Elastic moduli and refractive index of γ-Ge3N4.

Germanium nitride, having cubic spinel structure, γ-Ge3N4, is a wide band-gap semiconductor with a large exciton binding energy that exhibits high hardness, elastic moduli and elevated thermal stability up to approximately 700°C. Experimental data on its bulk and shear moduli (B0 and G0, respectively) are strongly limited, inconsistent and, thus, require verification. Moreover, earlier first-principles density functional calculations provided significantly scattering B0 values but consistently predicted G0 much higher than the so far available experimental value. Here, we examined the elasticity of polycrystalline γ-Ge3N4, densified applying high pressures and temperatures, using the techniques of laser ultrasonics (LU) and Brillouin light scattering (BLS) and compared with our extended first-principles calculations. From the LU measurements, we obtained its longitudinal- and Rayleigh wave sound velocities and, taking into account the sample porosity, derived B0 = 322(44) GPa and G0 = 188(7) GPa for the dense polycrystalline γ-Ge3N4. While our calculations underestimated B0 by approximately 17%, most of the predicted G0 matched well with our experimental value. Combining the LU- and BLS data and taking into account the elastic anisotropy, we determined the refractive index of γ-Ge3N4 in the visible range of light to be n = 2.4, similarly high as that of diamond or GaN, and matching our calculated value. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Effect of refracted light distribution on the photoelastic generation of zero-group velocity Lamb modes in optically low-absorbing plates.

Zero-group velocity (ZGV) Lamb modes are associated with sharp local acoustic resonances and allow, among other features, local measurement of Poisson's ratio. While the thermoelastic generation of Lamb waves in metal plates has been widely studied, the case of materials of low-optical absorption remains unexplored. In materials such as glasses, the generation of bulk elastic waves has been demonstrated to be sensitive to the refracted light distribution. In this paper, a detailed analysis of the effect of light refraction on the laser-based generation of ZGV Lamb modes is presented. Experiments are performed on a bare glass plate without the need for an additional layer for light absorption or reflection. Using an appropriate tilted volume source, it is shown that the laser-ultrasonic technique allows non-contact measurement of the Poisson's ratio.

Investigation of interfacial stiffnesses of a tri-layer using Zero-Group Velocity Lamb modes.

Zero-Group Velocity (ZGV) Lamb waves are studied in a structure composed of two plates bonded by an adhesive layer. The dispersion curves are calculated for a Duralumin/epoxy/Duralumin sample, where the adhesion is modeled by a normal and a tangential spring at both interfaces. Several ZGV modes are identified and their frequency dependence on interfacial stiffnesses and on the bonding layer thickness is numerically studied. Then, experiments achieved with laser ultrasonic techniques are presented. Local resonances are measured using a superimposed source and probe. Knowing the thicknesses and elastic constants of the Duralumin and epoxy layers, the comparison between theoretical and experimental ZGV resonances leads to an evaluation of the interfacial stiffnesses. A good agreement with theoretical dispersion curves confirms the identification of the resonances and the parameter estimations. This non-contact technique is promising for the local evaluation of bonded structures.

Optically Controlled Nano-Transducers Based on Cleaved Superlattices for Monitoring Gigahertz Surface Acoustic Vibrations.

Surface acoustic waves (SAWs) convey energy at subwavelength depths along surfaces. Using interdigital transducers (IDTs) and opto-acousto-optic transducers (OAOTs), researchers have harnessed coherent SAWs with nanosecond periods and micrometer localization depth for various applications. These applications include the sensing of small amount of materials deposited on surfaces, assessing surface roughness and defects, signal processing, light manipulation, charge carrier and exciton transportation, and the study of fundamental interactions with thermal phonons, photons, magnons, and more. However, the utilization of cutting-edge OAOTs produced through surface nanopatterning techniques has set the upper limit for coherent SAW frequencies below 100 GHz, constrained by factors such as the quality and pitch of the surface nanopattern, not to mention the electronic bandwidth limitations of the IDTs. In this context, unconventional optically controlled nanotransducers based on cleaved superlattices (SLs) are here presented as an alternative solution. To demonstrate their viability, we conducted proof-of-concept experiments using ultrafast lasers in a pump-probe configuration on SLs made of alternating AlxGa1-xAs and AlyGa1-yAs layers with approximately 70 nm periodicity and cleaved along their growth direction to produce a periodic nanostructured surface. The acoustic vibrations, generated and detected by laser beams incident on the cleaved surface, span a range from 40 to 70 GHz, corresponding to the generalized surface Rayleigh mode and bulk modes within the dispersion relation. This exploration shows that, in addition to SAWs, cleaved SLs offer the potential to observe surface-skimming longitudinal and transverse acoustic waves at GHz frequencies. This proof-of-concept demonstration below 100 GHz in nanoacoustics using such an unconventional platform might be useful for realizing sub-THz to THz coherent surface acoustic vibrations in the future, as SLs can be epitaxially grown with atomic-scale layer width and quality.

Acoustic beam steering by light refraction: illustration with directivity patterns of a tilted volume photoacoustic source.

The symmetry of a thermoelastic source resulting from laser absorption can be broken when the direction of light propagation in an elastic half-space is inclined relatively to the surface. This leads to an asymmetry of the directivity patterns of both compressional and shear acoustic waves. In contrast to classical surface acoustic sources, the tunable volume source allows one to take advantage of the mode conversion at the surface to control the directivity of specific modes. Physical interpretations of the evolution of the directivity patterns with the increasing light angle of incidence and of the relations between the preferential directions of compressional- and shear-wave emission are proposed. In order to compare calculated directivity patterns with measurements of normal displacement amplitudes performed on plates, a procedure is proposed to transform the directivity patterns into pseudo-directivity patterns representative of the experimental conditions. The comparison of the theoretical with measured pseudo-directivity patterns demonstrates the ability to enhance bulk-wave amplitudes and to steer specific bulk acoustic modes by adequately tuning light refraction.

Time-domain Brillouin scattering theory for probe light and acoustic beams propagating at an angle and acousto-optic interaction at material interfaces.

A theory has been developed to interpret time-domain Brillouin scattering (TDBS) experiments involving coherent acoustic pulse (CAP) and light pulse beams propagating at an angle to each other. It predicts the influence of the directivity pattern of their acousto-optic interaction on TDBS signals when heterodyne detection of acoustically scattered light is in backward direction to incident light. The theory reveals relationships between the carrier frequency, amplitude and duration of acoustically induced "wave packets" in light transient reflectivity signals, and factors such as CAP duration, widths of light and sound beams, and their interaction angle. It describes the transient dynamics of these wave packets when the light and CAP encounter material interfaces, and how the light scattering by the incident CAP transforms into scattering by the reflected and transmitted CAPs. The theory suggests that single-point TDBS experiments can determine not only depth positions of buried interfaces but also their local inclinations/orientations.

Time-domain Brillouin scattering for evaluation of materials interface inclination: Application to photoacoustic imaging of crystal destruction upon non-hydrostatic compression.

Time-domain Brillouin scattering (TDBS) is a developing technique for imaging/evaluation of materials, currently used in material science and biology. Three-dimensional imaging and characterization of polycrystalline materials has been recently reported, demonstrating evaluation of inclined material boundaries. Here, the TDBS technique is applied to monitor the destruction of a lithium niobate single crystal upon non-hydrostatic compression in a diamond anvil cell. The 3D TDBS experiments reveal, among others, modifications of the single crystal plate with initially plane-parallel surfaces, caused by non-hydrostatic compression, the laterally inhomogeneous variations of the plate thickness and relative inclination of opposite surfaces. Our experimental observations, supported by theoretical interpretation, indicate that TDBS enables the evaluation of materials interface orientation/inclination locally, from single point measurements, avoiding interface profilometry. A variety of observations reported in this paper paves the way to further expansion of the TDBS imaging use to analyze fascinating processes/phenomena occurring when materials are subjected to destruction.

Nonlinear generation of a zero group velocity mode in an elastic plate by non-collinear mixing.

Zero Group Velocity (ZGV) modes are peculiar guided waves that can exist in elastic plates or cylinders, and have proved to be very sensitive tools in characterizing materials or thickness variations with sub-percent accuracy at space resolutions of about the plate thickness. In this article we show theoretically and experimentally how such a mode can be generated as the sum-frequency interaction of two high amplitude primary waves, and then serve as a local probe of material non-linearity. The solutions to the phase matching condition, i.e. condition for a constructive non-linear effect, are obtained numerically in the mark of classical, quadratic non-linearity. The coupling coefficients that measure the transfer rate of energy as a function of time from primary to secondary modes are derived. Experiments are conducted on an aluminum plate using piezo-electric transducers and a laser interferometer, and explore the interaction for incident symmetric and anti-symmetric fundamental Lamb modes. In an experiment operated without voltage amplifier we demonstrate that the resonant nature of these ZGV modes can be leveraged to accumulate energy from long excitations and produce detectable effects at extraordinarily low input power even in such weakly non-linear material.

In-Situ Imaging of a Light-Induced Modification Process in Organo-Silica Films via Time-Domain Brillouin Scattering.

We applied time-domain Brillouin scattering (TDBS) for the characterization of porogen-based organosilicate glass (OGS) films deposited by spin-on-glass technology and cured under different conditions. Although the chemical composition and porosity measured by Fourier-transform infrared (FTIR) spectroscopy and ellipsometric porosimetry (EP) did not show significant differences between the films, remarkable differences between them were revealed by the temporal evolution of the Brillouin frequency (BF) shift of the probe light in the TDBS. The observed modification of the BF was a signature of the light-induced modification of the films in the process of the TDBS experiments. It correlated to the different amount of carbon residue in the samples, the use of ultraviolet (UV) femtosecond probe laser pulses in our optical setup, and their intensity. In fact, probe radiation with an optical wavelength of 356 nm appeared to be effective in removing carbon residue through single-photon absorption processes, while its two-photon absorption might have led to the breaking of Si-CH3 bonds in the OSG matrix. The quantum chemical calculations confirmed the latter possibility. This discovery demonstrates the possibility of local modifications of OSG films with a nanometric resolution via nonlinear optical processes, which could be important, among other applications, for the creation of active surface sites in the area-selective deposition of atomic layers.

Effect of laser beam incidence angle on the thermoelastic generation in semi-transparent materials.

When a laser beam is absorbed in a semi-transparent material, a volume acoustic source is created owing to penetration of the laser beam inside the material and to thermoelastic transduction. Many experimental and theoretical studies have been conducted to better understand this ultrasound generation process with normal laser light incidence on the material surface. The purpose of this paper is to analyze the effects of the asymmetry caused by oblique incidence of a laser line source on the generation of acoustic waves in semi-transparent isotropic materials. Experiments on a glass plate demonstrate that such an obliquely incident laser light strongly affects bulk acoustic waves generation. Compressional and shear waves are enhanced and the loss of symmetry of the acoustic source causes asymmetrical behavior of the acoustic waves. Surprisingly, compressional-wave amplitude decreases whereas shear-wave amplitude increases in the region where the electromagnetic energy is refracted. This feature is explained by semi-analytical calculations.

Photoacoustic 3-D imaging of polycrystalline microstructure improved with transverse acoustic waves.

Non-invasive fast imaging of grain microstructure of polycrystalline ceria with sub-micrometric spatial resolution is performed via time-domain Brillouin scattering. The propagation of a nanoacoustic pulse is monitored down to 8 µm deep in a 30 × 30 µm2 area. Grains boundaries are reconstructed in three-dimensions via a two-step processing method, relying on the wavelet synchro-squeezed transform and the alphashape algorithm. Imaging contrast is improved by taking advantage of stronger sensitivity to anisotropy of transverse acoustic waves, compared with longitudinal waves. Utilization of transverse waves in the image processing reveals additional boundaries, confirmed by an electron backscattering diffraction pattern but not discerned using longitudinal waves. A buried inclined interface between differently oriented grains is identified by monitoring changes in amplitude (phase) of the portion of the signal associated with transverse (longitudinal) waves. Estimates of the inclination angle of this interface prove the sensitivity of our laser ultrasonic method to image inclined boundaries.

Evaluation of Optical and Acoustical Properties of Ba1-xSrxTiO3 Thin Film Material Library via Conjugation of Picosecond Laser Ultrasonics with X-ray Diffraction, Energy Dispersive Spectroscopy, Electron Probe Micro Analysis, Scanning Electron and Atomic Force Microscopies.

Wide-range continuous spatial variation of the film composition in lateral compositionally graded epitaxial films requires the development of high throughput measurement techniques for their local and non-destructive characterization with the highest possible spatial resolution. Here we report on the first application of the picosecond laser ultrasonics (PLU) technique for the evaluation of acoustical and optical parameters of lateral compositionally graded film, the Ba1-xSrxTiO3 (0 ≤ x ≤ 1) material library. The film was not dedicatedly prepared for its opto-acousto-optic evaluation by PLU, exhibiting significant lateral variations in thickness and surface roughness. Therefore, the achieved measurements of the sound velocity and of the optical refractive index, and characterization of the surface roughness confirm the robustness of the PLU technique for thin film evaluation. We hope that the first measurements of the acoustical and optical properties of epitaxial grown Ba1-xSrxTiO3 (0 ≤ x ≤ 1) by PLU technique accomplished here provide the parameters required for more extended predictive design of the phononic, photonic and phoxonic mirrors and cavities with superior properties/functionalities for novel multifunctional nanodevices.

Imaging grain microstructure in a model ceramic energy material with optically generated coherent acoustic phonons.

Characterization of microstructure, chemistry and function of energy materials remains a challenge for instrumentation science. This active area of research is making considerable strides with methodologies that employ bright X-rays, electron microscopy, and optical spectroscopy. However, further development of instruments capable of multimodal measurements, is necessary to reveal complex microstructure evolution in realistic environments. In this regard, laser-based instruments have a unique advantage as multiple methodologies are easily combined into a single instrument. A pump-probe method that uses optically generated acoustic phonons is expanding standard optical characterization by providing depth resolved information. Here we report on an extension of this method to image grain microstructure in ceria. Rich information regarding the orientation of individual crystallites is obtained by noting how the polarization of the probe beam influences the detected signal amplitude. When paired with other optical microscopies, this methodology will provide new perspectives for characterization of ceramic materials.

High-Frequency Elastic Coupling at the Interface of van der Waals Nanolayers Imaged by Picosecond Ultrasonics.

Although the topography of van de Waals (vdW) layers and heterostructures can be imaged by scanning probe microscopy, high-frequency interface elastic properties are more difficult to assess. These can influence the stability, reliability, and performance of electronic devices that require uniform layers and interfaces. Here, we use picosecond ultrasonics to image these properties in vdW layers and heterostructures based on well-known exfoliable materials, i.e., InSe, hBN, and graphene. We reveal a strong, uniform elastic coupling between vdW layers over a wide range of frequencies of up to tens of gigahertz (GHz) and in-plane areas of 100 µm2. In contrast, the vdW layers can be weakly coupled to their supporting substrate, behaving effectively as free-standing membranes. Our data and analysis demonstrate that picosecond ultrasonics offers opportunities to probe the high-frequency elastic coupling of vdW nanolayers and image both "perfect" and "broken" interfaces between different materials over a wide frequency range, as required for future scientific and technological developments.

Picosecond laser ultrasonics for imaging of transparent polycrystalline materials compressed to megabar pressures.

Picosecond laser ultrasonics is an all-optical experimental technique based on ultrafast high repetition rate lasers applied for the generation and detection of nanometric in length coherent acoustic pulses. In optically transparent materials these pulses can be detected not only on their arrival at the sample surfaces but also all along their propagation path inside the sample providing opportunity for imaging of the sample material spatial inhomogeneities traversed by the acoustic pulse. Application of this imaging technique to polycrystalline elastically anisotropic transparent materials subject to high pressures in a diamond anvil cell reveals their significant texturing/structuring at the spatial scales exceeding dimensions of the individual crystallites.