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## Solution of problem 3

Solution 3. Change of the coordinate system.
For the problem, see p. .

The new origin has the coordinates referred to the present origin . Therefore, the change of coordinates consists of subtracting 0, from the old values, i.e. leave the coordinate unchanged, add to the coordinate, and subtract from the coordinate.

The new coordinates are

(i) (ii) (iii) This oxygen atom is obviously not the one (0,0.067,0.198) listed by the Structure Reports but must be a symmetrically equivalent one. Therefore, it is necessary to determine also the new coordinates of the other oxygen atoms.

(iv) The coordinates of the other oxygen atoms are (normalized ): The first one of these oxygen atoms corresponds to the one representing the results of the later refinement with higher accurancy. The distance is reduced from 1.62 Å to 1.61 Å.

The change of basis to the primitive cell is described by the matrix .

One determines the inverse matrix by which the coordinates are transformed using the formula (5.3.6): . The coordinates x are those referred to the origin in .

(v)
The new coordinates of the first atom are (vi)
The new coordinates of the first atom are (vii)
The new coordinates of the first atom are .     Next: Index Up: Solution of the exercises Previous: Solution of problem 2