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The orthorhombic and rhombohedral structures of ferroelectric potassium niobate have been determined by neutron diffraction measurements on powdered crystals, using the profile refinement technique to analyse the data. In the orthorhombic phase at 22 degrees C the atomic displacements along (011) from the cubic perovskite positions are delta (K)=-0.006+ or-9 AA, delta (Nb)= 0.070 AA, delta (O I)=-0.138+ or-6 AA and delta (O II) identical to delta (O III)=-0.125+ or-4 AA. In the rhombohedral phase at 23oK, the displacements are along (111); delta (K)=-0.013+ or-32 AA, delta (Nb)= 0.078 AA and delta (O I) identical to delta (O II) identical to delta (O III)=-0.140+ or-4 AA. As a check on the profile technique, the tetragonal structure was redetermined, and good agreement obtained with the previous single-crystal work, with displacements along (001) of delta (K)=-0.014+ or-26 AA, delta (Nb)= 0.063 AA, delta (O I)=-0 …