Piezoelectric Creep Research Articles

Bimorph mirrors at synchrotron beamlines: from walking to flying

With brighter synchrotron sources, automated sample changers, and faster detectors, there is a strong scientific need for rapid and precise variation of the X-ray beam profile, rather than the “set and forget” operation of years past. Piezoelectric bimorph deformable mirrors already allow quick beam profile changes without the heat generation and wear of mechanical devices. Now, their early technological limitations – excessively constraining holders, progressive “junction effect” distortion, and communication bottlenecks with power supplies – are being overcome by a collaboration of scientists and engineers both in industry and at Diamond Light Source. A new generation of bimorph mirrors maintains a stable figure over extended periods of operation. Improved holders and flexible electrical connectors are greatly reducing the mechanical strain imparted to bimorphs, thereby improving their speed, accuracy, and stability. A more sophisticated high voltage power supply has on-board signal processing capacity, allowing large focusing changes within seconds and providing programmable time-varying voltage profiles to counteract piezoelectric creep. The communication between beamline systems and power supplies is being freed of bottlenecks and now runs stably up to 1 Hz. Early tests have already shown that bimorph mirrors can repeatedly switch the size of an X-ray beam in well under 10 seconds. Bimorph mirrors at synchrotron beamlines are now growing beyond the largely static operation of the past and gaining a new dynamism through development projects that are now well advanced. We report on how these endeavours will make it easier for beamlines to utilise the full potential of bimorph mirrors.

Piezoelectric creep in LiNbO3, PMN-PT and PZT-5A at low temperatures

Creep and hysteresis were directly measured for shear displacements of three widely used piezoelectric materials: 41° X-cut lithium niobate (LiNbO3), single crystal lead magnesium niobate-lead titanate (PMN-PT), and ceramic lead zirconium titanate (PZT-5A). Measurements were made at temperatures between 0.1 K and 310 K and at voltages up to 150 V. No creep or hysteresis was seen for the single domain lithium niobate transducer. PMN-PT exhibited large creep and hysteresis with a strong temperature dependence even at temperatures as low as 10 K. The temperature dependence was complicated and included an unusual region of negative creep around 250 K. The ceramic PZT-5A had significant creep near room temperature, which disappeared below about 35 K. The widths of the measured hysteresis loops mirrored the magnitudes of the creep that produces the hysteresis. We discuss the behavior of the three materials in terms of intrinsic and extrinsic mechanisms of piezoelectricity. Our results provide guidance in selecting materials for piezoelectric actuators for precise positioning applications like scanning tunneling microscopy. Although it is seldom used in actuator stacks, lithium niobate is the best choice for many cryogenic applications.

Dynamic adaptive X-ray optics. Part II. High-speed piezoelectric bimorph deformable Kirkpatrick-Baez mirrors for rapid variation of the 2D size and shape of X-ray beams.

The tangential curvature of actively bent X-ray mirrors at synchrotron radiation and X-ray free-electron laser (XFEL) facilities is typically only changed every few hours or even days. This operation can take tens of minutes for active optics with multiple bending actuators and often requires expert guidance using in situ monitoring devices. Hence, the dynamic performance of active X-ray optics for synchrotron beamlines has historically not been exploited. This is in stark contrast to many other scientific fields. However, many areas of synchrotron radiation and XFEL science, including macromolecular crystallography, could greatly benefit from the ability to change the size and shape of the X-ray beam rapidly and continuously. The advantages of this innovative approach are twofold: a large reduction in the dead time required to change the size of the X-ray beam for different-sized samples and the possibility of making multiple changes to the beam during the measurement of a single sample. In the preceding paper [Part I; Alcock, Nistea, Signorato & Sawhney (2019), J.Synchrotron Rad. 26, 36-44], which accompanies this article, high-speed visible-light Fizeau interferometry was used to identify the factors which influence the dynamic bending behaviour of piezoelectric bimorph deformable X-ray mirrors. Building upon this ex situ metrology study, provided here is the first synchrotron radiation beamline implementation of high-speed adaptive X-ray optics using two bimorphs operating as a Kirkpatrick-Baez pair. With optimized substrates, novel opto-mechanical holders and a next-generation high-voltage power supply, the size of an X-ray beam was rapidly and repeatedly switched in <10 s. Of equal importance, it is also shown that compensation of piezoelectric creep ensures that the X-ray beam size remains stable for more than 1 h after making a major change. The era of high-speed adaptive X-ray optics for synchrotron radiation and XFEL beamlines has begun.

Dynamic adaptive X-ray optics. Part I. Time-resolved optical metrology investigation of the bending behaviour of piezoelectric bimorph deformable X-ray mirrors.

Piezoelectric bimorph deformable mirrors (`bimorphs') are routinely used on many synchrotron and free-electron laser beamlines to provide active variation in the size and shape of the X-ray beam. However, the time-domain potential of such optics has never been fully exploited. For the first time, the fast dynamic bending response of bimorphs is investigated here using Fizeau interferometry. Automated scripts for acquisition and analysis were developed to collect Fizeau data at a rate of 0.1 Hz to record dynamic changes in the optical surface as voltages were applied to the electrodes of the piezoelectric actuators. It is demonstrated that residual drift in the tangential radius of curvature of a bimorph can be significantly reduced using enhanced opto-mechanical holders and a fast programmable high-voltage power supply. Further improvements are achieved by applying small opposing voltages to compensate for piezoelectric creep. The present study shows that bimorphs can truly be used as high-speed adaptive optics for the X-ray domain, even without closed-loop feedback correction. This opens the possibility for relatively simple real-time tuning of the profile of X-ray bimorphs. Part II of this study [Alcock, Nistea, Signorato, Owen, Axford, Sutter, Foster & Sawhney (2019), J. Synchrotron Rad. 26, 45-51] builds upon these results and demonstrates how bimorphs can rapidly provide customisable sizes and shapes of synchrotron X-ray beams, specifically tailored to suit the experimental samples being investigated.

Making a commercial atomic force microscope more accurate and faster using positive position feedback control

This paper presents experimental implementation of a positive position feedback (PPF) control scheme for vibration and cross-coupling compensation of a piezoelectric tube scanner in a commercial atomic force microscope (AFM). The AFM is a device capable of generating images with extremely high resolutions down to the atomic level. It is also being used in applications that involve manipulation of matter at a nanoscale. Early AFMs were operated in open loop. Consequently, they were susceptible to piezoelectric creep, thermal drift, hysteresis nonlinearity, and scan-induced vibration. These effects tend to distort the generated image and slow down the scanning speed of the device. Recently, a new generation of AFMs has emerged that utilizes position sensors to measure displacements of the scanner in three dimensions. These AFMs are equipped with feedback control loops that work to minimize the adverse effects of hysteresis, piezoelectric creep, and thermal drift on the obtained image using proportional-plus-integral (PI) controllers. These feedback controllers are often not designed to deal with the highly resonant nature of an AFM's scanner nor with the cross coupling between various axes. In this paper we illustrate the improvement in accuracy and imaging speed that can be achieved by using a properly designed feedback controller such as a PPF controller. Such controllers can be incorporated into most modern AFMs with minimal effort since they can be implemented in software with the existing hardware. Experimental results show that by implementing the PPF control scheme, relatively good images in comparison with a well-tuned PI controller can still be obtained up to line scan of 60 Hz.

Correction for piezoelectric creep in scanning probe microscopy images using polynomial mapping.

We describe a method for using polynomial mapping to correct scanning probe microscope images for distortion due to piezoelectric creep. Because such distortion varies from image to image, this method can be used when the actual locations of some features within an image are known absolutely, or in a series of images in which the actual locations of some features are known not to vary. While the general case of polynomial mapping of degree N requires the determination of 2(N+ 1)2 matrix elements by regression, we find that by understanding the mechanism by which piezoelectric creep distorts scanning probe microscope images, we can fix most of these coefficients at 0 or 1 a priori, leaving only 2(N+ 1) coefficients to be determined by regression. We describe our implementation of this strategy using the Interactive Data Language (IDL) programming language, and demonstrate our technique on a series of atomic force microscopy (AFM) images of diblock copolymer microdomains. Using our simplified scheme, we are able to reduce the effects of distortion in an AFM image from 5% of the scan width to a single pixel, using only five reference points.

New method to estimate step heights in scanning-probe microscope images

A new algorithm, the polynomial step-function fit (PSFF), is presented. The PSFF algorithm extracts step heights from noisy and distorted scanning-probe microscope (SPM) images. A one-dimensional, line-by-line implementation as well as a two-dimensional, full-image version are presented. The PSFF algorithm allows the correction of image distortions due to nonlinearities in the piezoelectric scanner and Abbé offset errors, but piezoelectric creep and hysteresis must be corrected separately, and may set the ultimate physical limitations on the accuracy of the PSFF algorithm. The PSFF algorithm is demonstrated with a real sample.

A prescan method improving the reproducibility of force-distance curves obtained with a piezoelectric tube scanner

We present a method based on pre- and postscanning a piezoelectric tube scanner used in a force probe that improves the reproducibility of the scan lengths. Instead of prescanning in the same direction as when acquiring data (the z direction), which could destroy a sensitive surface, we perform lateral (x/y direction) prescans. As lateral motions of the tube scanner involve out of phase elongations and compressions of the tube in the z direction, these kinds of prescans will have a stabilizing effect on the z motion as well. By adding an additional postscan in the ±z directions, we reduce the piezoelectric creep following the data acquisition scan. When comparing the lengths of z scans with and without the pre/postscan procedure, preceded by a z voltage step 60 s before data acquisition, the deviation between four consecutive scans improved from 12% to 1.4%.

Control electronics for atomic force microscopy

The control electronics for the atomic force microscope (AFM) are described. The set of electronic devices described here allow convenient operation of an atomic force microscope. The key device is the force controller, which automates the otherwise tedious and time-consuming readjustment of the force to a preset value by controlling two gated feedback loops. The preset value of the force can be easily changed by simply turning a potentiometer. This automated system allows us to obtain reliable data, with known forces, despite piezoelectric creep and thermal drift in the force determining mechanical setup. The electronic devices and concepts presented here work for AFMs that use tunneling, capacitance measurements, or optical interference to sense small deflections of the spring.