If a paramagnetic substance obeys a Curie or Weiss law, — varying linearly with the temperature, on the X basis of the theory it is possible to deduce a value for the molec ular magnetic moment from the value of the Curie constant.
In either case, since
gram molecular moment is given by
.
In 1911 Weiss, from measurements then available, concluded that there was a fundamental unit magneton of which all atomic or molecular moments were multiples, the unit magnetic moment per gram molecule, M,,, being equal to 1,123.5. (This gives for the unit magnetic moment per molecule, the magneton, the value 1,123.5 1.85 X
unit pole X cm.) Subsequent results 6.06X
have shown that magnetic moments, calculated in the way in dicated, cannot generally be expressed as integral multiples of the Weiss unit. None the
the unit is a convenient one in terms of which to express calculated moments, which are usually given as p magnetons; The magnetic characteristic of normal paramagnetics can, then, be summarized by giving the values of p and 0, which may be de duced from the measurements. The results obtained for a number of normal paramagnetics will be considered, and their significance will then be further discussed in the light of the quantum theory. Many "abnormal" paramagnetics do not obey a Weiss or Curie law; these will be discussed in a later section.
The paramagnetic gases, oxygen and nitric oxide, are of particular interest, as for them the conditions under which Langevin's theory is applicable would be expected to prevail. Oxygen was investigated over a range of temperatures from 2o° to 45o° C by Curie, and the susceptibility was found to vary in versely as the absolute temperature. Measurements of Onnes and Perrier show that the Curie law holds closely down to —113° C. Assuming the Curie law, the molecular moment may be deduced from measurements at a single temperature, of which the most accurate are those of P. Weiss, E. Bauer and A. Piccard (192o), based on the measurement of the difference of pressure of two points of the gas, one in a field H, the other in zero field. Their results for
and NO at 20° C, and the deductions, are given in the following table:— The value for the Curie constant per gram (C= x T) which may be deduced from Curie's measurements, as compared with -0316 in the table, is .0307, from those of Onnes and Oosterhuis, -0303. As both these sets of experiments were carried out with high gas pressures, when a Weiss instead of a Curie law may be anticipated, they are not inconsistent with an invariable value of the Curie constant.
The susceptibility of oxygen in the liquid and solid state has been measured by Perrier and Onnes. The results, together with those of Onnes and Oosterhuis for the gas are shown in the diagram. For the liquid Curie's law was no longer obeyed. As the density of the pure liquid varies with temperature, experiments were made on mixtures of liquid oxygen and (feebly diamagnetic) liquid nitrogen. Between 6o° and 8o° absolute, the results agreed with the formula x =
The Curie constant agrees with T — 0 that found by Bauer and Piccard with the gas. The molecular field correction 0 was found to be negative (indicating a negative mole cular field) and to vary approximately linearly with the concen tration of the oxygen, from —2.2° for .o81 to
for -746. (If p is the fractional concentration, 0= —4op). Solidification (at about 57° A) results in a sudden decrease in the susceptibility, and a large increase in 0 is indicated. Below 33° apparently a new allotropic modification is formed, which has the anomalous char acteristic that the susceptibility decreases with decrease of tem perature down to 13°.
Outside oxygen and nitric oxide nearly all gases are diamagnetic. Taylor and Lewis have found that chlorine dioxide dissolved in carbon tetrachloride is paramagnetic, the molecular susceptibility being 1.3 X
indicating a Weiss magneton value of about 8.7; and there is some evidence that nitrogen dioxide,
is para magnetic.
The paramagnetic solutions which have been most investigated are those of salts of the first transition group of elements (from scandium of atomic number 21, to nickel, 28). Dilute solutions, for the range of temperature over which they can be investigated, generally follow Curie's law very closely. The paramagnetism can be attributed to the metallic ion. From the susceptibility of the solution, knowing the susceptibility of water, that of the dissolved substance may be calculated in the way already indicated. From this the ionic susceptibility of the metallic ion may be determined, by cor recting for the effect of the dia magnetic ions present ; from the ionic susceptibility, assuming Curie's law to hold, the ionic moment may be calculated, and expressed in Weiss magnetons. If the paramagnetic ions are all of one kind, and do not change their character with change in con centration, the magneton value, p, would be expected to be inde pendent of concentration; e.g., for
Bruins found that the p value (16-05±-03) remained con stant to within -4% with concen trations ranging from -6 to 22%.