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Principle Neumann

Curie understood that under stress, or in the presence of external electric or magnetic fields, the symmetry of a system is changed. The Neumann principle still applies but should no longer be based on the symmetry of the isolated crystal, but on that of the combined system of crystal and external field, as we have considered in Sect. 3.9. In the case of ammonia, application of an electric field has the Coov symmetry of a polar vector. The symmetry that results from the superposition of the field with the molecular point group 3 depends on the orientation (see Appendix B). In the coordinate frame of Fig. 3.1 one has ... [Pg.104]

If the field is oriented along the z-direction, it will keep the C3 symmetry of the molecule. This is also in line with the existence of a permanent dipole in the z-direction according to the Neumann principle since a charge dipole has the same symmetry as an electric field. If an external field is applied in the jc-direction, the symmetry is reduced to the reflection group, Cg = E, ai. In the presence of such a field, displacement of charge in the jc-direction is compatible with the extended symmetry principle, which means that ammonia can acquire an induced dipole moment in the x-direction. However, a field along jc cannot induce a dipole moment in the y-direction since the ai reflection plane is incompatible with the displacement of charge across the plane of symmetry. [Pg.104]

The symmetry-properties correlation is summarized by the Neumann principle, according which the symmetry elements associated to any physical property of a crystalline system must contain the symmetry elements of the point group to which the crystal in focus belongs. ... [Pg.176]

Nenitzescu reaction 100 Neumann principle, tensor properties 201 neural networks 810 neutron scattering 680-698 Newton equations, molecular modelling 74 nickel, X ray absorption curve 622 nitro, terminal substituents 147 nitrogen saturation, phase transitions 357... [Pg.938]

When we are dealing with the question of whether a material can be spontaneously polarized or not, or whether some external action can make it polarized, there are two principles of great generality which are extremely useful, the Neumann principle and the Curie principle. Good discussions of these principles are found in a number of books, for instance [24, 36, 89]. The first of... [Pg.1559]

The second, from 1894, after Pierre Curie, says that a medium subjected to an external action changes its point symmetry so as to preserve only the symmetry elements common with those of the influencing action. Symbolically we may write the Neumann principle as... [Pg.1559]

The Neumann and Curie principles have long been the dominating symmetry principles in condensed-matter physics. Both can be formulated in a number of different ways. For instance, the Neumann principle may be stated as follows the symmetry elements of an intrinsic property must include the symmetry elements of the medium . This formulation stresses that every physical property may and often does have higher symmetry, but never less than the medium. [Pg.1559]

How can we know that the Neumann principle is always valid Consider, for the sake of argument, that the crystal group K had a symmetry operation that was not contained in the property group P. Then, under the action of this operation, the crystal would on the one hand coincide with itself, and on the other, change its physical properties. This inherent contradiction proves the validity of the principle. This principle is often used in two ways, although it works strictly in only one direction. Evidently, it can be used to End out if a certain property is permitted in a medium, the syimnetry of which is known. However, it may and has also been used (with caution) as an aid in the proper crys-... [Pg.1560]

The general application of the Neumann principle in condensed matter is normally much more formalized (for instance, involving rotation matrices) than we will have use for. Few textbooks perform such demonstrations on an elementary level, but there are exceptions, for example, the excellent treatise by Nussbaum and Phillips [90]. For a liquid crystal, we illustrate the simplest way of using the symmetry operations of the medium in Fig. 13. (The same discussion, in more detail, is given in [46]). We choose the z-direction along the director as shown in Fig. 13a and assume that there is a nonzero polarization P=(Px, Py, Pz) i nematic or smectic A. Rotation by 180° around the y-axis transforms and P into and -P, and hence both of these components must be zero, because this rotation is a symmetry operation of the medium. Next, we rotate by 90 ° around the z-axis, which transforms the remaining Py into P. If therefore Py were nonzero, we would see that the symmetry operations of the medium are not synunetry operations of the property, in violation of Neumann s principle. Hence P =0 and P will vanish. [Pg.1560]

For orthorhombic, monoclinic, and triclinic symmetry the indicatrix is a triaxial ellipsoid. The orthorhombic system has three orthogonal twofold rotation axes. This means that the indicatrix, representing the optical properties, must have the same symmetry axes (Neumann principle). Therefore the three principal axes of the indicatrix coincide with the three crystallographic axes and are fixed in space, whatever the wavelength. This is not so for the monoclinic symmetry represented by the smectic C. Because the symmetry element of the structure must always be present in the property (again the Neumann principle), the crystallographic C2 axis perpendicular to the tilt plane is now the twofold axis of the indicatrix and the tensor, but no other axes are fixed. This means that there is ambiguity in... [Pg.1627]

In Eq. (338) y is already written in the molecular frame of reference in which it is diagonalized, as illustrated in Fig. 76, with the principal axes 1, 2, and 3. Because the C2 axis perpendicular to the tilt plane has to appear in the property (Neumann principle - we use it here even for a dynamic parameter), this has to be the direction for y2. As for the other directions, there are no compelling arguments, but a natural choice for a second principal axis is along the director. We take this as the 3 direction. The remaining axis 1 is then in the tilt plane, perpendicular to n. The 3 axis is special because, along n, the rotation is supposed to be characterized by a very low viscosity. In other words, we assume that the eigenvalue is very small, i.e., yi[Pg.1633]

Neumann principles, ferroelectrics 541 ff, 609, 615 nickel, ligands 914 f, 924 nitration, hydrocarbon cores 709 nitrile ligands, metallomesogens 902 nitro derivatives, polycatenars 878 nitrobenzene derivatives, chaige transfer 948 nitrobiphenylcarboxylic acids, synthesis 433 nitroester, phasmids 866 nomenclature... [Pg.2031]

Contrary to what appears at a first sight, the integral relations in Eqs. (9) and (10) are not based on causality. However, they can be related to another principle [39]. This approach of expressing a general principle by mathematical formulas can be traced to von Neumann [242] and leads in the present instance to an equation of restriction, to be derived below. According to von Neumann complete description of physical systems must contain ... [Pg.111]

The second axiom, which is reminiscent of Mach s principle, also contains the seeds of Leibniz s Monads [reschQl]. All is process. That is to say, there is no thing in the universe. Things, objects, entities, are abstractions of what is relatively constant from a process of movement and transformation. They are like the shapes that children like to see in the clouds. The Einstein-Podolsky-Rosen correlations (see section 12.7.1) remind us that what we empirically accept as fundamental particles - electrons, atoms, molecules, etc. - actually never exist in total isolation. Moreover, recalling von Neumann s uniqueness theorem for canonical commutation relations (which asserts that for locally compact phase spaces all Hilbert-space representations of the canonical commutation relations are physically equivalent), we note that for systems with non-locally-compact phase spaces, the uniqueness theorem fails, and therefore there must be infinitely many physically inequivalent and... [Pg.699]

Neumann, E. Principles of electric field effects in chemical and biological systems, in Topics in Bioelectrochemistry and Bioenergetics, Vol. 4, (ed.) Milazzo, G., New York, Wiley 1981... [Pg.259]

From this general law it is possible to infer probable properties, since according to the principle of Neumann the properties cannot be less symmetrical than the structure. Neumann s principle states that "The symmetry elements of any physical property of a crystal must include the symmetry elements of the point group of the crystal". Thus, a centro-symmetric crystal cannot by pyroelectric, since it would require that the two symmetrically related ends behave differently towards a change of temperature. [Pg.81]

Neumann, G., and W. J. J. Pierson, Principles of Physical Oceanography, Prentice-Hall, Englewood Cliffs, NJ, 1966. [Pg.1239]

The diffusivity tensor has special forms for particular choices of coordinate axes if the diffusing body itself has special symmetry (e.g., if it is crystalline). Neumann s principle states ... [Pg.90]

A consequence of Neumann s symmetry principle is that direct tensor Onsager coefficients (such as in the diffusivity tensor) must be symmetric. This is equivalent to the addition of a center of symmetry (an inversion center) to a material s point group. Thus, the direct tensor properties of crystalline materials must have one of the point symmetries of the 11 Laue groups. Neumann s principle can impose additional relationships between the diffusivity tensor coefficients Dij in Eq. 4.57. For a hexagonal crystal, the diffusivity tensor in the principal coordinate system has the form... [Pg.90]

Additional symmetries arise when the tensors Xj and/or Y, are symmetric, and from crystal symmetry in accordance with Neumann s principle, as seen in Section 15.2. These symmetries are properties of the tensor and the crystal point group, and, if different physical properties may be represented by the same kind of tensor, it will exhibit the same structure, irrespective of the actual physical property under consideration. [Pg.288]

This principle seems to have been first recognized by Neumann, F. E. See Shubnikov, A. V. Koptsik, V. A. Symmetry in Science and Art Plenum Press New York, 1974, p. 334. Donaldson, J. D. Ross, S. D. Symmetry and Stereochemistry John Wiley and Sons, Inc. New York, 1972, p. 132. [Pg.75]

The BOC-MP model is a simple, truly back-of-the-envelope model that can be directly used by practitioners in the field. It efficiently describes and interrelates a wide variety of chemisorption phenomena. Most important, the model maps out metal surface reactions providing insight into both regularities and details. We have considered a number of examples of different complexity. In principle, any metal surface reaction can be treated this way. The only requirement is to retain the rigor and simplicity of the model projections. As John von Neumann put it, if a style, classical in the beginning, turns to resemble baroque, this is a sign of danger. [Pg.156]

There are two important points to remember regarding the applicability of Neumann s principle. First, forces imposed on a crystal, including mechanical stresses and electric fields, can have any arbitrary direction or orientation. These types... [Pg.3]


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