Role of Magnetic Exchange Interactions in the Magnetization Relaxation of {3d–4f} Single‐Molecule Magnets: A Theoretical Perspective

Combined density functional and ab initio calculations are performed on two isomorphous tetranuclear {Ni₃^IIILn^III} star‐type complexes [Ln=Gd ( 1 ), Dy ( 2 )] to shed light on the mechanism of magnetic exchange in 1 and the origin of the slow magnetization relaxation in complex 2 . DFT calculations correctly reproduce the sign and magnitude of the J values compared to the experiments for complex 1 . Acute ?Ni?O?Gd bond angles present in 1 instigate a significant interaction between the 4f_xyz orbital of the Gd^III ion and 3d orbital of the Ni^II ions, leading to rare and strong antiferromagnetic Ni???Gd interactions. Calculations reveal the presence of a strong next‐nearest‐neighbour Ni???Ni antiferromagnetic interaction in complex 1 leading to spin frustration behavior. CASSCF+RASSI‐SO calculations performed on complex 2 suggest that the octahedral environment around the Dy^III ion is neither strong enough to stabilize the m_J |±15/2〉 as the ground state nor able to achieve a large ground‐state–first‐excited‐state gap. The ground‐state Kramers doublet for the Dy^III ion is found to be the m_J |±13/2〉 state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY_ANISO program, we have extracted the J_NiDy interaction as ?1.45 cm^?1. The strong Ni???Dy and next‐nearest‐neighbour Ni???Ni interactions are found to quench the QTM to a certain extent, resulting in zero‐field SMM behavior for complex 2 . The absence of any ac signals at zero field for the structurally similar [Dy(AlMe₄)₃] highlights the importance of both the Ni???Dy and the Ni???Ni interactions in the magnetization relaxation of complex 2 . To the best of our knowledge, this is the first time that the roles of both the Ni???Dy and Ni???Ni interactions in magnetization relaxation of a {3d–4f} molecular magnet have been established.     

Common fixed points of two maps in cone metric spaces

We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.      

Approximation of fixed points of uniformly R-subweakly commuting mappings

We introduce a new class of uniformly R-subweakly commuting mappings and then using this class study the problem of approximation of common fixed points of asymptotically S-nonexpansive mappings in a Banach space with uniformly Gâteaux differentiable norm.     

Changes in the zeta-potential of copper ferrocyanide sol by gradual addition of electrolytes

Summary Zeta-potential of copper ferrocyanide sol falls, and its hydrogen ion concentration increases continuously with the addition of chlorides of potassium, barium, and aluminium till the sol falls to coalescence. The effect of thorium nitrate on the above sol is quite distinct from the rest in the sense that with its addition zeta-potential first falls rapidly, attains a minima, and then it again rises. The lowering of zeta-potential as well as the increase in hydrogen ion concentration of this sol by the cations of different valencies follows the Hardy-Schulze rule.

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Zusammenfassung Das Zeta-Potential von Kupfer-Ferro-Cyanid-Sol sinkt, und seine Wasserstoffkonzentration steigt kontinuierlich mit Zufügung der Chloride von Kalium, Barium und Aluminium, bis das Sol ausf?llt. Der Effekt von Thoriumnitrat ist v?llig verschieden. Das Zeta-Potential f?llt zuerst sehr stark, erreicht ein Minimum und steigt dann wieder. Die Erniedrigung des Zeta-Potentials wie auch der Anstieg der Wasserstoffionenkonzentration dieses Soles durch Kationen verschiedener Wertigkeit entspricht der Hardy-SchulzeRegel.

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We thank Dr. M. O. Farooq for his kind interest in the work.     

Forced convective mass transfer studies from spheroids

In order to obtain information on the effect of shape on mass transfer, overall mass transfer rates were measured from naphthalene spheroids suspended in a wind tunnel (Schmidt number 2.4). Spheroidal shapes which included spheres, oblate spheroids and spheroids with composite halves were employed for the study. The ratio of the minor to major axes of the spheroids ranged from 1∶1 to 1∶4. The data obtained from one-hundred and fifty six experimental runs were best correlated by the use of Pasternak and Gauvin's characteristic dimension defined as total surface area of the body divided by maximum perimeter normal to flow. The correlations for the ranges 200 < Re < 2000 and 2000 < Re < 32000 are as follows. $$\begin{gathered} Sh = 0.62 (Re)^{0.5} (Sc)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \hfill \\ Sh = 0.26 (Re)^{0.6} (Sc)^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \hfill \\ \end{gathered}$$ which correlated the data with standard deviation of 3.75% and 3.50% respectively.     

A novel technique for mass transfer studies

An optical technique using microdensitometer has been demonstrated to measure mass transfer rates to a flat plate. Not only that this technique enabled measurements from extremely small areas but also the accuracy and reproducibility of the results were found to be excellent. A dyeing process consisting of a flat polymer film held parallel to the direction of liquid flow was chosen as a model system in which the mass transfer rates are determined by a number of mechanisms. The fundamental concepts thus obtained can be extended to apply more generally to all mass transfer processes.

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Zusammenfassung Mit Hilfe eines Mikrodichtemessers wird eine neue Technik demonstriert, um Stoffübertragungsdaten auf eine ebene Platte zu messen. Diese Technik ermöglicht nicht nur Messungen bei extrem kleinen Mächen, auch die Genauigkeit und Reproduzierbarkeit der Ergebnisse ist ausgezeichnet. Ein Färbungsprozeß, bei dem ein ebener, polymerer Film parallel zur Richtung des Flüssigkeitsstromes gehalten wird, wird als Modellsystem gewählt. Die Stoffübertragungsraten werden durch eine Anzahl von Mechanismen bestimmt. Die so erhaltenen grundlegenden Begriffe können erweitert werden, um sie allgemein auf alle Stoffübertragungsvorgänge anzuwenden.

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Magnetically guided fast electrons in cylindrically compressed matter

Fast electrons produced by a 10 ps, 160 J laser pulse through laser-compressed plastic cylinders are studied experimentally and numerically in the context of fast ignition. K(α)-emission images reveal a collimated or scattered electron beam depending on the initial density and the compression timing. A numerical transport model shows that implosion-driven electrical resistivity gradients induce strong magnetic fields able to guide the electrons. The good agreement with measured beam sizes provides the first experimental evidence for fast-electron magnetic collimation in laser-compressed matter.     

An application of a fixed point theorem to best simultaneous approximation

Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.