Warming can lengthen or shorten a solid

Compare two hypothetical samples of the same starting length. One has a positive linear expansion coefficient; one has a negative coefficient. The coefficients are editable examples, not material specifications.

Starting length (millimetres)Temperature change (kelvin)Sample A coefficient (millionths per kelvin)Sample B coefficient (millionths per kelvin)

Default: Sample A lengthens by 115 micrometres; Sample B shortens by 45 micrometres.

Formula and limits

For a small temperature interval, ΔL=αL₀ΔT. The displayed coefficients are in 10⁻⁶/K. A cubic isotropic material has approximately ΔV/V≈3αΔT for a sufficiently small change.

Real coefficients vary with temperature, crystal phase and direction. A phase transition, moisture, constraints or microstructure can change the result. This is an ideal freely expanding sample calculation, not an engineering tolerance, composite design or measurement of a named specimen.

Background: Research on zirconium tungstate’s vibrational mechanisms. This page sends no information.