The crystal structure of magnesium boron nitride in the low-pressure phase, Mg3BN3(L), has been solved ab initio from X-ray powder data. The cell is hexagonal (space group P63/mmc, Z = 2) with a = 3.54453 (4), c = 16-03536 (30)/k. Initial positional parameters for the Mg atoms were obtained from Patterson functions generated by 50 integrated intensities derived from a whole-powder pattern decomposition. The remaining atoms were located by trial-and-error model building, followed by Rietveld refinements (R,p = 8.5%). The structure can be described as consisting of ABB'BACC'CA... layers perpendicular to the c axis with linear N-~-B~N molecular anions at position A, Mg 2+ at positions B and C and Mg 2+ with three coordinating N atoms at positions B' and C', although Mg3BN3(L) is not a layer compound. A very similar structure has also been obtained by applying standard direct methods to the same intensity data. A high-quality electrondensity map has been calculated from the structurefactor data using the maximum-entropy method.
For an equation representing creep strain-time relationship curves of high temperature materials, the equations which represent from the primary creep region to the tertiary creep region using exponential functions such as the modified θ projection [3] have already been proposed. However, the estimated values by the modified θ projection don't necessarily coincide with the measured values, and deviations occur between the estimated values and the measured values [8]. Then in this paper, we propose a new creep equation using the Discrete Cosine Transform (DCT). According to this equation, all the estimated values coincide with the measured values and each interpolated value between the measured points gives a reasonable value. Therefore it is possible to express a creep curve quite well from the primary creep region to the tertiary creep region by using the DCT.
It is well-known that the creep equation obtained by the modified θ projection [2] describes well from the primary creep region to the tertiary creep region. However, unlike the power law such as that applied by the Bailey-Norton method, the stress variables and temperature variables are not found in the equation coefficients. Therefore, the users of this equation must find functions containing temperature variables and stress variables to display the equation coefficients. Thus, among the three coefficients A, α, and B included in the equation of the modified θ projection, the rate constant α, which exerts the largest influence on the curvature and the minimum creep strain rate of the creep curve [3], was selected as the object of investigation. Moreover, by considering the Cr-Mo-V steel and the Ni-based superalloy as examples, the expression of α was investigated. As a result, it was found that the discrete cosine transform and series can be applied not only to the coefficients of the creep equation but also to the creep equation itself. It is very important that the Fourier transform, which is considered to be applicable only to periodic functions, can be applied to non-periodic functions like a creep equation or its coefficients without apodizing such as windowing [9].
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