Undistorted Configuration Research Articles

On isotropic tensors and elastic moduli

AbstractThe use of even-order isotropic tensors in non-linear elasticity theory is discussed in this paper. A notation is adopted through which these tensors can be represented conveniently so that their interdependence is clearly shown. Information about the number of independent elastic constants required is then readily available for use in an expansion of the stress to various orders in the strain relative to the undistorted configuration of the elastic material in question.For an incompressible isotropic hyperelastic solid, it is shown that each principal component of the distortional part of the stress is expressible as a function only of the corresponding principal component of strain to the fourth order. Under certain conditions, which are not too restrictive, this result can be extended to higher orders.

Molecular Structures of Gaseous Hexabromo- and ortho-Dibromobenzene as Determined by Electron Diffraction

The molecular structures of hexabromo- and ortho-dibromobenzene have been studied by least-squares refinements based on gaseous electron-diffraction intensity data. The equilibrium conformation of ortho-dibromobenzene is found to be planar with C2v symmetry and with an angle of 63.6°±0.5° between the two carbon—bromine bonds. For hexabromobenzene, the ortho-bromine—bromine distance indicates a distorted structure possessing S6 symmetry with every second bromine atom above and below the plane of the benzene ring. The other bromine—bromine and the nonbonded carbon—bromine distances, however, are in better agreement with a planar and undistorted configuration. Possible structures of this molecule are discussed in the text. The most important molecular parameters and estimated standard deviations are listed in Table IV. Accurate partial-wave scattering factors for the atomic scattering of 40-keV electrons have been applied in some refinements. The results are compared with the results obtained using scattering factors according to the first Born approximation, and a better agreement with the experimental data is observed for the former scattering factors.

Symmetry of Transition Metal Impurity Sites in Crystals as Inferred from Optical Spectra

The polarized optical spectra of several transition metal ion impurities in crystals with the wurtzite structure; Cs2ZnX4 (where X−=Cl− or Br−); and Al2O3 have been measured at temperatures ranging from that of liquid helium to room temperature. In all these cases the transition metal ion substitutes for a cation of pure compound. The gross features of the spectra are explained by crystal field theory for the impurity ions in a potential field arising from the nearest-neighbor ligands in their undistorted configuration. The finer details of the spectra and the polarization effects which are observed are used to infer the actual site symmetry of the impurity ion. The trigonal field splitting compared to the calculated value indicates that certain ions in Al2O3 are displaced from the aluminum site along the threefold axis. The breadth of certain bands, and in some cases the lattice vibration progressions which are observed, have been interpreted as being due to a reduction in the symmetry of the electronically exicted ion and its ligand environment from that of the ground-state configuration. In the case of Mn3+ in corundum there is very good evidence for a highly distorted site, presumably due to the Jahn-Teller effect.

Investigation of Bloch wall fine structures by magnetic force microscopy

Using a magnetic force microscope (MFM), measurements have been performed on single crystal iron whiskers. These samples exhibit a comparatively simple magnetic domain structure and a high degree of crystallographic perfection. STM measurements yield an average surface corrugation of about 3 nm. These nearly ideal boundary conditions permit an investigation of the undistorted surface configuration of Bloch walls in a cubic bulk crystal. Interactions between the stray field configuration of the sample and a ferromagnetic microscope tip have been measured with a new MFM device which is based on direct compliance detection. Measurements have been performed in the constant-current mode, as well as in the constant-compliance, mode. Control observation by means of the Kerr magneto-optic effect permit an interpretation of the obtained MFM data in terms of isolated 180° Bloch walls. The fine structure of these walls has been analysed and compared with results obtained from model calculations.