A method to determine the effective electrostatic tip radius of arbitrarily shaped conducting tips in atomic force microscopy is presented. The method is based on the finding that for conductive samples, the electrostatic force can be separated into two contributions: one from a constant background that depends only on the macroscopic shape of the tip (cone or pyramid and cantilever), and another that depends only on the radius of curvature of the tip apex. Based on a simple theoretical expression derived from the generalized image charge method, we show that the tip radius can be directly determined from experimental force-distance characteristics. For irregular tip shapes, we show that the measured tip radius is the average of two principal curvatures, in agreement with tip shape images obtained by scanning electron microscopy.

In this study, we show that the correct determination of surface morphology using scanning force microscopy (SFM) imaging and power spectral density (PSD) analysis of the surface roughness is an extremely demanding task that is easily affected by experimental parameters such as scan speed and feedback parameters. We present examples were the measured topography data is significantly influenced by the feedback response of the SFM system and the PSD curves calculated from this experimental data do not correspond to that of the true topography. Instead, either features are "lost" due to low pass filtering or features are "created" due to oscillation of the feedback loop. In order to overcome these serious problems we show that the interaction signal (error signal) can be used not only to quantitatively control but also to significantly improve the quality of the topography raw data used for the PSD analysis. In particular, the calibrated error signal image can be used in combination with the topography image in order to obtain a correct representation of surface morphology ("true" topographic image). From this "true" topographic image a faithful determination of the PSD of surface morphology is possible. The corresponding PSD curve is not affected by the fine-tuning of feedback parameters, and allows for much faster image acquisition speeds without loss of information in the PSD curve.

Thermal fluctuation of the cantilever position sets a fundamental limit for the precision of any Scanning Force Microscope. In the present work we analyse how these fluctuations limit the determination of the resonance frequency of the tip-sample system. The basic principles of frequency detection in Dynamic Scanning Force Microscopy are revised and the precise response of a typical frequency detection unit to thermal fluctuation of the cantilever is analysed in detail. A general relation for thermal frequency noise is found as a function of measurement bandwidth and cantilever oscillation. For large oscillation amplitude and low bandwidth, this relation converges to the result known from the literature, while for low oscillation amplitude and large bandwidth we find that the thermal frequency noise is equal to the width of the resonance curve and therefore stays finite, contrary to what is predicted by the relation known so far. The results presented in this work fundamentally determine the ultimate limits of Dynamic Scanning Force Microscopy. 1 arXiv:1002.4284v2 [cond-mat.mes-hall]

The biallelic pathogenic repeat (AAGGG)400–2000 intronic expansion in the RFC1 gene has been recently described as the cause of cerebellar ataxia, neuropathy, vestibular areflexia syndrome (CANVAS) and as a major cause of late‐onset ataxia. Since then, many heterozygous carriers have been identified, with an estimated allele frequency of 0.7% to 4% in the healthy population. Here, we describe in two affected CANVAS sisters the presence of the nonsense c.724C > T p.(Arg242*) variant in compound heterozygosity with the pathogenic repeat expansion in the RFC1 gene. Further RNA analysis demonstrated a reduced expression of the p.Arg242* allele in patients confirming an efficient nonsense‐mediated mRNA decay. We also highlight the importance of considering the sequencing of the RFC1 gene for the diagnosis, especially in patients with CANVAS diagnosis carriers of the AAGGG repeat expansion.

A method to precisely calibrate the oscillation amplitude in dynamic scanning force microscopy is described. It is shown that the typical electronics used to process the dynamic motion of the cantilever can be adjusted to transfer the thermal noise of the cantilever motion from its resonance frequency to a much lower frequency within the typical bandwidth of the corresponding data acquisition electronics of a scanning force microscopy system. Based on this concept, two procedures for the calibration of the oscillation amplitude are proposed. One is based on a simple calculation of the root mean square deviation measured at the outputs of the electronics used to process the dynamic motion of the cantilever, and the second one is based on analysis of the corresponding spectrum and the calculation of the quality factor, the resonance frequency and the signal strength.We show that the proposed scheme for amplitude calibration using thermal noise is experimentally and theoretically robust, with soft as well as with hard cantilevers. Moreover, it is directly related to well-defined quantities such as the force constant and thermal energy, in contrast to the calibration using amplitude versus distance curves, which requires non-trivial a priori assumptions regarding the amplitude versus distance relation.

In this work we describe two simple and compact submicrometer-precision sample holders that are easily integrated into a Scanning Force Microscopy (SFM) system. The designs are based on a traditional kinematic mounting or on self-adjustment of the sample holder and the upper piece of the piezoelectric scanner. With these sample holders the sample position is automatically recovered to within about 100 nm. The setup allows ex situ manipulation of the sample and SFM imaging of the same region without the aid of an optical microscope, positioning marks, and tedious re-allocation.

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