The 100th anniversary of the four-point probe technique: the role of probe geometries in isotropic and anisotropic systems

The electrical conductivity of solid-state matter is a fundamental physical property and can be precisely derived from the resistance measured via the four-point probe technique excluding contributions from parasitic contact resistances. Over time, this method has become an interdisciplinary characterization tool in materials science, semiconductor industries, geology, physics, etc, and is employed for both fundamental and application-driven research. However, the correct derivation of the conductivity is a demanding task which faces several difficulties, e.g. the homogeneity of the sample or the isotropy of the phases. In addition, these sample-specific characteristics are intimately related to technical constraints such as the probe geometry and size of the sample. In particular, the latter is of importance for nanostructures which can now be probed technically on very small length scales. On the occasion of the 100th anniversary of the four-point probe technique, introduced by Frank Wenner, in this review we revisit and discuss various correction factors which are mandatory for an accurate derivation of the resistivity from the measured resistance. Among others, sample thickness, dimensionality, anisotropy, and the relative size and geometry of the sample with respect to the contact assembly are considered. We are also able to derive the correction factors for 2D anisotropic systems on circular finite areas with variable probe spacings. All these aspects are illustrated by state-of-the-art experiments carried out using a four-tip STM/SEM system. We are aware that this review article can only cover some of the most important topics. Regarding further aspects, e.g. technical realizations, the influence of inhomogeneities or different transport regimes, etc, we refer to other review articles in this field.

Evaluation of reproductive barriers contributes to the development of novel interspecific hybrids in the Kalanchoe genus

Background: Interspecific hybridization is a useful tool in ornamental breeding to increase genetic variability and introduce new valuable traits into existing cultivars. The successful formation of interspecific hybrids is frequently limited by the presence of pre- and post-fertilization barriers. In the present study, we investigated the nature of hybridization barriers occurring in crosses between Kalanchoe species and evaluated possibilities of obtaining interspecific hybrids. Results: The qualitative and quantitative analyses of pollen tube growth in situ were performed following intra-and interspecific pollinations. They revealed occurrence of pre-fertilization barriers associated with inhibition of pollen germination on the stigma and abnormal growth of pollen tubes. Unilateral incongruity related to differences in pistil length was also observed. The pollen quality was identified as a strong factor influencing the number of pollen tubes germinating in the stigma. In relation to post-fertilization barriers, endosperm degeneration was a probable barrier hampering production of interspecific hybrids. Moreover, our results demonstrate the relation of genetic distance estimated by AFLP marker analysis of hybridization partners with cross-compatibility of Kalanchoe species. At the same time, differences in ploidy did not influence the success of interspecific crosses. Conclusions: Our study presents the first comprehensive analysis of hybridization barriers occurring within Kalanchoe genus. Reproductive barriers were detected on both, pre- and post-fertilization levels. This new knowledge will contribute to further understanding of reproductive isolation of Kalanchoe species and facilitate breeding of new cultivars. For the first time, interspecific hybrids between K. nyikae as maternal plant and K. blossfeldiana as well as K. blossfeldiana and K. marnieriana were generated.