Crystallographic Direction to Point: What is the first step to convert a crystallographic direction to a head-tail point representation?

• A. Head-tail calculation
• B. Multiply to clear fractions
• C. Put in brackets and put dash line over negative signs
• D. Divide by the highest common factor

Answer: (A)

The main idea is to treat a crystallographic direction as a displacement from tail to head and form the head-tail vector that points to the lattice point defined by the direction. That is exactly what the head-tail calculation does: it converts the direction [uvw] into the actual displacement vector from the origin to the point with coordinates proportional to (u, v, w). For example, a direction [2 4 6] corresponds to a head at (2, 4, 6) in lattice units, i.e., the head-tail vector from the origin to that point. After this step, you would typically simplify to the smallest integer triple (by dividing by the greatest common factor) or clear fractions if present, but those come after establishing the head-tail vector. The other steps are formatting or normalization steps that follow once you have the basic head-tail vector.