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High-Q pure forsterite (Mg 2 SiO 4 ) ceramics with Qf = 240,000 GHz were developed by the usual solid sintering process, using raw materials of highly purified MgO and SiO 2 .The τ f (temperature coefficient of the resonant frequency) was a large and negative: -60 to -70 ppm/ºC. To adjust the τ f value to zero, rutile (TiO 2 ) with high τ f (450 ppm/ºC) was added. When sintering temperature was selected as low as possible, TiO 2 remained in the forsterite specimen, which raised τf from a negative to positive values. For instance, the 30 wt% TiO 2 added forsterite ceramics sintered at 1200ºC yield a high density (3.3 g/cm 3 ), which same as that of the same forsterite ceramics sintered at 1350ºC. A part of added TiO 2 works for sintering aid and residual ones do for arising the τf value from negative to positive. Improved forsterite ceramics have τ f = 0 ppm/˚C, ε r = 11 and Qf = 82,000 GHz, when they contains 24 wt% of TiO 2 and sintered at 1200ºC for 2h.

A method of stress analysis for a two dimensional crack, which is subjected to internal gas pressure, and situated parallel to a free surface of a material, is presented. It is based on the concept of continuously distributed edge dislocations of two kinds, i.e. one with Burgers vector normal to the free surface and the other with Burgers vector parallel to it.Stress fields of individual dislocations are chosen so as to satisfy stress free boundary conditions at the free surface, by taking account of image dislocations. Distributions of both kinds of dislocations in the crack are derived so as to give the internal gas pressure and, at the same time, to satisfy shear stress free boundary conditions on the crack surface. Stress fields try, ~ryy and trxy in the sub-surface layer are then determined from them. They have square root singularities at the crack-up.

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