Quantitative elastic modulus measurement by magnetic force modulation microscopy

It is experimentally demonstrated that magnetic force modulation microscopy (MFMM) is a technique allowing quantitative elastic modulus measurements. A model of the cantilever–tip–sample interaction taking into account the lateral contact stiffness (i.e., the friction effects at the level of the tip–sample contact), the position of the magnetic force applied to the cantilever with respect to the tip position, as well as the inclination of the cantilever arm with respect to the sample surface is presented. The model shows that MFMM is much less sensitive to lateral force than the other modulation techniques and thus, in contrast to the latter, that the contrast of the stiffness images can be interpreted as a true elasticity contrast and not as a mixture of friction and elasticity. Thanks to the study of the normal contact stiffness versus normal load that allows the characterization of contact between tip and sample, it is possible to perform quantitative elastic modulus measurements with a dynamic modulation method.     

Prototype cantilevers for quantitative lateral force microscopy

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.     

A new calibration method of the lateral contact stiffness and lateral force using modulated lateral force microscopy

We describe a new calibration method for lateral contact stiffness using modulated lateral force microscopy, a technique that offers some advantages with respect to the more classical friction force microscopy currently used for characterizing the friction properties of materials. The calibration method is based on the study of the lateral contact stiffness versus applied load and on the use of elasticity contact theories to determine by fit the calibration coefficient, allowing the scaling of experimental data. The method is tested by measuring the friction coefficient and shear strength of silicon and mica samples, respectively, and compared with results from the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Carbon nanotubes: a promising standard for quantitative evaluation of AFM tip apex geometry

The direct contact between tip and sample in atomic force microscopy (AFM) leads to demand for a quantitative knowledge of the AFM tip apex geometry in high-resolution AFM imaging and many other types of AFM applications like force measurements and surface roughness measurements. Given, the AFM tip apex may change continuously during measurements due to wear or during storage due to oxidation, it is very desirable to develop an easy and quick way for quantitative evaluation of AFM tip radius when necessary. In this study, we present an efficient method based on Zenhausern model (Scanning 14 (1992) 212) by measuring single-wall carbon nanotubes deposited on a flat substrate to reach this goal. Experimental results show the method can be used for routine quantitative evaluation of AFM tip apex geometry for tips with effective radii down to the nanometer scale.     

Amplitude and frequency modulation torsional resonance mode atomic force microscopy of a mineral surface

Scanning probe imaging in a shear force mode allows for the characterization of in-plane surface properties. In a standard AFM, shear force imaging can be realized by the torsional resonance mode. In order to investigate the imaging conditions on mineral surfaces, a torsional resonance mode atomic force microscope was operated in amplitude (AM) and frequency modulation (FM) feedback. Freshly cleaved chlorite was investigated, which showed brucite-like and talc-like surface areas. In constant amplitude FM mode, a slight variation in energy dissipation was observed between both surfaces. Amplitude and frequency vs. distance curves revealed that the tip was in repulsive contact with the specimen during imaging.     

压电力传感器晶片与电极接触刚度影响研究*

以压电力传感器为核心的多分量测量系统是航空、航天等领域重要的力学测量装置。压电力传感器中晶片与电极结合面接触刚度是基础性能参数,对压电力传感器的分载效应及灵敏度,多分量测量系统的整体刚度及静、动态性能有直接影响。由于尚无对该参数的研究,导致在设计封装压电力传感器过程中缺少相应的理论依据,在使用多分量测量系统时存在标定困难等问题。针对以上问题,研究晶片与电极结合面接触刚度的影响因素,建立基于分形理论的接触刚度模型,优化了晶面表面形貌、压电材料、电极材料、预紧力等参数。在此基础上,研究接触刚度对传感器性能——刚度、灵敏度、固有频率等影响,提出一种以接触刚度为约束的晶片表面形貌优化方法。基于结构函数法,建立分形理论与实际工程测量参数的联系,通过两种压电晶体——石英与硅酸镓镧,四种电极材料——钛合金、不锈钢、黄铜、铝,试验验证了理论模型。试验表明,优化晶片表面分形参数、提高预紧力、选用弹性模量小的电极有助于提高晶片与电极接触刚度,进而提高传感器的整体刚度、灵敏度和固有频率。研究为高性能压电力传感器的设计提供了理论参考。     

Chemical force microscopy of microcontact-printed self-assembled monolayers by pulsed-force-mode atomic force microscopy

A novel chemically sensitive imaging mode based on adhesive force detection by previously developed pulsed-force-mode atomic force microscopy (PFM-AFM) is presented. PFM-AFM enables simultaneous imaging of surface topography and adhesive force between tip and sample surfaces. Since the adhesive forces are directly related to interaction between chemical functional groups on tip and sample surfaces, we combined the adhesive force mapping by PFM-AFM with chemically modified tips to accomplish imaging of a sample surface with chemical sensitivity. The adhesive force mapping by PFM-AFM both in air and pure water with CH3- and COOH-modified tips clearly discriminated the chemical functional groups on the patterned self-assembled monolayers (SAMs) consisting of COOH- and CH3-terminated regions prepared by microcontact printing (microCP). These results indicate that the adhesive force mapping by PFM-AFM can be used to image distribution of different chemical functional groups on a sample surface. The discrimination mechanism based upon adhesive forces measured by PFM-AFM was compared with that based upon friction forces measured by friction force microscopy. The former is related to observed difference in interactions between tip and sample surfaces when the different interfaces are detached, while the latter depends on difference in periodic corrugated interfacial potentials due to Pauli repulsive forces between the outermost functional groups facing each other and also difference in shear moduli of elasticities between different SAMs.     

A torsional resonance mode AFM for in-plane tip surface interactions

Changing the method of tip/sample interaction leads to contact, tapping and other dynamic imaging modes in atomic force microscopy (AFM) feedback controls. A common characteristic of these feedback controls is that the primary control signals are based on flexural deflection of the cantilever probes, statically or dynamically. We introduce a new AFM mode using the torsional resonance amplitude (or phase) to control the feedback loop and maintain the tip/surface relative position through lateral interaction. The torsional resonance mode (TRmode™) provides complementary information to tapping mode for surface imaging and studies. The nature of tip/surface interaction of the TRmode facilitates phase measurements to resolve the in-plane anisotropy of materials as well as measurements of dynamic friction at nanometer scale. TRmode can image surfaces interleaved with TappingMode™ with the same probe and in the same area. In this way we are able to probe samples dynamically in both vertical and lateral dimensions with high sensitivity to local mechanical and tribological properties. The benefit of TRmode has been proven in studies of water adsorption on HOPG surface steps. TR phase data yields approximately 20 times stronger contrast than tapping phase at step edges, revealing detailed structures that cannot be resolved in tapping mode imaging. The effect of sample rotation relative to the torsional oscillation axis of the cantilever on TR phase contrast has been observed. Tip wear studies of TRmode demonstrated that the interaction forces between tip and sample could be controlled for minimum tip damage by the feedback loop.     

Lateral force microscopy of multiwalled carbon nanotubes

Carbon nanotubes are usually imaged with the atomic force microscope (AFM) in non-contact mode. However, in many applications, such as mechanical manipulation or elasticity measurements, contact mode is used. The forces affecting the nanotube are then considerable and not fully understood. In this work lateral forces were measured during contact mode imaging with an AFM across a carbon nanotube. We found that, qualitatively, both magnitude and sign of the lateral forces to the AFM tip were independent of scan direction and can be concluded to arise from the tip slipping on the round edges of the nanotube. The dependence on the normal force applied to the tip and on the ratio between nanotube diameter and tip radius was studied. We show that for small values of this ratio, the lateral force signal can be explained with a simple geometrical model.     

Effect of contact stiffness on wedge calibration of lateral force in atomic force microscopy

Quantitative friction measurement of nanomaterials in atomic force microscope requires accurate calibration method for lateral force. The effect of contact stiffness on lateral force calibration of atomic force microscope is discussed in detail and an improved calibration method is presented. The calibration factor derived from the original method increased with the applied normal load, which indicates that separate calibration should be required for every given applied normal load to keep the accuracy of friction measurement. We improve the original method by introducing the contact factor, which is derived from the contact stiffness between the tip and the sample, to the calculation of calibration factors. The improved method makes the calculation of calibration factors under different applied normal loads possible without repeating the calibration procedure. Comparative experiments on a silicon wafer have been done by both the two methods to validate the method in this article.     

Evaluating local elasticity of the metal nano-films quantitatively based on referencing approach of atomic force acoustic microscopy

Traditional technique such nanoindenter(NI) can’t measure the local elastic modulus at nano-scale(lateral). Atomic force acoustic microscopy (AFAM) is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper(Cu) film with 110 nm thickness, zinc(Zn) film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples (it’s elastic modulus is known), and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values MCu=105-130 GPa, MZn=88.44 GPa and MGlass=50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160μm, 225μm and 520μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.     

Novel operation mode for eliminating influence of inclination angle and friction in atomic force microscopy

The accuracy of topography imaging in contact force mode of atomic force microscopy (AFM) depends on the one-to-one corresponding relationship between the cantilever deflection and the tip–sample distance, whereas such a relationship cannot be always achieved in the presence of friction and incline angle of sample surface. Recently, we have developed a novel operation mode in which we keep the van der Waals force as constant instead of the applied normal force, to eliminate the effect of inclination angle and friction on topography imaging in the contact force mode. We have improved our AFM to enable the new operation mode for validation. Comparative experiments have been performed and the results have shown that the effect of friction and inclination angle on topography imaging in contact mode of AFM can be eliminated or at least decreased effectively by working in the new operation mode we present.     

Forces de surface et contact : les derniers nanomètres

Surface and contact forces: the last nanometres. We describe the use of surface force measurements to characterize contact properties of oxide surfaces. This technique is highly sensitive and permits us to evidence various phenomena related to surface interactions and surface mechanical response. Examples will be presented, dealing with adhesion (adhesion energy, interaction range for oxide powders and metal–oxide interfaces) and the mechanical response of adsorbed organic layers (elasticity modulus, toughness).     

Quantitative imaging of Young's modulus of solids: a contact-mechanics study

We developed equipment and methods for measuring quantitatively the local Young's modulus of solids. It consists of an electrodeless langasite oscillator and line antennas, and oscillator vibrations are generated and detected contactlessly. A constant biasing force results from oscillator mass and is independent of surface roughness. The effect of material anisotropy on the measured stiffness is theoretically discussed for studying the limitation of the quantitative measurement. The microscopy has been applied to polycrystalline copper, and the measured modulus is compared to calculations based on electron-backscatter-diffraction measurements. Also, we applied it to a duplex stainless steel and an embedded silicon-carbide fiber. The results reveal textured regions, defects with high sensitivity, and even stiffness distribution in a single grain.     

Origin of phase shift in atomic force microscopic investigation of the surface morphology of NR/NBR blend film

Atomic force microscopy (AFM) was used to study the morphology and surface properties of NR/NBR blend. Blends at 1/3, 1/1 and 3/1 weight ratios were prepared in benzene and formed film by casting. AFM phase images of these blends in tapping mode displayed islands in the sea morphology or matrix-dispersed structures. For blend 1/3, NR formed dispersed phase while in blends 1/1 and 3/1 phase inversion was observed. NR showed higher phase shift angle in AFM phase imaging for all blends. This circumstance was governed by adhesion energy hysteresis between the device tip and the rubber surface rather than surface stiffness of the materials, as proved by force distance measurements in the AFM contact mode.     

Dual resonance excitation system for the contact mode of atomic force microscopy

We propose an improved system that enables simultaneous excitation and measurements of at least two resonance frequency spectra of a vibrating atomic force microscopy (AFM) cantilever. With the dual resonance excitation system it is not only possible to excite the cantilever vibrations in different frequency ranges but also to control the excitation amplitude for the individual modes. This system can be used to excite the resonance frequencies of a cantilever that is either free of the tip-sample interactions or engaged in contact with the sample surface. The atomic force acoustic microscopy and principally similar methods utilize resonance frequencies of the AFM cantilever vibrating while in contact with the sample surface to determine its local elastic modulus. As such calculation demands values of at least two resonance frequencies, two or three subsequent measurements of the contact resonance spectra are necessary. Our approach shortens the measurement time by a factor of two and limits the influence of the AFM tip wear on the values of the tip-sample contact stiffness. In addition, it allows for in situ observation of processes transpiring within the AFM tip or the sample during non-elastic interaction, such as tip fracture.     

Probability Model for the intermolecular force with surface roughness considered

This paper studies the intermolecular force considering both the roughness of the air-bearing surface and the disk surface by simulation. A model is developed to deal with the intermolecular force, the contact force and the air-bearing force based on the probability distributions of the roughness of the surfaces. The intermolecular force is linked with the contact force when its repulsive term is stronger than its attractive term. In such a case, all the intermolecular force, the contact force and the air-bearing force can be extended to the various flying height regions. Some interesting results are observed and discussed. It is found that both the Hamaker constant and the surface roughness have significant influences on the intermolecular pressure. Compared with the intermolecular pressure with smooth surfaces, that with the surface roughness considered shows greater attractive pressure at the flying height higher than 0.7 nm approximately, but much smaller values between 0.26 and 0.7 nm approximately. A negative stiffness region exists when the minimum flying height is between −0.2 and 1.2 nm for the case studied in this paper. It shows that the Probability Model is suitable for the intermolecular force calculation with the surface roughness considered.     

Analysis of the contact probe mechanism for micro-coordinate measuring machines

High precision contact scanning probes for measuring miniature components on micro- and nano-coordinate measuring machines requires sensitive mechanisms. This paper analyzes the mechanism of a developed contact probe in order to find its optimal dimensions. The contact probe is composed of a fiber stylus with a ball tip, a mechanism with a wire-suspended floating plate, and focus sensors. The wires experience elastic deformation when a contact force is applied. The probe mechanism with a four-wire floating plate is studied. Stiffness analysis is carried out using the theory of elasticity. It is found that, with a proper stylus length, a contact probe with uniform stiffness can be designed.     

Analysis of photopolymerized acrylic films by AFM in pulsed force mode

This paper highlights the potential of atomic force microscopy in the pulsed force mode to investigate the photopatterning of acrylic‐based films. The pulsed force mode is a nonresonant mode designed to allow approach curves to be recorded along the scanning path. It thereby provides the topography of the sample and a direct and simple local characterization of adhesion and stiffness. This mode can be used either for imaging or for locally probing the mechanical properties of a surface. In particular, a correlation between stiffness and conversion of the monomer was established. The close examination of the pulsed force mode signal brought accurate information on the photoinduced modification of the film. Polymer films with submicron photopatterning generated by interferometric illumination were analyzed by pulsed force mode. It was established that the gradient of mechanical properties throughout the films was strongly dependant on the irradiation conditions.