Entwicklung eines Prüfstandes zur rückführbaren Kalibrierung von Cantilevern

Zur rückführbaren Messung von Kräften im Bereich von Nanonewton werden typischerweise AFM Cantilever verwendet, deren Durchbiegung in guter Näherung proportional zur eingeleiteten Kraft ist. Die Proportionalitätskonstante zwischen den Größen wird durch die Steifigkeit des Cantilevers beschrieben. In dieser Arbeit wird die Konzeption, Entwickelung und Analyse eines Prüfstandes zur Vermessung der Steifigkeiten von Cantilevern beschrieben. Dazu wird der Cantilever an einem Halter befestigt und durch einen Piezoantrieb auf die Oberfläche eines Diamanttasters gedrückt. Die Auslenkung des Cantilevers wird durch ein Differenzinterferometer und die dafür notwendige Kraft mit einer neu entwickelten EMK-Wägezelle gemessen. Der Mechanismus der monolithischen Wägezelle ist durch die Verwendung eines einzelnen Drehgelenks sehr weich und ermöglicht dadurch eine hohe Kraftauflösung. Die Position des Wägebalkens wird durch ein weiteres Differenzinterferometer gemessen und mit einem PID-Regler zu Null geregelt. In zwei unabhängigen Verfahren wurde in guter Übereinstimmung die effektive Kraftkonstante der Wägezelle auf Bl = 25,9 mN/A bestimmt. Der Prüfstand wurde hinsichtlich seiner Eigenschaften untersucht und die Einflussgrößen auf die Messunsicherheit der Cantileversteifigkeit identifiziert. Die Kalibrierung eines weichen Cantilever ergab eine relative Messunsicherheit von 1,5 % (k = 2) bei einer Kalibrierkraft < 100 nN. Bei der anschließenden Untersuchung der Spitze waren keine Schäden festzustellen. Die Messung eines zweiten Cantilevers ergab eine gute Wiederholbarkeit der Kalibrierergebnisse. Außerdem wurden die durch diesen Prüfstand erzielten Ergebnisse mit den Resultaten eines an deren Prüfstandes verglichen und zeigten gute Übereinstimmung.Traceable measurements of forces in the range of Nanonewtons are typically done with AFM cantilevers. As a good approximation, the cantilever deflection is proportional to the applied force. This thesis describes the development of a calibration device that measures the stiffness of cantilevers by pushing them on a diamond surface. The cantilever is moved by a piezo stage while an interferometer measures its position. A novel load cell measures the force that is applied to the diamond according to the electromagnetic force compensating principle. Its single pivot design results in a soft mechanism that deflects under the load of the cantilever force. The deflection of the load cell is measured by another interferometer with a sub nanometer resolution. During the force measurement, the current through the coil is controlled by a PID controller. The effective force constant of the load cell has been measured in two independent ways with a good agreement. In several experiments, the metrological properties of the device were determined as well as the contribution factors to the uncertainty of the cantilever stiffness. A calibration of a small cantilever resulted in relative uncertainty of 1,5 % (k = 2) with a calibration force of < 100 nN. The imaging of the cantilever with a SEM microscope showed that the tip was not damaged. A second cantilever was calibrated multiple times and showed a good repeatability. The determined stiffness shows a good agreement with the results of a similar calibration device

The morphology, evolution and seismic visibility of partial melt at the core-mantle boundary: Implications for ULVZs

SUMMARY Seismic observations indicate that the lowermost mantle above the core–mantle boundary (CMB) is strongly heterogeneous. Body waves reveal a variety of ultra-low velocity zones (ULVZs), which extend not more than 100 km above the CMB and have shear velocity reductions of up to 30 per cent. While the nature and origin of these ULVZs remain uncertain, some have suggested they are evidence of partial melting at the base of mantle plumes. Here we use coupled geodynamic/thermodynamic modelling to explore the hypothesis that present-day deep mantle melting creates ULVZs and introduces compositional heterogeneity in the mantle. Our models explore the generation and migration of melt in a deforming and compacting host rock at the base of a plume in the lowermost mantle. We test whether the balance of gravitational and viscous forces can generate partially molten zones that are consistent with the seismic observations. We find that for a wide range of plausible melt densities, permeabilities and viscosities, lower mantle melt is too dense to be stirred into convective flow and instead sinks down to form a completely molten layer, which is inconsistent with observations of ULVZs. Only if melt is less dense or at most ca. 1 per cent more dense than the solid, or if melt pockets are trapped within the solid, can melt remain suspended in the partial melt zone. In these cases, seismic velocities would be reduced in a cone at the base of the plume. Generally, we find partial melt alone does not explain the observed ULVZ morphologies and solid-state compositional variation is required to explain the anomalies. Our findings provide a framework for testing whether seismically observed ULVZ shapes are consistent with a partial melt origin, which is an important step towards constraining the nature of the heterogeneities in the lowermost mantle and their influence on the thermal, compositional and dynamic evolution of the Earth.ER

FPGA-based signal processing of a heterodyne interferometer

A heterodyne interferometer and a data acquiring algorithm have been developed to measure the movement of a mirror in one dimension, as well as its rotation around two axis. The interferometer uses spatially separated beams to reduce periodic optical non-linearities, furthermore the optical set-up was designed for low drift, few number of optical elements and easy adjustment. The FPGA-based signal processing is based on an undersampling technique with the aim to minimise the calculation effort. The working principles of the interferometer and the electronics are described and their remaining non-linearities are investigated. Finally, the z-position, the tip and tilt angle of a planar stage are measured with the described system as an example of use

Unsicherheitsbeiträge der Krafteinleitung bei der Kalibrierung der Federkonstanten von AFM Cantilevern

Bei der Kalibrierung der Federsteifigkeit von AFM Cantilevern liefert deren Fehlausrichtung bezüglich des Kalibriersystems einen signifikanten Beitrag zur Messunsicherheit. In dieser Veröffentlichung werden diese Messunsicherheitsbeiträge auf Basis von analytischen und numerischen Modellen beschrieben sowie mit geeigneten Messungen überprüft. Das Ziel ist die Reduzierung der Messunsicherheit der Federsteifigkeit

Delayed improvement of depression and anxiety after transcatheter aortic valve implantation (TAVI) in stages of extended extra-valvular cardiac damage

Background: Depression and anxiety are frequently occurring and likely to be linked to the severity of cardiac diseases like aortic stenosis (AS). This seems to be of interest since a staging classification of extra-valvular cardiac damage in AS has been introduced and shown to be of prognostic relevance. Objective: The current study aimed to investigate the frequency of depression and anxiety in association to staging and their dynamics after transcatheter aortic valve implantation (TAVI). Methods: A total number of 224 AS patients undergoing TAVI were classified according to the 2017 staging classification into stage 0 to 4 and further dichotomized into group A (stage 0 to 2) and B (stage 3 and 4). Using the Hospital Anxiety and Depression Scale (HADS-D), patients were assigned to depressive versus non-depressive or anxious versus non-anxious per staging group respectively, and analyzed at baseline, 6 weeks, 6 months and 12 months after TAVI. Results: After dichotomization, 158 patients (70.5%) were assigned to group A and 66 patients (29.5%) to group B. The part showing pathologic values for depression was 25.4% (57/224 patients) in the entire collective, 26.6% (42/158 patients) in group A and 22.7% (15/66 patients) in group B (p = n.s.). The proportion showing pathologic values for anxiety was 26.8% (60/224 patients) in the entire collective and did not differ between group A (24.7%, 39/158 patients) and B (31.8%, 21/66 patients) (p = n.s.). In patients revealing pathologic values for depression or anxiety prior to TAVI, there were significant and stable improvements over time observable already in short-term (6 weeks) follow-up in group A, and likewise, but later, in long-term (6/12 months) follow-up in group B. Conclusions: Although of proven prognostic relevance, higher stages of extra-valvular cardiac damage are not associated with higher rates of pre-existing depression or anxiety. The TAVI procedure resulted in a persisting reduction of depression and anxiety in patients showing pathologic values at baseline. Notably, these improvements are timely delayed in higher stage

The importance of grain size to mantle dynamics and seismological observations

Abstract: Grain size plays a key role in controlling the mechanical properties of the Earth's mantle, affecting both long‐time‐scale flow patterns and anelasticity on the time scales of seismic wave propagation. However, dynamic models of Earth's convecting mantle usually implement flow laws with constant grain size, stress‐independent viscosity, and a limited treatment of changes in mineral assemblage. We study grain size evolution, its interplay with stress and strain rate in the convecting mantle, and its influence on seismic velocities and attenuation. Our geodynamic models include the simultaneous and competing effects of dynamic recrystallization resulting from dislocation creep, grain growth in multiphase assemblages, and recrystallization at phase transitions. They show that grain size evolution drastically affects the dynamics of mantle convection and the rheology of the mantle, leading to lateral viscosity variations of 6 orders of magnitude due to grain size alone, and controlling the shape of upwellings and downwellings. Using laboratory‐derived scaling relationships, we convert model output to seismologically observable parameters (velocity and attenuation) facilitating comparison to Earth structure. Reproducing the fundamental features of the Earth's attenuation profile requires reduced activation volume and relaxed shear moduli in the lower mantle compared to the upper mantle, in agreement with geodynamic constraints. Faster lower mantle grain growth yields best fit to seismic observations, consistent with our reexamination of high‐pressure grain growth parameters. We also show that ignoring grain size in interpretations of seismic anomalies may underestimate the Earth's true temperature variations