Question: Concern the crystal lattice for titanium, which has the hexagonal structure shown on the left in the accompanying figure. The vectors in R 3 form

Concern the crystal lattice for titanium, which has the hexagonal structure shown on the left in the accompanying figure. The vectors 2.6 -1.5 0 0 3 0 0 0 4.8

in R³ form a basis for the unit cell shown on the right. The numbers here are Angstrom units (1 A = 10^-8 cm). In alloys of titanium, some additional atoms may be in the unit cell at the octahedral and tetrahedral sites (so named because of the geometric objects formed by atoms at these locations).

One of the tetrahedral sites is

Determine the coordinates of this site relative to the standard basis of R³.

2.6 -1.5 0 0 3 0 0 0 4.8

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