K.F. Niessen

Ratio of exchange integrals in connection with angles between partial magnetizations in ferrimagnetic spinels

Synopsis Allowing the spin direction of magnetic ions in one sublattice of (octahedral) B-sites to differ from that in the other sublattice of B-sites (as assumed by Yafet and Kittel for a spinel with only one kind of magnetic ions) a mixed crystal spinel containing two kinds of magnetic ions is considered, taking into account the different physical nature of the ions. Here a situation may be realized where the partial magnetizations are neither parallel nor antiparallel but where in one sublattice (say BinI) two special spin directions occur for the two kinds of magnetic ions and in the other (BinII) another couple of spin directions lying with the former set symmetrical with respect to the single spin direction of ions on the (tetrahedral) A-sites. The A-A interaction is neglected and consequently a subdivision of the A-lattice is not taken into account. Compositions of the mixed crystal are possible where such a non-rectilinear case is just possible, i.e. where the mutual deviations of the spin directions on the B-sites are very small, their angles with the spin direction on A-sites being nearly π. From three of such compositions the ratios of exchange integrals can be determined.

Curie temperature of nickel-zinc ferrites as a function of the nickel-zinc ratio

Abstract In a series of mixed crystals of nickel ferrite (or any other ferromagnetic ferrite Me2+Fe2O4 and zinc ferrite the ratio of the Curie temperature to that of the zinc-free ferrite, can be calculated by means of a generalisation of Neels extension of the Weiss theory to ferrites. In this generalisation the interations of all magnetic ions are taken into account. The dependency of the Curie temperature on composition leads to the prediction that zinc ferrite is antiferromagnetic.

On the deviations between theoretical and experimental values of the specific heat of superconductors

Abstract The deviations mentioned in the title are explained qualitatively by the combination of two effects, the more important of which is based on the assumption that the thickness of H e i s e n b e r gs superconducting layer, covering part of the Fermi surface, does not fall abruptly to zero at the boundary of the layer. The other effect, which was more obvious but appeared to be of less importance, comes into play when the thickness of the superconducting layer decreases with increasing temperature.

The energy of the normal electrons in a superconductor as a function of temperature and thickness of the superconducting layer on the fermi surface

Abstract In order to need simpler calculations Heisenbergs assumption about the superconducting layer covering a part of the Fermi surface is modified in so far that a layer is assumed of thickness Δ (by which is meant the difference of the energies corresponding to the upper and lower surfaces of the layer), which layer, covering a part ω of the Fermi surface, is entirely inaccessible to normal electrons. A formula for the energy of the normal electrons is derived which is a function of ω, T and Δ and which for Δ 》 kT coincides with Koppes expression in the Heisenberg theory but for Δ 《 kT is identical with the value well known from Sommerfelds theory of metals. A special case is used to express the number of superconducting electrons per cubic centimetre at T = 0 in the transition temperature and the number of normal electrons. See equation (33).

On one of Heisenberg's hypotheses in the theory of specific heat of superconductors

Abstract An assumption made by H e i s e n b e r g in K o p p es theory of the specific heat of superconductors is discussed. A comparison with an other problem at first sight seems to contradict this assumption but turns out to support it. Heisenbergs assumption is also confirmed in a direct way.

U¨ber die empfangsimpedanz einer empfangsantenne. I strahlungswiderstand

Abstract In dieser Arbeit wird die Empfangsimpedanz einer Empfangsantenne, d.h. die Strahlungsimpedanz der unbelastet gedachten Antenne, betrachtet und zwar bei einer Stromverteilung, die sich nach von Korshenewsky bei der Annahme einer flachen auffallenden Signalwelle einstellen wird, wenn der elektrische Vektor parallel der Antenne steht. In Fig. 4 findet man die Stromverteilungen auf einigen Empfangsantennen und in Fig. 5 die auf einigen in der Mitte gespeisten Sendeantennen abgebildet. In Fig. 6 sind diese von von Korshenewsky und von Labus herru¨hrenden Stromverteilungen zusammengebracht. In Teil I werd speziell der Empfangswiderstand der Empfangsantenne als Funktion der Antennenla¨nge (ausgedru¨ckt in Wellenla¨ngen) na¨her ausgearbeitet.

Spontaneous magnetization of nickel zinc ferrite as a function of the nickel zinc ratio

Synopsis The reduced spontaneous magnetization of nickel zinc ferrite (magnetization at T , divided by that at T = 0) is determined as a function of the reduced temperature T * ( T , divided by the Curie temperature T c ) and of the nickel zinc ratio f , defined by the following expression for the ratio between the numbers of nickel and zinc ions: Ni : Zn = f : (1 − f ). In the case T * ≪ 1 and in the case T * = 1 − Δ ( Δ ≪ 1) formulae for the reduced magnetization are given, holding for high values of f , for instance 1/2 f T * a graphical method must be used. The results are compared with the experimental curves of Guillaud and Roux, representing the reduced magnetization as a function of T * when several ferrites with a different nickel zinc ratio are considered, especially at low and intermediate values of T * . These curves diverge in a typical way. This can be explained qualitatively. For the nickel ions in nickel ferrite we are obliged to assume that, at T * = 0 · 3, four percent occupy tetrahedral interstices instead of octahedral interstices.

Zur prüfung der Paulingschen Hypothese über die bindung der atome in metallen

Zusammenfassung Versucht wird (leider mit negativem Erfolg) die Paulingsche Hypothese uber die Bindung der Atome im Metall plausibel zu machen und zwar unter Benutzung der Curietemperatur von Nickel.

Note on the “albedo” of a hydrogenated substance for slow moving neutrons

Zusammenfassung Die von O. Halpern und Mitarbeitern gefundene Formel fur die Albedo β = 1− 4 ✓3 1 ✓N wird erganzt, indem der folgende Term der Reihenentwicklung abgeschatzt wird. Die Formel lasst sich dann schreiben: β = 1− 4 ✓3 1 ✓N + 2.86 N

Curiekonstante und curietemperatur von nickellegierungen

Abstract Nach der Slaterschen Theorie des Ferromagnetismus werden die Curiekonstante (c) un die Curietemperatur (θ) einer Nickellegierung betrachtet als Funktion vom Gehalt (100x%) des hinzugefu¨gten Metalles, wobei besonders auf Effekte hingewiesen wird, die den Wert vondc/dx unddθ/dx beix = 0 beeinflussen. Zwei Fa¨lle werden dabei untersucht, die sich z.B. bei Ni-Cu Legierungen darin unterscheiden, dass im Fall I angenommen wird, dass alle Lo¨cher der Legierung sich im 3d-Ni Band befinden, wa¨hrend im Fall II die Mo¨glichkeit einer Verteilung der Lo¨cheru¨ber die 3d-Ba¨nder des Nickelsund des Kupfers betrachtet wird. Vermutet wird, dasz bei Ni-Cu und Ni-Zn die Lo¨cher sich in beiden Ba¨ndern befinden und dasz bei Legierungen von Nickel und hochvalenten Elementen die Lo¨cher nur im Nickel Band sitzen und zwar (0,6—px)/1—x pro Ni-Atom, wop die Valenz des zweiten Elementes ist. Diese Vermutung ist basiert auf den (immer geringen) Abweichungen zwischen−0.6/c0 (dc/dx)x = 0 undp und auf den Abweichungen zwischen−0,6/θ0 (dθ/dx)x = 0 undp, wobeic0 undθ0die Curieconstante resp. die Curietemperatur des reinen Ni sind. Die letzteren Abweichungen sind nihil bei Ni-Cu und Ni-Zn und sonst stark negativ. Vergleich hierzu die Tabellen A und B, die einer Arbeit von Hirone direkt, resp. indirekt entnommen sind.