Crystallography concept check A characteristic property of a crystal is the periodicity of its atomic structure (long-range order). Is this statement correct?

Introduction / Context:
Crystals are solids with atoms arranged in a repeating, periodic lattice exhibiting long-range order. This periodicity is foundational in solid-state physics, dictating band structures, diffraction patterns, and many physical properties.

Given Data / Assumptions:

• Ideal crystalline materials (ignoring defects and thermal vibrations).
• Periodic arrangement described by lattice vectors and a basis.
• Amorphous solids lack long-range translational periodicity.

Concept / Approach:

A crystalline solid possesses translational symmetry: shifting the crystal by integer combinations of primitive lattice vectors leaves it invariant. This periodicity leads to Bragg diffraction, reciprocal lattices, and the validity of Bloch’s theorem for electron wavefunctions. While real crystals include dislocations, vacancies, and thermal motion, the underlying long-range order remains their defining feature.

Step-by-Step Solution:

Verification / Alternative check:

Experimental X-ray, neutron, or electron diffraction from crystals shows sharp Bragg peaks at reciprocal lattice positions, directly evidencing periodicity.

Why Other Options Are Wrong:

(b) contradicts the definition; (c) periodicity persists at ordinary temperatures though thermal vibrations broaden peaks; (d) metals form crystals (e.g., FCC copper), so claiming false for all metals is incorrect; (e) amorphous solids explicitly lack such periodicity.

Common Pitfalls:

Confusing short-range order (present in many solids) with long-range periodic order (distinct to crystals); overlooking defects which do not negate the fundamental periodic lattice.

Final Answer:

True