Crystal field potential definition

The above picture of five possible kinds of the crystal field potentials (A0-A4) formed by ideally ordered CuOjt layers of OI and/or Oil types is definitely oversimplified. In reality, the oxygen distribution in the CuO, layers is not homogeneous, so that the crystal field potential varies from one R ion to another. For example, the Tm NMR studies of the TmBa2Cu306 sample at 4.2 K have shown the inhomogeneous halfwidth at a half maximum 6 for the Tm resonance line in a field Hq c to vary with frequency v according to the following expression (Egorov et al. 1992) ... 

In the definition mod simply means the addition or subtraction of multiples of q to the crystal quantum number p. For q, the minimum gf-value in the crystal-field potential different from zero is taken. The crystal-field quantum numbers for a given symmetry can be found in practice by writing down different series M + mq, so that these series together contain every integer between -/ and / (/ is the highest value for the / quantum number in the system under study). The number with the lowest absolute value in each series will be considered as a crystal quantum number p. This can be illustrated for the C3 symmetry q = 3). The crystal quantum numbers for a C3 symmetry in systems with an even number of electrons are p = 0, 0" and p = l. 

Here Ai are inverse mass parameters in WZ structure, corresponding to Luttinger parameters in ZB structure, me11 and me1 are k-dependent electron effective masses. D , aic and a2c are Bir-Pikus deformation potentials. Ai and 3A2,3 correspond to the crystal-field and spin-orbit splitting energies, respectively. The definition of several operators is given as L+ = (U iLy)/V2, a+ = (ax iay)/2,... 

With the availability of faster computers, BPTI was simulated in aqueous solution and in a solvated crystal with a more realistic (three-center) water model.92 The simulations were limited to 8 ps of equilibration and 12 ps of analysis, somewhat short for definitive conclusions to be drawn recently, a crystal simulation of BPTI that extended over 40 ps has been reported.322 The average structures obtained from the various simulations are compared in Table VII. In the three calculations made with the same empirical potential, the van der Waals solvent and static crystal field results yielded an average structure closer to the experimental crystal structure than did the vacuum calculation. The full crystal simulations, including crystal waters, gave an average structure still closer to the X-ray result, while the deviation from the crystal structure of the average structure obtained from the aqueous solution simulation was similar to the earlier vacuum result. 

The term electrochromism was apparently coined to describe absorption line shifts induced in dyes by strong electric fields (1). This definition of electrocbromism does not, however, fit within the modem sense of the word. Electrochromism is a reversible and visible change in transmittance and/or reflectance that is associated with an electrochemicaHy induced oxidation—reduction reaction. This optical change is effected by a small electric current at low d-c potential. The potential is usually on the order of 1 V, and the electrochromic material sometimes exhibits good open-circuit memory. Unlike the well-known electrolytic coloration in alkaU haUde crystals, the electrochromic optical density change is often appreciable at ordinary temperatures. 

The systematic study of piezochromism is a relatively new field. It is clear that, even within the restricted definition used here, many more systems win be found which exhibit piezochromic behavior. It is quite possible to find a variety of potential appUcations of this phenomenon. Many of them center around the estimation of the pressure or stress in some kind of restricted or localized geometry, eg, under a localized impact or shock in a crystal or polymer film, in such a film under tension or compression, or at the interface between bearings. More generally it conveys some basic information about inter- and intramolecular interactions that is useful in understanding processes at atmospheric pressure as well as under compression. 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

There is another way to interpret the progress of a hand that moves across the dial of a clock, when it measures time. Each position of the hand denotes a specific time, which is different from all others, and only repeats itself after a complete cycle of either 2tt or 47r, depending on the definition of a unit cycle as either 12 or 24 hours. The symmetry that describes the progress of the moving hand is equivalent to that of translational motion over a potential field that repeats at periodic intervals, for instance in a crystal. 

Th.e refinements of the theory, which have been worked out in particular by Houston, Bloch, Peierls, Nordheim, Fowler and Brillouin, have two main objects. In the first place, the picture of perfectly free electrons at a constant potential is certainly far too rough. There will be binding forces between the residual ions and the conduction electrons we must elaborate the theory sufficiently to make it possible to deduce the number of electrons taking part in the process of conduction, and the change in this number with temperature, from the properties of the atoms of the substance. In principle this involves a very complicated problem in quantum mechanics, since an electron is not in this case bound to a definite atom, but to the totality of the atomic residues, which form a regular crystal lattice. The potential of these residues is a space-periodic function (fig. 10), and the problem comes to this— to solve Schrodinger s wave equation for a periodic poten-tial field of this kind. That can be done by various approximate methods. One thing is clear if an electron... 

The results lately obtained, although very interesting and promising, definitely do not cover all the aspects and do not answer all the questions addressed by the fascinating field of lyotropic liquid crystals and their applications as drug delivery systems. Clearly, many additional experiments need to be carried out in order to clarify the detailed structure, the exact properties, and specific potential of these systems. We hope that we at least opened a new window and provided new thoughts and interest into this rapidly growing field of research. 

The field of co-crystals has elicited significant interest in the pharmaceutical industry recently with the potential to utilize this technology as means of enhancing physicochemical properties such as solubility and dissolution in addition to enhancements to particle properties that could aid drug product development,. e.g. improving both chemical and physical stability and indeed as a method to induce crystallization of materials that traditionally would have been isolated as an oil or an amorphous material. There is also considerable ongoing debate as to the theoretical definition of a co-crystal, how a co-crystal can be reliably synthesized, manufactured and characterized, coupled with the intellectual properties ramifications therein. This presentation will outline some of our recent research efforts (in-house external) into the synthesis of co-crystals, and will outline different techniques that can be utilized to characterize co-crystals. 

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