1. Introduction

Electromagnetic wave absorbers are important components in military and civil applications such as stealth, antennas, and integrated circuits designed to suppress radar cross-sections, electromagnetic stray waves, and interferences. When developing absorbers, it is important to ensure the optimal choice of constitutive materials, composition, and design of their structure to meet the increasing requirements for the performance characteristics of absorbers. To date, the development of absorbers relies on progress in several fields of modern science and technologies including material chemistry, polymer science, solid-state physics, optics, and electromagnetic theory (see textbooks [1,2], recent reviews [3–6] and references therein).

At present, the development of electromagnetic wave absorbers has been performed within the framework of the theory of metamaterials, which makes it possible to create electrically thin absorbers (in radio-engineering language, it means the same as optically thin, i.e., much thinner than the wavelength of the incident radiation). The main functional component of such absorbers is an impedance-matching layer that ensures the non-reflective operation conditions of the structure. Typically, such a layer is implemented in the form of a frequency-selective surface characterized by some reactive averaged surface impedance [7,8], which is made of a dense array of conductive patches [9–15]. The metamaterial-based absorbers have been implemented for spectral ranges from microwaves to visible [16–19] (see also a comprehensive review [20] on a general theory of electrically thin absorbers).

There are additional specific requirements for absorbers when they are used in harsh environments, typical for aerospace applications where high temperature and corrosion are a concern. Here, much interest is focused on studying various high-temperature absorbers made using novel materials with excellent electromagnetic wave absorption properties. These are high-temperature lossy ceramics, metal oxides, as well as carbon-based nanocomposites [21–25]. Although such bulk materials provide good absorption of electromagnetic radiation being sufficiently thick, the implementation of electrically thin absorbers requires conductive materials for fabrication of the patches able to withstand high temperatures. Of the possible materials that can satisfy this request, the best candidates are titanium and its alloys, since in addition to being lightweight, they have good conductivity, resistance to high temperatures, and corrosion [26]. In particular, several titanium-based absorber designs have been proposed for the microwave, infrared, and visible parts of the spectrum [27–32].

Therefore, it is important to involve new methods from titanium material science and assess their applicability for designing electrically thin metamaterial-based absorbers. Among such methods, there is a particular interest in titanium powder metallurgy techniques [33,34], especially blended elemental powder metallurgy (BEPM) [35]. Compared to other manufacturing techniques, BEPM makes it possible to cost-effectively produce a wide range of high-quality titanium alloys and structures based on them. The most cost-effective BEPM processes are based on the technology where alloying elements are added to titanium as elemental or master alloy powders. Traditionally this method includes the preparation of powder blends, their consolidation at room temperature, and sintering in a vacuum for the transformation of initial heterogeneous powder compacts into massive homogeneous alloys. Consolidation may be performed by low-cost conventional powder metallurgy processes such as die pressing, cold isostatic pressing, or direct powder rolling. The benefits of BEPM are alloy flexibility, refractory materials, homogeneity, near-net shape manufacturing, and cost-effectiveness, whereas the natural drawbacks are purity concerns, sintering challenges, and porosity [36].

Previously we have studied the mechanical properties and structure of TC4 alloys prepared with BEMP [37–39] (we should note that in the BEMP, TC4 alloy is one of the most commonly used). In the present paper, we extend the scope of our research to demonstrate the ability to produce low-cost titanium alloy parts for electrically thin metamaterial-based absorbers. In this regard, we perform a comparative study of structures consisting of titanium patches fabricated by using BEPM. To elucidate the differences in absorption properties of structures composed of titanium patches prepared under different conditions of the BEPM technological process, we utilize a well-known thin absorber design based on an artificial high-impedance surface [13,14]. This surface is an array of subwavelength square patches arranged on a lossy ceramic substrate. To ensure zero transmission, the structure is placed on a metal screen. A detailed description of the titanium alloy fabrication process, full-wave numerical simulation of the metamaterial-based absorber, methods of preparation of samples and their experimental characterization supplements this study. Based on the instrumental capabilities at our disposal, the microwave frequency range ($8-12$ GHz) was selected for the validating experiment.

2. Microwave absorber design

2.1 Outline of the problem

Our goal in this study is to evaluate the feasibility of using titanium alloys in the construction of an electrically thin metamaterial-based absorber, given that these alloys are prepared under different conditions of the BEPM process. Since we mainly focus on comparing the properties obtained for a constitutive material, here we use a well-known high-impedance surface design to implement a metamaterial platform of the absorber. This is a surface composed of a dense array of rectangular patches of the size $w$ and thickness $h_p$ that are supposed to be made from titanium with the conductivity $\sigma _\textrm {Ti}$. The patches are arranged in a lattice with the period $p$ deposited on a lossy dielectric substrate. The substrate is made from microwave ceramics with the thickness $h_s$ and relative complex permittivity $\varepsilon _\textrm {sub}$. On the back side, the structure is supported by a metal sheet (ground plate) to create conditions similar to the practical use of microwave absorbers.

Further, for definiteness, we assume that the structure is normally irradiated by a linearly polarized wave ($\textbf {k} = \{0,0,-k_z\}$), in which the electric field vector is oriented along the $y$-axis ($\textbf {E} = \{0, E_y, 0\}$). All characteristic dimensions of the structure, the orientation of the electromagnetic wave vectors of the incident wave, and the chosen Cartesian coordinate frame related to the problem under study are presented in Fig. 1.

 

Fig. 1. A sketch showing all the characteristic dimensions of an electrically thin metamaterial-based microwave absorber consisting of titanium patches periodically arranged on a lossy ceramic substrate supported by a metal sheet. Here, $p$ is the lattice constant, $w$ is the square patch width, $h=h_p+h_s$ is the overall sample thickness, and $\sigma _\textrm {Ti}$ and $\varepsilon _\textrm {sub}$ are the conductivity and permittivity of titanium and ceramics, respectively. The red dashed square outlines the array unit cell. The insets show the Cartesian coordinate frame and the configuration of the incident wave.

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2.2 Titanium patches preparation

Our comparative study is carried out by preparing and utilizing three different sets of patches for the absorber assembly. Of the three sets, one serves as a reference, which is made of a commercially available Ti–6Al–4V (TC4) titanium alloy, while the other two sets are prepared from self-fabricated alloys using BEPM.

In particular, the reference titanium material is purchased in the online store in the form of sheets with a thickness of $0.2$ mm. It is prepared by using conventional (non-powder) metallurgy techniques. All parameters of this material are specified by the manufacturer in the datasheet. Moreover, we additionally verified these parameters with our measurements, and a good correspondence was found. Measurements made by densitometer ETNALN (ET-320D) using the Archimedes method showed that the density of this material is $4.420$ g/cm$^3$, corresponding to generally accepted density values for the standard TC4 alloys. In what follows, we denote this material as ‘TC4-1’.

Two self-made materials are prepared from titanium powder using previously developed BEPM technique [38,39]. The fabrication procedure consists of several stages. First, the titanium sponge was heated and hydrogenated in a sintering furnace Sincere (WM121224), then milled in omni-directional planetary ball mill QM (QX2) and sieved to obtain TiH$_2$ powder with the desired particle size distribution ($120$ mesh). The master alloy powder is 60Al40V ($600$ mesh). The powders were mixed together in high efficiency double cone mixer NF-SB (ZX-0.02m3), the proportions suitable for producing the Ti–6Al–4V alloy and then blended for $4$ hours. The mixture was transferred to a die and subjected to cold isostatic pressing at $350$ MPa for $5$ min. Then the alloy was placed in a vacuum furnace and subjected to sintering at $1200^\circ$C with a heating rate of $10^\circ$C/min, isothermal holding for 4 hours, and finally, furnace cooling. The relative density of the material produced at this stage is 98.6%. We denote it as ‘TC4-2’.

Next, we apply mechanical processing for a part of the obtained TC4-2 material by performing the rolling. Hot rolling is a treatment for the BEMP alloys to reduce the porosity of the fabricated sample and increase its structural strength. The hot rolling takes place at $920^\circ$C with a rod roll forging machine ZHIKE (ZK-WS9F3) to obtain deformation with the cross-section reductions of 88%. After the rolling, the relative density of the material increases up to 99.8%. We denote this final material as ‘TC4-3’ (all additional information about TC4-2 and TC4-3 alloys characteristics, namely mechanical properties, phase compositions, microstructures, X-ray diffraction patterns, etc., one can find in Refs. [37–39]).

We apply two different fabrication procedures to produce the patches from the obtained titanium alloys. In particular, to fabricate the square patches from the sheet of the reference TC4-1 material, the high-precision CO$_2$ laser Sanke (40 W) was used. Respectively, rectangular prisms with dimensions of $4 \times 4 \times 50$ mm$^3$ were formed from the bulk TC4-2 and TC4-3 materials, from which patches were then produced by the electrical discharge machining (EDM) cutting method with the use of the HNK (HND320A) machine. The final geometric dimensions of the patches produced by these two methods coincide. They are $h_p=0.2$ mm and $w=4.0$ mm. The photos of the materials at the pre-fabrication and post-fabrication stages, as well as final patches made on their basis, are presented in Fig. 2(a).

 

Fig. 2. (a) Stages of fabrication of titanium patches and (b) photo of the samples of a metasurface-based absorber related to a ruler with a millimeter scale. Here $p=5.0$ mm, $w=4.0$ mm, and $h_p=0.2$ mm.

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We should note that using EDM results in some unwanted modification of the surface of patches which may reduce their conductivity. In particular, such a modification appears when the doped or carbon-based coolant is used as a dielectric medium in the EDM cutting. After the cutting, the surface of TC4-2 and TC4-3 alloys acquired oxidation due to the extensive heat and interaction with de-ionized water with EDM machine working fluid SOAP (dielectric medium). Therefore, we have performed mechanical grinding to the shiny surface to restore the conductivity of the patches.

The electrical conductivity of the reference and self-fabricated materials was measured by the four-point method [40] with the use of a power source GWINSTEK (GPD-33038), voltmeter Victor (VC890D), and custom-made probes. The radius of the probe tip is $0.3$ mm. During the measurements, the distance between adjacent probes is set at $1.0$ mm. The conductivity was measured three times for each sample at different probe positions. Since samples of the TC4-1, TC4-2, and TC4-3 alloys have different thicknesses and forms, the corresponding geometric correction factors for the sheet and bars with a rectangular cross-section are accounted for (see details in Ref. [41]). All measurements were performed at room temperature with 50% relative humidity. The measured conductivity and relative density of the materials prepared for this study are collected in Table 1. From the results obtained, it is clear that the conductivity of the TC4-2 and TC4-3 materials prepared by BEPM deteriorates somewhat after the post-fabrication stage, but remains at an acceptable level for implementing an electrically thin metamaterial-based absorber (this decrease in conductivity is associated with the residual manifestation of the oxidation of titanium, which occurs during EDM cutting). In fact, the measured conductivity values from Table 1 for pre-fabricated TC4-1, TC4-2, and TC4-3 alloys differ from the known conductivity of the Ti–6Al–4V alloy ($\sigma _\textrm {Ti} = 5.88\times 10^5$ S/m; see Table B.9 in Ref. [42]) by 1.7%, 2.9%, and 4.4%, respectively.

Table 1. Conductivity and relative density of the TC4 titanium alloys used for the patches fabrication

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2.3 Sample assembly

To test the performance of the resulting titanium materials, three metamaterial-based absorber prototypes were fabricated. To do this, the patches were fixed on the top side of a lossy dielectric substrate. They are arranged manually one by one with the use of a removable 3D-printed mask. The substrate is made of commercially available Al$_2$O$_3$-based JingWei-95 corrosion-resistant ceramics. The thickness of the layer is $h_s = 1$ mm, and according to the manufacturer’s datasheet, the relative permittivity of the ceramics is $\varepsilon = 9.25$, and the electric loss tangent is $\tan \delta \approx 0.01$ ($\varepsilon _\textrm {sub} = 9.25+i0.09$). The transverse size of the ceramic plate is $100\times 100$ mm$^2$ which allows us to dispose of 256 patches on it by constructing the array with the lattice period $p=5$ mm (i.e. the actual high-impedance surface is composed of $16 \times 16$ unit cells). To imitate a metallic ground plate, on the bottom side, the ceramic substrate is covered by adhesive copper foil with a thickness of $0.04$ mm. The photos of the fabricated samples of the metamaterial-based absorber consisting of patches produced from the TC4-1, TC4-2, and TC4-3 titanium alloys are shown in Fig. 2(b).

2.4 Numerical simulation

The full-wave numerical simulations of the absorber’s electromagnetic characteristics are performed using the commercial finite-element COMSOL Multiphysics solver. In the framework of the RF module of the solver, the Floquet-periodic boundary conditions are imposed on four sides of the unit cell to simulate the infinite two-dimensional array of patches. At the bottom side, the computational domain is terminated by the perfectly electric conductor (PEC) boundary. We dispose of a single port above the structure to radiate and receive plane electromagnetic waves with a required linear polarization. The port boundary conditions are placed on the interior boundary of a perfectly matched layer, adjacent to the air domain. This perfectly matched layer on the top of the unit cell absorbs the waves reflected from the structure and prevents unwanted re-reflection of the scattered fields inside the computational domain. The port boundary conditions automatically determine the reflection characteristics of the structure in terms of S-parameters. After simulation, we retrieve values of the reflection coefficient magnitude ($|R| = |\textrm {S11}|$) as a function of the frequency. Since the structure is terminated with the PEC boundary, there is no transmission, and the total absorption can be calculated as:

To estimate the basic characteristic of the structure under study as well as its operating frequency, we use an analytical model from Ref. [43] (see Appendix).

2.5 Measurement technique

We use a monostatic test bench with an open-ended waveguide to measure the reflection and absorption characteristics of our metamaterial-based absorber over a selected frequency range. We use an experimental method proposed earlier to measure the absorption level of microwave absorbers [44]. This method is based on the fact that standing waves occur between the antenna aperture and absorber due to a mismatch of the absorber impedance and the impedance of the free space (it resembles multiple reflection conditions existing between a mismatched generator and a load [45]). Therefore, the reflection and absorption characteristics of the structure can be obtained by measuring the reflection coefficient of the sample and several reference loads. They are the reflection coefficients of free space ($\textrm {S11}_\textrm {freespace}$), sample ($\textrm {S11}_\textrm {sample}$), and a metallic plate of the same size as the sample ($\textrm {S11}_\textrm {PEC}$). Then, the reflection coefficient of the metamaterial-based absorber can be calculated according to the next equation [44]:

In our experimental setup, the WR-90 open waveguide (AV-71135M) with a small aperture size ($22.86 \times 10.16$ mm$^2$) is used as an antenna. The waveguide is connected to the first port of the calibrated Rohde & Schwarz ZVA-50 vector network analyzer (VNA) via a $50$ Ohm coaxial cable. The sample is placed on a table covered by an RF absorber. The distance between the sample and waveguide edge is $60$ mm, which is the thickness of the polyethylene foam plate through which the measurements are taken. All measurements are conducted in an anechoic chamber at room temperature. The experimental setup used for this study is presented in Fig. 3 just for reference.

 

Fig. 3. Experimental setup for the measurement of reflection and absorption characteristics of a metamaterial-based absorber composed of titanium patches.

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3. Results and discussion

In the first stage of our study, we validate our numerical model of an electrically thin metamaterial-based absorber implemented in COMSOL by comparing the values of the reflection coefficient magnitude obtained in Ref. [14] and by our simulations for a structure with the same material and geometric parameters. In this initial model, all metallic elements of the absorber are assumed to be infinitely thin and made of PEC, while the dielectric substrate has thickness $h_s = 3.0$ mm and relative complex permittivity $\varepsilon _\textrm {sub} = 9.0+i0.222$ (these parameters correspond to the structure presented in Fig. 2 of Ref. [14]). The results are also referenced to those obtained from an analytical model (for the parameters of the analytical model, see Ref. [43] and Appendix). Then, to move on to using actual materials, we substitute PEC conditions for the patches with a finite thickness by values of conductivity corresponding to the TC4 titanium alloys listed in Table 1. The results of all these calculations are depicted in Fig. 4(a).

 

Fig. 4. Comparative curves of the simulated reflection coefficient magnitude (in decibels) and absorption coefficient (in percentages) of an electrically thin metamaterial-based absorber composed of patches made of PEC and TC4-1, TC4-2, and TC4-3 titanium alloys for two different thicknesses of the dielectric substrate. Breaks are inserted on the ordinate axes to demonstrate the differences in curves in an enlarged scale. The corresponding values of conductivity of titanium alloys are listed in Table 1 and the permittivity of the ceramic substrate is $\varepsilon _\textrm {sub} = 9.0+i0.222$. Here (a) $h_s=3.0$ mm, $w=4.9$ mm, and (b) $h_s=1.0$ mm, $w=4.0$ mm, while all other geometric parameters of the structure are given in the caption to Fig. 2.

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It can be concluded that all obtained numerical data are in good correspondence with each other and with the results of the analytical model. The structure has a resonance in absorption at a frequency of $3.2$ GHz with a level of $-30$ dB in theory, which is fully consistent with the results of Ref. [43], thereby verifying our numerical model. For this structure based on PEC, the resonance is quite narrowband, where the corresponding absorption peak reaches almost 100%, as is typical for electrically thin metamaterial-based absorbers. However, the results obtained from the full-wave numerical simulation of the structure based on patches made from ether PEC or titanium alloys demonstrate lower levels of absorption compared with the analytical prediction. This inconsistency in the analytical and numerical results is a solver artifact that depends on the density of the mesh, which COMSOL generates during the calculation (in this study, we use the default physics-controlled settings of the solver for normal mesh generation; in the case of using normal/fine/finer/extra fine mesh, our results do not change significantly, the value of reflection changes is less than 0.05 dB, and frequency changes are 0.05 GHz). The levels of absorption obtained in simulations are practically the same for all structures, regardless of whether they are made of PEC or titanium alloys. However, the absorption levels in these calculations are still quite high and are about 99.5%.

However, our numerical model must be further modified to provide operation of the structure in the specified frequency range ($8-12$ GHz). From the theory of electrically thin absorbers, it is known [20], that the change in the array period affects the surface impedance, while the thickness of the dielectric substrate determines the position of the resonance on the frequency scale and its bandwidth. Therefore, we fix the period and permittivity of the substrate while reducing its thickness and the width of patches to find corresponding geometric parameters of the structure that can be fabricated. In this parametric study, we estimate the operating frequency of the structure and its absorption performance using the analytical model. It is found that the acceptable structure characteristics can be obtained with parameters $h_s = 1.0$ mm and $w = 4.0$ mm, therefore, this structure was subjected to subsequent full-wave numerical simulations in COMSOL. The results of these simulations are presented in Fig. 4(b).

For the structures with a modified design, besides the fact that their resonant frequency shifts to the desired region around $9.28$ GHz, the bandwidth increases from $2$ GHz to $3.5$ GHz. The structures containing titanium patches with finite conductivity exhibit a slightly lower absorption level compared with those made of PEC. Our estimates show that when replacing PEC with titanium in the model, the absorption level decreases by 0.2%, 0.5%, and 1.6% for the TC4-1, TC4-2, and TC4-3 titanium alloys, respectively. Another peculiarity of the structures composed of titanium patches is that their corresponding resonances experience a slight red frequency shift. In particular, the frequency shift is $0.01$ GHz, $0.07$ GHz, and $0.08$ GHz for the structures made from the TC4-1, TC4-2, and TC4-3 titanium alloys, respectively, compared with the resonant frequency of the structure made from PEC. This frequency shift can be explained by the fact that the decreased conductivity of the titanium patches changes the balance of impedance matching conditions for the selected metasurface parameters, which also causes deterioration in the absorber characteristics. Nevertheless, based on the results of this preliminary numerical modeling, the overall conclusion can be made that although the finite conductivity of titanium somewhat reduces the absorption level of the structure, it remains satisfactory for the implementation of absorbers. Thus, the impedance matching provided by a surface consisting of patches made from titanium alloy is quite robust against conductivity degradation, which is also important when considering the use of the absorber at high temperatures where conductivity may become even lower [46].

Finally, we proceed to the results obtained in the microwave experiment. Since we do not have the necessary means for the production of ceramics, to prepare experimental samples of the absorber, we searched on the market for available materials whose dielectric properties are closest to those studied numerically. The necessary ceramics were found in the form of ready-made plates with the required thickness ($h_s=1.0$ mm), but having dielectric properties slightly different from the specified ones ($\varepsilon =9.25+i0.09$). To take this difference into account, the numerical model in COMSOL was refined, and new simulation data were collected. Then the corresponding measurements of the fabricated samples were carried out and all the results obtained were summarized in Fig. 5.

 

Fig. 5. Comparative curves of the simulated (dashed lines) and measured (solid lines) reflection coefficient magnitude (in decibels) and absorption coefficient (in percentages) of an electrically thin metamaterial-based absorber composed of patches made of TC4-1, TC4-2, and TC4-3 titanium alloys. The corresponding values of conductivity of titanium alloys are listed in Table 1 and the permittivity of the ceramic substrate is $\varepsilon _\textrm {sub} = 9.25+i0.09$. Here $h_s=1.0$ mm, $w=4.0$ mm, while all other geometric parameters of the structure are given in the caption to Fig. 2.

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At once, one can notice that the results of our simulation and experiment agree quite well when we consider that the significant reduction in absorption of actual structures arises from the much lower level of losses existing in commercial ceramics. Our experimental results confirm that the resonance in absorption appears at $9.16$ GHz, $9.21$ GHz, and $9.07$ GHz for the structures made of the TC4-1, TC4-2, and TC4-3 titanium alloys, respectively. The reflection value for the absorber based on the reference TC4-1 alloy is only slightly different from the corresponding COMSOL simulation data, whereas those for structures based on the TC4-2 and TC4-3 alloys differ more significantly, having a lower level of absorption approximately in 2 dB. However, the order of the appearance of the resonances on the frequency scale in the experiment is the same as in the simulation.

The absorption values of the structures made from the TC4-1, TC4-2, and TC4-3 titanium alloys are correspondingly 91%, 84%, and 80%. The lower absorption level of structures based on the self-fabricated BEPM alloys can be explained by the poor surface quality of patches that deteriorates their conductivity and brings imperfections in the surface of fabricated samples, leading to lower impedance matching between the free space and absorber.

The experiment showed that (i) dense arrays composed of patches made from titanium alloys prepared by BEPM methods can be used to realize efficient impedance matching between a lossy layer and free space, (ii) the relatively low conductivity of the titanium patches leads to a slight increase in reflection and, consequently, a decrease in absorption, and (iii) titanium alloys obtained by BEPM methods can be used in designs of electrically thin microwave absorbers. However, in this case, the EDM cutting method should be improved or modified to ensure that the conductivity of the post-fabricated alloys is no worse than the pre-fabricated ones.

4. Conclusions

In summary, we have performed a comparative study of the characteristics of an electrically thin metamaterial-based absorber composed of patches made from different TC4 titanium alloys. We used a standard design of the structure based on a high-impedance surface composed of an array of rectangular conductive patches located on a lossy dielectric substrate. To experiment, we have prepared three sets of patches from commercial (non-powder) and self-made (powder) titanium alloys. The latter ones are made using BEPM. When assembling the structure, the patches are fixed to a layer of commercial lossy ceramics. To measure the absorption properties of the prepared samples in the frequency domain, we used standard microwave equipment only. All our experimental studies are complemented by an analytical model and full-wave numerical calculations.

We have confirmed that titanium alloys made by BEPM can be used for producing conductive elements of metamaterial-based absorbers targeted to operate in harsh environments. It is possible since the structure is tolerant to the slightly degraded conductivity of titanium alloys produced from the powder. Nevertheless, the fabrication technique of patches based on the EDM cutting method requires revision and further improvement to prevent deterioration in the conductivity of the patches while maintaining their electrically smooth surface. It must be admitted that the problem of the roughness of the resulting surface of patches remains unexplored until the end since this feature is not included in our simulation method. We consider that the issue of the surface roughness is a call for future study.