Curie relation

Example 6. For paramagnetic materials the magnetic susceptibility may be measured experimentally and used to give information on the molecular magnetic dipole moment, and hence on the electronic structure of the molecules in the material. The paramagnetic contribution to the molar magnetic susceptibility of a material, xm, is related to the molecular magnetic dipole moment m by the Curie relation... 

Electron has associated with it a magnetic moment that is equal to 1 Bohr magneton, j,b- The electron magnetization given by the Curie relation is... 

Once again, these fluxes are not all independent and some care must be taken to rewrite everything so that syimnetry is preserved [12]. Wlien this is done, the Curie principle decouples the vectorial forces from the scalar fluxes and vice versa [9]. Nevertheless, the reaction temis lead to additional reciprocal relations because... 

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

Curie (Ci) A unit of radioactivity, related to the emission from 1 g of radium, it is equal to 3.7 x 10 disintegrations per gram per second. This unit has been replaced by the Becquerel (Bq) 1... 

Compressibility and pressure dependence of Curie temperature are directly measured changes in specific heat and thermal expansion are calculated from the Ehrenfest relation. 

This equation is called the Curie law and relates the equilibrium magnetization M0 to the strength of the magnetic field B0. The constants have the following meaning I is the nuclear spin quantum number (see below), y is the gyromagnetic ratio specific for a given isotope, h is Planck s constant, kB is Boltzmann s constant, N is the number of nuclei and T is the temperature. 

The activity is a measure of the quantity of radioactive material. For these radioactive materials it is customary to describe the activity as the number of disintegrations (transformations) per unit time. The unit of activity is the curie (Ci), which was originally related to the activity of one gram of radium, but is now defined as that quantity of radioactive material in which there are ... 

At ordinary temperatures die magnetic susceptibility is given approximate This relation was determined experimentally by Piene Curie. Preach physicist... 

It is a great pleasure to present the Proceedings of the 4th Conference of the Federation of European Zeolite Associations (FEZA) held in Paris, France, from September 2 to 6, 2008. The Conference was organized by the "French Group of Zeolites" (GFZ) and the University Pierre et Marie Curie, Paris under the auspices of FEZA on the theme Zeolites and Related Materials Trends, Targets and Challenges . 

Because there is no phase relation between the light emitted by different molecules, fluorescence can be considered as the result of three independent sources of light polarized along three perpendicular axis Ox, Oy, Oz without any phase relation between them. Ix, Iy, Iz are the intensities of these sources, and the total intensity is I = Ix + Iy + Iz. The values of the intensity components depend on the polarization of the incident light and on the depolarization processes. Application of the Curie symmetry principle (an effect cannot be more dissymmetric than the... 

Fig. 5.3. Relations between the fluorescence intensity components resulting from the Curie symmetry principle. The fluorescent sample is placed at the origin of the system of coordinates.

The average magnetization I is given by (15), where Bj a) is called a Brillouin function, and a by (16). When a 1, Bj(a) may be expanded, and, if we take only the first term, then (17) results. The paramagnetic susceptibility X is inversely proportional to the absolute temperature T. This relation is called the Curie law, and the proportionality constant C is the Curie constant. 

Fig. 11 Schematic drawings of inverse x vs temperature relations for paramagnetic samples (a) without interspin coupling, (b) with ferro- and (c) antiferro-magnetic interspin interactions. The slope of the lines is equal to the inverse of the Curie constants.

A vast amount of data based on dielectric constant measurements of substances in dilute solution in nonpolar solvents indicate that the theory is correct, but it looses validity and breaks down completely in the case of strongly polar media. It is interesting to notice that such a breakdown can be shown by the concept of the Curie point, introduced in connection with studies of magnetism but directly applicable to the case of dielectric constants. The dielectric constant can be related to the molar polarizability P and the molar concentration c by q. (21) and the value of P itself is given by Eq. (22). It is obvious that P increases as T dimin-... 

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