Zn2P2O7crystallizes in a thortveitite-like structure and features temperature-dependent polymorphism. At high temperatures (T> 500 K), the aristotype phase β-Zn2P2O7(C2/m,Z= 2,a≃ 6.60,b≃ 8.28,c≃ 4.53 Å, β ≃ 105.4°) is stable. At lower temperatures the lock-in phase α1-Zn2P2O7[at 350 K:I2/c,Z= 12,a= 20.1131 (13),b= 8.2769 (6),c= 9.109 (3) Å, β = 106.338 (16)°], a sixfold superstructure with commensurate modulation vectorq= (1/3, 0, 1/2), is stable. Between the stability ranges of the α1- and β-phases exists the intermediate, incommensurately modulated α2-Zn2P2O7phase with modulation wavevectorq≃ (0.33, 0, 0.40) andC2/m(α, 0, γ)0ssuperspace group symmetry. The α1→ α2lock-in phase transition atTL= 408 K is of first-order and features virtually no hysteresis. It is immediately followed by the second-order α2→ β transition to the non-modulated phase atTI≃ 430 K. This transformation is sluggish and even atT= 500 K very weak satellite reflections of the α2-phase were observed. Both phase transitions were analyzed with differential scanning calorimetry and high-temperature powder and single-crystal X-ray diffraction. The crystal structures of the α1- and α2-phases were refined from single crystal data collected atT= 350, 400, 405, 410, 415, 420, 425, 430, 450 and 500 K. Different models describing the slow transition from the incommensurately modulated α2- to the non-modulated β-phase were tested. In the model resulting in the best residuals, the bridging O atom of the [P2O7] group, which is located on a 2/mposition in the basic structure, is described as an overlap of an atom ordered in internal space and one atom disordered around the mirror plane. The occupancy of the ordered atom decreases with temperature until atT= 500 K virtually only the disordered atom remains. Simultaneously, the amplitude of the modulation functions of the remaining atoms decreases, so that theT= 500 K structure can be considered as theC2/maristotype structure, although the diffraction pattern still features satellite reflections of first order with very low intensities.
Optimization of the parameters in the RHIC single crystal heavy ion collimation