Thermal equilibrium, between different spin states

The phenomenon of spin equilibrium in octahedral complexes was first reported by Cambi and co-workers in a series of papers between 1931 and 1933 describing magnetic properties of tris(iV,iV-dialkyldithio-carbamato)iron(III) complexes. By 1968 the concept of a thermal equilibrium between different spin states was sufficiently well established that the definitive review by Martin and White described the phenomenon in terms which have not been substantially altered subsequently (112). During the 1960s the planar-tetrahedral equilibria of nickel(II) complexes were thoroughly explored and the results were summarized in comprehensive reviews published by Holm and coworkers in 1966 and 1973 ( 79, 80). Also, in 1968, Busch and co-workers... 

The existence of three polymorphs of III has been confirmed by Casey72), who has carried out seventeen preparations of the compound by two different methods and measured the magnetic susceptibility over a temperature range of 300—85 K. Within the experimental error, he found the same values for the transition temperature (212 3K) and the low-temperature magnetic moments (0.91, 1.35, and 1.65 B.M., respectively) for the three polymorphs as in Ref. 71. He further observed that, as with I65), the change from the HS state to the LS state at the transition temperature ( 213 K) took on the order of two hours to complete, and therefore concluded that a simple thermal equilibrium between the two spin states may be ruled out. 

Another powerful contrast parameter is spin-lattice, or Tj, relaxation. Spin-lattice relaxation contrast can again be used to differentiate different states of mobility within a sample. It can be encoded in several ways. The simplest is via the repetition time, between the different measurements used to collect the image data. If the repetition time is sufficiently long such that Tj )) Tj for all nuclei in the sample, then all nuclei will recover to thermal equilibrium between measurements and will contribute equally to the image intensity. However, if the repetition time is reduced, then those nuclei for which Tr < Tj will not recover between measurements and so will not contribute to the subsequent measurement. A steady state rapidly builds up in which only those nuclei with Tj contribute in any significant manner. As with -contrast, single images recorded with a carefully selected may be used to select cmdely a short component of a sample. 

The incident radiation induces transitions not only from the lower to the higher energy states but can also induce emission with equal probability. Consequently the extent of absorption will be proportional to the population difference between the two states. At thermal equilibrium the relative spin populations of the two Zeeman levels is given by a Boltzmann equation ... 

When nuclei with spin are placed in a magnetic field, they distribute themselves between two Zeeman energy states. At thermal equilibrium the number (N) of nuclei in the upper (a) and lower (j8) states are related by the Boltzmann equation (1) where AE=E — Ep is the energy difference between the states. In a magnetic field (Hq), E = yhHo and... 

Since interconversions between different states of symmetry (i.e., between ortho- and parahydrogen) are forbidden, the adjustment of the relative ratios of the two spin isomers to the values corresponding to the thermal equilibrium at an arbitrary temperature is normally very slow and, therefore, must be catalyzed. In the absence of a catalyst, dihydrogen samples retain their once achieved ratio and, accordingly, they can be stored in their enriched or separated forms for rather long periods (a few weeks or even a few years in favorable cases). 

Application of an oscillating magnetic field at the resonance frequency induces transitions in both directions between the two levels of the spin system. The rate of the induced transitions depends on the MW power which is proportional to the square of co = y B (the amplitude of the oscillating magnetic field) (see equation tbl.15.711 and also depends on the number of spins in each level. Since the probabilities of upward ( P) a and downward ( a) P)) transitions are equal, resonance absorption can only be detected when there is a population difference between the two spin levels. This is the case at thermal equilibrium where there is a slight excess of spins in the energetically lower P)-state. The relative population of the two-level system in thermal equilibrium is given by the Boltzmann distribution... 

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