Σm Values Research Articles

Evaluation of the modulation index of the standing wave Raman-Nath mode-locking device

The performance of an acoustooptic standing wave Raman-Nath deflector as active mode-locking switch is evaluated and compared with theory. The time averaged intensities of the diffracted beam up to the eight order are calculated for acoustic phase shifts up to Δϕ = 4. With fused quartz the highest attainable value of σm was 6.4 at 633 nm. In the theory describing the pulse width of homogeneously broadened AM mode-locked laser oscillators the modulation index σm is a parameter, given by δm = 2 Δϕ.

Linear free energy relations in intramolecular aromatic ipso-substitutions by substituted methyl radicals

Reaction of the 1-arylsulphonyl-2-iodomethylpiperidines (4) with tri(n-butyl)stannane induces a 1,4-aryl radical rearrangement to (5) together with the formation of the thiazines (6) and methyl derivatives (7); plots of the relative rate constants against σm and σp values give good linear correlations with a V-shaped curve for the 1,4 process.

WC-Co超硬合金の抗折力と引張強度との関係

The relation between transverse-rupture strength (σm) and tensile-rupture strength (σt) in cemented carbides was studied paying attention to the microstructural defect as a fracture source. The conventional WC-10 and 20%Co alloys with a mean carbide grain size of 1.3 μm were used as specimens. Hot-isostatically pressed WC-10%Co alloy was also used. The transverse-rupture test was done according to the JIS, and the dimensions of the tensile test specimen were 4.0 mmφ in gage section and 30 mm in length.The results obtained were as follows: (1) The ratios of \barσm⁄\barσt in this study were about 1.7 and 1.4 in conventional WC-10 and 20%Co alloys, respectively. These ratios were quantitatively explained, when the difference in dimensions of fracture sources between the two tests, the location of defects in the transverse-rupture test specimens and the overestimated value of σm (from usual beam formula) in particular in high cobalt alloys were taken into account. The ratio was confirmed to approach the value of 1.0, as the distribution of defect size within specimens became narrower. (2) For further confirmation of the above explanation, the exponent of Weibull’s equation was examined in both tests. It was found that the exponent did not generally coincide in each test, as expected from the above results. Thus, the strength of the alloy including the ratio of \barσm⁄\barσt was by no means considered to be explicable by Weibull’s theory.

Effect of ortho-substituents on methanesulfonic acid derivative of substituted aniline.

Formation and hydrolysis rates for methanesulfonic acid derivatives (MSD) of anilines including o-, m-, and p-carboxyaniline and various ortho-substituted anilines were studies as compared with those of the other substituted anilines. For o-, m-, and p-carboxyaniline, a practical pKa was discussed on the relationship between logarithm of formation or hydrolysis rate constant and pKa of the corresponding anilinium ion. Formation rates for the reaction of intramolecular H-bonding aniline with hydroxymethanesulfonate were about half to those for the other substituted anilines, which supported the assumption that the reactive H in NH2 group became half owing to the intramolecular H-bonding. In the cases of anilines substituted by negatively charged group, formation and hydrolysis rates were fairly correlated to Hammett σ value of negative group and both the rates were slower than those of the other anilines. Hammett σ values of NHCH2SO3-group were determined and the values of σm and σp were -0.10 and -0.57 respectively. From these observations the structure of intermediate of the reversible MSD reaction was proposed.

Stability Constants of Cu(II) Chelates with o-Phenylenediamine Derivatives

Abstract The stability constants of copper(II) chelates with o-phenylenediamine derivatives have been determined by the pH titration method. The measurements have been carried out at 25.0±0.1°C and μ=0.10(by KNO3). o-Phenylenediamine derivatives, which have a substituent group (CH3, CH3O, COOH, or Cl, etc.) at the 4 positions, were used as ligands. The overall stability constants of the copper chelates are of the order: CH3, CH3O, H, COO−, Cl, COOH; their values were 8.50, 8.42, 7.72, 7.06, 5.76, and 5.35 respectively. The effects of substituent groups on the stability constants have been studied. The plot of the overall stability constants against the sum of Hammett σm and σp values was found to be linear. The chelate stability and acid dissociation constants of the acido complexes of 3,4-diaminobenzoic acid were determined by the use of an augmented matrix.

Transmission of substituent effects in pyridines. Part I. Alkaline hydrolysis of some 3- and 4-substituted methyl pyridinecarboxylates

The alkaline hydrolysis of methyl 5-X-picolinates, methyl 4-X-picolinates, and methyl 5-X-nicotinates (X = NO2, Br, H, MeO, or Me2N) in methanol–water (85% w/w) is reported. In each series, the effect of the substituent and ring nitrogen are additive and the rates may be correlated with Hammett σm and σp values.

The deactivating effect of a meta‐methoxy group in the methoxydechlorination of pyridine and pyrimidine derivatives

AbstractReactivity data and the activation parameters for the methoxydechlorination of some 2‐chloro‐4‐R‐pyridines and 4‐chloro‐6‐R‐pyrimidines have been determined. A methoxy group meta with respect to the reaction site is found to be deactivating as already observed in the quinoline series. This gives further support to the hypothesis that in N‐heteroaromatic systems a conjugative interaction of an electron‐releasing substituent with the aza group (s) is a factor in modifying the nucleophilic reactivity as predicted by Hammett's σm values.

Measurement of the Mean and Anomalous Absorption Coefficients with the Three‐Crystal X‐Ray Spectrometer

AbstractThe anomalous absorption coefficient 1/2 (σ1 — σ2) and the mean absorption coefficient σm are measured for the (220) and (111) reflections of Si single crystals for CuK radiation. The measured variation of the intensity of the diffracted beam with crystal‐thickness is composed of two exponential terms, one of which corresponds to strong absorption and the other to weak absorption of the wave field. The measurements are made with a three‐crystal X‐ray spectrometer which allows the relative angular position of the crystal under investigation to be controlled to within ±1″. The anomalous absorption coefficient is measured for the angle βr corresponding to equal to zero, values of 122 cm−1, and 75 cm−1 being obtained for the (220), and (111), reflections respectively. These values are smaller than those predicted theoretically due to the presence of imperfections in the crystals. The values of σm are 164 cm−1 and 154 cm−1 for the (220), and (111), reflections respectively, which agree with the theoretical values within the limits of experimental error.

RELATIVE DETERMINATION OF THE DENSITY OF SURFACE ROCKS AND THE MEAN DENSITY OF THE EARTH FROM VERTICAL GRAVITY MEASUREMENTS*

AbstractThe gravity difference between two stations, one at the surface and the other underground vertically below the former and at a given distance from it, depends on the mean density of the earth, σm as well as on the density of the layer of rock contained between the two stations. When one of these densities is known, the other can be computed from this gravity difference. The reliability of this determination depends on the relative accuracies with which σm and σ can be obtained.These accuracies are discussed in the paper. The mean density of. the earth has been determined with an accuracy of approximately 0.01 gr/cm3. The determination of the density of a layer of rock depends on density determinations of rock samples which are not representative of the layer as a whole. Thus the accuracy of the value of σ based on a number of sample determinations will depend on many factors, including the method of averaging the density values obtained from the samples and the degree of uniformity in the geology.To investigate the problem discussed above, three sets of gravity measurements were made under differing conditions. In each instance a number of pairs of stations vertically above each other were occupied on the surface and underground. The results computed from the data on each pair of stations in a set of measurements were considered as repeated measurements of the same quantity, and the most probable value was calculated.The results demonstrated that the accuracy varied with the conditions prevailing in the area where the observations were made. In Godstone Quarries the dip of the strata was negligible, the rocks fairly uniform and structural conditions undisturbed. Consequently, although the rock layer between the surface and underground stations was only of the order of a hundred feet, the mean density of the earth computed from the average density of the rock samples, was very close to the accepted standard value of 5.52 gr./cm3. This agreement, however, was easily upset when only one random sample density was assumed as representative of a given formation.In a different locality in Cumberland the observations were made in a mine and on the surface. The rock layer between the surface and the underground stations was approximately a thousand feet thick. One set of measurements followed a line parallel to a fault, the other a line crossing this fault. The results differed appreciably from the standard value of σm, particularly in the latter case.It is concluded that the gravity difference between a surface and an underground station can be used satisfactorily to determine the average density of a rock layer in situ and en bloc, using the standard value for the mean Earth density.