like materials can be expressed in terms of only theM–O–Xangle.

The Molecular Structures and Conformations of Bis(dichlorosilyl)amine and Bis(dichlorosilyl)methylamine in the Gas Phase: Determination by Electron Diffraction and by ab Initio Calculations

The gas-phase molecular structures of bis(dichlorosilyl)-amine, (HSiCl22NH, and bis(dichlorosilyl)methylamine, (SiHCl2)2NMe, have been investigated by electron diffraction and ab initio calculations on a MP2/6–31G* level. Because the latter suggest the presence of a mixture of two conformers for each molecule, attempts were made to fit the electron diffraction data in each case by two different models, one assuming the presence of only one conformation, and another allowing for two different conformers. The principal parameters (ra) from electron diffraction for (HSiCl2)2NH are (the appropriate ab initio calculated values are given in brackets []): r(Si-N) 171.9(2) [172.7], r(Si-Cl) 204.1(1)[204.5] pm; Si-N-Si 126.5(8) [127.4] N-Si-Cl 107.3(5) [110.8] and Cl-Si-Cl 106.5(3) [107.5]°. For (SiHCl2)2NMe: r(Si-N) 171.1(3) [171.5], r(Si-Cl) 204.0(9) [205.2], r(N-C) 149.7(10) [148.3] pm; Si-N-Si 124.9(13) [123.4], N-Si-Cl 109.7(5) [110.7] and Cl-Si-Cl 107.1(3) [107.2]° [110.8] and Cl-Si-Cl 106.5(3) [107.5]°. For (SiHCl2)2NMe: r(Si-N) 171.1(3) [171.5], r(Si-Cl) 204.0(9) [205.2], r(N-C) 149.7(10) [148.3] pm; Si-N-Si 124.9(13) [123.4], N-Si-Cl 109.7(5) [110.7] and Cl-Si-Cl 107.1(3) [107.2]°. For (HSiCl2)2NH three different conformers were found to fit the experimental data with the single-conformation model. In two of the conformers, the dichlorosilyl groups are twisted by Θ1 = 146.0(10)/Θ2 = 155.2(20)° and Θ1= 101.1(49)/Θ2 = 196.8(12)°; respectively counterclockwise from the positions in which the Si-H bonds eclipse the N-H bond. Both of these lead to nearly ideally staggered conformations of the two SiHCl2 groups when viewed along the Si–Si axis. In contrast, the third conformation is nearly eclipsed, with torsion angles Θ1 = 131.4(15)/Θ2 = 80.4(26)°. Planarity of the Si2NH group was assumed as suggested by ab initio calculation. For (HSiCl2)2NMe the experimental data could be suitably fitted by two conformers, in which the dichlorosilyl groups are twisted by Θ1= 161.8(13)/Θ2 = 63.1(23)° and Θ1 = 156.1(9)/ Θ2 = 177.1(15)° from the positions in which the Si-H bonls eclipse the N-C bond. The first of these structures has an eclipsed Si(NSi)Cl conformation and an Si…Cl nonbonded distance close to distance clse to the sum of the appropriate van der waals radii. MP2/6–31G* calculations support the GED bond lengths and bond angles of both molecules, but indicate different conformations for the most stable equilibrium geometries: the computed twists are Θ1 = 180/Θ2 = 180° and Θ1 = 177.0/ Θ2 = 183.0° for (HSiCl2)2NH and (HSiCl2)2NMe, respectively. Rotation about the Si—N bonds is a very facile process, cf. the computed [MP2/6–31G*//MP2/6–31G* + ZPE(SCF/6–31G*)] rotational barrier of 2.9 kJ. mol-1 for (HSiCl2)2NH.

Structure Deformations and Existence of the α-β Transition in MXO 4 Quartz-like Materials

The paramount importance of M- X interactions in determining the existence or nonexistence of an α-β transition can be shown by a general survey of all known or predicted quartz-like materials, MX O 4. This distance, M- X, defined as the nonbonded radius sum, prescribes structure packing. If the M-O and X -O distances increase, interterahedron distortion will increase in relation to the decrease of the M-O- X angle, 0, and decrease of the tilt angle, δ. From a structural point of view, a borderline value of δ ∼ 22° or θ ∼ 136° has been extrapolated for the existence of an α-β transition.

Synthesis and crystal structure of copper oxybromides [M 2Cu 3O 4Br 2 (M=Sr,Ba)

Two new members of copper oxybromides M 2Cu 3O 4Br 2 (M=Sr,Ba) have been prepared and studied by X-ray powder diffraction. They were determined to assume a tetragonal crystal structure with space group 14/mmm and lattice parameters a=5.4840(2) A ̊ , c=13.297(1) A ̊ for Sr 2Cu 3O 4Br 2 and a=5.5386(2) A ̊ , c=14.624(1) A ̊ for Ba 2Cu 3O 4Br 2. The structure is built of the sheets [Cu 3O 4] and the fluorite-type layers [M 2Br 2] stacking alternatively along [001]. The [Cu 3O 4] layer can be described as the well-known sheets [CuO 2] in cuprate superconductors with the addition of Cu to the centers of the square units [CuO 2] at a period of √2a p ×√2 a p . In the alkaline-earth copper oxyhalide systems, M 2CuO 2X 2 can be obtained only with the low ionic radius sum r M+ X of M 2+ and X −, while M 2Cu 3O 4X 2 was got only with a high r M+ X where M=Ca,Sr,Ba and X=Cl,Br.

Left ventricular midwall mechanics in systemic arterial hypertension. Myocardial function is depressed in pressure-overload hypertrophy.

Left ventricular (LV) midwall geometry has been described conventionally as the sum of the chamber radius and half of the wall thickness; this convention is based on the assumption of uniform transmural thickening during systole. However, theoretical considerations and experimental data indicate that the inner half (inner shell) of the LV wall thickens more than the outer half (outer shell). Thus, an end-diastolic circumferential midwall fiber exhibits a relative migration toward the epicardium during systole. As a result, the conventional method provides an overestimate of the extent of the midwall fiber shortening. We developed an ellipsoidal model with a concentric two-shell geometry (nonuniform thickening) to assess midwall fiber length transients throughout the cardiac cycle. This modified midwall method was used in the analysis of LV cineangiograms from 15 patients with systemic arterial hypertension and 14 normal subjects. Study groups were classified according to LV mass index (LVMI): 14 normal subjects (group I), eight hypertensive patients with a normal LVMI (group II), and seven hypertensive patients with an increased LVMI (group III). There were no significant differences in LV end-diastolic pressure or volume among the three groups; the ejection fraction was slightly greater in group II (70 +/- 5%) than in groups I (65 +/- 8%) and III (66 +/- 4%), but this trend did not achieve statistical significance. Values for endocardial and conventional midwall fractional shortening (FS) were also similar in the three groups. By contrast, FS by the concentric two-shell geometry (modified midwall method) in group III (16 +/- 2%) was significantly less than that seen in groups I and II (21 +/- 4% and 21 +/- 5%, respectively; both p less than 0.05). This difference achieves greater importance when it is recognized that mean systolic circumferential stress was lower in group III (151 +/- 22 g/cm2) than in groups I and II (244 +/- 37 g/cm2 and 213 +/- 38 g/cm2, respectively; both p less than 0.01). The midwall stress-shortening coordinates in six of the seven group III patients were outside the 95% confidence limits for the normal (group I) subjects. Thus, despite a normal ejection fraction, systolic function is subnormal in hypertensive patients with LV hypertrophy. Chamber dynamics provide an overestimate of myocardial function, especially when LV wall thickness is increased. This is due to a relatively greater contribution of inner shell thickening in pressure-overload hypertrophy.

Structural and Electronic Properties of TXF-TCNQ (X ˭ S, Se, Te)

Abstract We report the crystal structure and physical properties of TTeF-TCNQ, compare the electrical conductivities of TXF-TCNQ (X ˭ S, Se, Te) by performing tight-binding band calculations on TXF-TCNQ, and examine the differences in the packing patterns of TXF-TCNQ (X ˭ S, Se, Te) by carrying out ab initio SCF-MO/MP2 calculations on appropriate model systems. The electrical conductivity of TXF-TCNQ increases as X varies from S to Se to Te. This increase is primarily caused by the conductivity enhancement in the donor stacks. In TXF-TCNQ (X ˭ S, Se) the C-H bonds of both the donor and the acceptor molecules make intermolecular contacts shorter than the van der Waals radii sums, but in TTeF-TCNQ only the C-H bonds of the donor molecules do. This difference in the packing patterns was rationalized on the basis of the C-H…X and N(sp)…X (X ˭ S, Se, Te) contact interaction energies estimated by ab initio SCF-MO/MP2 calculations on H3C-H…XH2 and H-C≡N…XH2.

Calculation of heteronuclear single bond enthalpies from pauling electronegativities

Abstract Modifications to the Pauling method of calculating single bond enthalpies are proposed. First, because bond polarity produces a decrease in equilibrium bond length which strengthens the bond, a correction is made for any deviation in the actual bond length from the covalent radius sum. Secondly, because charge-transfer from a less to a more electronegative atom is exothermic only until electronegativity equalization is achieved, a saturation effect is observed for large electronegativity differences. A correction for the effect is provided. The modified Pauling method is shown to be more accurate than the original Pauling method and valid over the entire range of bond polarity.

The Synthesis, Crystal Structure, Electrical Conductivity and Band Electronic Structure of (BPDT-TTF)2lCl2

Abstract (BPDT-TTF)2ICl2 is a synthetic metal salt composed of the electron donor molecule bis(propylenedithio)tetrathiafulvalene (BPDT-TTF, C12H12Sk) and the linear iododichloride anion, ICl2 −. The crystal structure of (BPDT-TTF)2ICl2, determined at 298 K and 120 K, closely resembles those of the organic metals and semiconductors based on bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF, C10H8H8), in that all of these materials contain sheetlike donor molecule networks sandwiched between anion layers. In contrast to the (BEDT-TTF)2X salts, however, there is a total absence of S···S contact distances less than ∼3.6 A (the van der Waals radius sum) within the donor-molecule network of (BPDT-TTF)2ICl2. In addition, each stack of BPDT-TTF molecules is also strongly dimerized. The lack of short S···S contact distances at both 298 K and 120 K appears to be a consequence of the bulky propylene groups of BPDTTTF compared to the smaller ethylene groups of the BEDT-TTF molecule. Based upon four-probe a.c. resistiv...

Electromagnetic processes in relativistic heavy ion collisions

Electromagnetic effects in relativistic heavy ion collisions with impact parameter larger than the sum of the nuclear radii are studied using the virtual photon method. With increasing value of the relativistic parameter γ the hardness of the virtual photon spectrum increases. This leads to interesting new effects which will also have to be considered in the design of future relativistic heavy ion machines and experiments. The excitation of high-lying giant E1 and E2 multipole resonances is calculated as well as electromagnetic pion production. Coulomb bremsstrahlung is calculated and compared to the bremsstrahlung emitted in the more violent central nuclear collisions. K-shell ionization and electron-positron pair production is studied. The latter process has a very large cross section for heavy ions and contributes significantly to the stopping power of relativistic heavy ions in a dense medium.

Structure and Properties of Thallium(I) Formate Solutions

Abstract The structure of thallium(I) formate aggregates in concentrated aqueous thallium(I) formate solutions was investigated by the X-ray diffraction method at 25 °C for solutions A (10.77 mol dm−3) and B (3.493 mol dm−3). The former solution had the density of 3.189 g cm−3 and the CH2O⁄CTl mole ratio of 2.59, where Ci represents the total concentration of species i, and was an almost saturated solution at room temperature. From the analysis of the X-ray diffraction data of solution A, thallium(I) formate was found to be present as a tetramer Tl4(O2CH)4. The nearest interatomic distances between thallium(I) and atoms within the formate ions in the tetramer were determined as Tl–O: 2.79(1) Å and Tl···C: 3.33(2) Å. The nonbonding Tl···Tl distances within the aggregate were estimated to be 3.92(1) Å, 4.34(1) Å, and 4.79(1) Å. The Tl–OH2 bond length was also determined to be 3.22(3) Å, which was much larger than the distance expected from the sum of the ionic radius of thallium(I) ion (≈1.4 Å) and size of a water molecule (≈1.4 Å). A comparison of the radial distribution function of solution A with that of solution B, which had the CH2O⁄CTl mole ratio of 13.5, indicated that the aggregate decomposed by dilution. Raman spectra of four different thallium(I) formate aqueous solutions of 3.493 to 10.77 mol dm−3 were measured and the frequencies of the C–O and C=O stretchings of formate ions in the solutions were compared with those of free formate ion. Band shifts of the two frequencies observed for concentrated thallium(I) formate solutions indicated the existence of bridge-type formate ions coordinated to thallium(I) ions, and the result agreed with that observed by the X-ray diffraction analysis. Densities, refractive indices, viscosities and conductivities were measured for thallium(I) formate aqueous solutions with varying concentrations.

Analysis of the unit cell dimensions of phases with the BaAl 4 (ThCr 2Si 2) structure I: Rare earth phases of manganese, iron, cobalt, nickel or copper with silicon or germanium

We analysed the unit cell dimensions of MN 2X 2 phases (M ≡; rare earth; N ≡; Mn, Fe, Co, Ni, Cu; X ≡; Si, Ge) with the tetragonal BaAl 4 structure on the basis of plots of the slopes, versus the diameter D M of the M component, of the differences of the appropriate radius sums and the calculated interatomic distances for the M-N, M-X, N-X and X-X contacts of interest. Ten series of phases were examined. The M-N and/or the M-X contacts are responsible for the dependences of a and c on D M in the series of phases formed with N and X kept constant and M varied. The N-X contacts largely control the relative sizes of a and c such that in the phase formed by the smallest M component the N-X distance is equal to the sum of the radii of N and X for coordination number 4. The phases of the five transitional and noble metals behave differently, whereas the silicon and germanium phases behave similarly.

Some systematics of the garnet structure

Equations relating the positional parameters of the anion in the oxide garnets to the mean constituent ionic radii of the cations occupying the {X}, [Y], and (Z) sites have been derived from published garnet structures using multiple regression analysis: x = 0.0278(22)r { X} +0.0123(28)r [ Y] −0.0482(16)r( Z) +0.0141 y = −0.0237(25)r { X} +0.0200(32)r [ Y] + 0.0321(18)r( Z) +0.0523 z = −0.0102(20)r { X} +0.0305(25)r [ Y] −0.0217(14)r( Z) +0.6519 Variations of mean bond lengths with constituent ionic radius are examined for the garnet structures. Deviations of mean bond length from the sum of the constituent ionic radii may be correlated with the ionic radius of the cations at the other sites in the structure.

Structures and stabilities of the group IIIa dihydrides

The CaF 2-type dihydrides of the group IIIa elements represent a relatively large family of similar metallic hydrides for which relationships between interatomic distances and stabilities can be derived. Available data for the thermodynamic properties of formation of these dihydrides were assembled and the enthalpies and free energies of formation are compared with the metal-hydrogen distances in the hydrides. The data show that for these hydrides there is a maximum in the stability-distance curve; the most stable dihydrides are HoH 2 and DyH 2 with metal-hydrogen distances of 2.237Å and 2.252 Å respectively. A modified Born-Mayer ionic model is applied to this family of dihydrides. In addition to the usual Coulomb (attraction) and overlap (repulsion) terms, an additional attraction term is introduced to take into account residual metallic cohesion in the hydride lattice. The results obtained from this model are compared with the thermochemical data using the BornHaber cycle. In making this comparison a parameter β (which has units of length) is introduced which accounts for the influence of the 4f electronic structure on the repulsive potential for the lanthanide dihydrides. It is shown that the relation between stability and the sum of the metallic radius and the tetrahedral hole radius (in the metal) is similar to that between stability and the actual metal-hydrogen distance in these dihydrides. This similarity is used to rationalize observed correlations between stability and tetrahedral hole sizes in intermetallic compound hydrides.

Optical model analysis forO16+Pb208: Evidence for dynamic shape or density changes

For the reaction /sup 16/O + /sup 208/Pb, experimental data are available for cross sections for complete fusion and all reactions from 80 --102 MeV and for elastic scattering from 80 to 313 MeV. Most of these data can be adequately described by an energy-independent spherical optical potential with the proximity formulation for the real part and a Woods-Saxon form for the imaginary part. Three parameters have been varied, radius and surface width in the proximity potential and radius in the imaginary potential. The sum of the equivalent sharp radii of the interacting nuclei must be enlarged significantly in order to fit the fusion and scattering data. As a consequence, the sum of the ''best fit central radii'' for /sup 16/O and /sup 208/Pb is approx. = 0.8 fm larger than the sum of the independently measured radii. If the proximity formulation is correct this implies dynamical shape or density adjustments during the collision.

Effective solid angle of scintillation counter for fast neutrons

The effective solid angle of a cylindrical scintillation counter is derived in closed form for two particular isotropic sources of fast neutrons of practical interest: a point source on axis and a symmetrically placed uniform disc source of the same size as the counter face, for arbitrary source-to-detector distance. Series solutions are also obtained for a point source off axis and for a smaller disc source (restricted to a source distance exceeding the sum of the counter radius and the offset from the axis or the disc radius, respectively).

Electromagnetic pion radius and dispersion sum rules

A general set of dispersion sum rules is considered for the pion form factor G( t) in the mixed-modulus phase representation. The connection between the distribution of the G( t) complex zeros and the sizes of dispersion integrals along the cut is stated. Under the assumption that G( t) ∼ t α at large t the following restriction on the asymptotic behaviour of G( t) is obtained: | G( t)| ⩾ at −2 ( a>0). Using present experimental data we evaluate the electromagnetic mean squared radius, r π = 0.71 ± 0.30 fm.

The hydrated proton H+(H2O)n. II. A spectroscopic study and normal coordinate treatment of the oxonium ions H3O+ and D3O+

A spectroscopic study and a normal coordinate treatment (NCT) of the oxonium ions H3O+ and D3O+ in solid H3O+CH3C6H4SO3− and D3O+CH3C6H4SO3− were made. Neutron diffraction studies indicated a pyramidal, C3ν symmetry for the oxonium ions. Based on this symmetry, the observed frequencies for H3O+ and D3O+ were assigned and a NCT attempted using the general valence force field and the Urey-Bradley force field. Comparison of the fundamental vibrations in various oxonium compounds was made. It was demonstrated that a relationship between the OH stretching frequencies in H3O+ and D3O+ ions vs R (the O⋯O distance) exists, as well as a relationship between the stretching frequency shift (Δνs) and R. The failure of past investigators to recognize this trend may have contributed to the confusion regarding the assignments. This is the first confirmation of such a trend existing in oxonium compounds. It is suggested that the stretching mode frequencies in H3O+ and D3O+ are dependent on R. When Rx-y is greater than the X–H⋯Y van der Waals radius sum, the asymmetric stretching vibration (ν3,e) is at higher frequency than the symmetric stretching vibration (ν1,a1); where Rx-y is less, the stretching mode frequencies are inverted.

The crystal structure of the molybdenum boride Mo 1− xB 3

The structure of Mo 1− x B 3, with x close to 0.20, has been investigated using powder diffractometry, in conjunction with the electron microprobe and chemical analysis. The range of homogeneity of the compound is very small and does not include the stoichiometric composition. The structure is described in the hexagonal space group P6 3 mmc with the axes a = 5.2026 (2) Å and c = 6.3489 (3) Å. No significant variations in cell dimensions were observed. There are four formula units per unit cell with molybdenum at 2( b) (occupancy 60%) and 2( c) and boron at 12( i) with x = 0.333. The refinement was performed with least-squares and Fourier difference techniques. The final R value, based on intensities, was 8.8%. The structure may be described as a stacking of two-dimensional boron nets and highly defect metal layers. The molybdenum-boron distance exceeds the radius sum by 3%, while the Mo-Mo distances are 7 and 13% longer than the radius sum. There are holes in the structure, which are large enough to accommodate boron atoms. However, there is no evidence that these holes are even partially filled.

Ionic radii for use in geochemistry

The ionic radii proposed by Shannon and Prewitt as the effective values in oxides and fluorides have been analysed for their conformity with the radius ratio principles of crystal chemistry. It is shown that a set of values intermediate between the “IR” and “CR” values of Shannon and Prewitt provides the best conformity in this respect, and a table of the values adopted is provided in periodic form. These values correspond to a VI co-ordinate oxygen radius of 1.32 Å and a VI co-ordinate fluorine radius of 1.25 Å, and the radii of the cations are therefore appreciably larger than those previously accepted, although not as large as Shannon and Prewitt's “CR” values. It is suggested that the radii obtained are the most suitable for use in silicate geochemistry, and constitute a major improvement over previous values for this particular purpose. Although it is impossible to maintain the accuracy with which radius sums represent interatomic distances and at the same time to extend the range of the radii to other anions, it seems desirable to provide compatible (although only very approximate) values of radii for Cl, Br, I, S and Se anions. Use of the new cation radii with these anion radii cannot be expected to be an improvement over the use of older radii, but should be about as satisfactory. The changes of cation radii relative to one another, as compared with Ahrens' radii, are tabulated in order to draw attention to their possible geochemical significance, and the implications are discussed in the case of scandium.