Structural refinements of time-of-flight neutron powder diffraction data for Mg(OD)(2) and inelastic neutron scattering measurements for Mg(OH)2 demonstrate that the mechanism of thermal contraction is primarily the reduction of the octahedral thickness and secondarily the reduction of the interlayer thickness. The contraction of the octahedral layer thickness is 4 times as great as the contraction of the interlayer thickness over the temperature interval 300-15 K. The volume of brucite at 15 K is equivalent to that at 0.2 GPa which should not be sufficient to observe the H-bonding between the octahedral layer that occurs at high pressure; however, the three-site split-atom model, in which the O-D direction makes an angle a with the 3-fold c axis, provides a better fit to the data for each temperature than the single-site model. The O-D distance from the single-site model is markedly shortened by the large atomic displacement parameter of the D atom, but if the O-D distance is corrected for "riding" motion, it lengthens roughly to the same values determined from the three-site split-atom model. The temperature dependence of the lattice parameters are given by a = 3.1435 + 2.911 x 10(-5)T + 9.944 x 10(-8)T(2) -1.965 x 10(-11)T(3) -4.789 x 10(-13)T(4), c = 4.7478 + 1.793 x 10(-4)T + 4.496 x 10(-7)T(2) + 3.910 x 10(-10)T(3), V = 40.635 + 2.330 x 10(-3)T + 5.592 x 10(-6)T(2) + 1.748 x 10(-9)T(3), for T in degrees C. The vibrational spectrum of hydrogen in Mg(OH)(2) at 15 K obtained from inelastic scattering measurements shows a sharp OH stretch band at 461.8 meV, an E-u OH libration at 47.5 meV, and other broad features due to lattice vibrations and combination excitations. No evidence of enhanced hydrogen bonding was found at low temperatures.