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The van der Pauw method for two-dimensional samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the dimensionless parameter related to the geometry of the isolated hole, known as the Riemann modulus. The parameter is invariant under conformal mappings. Experimental verification of the method is presented.

Explicit results of the van der Pauw method for a sample containing an isolated hole are presented together with experimental confirmation. Results of measurements and numerical analysis strongly suggest that four probe resistivities obey inequality similar in the form to the famous van der Pauw equation. The inequality seems to be valid for any sample with an isolated hole and contacts located on the same edge, however rigorous proof is not given. The inequality can be used for experimental detection of the sample quality.Comment: 6 pages plus 4 figure

The powder samples of (x = 4, 5 and 6) alloys have been measured by means of magnetization, Mössbauer effect, x-ray and neutron diffraction techniques in the temperature range 1.5 - 400 K. Both neutron and x-ray diffraction experiments showed that the positions f in all samples are occupied by iron, while the iron atoms in the samples with x = 5 and 6 locate also at j sites. A little f - j disorder exists in . The paper shows a change of the magnetic structure with an increase of iron content. The magnetic moments lie in a basal a - b plane. Iron atoms in alloy order antiferromagnetically. and alloys exhibit in general a ferromagnetic behaviour. However a detailed distribution of magnetic moments among different sites could not be determined unambiguously from the neutron data only. Nevertheless, combining information from neutron and Mössbauer experiments, one can infer that the ordering among iron atoms must be non-collinear. A magnetic ordering among uranium atoms has been found in only. Low-temperature thermal expansion varies nonlinearly with temperature and in all samples is negligible at low temperatures.

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The Mössbauer measurements performed on powdered single crystals of FeTe 0.5 Se 0.5 (T c ~ 14.7 K) reveal minor content of two impurity phases, identified as Fe 3 O 4 and Fe 7 Se 8 , among the major tetragonal phase. From the shape of impurity subspectra it follows that Fe 7 Se 8 behaves in superparamagnetic manner, most likely because of randomly distributed Fe vacancies in the lattice structure of Fe-Te-Se. The magnetite content in the powdered absorber exposed to ambient air conditions remains unchanged during period of 16 months. Ageing effects were observed for the samples stored under argon atmosphere and small increase of the isomer shift of the doublet was detected. Presented temperature dependence of the hyperfine parameters can be explained as due to possible orthorhombic distortion or to temperature behaviour of impurity phases Fe 3 O 4 and Fe 7 Se 8 . Strong tendency to formation of crystalline texture of powdered sample is observed.

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