Kenji Hagiya

The structures of Ca2CoSi2O7, Ca2MgSi2O7, and Ca-2(Mg0.55Fe0.45)Si2O7 have been determined in the temperature range between 297 and 773 K with arbitrary intervals. The structures of the incommensurate phase of the three compounds are characterized by the presence of the six-, seven-, and eight-coordinated Ca-O polyhedra and of the bundles along the c-axes consisting of four arrays of the six-coordinated Ca-O polyhedra and an array of (TO4)-O-1 (T-1: Co, Mg, or Mg-Fe) tetrahedra in the structures. The number of bundles in each material decreases at elevated temperatures. The incommensurate phase undergoes a phase transition into the normal phase at 493 K in Ca2CoSi2O7, at 360 K in Ca2MgSi2O7, and at 510 K in Ca-2(ME0.55Fe0.45)Si2O7. The features of the structures of the normal phase are almost the same as those found in the basic structures (the averaged structures of the incommensurate structures), and this fact implies that the characteristics of the structures, such as the six-coordinated Ca-O polyhedra or fragments of the bundles, should be partially preserved at higher temperatures both in the incommensurate structures and also in the structures of the normal phase. Analyses of anisotropic displacement parameters clarified that disorder of the modulation waves is developed in the structures at higher temperatures. The evolution of a disorder in the structures was ascertained by observation of the circular diffuse streaks in the vicinity of the transition temperature between the incommensurate and normal phases.

The incommensurate structure of (Sr0.13Ca0.87)(2)CoSi2O7 at room temperature has been determined from single-crystal X-ray diffraction data. The compound has a non-centrosymmetric tetragonal basic cell of a = 7.8743 (4) and c = 5.0417 (2) Angstrom with the space group P (4) over bar 2(1)m. The refinements of the basic structure converged to R = 0.038 for 757 main reflections. The two-dimensional incommensurate structure is characterized by the wavevectors q(1) = 0.286 (3)(a* +b*) and q(2) = 0.286 (3)( -a* +b*), where a*, b* are the reciprocal lattice vectors of the basic structure. With the (3 + 2)dimensional superspace group P-p4mg(P (4) over bar 21m), the refinements converged to R = 0.071 for 1697 observed reflections (757 main and 940 satellite reflections). The structure is described in terms of displacement of the atoms, rotation, distortion of CoO4 and SiO4 tetrahedra, and the partial ordering of the Sr and Ca atoms accompanied with the modulation. Correlated evolution of these features throughout the crystal gives rise to various oxygen coordination around Ca/Sr. Comparison of the derived modulated structure to that of Ca2CoSi2O7 clarified that the partial substitution of Ca by large alkaline-earth atoms such as Sr should decrease the distortion of the polyhedra around the cations.

The incommensurate modulation in a synthetic iron-bearing åkermanite, Ca₂(Mg, Fe)Si₂O₇, has been determined at room temperature by the five-dimensional refinements of the structure. The basic structure is tetragonal P-42₁m with unit-cell dimensions a=7.8679(3), c=5.0144(2)Å, V=310.41(2)ų, Z=2, M=286.69, D_x=3.067Mg·m⁻³, MoKα with graphite monochromator, μ=3.199mm⁻¹, F(000)=284.49, Mg/(Mg+Fe)=0.554(6), R=0.065 for 770 unique reflections. The modulated structure is also tetragonal P_P4mg^p-42_1m, k₁=0.295(2)×(a^*+b^*), k₂=0.295(2)×(-a^*+b^*), where k₁, k₂ are the wave vectors and a^*, b^* the reciprocal lattice vectors of the basic structure. R=0.136 for 3965 unique reflections. The modulation is caused mainly by the shifts of Ca and O atoms, and substitutional modulation at (Mg, Fe) sites was not detected in the present studies. Six-coordinated Ca forming a distorted oxygen octahedra exists in the modulated structure and most of them form clusters together with the flattened (Mg,Fe)O₄ tetrahedra. The number of the clusters in the present material is less than that in Co-åkermanite. The reason may be attributed to the disorder of the modulation amplitudes and wavelength.