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Explicit formulas for the calculation of stress are presented based on the stress theorem and the local-density-functional approximation.Norm-conserving pseudopotentials are applied in a planewave basis for calculations on the semiconductors Si, Ge, and GaAs. Besides the lattice constants and bulk moduli, complete sets of elastic constants are given, together with the optical I phonon frequencies and interna1-strain parameter g. E1ectronic charge density structure factors, deformation potentials, and strain-induced splittirigs of phonons are given, as well as the nonlinear thirdorder elastic constants. Good agreement with experiment is found throughout, except for persistent deviations from the x-ray diffraction values for g.

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The calibration parameters of a vector magnetometer are estimated only by the use of a scalar reference magnetometer. The method presented in this paper differs from those previously reported in its linearized parametrization. This allows the determination of three offsets or signals in the absence of a magnetic field, three scale factors for normalization of the axes and three non-orthogonality angles which build up an orthogonal system intrinsically in the sensor. The advantage of this method compared with others lies in its linear least squares estimator, which finds independently and uniquely the parameters for a given data set. Therefore, a magnetometer may be characterized inexpensively in the Earth's magnetic-field environment. This procedure has been used successfully in the pre-flight calibration of the state-of-the-art magnetometers on board the magnetic mapping satellites Ørsted, Astrid-2, CHAMP and SAC-C. By using this method, full-Earth-field-range magnetometers (±65536.0 nT) can be characterized down to an absolute precision of 0.5 nT, non-orthogonality of only 2 arcsec and a resolution of 0.2 nT.