High pressure studies of actinide intermetallics

Hyperfine Interactions - Magnetic properties of NpOs2,NpAl2. NpCo2Si2, NpAs, and NpSn3 are investigated by high pressure Mössbauer spectroscopy using the 60 keV transition in237Np. A wide...     

Observation of paramagnetic relaxation in the NpCu4Al8 intermetallic compound

²³⁷Np Mössbauer spectroscopy between 77 and 4.2 K was carried out in connection with neutron diffraction studies between 300 and 2 K on the tetragonal intermetallic NpCu₄Al₈. The Mössbauer spectra give an isomer shift of + 14.3 mm/s vs. NpAl₂ indicating the non-Kramers Np³⁺(⁵I₄)-ion to be present. Below 45 K the onset of magnetic hyperfine splitting is observed. It develops into a fully resolved Zeeman pattern at 4.2 K with B_eff≈330 T. Neutron diffraction finds no evidence for magnetic order over the whole temperature range scanned. All these results can consistently be explained by paramagnetic relaxation phenomena involving a low lying Γ^t₅ doublet closely followed by a Γ^t₄ singlet as the tetragonal crystalline field states of the Np³⁺ ion.     

Magnetic properties of NpM4Al8−x (M=Cr,Fe, Cu) intermetallics: Mössbauer effect and neutron diffraction studies

Mössbauer effect and neutron diffraction studies on the tetragonal NpM₄Al_8?x (M=Cr, Fe, Cu) of the 14/mmm space group are reported. In NpFe₄Al_8?x, both the Np and Fe sites order magnetically at close temperatures: the Np order ferromagnetically at 115(15) K (μ(Np)) ～ 0.6 μ_B and the Fe moments order antiferromagnetically at 130(10) K (μ(Fe) = 1.05(15) μ_B) with a ++?? sequence. In NpCr₄Al_8?x, the Np order magnetically around 50K. From the susceptibility data we conclude possible antiferromagnetic order of both Np and Cr sites. NpCu₄Al_8?x does not order magnetically down to at least 2 K. The magnetic hyperfine splitting observed below 45 K is explained by slow paramagnetic relaxation. The Np isomer shifts and also its magnetic behavior point to a trivalent ion (⁵I₄ Hund's rule ground state). The observed relaxation and magnetic phenomena are discussed in terms of crystalline electric field effects. In contrast to the isostructural rare-earth RM₄Al₈ compounds with practically independent order of R and M magnetic sublattices, we show that Np and M sublattices in NpM₄Al₈ are strongly coupled. This is caused by hybridization of both Np and M atoms with Al.     

Magnetic and hyperfine properties of NpFe2−xCoxSi2 tetragonal systems

Magnetization, ²³⁷Np Mössbauer effect and neutron diffraction studies of the tetragonal NpFe_2?xCo_xSi₂ (x = 0, 1, 1.5, 2) intermetallic compounds were performed. The Mössbauer studies of the²³⁷Np show a magnetic order below 87 (3)_, 15 (3), 37 (3), 42 (3) K, hyperfine fields of 2535 (50), 1600 (50), 2210 (50), 2600 (50) MHz and isometric shifts of -2.3 (3), +7.6 (3), 0 (3), -2.9 (3) mm/s (relative to NpAl₂), respectively. An extremely low magnetization of non-saturated character (at 4.2 K, 20 KOe) is observed.A polycrystalline ingot sample of NpCo₂Si₂ was studied by neutron diffraction at temperatures from 2 to 160 K. Five superlattice lines were observed at temperatures below 46 K and are consistent with an antiferromagnetic structure of the Np(2a) sublattice of type I with T_N = 46 (3) K. The Np ion magnetic moment consistent with the diffracted intensities is 1.5 (1) μ_B with no localized moment on the Co ion.A direct correlation between the Isomer shift, Hyperfine fields and ordering temperature is reported for the first time. This unusual correlation can be explained only if strong f-d, f-s hybridization are assumed.     

Unfair allocation of gains under the Equal Price allocation method in purchasing groups

Certain purchasing groups do not flourish. A supposed reason for this is a creeping dissatisfaction among various members of a group with the allocation of the cooperative gains. In this paper, we analyze unfairness resulting from using the commonly used Equal Price (EP) method for allocating gains under the assumption of continuous quantity discounts. We demonstrate that this unfairness is caused by neglecting a particular component of the added value of individual group members. Next, we develop two fairness ratios and tie these to fairness properties from cooperative game theory. The ratios show among other things that being too-big a player in a purchasing group can lead to decreasing gains. They can be used to assess if EP is an unfair method in specific situations. Finally, we discuss measures a purchasing group could consider in order to attenuate perceived unfairness. Thereby, the group may improve its stability and prosperity.