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The control of thermal expansion represents a challenge in materials design. This work shows that the length of the lattice parameter is a key element for controlling thermal expansion. By varying the lattice parameter through external pressure, chemical or other methods, the single-well potential energy of the polyhedra rotations (or of the atomic transverse vibrations) responsible for negative thermal expansion (NTE), can be turned into a quartic anharmonic potential or into a double-well potential, thus enhancing or suppressing the NTE, respectively. This result applied to framework materials should be taken into account to overcome the challenge of controlling thermal expansion.