Curie Symmetry Principle Research Articles

Ballistic Thermoelectricity

The analysis of Local thermo-EMF in p-n junctions made it possible to reveal the phenomenological features of ballistic thermoelectricity. By the Curie Symmetry Principle, in polar structures of p-n junctions, the thickness of which is of the order of the electron mean free path, the contribution of ballistic effects to the formation of the total EMF is decisive. This ballistic contribution to thermo-EMF provides both high output voltages and high efficiency of DIRECT energy conversion.

Dissymmetry of Collective Crystal Growth

The statistical regularities of collective crystal growth under isotropic/anisotropic conditions are described based on the adsorption-fluctuation dislocation growth model. A version of realization of the Curie symmetry principle for an open stationary nonequilibrium system, described by random processes, is presented. The form of manifestation of the Curie principle is shown to depend not only on the physical conditions of the crystallization process but also on the structure of transitions between morphotypes (a Markov chain).

Нелинейные определяющие соотношения для трансверсально-изотропных материалов классов симметрии С∞ и С∞h

Transversely isotropic materials feature infinite-order symmetry axes. Depending on which other symmetry elements are found in the material structure, five symmetry groups may be distinguished among transversely isotropic materials. We consider constitutive equations for these materials. These equations connect two symmetric second-order tensors. Two types of constitutive equations describe the properties of these five material groups. We derived constitutive equations for materials belonging to the C∞ and C∞h symmetry groups in the tensor function form. To do this, we used corollaries of Curie's Symmetry Principle. This makes it possible to obtain a fully irreducible form of the tensor function.

Toward the Targeted Design of Molecular Ferroelectrics: Modifying Molecular Symmetries and Homochirality.

Although the first ferroelectric discovered in 1920 is Rochelle salt, a typical molecular ferroelectric, the front-runners that have been extensively studied and widely used in diverse applications, such as memory elements, capacitors, sensors, and actuators, are inorganic ferroelectrics with excellent electrical, mechanical, and optical properties. With the increased concerns about the environment, energy, and cost, molecular ferroelectrics are becoming promising supplements for inorganic ferroelectrics. The unique advantages of high structural tunability and homochirality, which are unavailable in their inorganic counterparts, make molecular systems a good platform for manipulating ferroelectricity. Remarkably, based on the Neumann's principle and the Curie symmetry principle defining the group-to-subgroup relationship, we have found some outstanding high-temperature molecular ferroelectrics, like diisopropylammonium bromide (DIPAB) with a large spontaneous polarization up to 23 μC/cm2 ( Fu, D. W.; et al. Science 2013 , 339 , 425 ). However, their application potential is severely limited by the uniaxial nature, leading to major issues in finding proper substrates for thin-film growth and achieving high thin-film performance. Inspired by the commercialized inorganic ferroelectrics like Pb(Zr, Ti)O3 (PZT), where the multiaxial nature contributes greatly to the optimized ferroelectric and piezoelectric performance, developing high-temperature multiaxial molecular ferroelectrics is an imminent task. In this Account, we review our recent research progress on the targeted design of multiaxial molecular ferroelectrics. We first propose the "quasi-spherical theory", a phenomenological theory based on the Curie symmetry principle, to modify the spherical cations to a low-symmetric quasi-spherical geometry for acquiring the highly symmetric paraelectric phase and the polar ferroelectric phase of multiaxial ferroelectrics simultaneously. Besides the sizes and weights of the cation and anion, the intermolecular interactions are particularly crucial for decelerating the molecular rotation at low temperature to reasonably induce ferroelectricity. It means that the momentums of the cation and anion should be matched, so we describe the "momentum matching theory". In particular, introducing homochirality, a superiority of molecular materials over the inorganic ones, was demonstrated as an effective approach to increase the incidence of ferroelectric crystal structures. Thanks to the striking chemical variability and structure-property flexibility of molecular materials, our research efforts outlined in this Account have led to and will further motivate the richness and the application exploration of high-temperature, high-performance multiaxial molecular ferroelectrics, along with the implementation and perfection of the targeted design strategies.

Lattice Symmetry of Nanothin Crystals, Direct and Reciprocal Space Isomorphism, and the Curie Symmetry Principle

The symmetry of direct and reciprocal lattices and the symmetry of bend contours present in the electron microscopy images of nanothin crystals with elastic rotational distortion of the lattice are examined using the example of nanothin selenium crystals.

Applications of Curie symmetry principle in molecular ferroelectrics

Applications of Curie symmetry principle in molecular ferroelectrics

A displacive-type metal crown ether ferroelectric compound: Ca(NO3)2(15-crown-5).

Following the Curie symmetry principle and Aizu rule, we discovered there is a centrosymmetric-to-noncentrosymmetric phase transition in Ca(NO3)2(15-crown-5) at Tc = 205 K. The transition was confirmed by differential scanning calorimetry and second harmonic generation measurements. The transition gives rise to excellent ferroelectricity, such as a giant dielectric anomaly, with faster polarization switching (5×10(-5) s) of up to 10(7) times without showing fatigue. The ferroelectric mechanism is attributable to the coordination environmental distortion of the central Ca atom. This finding can throw light on the further research in metal-organic ferroelectrics.

A Displacive‐Type Metal Crown Ether Ferroelectric Compound: Ca(NO3)2(15‐crown‐5)

AbstractFollowing the Curie symmetry principle and Aizu rule, we discovered there is a centrosymmetric‐to‐noncentrosymmetric phase transition in Ca(NO3)2(15‐crown‐5) at Tc=205 K. The transition was confirmed by differential scanning calorimetry and second harmonic generation measurements. The transition gives rise to excellent ferroelectricity, such as a giant dielectric anomaly, with faster polarization switching (5×10−5 s) of up to 107 times without showing fatigue. The ferroelectric mechanism is attributable to the coordination environmental distortion of the central Ca atom. This finding can throw light on the further research in metal–organic ferroelectrics.

Will Kleber, Hans-Joachim Bautsch, Joachim Bohm, Einführung in die Kristallographie

This book is the classic German language textbook on Crystallography! It has first been published in 1956. Since then, the (VEB) Verlag Technik, Berlin, published a total of 18 editions up to 1998. In 2010, the Oldenbourg Verlag Munich published the 19th edition, with which this book review is mainly concerned. Up to 1970, i.e., the 10th German edition and 1st English edition (under the title An Introduction to Crystallography), Will Kleber was the sole author. Since then Irmgard Kleber, Hans-Joachim Bautsch, Joachim Bohm, and most recently Detlev Klimm worked on the subsequent editions. All of these authors followed the didactic approach of Will Kleber while incorporating newer results and expanding the references and index. All of crystallography is treated comprehensively under the five main sections: (i) crystal structure and morphology, (ii) crystal chemistry, (iii) physical-chemical crystallography, (iv) crystal physics, and (v) structure analysis of crystals. There are a total of 413 pages of text and an addendum (Wulff net, Schmidt net and birefringence/interference table). Very notable additions of recent years in the crystal physics section are the symmetry groups of fields and Curie's symmetry principle as well as an introduction to the tensor formalism. Otherwise, this reviewer feels that especially the sections on structure analysis and crystal chemistry need updating. With respect to the described crystal structure types, the crystal chemistry section is partially outdated. There are no descriptions of modern materials, modular structures, nano-structured materials, and biological macromolecule structures. This reviewer missed also an introduction to group-subgroup symmetry relations between crystal structures (i.e. Bärnighausen trees). Open-access Internet resources such as the “Bilbao Crystallographic Server” (http://www.cryst.ehu.es/) and the “Crystallography Open Database” (www.crystallography.net) should be mentioned in future editions of the book, since the latter database possesses more than 200,000 (unit cell parameters, space group and setting, atomic coordinates, …, full bibliography) entries. In the structure analysis section, the Weissenberg method (of 1924) and other film-based methods of X-ray diffraction data collection are covered extensively while position sensitive X-ray detectors are not even mentioned. Similarly, transmission electron microscopy (TEM) and electron diffraction are covered within nine pages only that seem to have not changed much over recent years. As a result, instrumental (such as TEM-lens aberration correction) and methodical (e.g., precession electron diffraction based crystallography) breakthroughs are ignored although there is an atomic-resolution phase-contrast TEM image on the front cover of the book. As for this front cover image, it would be of higher pedagogical value if it were to show a length scale marker. Also a model of the crystal structure could be shown on the book cover in three dimensions next to this image (rather than sketched into the two-dimensional experimental data). As far as this reviewer is aware, there were no more English language editions since 1970. This is a real pity as generations of materials science and crystallography students in the English speaking parts of the world have missed out on this classical textbook. There are indeed a few classical books, e.g., John von Neumann’s, Mathematische Grundlagen der Quantummechanik (Julius Springer-Verlag, Berlin, 1932, Springer 1968 and 1996; translated into English 1949: Mathematical Foundations of Quantum Mechanics, Princeton Landmarks in Mathematics, 12th printing, 1996), that never need updating. Will Kleber's book, however, needs updating in future editions because it aims to cover classical and topical theories as well as experiments comprehensively. Because its original approach to introducing crystallography has still lots of merits, a 20th German/2nd English edition of his book would be very valuable for the education of new generations of materials scientists and crystallographers worldwide. Active research scientists/educators such as Detlef Klimm who “grew up” with “The Kleber”, utilized it as main textbook while studying crystallography as undergraduates and/or graduates (and are now in their forties to mid-fifties), could be the authors of such new editions.

Symmetry Rules: How Science and Nature Are Founded on Symmetry. By Joe Rosen. Springer: Berlin. 2008, XIV, 305 p. 86 illus., Hardcover. CHF 70. ISBN: 978-3-540-75972-0

This book belongs to the book series The Frontiers Collection, edited by A.C. Elitzur, M.P. Silverman, J. Tuszynski, R. Vaas and H.D. Zeh.[...]

Curie symmetry principle and growth of single crystals

Application of the symmetry principle, proposed by Pierre Curie, to the growth of single crystals is considered. The basic concepts of this principle and the rules for alignment of the crystallographic symmetry of a seed crystal with the external symmetry of the thermal field formed by the crucible with a melt are shown. The modified Stepanov method, developed at the General Physics Institute, Russian Academy of Sciences, on the basis of the Czochralski and Stepanov methods, is described, and its advantages are demonstrated. Examples of application of this technique to the growth of complex oxide crystals are given.

The Clausius inequality: Implications for non-equilibrium thermodynamic steady states with NEMD corroboration

The Clausius inequality for closed systems was deduced from the Riemann integration of closed Carnot cycle loops for irreversible transitions. The corresponding inequalities for open system Carnot cycles are derived here. Their properties indicate that no new non-equilibrium entropy is evident as has been proposed over the decades. It is proven that a sequence of points along a non-equilibrium state space must have excess variables augmenting those for the equilibrium situation and therefore the principle of local equilibrium (PLE) used extensively to describe non-equilibrium systems is an approximation. To demonstrate the breakdown of the principle, verification of the theorem, and the presence of new phenomena, an ab initio steady-state simulation of a simple dimer reaction 2 A ↔ A 2 under non-equilibrium conditions was performed and the results compared to the equilibrium conditions to show the regime of breakdown of the principle. The novel dimer reaction presented has a cyclical pathway found in many natural processes, such as laser photochemistry. It is suggested that such reaction pathways can exist and awaits experimental verification. A new algorithm to conserve momentum and energy at the potential switches of the dimer is applied effectively. New atomic and molecular flux flows not present under equilibrium conditions are shown to exist, where the net rate of reaction along the cell is not zero but small, unlike the zero rate equilibrium requirement, leading to the flux presence. The equilibrium constant is also shifted from the value at thermodynamical equilibrium. Unless reinterpreted differently, it is shown that the so-called Curie symmetry principle, fundamental in deciding on the feasibility of flux–force couplings in both theory and experiment in all physical theories, cannot apply to such experimental results. Hence, a far greater freedom in selecting appropriate force–flux couplings is indicated than would be the case if the Curie principle, as commonly interpreted is adopted.

Spontaneous Symmetry Breaking and Chance in a Classical World

This essay explores the nature of spontaneous symmetry breaking (SSB) in connection with a cluster of interrelated concepts such as Curie's symmetry principle, ergodicity, and chance and stability in classical systems. First, a clarification of the two existing senses of SSB is provided and an argument developed for a proposal for SSB, in which not only the possibilities but also the actual breakings are referred to. Second, a detailed analysis is given of classical SSB that answers the questions: (i) how we are justified in regarding it as a matter of chance, and (ii) why the breakings in it are equally probable. The answer provides some support to the applicability of ergodicity in special systems (such as ours).

Symmetry of the Fréedericksz transition in nonchiral nematic liquid crystals.

The Fr\'eedericksz transition is a nonuniaxial, nonchiral nematic liquid crystal (LC) in the presence of the electric E field is considered using the Curie symmetry principle. All possible symmetries of (i) the LC point symmetry group ${\mathit{G}}_{\mathit{N}}$, (ii) the strong boundary LC orientation at the infinite plane-parallel plates of slab, and (iii) the direction of the E field are analyzed. The free energy polynomial J(${\mathit{c}}_{\mathit{i}}$) is expressed in terms of the invariant polynomials of components of the three-dimensional axial vector c. Possible primary and secondary bifurcations are determined for all classes of nonchiral nematic LC's (biaxial, tetrahedral, cubic, and icosahedral). It is shown that different kinds of such LC's, subjected to the E fields of different orientations, can be described by the same polynomial J(${\mathit{c}}_{\mathit{i}}$), invariant with respect to the action of a symmetry group ${\mathit{G}}_{\mathrm{Fr}}$ of the Fr\'eedericksz transition. In the framework of the symmetry approach, the influence of the thermal fluctuations of the nematic directors on the Fr\'eedericksz transition is studied and mean squares of these fluctuations are found.

Significance of low symmetry fabrics in magmatic rocks : J Struct Geol V13, N3, 1991, P337–347

Abstract The significance of low symmetry fabrics (monoclinic and triclinic) in magmatic rocks is studied using theoretical models describing the motion of rigid markers embedded in a slowly deforming ductile matrix. In agreement with Curie's Symmetry Principle, the development of these fabrics requires a non-coaxial strain-path. Simulations of monoclinic fabrics indicate that their characteristics depend on: (a) the strain regime and the amount of strain, and (b) the morphological composition of the population of rigid markers. Natural monoclinic fabrics contain precious information about the strain regime they result from: type of the non-coaxial strain-path involved (simple shear, non-coaxial flattening, etc.), orientation of its axes and sense of shear. The magnitude of the finite strain may eventually be estimated provided that the shape of the markers is precisely known.

Significance of low symmetry fabrics in magmatic rocks

The significance of low symmetry fabrics (monoclinic and triclinic) in magmatic rocks is studied using theoretical models describing the motion of rigid markers embedded in a slowly deforming ductile matrix. In agreement with Curie's Symmetry Principle, the development of these fabrics requires a non-coaxial strain-path. Simulations of monoclinic fabrics indicate that their characteristics depend on: (a) the strain regime and the amount of strain, and (b) the morphological composition of the population of rigid markers. Natural monoclinic fabrics contain precious information about the strain regime they result from: type of the non-coaxial strain-path involved (simple shear, non-coaxial flattening, etc.), orientation of its axes and sense of shear. The magnitude of the finite strain may eventually be estimated provided that the shape of the markers is precisely known.

Complexity transmission during replication

The transmission of complexity during DNA replication has been investigated to clarify the significance of this molecular property in a deterministic process. Complexity was equated with the amount of randomness within an ordered molecular structure and measured by the entropy of a posteriori probabilities for discrete (monomer sequences, atomic bonds) and continuous (torsion angle sequences) structural parameters in polynucleotides, proteins, and ligand molecules. A theoretical analysis revealed that sequence complexity decreases during transmission from DNA to protein. It was also found that sequence complexity limits the attainable complexity in the folding of a polypeptide chain and that a protein cannot interact with a ligand moiety of higher complexity. The analysis indicated, furthermore, that in any deterministic molecular process a cause possesses more complexity than its effect. This outcome broadly complies with Curie's symmetry principle. Results from an analysis of an extensive set of experimental data are presented; they corroborate these findings. It is suggested, therefore, that complexity governs the direction of order-order molecular transformations. Two biological implications are (i) replication of DNA in a stepwise, repetitive manner by a polymerase appears to be a necessary consequence of structural constraints imposed by complexity, and (ii) during evolution, increases in complexity had to involve a nondeterministic mechanism. This latter requirement apparently applied also to development of the first replicating system on earth.