Abstract
A molecular dynamics simulation of quartz at different temperatures both in the a and in the β phase has been conducted. The α-β phase transition could be observed. A phonon analysis of the β-phase confirms and rounds out in a quantitative way the origin of the incommensurate (ic) modulated phase. In particular it traces the optic soft mode at Γ becoming (to a good approximation) a so-called rigid unit mode (RUM) at q≠0, and elucidates its coupling to the transverse acoustic mode which precipitates the incommensurate transition. This success underpins and illuminates the concept of RUMs and their role in structural phase transitions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aslanyan TA, Levanyuk AP (1979) On the Possibility of an Incommensurate Phase near the α-β Transition Point in Quartz. Solid State Commun 31:547–550
Aslanyan TA, Levanyuk AP, Vallade M, Lajzerowicz J (1983) Various Possibilities for the Formation of Incommensurate Super-structure near the α-β Transition in Quartz. J Phys C16:6705–6712
Axe JD, Shirane G (1970) Study of the α-β Quartz Phase Transformation by Inelastic Neutron Scattering. Phys Rev B1:342–348
Axe JD, Harada J, Shirane G (1970) Anomalous Acoustic Dispersion in Centrosymmetric Crystals with Soft Optic Branches. Phys Rev B1:1227–1234
Barron THK, Huang CC, Pasternak A (1976) Interatomic Forces an Lattice Dynamics of α-. J Phys C 9:3925–3940
Berge B, Dolino G, Vallade M (1984) Incommensurate Phase of Quartz II: Brillouin Scattering Studies. J Phys 45:715–724
Berge B, Bachheimer JP, Dolino G, Vallade M (1986) Inelastic Neutron Scattering Study of Quartz near the Incommensurate Phase Transition. Ferroelectrics 66:73–84
Boysen H, Dorner B, Frey F, Grimm H (1980) Dynamic Structure Determination for two Interacting Modes at the M-Point in α and β Quartz by Inelastic Neutron Scattering. J Phys C13:6127–6146
Cohen ML, Heine V (1970) The Fitting of Pseudopotentials to Experimental Data and their Subsequent Application. Solid State Phys 24:78–80
Dolino G (1986) The Incommensurate Phase of Quartz. In: Blinc R, Levanyuk AP (eds) Incommensurate Phases in Dielectrics, Vol. 2, North Holland, Amsterdam, pp 205–232
Dolino G, Berge B, Vallade M, Moussa F (1989) Inelastic Neutron Scattering Study of the Origin of the Incommensurate Phase of Quartz. Phys Rev B156:15–16
Dorner B, Grimm H, Rzany H (1980) Phonon Dispersion Branches in α-Quartz. J Phys C13:6607–6612
Dove MT (1988) Molecular Dynamics Simulation in Solid State Sciences. In: Salje EK (ed) Physical Properties and Thermodynamic Behaviour of Minerals, NATO ASI Series, Vol. 225. Reidel, Dordrecht, pp 501–590
Dove MT, Lynden-Bell RM (1986) A Model of the Paraelectric Phase of Thiourera. Philos Mag 54:443–463
Elcombe MM (1967) Some Aspects of Lattice Dynamics of α-Quartz. Proc Phys Soc 91:947–958
Giddy A (1991) Thesis, University of Cambridge, UK
Giddy A, Dove MT, Heine V, Chen XJ (1991) (to be published)
Gouhara K, Kato N (1984) Refined Observations of Satellite Reflections in the Intermediate Phase of Quartz. J Phys Soc Japan 53:2177–2180
Grimm H, Dorner B (1975) On the Mechanism of the α-β Phase Transformation of Quartz. Phys Chem Solids 36:407–413
Heine V (1988) The Microscopic Mechanisms of Complex Structural Phase Transitions. In: Salje EK (ed) Physical Properties and Thermodynamic Behaviour of Minerals, NATO ASI Series, Vol 225. Reidel, Dordrecht, pp 1–15
Heine V, McConnell JDC (1984) The Origin of Incommensurate Structures in Insulators. J Phys C17:1199–1220
Heine V, Lynden-Bell RM, McConnell JDC, McConnell IR (1984) The Structure of The Incommensurate Modulated Phase of NaNO2. Z Phys B — Condensed Matter 56:229–239
McConnell JDC (1988) The Structure of Incommensurate Materials. In: Electron Beam Imaging of Non-crystalline Materials, IOP Short Meetings Series No 11., London, pp 1–18
McConnell JDC, Heine V (1984) An Aid to the Structural Analysis of Incommensurate Phases. Acta Crystallogr A40:473–482
McMillan PF, Hess AC (1990) Ab Initio Valence Force Field Calculations for Quartz. Phys Chem Minerals 17:97–107
Megaw HD (1973) Crystal Structures. WB Saunders, London, p 433
Kihara K (1990) Temperature Dependence of the Structure of Quartz. Eur J Mineral 2:63–70
Pawley GS, Thomas GW (1982) The Implementation of Lattice Calculations on the DAP. J Comp Phys 47:165–178
Striefler ME, Barsch GR (1975) Lattice Dynamics of α-Quartz. Phys Rev B12:4553–4566
Tautz FS, Dove MT (1991) to be published
Tauneyuki S, Tsukada M, Aoki H, Matsui Y (1988) First Principles Interatomic Potential of Silica Applied to Molecular Dynamics. Phys Rev Lett 61:869–872
Tsuneyuki S, Aoki H, Tsukada M (1990) Molecular-Dynamics Study of the a to β Structural Phase Transition of Quartz. Phys Rev Lett 64:776–779
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tautz, F.S., Heine, V., Dove, M.T. et al. Rigid unit modes in the molecular dynamics simulation of quartz and the incommensurate phase transition. Phys Chem Minerals 18, 326–336 (1991). https://doi.org/10.1007/BF00200190
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00200190