Calcite (CaCO3) is one of the most abundant minerals on earth and plays an important role in a wide range of different fields including, for example, biomineralization and environmental geochemistry. Consequently, surface processes and reactions such as dissolution and growth as well as (macro)molecule adsorption are of greatest interest for both applied as well as fundamental research. An in-depth understanding of these processes requires knowledge about the detailed surface structure in its natural state which is quite often a liquid environment. We have studied the most stable cleavage plane of calcite under liquid conditions using frequency modulation atomic force microscopy. Using this technique, we achieved true atomic-resolution imaging, demonstrating the high-resolution capability of frequency modulation atomic force microscopy in liquids. We could reproduce contrast features reported before using contact mode atomic force microscopy, originating from the protruding oxygen atom of the carbonate groups. Besides this contrast, however, our results, indeed, indicate that we obtain more detailed structural information, revealing the calcium sublattice of the (1014) cleavage plane.

Calcite is a mineral of fundamental importance that plays a crucial role in many fields of research such as biomineralization, biomolecule adsorption, and reactivity as well as industrial and daily life applications. Consequently, the most stable cleavage plane of calcite has been studied extensively using both direct imaging techniques such as atomic force microscopy as well as spectroscopic and diffraction techniques. Several surface structures have been reported for the (1014) cleavage plane of calcite differing from the simple bulk-truncated structure and an ongoing controversy exists in literature whether the cleavage plane exhibits a (2 x 1) reconstruction or not. We study the (1014) cleavage plane using high-resolution noncontact atomic force microscopy (NC-AFM) under ultrahigh vacuum conditions and obtain a clear signature of the (2 x 1) reconstruction. This reconstruction is observed in very narrow tip-surface distance ranges only, explaining why in some experiments the reconstruction has been observed and in others not. Moreover, as all sample preparation is performed in ultrahigh vacuum, the possibility of the (2 x 1) reconstruction being adsorbate-induced appears rather unlikely. Additionally, tip-induced surface changes are ruled out as origin for the observed reconstruction either. In conclusion, our study suggests that the (2 x 1) reconstruction is a true surface property of the (1014) cleavage plane of calcite.

SummaryThe noise of the frequency-shift signal Δf in noncontact atomic force microscopy (NC-AFM) consists of cantilever thermal noise, tip–surface-interaction noise and instrumental noise from the detection and signal processing systems. We investigate how the displacement-noise spectral density d z at the input of the frequency demodulator propagates to the frequency-shift-noise spectral density d Δ f at the demodulator output in dependence of cantilever properties and settings of the signal processing electronics in the limit of a negligible tip–surface interaction and a measurement under ultrahigh-vacuum conditions. For a quantification of the noise figures, we calibrate the cantilever displacement signal and determine the transfer function of the signal-processing electronics. From the transfer function and the measured d z, we predict d Δ f for specific filter settings, a given level of detection-system noise spectral density d z ds and the cantilever-thermal-noise spectral density d z th. We find an excellent agreement between the calculated and measured values for d Δ f. Furthermore, we demonstrate that thermal noise in d Δ f, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A system with a low-noise signal detection and a suitable cantilever, operated with appropriate filter and feedback-loop settings allows room temperature NC-AFM measurements at a low thermal-noise limit with a significant bandwidth.

Sperm cells swim through the fluid by a periodic wave-like beating of their flagellum. At low Reynolds numbers and in confinement, the directed motion of sperm and other microswimmers is strongly influenced by steric and hydrodynamic wall interactions. We model sperm motility in mesoscale hydrodynamics simulations by imposing a planar traveling bending wave along the flagellum. Sperm are simulated swimming in curved, straight, shallow and zigzag-shaped microchannels. Changes in the sidewall modulations and the imposed beat pattern allow the identification of a strong dependence of the surface attraction on the beat-shape envelope of the sperm cell. For swimming in zigzag microchannels, the deflection-angle distribution at sharp corners is calculated and found to be in good agreement with recent microfluidic experiments. The simulations reveal a strong dependence of the deflection angle on the orientation of the beat plane with respect to the channel sidewall, and thus deepen the understanding of sperm navigation under strong confinement. Detachment of sperm, while swimming along curved walls, is dominated by the change of beat-plane orientation. Therefore, either the emergence of a nonplanar component of the flagellar beat with increasing wavelength or the strong confinement in shallow channels drastically increases wall attraction. Our simulation results reveal a consistent picture of passive sperm guidance that is dominated by the steric interactions of the beat pattern with the nearby surfaces.

A key issue for high-resolution frequency-modulation atomic force microscopy imaging in liquids is minimizing the frequency noise, which requires a detailed analysis of the corresponding noise contributions. In this paper, we present a detailed description for modifying a commercial atomic force microscope (Bruker MultiMode V with Nanoscope V controller), aiming at atomic-resolution frequency-modulation imaging in ambient and in liquid environment. Care was taken to maintain the AFMs original stability and ease of operation. The new system builds upon an optimized light source, a new photodiode and an entirely new amplifier. Moreover, we introduce a home-built liquid cell and sample holder as well as a temperature-stabilized isolation chamber dedicated to low-noise imaging in liquids. The success of these modifications is measured by the reduction in the deflection sensor noise density from initially 100 fm/√Hz to around 10 fm/√Hz after modification. The performance of our instrument is demonstrated by atomically resolved images of calcite taken under liquid conditions.

One contribution of 17 to a Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

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The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior. Graphic abstract