Question 1 For the plane shown below in the the hexagonal unit cell, determine: a. The indices referenced by the 3-axis coordinate system (a1,a2 and z). b. Convert these indices into an index set referenced to the 4-axis scheme (a1,a2,a3 and z).

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The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.