Abstract
Calculations of the rigid unit mode (RUM) spectrum of the high-temperature phase of SiO2 tridymite are used to explain the patterns of diffuse scattering seen in transmission electron microscopy experiments. These results show that RUM's can occur with wave vectors on curved surfaces in reciprocal space rather than being confined to symmetry points, lines or planes. The fact that the calculations reproduce the detail seen in the diffuse scattering provides a striking nontrivial confirmation of the validity of the rigid unit mode model.
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Berge B, Bachheimer JP, Dolino G, Vallade M, Zeyen CME (1986) Inelastic neutron scattering study of quartz near the incommensurate phase transition. Ferroelectrics 66: 73–84
Bethke J, Dolino G, Eckold G, Berge B, Vallade M, Zeyen CME, Hahn T, Arnold H, Moussa F (1987) Phonon dispersion and mode coupling in high-quartz near the incommensurate phase transition. Europhys Lett 3: 207–212
Boysen H (1990) Neutron scattering and phase transitions in leucite. In: Salje EKH (ed) Phase transitions in ferroelastic and co-elastic crystals, pp 334–349. Cambridge University Press, Cambridge
Dolino G, Berge B, Vallade M, Moussa F (1989) Inelastic neutron scattering study of the origin of the incommensurate phase of quartz. Physica B156: 15–16
Dolino G, Berge B, Vallade M, Moussa F (1992) Origin of the incommensurate phase of quartz: I. Inelastic neutron scattering study of the high temperature β phase of quartz. Journal de Physique 12: 1461–1480
Dove MT (1993) Introduction to Lattice Dynamics. Cambridge University Press, Cambridge
Dove MT, Giddy AP, Heine V (1992) On the application of mean- field and Landau theory to displacive phase transitions. Ferroelectrics 136: 33–49
Dove MT, Giddy AP, Heine V (1993) Rigid unit mode model of displacive phase transitions in framework silicates. Trans Amer Cryst Assoc 27: 65–74
Dove MT, Heine V, Hammonds KD (1995a) Rigid unit modes iri framework silicates. Mineralogical Mag 59: 629–639
Dove MT, Chen X, Giddy AP, Hammonds KD, Heine V (1995b) Simplicity in complexity: structural phase transitions in silicate framework structures. Phys Rev Lett (submitted)
Giddy AP, Dove MT, Pawley GS, Heine V (1993) The determination of rigid unit modes as potential soft modes for displacive phase transitions in framework crystal structures. Acta Crystallogr A49: 697–703
Hammonds KD, Dove MT, Giddy AP, Heine V (1994) CRUSH: a FORTRAN program for the analysis of the rigid unit mode spectrum of a framework structure. Amer Mineral 79: 1207–1209
Hammonds KD, Dove MT, Giddy AP, Heine V, Winkler B (1995) Rigid unit phonon modes and structural phase transitions in framework silicates. Amer Mineral (submitted)
Hatch DM, Ghose S (1991) The α-β phase transition in cristobalite, SiO2. Phys Chem Minerals 17: 554–562
Hua GL, Welberry TR, Withers RL, Thompson JG (1988) An electron diffraction and lattice-dynamical study of the diffuse scattering in β-cristobalite, SiO2. J Appl Crystallogr 21: 458–465
Phillips BL, Thompson JG, Xiao Y, Kirkpatrick RJ (1993) Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO2 and A1PO4 from 31P, 27Al and 29Si NMR spectroscopy from 770 K. Phys Chem Minerals 20: 341–352
Sollich P, Heine V, Dove MT (1994) The Ginzburg interval in soft mode phase transitions: consequences of the Rigid Unit Mode picture. J Phys Cond Matter 6: 3171–3196
Spearing DR, Farnan I, Stebbins JF (1992) Dynamics of the α-β phase transitions in quartz and cristobalite as observed by in situ high-temperature 29Si and 17O NMR. Phys Chem Minerals 19: 309–321
Swainson IP, Dove MT (1993) Low-frequency floppy modes in β-cristobalite. Phys Rev Lett 71: 193–196
Swainson IP, Dove MT (1995a) Molecular dynamics simulation of α- and β-cristobalite. J Phys Cond Matter 7: 1771–1788
Swainson IP, Dove MT (1995b) On the thermal expansion of β-cristobalite. Phys Chem Minerals 22: 61–65
Tautz FS, Heine V, Dove MT, Chen X (1991) Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition. Phys Chem Minerals 18: 326–336
Vallade M, Berge B, Dolino G (1992) Origin of the incommensurate phase of quartz: II. Interpretation of inelastic neutron scattering data. Journal de Physique. I. 2: 1481–1495
Welberry TR, Hua GL, Withers RL (1989) An optical transform and Monte Carlo study of the disorder in β-cristobalite SiO2. J Appl Crystallogr 22: 87–95
Withers RL, Thompson JG, Welberry TR (1989) The structure and microstructure of α-cristobalite and its relationship to β-cristobalite. Phys Chem Minerals 16: 517–523
Withers RL, Thompson JG, Xiao Y, Kirkpatrick RJ (1994) An electron diffraction study of the polymorphs of SiO2-tridymite. Phys Chem Minerals 21: 421–433
Xiao Y, Kirkpatrick RJ (1993) Structural phase transitions of tridymite: a 29Si NMR investigation. Amer Mineral 78: 241–244
Xiao Y, Kirkpatrick RJ, Kim YJ (1994) Investigation of tridymite by 29Si MAS NMR-modulated structures and structural phase transitions. Phys Chem Minerals 22: 30–40
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Dove, M.T., Hammonds, K.D., Heine, V. et al. Rigid unit modes in the high-temperature phase of SiO2 tridymite: calculations and electron diffraction. Phys Chem Minerals 23, 56–62 (1996). https://doi.org/10.1007/BF00202994
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DOI: https://doi.org/10.1007/BF00202994