Constant Curie

A plot of X vs T for C50 w as used to estimate a Curie constant of 8.6 x 10 /mole, which corresponds to 1.7 X 10 electron spins per carbon atom in Cgo- It is possible that the paramagnetic upturn is caused by a small amount of within the sample. To examine this point, we sealed a Cgg sample under a vacuum of 2 x 10 Torr in a chamber located at... 

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

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.

Static dielectric measurements [8] show that all crystals in the family exhibit a very large quantum effect of isotope replacement H D on the critical temperature. This effect can be exemphfied by the fact that Tc = 122 K in KDP and Tc = 229 K in KD2PO4 or DKDP. KDP exhibits a weak first-order phase transition, whereas the first-order character of phase transition in DKDP is more pronounced. The effect of isotope replacement is also observed for the saturated (near T = 0 K) spontaneous polarization, Pg, which has the value Ps = 5.0 xC cm in KDP and Ps = 6.2 xC cm in DKDP. As can be expected for a ferroelectric phase transition, a decrease in the temperature toward Tc in the PE phase causes a critical increase in longitudinal dielectric constant (along the c-axis) in KDP and DKDP. This increase follows the Curie-Weiss law. Sc = C/(T - Ti), and an isotope effect is observed not only for the Curie-Weiss temperature, Ti Tc, but also for the Curie constant C (C = 3000 K in KDP and C = 4000 K in DKDP). Isotope effects on the quantities Tc, P, and C were successfully explained within the proton-tunneling model as a consequence of different tunneling frequencies of H and D atoms. However, this model can hardly reproduce the Curie-Weiss law for Sc-... 

Figure 6.39(a) shows the vs. T curve, normalized to the RT value, for a 100 nm thick a-/ -NPNN/glass film obtained from electron paramagnetic resonance (EPR) measurements with the static magnetic field applied perpendicular to the substrate plane. As previously shown in Fig. 3.19, the molecular a -planes are parallel to the substrate s surface. The data points closely follow the Curie-Weiss law = (T — w)/C, where C stands for the Curie constant. In this case w — —0.3 K, indicating that the net intermolecular interactions are weakly anfiferromagnetic. No hint of a transition at low temperature is observed. These results coincide with those derived from SQUID measurements on a single a-p-NPNN crystal (Tamura etal, 2003), where 0.5 < w < 0, which are displayed in Fig. 6.40. 

By using this low temperature superimposed susceptibility, the transition temperature and the Curie constant immediately above Tc, Dunlap et al. found that NpOs2 fulfilled the Murata-Doniach requirements for a weak itinerant ferromagnet ... 

The paramagnetic susceptibility of pure FeAl204 (x = 2) gives a Weiss constant 0 = -144 K and a molar Curie constant (emu) = 3.80 K, somewhat large for high-spin Foa ions with a spin-only moment however, there is no apparent antiferromagnetic ordering of the FeA -ion spins down to 9.5 K, where a peak in the susceptibility has been associated with a local Jahn-Teller distortion about the Fe ions ... 

When the theory gives a non-integral value of the moment, it is not entirely clear what value of the Curie constant should be taken in (25). Our belief is that the moment will be changing with a frequency k T Jh from one integral number to another, and only if T>> TK can a formula of type (25) be used. The susceptibility under these conditions will always be of the form... 

The Curie constant C = g2p xNoS(S + )/3koT. determined from 11%-T curve shown in fig. 1 lb gives a spin of S = 3, when the nominal value of the Mn concentration, x — 0.053, is used. Here No is the cation density, g (= 2.0) the Lande factor of the Mn ions, /tb is the Bohr magneton, k is the Boltzmann constant. Judging from this value of 5, some ferromagnetic clusters exist already above 7c. 

The value of the Bohr magneton is 0.927 X 10 ° erg gauss"1. The magnetic moment ju is hence related to the molar Curie constant by the equation... 

In a graph of 1/xmoiar against T, the points lie on a straight line if the Weiss equation is valid. Measurements for three salts of cobalt(II) are shown in Figure X-l. It is seen that the curves are straight lines except at very low temperatures. Their slopes are the same the slope is the reciprocal of the Curie constant, and accordingly the cobalt (II) atom has the same magnetic moment in the three substances. 

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