We use time-of-flight neutron powder diffraction to examine static displacive disorder in three different pyrochlore A(2)B(2)O(6)O' compounds with Bi on the A site. The compounds (Bi1.5Zn0.5)(Nb1.5Zn0.5)O6O' (BZN), (Bi1.5Zn0.5)(Ta1.5Zn0.5)O6O' (BZT), and (Bi1.5Zn0.5)(Sb1.5Zn0.5)O6O' (BZS), are of interest - particularly BZN - for their high dielectric constants in the absence of any phase transition from the cubic high temperature phase. The local structures of the three compounds is characterized by displacive disorder from the ideal pyrochlore positions for both the A and O' sites, with the precise nature of the disorder being quite similar. However the extent of displacive disorder is different, despite the B-O networks being nearly identical in the three compounds. The reported dielectric constants of the three compounds are related to the extent of local displacement, and BZN, with the largest extent of local atomic displacement of A and O', is also reported to have the largest dielectric constant at 1 MHz. The dielectric constants are also related to the magnitudes of the thermal parameters of the different ions. The strongest correlation is found to involve the thermal parameter on the B site (Nb, Ta, or Sb). (C) 2006 Elsevier Ltd. All rights reserved.