This review discusses current applications of high-resolution continuum source electrothermal atomic absorption spectrometry (HR-CS ETAAS) for quantitative analysis. Analytical approaches for samples of various compositions are considered, including environmental objects, food products, plant and biological materials, metal-containing samples, crude oil and petroleum products, and cosmetics. The following methodological solutions are presented in order to achieve low detection and determination limits: the use of various modifiers, optimisation of graphite furnace heating programms, preliminary extraction and concentration procedures. The differences between simultaneous multielement determination and sequential determination within a single aliquot are highlighted. An analysis of the regulatory framework is provided, covering current standards for HR-CS ETAAS methods and certified procedures included in the Federal Information Fund for Ensuring the Uniformity of Measurements. The review demonstrates that CS ETAAS is a highly sensitive, accurate, and cost-effective analytical tool, remaining competitive among modern spectrometric techniques and its further development is linked to the expansion of multielement analytical methodologies for complex matrices.
Nonparametric methods of estimation in stochastic systems are certainly more general than parametric estimation methods. The latter assume the presence of a priori information, which ultimately assumes the knowledge of the number of estimated parameters and the structure of the system itself. In nonparametric methods, such information is not required. The paper objective: to develop methods for nonparametric estimation of dependence measures for complexly organized random processes. The article introduces a measure of dependence that links k pairs of random processes. Such a measure, based on the use of conditional mathematical expectations of processes, can be considered as a further generalization of dispersion functions. Convergence with probability 1 of nonparametric estimates of such a measure is derived using sample data. These estimates are used to construct sample analogues of some nonlinear measures of stochastic dependence of random processes, in particular, to obtain a consistent measure of dependence in the sense of Kolmogorov, i.e., a measure that vanishes if and only if the given random processes are stochastically independent. As a direct consequence, the consistency of the measure of dependence in the sense of Rényi, i.e., a measure that satisfies the corresponding Rényi axioms, will immediately follow from the obtained results. The developed estimation algorithms converging with probability 1 do not require any a priori information about the system and can be used to construct input-output mappings of nonlinear systems without any special requirements for the system.
Solving the problem of operational nondestructive evaluation of cast aluminum matrix composites is of great practical importance for improving their production technology. The purpose of the work is ultrasonic and microscopic studies of a promising aluminum matrix composite obtained by casting with mechanical mixing of reinforcing hollow ceramic microspheres. Optical and scanning electron microscopy, hydrostatic weighing, and ultrasonic echo method were used to study specimens with different volume fractions of pores and reinforcing microspheres. It is shown that saturation of aluminum matrix with reinforcing hollow microspheres consisting mainly of aluminum oxide makes it possible to obtain the composite less dense than the initial alloy. The main characteristic of the composite structure affecting its properties is the total volume fraction of micropores and reinforcing microspheres. It was found that in the studied specimens, the heterogeneity of the distribution and the average size of the pores and reinforcing microspheres do not affect the propagation velocities of ultrasonic waves and elastic properties. The density, ultrasonic wave velocities, Young’s modulus, and Poisson’s ratio decrease monotonously with an increase in the total volume fraction of micropores and hollow microspheres. It is concluded that the Poisson’s ratio can be used as an informative parameter for rapid quality control of the composite. The results obtained can be used to improve the technique of nondestructive quality control of produced aluminum matrix composites reinforced with hollow ceramic microspheres.
Alumina ceramic specimens with a submicron equiaxed grain microstructure exhibit the highest mechanical performance. However, for certain ratios of fine and coarse grains, the presence of abnormally grown grains may be regarded not as a defect but as a strengthening phase, enabling improved properties, in particular high flexural strength. The aim of this work is to investigate the effect of the volume fraction of abnormally large grains on the strength and fracture toughness of alumina-based ceramics. Abnormal grain growth was achieved during pressureless sintering of submicron α-Al 2 O 3 powder. It is shown that, under sintering at a constant heating rate up to a relative density of ~97%, the microstructure consists of equiaxed grains (size ~0.7 μm) and abnormally grown grains (5 vol. %, size >10 μm). By varying the sintering parameters, ceramics with different volume fractions of abnormally grown grains were produced. Increasing the fraction of abnormally grown grains from 5 to 15 vol. % increases the strength and fracture toughness by more than 1.5 times. The improved mechanical properties are attributed to deflection of the crack path from a straight trajectory as the crack bypasses abnormally large grains. The results obtained and the proposed approach may be used to optimise pressureless sintering routes for enhancing the mechanical properties of ceramics.
Thin carbon foils are widely used in various fields, including charged particle accelerators. The aim of the work is to study the effect of a high-energy electron beam on the surface structure of a carbon film. Influence of this effect on the service life of charged carbon films was analyzed by bombarding a carbon foil with a beam of high-energy particles. Comparative electron microscopic studies and X-ray spectral microanalysis of the elemental composition of a carbon foil sample after exposure to a high-energy electron beam have been performed. It has been found that in the irradiation area, warping and cracking of the film along the periphery are observed, followed by destruction and separation of the irradiation zone from the foil base. The high-energy effect of charged particles on the foil leads to thermal and radiolytic destruction of the material and the adhesive substrate, accompanied by surface chemical processes. The results obtained can be used to improve the technology for producing stripper carbon foils and increase their service life in charged particle accelerators.
Tungsten carbide-based ceramics and hard alloys are widely used as the base for metal-cutting and metalworking tools. The purpose of the work is a metallographic study of the effect of large graphite particles in the initial powder on the grain structure of tungsten carbide-based ceramics produced by spark plasma sintering. Before sintering the ceramic samples, large graphite particles of 50 – 500 μm in size were introduced into the initial powder. Digital image processing and statistical analysis methods were used in the work. It was found that an area of large grains of ~10 μm in size (with a submicron grain size in the material bulk) is formed around the graphite particles identified in metallographic sections of the samples. Similar effect upon contact between the workpiece and the graphite tooling is a consequence of carbon diffusion in tungsten carbide. The area thickness does not depend (within the error limits) on the graphite particle size and is 44 ± 9 μm. It was shown that the size distribution of coarse-grained areas can be approximated by lognormal and exponentially modified Gaussian distributions (the distribution modes are 47 ± 4 and 53 ± 7 μm, respectively). The results obtained and the proposed approach can be used to improve digital image processing techniques for metallographic analysis of the microstructure of materials.
The photometric method is cost-effective and easy to use, and the results of silicon determination using this method are highly reproducible. At the same time, it is more difficult to take into account the effect of the matrix on the results of photometric determination of silicon with the molybdenum blue reagent than for the determination by the ICP AES method. The procedures of GOST 12346–78 for steels and GOST 2642.3–2014 for refractory materials were tested for photometric determination of silicon in samples of complex variable composition. A universal method of sample preparation is proposed for the decomposition of samples of various compositions — catalysts based on aluminum oxide, ore, and functional composite materials. It is shown that the developed combined technique is suitable for all analyzed materials with different silicon content. The addition of EDTA during the dissolution of the melt makes it possible to mask impurities affecting the photometric determination of silicon due to the formation of strong EDTA complexes. The results of the determination of silicon in these samples obtained by the photometric method agree with the results of the ICP AES method within an error of 5%. It is noted that the results of photometric determination of silicon in ore materials are characterized by lower precision ( s r ≥ 0.09), which is associated with the complex variable composition of these samples. At the same time, the precision of the results of silicon determination in other materials by this method is higher than those obtained by the ICP AES method.
Eddy current testing of the quality of soldering of current-carrying joints of stators of hydro- and turbogenerators is carried out when commissioning new units, as well as after their scheduled repairs. The objective of this study is to investigate the specific electrical conductivity of connecting strips of current-carrying joints made of M1 copper semi-finished products and to eliminate the influence of adjacent joints on the testing results. When hot-rolled busbars are used as connecting strips in current-carrying joints of turbogenerator stator windings, significant variability (from 2 to 4.4%) in their electrical conductivity across their thickness and from product to product is observed. The error in determining the solder integrity of sidewalls using an eddy current transducer (ECT) can reach 52.8%. This must be taken into account when developing eddy current testing tools for soldering such joints, with electrical conductivity determined at the same frequencies at which the testing will be performed. It has been demonstrated that conductivity variability does not affect solder quality testing results when inspecting current-carrying joints in hydrogenerator stator windings, as the current-carrying rods and connecting strips in this case consist of soft copper busbars manufactured from rod using the upward casting method. However, the influence of adjacent connections on the ECT signals is significant. A method for eliminating this influence is proposed, consisting of shielding the ECT windings with a two-layer screen made of transformer steel. The obtained results can be used to improve the reliability of solder joint inspection in power equipment and to refine the methodology for use with other types of connections, as well as in conditions of complex electromagnetic interference.
The aim of this study is to investigate the physical and mechanical properties of polymethyl methacrylate (PMMA) brand Plexiglas GS 0Z00 due to the absence of stress-strain curves in open databases, such as CAMPUS or MATDAT. In addition, the mantioned databases contain curves only for tension. Stress-strain curves are necessary for more accurate calculation of the stress-strain state of the body. To determine the performance characteristics of the material, the samples were exposed to climatic action. The results of the experimental study of the physical and mechanical properties of the material before/ after climatic action are presented. Various models that determine the relationship between stresses and strains (the Menges model, the model based on the logistic function) at temperatures below the glass transition temperature are considered. Numerical values of the model parameters are obtained in accordance with the experimental data. The results of tensile-compressive tests at a constant strain rate from 1 to 10 mm/min (from = 3.3 %/min to 33.33 %/min) are compared with the results of tensile-compressive tests of the material at the same rates and room temperature, but after exposing the samples to open air for six months. In addition, the physical and mechanical properties of the material for different ambient temperatures are determined. Stress-strain curves of the material at room temperature are constructed for further use in modeling the stress-strain state of bodies. It is noted that at a deformation of no more than 4%, the Menges model and the model based on the logistic function have proven themselves well. The parameters of both functions for the selected material are presented in the paper. The material has a tendency to embrittlement after climatic aging. The physical and mechanical properties of the material depend on the ambient temperature and the rate of the applied load.
The study presents the methodology and results of investigation into the viscoelasticity of polymethyl methacrylate (PMMA) and polyamide PA-6 in tensile and compressive testing. The experiments enabled the separation of the volumetric and deviatoric components of the strain tensor. A significant dependence of the shear modulus and a weak dependence of the bulk modulus on hydrostatic stress were revealed. The features of PMMA viscoelastic deformation were studied over a wide range of operating temperatures. It was found that the ratio of the elastic and viscous strain intensities is weakly dependent on both hydrostatic stress and temperature of the medium. Constitutive equations are presented for viscoelasticity under a volumetric stress state at various combinations of elastic and viscous strain rates in the stress range from the creep limit to the forced elasticity limit, as well as during recovery after complete unloading. The equations do not explicitly include time and accumulated viscous strain, so they are applicable to processes with arbitrary strain or stress growth patterns. Comparison with experiment confirmed the high modeling accuracy of viscous PMMA deformation for prescribed law of elastic strain change. Several successive stages of viscoelastic deformation during loading and subsequent unloading were revealed. At the first stage, viscous strain does not increase, at the second stage, it increases only with increasing load, at the third stage, it also increases under constant load. Upon load reversal, the viscous strain rate decreases to zero, then changes sign and increases, approaching the elastic strain rate. The developed mathematical apparatus is intended for modeling the cyclic alternating loading of a spherical shell with internal and external pressure under operating conditions of a manned submersible vehicle.
Dairy products are frequently adulterated with non-dairy fats, including beef fat. Traditional methods for authenticating milk fat are based on the analysis of fatty acid, sterol, and triglyceride compositions. This study presents a novel approach using isotope mass spectrometry, based on the difference in carbon isotope ratios between cow’s milk fat and adipose tissue. The method involves the preparation of fatty acid methyl esters (FAMEs) via alkaline treatment, followed by their separation using gas chromatography, burning in the element analyser, and detection by an isotope mass spectrometer. It is shown that sample preparation has no significant effect on the carbon isotopic characteristics of FAMEs. The differences in δ 13 C values between methyl esters of stearic and palmitic acids (δ 13 C C 18:0 – δ 13 C C 14:0 ) and stearic and myristic acids (δ 13 C C 18:0 – δ 13 C C 14:0 ) were determined. Based on the sum of these differential values, criteria were established to detect the presence of beef fat in butter samples: less that –8‰ — natural butter; from –8 to –2‰ — butter with addition of more than 15% of beef fat; over –2‰ — beef fat. If the beef fat content is less than 15%, the samples cannot be distinguished from natural butter by this method. The proposed approach for determining the authenticity of milk fat is less work-consuming and more rapid than the traditional one.
For mechanical multi-cycle tests and fatigue strength studies of steel specimens, a simple portable bench unit has been created. Such tests are especially relevant in the study of specimens obtained with the help of additive technologies, which have specific features due to the specific production technology, consisting in the construction of the finished product by layer-by-layer build-up of powder material. The most convenient scheme of cyclic loading of the test specimen based on cantilever bending and possessing a number of advantages: simplicity of realization, testing performance, relatively low cost, adaptability and variability to loading conditions and additive technologies research, versatility, etc., was used when creating the stand. The block diagram of the stand, its appearance, the shape of the specimen loading cycle are presented, and the operation of the portable stand is described. The micromagnetic method — the Barkhausen effect method, which is closely related to the domain structure of the material, was used as a method for studying the kinetics of fatigue damage accumulation in the samples. Multi-cycle bending tests were carried out on specimens made of 09G2S low-alloy structural steel manufactured in accordance with GOST by additive technology (by selective laser fusion/sintering) and by casting. Experimental dependences of the influence of the number of loading cycles on the intensity of magnetic noise in the samples of one of the batches at low stress amplitude in the range of loading cycles variation from 1.5 × 10 6 to 6.9 × 10 6 are presented, as a result, the performance and efficiency of the stand are demonstrated. The bench allows to test small-sized specimens and to study in detail the process of fatigue damage accumulation with the growth of the basic value of the number of loading cycles and has the ability, if necessary, to set the required loading algorithm for multi-cycle tests and can be used in factory and laboratory conditions.
In use of technical systems and impact on them total loadings, physical fields and corrosion environments initiation in zones of high concentration of stresses of their elements not only fields of stresses and strains, but also fields of damages takes place. At the same time depending on conditions of loading and environment various mechanisms of damages accumulation and fracture are realized. Among these mechanisms are the most dangerous such which taking into account of long static and thermomechanical cyclic loading lead to catastrophic (avalanche) fracture. At the same time identification and analysis of physically connected specificities of not isothermal and statistical mechanisms of accumulation of damages to material plays a very important role when forming criteria of achievement of various types of limit states which are described by the corresponding state equations with the parameters of criteria characteristics of mechanical properties of materials entering them. It is shown that in the direction of working out of materials criteria base of structural strength and technogenic safety justification of models of damages summation at complex impact conditions of the damaging operational factors is perspective. At the same time in addition to standard characteristicses of mechanical properties of structural materials it is necessary to include in the content of criteria base of structural materials science characteristicses of crack resistance, fatigue, cold resistance, corrosion resistance, characteristics of resistance to elastic and plastic strains, characteristics of cyclic hardening, softening and stabilization of material at repeated elastoplastic deformation in the wide range of temperatures of operational loading. New, perspective integrated criteria of safety of operation of technosphere objects is the criteria of unacceptable (critical) technogenic risk considering on the basis of criteria base of structural materials science probability of initiation to them of damages, refusals, fractures, emergency and catastrophic situations at all stages of a lifetime at design, beyond design basis and hypothetical situations.
Anisotropic thick films of hexagonal barium ferrite BaFe 12 O 19 are used in the design and manufacture of microstrip microwave electronics devices, spinwave electronics devices and magnonics. The aim of the work is to study the crystal structure and magnetic properties of BaFe 12 O 19 films of different thicknesses. The films were obtained by the method of slip casting. The starting material is ferritized barium hexaferrite powder synthesized using standard ceramic technology. Polyvinyl butyral was used as a film-forming agent, ethyl alcohol, butyl acetate and dibutyl phthalate were used as solvents. The ratio of BaFe 12 O 19 powder to solvent film-forming agent was 70/30, and the thickness of the obtained films after sintering was 73, 340, and 770 μm. X-ray phase analysis of the samples was performed using an automated X-ray diffractometer DRON-4, the magnetic hysteresis loops of the study objects were recorded at room temperature. It is established that the main phase of the films is barium hexaferrite (crystal lattice parameters: a = 5.88 Å, c = 23.19 Å). The impurity found on the diffractograms probably refers to the film-forming agent and solvent. It is shown that the coercive force of the synthesized films is ~3 kOe, the residual specific magnetization is 20 – 26 emu/g, and the degree of magnetic texture is in the range of 10.98 – 15.7, which indicates the anisotropy of the samples. The results obtained can be used in the manufacture and improvement of devices for magnetoelectronics, microwave microelectronics, as well as spinwave electronics and magnonics.
Ceramic materials based on aluminum oxide (Al 2 O 3 ) are widely used in industry due to their unique combination of high hardness, thermal stability, and chemical inertness. The objective of this work is to review studies on the performance characteristics of ceramic cutting tools based on aluminum oxide. Key factors determining tool performance were examined, including the chemical purity of starting powders, composition modification of ceramics tailored to operating conditions, material microstructure (grain size, porosity, grain boundary state), and residual stresses arising during sintering. It is demonstrated that the wear resistance of Al 2 O 3 -based ceramics is primarily governed by the stability of grain boundaries (absence of amorphous phases and pores located along grain boundaries). Hardness, which depends on grain size, also exerts an influence. It was found that the lowest wear occurs in ceramics with grain sizes of 0.4 – 0.65 μm. A procedure for evaluating ceramic strength is proposed, incorporating the calculation of critical stress required for crack propagation along grain boundaries. It was established that, following grinding, the strength of conventional sintered ceramics increases by 30%, whereas the strength of ceramics sintered in a hydrogen atmosphere decreases by 10%. The research findings can be applied to develop new methods for controlling grain boundary structure and mitigating the impact of structural defects on the performance characteristics of ceramic cutting tools.
An overview of the information indicated in the passports of reference materials (RM) or certified reference materials (CRM) from the world’s leading manufacturers for the substances of anticoagulant rodenticides of the 4-hydroxycoumarin series is presented. Most of the characteristics in the passports are presented without taking into account uncertainties and specifying the methods by which the values given were obtained, which does not allow researchers to unambiguously assess the validity of the substance, and the quantity of the standard sample does not allow the consumer to reproduce at least some of these characteristics. As an alternative, the use of technical substances for the analysis of rodenticidal product products is considered. The stages of the input control procedure are proposed as part of the supplier assessment, which would take into account the specifics of the substances under consideration (tautomeric transformations, polymorphism, and rich isomeric composition). Using the example of the dif-nakum substance, the nonequivalence of the spectral characteristics of cis / trans isomers is demonstrated, which must be taken into account when using spectrophotometric or fluorimetric detectors. It is noted that the determination of the isomeric ratio is an important characteristic of the substance and is indicated in the passports for technical substances, but not in the documentation for standards, and this limits the use of the additive method in the analytical determination of the substance. It is proposed to provide the ISI testers with a sample of the technical substance from which the test sample was prepared, indicating in the research assignment the concentration range and the possible range of substances used. In this case, the participants of the ICI have the opportunity to carry out a full-fledged entrance control, confirm the authenticity of the substance, and then quantify its content in the assessment sample. The information provided is of interest both to manufacturers of rodenticide products and to potential providers of interlaboratory benchmarking tests, manufacturers of standard samples of pesticides and laboratories engaged in the analysis of products in the field of «pest control».
The development of simple and rapid methods for determining various biomarkers in blood plasma is necessary both to ensure prompt monitoring of the functional state of athletes and to validate new biomarkers. In particular, the key transmethylation intermediates S -adenosylmethionine ( SAM ) and S -adenosylhomocysteine ( SAH ) are considered to be potential early markers of impaired long-term adaptation of athletes to physical exertion. A technique for the determination of these compounds in blood plasma by liquid chromatography-tandem mass spectrometry (HPLC-MS/MS) has been developed: acceptable conditions have been found to ensure a balance of sensitivity, selectivity and expressiveness of the analysis. For chromatographic separation of the determined metabolites under gradient elution conditions, a Zorbax Eclipse XDB-C18 reversed-phase column and a water-methanol mixture as the mobile phase were used. The values of the declusterization potential have been optimized, fragmentation of SAM and SAH precursor ions has been studied, and the effect of collision energy on the signal intensity of characteristic fragment ions has been investigated. Product ions with m / z 250 and 136, respectively, were selected to determine SAM and SAH . The metrological characteristics of the developed technique and the matrix effect in the determination of analytes are evaluated: the limit of quantification of SAM and SAH is 1 ng/mL, the linear dynamic range is 1 – 500 and 1 – 1000 ng/mL, respectively. The correctness of the technique within a separate series of analysis and between series was confirmed by analyzing samples of known composition. The duration of the analysis does not exceed 4 min.
An electrochemical method for the determination of sulfur-containing compounds in motor fuels using square-wave voltammetrys developed. The relevance of the research is driven by increasingly stringent environmental regulations governing sulfur content in gasoline and diesel fuels in accordance with the Euro 5 and Euro 6 standards. Carbon-based electrodes fabricated by screen-printing on a dielectric substrate and modified with a bismuth film were employed as sensing elements. The use of such electrodes ensures environmental safety and high reproducibility of analytical characteristics. The conditions for bismuth electrodeposition used to modify the voltammetric sensor were optimized by means of cyclic voltammetry and electrochemical impedance spectroscopy. Model solutions of dibutyl sulfide were used plotting the calibration curve. It has been shown that preliminary accumulation of the analyte for 60 sec increases the sensitivity of determination by 30%. The detection limit calculated according to the 3σ-criterion was 0.05 mg/L, relative standard deviation did not exceed 10%. The developed technique has been tested in the analysis of real samples of gasoline with different octane ratings and diesel fuel. The obtained sulfur contents allowed as to classify all the samples as Euro 5 class. A comparison of the obtained results with those derived from potentiometric titration and X-ray fluorescence analysis according to ASTM D2622 showed good agreement. The developed electrochemical technique can be used for rapid and reliable quality control of motor fuels in both production and analytical laboratory environments.
This paper presents the Crack Tip Opening Angle (CTOA) as an effective fracture mechanics criterion for preventing risks associated with pipelines transporting hazardous gases such as hydrogen and ammonia. CTOA is used as a global parameter to characterize resistance to ductile crack propagation and to predict crack arrest conditions in pressurized pipelines. Unlike initiation-based fracture parameters, CTOA directly describes steady-state crack growth and is therefore well suited for assessing long-running cracks that may lead to catastrophic failures. The paper reviews the fracture behavior of pipeline steels, distinguishing between crack initiation and propagation, and highlights the advantages and limitations of the CTOA approach. Several CTOA measurement techniques are discussed, including direct optical methods, indirect load — displacement curve analysis, and fracture surface microtopography. The influence of material properties, specimen geometry, thickness, loading mode, and plastic constraint on CTOA values is examined, with particular emphasis on the significant scatter observed in experimental data. CTOA is implemented in finite element simulations using a node-release technique to model ductile crack propagation and arrest under internal pressure. The predicted arrest pressure and crack length are compared with established approaches such as the Battelle Two-Curves Method, showing good agreement. Once crack arrest is determined, the resulting breach size is used to calculate gas outflow rates. Finally, gas dispersion modeling, combined with CTOA-based fracture analysis, enables the determination of safety distances for toxic or explosive gas releases. A case study using ammonia and the ALOHA dispersion software demonstrates how CTOA can be integrated into a risk-based framework to ensure that lethal risk remains below regulatory thresholds over the pipeline’s service life.
The paper deals with a modified notch failure assessment diagram taking into account in-plane and out-of-plane constraint parameters in terms of nonsingular T xx - and T zz -stresses in the fracture process zone ahead of the notch tip front. A local failure criterion based on an average maximum tangential stress in the fracture process zone has been proposed to describe notch failure assessment curves. The average maximum tangential stress is assumed to be equal to the local strength in the fracture process zone which is calculated by means of the Huber – Mises plasticity criterion taking into account nonsingular T xx - and T zz -stresses. To reflect the combined effect of the constraint parameters, it is proposed to use the T z -parameter, which is a complex parameter of constraint at the notch tip front of a three-dimensional solids and reflects the constraint both perpendicular and along the notch tip front through the components of non-singular T xx - and T zz -stresses, respectively. It was established that there is the significant effect of the elastic stress concentration factor, out-of-plane notch tip constraints and T z -parameter on notch failure assessment curves in the case of three-dimensional solids. Notch failure assessment curves shift along the abscissa axis as the theoretical stress concentration factor increases. Besides, notch failure assessment curves for three-dimensional solids are located between the curves corresponding to the conditions of plane stress and plane strain. In the case of an unlimited theoretical stress concentration factor, the notch failure assessment curves for a notched solid transform into the failure assessment curves for a solid with the crack.
