Optical spectroscopy combined in situ with instrumented indentation

Optical spectroscopy is one of the most powerful tools used in chemical and physical sciences to study the structure and composition of a wide range of materials.^1,2 The development of experimental research methods implies not only increasing the accuracy of a particular measurement method but also the possibility of combining different measurements in the course of a single experiment.³ A striking example of such an approach is the use of optical spectroscopy to study the structural characteristics of the deformed material in the area under the indenter in indentation methods (local loading of the surface with a sharpened tip in order to measure mechanical properties).^4,5

For quite a long time, such combined studies were limited and were carried out only for transparent materials.⁵ Viewing the area under the indenter was hindered by the effect of total internal reflection, which prevents the passage of light into the area of interest. The traditional geometry of the indenter as a three- or four-sided pyramid and the high value of the refractive index of the diamond used to manufacture such a pyramid did not allow observation of the indentation area through the indenter in situ.

Therefore, the application of spectroscopic methods simultaneously with indentation was possible either when observing from the side of the sample, if it was transparent, or through the specially faceted side faces.⁶ As a rule, such studies were carried out after the end of the indentation process by traditional optical methods⁷ or by Raman spectroscopy,⁸ when all structural rearrangements in the material had already been completed.

The indenter-objective design proposed in the article⁹ solves this problem—the absence of the possibility of optical observation of the area under the indenter—and allows creating new devices and methods for studying the complex tense state of the material in the indentation area by a wide range of optical methods.

This Tutorial article discusses options for the design of an indenter-objective and approaches to its fabrication and control of the main performance characteristics. The possibilities of such an instrument from the point of view of visual investigation of the character of fracture of films and coatings, search for phase transitions in the indentation area by Raman spectroscopy, and application of Brillouin spectra to study the variability of elastic moduli of deformed polymer material are also considered. This approach can be extremely productive in the study of high-molecular weight materials and pharmaceuticals prone to the formation of polycrystalline structures and different conformational states.

Indentation experiments were carried out using a NanoScan nanoindenter (TISNCM, Russia), and combined Raman measurement was carried out using NanoScan indentation module integrated with a Renishaw InVia microscope. Combined Raman-Brillouin spectral measurements were carried out using a microscope “Nanofinder 30A/Brillouin/Raman” (Tokyo Instruments, Japan).

Typically, Berkovich tips are used for instrumented indentation, having the shape of a regular triangular pyramid with an angle between the height and the face α1 = 65.3°.¹⁰ The flat base of the indenter is usually perpendicular to the height of the pyramid. When such a pyramid is illuminated from the base by a beam of light parallel to its height, the angle between the direction of light and the perpendicular to the face will be a2 = 24.7°, which exceeds the angle of total internal reflection for a diamond having a refractive index of 2.4. Therefore, it is impossible to observe the surface of the material through the base and top of the Berkovich pyramid. When the tip is pushed into the material to some depth, the condition of total internal reflection may be violated, and the contact area will be visible due to the diffusely scattered part of the incident light. The rays mirrored from the face of the pyramid do not return to the microscope and do not participate in image formation.⁹ 

To overcome this difficulty, an indenter geometry is proposed, in which two centrally symmetrical Berkovich pyramids are formed at opposite ends of the diamond cylinder, that is, rotated relative to each other by 60°. These pyramids actually form three plane-parallel plates through which a quasi-parallel beam of light from the microscope passes, without undergoing complete internal reflection, both to the sample and back.^11,12

This approach, which allows observing the surface through an indenter, can be implemented for tips in the form of Vickers, Knoop, and any other self-similar indenters. The indenter-objective can also be in the form of a rotation figure, which is especially valuable when studying the stress-strain diagram by the method of instrumental indentation.

By adjusting the vertical size of such an indenter, it is possible to achieve that the objective surface formed by the lower part of the indenter collects optical rays in the focus of the objective formed by the upper surface. Then, the quasi-parallel beam of light reflected by the sample surface will remain quasi-parallel even after passing the indenter, and we will get a full-fledged, only inverted and enlarged or reduced image of the indentation area and its surroundings.

The hybrid form of the indenter-objective requires special mention when the tip of the upper (non-working) pyramidal part is cut off from it. The peripheral part of the observed surface is projected into this area at the indenter-objective, therefore, having formed a polished platform there, we get the opportunity to look into the area located directly under the top of the indenter and in its vicinity. In this area, the indenter and the sample are in direct mechanical and optical contact, and full internal reflection will not interfere with spectral studies directly under the tip of the indenter.

Due to the unique possibility of combining optical imaging and mechanical testing functions in a single tool, a new type of indenter is commonly called an indenter-objective, and the observation method is transparent tip imaging (TTI).⁹ 

Figure 1 shows how refracted light rays pass through a transparent indentor and form images.

Berkovich tip shape was chosen because it requires only three pairs of faces to be oriented in parallel. It is possible to use different tip shapes, like Vickers, cube-corner, or sphere, if we satisfy related geometric requirements in production.

Analysis of the optical path of the rays through the indenter-objective leads to the conclusion that the point of the surface lying under the face of the indenting end near the indenting tip is displayed on the surface of the non-indenting end at a distance from its vertex. The displacement of this point in the observation plane coincides with the displacement of the entire sector observed through the pair of faces of the indenting and non-indenting ends. Thus, in order to observe the area directly under the indenter, it is necessary that the surface of the non-indenting end has sufficient dimensions.

In order to maximize the use of the cross-sectional area of the indenter, its height and width must be in a certain ratio.

Figure 2 shows a modification of the diamond indenter-objective holder, which allows it to be used in almost any device designed for micro- and nanoindentation. Diamond crystal is fixed with titanium-based alloys by soldering in vacuum. This makes us sure that no significant strain is induced in indenter.

Direct observation of the surface through the indenter-objective leads to the splitting of the image into three sectors, which must be programmatically rearranged and re-stitched so that a coherent image is obtained. An example of this kind of processing of the resulting image is shown in Figs. 3–7. The arrows in Fig. 3(a) designate the position of the indenter tip on the raw optical image. It is also possible to see and study the untouched part of the surface under a transparent indentor.

The image quality as observed though the indenter is completely determined by the optical performance of the microscope. That is, the presence of the diamond indenter-objective in the optical path does not make the image quality worse, if the indenter is prepared properly.

Diamond polishing is a proven technology, and there were no problems with the surface quality and the level of diamond indented faces roughness. The main inaccuracy of manufacturing with the traditional approach to diamond cutting turned out to be the wedge shape of all three plane-parallel plates formed by opposing faces.

The wedge shape was studied using an optical dioptrimeter. This device allows not only to measure the optical strength of lenses and fix their asphericity, but also to measure the magnitude of the wedge shape of the object under study. The measurements showed a negligible optical power of the lens formed by the opposite sides and a rather significant wedge shape, which reached several hundredths of a radian in the most unsuccessful copies of the indenter-objective. At the same time, the direction of deflection of the light beam is due to randomness of prismaticity.

To eliminate this disadvantage, which makes it difficult to stitch three sectors of the surface visible through the indenter-objective, a special technique has been developed that guarantees the plane-parallelism of the opposite faces. First, a Berkovich pyramid is formed on a cylindrical billet using the standard method. Then, a half-finished indenter-objective is glued to a plane-parallel base and the face lying opposite is formed. And so it repeats three times for each of the faces.

The natural inaccuracy in the arrangement of the vertices on top of each other does not significantly affect the quality of the image stitching, since the indentation area is projected onto a flat face away from the top of the pyramid.

For spectral studies, an important factor is the size of the focusing spot of the probing radiation, and here the indenter-objective has one feature associated with the fact that all three plane-parallel plates forming an antisymmetric figure are turned by a significant 24.7° angle. This circumstance, when using a wide-angle probing beam, leads to the appearance of caustics in the focusing area. To minimize the amount of this erosion, a second plane-parallel plate can be used, if turned by 24.7°, but in the opposite direction.

High-quality diamonds suitable for the manufacture of transparent indenters can be obtained in one of two types of technological processes. An older method, the High Pressure High Temperature (HPHT) method, is based on growing a crystal from a carbon melt around a seed at extremely high pressure and high temperature.¹³ A newer process of growing chemical vapor deposition (CVD) diamonds is carried out inside a chamber filled with carbon-containing gas, during ionization of which pure carbon is deposited on a thin plate grown by the HPHT method. The process of growing diamonds by chemical vapor deposition has several advantages over the process at high temperature and high pressure. High pressure is not required in the CVD method, and the temperature is 800 °C, which significantly reduces the cost. Achieving high gas pressure and increasing the power of microwave discharges can provide a growth rate above 50 μm/h, which makes it possible to obtain single-crystal samples with a thickness of millimeters.¹⁴ 

Nevertheless, it is important to monitor the quality of the crystal obtained by the CVD method, in particular, it is necessary to avoid grain boundaries, as in polycrystalline films; otherwise, it will not be possible to produce an indenter-objective by mechanical polishing—it will chip off.

The control of defects in diamonds is important when they are supposed to be used for the production of devices. Since the diamond has a very dense crystal lattice, the introduction of foreign atoms into the diamond, i.e., the appearance of point defects, is difficult. However, some impurities in diamonds have been identified (a list of optically active defects can be found in Ref. 15).

Extended defects representing dislocations in concentrations from 10⁴ to 10⁶ cm⁻² are also detected in CVD diamond films. This is several orders of magnitude lower than in natural diamonds, but usually higher than the typical densities found in synthetic HPHT crystals (<10⁴ cm⁺²). The strong stress field that surrounds dislocations generates double refraction, which makes the use of such crystals unsuitable for optical applications requiring a high degree of uniformity.¹⁶ 

X-ray topography methods allow to visualize defects (dislocations, twins, inclusions, impurity inhomogeneities, etc.) present in the crystal volume, to determine their type, some characteristics, and distribution features. Compared with other methods of detecting defects (etching, decoration, electron microscopic studies of thinned crystals), x-ray topography methods have a number of significant advantages. In particular, they do not require crystal destruction, they are distinguished by high sensitivity and the ability to study the volumetric location and characteristics of a wide range of defects in relatively large samples.¹⁷ 

Cutting of diamond blanks is carried out using a laser, and further shaping them into the required shape is carried out by machining. At the moment, there is no laser cutting technology that would allow achieving acceptable surface roughness. The minimum possible roughness—no more than 0.5 nm can be achieved by polishing with different intensities depending on the crystallographic orientation of the diamond substrate relative to the direction of rotation of the cast iron grinding wheel (scaife). The optimization of the technology proposed in Refs. 13, 18, and 19 makes it possible to obtain super-smooth surfaces in a relatively short time of <10 min.

Such primary control of the tip geometry as the coincidence of the angles of inclination of the faces with the specified values can be carried out by confocal 3D profilometry.²⁰ High speed of measurements is one of the main advantages of this method in comparison with the contact method for determining the surface relief. However, for roughness control, it is necessary to use an atomic force microscope, since this device has a significantly higher spatial resolution than a 3D profilometer.

The performance quality of the indenter-objective can also be monitored using an optical dioptrimeter, which is a standard equipment used in the control of optical elements. An important feature of this device is the multiplicity of controlled parameters. First, it measures the optical force with an accuracy not worse than 0.1 diopters, that is, it is able to record the large-scale undulation and hilly surface of the indenter. Roughness, that is, poor optical quality, will manifest itself in the form of a haze surrounding the test optical image in the form of a circle consisting of bright dots. The blurring of the points forming a circle in one of the directions indicates the cylindrical nature of the part being tested. A key feature that is extremely important when testing an indenter-objective is the ability to measure the deviation of the light beam from the optical axis of the diopter. This feature allows you to find the center of the lenses and fix the level of their wedge shape. The image of the test circle observed through the indenter-objective splits into three circles, since such an indenter behaves like three plane-parallel plates rotated at an angle of 120°. Ideally, all these three circles should merge into one with minimal mutual displacement. In reality, with the classical method of cutting with the interception of the indenter-objective in the collet clamp and the formation of the second vertex in an independent way, the misalignment of the planes and the resulting wedge shape reached several tens of mrad. Such a level of plane-parallelism mismatch significantly spoiled the image synthesized by rotating three sectors. The use of a new technique for sharpening the indenter by gluing it onto a pre-formed face made it possible to reduce the wedge shape to a level of less than 1 mrad, which is quite acceptable, and allows you to work with a large magnification in all three sectors simultaneously.

A disadvantage of the HPHT method is that diamonds are in contact with nitrogen during the growth process, which results in a yellowish and brownish tint. For simple observations of the indentation area, the coloring of a transparent indenter is not a significant obstacle. However, for spectroscopic studies through an indented-objective, the presence of spurious peaks in the spectrum is undesirable. The presence of impurities, in particular nitrogen, widens the peaks in the Raman spectrum of diamond. Saturation of diamond with boron leads to a shift in the peaks' intensity and to an increase in the intensity of the background spectrum.^21–24 

During measurement, the contact area (as well as spectra collecting area) is usually more than 1 μm², so significant image distortions or other artifacts due to diffraction effects are neither expected nor observed. For problems where the resolution requirements are higher, the impact of diffraction shall be analyzed in detail.

The simplest and most obvious application of this type of indenter is the possibility of optical imaging during indentation and observation of the indentation or scratching process in live video mode. One shot from such a video is shown in Fig. 8. Of particular interest in this kind of observation is the behavior of the material outside the area of direct contact between the indenter and the material, that is, the area that is inaccessible when observed through a conventional pyramidal indenter. This possibility in combination with the increasingly popular methods of digital image correlation (DIC)^25,26 opens up wide possibilities for studying the dynamics of deformation processes along the perimeter of the print. By using TTI with a confocal optical 3D profilometer, it is possible to study the details of formed pileups, for example, is height correction required for precise measurements.

The proposed approach makes it possible to simplify the task of targeted positioning of the indenter vertex. It also opens up the possibility of quantitative measurement of the unrecoverable imprint and analysis of the nature of deformation of the sample surface and the formation of cracks in it, plastic bulk and elastic deflection of the surface contour directly during the test (indentation, scratching, etc.). Moreover, by a detailed analysis of the brightness of the indentation area, it is possible to register a change in the reflection coefficient from the diamond face at the place of direct contact of the diamond with the deformed surface, which allows determining the size of the actual contact area of the material with the indenter.

This circumstance is especially important when working with elastic materials and materials with a high level of elastic recovery of the print. At the same time, there are no restrictions on the level of transparency of the tested material. Since optical and spectrometric observations occur from the side of the diamond indenter-objective, the requirement for transparency of the sample is eliminated.

It is possible to use TTI for studying the properties of very soft organic material. For this area of research, we do not set up any limitations for the usage of transparent indentor. We do not know of such experiments, except for pharmacology application, which is discussed further.

Such opportunities are important when working with heterogeneous materials with a grain size in the range of (1–100) μm,²⁷ and various kinds of multilayer coatings that can peel off during operation.^28,29

Localization of pressure induced phase transitions, provided we know what the strained state is there, allows us to find out at what pressure magnitude the transition occurs. There are many simulations^30,31 of indentation experiments with Berkovich tip, and one may use them to find out details about strain distribution. Detailed information about the change in the properties of the material during indentation and variability along the surface can be obtained by using optical spectroscopy methods by observing the sample through an indenter-objective. An example of setting a task for this kind of research can be the article,³² where the authors try to distinguish different crystalline forms of a molecular crystal by purely mechanical methods. The connection of Raman spectroscopy methods carried out through an indenter-objective to the problem they are solving would significantly expand the amount of information received and confidently distinguish different conformational states.

An example of this kind of investigation of the process of diamond-like carbon (DLC) film detachment, that is, changes in the state of matter, using Raman spectroscopy is the work.³³ This can be done by registering shifting and changing the width of peaks on the spectra (for example, by raster scanning).

In Ref. 33, it is shown that by mapping the Raman spectra, the region of DLC film detachment can be clearly observed. However, the film remains continuous. 3D image of the indent is shown in Fig. 9.

This experiment, or the similar one, is the best example of how the results obtained with TTI correspond with others.

Under pressure, phase transformations occur in a number of materials. In various applied fields such as superconductivity and pharmacology, the production of amorphous alloys, the conditions under which these transitions occur, the stability of the formed phases, and their other properties are studied.^34,35

With developed plastic deformation, phase transitions and states that are stable only in the stressed state are often observed in the substance. Examples of this kind of research are the works in Refs. 11 and 36.

The data obtained using an indenter-objective and a Raman spectrometer unambiguously indicate the occurrence of well-known silicon phases in the indentation region. Measurements of the Raman shift were made at a fixed position of the focusing area of the probing laser radiation relative to the tip of the indenter. At the same time, as the load on the indenter increases and the area of the material subjected to plastic deformation expands, a well-noticeable change in the measured Raman spectrum occurs.

This change of spectrum is due to the high level of heterogeneity of the stress state of the material in the area under the indenter and a kind of averaging of the recorded spectrum, in both area and depth of the material under study. This circumstance—the averaging of the measured spectrum over the area of the illuminated spot—should be taken into account when studying the stress state of the material and the resulting phase transitions.

A relevant study of silicon phase transformations under pressure during indentation is Ref. 37, where the authors use Raman microspectroscopy. They have detected the formation of metastable Si phases. If one can localize phases and provided that the distribution of strain in sample is known from simulations, one can figure out at what pressure the transition starts. Spectra quantitative comparison is provided in Ref. 12.

Modern optical spectroscopy has a wide range of methods for studying various properties of materials. In this work, the elastic modulus of transparent samples and their change during indentation were determined using a diamond indenter-objective and the method of spontaneous light scattering spectroscopy on thermal vibrations in solids (acoustic phonons). This method, provided that the angle of incidence of light varies and the polarization of the incident laser and the detected scattered radiation are controlled, makes it possible to measure the full tensor of the elastic modulus.³⁸ For the optical configuration of the indenter-objective, the determination of all components of the elasticity tensor is difficult due to physical limitations on the magnitude of the angle of incidence of radiation on the sample. At the same time, the main parameter used to determine elastic constants is the spectral shift of the Mandelstam–Brillouin radiation line.³⁹ As noted above, the input of a laser beam and the registration of a spectral signal through a transparent diamond indenter are performed in the geometry of reverse 180° scattering. Spectral measurements carried out at several points were taken, and the most diverse data were obtained at contact and pileup zones. Spectra are shown in Fig. 10.

A single peak corresponding to the scattering of laser light on longitudinal acoustic phonons is observed in the radiation spectrum of isotropic materials. The spectral shift of this peak v makes it possible to calculate the velocity of longitudinal acoustic waves V in the medium and the elastic modulus E of the P-wave, knowing the wavelength of the laser in vacuum, the refractive index, and the density of the material.⁴⁰ 

The sample was brought to the indenter using a micrometer screw until an image of the indenter print appeared on the microscope camera (Fig. 10). Then, with a fixed supply, scattered radiation spectra were recorded at selected points along the sample surface and in depth. The data on the shift of spectral lines obtained by fitting the Stokes component of the pseudo-Voight curve allow us to obtain a spatial distribution of the dependence of the velocity of acoustic waves (elastic properties of the medium) in the deformation region created by the tip of the indenter. Calculations were made under the assumption of a constant density of the material. Without such assumption, one may expect that in the region of plastic deformation, the speed of sound will increase even more due to the density increase under isotropic compression.

Spectral measurements were carried out using a microscope “Nanofinder 30A/Brillouin/Raman” (Tokyo Instruments, Japan). An exciting laser with a wavelength of 532 nm was used, lenses 10X0.25 and 20X0.45. Characteristic spatial resolution for such measurements lies in the range of 10–40 μm, depending on the lens used.

Figure 10 shows the Mandelstam–Brillouin scattering spectra measured along the sample surface at several points. Figures 11 and 12 show the dependences of the calculated acoustic velocity as a function of the distance from the top of the indenter along the surface and into the depth of the sample. The calculations assumed the value of the refractive index to be constant and equal to 1.5983 (at a wavelength of 532 nm).

The conducted studies have shown the possibility and prospects of applying Mandelstam–Brillouin confocal spectroscopy to the problems of studying the distribution of mechanical properties of transparent samples when exposed to them with an indenter-objective.

Just like any other indenter tip, the transparent diamond indentor, which we presented here, is wearing during exploitation. How long does take to round the tip depends on what type of experiment is being performed (indentation/scratching/other) and on what sample is made of. For soft samples like polymers, it is known that the tip may remain sharp during thousands of indentations; meanwhile, scratching ceramic may cause indenter breaking quite soon. It is required that tip's rounded area is less than 10% of full contact area. One may check imperfection of tip with the standard procedure of obtaining dependency for contact area on indentation depth.

For indentor transparency, it is also necessary to keep it clean. For tip cleaning, we recommend to push it into soft material like polytetrafluoroethylene or polycarbonate.

The results presented in this work indicate broad possibilities for the use of the proposed indenter-objective design for comprehensive studies of the complex tense state of matter under the indenter, studies of heterogeneous materials, studies of multilayer coatings, and phase transitions inherent in various types of deformation and microfracture modes of matter. Especially promising is the coupling of optical methods with the mode of instrumented indentation, which has wide possibilities in terms of mapping the mechanical properties of any materials. TTI technique allows collecting data from both loaded and not loaded areas under an indentor, when the load is applied. The combination of advanced methods of optical and mechanical tests in one device is of undoubted interest for a wide range of researchers.

The study was carried out using the equipment of the TISNCM Center of Collective Use. The authors acknowledge I. Kudryashov and K. Budich from Tokyo Instruments, Japan for conducting experiments on Raman-Brillouin spectra measurements.

The authors have no conflicts to disclose.

A. Useinov: Conceptualization (equal); Investigation (equal); Supervision (equal); Writing – original draft (equal). V. Reshetov: Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). A. Gusev: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal). E. Gladkih: Investigation (equal); Methodology (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.