Biaxial Symmetry Research Articles

Anisotropy modifications and domain-wall behavior in grooved films

Patterns of 5-μm-wide grooves on 25-μm centers were partially etched in the easy and/or hard directions in uniaxial Permalloy films; 20-μm-diameter circles or 25-μm centers were also etched. The easy direction grooves modified the anisotropy of the films to produce an NDRO behavior, while the hard direction grooves resulted in biaxial symmetry. Coercive force of the easy direction grooved films increased as a result of the lower energy of 180° walls in the thinner grooved regions. Pairs of crossties and the Bloch lines between them were confined to grooves in the hard direction. Creep sensitivity was markedly decreased in hard direction grooved films. This creep control probably results from the limitation of Bloch-line motion by the hard direction grooves, in agreement with several recent suggestions concerning the mechanism of creep in crosstie walls.

Anisotropy modification and domain-wall behavior in grooved films

Patterns of 5-μm-wide grooves on 25-μm centers were partially etched in the easy and/or hard directions in uniaxial Permalloy films; 20-μm-diameter circles or 25-μm centers were also etched. The easy direction grooves modified the anisotropy of the films to produce an NDRO behavior, while the hard direction grooves resulted in biaxial symmetry. Coercive force of the easy direction grooved films increased as a result of the lower energy of 180° walls in the thinner grooved regions. Pairs of crossties and the Bloch lines between them were confined to grooves in the hard direction. Creep sensitivity was markedly decreased in hard direction grooved films. This creep control probably results from the limitation of Bloch-line motion by the hard direction grooves, in agreement with several recent suggestions concerning the mechanism of creep in crosstie walls.

General description of optical (dichroic) orientation factors for relating optical anisotropy of bulk polymer to orientation of structural units. Part II. Fourth moments of orientation distribution and polarized fluorescence

AbstractA general description is given for relations among the optical quantities obtained from fluorescence polarization measurements on bulk polymer stained by fluorescent groups: the moments of distribution of orientations of the fluorescent groups, and those of the structural units of the polymer (chain segments) on which the groups are adsorbed. Two assumptions as to the biaxial symmetry of the bulk polymer and the cylindrical symmetry of the optical anisotropy of the fluorescent element, both for the absorption and emission processes, reduce the intensities of the polarized fluorescence to a 3 × 3 matrix L which is asymmetric (Lij ≠ Lji), as has frequently been observed in experiments. The components of the L matrix are related to those of the J matrix which is so defined as to describe the fourth moments of the distribution of orientations of the structural units on the basis of a random distribution of the rotational angle of the unit about the segment axis. It is found that the use of the method of fluorescence polarization combined with absorption dichroism and/or emission gives the values of the optical anisotropy ratios of the fluorescent unit, and that the effects of the thermal agitation of the structural unit can be separated from the moments of the orientation distribution for the simplest case.

Mathematics of the Polarized-Fluorescence Experiment

The polarized-fluorescence experiment for measurement of preferred orientation is analyzed mathematically. The intensity is dependent upon P and A, unit vectors describing the positions of the polarizer and analyzer, and upon the orientation distribution N(α, δ) of the chromophoric group of the polymer. In the case of biaxial or uniaxial symmetry, the intensity IPA for any combination of P and A vectors is expressed as linear combination of nine fundamental intensities characteristic of a given sample. These intensities form a 3×3 matrix, each entry Iij being the intensity obtained with P and A parallel to the ith and jth principal axes of the sample. Of the nine components of I, only five are independent for a biaxially oriented sample; two for uniaxial orientation. Each Iij is proportional to 〈xi2xj2〉Av, where xi and xj are the components of the chromophore vector along the corresponding principal axes. Calculated matrices are shown for several model distributions. Nishijima's P function is related to the Iij's, and the problem of measuring biaxial orientation is discussed. The Iij's are also shown to be directly related to the second-and fourth-order coefficients in the spherical harmonic expansion of N(α, δ). These coefficients can be measured directly by a few simple experiments involving spinning the sample between crossed or parallel polarizers. Thus, the experimental error in their determination can be minimized.

Determination of shadow-band structure from stellar scintillation measurements.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Determination of shadow-band structure from stellar scintillation measurements. Protheroe, W. M. Abstract On three nights in March, 1954, observations of stellar shadow band structure were made using the method described by Keller.' The observations were made with the i~-,'-inch refractor of the Emerson McMillin Observatory utilizing an RCA 6199 photomultiplier tube as the detector. The photocell output was recorded on magnetic tape and played back through a General Radio 762-B vibration analyzer. In this manner the time average of the frequency spectrum of the scintillation signal was obtained over the range from 2.5 to 450 cps. The observing technique utilized diaphrams with two one-inch apertures having center to center separations ranging from one to eleven inches. Since the shadow band pattern seems to show a biaxial symmetry about axes which are approximately perpendicular to each other, the observations with a given aperture spacing were made in duplicate, the line of centers being placed in coincidence with one and then the other axis of the pattern. Auto-correlation functions were then constructed from these observations using the root mean square fluctuations in light intensity integrated over all frequencies and also at 20, 150, and 250 cps. These curves have the following properties: I. They resemble zero-order Bessel functions and in general can be fitted fairly well by a single function of this type having a characteristic wave length around five or ten inches. A better fit can be obtained by the addition of one or two more zero-order Bessel functions having smaller amplitudes and other characteristic wave lengths. 2. The characteristic lengths associated with the one axis of symmetry are in general shorter than those associated with the other. 3. On one night, i6 March, the auto-correlation curves for one direction were essentially the same for all frequencies. A change in the shape of the auto-correlation curves with frequency was apparent in the other direction, however. This indicates that the amplitudes of the characteristic wave lengths measured in this direction depended on frequency. Such an effect is to be expected if the shadow band pattern is in motion along the direction of separation of the holes~ It was observed that this was the direction associated with the generally larger characteristic wave lengths. This work was sponsored in part by the Cambridge Air Force Research Center through a contract with the Ohio State University Research Foundation. s~. A. J. 59, 326, 5954. Perkins Observatory, Delaware, Ohio. Publication: The Astronomical Journal Pub Date: October 1954 DOI: 10.1086/107041 Bibcode: 1954AJ.....59..331P full text sources ADS |

Flexure with shear and associated torsion in prisms of uni-axial and asymmetric cross-sections

It is now well over eighty years ago since Barre de Saint-Venant reduced the problem of the beam of constant cross-section under the action of a single transverse load to the search for plane harmonic functions satisfying a certain condition round the boundary of the cross-section. The solutions due to Saint-Venant, which include the rectangular, elliptic and circular cross-sections, are all cases in which the cross-sections have two axes of symmetry at right angles, meeting of necessity in the centroid of the cross-section, and along these axes the single transverse load is resolved. These axes are principal axes, and his solution depends upon this fact. Some less useful solutions exist for the load along one axis of certain beams of such bi-axial symmetry of cross-section, the solutions not yet being known for the load along the perpendicular axis.