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A theoretical expression for a range of the d/P0 ratio in which two distinct states exist in the equilibrium condition has been derived as a function of Asa0d/K, where Asa0 is the azimuthal anchoring energy, K the elastic constant and d the cell thickness. An expression for the lower limit of azimuthal anchoring energy exhibiting two distinct states has been derived. Theoretical calculations have been performed on the bi-stable energy curve which has two minimal energy levels corresponding to bi-stable states. It has been shown that the energy barrier between the two states mainly originates from the azimuthal anchoring energy and the height of the energy barrier is affected by the d/P0 ratio and cell thickness.

A new violet phosphor was synthesized by sintering under the reduction condition from the Sr–Al–O:Eu powder oxidized from an ethylenediaminetetraacetic (EDTA) complex on a polycrystalline alumina plate. The crystalline phase of violet phosphor was determined to be Sr7Al12O25 by the change in the crystallinity of the product with a change in the composition of the raw material. The emission wavelength of the phosphor was 410 nm for Sr7Al12O25:Eu2+. For the composition of Sr:Al:Eu = 6.86:8:0.14 in the EDTA complex with sintering at 1400 °C, Sr7Al12O25:Eu2+ was obtained only in the crystalline phase of Sr7Al12O25 and exhibited the highest emission intensity of 410 nm in our experiment. The sintering temperature at sintering and composition of metals in the EDTA complex affected the emission wavelength change from 410 to 460 nm because of change in crystallinity. These changes indicate that the emission color in the range from violet to green is controlled by composition change or sintering temperature.

The transition process between bistable states in the bistable nematic (Bi-Nem) cell based on the anchoring breaking phenomenon has been strictly simulated by computer. In our simulation, the surface tilt angle dependence of the contribution of azimuthal anchoring to the surface free energy density has been taken into account. This leads to successful reproduction of the bistable operation of the Bi-Nem cells by the computer simulation. As a result, it has been clarified that in the transition process from the uniform state to the twisted state, the molecular orientation takes the 270 deg. twisted state at first and then changes toward to the 180 deg. twisted state. From our simulations, it is confirmed that the bistable transition occurs in limited regions of polar and azimuthal anchoring energy on the slave plate.