Realization of strong microwave absorption characteristics of Gd 5 Si 2 Ge 2 nanoparticles with materials data-driven discovery

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Bora, Bibhusita Mahanta, Shalabh Gupta, Praveen C. Ramamurthy, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3845175/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this study, we utilized a materials data-driven approach to investigate the microwave absorption characteristics of Gd 5 Si 2 Ge 2 nanocomposites. These results suggests that Gd 5 Si 2 Ge 2 nanocomposites possess highly efficient microwave absorption properties. It was observed that varying the loading of the Gd 5 Si 2 Ge 2 nanoparticles in a polymer matrix, such as polydimethylsiloxane (PDMS), resulted in changes in reflection loss (RL). However, it was also found that simply increasing the loading of the Gd 5 Si 2 Ge 2 nanoparticles in PDMS did not improve RL performance. To optimize the RL performance, we employed an electromagnetic data-driven methodology. Obtained results predict a remarkable RL of ≤ -60 dB for a composite containing 60 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS in the frequency range 8.2–18 GHz. This prediction was supported by experimental data, which showed a minimum RL value of -57 dB with multiple RL≤-10 dB bandwidth. These findings validate the proposed proof of concept of utilizing data-driven methodology to obtain broadband and robust microwave absorption characteristics in Gd 5 Si 2 Ge 2 nanocomposites. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Microwave absorption materials play a crucial role in a wide range of applications, from radar and communication systems to medical imaging and electromagnetic (EMI) interference shielding [ 1 – 4 ]. In telecommunications, microwave absorption materials are used to control the transmission and reception of signals through antennas and other devices [ 5 – 7 ]. In radar, the absorption of microwaves by materials allows for the detection and imaging of objects. In medical treatment, microwave absorption materials are used in procedures such as hyperthermia, in which cancer cells are targeted with high-energy microwaves to kill them [ 8 – 9 ]. The strong properties that make a material suitable for microwave absorption include its dielectric constant and loss tangent, which determine how effectively it can absorb microwave energy [ 10 – 11 ]. The development of new microwave absorption materials with improved performance is an active area of research, as these materials have the potential to significantly enhance the capabilities of a wide range of technologies [ 10 , 12 ]. Ferrites or a combination of electrical and magnetic materials have been proposed for microwave absorption [ 13 – 14 ]. However, reports on Gd-based materials for microwave absorption are limited. In our previous work [ 15 ], we studied the microwave absorption properties of Gd 5 Si 4 nanoparticles by incorporating them into a polydimethylsiloxane matrix (PDMS) and found that Gd 5 Si 4 nanoparticles loaded polymer nanocomposites exhibit better microwave absorption properties (Reflection Loss or RL) than some of the ferrites [ 15 ]. In another study, Gd 5 Si4 nanoparticles were loaded to PVB-PEDOT:PSS blends to tune the microwave absorption bandwidth (RL ≤-10 dB bandwidth) [ 16 ]. Gd 5 Si 2 Ge 2 has been reported for some of the potential applications such as healthcare applications [ 17 ]. However, its electromagnetic properties (permittivity and permeability) especially in high-frequency region (8–18 GHz) is not investigated before. Furthermore, optimization of filler loading in polymer matrix for the most realistic microwave absorption is another challenge [ 10 , 12 ]. Materials data-driven discovery have been reported to overcome such problems viz., it describes how a mathematical model of the electromagnetic response of a material can be used to simulate, predict, and optimize their microwave absorption performance [ 18 , 19 ]. The most promising microwave absorption characteristics of composites or hybrids could be realized through materials data-driven discovery [ 20 – 23 ]. This work aims to evaluate the microwave absorption characteristics, especially in X-band (8.2–12.4 GHz) and Ku-band (12.4–18 GHz) of Gd 5 Si 2 Ge 2 nanoparticles and optimize the Gd 5 Si 2 Ge nanoparticles loading in the polymer matrix (PDMS) which is widely used for electronics for microwave absorption with an electromagnetic data-driven method. Experimental Gd 5 Si 2 Ge 2 nanoparticles synthesis Polycrystalline samples of Gd 5 Si 2 Ge 2 were prepared by arc melting at the Materials Preparation Center of Ames Laboratory using > 99.99 wt.%.11 The samples were heat treated at 1273K for 24 h to reduce or eliminate the amount of orthorhombic I phase present in the sample. They were then cooled at a rate of 10°C/min. It is our experience that slow cooling produces a more phase pure sample than quenching. The sample was remelted six times, turning over each time to ensure homogeneity. The last melting was completed by shutting OFF power to the arc, allowing for the highest cooling rates to avoid the formation of neighboring phases. No further heat treatment was performed on the as-cast sample. This process usually leads to phase-pure alloys [ 24 , 25 ]. To obtain the submicrometer of Gd 5 Si 2 Ge 2 , the as-cast material was grounded in a mortar and sieved to obtain a powder with a particle size of 53 µ m or smaller. The particles were further processed by high-energy ball-milling using a SPEX 8000 M mill without adding any liquid processing agent. To prevent surface oxidation, all millings and subsequent manipulations were performed in a glove box under an argon atmosphere. In a typical milling procedure, 4 g of bulk powder was milled with ∼14.5 g of stainless-steel balls consisting of 2 balls of 11.1 mm diameter and 4 balls of 6.3 mm diameter. The powder was milled for 2 h. The bulk and all the ball-milled samples were analyzed for their particle size, morphology, composition, crystal structure, and magnetic properties [ 26 ]. PDMS- Gd 5 Si 2 Ge nanocomposites preparation The PDMS-Gd 5 Si 2 Ge 2 nanocomposites were synthesized through facile solution processing. Various weight percentages (wt %) of Gd 5 Si 2 Ge 2 nanoparticles viz., 1%, 10%, 50% and 80% were dispersed in PDMS and the curing agent (PDMS to curing agent ratio 10:1) was slowly added and kept for stirring another 20 minutes. Finally, PDMS-Gd 5 Si 2 Ge 2 mixture was poured into the X-band and Ku-band sample holders and dried in a vacuum oven at 60 ± 5°C (400 Torr pressure) for 6 h. Characterization The surface morphology of the Gd 5 Si 2 Ge 2 nanoparticles and PDMS-Gd 5 Si 2 Ge 2 nanocomposites were recorded using a scanning electron microscope (Zeiss ULTRA 55 SEM by GEMINI technology). The electromagnetic parameters (relative permittivity and permeability) of the samples were measured using a vector network analyzer (VNA, Agilent N5230A) through the industrial standard waveguide method. The full two-port calibration of the VNA (thru-reflect line or TRL) was carried out in the X-band (8.2–12.4 GHz) and Ku-band (12.4–18 GHz) and S parameters ( S 11 , S 21 , S 12 , S 22 ) were measured for the fabricated samples. From the recorded S -parameters, the complex permittivity ( \({\epsilon }_{r}= \epsilon ΄-i\epsilon ˝\) ) and permeability ( \({\mu }_{r}= \mu ΄-i\mu ˝\) ) were evaluated using standard Nicholson-Ross-Weir (NRW) method [ 27 , 28 ]. The microwave simulations of the PDMS-Gd 5 Si 2 Ge 2 nanocomposites were carried out using commercial computer simulation technology (CST- Microwave studio 2018) software [ 29 , 30 ]. Results and Discussion Figure 1 (a) shows the recorded TEM image of the synthesized Gd 5 Si 2 Ge nanoparticles. The particles were first deposited on a silicon dioxide substrate in another study [ 31 , 32 ]. A femtosecond laser was used in the pulsed laser deposition technique to obtain a non-thermal deposition which resulted in the same phase and composition of the original polycrystalline bulk target of Gd 5 Si 2 Ge 2 . The TEM sample was prepared by scraping off the deposited particles of Gd 5 Si 2 Ge 2 on a TEM grid. The smallest particle having a diameter less than 100 nm was identified and imaged on the JEM-F200 Cold FEG Electron Microscope at the Nano Characterization Center of Virginia Commonwealth University. The image shows a particle having a core of crystalline Gd 5 Si 2 Ge 2 phase and a small protective shell of an amorphous phase. The amorphous phase is considered to be Gd 2 O 3 formed due to exposure of the nanoparticles to the environment while taking them out of the glove box and while placing them on the TEM grids. The amorphous shell protects against further oxidation of Gd 5 Si 2 Ge 2 particles. The recorded surface morphologies of the synthesized Gd 5 Si 2 Ge 2 nanoparticles are shown in Fig. 1 (b-c) . The SEM images show Gd 5 Si 2 Ge 2 nanoparticles (70–100 nm) with irregular shapes and varying sizes. These irregular shapes have the advantage of providing a higher surface area and making it easier to form connections within the polymer matrix, which leads to reaching the percolation threshold easily [ 16 ]. The X-ray diffraction pattern of Gd 5 Si 2 Ge 2 nanoparticles, is shown in Fig. S1 ( Supporting information ) . Figure 1 (d) and Fig. 1 (e) show the variation of the real (ε′) and imaginary (ε″) parts of the complex electric permittivity of various Gd 5 Si 2 Ge 2 nanoparticles wt% loaded viz., 1%, 10%, 50% and 80% PDMS- Gd 5 Si 2 Ge 2 nanocomposite in the frequency range 8.2–18 GHz respectively. The real part represents the ability of a material to store electric energy and is related to the amount of polarization, while the imaginary part corresponds to the electric energy dissipation inside the material [ 14 – 18 ]. Similarly, the real and imaginary parts of complex magnetic permeability (µ′ and µ″) represent the storage and dissipation of magnetic energy respectively [ 33 – 36 ]. The recorded µ′ and µ″ of various Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS- Gd 5 Si 2 Ge 2 nanocomposite is shown in Fig. 1 (f) and Fig. 1 (g) respectively. As seen, the ε΄ value increases as the Gd 5 Si 2 Ge 2 nanoparticles loading to PDMS increases, for example, the ε΄ value varies from ~ 2.9, ~ 3.4, ~ 5.1 and ~ 6.3 for 1 wt%, 10 wt%, 50 wt% and 80 wt% respectively, whereas the ε΄ of PDMS was ~ 2.5. The corresponding recorded ε˝ of 1 wt%, 10 wt%, 50 wt% and 80 wt% respectively, were ~ 0.05, ~ 0.13, ~ 0.49 and ~ 0.7. The observed variation in ε΄ and ε˝ as the Gd 5 Si 2 Ge 2 nanoparticles wt% increases are thought to be due to interfacial polarization. The permeability of PDMS-Gd 5 Si 2 Ge 2 nanocomposites varies greatly between 12.4 and 18 GHz in presence of different Gd 5 Si 2 Ge 2 nanoparticles. This variation in permeability, which ranges from 1.15 to 1.37, can be attributed to limitations in the GHz range known as Snoek's limitation [ 12 ]. Additionally, multiple peaks in the permeability, with the highest peak being 1.37, may be caused by natural and exchange resonances. These fluctuations in permeability are largely due to factors such as hysteresis loss, domain wall resonance, natural and exchange resonances, and eddy current effects [ 33 – 36 ]. However, it is worth noting that domain wall resonance is more prominent at frequencies of 1-100 MHz, and hysteresis loss can be disregarded for weak applied fields [ 33 – 36 ]. It can be observed from Fig. 1 (a-f) that the electromagnetic response of the PDMS-Gd 5 Si 2 Ge 2 nanocomposites is primarily influenced by the Gd 5 Si 2 Ge 2 nanoparticles present in PDMS. This suggests that the electromagnetic responses of the system can be predicted and modeled. As previously mentioned, the dielectric constant values can have a significant impact on the reflection loss (RL) at specific thicknesses ( d ), and it is expressed as [ 8 – 12 ], $$\text{R}\text{e}\text{f}\text{l}\text{e}\text{c}\text{t}\text{i}\text{o}\text{n} \text{l}\text{o}\text{s}\text{s} \left(\text{R}\text{L}\right)=20log\left|\frac{{Z}_{in}-{Z}_{0}}{{Z}_{in}+{Z}_{0}}\right|\left(dB\right)$$ 1 Where Z in is the input impedance, which can in turn be written as, $${Z}_{in}={Z}_{0}\sqrt{\frac{{\mu }_{r}}{{\epsilon }_{r}}}tanh\left(j\frac{2\pi fd\sqrt{{\mu }_{r}{\epsilon }_{r}}}{c}\right)$$ 2 Where Z 0 is the characteristic impedance of free space (= 377 Ω) and c is the velocity of light. The RL value of -10 dB corresponds to 90% absorption and is preferred for real-time applications [ 8 – 16 ]. Figure 1 (h-k) illustrates the variation of RL for 1–9 mm of 1 wt%, 10 wt%, 50 wt% and 80 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite. It can be seen that the minimum RL value (RL min ) and the RL ≤ -10 dB bandwidth strongly depend on the Gd 5 Si 2 Ge 2 nanoparticles loading and corresponding thickness. As shown in Fig. 1 (j) , the RL min of -14 dB was obtained for 10 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite at 9 mm, and a significantly improved RL of -35 dB was obtained for 50 wt% Gd 5 Si 2 Ge 2 nanoparticles at 7 mm. However, the RL value was not very promising for 80 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite till 9 mm indicating that increasing the Gd 5 Si 2 Ge 2 nanoparticles loading in the PDMS will not improve the RL value. As depicted in Fig. 1 (h-k) , the RL min value is found to be dependent on the thickness of the sample. As the thickness increases, a shift towards lower frequency regions is observed. This can be attributed to the quarter wavelength resonance phenomenon, in which a specific matching frequency-thickness co-ordinate ( \({f}_{m}, {d}_{m}\) ) is associated with RL min . This relationship can be described mathematically by the equation [ 12 ], $${d}_{m}=\raisebox{1ex}{$n\lambda $}\!\left/ \!\raisebox{-1ex}{$4$}\right.=nc/\left(4{f}_{m}\sqrt{\left|{\epsilon }_{r}\right|\left|{\mu }_{r}\right|} \right) n=1, 3, 5\dots$$ 3 This equation illustrates that as the thickness increases, the RL min shifts towards lower frequency regions. Data-driven techniques are proving to be a valuable asset in the simulation of material response, as they not only reduce the time and costs associated with experimental runs but also enable the development of more efficient materials [ 18 – 23 ]. In the realm of microwave-absorbing materials, the utilization of these methods can lead to the creation of a set of normalized materials data sets [ 18 – 23 ]. This would facilitate the functionalization of the material response across a range of variables and allow for the application of data-driven techniques to fine-tune the synthesis process, ultimately leading to the identification of an optimal formulation, as illustrated in Fig. 2 . However, despite the potential benefits, the current state of research in the field of microwave absorbing materials has yet to fully embrace data-driven approaches for materials discovery. This lack of a systematic approach not only incurs additional time and resources but also hinders the advancement of the field in the search for novel microwave-absorbing materials [ 18 – 23 ]. It is believed that the integration of data-driven methods can greatly enhance our capability to simulate material response and optimize material performance [ 37 ]. To fully realize the RL and electromagnetic properties of Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite, the ε΄, ε˝, µʹ and µʺ were modeled based on data from experiments using 1 wt%, 10 wt%, 50 wt% and 80 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite. The model covers a range of Gd 5 Si 2 Ge 2 nanoparticles loading from 1 wt% to 80 wt%, with intervals of 0.5 wt%. Numerical models were employed to create a third-order polynomial function for each parameter using cubic spline interpolation [ 38 , 39 ]. This method was considered ideal as third-order polynomials require n + 1 data points to determine their coefficients, and cubic functions are commonly used in engineering to model physical systems [ 38 ]. Each of the four weight percentages were analyzed with the same frequency set, and each frequency response point tested between 12.4 GHz to 18 GHz for the four weight percentages could be fitted with an interpolating polynomial for modeling, as shown in Fig. 3 (a-d) using a Python code. As shown in Fig. 1 (h-k) and from Eq. 1 it was observed that RL min value is associated with a specific d value. In this work, a reverse engineering approach utilizing the genetic algorithm (GA) was employed to simulate and evaluate the optimal d value of Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite for achieving the best RL performance [ 40 ]. The GA is a type of optimization method that mimics the process of natural evolution and can be used to find the optimal solution to a problem by iteratively improving a solution through selection, recombination, and mutation [ 40 – 42 ]. To use GA to optimize the d value of a material to minimize RL, a "fitness function" representing the objective to be optimized must be defined. Herin, the fitness function is the RL that occurs for a given d value range of the material. The commercial CST-microwave studio (2018) software was used for the d value optimization, which has an in-built GA and microwave simulation integration function [ 40 ]. The highly non-monotonic and non-linear dependence of RL and filler loading make this simulation-assisted optimization framework an ideal candidate for achieving the best results. The predicted data sets (Fig. 3 (a-d) ) were used as an input parameter for the CST simulation with RL min target value to optimize the d value. The simulated RL min value and corresponding loading and the optimize d value are shown in Fig. 3 (e) . Through simulation, the optimized RL min value was found − 60.5 dB for 60 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite at 7 mm (Fig. 3 (e) ). Figure 3 (f) shows the predicted 3D RL plot with corresponding d (1–9 mm with 0.1 mm interval) and frequency of 60 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite. To verify the accuracy of the predictions, the 60 wt % Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite was fabricated (like previous) and \(\epsilon ΄\) , \(\epsilon ˝\) , \(\mu ΄\) and \(\mu ˝\) were measured in 8.2–18 GHz. The comparison of the predicted and experimental \(\epsilon ΄\) , \(\epsilon ˝\) , \(\mu ΄\) and \(\mu ˝\) were shown in Fig. 4 (a) , Fig. 4 (b) , Fig. 4 (c) and Fig. 4 (d) respectively. The comparison of the predicted and experimental dielectric loss tangent, \(tan{\delta }_{e}=\frac{\epsilon ˝ }{\epsilon ΄}\) , and magnetic loss tangent, \(tan{\delta }_{\mu }=\frac{\mu ˝ }{\mu ΄}\) are shown in Fig. 4 (e) and Fig. 4 (f) respectively. The rate of electromagnetic (EM) attenuation can be determined using the EM attenuation constant (α), which is calculated as, \(\alpha =Re\left[iw{c}^{-1}{\left({\epsilon }_{r}{\mu }_{r}\right)}^{\frac{1}{2}}\right]\) , where \(i=\sqrt{-1}\) []. Figure 4 (g) shows the variation of the predicted and experimental \(\alpha\) values (60 wt% Gd 5 Si 2 Ge 2 nanoparticles loaded PDMS nanocomposite) with frequency (GHz) and indicates that the experimentally obtained EM attenuation is stronger than the predicted attenuation. Figure 4 (h) shows a comparison of the experimental and predicted RL for a PDMS nanocomposite loaded with 60 wt % Gd 5 Si 2 Ge 2 nanoparticles with a thickness of 7 mm. The comparison of the simulated and experimental RL spectra in Fig. 4 (h) reveals an excellent match, with an RL min value of -57 dB achieved, validating the proof-of-concept of the data-driven method. Additionally, the fabricated optimized sample demonstrated a better absorption bandwidth (RL ≤ -10 dB), specifically within the range of 12 GHz-16 GHz, compared to the simulated RL. Conclusion In this study, we have demonstrated the effectiveness of using predictive modeling for the development of high-performing microwave absorption materials based on Gd 5 Si 2 Ge 2 nanoparticles. We used multidimensional mathematical models to optimize the electromagnetic response of Gd 5 Si 2 Ge 2 nanoparticles materials. These models allowed us to systematically determine the optimal loading of the Gd 5 Si 2 Ge 2 nanoparticles (60 wt%) to polymer matrix (PDMS), which we were then able to experimentally verify. The resulting PDMS nanocomposite exhibited an RL of -57 dB with multiple absorption bandwidth (RL ≤ -10 dB). This work presents a new and widely applicable methodology for materials discovery in the field of microwave absorption and marks the multidimensional mathematical models that have been used to fine-tune the electromagnetic response of materials for this purpose. Declarations Funding Declaration Work at VCU was partially funded by National Science Foundation, Award Number: 1726617, Project Investigator (PI): Prof. Ravi L. Hadimani. Competing Interest Declaration The authors declare no competing interests. Acknowledgement The authors would like to acknowledge Prof. K. J. Vinoy, Department of Electrical and Communication Engineering, Indian Institute of Science (IISc), India, for providing the VNA facility. Data Availability Statement Data sets generated during the current study are available from the corresponding author on reasonable request. References A. Iqbal, F. Shahzad, K. Hantanasirisakul, M. K. Kim, J. Kwon, J. Hong, H. Kim, D. Kim, Y. Gogotsi, C. M. 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Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3845175","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":267956258,"identity":"34d5c1f7-e831-4984-ba69-4d3bd1192ce9","order_by":0,"name":"Pritom J. Bora","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYBACxgYgkcDAwAPiHPhQASSZmRsIaWFsAGkB6mF8OOMMSAsjfi0wi0DWMBvztiEEcALmGcnHHzzccU/Gnr07TZp3Xm00fztQy4+KbbitmJGW2JB4ppiHh+fsNsm5247nzjjM2MDYc+Y2Hi05hg2JbQk8PBK52yTebjuW2wDUwszYRqwW3jnHcueTomWzIW9DTe4Gglp6niXOSDwD1HLm7MaHM44dyN0I1HIQn18M25MPfPy5I8Gevb13w4EPNXW5884fPvjgRwUeLRMSUCLiMJg8gFM9EMjzH0DRUodP8SgYBaNgFIxQAAAw9GH0pzr6sgAAAABJRU5ErkJggg==","orcid":"","institution":"Indian Institute of Science","correspondingAuthor":true,"prefix":"","firstName":"Pritom","middleName":"J.","lastName":"Bora","suffix":""},{"id":267956259,"identity":"8d021914-ce1f-4cbb-b4a9-a16e7fb0ff2a","order_by":1,"name":"Bibhusita Mahanta","email":"","orcid":"","institution":"Indian Institute of Science","correspondingAuthor":false,"prefix":"","firstName":"Bibhusita","middleName":"","lastName":"Mahanta","suffix":""},{"id":267956260,"identity":"da9ca6bc-f8a1-4fb3-af15-3f3b60a1aea9","order_by":2,"name":"Shalabh Gupta","email":"","orcid":"","institution":"Virginia Commonwealth University","correspondingAuthor":false,"prefix":"","firstName":"Shalabh","middleName":"","lastName":"Gupta","suffix":""},{"id":267956261,"identity":"532c4e3b-aafa-4b12-82e9-f2203b36a672","order_by":3,"name":"Praveen C. Ramamurthy","email":"","orcid":"","institution":"Indian Institute of Science","correspondingAuthor":false,"prefix":"","firstName":"Praveen","middleName":"C.","lastName":"Ramamurthy","suffix":""},{"id":267956262,"identity":"02150a06-5bab-4bc9-8c7f-7686b12e361e","order_by":4,"name":"Ravi L. Hadimani","email":"","orcid":"","institution":"Virginia Commonwealth University","correspondingAuthor":false,"prefix":"","firstName":"Ravi","middleName":"L.","lastName":"Hadimani","suffix":""}],"badges":[],"createdAt":"2024-01-08 10:44:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3845175/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3845175/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49980414,"identity":"78813fe7-fe0d-485c-a33a-4fa4788dc123","added_by":"auto","created_at":"2024-01-22 15:30:15","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":674340,"visible":true,"origin":"","legend":"\u003cp\u003eRecorded (a) TEM image, (b-c) surface morphology of the synthesized Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles\u003cem\u003e.\u0026nbsp; \u003c/em\u003eVariation of \u003cstrong\u003e(d)\u003c/strong\u003e real permittivity (εʹ), \u003cstrong\u003e(e)\u003c/strong\u003e imaginary permittivity (εʺ), \u003cstrong\u003e(f)\u003c/strong\u003e real permeability (µʹ) and \u003cstrong\u003e(g)\u003c/strong\u003e imaginary permeability (µʺ) of the different wt % of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS-\u003cem\u003e \u003c/em\u003eGd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites in the frequency range 8.2-18 GHz.\u0026nbsp; Thickness dependent (1-9 mm) RL of \u003cstrong\u003e(h)\u003c/strong\u003e 1 wt%, \u003cstrong\u003e(i)\u003c/strong\u003e 10 wt%, \u003cstrong\u003e(j)\u003c/strong\u003e 50 wt% and \u003cstrong\u003e(k)\u003c/strong\u003e 80 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e \u003c/em\u003enanoparticles loaded PDMS-\u003cem\u003e \u003c/em\u003eGd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites in the frequency range 8.2-18 GHz.\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/6b5d5ba4113dc04438d9431a.jpeg"},{"id":49980031,"identity":"be23f7ed-7f41-4d11-9205-6fc874a1019e","added_by":"auto","created_at":"2024-01-22 15:22:15","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":499934,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic representation of the proposed materials data-driven discovery for best RL performance.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/27f7713c9bd6e31c5211f7aa.jpeg"},{"id":49980030,"identity":"a8be4952-f232-4d19-ad8b-2a105a501f16","added_by":"auto","created_at":"2024-01-22 15:22:15","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":642091,"visible":true,"origin":"","legend":"\u003cp\u003ePredicted (a) ε΄, (b) ε˝, (c) µ΄ and (d) µ˝ \u0026nbsp;in 8.2-18 GHz of different Gd5Si2Ge nanoparticles wt% loading (1.5-80 wt%) in PDMS. (e) Simulated RLmin with the optimized thickness (d value) based on the predicted ε΄, ε˝, µ΄ and µ˝ for 1.5-80 wt% Gd5Si2Ge2 nanoparticles loaded PDMS nanocomposite. (f) Predicted 3D RL plot of 60 wt% Gd5Si2Ge2 nanoparticles loaded PDMS nanocomposite. \u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/5c541a96904b3261f4e05dca.jpeg"},{"id":49980033,"identity":"8ca3c853-d815-4e86-83aa-9e986712d8ea","added_by":"auto","created_at":"2024-01-22 15:22:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":118559,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/3d7e066feaede680eeb8ebd0.png"},{"id":50150920,"identity":"7e3f9276-8269-41e0-b94b-62731573b9c5","added_by":"auto","created_at":"2024-01-25 10:08:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":780103,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/f550beb6-389d-4b2a-a9dd-2092e29011b2.pdf"},{"id":49980415,"identity":"0ed9426b-ade1-4aae-8b41-33aea7719416","added_by":"auto","created_at":"2024-01-22 15:30:15","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":102453,"visible":true,"origin":"","legend":"","description":"","filename":"FinalSupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-3845175/v1/6a87edbe18d68049b84de55e.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Realization of strong microwave absorption characteristics of Gd 5 Si 2 Ge 2 nanoparticles with materials data-driven discovery","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMicrowave absorption materials play a crucial role in a wide range of applications, from radar and communication systems to medical imaging and electromagnetic (EMI) interference shielding [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. In telecommunications, microwave absorption materials are used to control the transmission and reception of signals through antennas and other devices [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. In radar, the absorption of microwaves by materials allows for the detection and imaging of objects. In medical treatment, microwave absorption materials are used in procedures such as hyperthermia, in which cancer cells are targeted with high-energy microwaves to kill them [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The strong properties that make a material suitable for microwave absorption include its dielectric constant and loss tangent, which determine how effectively it can absorb microwave energy [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The development of new microwave absorption materials with improved performance is an active area of research, as these materials have the potential to significantly enhance the capabilities of a wide range of technologies [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFerrites or a combination of electrical and magnetic materials have been proposed for microwave absorption [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, reports on Gd-based materials for microwave absorption are limited. In our previous work [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], we studied the microwave absorption properties of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e4\u003c/sub\u003e nanoparticles by incorporating them into a polydimethylsiloxane matrix (PDMS) and found that Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e4\u003c/sub\u003e nanoparticles loaded polymer nanocomposites exhibit better microwave absorption properties (Reflection Loss or RL) than some of the ferrites [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. In another study, Gd\u003csub\u003e5\u003c/sub\u003eSi4 nanoparticles were loaded to PVB-PEDOT:PSS blends to tune the microwave absorption bandwidth (RL \u0026le;-10 dB bandwidth) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eGd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e has been reported for some of the potential applications such as healthcare applications [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. However, its electromagnetic properties (permittivity and permeability) especially in high-frequency region (8\u0026ndash;18 GHz) is not investigated before. Furthermore, optimization of filler loading in polymer matrix for the most realistic microwave absorption is another challenge [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Materials data-driven discovery have been reported to overcome such problems viz., it describes how a mathematical model of the electromagnetic response of a material can be used to simulate, predict, and optimize their microwave absorption performance [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The most promising microwave absorption characteristics of composites or hybrids could be realized through materials data-driven discovery [\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis work aims to evaluate the microwave absorption characteristics, especially in X-band (8.2\u0026ndash;12.4 GHz) and Ku-band (12.4\u0026ndash;18 GHz) of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles and optimize the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe nanoparticles loading in the polymer matrix (PDMS) which is widely used for electronics for microwave absorption with an electromagnetic data-driven method.\u003c/p\u003e"},{"header":"Experimental","content":"\u003cp\u003e \u003cstrong\u003eGd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles synthesis\u003c/strong\u003e \u003cp\u003ePolycrystalline samples of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e were prepared by arc melting at the Materials Preparation Center of Ames Laboratory using\u0026thinsp;\u0026gt;\u0026thinsp;99.99 wt.%.11 The samples were heat treated at 1273K for 24 h to reduce or eliminate the amount of orthorhombic I phase present in the sample. They were then cooled at a rate of 10\u0026deg;C/min. It is our experience that slow cooling produces a more phase pure sample than quenching. The sample was remelted six times, turning over each time to ensure homogeneity. The last melting was completed by shutting OFF power to the arc, allowing for the highest cooling rates to avoid the formation of neighboring phases. No further heat treatment was performed on the as-cast sample. This process usually leads to phase-pure alloys [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. To obtain the submicrometer of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e, the as-cast material was grounded in a mortar and sieved to obtain a powder with a particle size of 53 \u003cem\u003e\u0026micro;\u003c/em\u003em or smaller. The particles were further processed by high-energy ball-milling using a SPEX 8000 M mill without adding any liquid processing agent. To prevent surface oxidation, all millings and subsequent manipulations were performed in a glove box under an argon atmosphere. In a typical milling procedure, 4 g of bulk powder was milled with \u0026sim;14.5 g of stainless-steel balls consisting of 2 balls of 11.1 mm diameter and 4 balls of 6.3 mm diameter. The powder was milled for 2 h. The bulk and all the ball-milled samples were analyzed for their particle size, morphology, composition, crystal structure, and magnetic properties [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003ePDMS- Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe nanocomposites preparation\u003c/h2\u003e \u003cp\u003eThe PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites were synthesized through facile solution processing. Various weight percentages (wt %) of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles viz., 1%, 10%, 50% and 80% were dispersed in PDMS and the curing agent (PDMS to curing agent ratio 10:1) was slowly added and kept for stirring another 20 minutes. Finally, PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e mixture was poured into the X-band and Ku-band sample holders and dried in a vacuum oven at 60\u0026thinsp;\u0026plusmn;\u0026thinsp;5\u0026deg;C (400 Torr pressure) for 6 h.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eCharacterization\u003c/h2\u003e \u003cp\u003eThe surface morphology of the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles and PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites were recorded using a scanning electron microscope (Zeiss ULTRA 55 SEM by GEMINI technology). The electromagnetic parameters (relative permittivity and permeability) of the samples were measured using a vector network analyzer (VNA, Agilent N5230A) through the industrial standard waveguide method. The full two-port calibration of the VNA (thru-reflect line or TRL) was carried out in the X-band (8.2\u0026ndash;12.4 GHz) and Ku-band (12.4\u0026ndash;18 GHz) and \u003cem\u003eS\u003c/em\u003e parameters (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e21\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e12\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003e22\u003c/em\u003e\u003c/sub\u003e) were measured for the fabricated samples. From the recorded \u003cem\u003eS\u003c/em\u003e-parameters, the complex permittivity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\epsilon }_{r}= \\epsilon ΄-i\\epsilon ˝\\)\u003c/span\u003e\u003c/span\u003e) and permeability (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\mu }_{r}= \\mu ΄-i\\mu ˝\\)\u003c/span\u003e\u003c/span\u003e) were evaluated using standard Nicholson-Ross-Weir (NRW) method [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The microwave simulations of the PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites were carried out using commercial computer simulation technology (CST- Microwave studio 2018) software [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e shows the recorded TEM image of the synthesized Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe nanoparticles. The particles were first deposited on a silicon dioxide substrate in another study [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. A femtosecond laser was used in the pulsed laser deposition technique to obtain a non-thermal deposition which resulted in the same phase and composition of the original polycrystalline bulk target of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e. The TEM sample was prepared by scraping off the deposited particles of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e on a TEM grid. The smallest particle having a diameter less than 100 nm was identified and imaged on the JEM-F200 Cold FEG Electron Microscope at the Nano Characterization Center of Virginia Commonwealth University. The image shows a particle having a core of crystalline Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e phase and a small protective shell of an amorphous phase. The amorphous phase is considered to be Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e formed due to exposure of the nanoparticles to the environment while taking them out of the glove box and while placing them on the TEM grids. The amorphous shell protects against further oxidation of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e particles.\u003c/p\u003e \u003cp\u003eThe recorded surface morphologies of the synthesized Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u003cb\u003e(b-c)\u003c/b\u003e. The SEM images show Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles (70\u0026ndash;100 nm) with irregular shapes and varying sizes. These irregular shapes have the advantage of providing a higher surface area and making it easier to form connections within the polymer matrix, which leads to reaching the percolation threshold easily [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The X-ray diffraction pattern of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles, is shown in \u003cb\u003eFig.\u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e (\u003c/b\u003e\u003cb\u003eSupporting information\u003c/b\u003e\u003cb\u003e)\u003c/b\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(d) and\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(e)\u003c/b\u003e show the variation of the real (ε\u0026prime;) and imaginary (ε\u0026Prime;) parts of the complex electric permittivity of various Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles wt% loaded viz., 1%, 10%, 50% and 80% PDMS- Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposite in the frequency range 8.2\u0026ndash;18 GHz respectively. The real part represents the ability of a material to store electric energy and is related to the amount of polarization, while the imaginary part corresponds to the electric energy dissipation inside the material [\u003cspan additionalcitationids=\"CR15 CR16 CR17\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Similarly, the real and imaginary parts of complex magnetic permeability (\u0026micro;\u0026prime; and \u0026micro;\u0026Prime;) represent the storage and dissipation of magnetic energy respectively [\u003cspan additionalcitationids=\"CR34 CR35\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The recorded \u0026micro;\u0026prime; and \u0026micro;\u0026Prime; of various Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS- Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposite is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(f)\u003c/b\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(g)\u003c/b\u003e respectively. As seen, the ε΄ value increases as the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loading to PDMS increases, for example, the ε΄ value varies from ~\u0026thinsp;2.9, ~\u0026thinsp;3.4, ~ 5.1 and ~\u0026thinsp;6.3 for 1 wt%, 10 wt%, 50 wt% and 80 wt% respectively, whereas the ε΄ of PDMS was ~\u0026thinsp;2.5. The corresponding recorded ε˝ of 1 wt%, 10 wt%, 50 wt% and 80 wt% respectively, were ~\u0026thinsp;0.05, ~\u0026thinsp;0.13, ~\u0026thinsp;0.49 and ~\u0026thinsp;0.7. The observed variation in ε΄ and ε˝ as the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles wt% increases are thought to be due to interfacial polarization. The permeability of PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites varies greatly between 12.4 and 18 GHz in presence of different Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles. This variation in permeability, which ranges from 1.15 to 1.37, can be attributed to limitations in the GHz range known as Snoek's limitation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Additionally, multiple peaks in the permeability, with the highest peak being 1.37, may be caused by natural and exchange resonances. These fluctuations in permeability are largely due to factors such as hysteresis loss, domain wall resonance, natural and exchange resonances, and eddy current effects [\u003cspan additionalcitationids=\"CR34 CR35\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. However, it is worth noting that domain wall resonance is more prominent at frequencies of 1-100 MHz, and hysteresis loss can be disregarded for weak applied fields [\u003cspan additionalcitationids=\"CR34 CR35\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. It can be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u003cb\u003e(a-f)\u003c/b\u003e that the electromagnetic response of the PDMS-Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites is primarily influenced by the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles present in PDMS. This suggests that the electromagnetic responses of the system can be predicted and modeled.\u003c/p\u003e \u003cp\u003eAs previously mentioned, the dielectric constant values can have a significant impact on the reflection loss (RL) at specific thicknesses (\u003cem\u003ed\u003c/em\u003e), and it is expressed as [\u003cspan additionalcitationids=\"CR9 CR10 CR11\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e],\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\text{R}\\text{e}\\text{f}\\text{l}\\text{e}\\text{c}\\text{t}\\text{i}\\text{o}\\text{n} \\text{l}\\text{o}\\text{s}\\text{s} \\left(\\text{R}\\text{L}\\right)=20log\\left|\\frac{{Z}_{in}-{Z}_{0}}{{Z}_{in}+{Z}_{0}}\\right|\\left(dB\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ein\u003c/em\u003e\u003c/sub\u003eis the input impedance, which can in turn be written as,\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${Z}_{in}={Z}_{0}\\sqrt{\\frac{{\\mu }_{r}}{{\\epsilon }_{r}}}tanh\\left(j\\frac{2\\pi fd\\sqrt{{\\mu }_{r}{\\epsilon }_{r}}}{c}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the characteristic impedance of free space (=\u0026thinsp;377 Ω) and \u003cem\u003ec\u003c/em\u003e is the velocity of light.\u003c/p\u003e \u003cp\u003eThe RL value of -10 dB corresponds to 90% absorption and is preferred for real-time applications [\u003cspan additionalcitationids=\"CR9 CR10 CR11 CR12 CR13 CR14 CR15\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(h-k)\u003c/b\u003e illustrates the variation of RL for 1\u0026ndash;9 mm of 1 wt%, 10 wt%, 50 wt% and 80 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite. It can be seen that the minimum RL value (RL\u003csub\u003emin\u003c/sub\u003e) and the RL \u0026le; -10 dB bandwidth strongly depend on the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loading and corresponding thickness. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(j)\u003c/b\u003e, the RL\u003csub\u003emin\u003c/sub\u003e of -14 dB was obtained for 10 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite at 9 mm, and a significantly improved RL of -35 dB was obtained for 50 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles at 7 mm. However, the RL value was not very promising for 80 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite till 9 mm indicating that increasing the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loading in the PDMS will not improve the RL value.\u003c/p\u003e \u003cp\u003eAs depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u003cb\u003e(h-k)\u003c/b\u003e, the RL\u003csub\u003emin\u003c/sub\u003e value is found to be dependent on the thickness of the sample. As the thickness increases, a shift towards lower frequency regions is observed. This can be attributed to the quarter wavelength resonance phenomenon, in which a specific matching frequency-thickness co-ordinate (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{m}, {d}_{m}\\)\u003c/span\u003e\u003c/span\u003e) is associated with RL\u003csub\u003emin\u003c/sub\u003e. This relationship can be described mathematically by the equation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e],\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${d}_{m}=\\raisebox{1ex}{$n\\lambda $}\\!\\left/ \\!\\raisebox{-1ex}{$4$}\\right.=nc/\\left(4{f}_{m}\\sqrt{\\left|{\\epsilon }_{r}\\right|\\left|{\\mu }_{r}\\right|} \\right) n=1, 3, 5\\dots$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis equation illustrates that as the thickness increases, the RL\u003csub\u003emin\u003c/sub\u003e shifts towards lower frequency regions.\u003c/p\u003e \u003cp\u003eData-driven techniques are proving to be a valuable asset in the simulation of material response, as they not only reduce the time and costs associated with experimental runs but also enable the development of more efficient materials [\u003cspan additionalcitationids=\"CR19 CR20 CR21 CR22\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. In the realm of microwave-absorbing materials, the utilization of these methods can lead to the creation of a set of normalized materials data sets [\u003cspan additionalcitationids=\"CR19 CR20 CR21 CR22\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. This would facilitate the functionalization of the material response across a range of variables and allow for the application of data-driven techniques to fine-tune the synthesis process, ultimately leading to the identification of an optimal formulation, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. However, despite the potential benefits, the current state of research in the field of microwave absorbing materials has yet to fully embrace data-driven approaches for materials discovery. This lack of a systematic approach not only incurs additional time and resources but also hinders the advancement of the field in the search for novel microwave-absorbing materials [\u003cspan additionalcitationids=\"CR19 CR20 CR21 CR22\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. It is believed that the integration of data-driven methods can greatly enhance our capability to simulate material response and optimize material performance [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo fully realize the RL and electromagnetic properties of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite, the ε΄, ε˝, \u0026micro;ʹ and \u0026micro;ʺ were modeled based on data from experiments using 1 wt%, 10 wt%, 50 wt% and 80 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite. The model covers a range of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loading from 1 wt% to 80 wt%, with intervals of 0.5 wt%. Numerical models were employed to create a third-order polynomial function for each parameter using cubic spline interpolation [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. This method was considered ideal as third-order polynomials require n\u0026thinsp;+\u0026thinsp;1 data points to determine their coefficients, and cubic functions are commonly used in engineering to model physical systems [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Each of the four weight percentages were analyzed with the same frequency set, and each frequency response point tested between 12.4 GHz to 18 GHz for the four weight percentages could be fitted with an interpolating polynomial for modeling, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e \u003cb\u003e(a-d)\u003c/b\u003e using a Python code. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e \u003cb\u003e(h-k)\u003c/b\u003e and from Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e it was observed that RL\u003csub\u003emin\u003c/sub\u003e value is associated with a specific \u003cem\u003ed\u003c/em\u003e value. In this work, a reverse engineering approach utilizing the genetic algorithm (GA) was employed to simulate and evaluate the optimal \u003cem\u003ed\u003c/em\u003e value of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite for achieving the best RL performance [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. The GA is a type of optimization method that mimics the process of natural evolution and can be used to find the optimal solution to a problem by iteratively improving a solution through selection, recombination, and mutation [\u003cspan additionalcitationids=\"CR41\" citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. To use GA to optimize the \u003cem\u003ed\u003c/em\u003e value of a material to minimize RL, a \"fitness function\" representing the objective to be optimized must be defined. Herin, the fitness function is the RL that occurs for a given \u003cem\u003ed\u003c/em\u003e value range of the material. The commercial CST-microwave studio (2018) software was used for the \u003cem\u003ed\u003c/em\u003e value optimization, which has an in-built GA and microwave simulation integration function [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. The highly non-monotonic and non-linear dependence of RL and filler loading make this simulation-assisted optimization framework an ideal candidate for achieving the best results. The predicted data sets (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e \u003cb\u003e(a-d)\u003c/b\u003e) were used as an input parameter for the CST simulation with RL\u003csub\u003emin\u003c/sub\u003e target value to optimize the \u003cem\u003ed\u003c/em\u003e value. The simulated RL\u003csub\u003emin\u003c/sub\u003e value and corresponding loading and the optimize \u003cem\u003ed\u003c/em\u003e value are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(e)\u003c/b\u003e. Through simulation, the optimized RL\u003csub\u003emin\u003c/sub\u003e value was found \u0026minus;\u0026thinsp;60.5 dB for 60 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite at 7 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(e)\u003c/b\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u003cb\u003e(f)\u003c/b\u003e shows the predicted 3D RL plot with corresponding d (1\u0026ndash;9 mm with 0.1 mm interval) and frequency of 60 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite.\u003c/p\u003e \u003cp\u003eTo verify the accuracy of the predictions, the 60 wt % Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite was fabricated (like previous) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon ΄\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon ˝\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu ΄\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu ˝\\)\u003c/span\u003e\u003c/span\u003ewere measured in 8.2\u0026ndash;18 GHz. The comparison of the predicted and experimental \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon ΄\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon ˝\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu ΄\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu ˝\\)\u003c/span\u003e\u003c/span\u003ewere shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(a)\u003c/b\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(b)\u003c/b\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(c) and\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(d)\u003c/b\u003e respectively. The comparison of the predicted and experimental dielectric loss tangent, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(tan{\\delta }_{e}=\\frac{\\epsilon ˝ }{\\epsilon ΄}\\)\u003c/span\u003e\u003c/span\u003e, and magnetic loss tangent, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(tan{\\delta }_{\\mu }=\\frac{\\mu ˝ }{\\mu ΄}\\)\u003c/span\u003e\u003c/span\u003e are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(e)\u003c/b\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(f)\u003c/b\u003e respectively. The rate of electromagnetic (EM) attenuation can be determined using the EM attenuation constant (α), which is calculated as, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha =Re\\left[iw{c}^{-1}{\\left({\\epsilon }_{r}{\\mu }_{r}\\right)}^{\\frac{1}{2}}\\right]\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i=\\sqrt{-1}\\)\u003c/span\u003e\u003c/span\u003e []. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(g)\u003c/b\u003e shows the variation of the predicted and experimental \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e values (60 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS nanocomposite) with frequency (GHz) and indicates that the experimentally obtained EM attenuation is stronger than the predicted attenuation. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(h)\u003c/b\u003e shows a comparison of the experimental and predicted RL for a PDMS nanocomposite loaded with 60 wt % Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles with a thickness of 7 mm. The comparison of the simulated and experimental RL spectra in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u003cb\u003e(h)\u003c/b\u003e reveals an excellent match, with an RL\u003csub\u003emin\u003c/sub\u003e value of -57 dB achieved, validating the proof-of-concept of the data-driven method. Additionally, the fabricated optimized sample demonstrated a better absorption bandwidth (RL \u0026le; -10 dB), specifically within the range of 12 GHz-16 GHz, compared to the simulated RL.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this study, we have demonstrated the effectiveness of using predictive modeling for the development of high-performing microwave absorption materials based on Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles. We used multidimensional mathematical models to optimize the electromagnetic response of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles materials. These models allowed us to systematically determine the optimal loading of the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles (60 wt%) to polymer matrix (PDMS), which we were then able to experimentally verify. The resulting PDMS nanocomposite exhibited an RL of -57 dB with multiple absorption bandwidth (RL \u0026le; -10 dB). This work presents a new and widely applicable methodology for materials discovery in the field of microwave absorption and marks the multidimensional mathematical models that have been used to fine-tune the electromagnetic response of materials for this purpose.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWork at VCU was partially funded by National Science Foundation, Award Number: 1726617, Project Investigator (PI): Prof. Ravi L. Hadimani.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interest Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to acknowledge Prof. K. J. Vinoy, Department of Electrical and Communication Engineering, Indian Institute of Science (IISc), India, for providing the VNA facility. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData sets generated during the current study are available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eA. Iqbal, F. Shahzad, K. Hantanasirisakul, M. K. Kim, J. Kwon, J. Hong, H. Kim, D. Kim, Y. Gogotsi, C. M. Koo, \u003cem\u003eScience (1979)\u003c/em\u003e \u003cstrong\u003e2020\u003c/strong\u003e, DOI 10.1126/science.aba7977.\u003c/li\u003e\n\u003cli\u003eZ. Zhao, L. Zhang, H. Wu, \u003cem\u003eAdvanced Materials\u003c/em\u003e \u003cstrong\u003e2022\u003c/strong\u003e, \u003cem\u003e34\u003c/em\u003e, 2205376.\u003c/li\u003e\n\u003cli\u003eZ. Wu, K. Pei, L. Xing, X. Yu, W. You, R. 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Goldberg, \u003cem\u003eIEEE Trans Electromagn Compat\u003c/em\u003e \u003cstrong\u003e1996\u003c/strong\u003e, \u003cem\u003e38\u003c/em\u003e, 518.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3845175/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3845175/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, we utilized a materials data-driven approach to investigate the microwave absorption characteristics of Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites. These results suggests that Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites possess highly efficient microwave absorption properties. It was observed that varying the loading of the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles in a polymer matrix, such as polydimethylsiloxane (PDMS), resulted in changes in reflection loss (RL). However, it was also found that simply increasing the loading of the Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles in PDMS did not improve RL performance. To optimize the RL performance, we employed an electromagnetic data-driven methodology. Obtained results predict a remarkable RL of \u0026le; -60 dB for a composite containing 60 wt% Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanoparticles loaded PDMS in the frequency range 8.2\u0026ndash;18 GHz. This prediction was supported by experimental data, which showed a minimum RL value of -57 dB with multiple RL\u0026le;-10 dB bandwidth. These findings validate the proposed proof of concept of utilizing data-driven methodology to obtain broadband and robust microwave absorption characteristics in Gd\u003csub\u003e5\u003c/sub\u003eSi\u003csub\u003e2\u003c/sub\u003eGe\u003csub\u003e2\u003c/sub\u003e nanocomposites.\u003c/p\u003e","manuscriptTitle":"Realization of strong microwave absorption characteristics of Gd 5 Si 2 Ge 2 nanoparticles with materials data-driven discovery","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-22 15:22:10","doi":"10.21203/rs.3.rs-3845175/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"df578cd8-5d25-4a4a-9cce-8dbfb9c281e1","owner":[],"postedDate":"January 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-01-25T10:00:12+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-22 15:22:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3845175","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3845175","identity":"rs-3845175","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}