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Quaternions and Cauchy Classical Theory of Elasticity

Danielewski Marek, Sapa Lucjan

Advances in Manufacturing Science and Technology

2020

Vol. 44, nr 2

67--70

Developed by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.

The structure and optical properties of lead-free transparent KNLTN-La0.01 ceramics prepared by conventional sintering technique

Yang W L, Xiu H J, Xiong Y L, Wang J, Yuan C X, Wei J, Zhou Z X

Materials Science Poland

2014

Vol. 32, No. 4

597--603

(Na0.52K0.44Li0.04)0.97La0.01Ta0.20Nb0.80O3 (KNLTN–La0.01) lead-free subtransparent ceramics was prepared by a conventional sintering technique. The structure and the optical properties of the ceramics were investigated. The room temperature crystallographic indexing revealed the ABO3 perovskite type, tetragonal phase and P4mm point group in the ceramics. The surface and fractured surface SEM micrographs showed a dense microstructure with few micropores in KNLTN–La0.01 ceramics, which was obviously better than for the pure KNLTN ceramics. The refractive indexes of the films were investigated by an ellipsometer and the results show that the KNLTN–La0.01 subtransparent ceramics reveals significant wavelength dependent dispersion. The refractive index ranges from 2.14 to 2.06 with the wavelength increase from 380 nm to 900 nm. The dispersive behavior was analyzed by three parameters of Cauchy dispersion model and the values of the parameters A, B and C are 2.0610±0.0005, 0.0054±0.0003 and 0.00069±0.00004, respectively.