Young guard cells function dynamically despite low mechanical anisotropy but gain efficiency during stomatal maturation in Arabidopsis thaliana.

Stomata are pores at the leaf surface that enable gas exchange and transpiration. The signaling pathways that regulate the differentiation of stomatal guard cells and the mechanisms of stomatal pore formation have been characterized in Arabidopsis thaliana. However, the process by which stomatal complexes develop after pore formation into fully mature complexes is poorly understood. We tracked the morphogenesis of young stomatal complexes over time to establish characteristic geometric milestones along the path of stomatal maturation. Using 3D-nanoindentation coupled with finite element modeling of young and mature stomata, we found that despite having thicker cell walls than young guard cells, mature guard cells are more energy efficient with respect to stomatal opening, potentially attributable to the increased mechanical anisotropy of their cell walls and smaller changes in turgor pressure between the closed and open states. Comparing geometric changes in young and mature guard cells of wild-type and cellulose-deficient plants revealed that although cellulose is required for normal stomatal maturation, mechanical anisotropy appears to be achieved by the collective influence of cellulose and additional wall components. Together, these data elucidate the dynamic geometric and biomechanical mechanisms underlying the development process of stomatal maturation.

PECTATE LYASE LIKE12 patterns the guard cell wall to coordinate turgor pressure and wall mechanics for proper stomatal function in Arabidopsis.

Plant cell deformations are driven by cell pressurization and mechanical constraints imposed by the nanoscale architecture of the cell wall, but how these factors are controlled at the genetic and molecular levels to achieve different types of cell deformation is unclear. Here, we used stomatal guard cells to investigate the influences of wall mechanics and turgor pressure on cell deformation and demonstrate that the expression of the pectin-modifying gene PECTATE LYASE LIKE12 (PLL12) is required for normal stomatal dynamics in Arabidopsis thaliana. Using nanoindentation and finite element modeling to simultaneously measure wall modulus and turgor pressure, we found that both values undergo dynamic changes during induced stomatal opening and closure. PLL12 is required for guard cells to maintain normal wall modulus and turgor pressure during stomatal responses to light and to tune the levels of calcium crosslinked pectin in guard cell walls. Guard cell-specific knockdown of PLL12 caused defects in stomatal responses and reduced leaf growth, which were associated with lower cell proliferation but normal cell expansion. Together, these results force us to revise our view of how wall-modifying genes modulate wall mechanics and cell pressurization to accomplish the dynamic cellular deformations that underlie stomatal function and tissue growth in plants.

Protocol for mapping the variability in cell wall mechanical bending behavior in living leaf pavement cells.

Mechanical properties, size and geometry of cells, and internal turgor pressure greatly influence cell morphogenesis. Computational models of cell growth require values for wall elastic modulus and turgor pressure, but very few experiments have been designed to validate the results using measurements that deform the entire thickness of the cell wall. New wall material is synthesized at the inner surface of the cell such that full-thickness deformations are needed to quantify relevant changes associated with cell development. Here, we present an integrated, experimental-computational approach to analyze quantitatively the variation of elastic bending behavior in the primary cell wall of living Arabidopsis (Arabidopsis thaliana) pavement cells and to measure turgor pressure within cells under different osmotic conditions. This approach used laser scanning confocal microscopy to measure the 3D geometry of single pavement cells and indentation experiments to probe the local mechanical responses across the periclinal wall. The experimental results were matched iteratively using a finite element model of the experiment to determine the local mechanical properties and turgor pressure. The resulting modulus distribution along the periclinal wall was nonuniform across the leaf cells studied. These results were consistent with the characteristics of plant cell walls which have a heterogeneous organization. The results and model allowed the magnitude and orientation of cell wall stress to be predicted quantitatively. The methods also serve as a reference for future work to analyze the morphogenetic behaviors of plant cells in terms of the heterogeneity and anisotropy of cell walls.

Cell twisting during desiccation reveals axial asymmetry in wall organization.

Plant cell size and shape are tuned to their function and specified primarily by cellulose microfibril (CMF) patterning of the cell wall. Arabidopsis thaliana leaf trichomes are unicellular structures that act as a physical defense to deter insect feeding. This highly polarized cell type employs a strongly anisotropic cellulose wall to extend and taper, generating sharply pointed branches. During elongation, the mechanisms by which shifts in fiber orientation generate cells with predictable sizes and shapes are unknown. Specifically, the axisymmetric growth of trichome branches is often thought to result from axisymmetric CMF patterning. Here, we analyzed the direction and degree of twist of branches after desiccation to reveal the presence of an asymmetric cell wall organization with a left-hand bias. CMF organization, quantified using computational modeling, suggests a limited reorientation of microfibrils during growth and a maximum branch length limited by the wall axial stiffness. The model provides a mechanism for CMF asymmetry, which occurs after the branch bending stiffness becomes low enough that ambient bending affects the principal stresses. After this stage, the CMF synthesis results in a constant bending stiffness for longer branches. The bending vibration natural frequencies of branches with respect to their length are also discussed.

Influence of tessellation morphology on ultrasonic scattering.

Material properties, such as hardness, yield strength, and ductility, depend on the microstructure of the material. If the microstructural organization can be quantified nondestructively, for example, with ultrasonic scattering techniques, then it may be possible to predict the mechanical performance of a component. Three-dimensional digital microstructures have been increasingly used to investigate the scattering of mechanical waves within a numerical framework. These synthetic microstructures can be generated using different tessellation algorithms that result in different grain shapes. In this study, the variation of ultrasonic scattering is calculated for microstructures of different morphologies for a nickel polycrystal. The ultrasonic properties are calculated for the Voronoi, Laguerre tessellations, and voxel-based synthetic microstructures created by DREAM.3D. The results show that the differences in the two-point statistics and ultrasonic attenuation for different morphologies become more significant at wider size distributions and higher frequencies.

Propagation of leaky Rayleigh waves along a curved fluid-solid interface.

A characteristic equation is derived for a leaky Rayleigh wave (LRW), propagating on a curved fluid-solid interface. The equations of motion for the curved solid and fluid are formulated using the constitutive equations of a homogenous isotropic curved solid and an inviscid fluid, respectively. The displacement potential functions are used to simplify the derivation. The interface conditions are used to ensure continuities of the mass, momentum, and energy across the interface. Then, with the consideration of the interface radius of the curvature, the characteristic equation for the LRW is established and solved numerically by Muller's method. One important outcome is that there is weaker directional dependence for the velocity of the LRWs on the radius of curvature in comparison with the Rayleigh waves at an air-solid interface. However, the numerical results show a strong directional dependence for the attenuation due to the LRW leakage on the complex curvatures. Moreover, a quantitative relation between the curvature and attenuation caused by the leakage for different materials is shown. The results are significant especially with respect to relevant future applications of ultrasonic testing.

Ultrasound in situ characterization of hybrid additively manufactured Ti6Al4V.

A major barrier for the full utilization of metal additive manufacturing (AM) technologies is quality control. Additionally, in situ real time nondestructive monitoring is desirable due to the typical high value and low volume of components manufactured with metal AM. Depending on the application, characteristics such as the geometrical accuracy, porosity, defect size and content, and material properties are quantities of interest for in situ nondestructive evaluation (NDE). In particular, functionally tailored components made with hybrid processing require quantitative NDE of their microstructure and elastic properties. Ultrasonic NDE is able to quantify these relevant characteristics. In this work, an ultrasonic measurement system is used to collect in situ real time measurements during the manufacturing of samples made with a hybrid process, which combines directed energy deposition with milling. In addition to quantifying ultrasonic properties, the measurements are used to gather insight on other geometry, material, and process effects. The results show the utility of ultrasound to evaluate relevant properties during manufacturing of a functionalized material domain, while providing perspective on additional material evolution information obtained from ultrasonic signals.

Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures: Phase velocity variations.

In most theoretical work related to effective properties of polycrystals, the media are assumed to be infinite with randomly oriented grains. Therefore, the bulk material has absolute isotropy because each direction includes an infinite number of grains with infinite possibilities for grain orientation. However, real samples will always include a finite number of grains such that the inspection volume will have some associated anisotropy. Thus, bounds on the bulk properties are expected for a given measurement. Here, the effect of the number of grains on the variations of elastic anisotropy is studied using synthetic polycrystals comprised of equiaxed cubic grains (17 volumes with 100 realizations each). Voigt, Reuss, and self-consistent techniques are used to derive the effective elastic modulus tensor. The standard deviation of the average elastic modulus is then quantified for several materials with varying degrees of single-crystal anisotropy and is shown to be inversely proportional to the square root of the number of grains. Finally, the Christoffel equation is used to study the relevant phase velocities. With appropriate normalization, a master curve is derived with respect to the finite sample size, which shows the expected variations of phase velocity for the longitudinal, fast shear, and slow shear modes.

Ultrasonic wave propagation predictions for polycrystalline materials using three-dimensional synthetic microstructures: Attenuation.

Ultrasonic attenuation plays a crucial role in inspection for heterogeneous materials such that theoretical models are critical for improved measurements. In this article, several assumptions often used in these models are examined with respect to their influence on attenuation. Here, dream.3d software is used to generate 10 ensembles with different volumes, each containing 50 realizations of equiaxed grains with cubic single-crystal symmetry, from which attenuations are calculated. Comparisons are then made with attenuation values derived from classical theories. These theories often decouple the spatial and tensorial components of the microstructure, assume statistical isotropy, and use a spatial correlation function that has a specific exponential form. The validity of these assumptions is examined by calculation of the spatial statistics to obtain the attenuations in their most general form. The results of Voigt-averaged results for nickel at 15 MHz show that the longitudinal and transverse attenuations are about one-third and one-fourth of those obtained from the theory, respectively. Such a difference is attributed to the relevant spatial correlation functions. The results also show a slight anisotropy in the attenuation. Finally, for microstructures with narrow grain size distributions and weak texture, the decoupling assumption is shown to be valid.

Generalized ultrasonic scattering model for arbitrary transducer configurations.

Ultrasonic scattering in polycrystalline media is directly tied to microstructural features. As a result, modeling efforts of scattering from microstructure have been abundant. The inclusion of beam modeling for the ultrasonic transducers greatly simplified the ability to perform quantitative, fully calibrated experiments. In this article, a theoretical scattering model is generalized to allow for arbitrary source and receiver configurations, while accounting for beam behavior through the total propagation path. This extension elucidates the importance and potential of out-of-plane scattering modes in the context of microstructure characterization. The scattering coefficient is explicitly written for the case of statistical isotropy and ellipsoidal grain elongation, with a direct path toward expansion for increased microstructural complexity. Materials with crystallites of any symmetry can be studied with the present model; the numerical results focus on aluminum, titanium, and iron. The amplitude of the scattering response is seen to vary across materials, and to have varying sensitivity to grain elongation and orientation depending on the transducer configuration selected. The model provides a pathway to experimental characterization of microstructure with optimized sensitivity to parameters of interest.

Flaw detection with ultrasonic backscatter signal envelopes.

Ultrasound is a prominent nondestructive testing modality for the detection, localization, and sizing of defects in engineering materials. Often, inspectors analyze ultrasonic waveforms to determine if echoes, which stem from the scattering of ultrasound from a defect, exceed a threshold value. In turn, the initial selection of the threshold value is critical. In this letter, a time-dependent threshold or upper bound for the signal envelope is developed based on the statistics governing the scattering of ultrasound from microstructure. The utility of the time-dependent threshold is demonstrated using experiments conducted on sub-wavelength artificial defects. The results are shown to enhance current nondestructive inspection practices.

Focused electron-beam-induced deposition for fabrication of highly durable and sensitive metallic AFM-IR probes.

We report on the fabrication of metallic, ultra-sharp atomic force microscope tips for localized nanoscale infrared (IR) spectrum measurements by using focused electron-beam-induced deposition of platinum or tungsten. The tip length can be controlled by changing the duration time of the electron beam. Probes of 12.0 ± 5.0 nm radius-of-curvature can be routinely produced with high repeatability and near-100% yield. The near-field-enhancement appears stronger at the extremity of the metallic tip, compared with commercial pristine silicon-nitride probe tip. Finally, the performance of the modified metallic tips is demonstrated by imaging PVDF and PMMA thin films, which shows that spatial resolution is greatly enhanced. In addition, the signal intensity of the localized nanoscale IR spectrum is increased offering greater sensitivity for chemical IR imaging.

Numerical analysis of longitudinal ultrasonic attenuation in sintered materials using a simplified two-phase model.

Techniques of quantitative nondestructive evaluation using attenuation of ultrasonic waves have been proposed as a potential tool for monitoring sintering processes because of the direct connection between the changes of wave propagation characteristics and microstructure properties. However, the influence of these changes during sintering on sound propagation remains unclear. In addition to theoretical investigations, numerical models can be utilized to provide key information for interpreting experimental data quantitatively. In this article, a simplified two-phase model using Voronoi polycrystals is applied to study wave propagation through sintered materials. Finite element simulations are developed with various material and geometric parameters of the two-phase model. Example longitudinal attenuation results are obtained and compared with the scattering theory for different input wave frequencies. The comparison of the numerical results with the theory shows the dependence of the attenuation on the parameters of the correlation function and the two-phase geometry. The results also validate the correlation function formula used in the theory. The influence of the input wave frequency and material properties on the correlation lengths is also discussed. Such numerical models can be used to verify theoretical models efficiently and to design further experimental methods for characterization of microstructures.

Transverse-to-transverse diffuse ultrasonic scattering.

Ultrasonic scattering occurs when elastic waves interact with interfaces within heterogeneous media. Diffuse ultrasonic backscatter measurements are used to capture the effective grain scattering within a polycrystal for extracting microstructural information. Recently, a mode-conversion scattering model was developed to describe the longitudinal-to-transverse ultrasonic scattering within polycrystalline materials and successfully applied to determine the material spatial correlation length L by fitting experimental results with the theoretical model. The mode-conversion model may allow additional microstructural information, such as grain shape, to be assessed. In this article, a theoretical extension of the previous mode-conversion ultrasonic scattering model is presented. The transverse-to-transverse (T-T) scattering can be measured by an experimental configuration with both source and receiving transducers oriented at angles between the first and second critical angles, including pitch-catch and pulse-echo measurements. The model is used to determine the correlation length from a sample of 1040 steel through pulse-echo T-T scattering measurements using 7.5 and 10 MHz transducers. The results show that the derived T-T model works well for lower frequencies but the results for higher frequencies reveal deficiencies in the model.

Ultrasonic attenuation of polycrystalline materials with a distribution of grain sizes.

Elastic wave scattering at grain boundaries in polycrystalline media can be quantified to determine microstructural properties. The amplitude drop observed for coherent wave propagation (attenuation) as well as diffuse-field scattering events have been extensively studied. In all cases, the scattering shows a clear dependence on grain size, grain shape, and microstructural texture. Models used to quantify scattering experiments are often developed assuming dependence on a single spatial length scale, usually, mean grain diameter. However, several microscopy studies suggest that most metals have a log normal distribution of grain sizes. In this study, grain size distribution is discussed within the context of previous attenuation models valid for arbitrary crystallite symmetries. Results are presented for titanium using a range of distribution means and widths assuming equiaxed grains and no preferred crystallographic orientation. The longitudinal and shear attenuations are shown to vary with respect to the frequency dependence for varying distribution widths even when the volumetric mean grain size is held constant. Furthermore, the results suggest that grain size estimates based on attenuation can have large errors if the distribution is neglected. This work is anticipated to play an important role in microstructural characterization research associated with ultrasonic scattering.

Diffuse ultrasonic backscatter using a multi-Gaussian beam model.

Diffuse ultrasonic backscatter is widely used to evaluate microstructural parameters of heterogeneous materials. Recent singly scattered response (SSR) models utilize a single-Gaussian beam (SGB) assumption which is expected to have limitations. Following a similar formalism, a model is presented using a multi-Gaussian beam (MGB) assumption to characterize the transducer beam for longitudinal-to-longitudinal scattering at normal incidence through an interface with arbitrary curvature. First, the Wigner transform of the transducer field is defined using conjugate double-layer MGB expressions. The theoretical analysis shows that ten groups of Gaussian beams are sufficient for convergence. Compared with the SGB-SSR curve, the shape of MGB-SSR curve is positive skewed. Differences between the MGB-SSR model and the SGB-SSR model are quantified and shown to be complex functions of frequency, sample curvature, transducer parameters, and focal depth in the material. Finally, both models are used to fit experimental spatial variance data from a 304 stainless steel pipe with planar, convex, and concave surfaces. The results show that the MGB-SSR has some characteristics suggesting a better fit to the experiments. However, both models result in grain size estimates within the uncertainty of the optical microscopy suggesting that the SGB is sufficient for normal incidence pulse-echo measurements.

Stress-dependent ultrasonic scattering in polycrystalline materials.

Stress-dependent elastic moduli of polycrystalline materials are used in a statistically based model for the scattering of ultrasonic waves from randomly oriented grains that are members of a stressed polycrystal. The stress is assumed to be homogeneous and can be either residual or generated from external loads. The stress-dependent elastic properties are incorporated into the definition of the differential scattering cross-section, which defines how strongly an incident wave is scattered into various directions. Nine stress-dependent differential scattering cross-sections or scattering coefficients are defined to include all possibilities of incident and scattered waves, which can be either longitudinal or (two) transverse wave types. The evaluation of the scattering coefficients considers polycrystalline aluminum that is uniaxially stressed. An analysis of the influence of incident wave propagation direction, scattering direction, frequency, and grain size on the stress-dependency of the scattering coefficients follows. Scattering coefficients for aluminum indicate that ultrasonic scattering is much more sensitive to a uniaxial stress than ultrasonic phase velocities. By developing the stress-dependent scattering properties of polycrystals, the influence of acoustoelasticity on the amplitudes of waves propagating in stressed polycrystalline materials can be better understood. This work supports the ongoing development of a technique for monitoring and measuring stresses in metallic materials.

Mode-converted ultrasonic scattering in polycrystals with elongated grains.

Elastic wave scattering is used to study polycrystalline media for a wide range of applications. Received signals, which include scattering from the randomly oriented grains comprising the polycrystal, contain information from which useful microstructural parameters may often be inferred. Recently, a mode-converted diffuse ultrasonic scattering model was developed for evaluating the scattered response of a transverse wave from an incident longitudinal wave in a polycrystalline medium containing equiaxed single-phase grains with cubic elastic symmetry. In this article, that theoretical mode-converted scattering model is modified to account for grain elongation within the sample. The model shows the dependence on scattering angle relative to the grain axis orientation. Experimental measurements were performed on a sample of 7475-T7351 aluminum using a pitch-catch transducer configuration. The results show that the mode-converted scattering can be used to determine the dimensions of the elongated grains. The average grain shape determined from the experimental measurements is compared with dimensions extracted from electron backscatter diffraction, an electron imaging technique. The results suggest that mode-converted diffuse ultrasonic scattering has the potential to quantify detailed information about grain microstructure.

Stress-dependent second-order grain statistics of polycrystals.

In this article, the second-order statistics of the elastic moduli of randomly oriented grains in a polycrystal are derived for the case when an initial stress is present. The initial stress can be either residual stress or stresses generated from external loading. The initial stress is shown to increase or decrease the variability of the grain's elastic moduli from the average elastic moduli of the polycrystal. This variation in the elastic properties of the individual grains causes acoustic scattering phenomenon in polycrystalline materials to become stress-dependent. The influence of the initial stress on scattering is shown to be greater than the influence on acoustic phase velocities, which defines the acoustoelastic effect. This work helps the development of scattering based tools for the nondestructive analysis of material stresses in polycrystals.