Bond Strain Research Articles

Particle flow simulation of fracture responses and anchoring mechanisms of cemented materials subjected to static-dynamic combined loads

This study aims to reveal the evolution of energy, cracks, force chain, and ultimate failure modes of cemented gangue backfill materials subjected to static-dynamic combined loads, as well as the reinforcement mechanisms of pre-tightening bolts on mechanical performance and progressive damage. The particle flow models with various fractal dimensions (D) of particle size distribution were established, and irreversible damage accumulation during dynamic loading was achieved through a nonlinear parallel-bonded stress corrosion model. The simulation results show that, compared to uniaxial compression, the energy release lag at peak strength is eliminated under static-dynamic combined loading, and the brittle failure feature becomes more pronounced. The filling effect of fine aggregates optimizes the uniformity of internal stress distribution, with the peak parallel bond strain energy increasing by 9.60%, 8.42%, and 14.81% as D increases from 2.1 to 2.85. At initial dynamic loading, the instantaneous increase in axial stress reaches the crack initiation stress, significantly increasing the number of tensile cracks. As pre-static load increases, the model sample is subjected to a higher internal stress environment during dynamic loading, leading to more remarkable force chain breakage observed at peak strength. Shear failure, including oblique shear failure and tensile-shear mixed failure, is the primary failure mode under static-dynamic combined loading. The additional constraints provided by bolts increase strain energy stored in particles and contacts and reduce the crack number at peak strength, with the constraining effect exhibiting more pronounced as preload increases. For anchored samples, the end of pallets is the initiation point for shear cracks, which extend along the edge of the preload concentration area, while tensile cracks initiating from the sample ends propagate toward the preload concentration area.

Modeling via peridynamics for damage and failure of hyperelastic composites

Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based peridynamics (PD) framework with multiple advancements. First, we develop a PD bond strain model grounded in the nonlinear Piola-Kirchhoff stress-stretch relationship, precisely capturing hyperelasticity and ensuring full compliance with thermodynamic laws and kinematics in large deformation scenarios. Second, our framework employs a particle discretization technique that not only sidesteps the mesh distortion issues commonly encountered in grid-based methods subjected to large deformation but also significantly lowers the computational complexity due to the ease of numerical implementation of random inclusion distributions. Third, we propose, for the first time, a refined 3D hyperelastic model within the PD framework that enables a more comprehensive and accurate prediction of material responses to external loads, surpassing the limitations of conventional 2D simulations. Validation against experimental data demonstrates that our model accurately captures key physical phenomena in hyperelastic composites, such as spontaneous crack initiation and propagation, interface debonding, crack coalescence, and the formation of non-smooth crack surfaces. Crucially, this framework is versatile and adaptable to a wide range of engineered composite systems with different inclusions and matrices, making it a powerful tool for predicting and analyzing large deformation behaviors in various advanced applications.

Synthesis of group-IV ternary and binary semiconductors using epitaxy of GeH3Cl and SnH4

Ge1−x−ySixSny alloys were grown on Ge buffers via reactions of SnH4 and GeH3Cl. The latter is a new CVD source designed for epitaxial development of group-IV semiconductors under low thermal budgets and CMOS-compatible conditions. The Ge1−x−ySixSny films were produced at very low temperatures between 160 and 200 °C with 3%–5% Si and ∼5%–11% Sn. The films were characterized using an array of structural probes that include Rutherford backscattering, x-ray photoelectron spectroscopy, high-resolution x-ray diffraction, scanning transmission electron microscopy, and atomic force microscopy. These studies indicate that the films are strained to Ge and exhibit defect-free microstructures, flat surfaces, homogeneous compositions, and sharp interfaces. Raman was used to determine the compositional dependence of the vibrational modes indicating atomic distributions indistinguishable from those obtained when using high-order Ge hydrides. For a better understanding of the growth mechanisms, a parallel study was conducted to investigate the GeH3Cl applicability for synthesis of binary Ge1−ySny films. These grew strained to Ge, but with reduced Sn compositions and lower thicknesses relative to Ge1−x−ySixSny. Bypassing the Ge buffers led to Ge1−ySny-on-Si films with compositions and thicknesses comparable to Ge1−ySny-on-Ge; but their strains were mostly relaxed. Efforts to increase the concentration and thickness of Ge1−ySny-on-Si resulted in multiphase materials containing large amounts of interstitial Sn. These outcomes suggest that the incorporation of even small Si amounts in Ge1−x−ySixSny might compensate for the large Ge–Sn mismatch by lowering bond strains. Such an effect reduces strain energy, enhances stability, promotes higher Sn incorporation, and increases critical thickness.

Experimental and analytical investigations on bond–slip behavior of steel reinforcement inUHPFRCconsidering yielding

AbstractThe bond behavior between ultra‐high‐performance fibre‐reinforced concrete (UHPFRC) and steel rebars plays an important role in the load‐bearing capacity and serviceability of structural members. A suitable bond–slip model is essential for predicting the load resistance and deformation capacity of members, after cracking of the UHPFRC. This paper studies the bond strength between ribbed steel bars and the surrounding UHPFRC before and after yielding of the steel reinforcement. To determine the corresponding bond–slip relationship, pull‐out tests, with varying embedment lengths of the reinforcement, namely 2 times and 10 times the rebar diameter, and diameter of reinforcing bars ranging from 10 mm to 16 mm were conducted. The bond stress, strain and slip along the embedment length of the steel rebars were measured by strain gauges and displacement transducers. Based on the test data, a bond stress–slip model was derived before (elastic stage) and after (inelastic stage) yielding of the reinforcement. The slip at the yield point is suggested through theoretical equations. The post‐yield bond–slip model is based on yield bond stress and frictional bond stress. The two‐part model was validated through iterative procedures and is able to predict the applied force, bond stress and strain distribution along the reinforcing bar. A comparison between the test data and analytical results demonstrates a good predictive capacity on the bond behavior of reinforcement in UHPFRC both before and after yielding of the reinforcement.

Theoretical study on the synthetic pathway of H and N co-doped diamonds

To search for potential n-type diamonds with shallow donor energy levels and low formation energies, the reaction energies, geometries, formation energies, electronic properties of hydrogen (H) and nitrogen (N) co-doped diamond have been investigated by density functional theory (DFT) and hybrid density functional theory (HSE06). The results of the investigations on isolated H- and N-doped diamonds do not meet the criteria for shallow n-type donors, in agreement with previous findings. Subsequently, the effect of the addition of N atoms as a co-dopant with H is investigated, which varies with the H:N ratio and whether H is substitutional or interstitial. By the results of the electronic structure, it is found that only the HN4 co-doped diamond is likely to exhibit a shallow donor, with a shallow donor level of 0.147 eV and formation energy of 0.02 eV. Then, the stability of the HN4 defect is analyzed, and the HN4 defect is more stable compared to the H-N3 + N and H-N2 + N2 defects, and its decomposition energy is also very large. Further, the bond strain brought by HN4 defect is considered, showing that the local bond strain of the HN4 defect is intermediate between that of the boron (B) and N defects, which proves that the defect can be realized. Finally, a non-molecular synthetic route for the preparation of HN4 defect is proposed by combining H-N + N3V or N2 + H-N2 defects.

Understanding Strain and Failure of a Knot in Polyethylene Using Molecular Dynamics with Machine-Learned Potentials.

A neural network potential (NNP) has been developed by fitting to ab initio electronic structure data on hydrocarbons and is used to study failure of linear and knotted polyethylene (PE) chains. A linear PE chain must be highly strained before breaking as the stress is equally distributed across the chain. In contrast, the stress in a PE chain with a 31 or overhand knot, accumulates at the knot's entrance/exit. We find the strain energy is greatest when the bond length and angle are strained simultaneously, and that the knot weakens the chain by increasing the variance of the C-C-C angle, thereby allowing rupture at lower bond strains. We extend our analysis to both 51 and 52 knots and find that both break at the entrance/exit of a loop. Notably, molecular scale PE knots exhibit many of the same characteristics as knots in a macroscopic rope, with stick-slip phenomena upon tightening and similar points of failure.

Efficient photocatalytic degradation of diclofenac drug using the Zn1-x-yPrxAlyO photocatalyst under UV light irradiation.

Herein, we report the efficient photocatalytic degradation of the diclofenac drug using the Zn1-x-yPrxAlyO photocatalyst [x, y] = (0.00, 0.00), (0.03, 0.01), (0.03,0.03) under UV light irradiation. The analysis of the structure reveals that the Pr3+ and Al3+ cations insertion into the ZnO lattice leads to a decrease in the lattice constant (a and c), Zn-O bond length, strain lattice, and crystallite size. These alterations are linked to the high degree of atomic disorder triggered by the dopants, which produce stress and strain in the ZnO structure. The Raman measurements confirmed the structural phase and showed changes in the position and intensity of the E2High mode, associated with oxygen vibrations and material crystallinity. The presence of the dopants reduces the concentration of VZn and VO++ type defects while increasing the levels of VO, VO+, and Oi defects, as observed from the fitting of the Photoluminescence spectra. Furthermore, it was noted that de Pr3+ and Al3+ cations insertion into ZnO increases the optical band gap, which is associated with the Moss-Burstein effect. The micrograph images show that dopants transform the morphology from quasi-spherical particles to irregular cluster structures. The textural analysis indicated that an increase in the concentration of Al3+ in the ZnO lattice led to a higher surface area, likely enhancing photocatalytic activity. The sample containing 3% Pr3+ and 3% Al3+ showed the highest photocatalytic activity and degraded up to 71.42% of diclofenac. In addition, experiments with scavengers revealed that hydroxyl radicals are the main species involved in the drug's photodegradation mechanism. Finally, the Zn1-x-yPrxAlyO compound is highly recyclable and stable.

First-principles calculations of structural and bonding properties of Li-doped tetrahedrite thermoelectrics

Tetrahedrite (copper antimony sulfosalt) is a promising p-type thermoelectric material due to its very low intrinsic thermal conductivity and moderately-high power factor, with one of the limitations being the lack of n-type variant to create a thermoelectric generator. In this paper, DFT calculations have been carried out to study tetrahedrite doped with Li into structural voids, LixCu12Sb4S13 (0≤x≤3). Enthalpies of formation show that the introduction of Li into both 6b and 24 g sites is energetically favorable. Dopants in those positions differently affect the rattling Cu(12e) behavior, as well as vary in the magnitude of induced local disorder. Topological analysis of charge density classifies tetrahedrite as a closed-shell, ionic system of interactions with some degree of covalency. The addition of Li increases bond strain and decreases structural stability. Electronic band structure shows that for x>2.0, material becomes n-type; however, results are not precisely conclusive on whether structure will be synthesizable, which should be determined experimentally.

Fatigue failure analysis of U75V rail material under Ⅰ+Ⅱ mixed-mode loading: Characterization using peridynamics and experimental verification

Fatigue failure behavior of U75V rail material under Ⅰ+Ⅱ mixed-mode loading is analyzed and characterized in this work. A fatigue crack propagation experiment was carried out on U75V rail material under mixed-mode loading for R = 0.1. Then, based on the Ordinary State-Based Peridynamic (OSB PD) theory, bond strain rate and bond energy release rate methods were used to characterize the fatigue failure behavior of the rail material. Finally, the simulation results were compared with experimental results in terms of crack propagation length, path and angle to evaluate the characterization effects of both methods. The conclusions were as follows: under single mode I loading, both methods could accurately characterize the fatigue failure behavior of the rail material. However, compared with the bond strain rate method, the bond energy release rate method could provide a more accurate characterization under I + II mixed-mode loading.

Unzipping hBN with ultrashort mid-infrared pulses.

Manipulating the nanostructure of materials is critical for numerous applications in electronics, magnetics, and photonics. However, conventional methods such as lithography and laser writing require cleanroom facilities or leave residue. We describe an approach to creating atomically sharp line defects in hexagonal boron nitride (hBN) at room temperature by direct optical phonon excitation with a mid-infrared pulsed laser from free space. We term this phenomenon "unzipping" to describe the rapid formation and growth of a crack tens of nanometers wide from a point within the laser-driven region. Formation of these features is attributed to the large atomic displacement and high local bond strain produced by strongly driving the crystal at a natural resonance. This process occurs only via coherent phonon excitation and is highly sensitive to the relative orientation of the crystal axes and the laser polarization. Its cleanliness, directionality, and sharpness enable applications such as polariton cavities, phonon-wave coupling, and in situ flake cleaving.

Tunable energy bandgap of Fe-doped (Bi, Li) co-substituted barium titanate

In this work, a polycrystalline Ba0.96(½ Bi, ½ Li)0.04Ti(1-x) FexO3; (0 ≤ x ≤ 0.08) ceramics have been synthesised using a solid-state reaction method. The prepared systems were explored to detect the impact of Fe substitution on the energy bandgap of the ceramics. XRD patterns confirmed that there is a structural phase transition from tetragonal (P4 mm) to hexagonal (P63/mmc) phase as the concentration of Fe increases. Rietveld refinement was performed to obtain the lattice information. Furthermore, Raman spectroscopic analysis confirmed the structural information obtained from XRD study. The average bond length variations, strain evolutions, crystallite size, and theoretical density have been calculated from the structural analysis. It is found that the lower Fe concentration with the tetragonal phase showed a strong Jahn-Teller effect. Meanwhile, the higher concentration of Fe led to phase transition to hexagonal phase with fewer structural distortions. The optical band gap species were investigated through UV-Vis. Following the onset of defects induced by acceptor ions, an exciting band gap reduction up to 2.09 eV for the sample with x = 0.08 was attained. ESR and PL spectroscopies analyses showed that in the hexagonal phase region more defects are formed giving rise to promoting band gap narrowing. Furthermore, the ac conductivity analysis indicates the appearance of defect levels due to the formation of oxygen vacancies. This study demonstrates that the right choice of Fe content in the host material can tune the energy band gap significantly in the BLBTF system and may be exploited in photovoltaics in the visible region.

Structural Analysis, Characterization, and First-Principles Calculations of Bismuth Tellurium Oxides, Bi6Te2O15

A single crystal of Bi6Te2O15 was obtained from the melt of the solid-state reaction of Bi2O3 and TeO3. Bi6Te2O15 crystallizes in the Pnma space group (No. 62) and exhibits a three-dimensional network structure with a =10.5831(12) Å, b = 22.694(3) Å, c = 5.3843(6) Å, α = β = γ = 90°, V = 1293.2(3) Å3, and Z = 4. The structure was determined using single-crystal X-ray diffraction. An asymmetric unit in the unit cell, Bi3Te1O7.5, uniquely composed of four Bi3+ sites, one Te6+ site, and nine O2− sites, was solved and refined. As a bulk phase, Bi6Te2O15 was also synthesized and characterized using powder X-ray diffraction (XRD), infrared (FT-IR) spectrometry, and the thermogravimetric analysis (TGA) method. Through bond valence sum (BVS) calculations from the single crystal structure, Bi and Te cations have +3 and +6 oxidation numbers, respectively. Each Bi3+ cation forms a square pyramidal structure with five O2− anions, and a single Te6+ cation forms a six-coordinated octahedral structure with O2− anions. Since the lone-pair electron (Lp) of the square pyramidal structure, [BiO5]7−, where the Bi+ cation occupies the center of the square base plane, exists in the opposite direction of the square plane, the asymmetric environments of all four Bi3+ cations were analyzed and explored by determining the local dipole moments. In addition, to determine the extent of bond strain and distortion in the unit cell, which is attributed to the asymmetric environments of the Bi3+ and Te6+ cations in Bi6Te2O15, bond strain index (BSI) and global instability index (GII) were also calculated. We also investigated the structural, electronic, and optical properties of the structure of Bi6Te2O15 using the full potential linear augmented plane wave (FP-LAPW) method and the density functional theory (DFT) with WIEN2k code. In order to study the ground state properties of Bi6Te2O15, the theoretical total energies were calculated as a function of reduced volumes and then fitted with the Birch–Murnaghan equation of state (EOS). The band gap energy within the modified Becke–Johnson potential with Tran–Blaha parameterization (TB-mBJ) revealed a value of 3.36 eV, which was higher than the experimental value of 3.29 eV. To explore the optical properties of Bi6Te2O15, the real and imaginary parts of the dielectric function, refraction index, optical absorption coefficient, reflectivity, the real part of the optical conductivity extinction function, and the energy loss function were also calculated.

Ultra-fast laser pulses as a probe of electron dynamics: A next generation QTAIM perspective

We investigate the construction of an ultra-fast laser probe to determine the response of the electron dynamics of ethane using next generation QTAIM (NG-QTAIM). This is undertaken by applying a pair of simulated left and right circularly polarized ultra-fast laser pulses of duration 10 fs. A proportional increase in the C-C BCP bond strain with peak electric field was discovered. NG-QTAIM was used to identify a characteristic morphology associated with ultra-fast laser probes. Candidate ultra-fast laser probes were selected on the basis of the ground state population remaining undisturbed at a time t = 15 fs.

Controllable toughness enhancement in graphene hybrid materials via planar twist-angle of carbon nanotubes

A controllable toughness enhancement in graphene hybrid materials via twist-angle of CNTs was first investigated. The mechanical properties, such as out-of-plane deformation, stress–strain curves, strain energy and interlayer loading transfer of Gr Hybrid model coupled by twist-angle CNTs were investigated by molecular dynamics simulations and nonlinear fracture mechanics theory. We find that these mechanical properties are sensitive to the existence of twist-angle CNTs in the Gr hybrid model. The crosslinking sites can be considered as structural defects. In addition, the CNTs exert a strengthening influence on the out-of-plane deformation, interlayer loading transfer as well as bond strain energies, thereby deflecting the crack paths of Gr Hybrid model under axial tension. Nevertheless, the existence of CNTs also triggers a reduction in the in-plane stress and the associated strain due to sp2 + sp3 hybrid state. We find that this abnormal improvement in toughness derives from the localization of the stress fields arising from their out-of-plane displacements at the interface, resulting in the stress fields being localized only at the crosslinking sites. These interfacial toughening strategies can redistribute crack tip stress in a wider range, avoid stress concentration, and at the same time realize a lot of energy dissipation by promoting crack deflection, thus achieving overall high toughness.

Cracking behavior of Sm2O3 ceramics and enhanced microwave dielectric properties with MgO addition: Insights from chemical bond characteristics and microstructure

Monoclinic Sm2O3 ceramics were prepared using the conventional solid-state sintering method. The influences of sintering temperature on structure, morphology, and performance of Sm2O3 ceramics were studied systematically. The excellent microwave dielectric properties (εr = 21.95, Q × f = 47,000 GHz, and τf = +30.15 ppm/°C) were achieved in Sm2O3 ceramic sintered at 1550 °C for 4 h. Interestingly, varying degrees of cracking were observed after the sintered samples were placed for a short time, with the extent depending on the sintering temperatures. The reasons for cracking were analyzed through chemical bond characteristics and microstructure. The analysis of bond valence and microstructure revealed that Sm2O3 ceramics sintered at higher temperatures exhibited larger bond strain index, global instability index, and interplanar spacings. These results suggest that the cracking of Sm2O3 ceramics originates from inner stress resulting from structural variations caused by variations in sintering temperatures. The effect of MgO addition on microwave dielectric properties and stability of Sm2O3 ceramics was also investigated. Phase identification and elemental distribution indicated that MgO existed as a secondary phase. The Sm2O3 ceramic with 20 wt% MgO addition exhibited optimal microwave dielectric properties: εr = 17.72, Q × f = 61,100 GHz, and τf = +2.4 ppm/°C. Importantly, cracking was not observed when MgO addition amounts were 5 wt% or higher. The attractive microwave dielectric properties and favorable stability confirm the possibility of the 5G applications for Sm2O3/MgO composite ceramics.

Testing the limits of the global instability index

The global instability index (GII) is a computationally inexpensive bond valence-based metric originally designed to evaluate the total bond strain in a crystal. Recently, the GII has gained popularity as a feature of data-driven models in materials research. Although prior studies have proven that GII is an effective predictor of structural distortions and decomposition energy when applied to small datasets, the wider use of GII as a global indicator of structural stability has yet to be evaluated. To that end, we compute GII for thousands of compounds in inorganic structure databases and partition compounds by chemical interactions underlying their stability to understand the GII values and their variations. Our results show that the GII captures relative chemical trends, such as electronegativity, even beyond the intended domain of strongly ionic compounds. However, we also find that GII magnitudes vary significantly with factors such as chemistry (cation–anion identities and bond character), geometry (connectivity), data source, and model bias, making GII suitable for comparisons within controlled datasets but unsuitable as an absolute, universal metric for structural feasibility.

Synergistic effects of mixing and strain in high entropy spinel oxides for oxygen evolution reaction

Developing stable and efficient electrocatalysts is vital for boosting oxygen evolution reaction (OER) rates in sustainable hydrogen production. High-entropy oxides (HEOs) consist of five or more metal cations, providing opportunities to tune their catalytic properties toward high OER efficiency. This work combines theoretical and experimental studies to scrutinize the OER activity and stability for spinel-type HEOs. Density functional theory confirms that randomly mixed metal sites show thermodynamic stability, with intermediate adsorption energies displaying wider distributions due to mixing-induced equatorial strain in active metal-oxygen bonds. The rapid sol-flame method is employed to synthesize HEO, comprising five 3d-transition metal cations, which exhibits superior OER activity and durability under alkaline conditions, outperforming lower-entropy oxides, even with partial surface oxidations. The study highlights that the enhanced activity of HEO is primarily attributed to the mixing of multiple elements, leading to strain effects near the active site, as well as surface composition and coverage.

Three-dimensional modeling and analysis of anisotropic materials with quasi-static deformation and dynamic fracture in non-ordinary state-based peridynamics

A general three-dimensional anisotropic model is proposed within the non-ordinary state-based peridynamic framework in this work. Three-dimensional peridynamic formulations for anisotropic solids are formulated, and two types of stress rate solutions, Green-Naghdi and Jaumann stress rate are implemented in this model, respectively. Moreover, the equivalent bond stress and corresponding equivalent bond strain are presented and calculated. The 3D-Hashin failure criterion is used among the numerical analysis of anisotropic materials through the equivalent bond strain. Various typical cases are performed by the proposed anisotropic peridynamic model and approach, including the numerical analyses of quasi-static deformation and dynamic fracture for anisotropic materials. The effectiveness and applicability of the proposed model are verified by precisely characterizing the quasi-static deformation and dynamic failure behavior.

Effect of lattice-induced strain on microwave dielectric polarization and properties: A case study of Ga-based garnet

In microwave dielectric materials, the phenomenon that the measured permittivity (εr) is inconsistent with the calculated permittivity (εr(C-M)) often occurs. In the present work, the intrinsic factors affecting the microwave dielectric properties of Ga-based garnet Ca3B1.5Ga3.5O12 (B = Nb, Ta) are studied by bond valence and the Phillips-Van Vechten-Levine (P-V-L) methods, and the relationship between lattice-induced strain effect and dielectric polarization is elucidated. Since the ionic polarizability of Nb5+ is lower than that of Ta5+, the εr(C-M) values of Ca3Nb1.5Ga3.5O12 (CNG) and Ca3Ta1.5Ga3.5O12 (CTG) are 11.06 and 12.17, respectively. However, this is the opposite trend of the measured values (15.00 and 12.62). The global instability index (GII) is equal to 0.013 and 0.044 v.u., respectively. Both the indexes, bond strain index (BSI) and GII, are related to the entire crystal structure. A stronger lattice-induced compressive strain and a higher degree of covalency lead to a lower measured εr, a higher Q×f, a higher temperature coefficient of permittivity τε, and a larger negative τf.

Correlation between structure and microwave dielectric properties of ordered olivine CaLnGaO4 (Ln = Pr, Yb) ceramics

The microwave dielectric properties of olivine-structured CaLnGaO4 (Ln = Pr, Yb) ceramics with a 1:1 order at the octahedra site were investigated using bond valance, P–V-L chemical bond theory, and Raman spectra. The theoretical permittivity εr(C-M) values are far below the porosity-corrected εr(Corr) values, indicating that the dielectric polarizabilities of CaLnGaO4 (Ln = Pr, Yb) were underestimated, and this phenomenon was mainly influenced by rattling cations. The difference in εr is mainly determined by the ionic polarizability per unit volume (αm/Vm). The τf values of CaLnGaO4 (Ln = Pr, Yb) did not decrease with the decrease of the εr, which was due to the larger positive temperature coefficient of dielectric constant (τε) and the higher coefficient of thermal expansion (αL) of CaPrGaO4 ceramic compared to CaYbGaO4, respectively. The difference in Q × f values between CaPrGaO4 and CaYbGaO4 is mainly due to the strain of chemical bonds and the Raman spectrum.