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Journal articles on the topic 'Incommensurate phase'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Kubli, Martin, Matteo Savoini, Elsa Abreu, Bulat Burganov, Gabriel Lantz, Lucas Huber, Martin Neugebauer, et al. "Kinetics of a Phonon-Mediated Laser-Driven Structural Phase Transition in Sn2P2Se6." Applied Sciences 9, no. 3 (February 4, 2019): 525. http://dx.doi.org/10.3390/app9030525.

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We investigate the structural dynamics of the incommensurately modulated phase of Sn 2P 2Se 6 by means of time-resolved X-ray diffraction following excitation by an optical pump. Tracking the incommensurable distortion in the time domain enables us to identify the transport effects leading to a complete disappearance of the incommensurate phase over the course of 100 ns. These observations suggest that a thin surface layer of the high-temperature phase forms quickly after photo-excitation and then propagates into the material with a constant velocity of 3.7 m/s. Complementary static structural measurements reveal previously unreported higher-order satellite reflection in the incommensurate phase. These higher-order reflections are attributed to cubic vibrational terms in the Hamiltonian.

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2

Caracas, Razvan. "A database of incommensurate phases." Journal of Applied Crystallography 35, no. 1 (January 22, 2002): 120–21. http://dx.doi.org/10.1107/s0021889801017083.

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A database of incommensurate phases is currently available at http://www.mapr.ucl.ac.be/~crystal/index.html. The present database offers a fast direct retrieval system for structural, physical and bibliographical data of incommensurate phases. The database contains data about inorganic, non-composite, non-magnetic and non-superconducting incommensurate phases only. Classification is according to the physical mechanisms responsible for the incommensurate phase transition. The main classes of incommensurate phases thus obtained are: theA2BX4dielectrics family, zone-centre lock-in transition phases, cooperative Jahn–Teller incommensurates, tetragonal tungsten bronzes, charge-density wave systems and miscellaneous incommensurate phases. The latter class, because of the lack of available data, is classified on a chemical basis in several subclasses: silicates, perovskites, Mn-bearing oxides, other oxides, group VI compounds, intermetallics and other compounds. The database contains a brief description of the main physical, chemical and structural features of each phase, as stated in the literature. This description is very material- and bibliography-dependent and it is preceded by the phase transition sequence.

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3

Gągor, Anna. "Phase transitions in ferroelectric 4-aminopyridinium tetrachloroantimonate(III) – revisited." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 74, no. 2 (March 21, 2018): 217–25. http://dx.doi.org/10.1107/s2052520618003669.

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New X-ray diffraction studies on the crystal structure of ferroelectric [4-NH2C5H4NH][SbCl4] indicate that in the broad temperature range from 240 to 304 K covering the three intermediate phases, the crystal structure is modulated. Phase II is incommensurately modulated with modulation vectorq= βb*, β varying from 0.60 to 0.66 and monoclinicC2/c(0β0)s0 superspace group. Ferroelectric phase III is commensurate withq= 2\over 3b*andCc(0β0)0 symmetry. Polar phase IV is incommensurately modulated with β varying from 0.66 to 0.70 andCc(0β0)0 superspace group. In all phases only first-order satellites are observed along theb*direction. Two types of periodic deformation are present in the structure of modulated phases. The 4-aminopyridinium cations are subjected to occupation modulation whereas [SbCl4]−nchains are displacively modulated. The paraelectric–ferroelectric phase transition is an example of the incommensurate–commensurate transition of the lock-in type. A new mechanism for this transformation is proposed.

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4

Jacobs, A. E. "The incommensurate phase of." Journal of Physics: Condensed Matter 8, no. 5 (January 29, 1996): 517–26. http://dx.doi.org/10.1088/0953-8984/8/5/002.

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5

Weigel, Dominique. "Commensurate incommensurate phase transitions." Phase Transitions 16, no. 1-4 (June 1989): 341–49. http://dx.doi.org/10.1080/01411598908245708.

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6

Markgraf, S. A., C. A. Randall, A. S. Bhalla, and R. J. Reeder. "Incommensurate phase in Ba2TiSi2O8." Solid State Communications 75, no. 10 (September 1990): 821–24. http://dx.doi.org/10.1016/0038-1098(90)90758-4.

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7

Röthlisberger, Francois, Friedrich Seifert, and Michael Czank. "Chemical control of the commensurate-incommensurate phase transition in synthetic melilites." European Journal of Mineralogy 2, no. 5 (October 4, 1990): 585–94. http://dx.doi.org/10.1127/ejm/2/5/0585.

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8

Aizu, Kêitsiro. "Twofold Incommensurate Phase as Analogs of Semicommensurate Phases. On the Transitions [Prototypic→Ordinarily (or Onefold) Incommensurate →Twofold Incommensurate]." Journal of the Physical Society of Japan 55, no. 5 (May 15, 1986): 1663–70. http://dx.doi.org/10.1143/jpsj.55.1663.

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9

Morelli, Rose, and M. B. Walker. "Novel mechanism for the incommensurate-to-incommensurate phase transition inNbTe4." Physical Review Letters 62, no. 13 (March 27, 1989): 1520–23. http://dx.doi.org/10.1103/physrevlett.62.1520.

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10

Chen, Z. Y., and M. B. Walker. "Superspace symmetry modes and incommensurate-to-incommensurate phase transition inNbTe4." Physical Review B 40, no. 13 (November 1, 1989): 8983–94. http://dx.doi.org/10.1103/physrevb.40.8983.

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11

Xu, Z., Dwight Viehland, and D. A. Payne. "An incommensurate-commensurate phase transformation in antiferroelectric tin-modified lead zirconate titanate." Journal of Materials Research 10, no. 2 (February 1995): 453–60. http://dx.doi.org/10.1557/jmr.1995.0453.

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Antiferroelectric tin-modified lead zirconate titanate ceramics (PZST), with 42 at. % Sn and 4 at. % Ti, were studied by hot- and cold-stage transmission electron microscopy and selected area electron diffraction techniques. The previously reported tetragonal antiferroelectric state is shown to be an incommensurate orthohombic state. Observations revealed the existence of incommensurate 1/x 〈110〉 superlattice reflections below the temperature of the dielectric maximum. The modulation wavelength for this incommensurate structure was found to be metastably locked-in near and below room temperature. An incommensurate-commensurate orthorhombic antiferroelectric transformation was then observed at lower temperatures. However, an intermediate condition was observed over a relatively wide temperature range which was characterized by an intergrowth of 〈110〉 structural modulations, which was strongly diffuse along the 〈110〉. These structural observations were correlated with dispersion in the dielectric properties in the same temperature range. No previous reports of an incommensurate orthorhombic antiferroelectric state or an incommensurate-commensurate orthorhombic antiferroelectric transformation are known to exist.

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12

Aleksandrova, I. P., A. A. Sukhovsky, and K. S. Aleksandrov. "Novel incommensurate phase in Cs3Bi2I9." Solid State Communications 105, no. 5 (February 1998): 323–26. http://dx.doi.org/10.1016/s0038-1098(97)10086-2.

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13

Sechovský, V., L. Havela, P. Svoboda, A. Purwanto, Allen C. Larson, R. A. Robinson, K. Prokeš, H. Nakotte, F. R. de Boer, and H. Maletta. "Incommensurate antiferromagnetic phase in UNiGe." Journal of Applied Physics 76, no. 10 (November 15, 1994): 6217–19. http://dx.doi.org/10.1063/1.358286.

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14

Golovko, V. A., and D. G. Sannikov. "Incommensurate phase of type-IV." Ferroelectrics 95, no. 1 (July 1989): 75–77. http://dx.doi.org/10.1080/00150198908245181.

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15

Janssen, T. "Phase Transitions in Incommensurate Composites." Ferroelectrics 412, no. 1 (January 2011): 4–7. http://dx.doi.org/10.1080/00150193.2011.542682.

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16

Mizuno, Motohiro, Tetsuo Asaji, Masahiko Suhara, and Yoshihiro Furukawa. "NQR and NMR Studies of Phase Transitions in R2Pb[Cu(NO2)6] (R = K, Rb, Tl, Cs, and NH4)." Zeitschrift für Naturforschung A 51, no. 5-6 (June 1, 1996): 721–25. http://dx.doi.org/10.1515/zna-1996-5-660.

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Abstract39K, 87, 85Rb, 133Cs, 205T1, and 1, 2H NMR spin-lattice relaxation times T1 and 14N NQR spin-lattice relaxation times T1Q were determined for R2Pb[Cu(NO2)6] (R = K, Rb, Tl, Cs, and NH4). T1 of 39K and 87Rb showed very short values in the incommensurate phase as compared with those in the other phases. When the commensurate-incommensurate phase transition point is approached from below, 14N T1Q of the R = K, Rb, Tl, and NH4 compounds showed rapid decrease. On the other hand, that of the R = Cs compound began to decrease first after passing beyond the corresponding transition point. The difference of the T1Q behavior may be ascribed to the difference of the condensed phonon mode in the incommensurate phase.

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17

Nagakura, Sigemaro, Yoshihiko Hirotsu, Naoki Yamamoto, Katsumi Miyagawa, Yuji Ikeda, and Yoshio Nakamura. "Modulated structures of Bi-based high-Tc superconducting oxides studied by High Resolution Electron Microscopy and electron diffraction." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 80–81. http://dx.doi.org/10.1017/s0424820100173534.

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In the superconducting Bi-Sr-Ca-Cu-O system, ideal compositions of the low Tc(Tc∼90 K) and the high Tc(Tc∼110K) phases are Bi2Sr2CaCu2Oy(y∼8:2212 phase) and Bi2Sr2Ca2 Cu3Oy (y∼10:2223 phase), respectively. The fundamental structures of these phases are tetragonal with parameters: at=bt=0.54 and ct=3.08 nm for the 2212 phase, and at=bt=0.54 and ct=3.71 nm for the 2223 phase. These phases have incommensurate structures with modulation along their b-axes. In this study, the modulated structures of Pb-doped 2212 and 2223 phases have been investigated by means of high resolution electron microscopy and electron diffraction. Samples Bi2-xPbxSr2CaCu2Oy(x=0-0.4, melt-quenched and annealed) and Bi2−xPbxSr2Ca2Cu3Oy(x=0-0.6, sintered) were observed in high resolution electron microscopes operating at 200 kV and 1 MV.Analysis of the incommensurate modulated structures of the 2212 and 2223 phases was made by using samples Bi2Sr2CaCu2Oy and Bi1.6Pb0.4Sr2Ca2Cu3Oy. The lattice parameters of the incommensurate superstructures are a=at and c=ct for both of these phases, but b∼5bt and b∼bt for the 2212 and 2223 phases, respectively.

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18

Randall, C. A., R. Guo, A. S. Bhalla, and L. E. Cross. "Microstructure-property relations in tungsten bronze lead barium niobate, Pb1−xBaxNb2O6." Journal of Materials Research 6, no. 8 (August 1991): 1720–28. http://dx.doi.org/10.1557/jmr.1991.1720.

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Transmission electron microscopy (TEM) has been used to explore details of the structural phase transitions and corresponding microstructural features in the solid solution of Pb1−xBaxNb2O6 (PBN) tungsten bronze ferroelectrics at compositions embracing the morphotropic phase boundary between orthorhombic and tetragonal ferroelectric phases. In addition to the ferroelectric domain structures that were consistent with the expected symmetries, incommensurate ferroelastic phases were observed. The “onset” and “lock-in” transition temperatures are a function of the Pb/Ba ratio, and for lead-rich compositions it appears that the incommensurate distortion may occur above the ferroelectric Curie temperature in the paraelectric phase.

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19

Noohinejad, Leila, Sander van Smaalen, Václav Petříček, and Andreas Schönleber. "Incommensurately modulated structure of morpholinium tetrafluoroborate and configurationalversuschemical entropies at the incommensurate and lock-in phase transitions." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 73, no. 5 (September 13, 2017): 836–43. http://dx.doi.org/10.1107/s2052520617009398.

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Morpholinium tetrafluoroborate, [C4H10NO]+[BF4]−, belongs to a class of ferroelectric compoundsABX4. However, [C4H10NO]+[BF4]−does not develop ferroelectric properties because the incommensurate phase belowTc,I= 153 K is centrosymmetric with superspace groupPnam(σ100)00sand σ1= 0.42193 (12) atT= 130 K; the threefold superstructure belowTc,II= 117–118 K possesses the acentric but non-ferroelectric space groupP212121. At ambient conditions, [C4H10NO]+[BF4]−comprises orientationally disordered [BF4]−anions accommodated in cavities between four morpholinium cations. A structure model for the incommensurately modulated phase, which involves modulated orientational ordering of [BF4]−together with modulated distortions and displacements of the morpholinium ions is reported. A mechanism is proposed for the phase transitions, whereby at low temperatures morpholinium cations are shaped around the tetrafluoroborate anion in order to optimize the interactions with one orientation of this anion and, thus, forcing [BF4]−into this orientation. This mechanism is essentially different from a pure order–disorder phase transition. It is supported by consideration of the transition entropy. The difference in configurational entropy between the disordered and incommensurate phases has been computed from the structure models. It is shown to be much smaller than the experimental transition entropy reported by Owczareket al.[Chem. Phys.(2011),381, 11–20]. These features show that the order–disorder contribution is only a minor contribution to the transition entropy and that other factors, such as conformational changes, play a larger role in the phase transitions.

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20

Guo, Ru, and Zhen-qing Yang. "The origin of the incommensurate phase and the incommensurate-commensurate transition." Ferroelectrics 66, no. 1 (February 1986): 189–94. http://dx.doi.org/10.1080/00150198608227884.

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21

Andersen, S., Y. X. Guo, and R. Høier. "Incommensurate Boundary Shifts in the AlMnSi Cubic Phase." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 2 (August 12, 1990): 522–23. http://dx.doi.org/10.1017/s0424820100136210.

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The icosahedral quasicrystalline (IQ) phases of rapidly solidified materials, and especially that of the AlMnSi type, have been subjected to intensive research in recent years. These phases have been found to be closely related to periodic phases of similar composition, and orientation relationships have been found between the IQ and its decomposition products. Consequently, they are also of great importance in the study of the IQs. The most recognized periodic phase in this respect is probably the primitive α-AlMnSi phase (a = 12.68 Å). The 138 atoms in the unit cell are arranged in large atomic clusters, the socalled Mackay Icosahedra, with slightly deformed icosahedral symmetry. These clusters are believed also to be the building blocks of the quasicrystals and of some additional periodic decomposition phases, the difference between the structures being realized through a different stacking of the clusters. A thorough understanding of these periodic phases is therefore clearly important. Here we present a study of some of the defects that frequently appear in the α-phase.

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22

Stöger, Berthold. "Symmetry reduction in thortveitites: incommensurability and polytypism." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C182. http://dx.doi.org/10.1107/s2053273314098179.

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For many years periodicity was the defining property of crystalline materials. The discovery of numerous aperiodic materials like incommensurately modulated phases or quasi-crystals led to a paradigm shift and since 1992 crystallinity is defined by the IUCr via the discreteness of the diffraction pattern [1]. A different class of materials lacking periodicity in three dimensions, albeit following strict building principles, are polytypes. Polytypes are composed of modules that can be arranged in different but energetically similar ways. On the example of the thortveitite family of compounds it will be shown that these seemingly disparate phenomena can be linked to the same underlying cause, namely symmetry reduction. Many bivalent transition metal diphosphates(V), diarsenates(V) and divanadates(V) of general formula M2X2O7 (X=P, As, V) crystallize in the thortveitite structure type. The high temperature β-M2X2O7 phases feature one crystallographically unique X2O7 group located on a centre of inversion. Due to the unfavourable X-O-X angle of 1800these phases transform on cooling into lower symmetry structures. Thus, numerous superstructures based on the thortveitite aristotype have been described. Incommensurate structures can be considered as superstructures with symmetry reduction by an index of ∞. The first example in the thortveitite family was described by Palatinus et al. [2]. Since then we found several other incommensuarte thortveitites with varying modulation functions and phase-transition behaviour. If the symmetry reduction leads to layers with different local symmetry, the resulting structures are order-disorder (OD) polytypes [3], resulting in twinning or diffuse scattering. In (Co,Ni)2As2O7 both features, incommensurate modulation and systematic twinning, are combined. An overview of the crystal-chemistry and the complex phase-transition behaviour of the incommensurately modulated and/or polytypic thortveitite phases will be given.

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23

de Boissieu, Marc. "Phonon and phasons : from incommensurate phases to quasicrystals." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C9. http://dx.doi.org/10.1107/s2053273314099902.

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Aperiodic crystals are long range ordered phases, which lack translational symmetry. They encompass incommensurately modulated phases, incommensurate composites phases and quasicrystals (1). Whereas their atomic structure is now well understood, even for the case of quasicrystals, the understanding of their physical properties remains a challenging problem. In particular, because of the aperiodic long range order, the lattice dynamics present a specific behavior. In particular, it can be shown theoretically that besides phonon, a supplementary excitation exits in all aperiodic phases named phason. Phason modes arise from the degeneracy of the free energy of the system with respect to a phase shift and are always diffusive modes (1). After a general introduction on the different class of aperiodic crystals, we will illustrate experimental results on phason modes. We will in particular demonstrate that these phason modes lead to a flexibility of the structure that might have important consequences for physical properties. We will also discuss their importance for the understanding of stabilizing mechanisms that lead to the long-range aperiodic order.

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24

Palatinus, Lukás, Mongi Amami, and Sander van Smaalen. "Structure of incommensurate ammonium tetrafluoroberyllate studied by structure refinements and the maximum entropy method." Acta Crystallographica Section B Structural Science 60, no. 2 (March 18, 2004): 127–37. http://dx.doi.org/10.1107/s0108768104000874.

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Incommensurately modulated ammonium tetrafluoroberyllate (AFB) occurs in a narrow temperature interval between the paraelectric room-temperature phase with space group Pnma (Ti = 178 K) and the ferroelectric low-temperature phase with space group Pna21 (Tc = 173 K). The structure is determined from accurate single-crystal X-ray diffraction data collected with synchrotron radiation at 175 K. The superspace group of the structure is Pnma(α00)0ss with α = 0.4796 (4). Both structure refinements and the maximum entropy method lead to the same structure model, which involves only single harmonic modulations. The building units of the structure are BeF_4^{2-} and NH_4^+ complex ions with approximately tetrahedral point symmetry. They are relatively rigid and the modulations consist mainly of translations of the tetrahedra and their rotations around a fixed axis. The modulation is related to changes in the network of the hydrogen bonds. The low-temperature superstructure can be described as a commensurately modulated structure with the same superspace symmetry. The first harmonic modulations of the low-temperature and incommensurate phases are related by a scale factor with a value of approximately two. In addition, the low-temperature phase exhibits a second harmonic modulation that is responsible for shifts along c and the ferroelectricity in this phase. The experimental data of the incommensurate phase do not contain any evidence for the presence of a second harmonic in the modulation functions. This suggests that the development of the second harmonic, i.e. the development of the spontaneous polarization, is responsible for the lock-in transition.

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25

Aizu, Kêitsiro. "Possibility of the Transition from an Incommensurate Phase Having Constant Phase Differences to an Incommensurate Phase Having Varying Phase Differences." Journal of the Physical Society of Japan 54, no. 11 (November 15, 1985): 4213–20. http://dx.doi.org/10.1143/jpsj.54.4213.

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26

Dolinšek, J., and R. Blinc. "A Note on the 14N Electric Field Gradient Notizen: Tensors in Incommensurate [N(CH3)4]2ZnCl4." Zeitschrift für Naturforschung A 42, no. 3 (March 1, 1987): 305–6. http://dx.doi.org/10.1515/zna-1987-0318.

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The 14N electric field gradient tensors of [N(CH3)4]2ZnCl4 have been re-determined in the paraelectric phase at 26 °C and in the incommensurate phase at 16 °C. The results in the incommensurate phase show the “non-local” nature of the 14N EFG tensor interaction.

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27

Dorner, B., B. Schmid, K. Kakurai, and D. Petitgrand. "The phase diagram of RbFeCl3 in a magnetic field perpendicular to the chain direction." Canadian Journal of Physics 73, no. 11-12 (November 1, 1995): 800–804. http://dx.doi.org/10.1139/p95-116.

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The temperature dependence of the position and line width of antiferromagnetic Bragg peaks were measured at different applied magnetic fields up to 1.4 T by means of elastic neutron scattering. Three different types of temperature dependences were observed that can be attributed to the commensurate–incommensurate, commensurate–paramagnetic, and incommensurate–paramagnetic phase transitions. Below 0.3 T the transition goes from commensurate to incommensurate. Between 0.3 and 0.5 T a phase boundary was observed, but there is some doubt as to whether the structure at temperatures below this boundary is commensurate. Between 0.5 and 1.2 T the phase transition goes directly from commensurate to paramagnetic at around 2.5 K. For fields higher than 1.3 T and temperatures above 1.5 K no commensurate phase could be identified. But above 1.2 T and still at 1.4 T there exists an incommensurate phase. Based on these temperature dependences at different magnetic fields, phase boundaries in the H–T phase space are proposed and compared with the phase diagram obtained by previous susceptibility measurements.

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28

RUSTAMOV, K. A., and B. R. GADJIEV. "THEORETICAL MODEL FOR THE HIGH-FREQUENCY DYNAMICAL SUSCEPTIBILITY IN THE IMPROPER SEGNETOELECTRICS." Modern Physics Letters B 07, no. 20 (August 30, 1993): 1335–42. http://dx.doi.org/10.1142/s0217984993001387.

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Description of the temperature and frequency dependences of the dynamical susceptibility in improper segnetoelectrics in the incommensurate phase near the incommensurate–commensurate phase transition is presented. The used model is based on the theory of three interacting nonlinear oscillators.

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29

Меньшенин, В. В. "Магнитные фазовые переходы в несоизмеримую магнитную структуру в соединении FeGe-=SUB=-2-=/SUB=-." Физика твердого тела 61, no. 3 (2019): 552. http://dx.doi.org/10.21883/ftt.2019.03.47251.269.

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AbstractA symmetry analysis of possible magnetic structures in an incommensurate magnetic phase in FeGe_2 compound, resulted from phase transitions from the paramagnetic phase, was performed based on a phenomenological consideration. It is shown that two possible approaches to a such an analysis, the first of which uses the magnetic representation of the space group, and the second one is based on the expansion of the magnetic moment in basis functions of irreducible representations of the space group of the paramagnetic phase, yield the same results. Space group irreducible representations are determined, according to which the transition to an incommensurate structure can occur. The set of these representations appears identical in both approaches. Ginzburg–Landau functionals for analyzing the transitions according to these representations are written. A renormalization group analysis of the second-order phase transitions from the paramagnetic state to the incommensurate magnetic structure is performed. It is shown that a helical magnetic structure can arise in the incommensurate phase as a result of two second-order phase transitions at the transitions temperature.

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30

Blanco, J. A., D. Gignoux, P. Morin, and D. Schmitt. "Incommensurate phase transitions in Gd compounds." Journal of Magnetism and Magnetic Materials 90-91 (December 1990): 166–68. http://dx.doi.org/10.1016/s0304-8853(10)80056-3.

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31

Vokhmyanin, A. P., S. Lee, K. H. Jang, A. A. Podlesnyak, L. Keller, K. Prokeš, V. V. Sikolenko, J. G. Park, Yu N. Skryabin, and A. N. Pirogov. "Commensurate–incommensurate phase transition in TbNi5." Journal of Magnetism and Magnetic Materials 300, no. 1 (May 2006): e411-e414. http://dx.doi.org/10.1016/j.jmmm.2005.10.179.

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32

Brand, Helmut R. "Phase dynamics for incommensurate nonequilibrium systems." Physical Review A 32, no. 6 (December 1, 1985): 3551–53. http://dx.doi.org/10.1103/physreva.32.3551.

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33

Benkert, C., and Volker Heine. "Excitations in Biphenyl's Incommensurate Phase III." Physical Review Letters 58, no. 21 (May 25, 1987): 2232–34. http://dx.doi.org/10.1103/physrevlett.58.2232.

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34

Benkert, C., V. Heine, and E. H. Simmons. "The incommensurate phase transition of biphenyl." Journal of Physics C: Solid State Physics 20, no. 22 (August 10, 1987): 3337–54. http://dx.doi.org/10.1088/0022-3719/20/22/007.

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35

Benkert, C., and V. Heine. "The incommensurate phase II of biphenyl." Journal of Physics C: Solid State Physics 20, no. 22 (August 10, 1987): 3355–67. http://dx.doi.org/10.1088/0022-3719/20/22/008.

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36

Samulionis, V., V. Valevicius, J. Banys, and A. Brilingas. "Ultrasonic Studies of Incommensurate Phase Transitions." Le Journal de Physique IV 06, no. C8 (December 1996): C8–405—C8–408. http://dx.doi.org/10.1051/jp4:1996887.

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37

Salnik, A., Yu P. Gololobov, and N. A. Borovoy. "The Incommensurate Phase Transformation in TlInS2Ferroelectric." Ferroelectrics 484, no. 1 (August 5, 2015): 62–68. http://dx.doi.org/10.1080/00150193.2015.1059716.

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38

Kobayashi, J. "Incommensurate phase transitions and optical activity." Physical Review B 42, no. 13 (November 1, 1990): 8332–38. http://dx.doi.org/10.1103/physrevb.42.8332.

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39

Sannikov, D. G., and V. A. Golovko. "New type of incommensurate phase transitions." Ferroelectrics Letters Section 8, no. 1 (December 1987): 15–18. http://dx.doi.org/10.1080/07315178708200649.

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40

Zubillaga, J., A. Lopez-Eharri, and M. J. Tello. "The incommensurate phase in tetramethylammonium tetrachloromanganate." Journal of Physics C: Solid State Physics 21, no. 24 (August 30, 1988): 4417–23. http://dx.doi.org/10.1088/0022-3719/21/24/008.

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41

Bendersky, L. A., and R. M. Waterstrat. "Incommensurate structure of the phase Zr3Rh4." Journal of Alloys and Compounds 252, no. 1-2 (May 1997): L5—L7. http://dx.doi.org/10.1016/s0925-8388(96)02417-6.

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42

Şentürk, E., L. Tümbek, F. Salehli, and F. A. Mikailov. "Incommensurate phase properties of TlGaSe2layered crystals." Crystal Research and Technology 40, no. 3 (January 27, 2005): 248–52. http://dx.doi.org/10.1002/crat.200410333.

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43

Barsamian, T. K., S. S. Khasanov, V. SH Shekhtman, YU M. Vysochanskii, and V. YU Slivka. "Incommensurate phase in proper ferroelectric Sn2P2Se6." Ferroelectrics 67, no. 1 (March 1986): 47–54. http://dx.doi.org/10.1080/00150198608227900.

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44

Hrabanski, Ryszard, and Adi Kassiba. "EPR study of K2ZnCl4in incommensurate phase." Ferroelectrics 222, no. 1 (February 1999): 221–25. http://dx.doi.org/10.1080/00150199908014819.

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45

Bosak, Alexei, Volodymyr Svitlyk, Alla Arakcheeva, Roman Burkovsky, Vadim Diadkin, Krystian Roleder, and Dmitry Chernyshov. "Incommensurate crystal structure of PbHfO3." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 76, no. 1 (February 1, 2020): 7–12. http://dx.doi.org/10.1107/s205252061901494x.

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Abstract:

Controversy in the description/identification of so-called intermediate phase(s) in PbHfO3, stable in the range ∼420–480 K, has existed for a few decades. A synchrotron diffraction experiment on a partially detwinned crystal allowed the structure to be solved in the superspace group Imma(00γ)s00 (No. 74.2). In contrast to some previously published reports, in the pure compound only one distinct phase was observed between Pbam PbZrO3-like antiferroelectric and Pm3m paraelectric phases. The modulation vector depends only slightly on temperature. The major structure modulation is associated with the displacement of lead ions, which is accompanied by a smaller amplitude modulation for the surrounding O atoms and tilting of HfO6 octahedra. Tilting of the octahedra results in a doubling of the unit cell compared with the parent structure.

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46

Parlinski, K., and F. Dénoyer. "Mechanisms of phase transitions between commensurate and incommensurate phases." Physical Review B 41, no. 16 (June 1, 1990): 11428–36. http://dx.doi.org/10.1103/physrevb.41.11428.

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47

Parlinski, K., S. Kwiecinski, and A. Urbanski. "Phase diagram of a hexagonal model with incommensurate phases." Physical Review B 46, no. 9 (September 1, 1992): 5110–15. http://dx.doi.org/10.1103/physrevb.46.5110.

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48

Uhrig, Go¨tz S., and Ruud Vlaming. "Incommensurate phases vs. phase separation for interacting spinless fermions." Physica B: Condensed Matter 194-196 (February 1994): 451–52. http://dx.doi.org/10.1016/0921-4526(94)90555-x.

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49

Walker, M. B., and Rose Morelli. "NbTe4: A model for a class of incommensurate-to-incommensurate phase transitions." Physical Review B 38, no. 7 (September 1, 1988): 4836–39. http://dx.doi.org/10.1103/physrevb.38.4836.

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50

Couzi, Michel, François Guillaume, and Kenneth D. M. Harris. "A phenomenological model for structural phase transitions in incommensurate alkane/urea inclusion compounds." Royal Society Open Science 5, no. 6 (June 2018): 180058. http://dx.doi.org/10.1098/rsos.180058.

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Abstract:

n -Alkane/urea inclusion compounds are crystalline materials in which n -alkane ‘guest’ molecules are located within parallel one-dimensional ‘host’ tunnels formed by a helical hydrogen-bonded arrangement of urea molecules. The periodic repeat distance of the guest molecules along the host tunnels is incommensurate with the periodic repeat distance of the host substructure. The structural properties of the high-temperature phase of these materials (phase I), which exist at ambient temperature, are described by a (3 + 1)-dimensional superspace. Recent publications have suggested that, in the prototypical incommensurate composite systems, n -nonadecane/urea and n -hexadecane/urea, two low-temperature phases II and ‘III’ exist and that one or both of these phases are described by a (3 + 2)-dimensional superspace. We present a phenomenological model based on symmetry considerations and developed in the frame of a pseudo-spin–phonon coupling mechanism, which accounts for the mechanisms responsible for the I ↔ II ↔ ‘III’ phase sequence. With reference to published experimental data, we demonstrate that, in all phases of these incommensurate materials, the structural properties are described by (3 + 1)-dimensional superspace groups. Around the temperature of the II ↔ ‘III’ transition, the macroscopic properties of the material are not actually associated with a phase transition, but instead represent a ‘crossover’ between two regimes involving different couplings between relevant order parameters.

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