Precise lattice parameters and linear least squares

13 Precise lattice parameters and linear least squares 

After the powder diffraction pattern has been successfully indexed, the next step is to establish the unit cell dimensions with the highest possible precision. By combining Eqs. 5.2 and 5.3 one can see that the errors in the lattice parameters only depend on the errors in the measured Bragg angles assuming that Miller indices and A, are known exactly  

By differentiating the right hand side of Eq. 5.28 we find that the absolute error in the interplanar distance, ad, is a function of both the error in Bragg angle, a0, and Bragg angle  

Ideally, the Bragg angles close to 0 = 90° (20 = 180°) should be available to claim the precision of the unit cell dimensions equivalent to that of the precision of the used wavelength. Unfortunately, measurements at 20 = 180° 

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