Single crystal X-ray intensity data were collected for four compositionally-intermediate olivine and humanities and their crystal structures were refined by full-matrix, least-squares techniques to investigate cation ordering. Forsterite from Langban, Sweden [(Mg₀.₅₁₉Mn₀.₄₈₂Ca₀.₀₀₃Fe₀.₀₀₁)₂SiO₄, Pbnm, a = 4.94(2) b = 10.419(4), c = 6.123(2)A] was refined to R=0.029 (R_W=0.028) using 731 unique structures factors with F_obs > ^2σFobs. The mean Si-O distance is 1.637A. Site refinements yielded Mg/(Mg+Mn) ratios of 0.92 in the M(2)0₆ octahedron (<M-0> = 2.209A) and a distribution coefficient (K_D) of 0.011. Tephroite from Madagascar [(Mn₀.₈₉₀Mg₀.₀₉₀Fe₀.₀₁₃Ca₀.₀₀₇)₂SiO₄, Pbnm, a = 4.879(2) b = 10.419(4), c = 6.234(2)A] was refined to R = 0.038 (R_W=0.049) using 773 structure factors. The mean si-0 distance is 1.640A. Site refinement yielding Mg/(Mg+Mn) ratios of 0.17 in the M(1)0₆ octahedron (<M-0> = 2.185A) and 0.00 in the M(2)0₆ octahedron (<M-0> = 2.227A) and a K_D of 0.00. Alleghanyite from the Sterling Mine, Ogdensburg, New Jersey [(Mn₀.₅₆₈Mg₀.₃₉₀Zn₀.₀₃₇Ca₀.₀₀₁)₅(F,OH)₂, P2₁/b, a = 4.815(2), b=10.574(3), c=9.083(3)A, α=108.74(2)°] was refined to R = 0.048 (R_W=0.053) using 1873 structures. The mean Si-0 distance is 1.629A. Site refinement with Zn assigned to M93) yielded Mg/(Mg+Mn) ratios of 0.14 in the M(1)0₆ octahedron (<M-0> = 2.212A). The M(3)0₄(F,0H)₂ site (<M-0> = 2.118A) is occupied by the 0.81 Mg, 0.10 Mn and 0.09 Zn atoms. Manganhumite from Langban, Sweden [(Mn₀.₆₈Mg₀.₃₀Fe₀.₀₁Ca₀.₀₁)₇ (Si0₄)₃(OH)₂, Pbnm, a = 4.815(1), b = 10.580(2), c=21.448(5)A] was refined to R = 0.051 (R_W = 0.081) using 1562 structures factors. Mean Si-0 distances for the isolated tetrahedra are <Si(1)-0> = 1.62A and <Si(2)-0> = 1.632A. Site refinement yielded Mg/(Mg+Mn) ratios of 0.30 in the M(1)0₆ octahedron (<M-0> = 2.222 and 2.206A), and 0.75 in the M(3)0₄ (OH)₂ octahedron (<M-0> = 2.117A). Mean octahedral bond distances are positive linear functions of effective ionic radii calculated from the refined site occupancies and f, one-half the number of fluorine atoms per formula unit times the number to monovalent ligands associated with the octahedron. <M(1)-0> = 1.445 + 0.9172 <r_M(1)> <M(2)-(O,OH,F)> = 1.541 + 0.8185 <r_M(2)> - 0.01649 f <M(3)-(O,OH,F)> = 1.502 + 0.8386 <r_M(3)> - 0.02122 f Magnesium, manganese and other cations are ordered on the octahedral sites according to size criteria, although ligancy may be the controlling factor where charge balance and crystal-field effects are involved. Characterization of a suite of naturally-equilibrated Mg-Mn olivines, from Langban, Sweden by electron probe microanalysis, X-ray powder diffraction and infrared spectroscopy and comparison with data in the literature for synthetic specimens demonstrate those unit cell parameters and infrared band positions are nonlinear functions of composition for ordered samples and that nonlinearity increases with the degree of order but that calculated specific gravity is a linear function of composition. / Ph. D.