We have calculated the initial magnetization curves and complete hysteresis loops for hard type-II superconductors. The critical-current density Jc is assumed to be a function of the internal magnetic field Hi according to Kim’s model, Jc(Hi)=k/(H0+‖Hi‖), where k and H0 are constants. As is the case for other critical-state models, additional assumptions are that bulk supercurrent densities are equal to Jc, and that the lower critical field is zero. Our analytic solution is for an infinite orthorhombic specimen with finite rectangular cross section, 2a×2b (a≤b), in which a uniform field H is applied parallel to the infinite axis. Assuming equal flux penetration from the sides, we reduced the two-dimensional problem to a one-dimensional calculation. The calculated curves are functions of b/a, a dimensionless parameter p=(2ka)1/2/H0, and the maximum applied field Hm. The field for full penetration is Hp=H0[(1+p2)1/2−1]. A related parameter is H*m=H0[(1+2p2)1/2−1]. Hysteresis loops were calculated for the different ranges of Hm : Hm<Hp, Hp<Hm<H*m, and H*m<Hm. The equations for an infinite cylindrical specimen of radius a are the same as those for a specimen with square cross section, a=b. In the limit p≪1 and a=b, our results reduce to those of the Bean model (Jc independent of Hi) for cylindrical geometry. Similarly, in the limit p≪1 and b→∞, the results are the same as those for a slab in the Bean model. For H>1.5 Hp, or H>0 when p≪1, the width of the hysteresis loop ΔM may be used to deduce Jc as a function of H: Jc(H)=ΔM(H)/[a(1−a/3b)].

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By combining nuclear magnetic relaxometry on 39 ferritin samples with different iron loading with magnetometry, results were obtained that suggest a new interpretation of the core structure and magnetic properties of ferritin. These studies provide evidence that, contrary to most earlier reports, the ferritin core is antiferromagnetic (AFM) even at body temperature and possesses a superparamagnetic (SPM) moment due to incomplete cancellation of antiparallel sublattices, as predicted by Néel's theory. This moment also provides a likely explanation for the anomalous T2 shortening in ferritin solution. However, the number of SPM moments derived from this model is less than the number of ferritin molecules determined chemically, and a similar discrepancy was found by retrospectively fitting previously published magnetometry data. In other words, only a fraction of the ferritin molecules seem to be SPM. The studies also provide evidence for paramagnetic (PM) Curie-Weiss iron ions at the core surface, where the local Néel temperature is lower; these ions are apparently responsible for the weaker T1 shortening. In fact, the conversion of uncompensated AFM lattice ions to PM ions could explain the small number of SPM particles. The apparent Curie Law behavior of ferritin thus appears to be a coincidental result of different temperature dependences of the PM and SPM components.

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A mononuclear vanadium(IV), a mononuclear vanadium(V), and a binuclear mixed valence vanadium(IV/V) complex with the ligand N-(2-hydroxyethyl)iminodiacetic acid (H(3)hida) have been structurally characterized. Crystal data for [VO(Hhida)(H(2)O)].CH(3)OH (1): orthorhombic; P2(1)2(1)2(1); a= 6.940(2), b = 9.745(3), c= 18.539(4) Å; Z = 4. Crystal data for Na[V(O)(2)(Hhida)(2)].4H(2)O (2): monoclinic; P2(1)/c; a = 6.333(2), b = 18.796(2), c = 11.5040(10) Å; beta = 102.53(2) degrees; Z = 4. Crystal data for (NH(4))[V(2)(O)(2)(&mgr;-O)(Hhida)(2)].H(2)O (3): monoclinic; C2/c; a = 18.880(2), b= 7.395(2), c = 16.010(2) Å; beta = 106.33(2) degrees; Z = 4. The mononuclear vanadium(IV) and vanadium(V) complexes are formed from the monoprotonated Hhida(2)(-) ligand, and their structural and magnetic characteristics are as expected for six-coordinate vanadium complexes. An interesting structural feature in these complexes is the fact that the two carboxylate moieties are coordinated trans to one another, whereas the carboxylate moieties are coordinated in a cis fashion in previously characterized complexes. The aqueous solution properties of the vanadium(IV) and -(V) complexes are consistent with their structures. The vanadium(V) complex was previously characterized; in the current study structural characterization in the solid state is provided. X-ray crystallography and magnetic methods show that the mixed valence complex contains two indistinguishable vanadium atoms; the thermal ellipsoid of the bridging oxygen atom suggests a type III complex in the solid state. Magnetic methods show that the mixed valence complex contains a free electron. Characterization of aqueous solutions of the mixed valence complex by UV/vis and EPR spectroscopies suggests that the complex may be described as a type II complex. The Hhida(2)(-) complexes have some similarities, but also some significant differences, with complexes of related ligands, such as nitrilotriacetate (nta), N-(2-pyridylmethyl)iminodiacetate (pmida), and N-(S)-[1-(2-pyridyl)ethyl]iminodiacetate (s-peida). Perhaps most importantly, the mixed valence Hhida(2)(-) complex is significantly less stable than the corresponding pmida and s-peida complexes of similar overall charge but very similar in stability to the nta and V(2)O(3)(3+) complexes with higher charges. Thus, there is the potential for designing stable mixed valence dimers.