Detailed neutron powder diffraction measurements have been carried out on two polymorphs of anhydrous magnesium sulfate, α-MgSO4 and β-MgSO4. α-MgSO4 is orthorhombic, space group Cmcm ( Z = 4); at 4.2 K the unit-cell dimensions are a = 5.16863 (3), b = 7.86781 (5), c = 6.46674 (5) Å, V = 262.975 (2) Å3 [ρcalc = 3040.16 (2) kg m−3], and at 300 K, a = 5.17471 (3), b = 7.87563 (5), c = 6.49517 (5) Å, V = 264.705 (2) Å3 [ρcalc = 3020.29 (2) kg m−3]. The axial and volumetric thermal expansion coefficients are positive at all temperatures and exhibit no unusual behaviour. Structures were refined at 4.2 and 300 K to RP < 3%; less precise structural parameters were determined during warming from 4.2 to 300 K. β-MgSO4 has a more complex structure, crystallizing in space group Pbnm ( Z = 4); the unit-cell dimensions at 4.2 K are a = 4.73431 (8), b = 8.58170 (12), c = 6.67266 (11) Å, V = 271.100 (5) Å3 [ρcalc = 2949.04 (5) kg m−3], and at 300 K, a = 4.74598 (7), b = 8.58310 (10), c = 6.70933 (10) Å, V = 273.306 (4) Å3 [ρcalc = 2925.42 (4) kg m−3]. The thermal expansivities of the a and c axes, and the volumetric thermal expansion coefficient, are positive at all temperatures and normally behaved. However, the thermal expansion of the b axis is both very small and negative below ∼125 K. Structural and thermal motion parameters for β-MgSO4 as a function of temperature are also reported. [ABSTRACT FROM AUTHOR]