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Die Studie konzentriert sich auf die Synthese dünner TiCrFeCoNi-Legierungen mit hoher Entropie mittels gepulsten Magnetronensputters und betont die entscheidende Rolle der Modulationsfrequenz bei der Steuerung der Filmeigenschaften. Die Shannon-Entropie wird als neuartige Messgröße zur Beurteilung der Komplexität und Homogenität der Filme eingesetzt und bietet neue Einsichten in die Struktur und das Verhalten des Materials. Die Forschung kombiniert theoretische Berechnungen und experimentelle Charakterisierungstechniken, um die Bildung und Stabilität der Legierung vorherzusagen, wobei das Potenzial zur Optimierung der Filmeigenschaften für verschiedene Anwendungen hervorgehoben wird.
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Abstract
This manuscript presents a comprehensive study of the synthesis of high-entropy TiCrFeCoNi alloy (HEA) thin films via pulsed magnetron sputtering (PMS).The research investigates the impact of various modulation frequencies on the material properties of the synthesized films. By employing Shannon entropy as a novel method to characterize the complexity and homogeneity of high-entropy thin films, we offer new insights into the synthesis process under various thermodynamic conditions. The initial characterization of the alloy, using calculated parameters such as mixing entropy, enthalpy of mixing, and others, sets the stage for a deeper understanding of the alloy's formation and stability. The experimental methodology encompasses target synthesis, sputtering system setup, sample synthesis, and comprehensive process and sample characterization, including EDS analysis, surface and cross-sectional analyses using SEM, and mechanical property assessments via nanoindentation. Results indicate that modulation frequency significantly influences the plasma discharge process, and consequently, the composition, microstructure, and mechanical properties of the HEA films. EDS analysis confirms the successful synthesis of the target alloy composition, and surface and cross-sectional analyses reveal the effects of modulation frequency on film morphology and structure. Mechanical property measurements highlight the variations in hardness and Young’s modulus among the synthesized films. The study elucidates the role of PMS parameters, especially modulation frequency, in controlling the synthesis of high-entropy thin films, paving the way for optimizing film properties for advanced material applications.
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1 Introduction
High-entropy alloys (HEAs) have emerged as a fascinating category of materials, exploiting the vast compositional space afforded by mixing multiple principal elements in equiatomic or near-equiatomic proportions. The interest in HEAs stems from their potential to achieve exceptional combinations of mechanical, chemical, and physical properties that are difficult or impossible to attain in conventional alloys.[1,2] HEA coating was synthesized by a plethora of synthesis techniques such as electrochemical deposition,[3] pulsed laser deposition,[4] and laser surface alloying,[5] pulsed magnetron sputtering[6] or high power impulse magnetron sputtering.[7] This study focuses on the synthesis of a high-entropy TiCrFeCoNi alloy thin film using pulsed magnetron sputtering (PMS), a technique known for its ability to produce high-quality coatings with superior adhesion and uniformity. The selection of the CrFeCoNi medium-entropy base for this study is due to its wide application in various alloy systems,[8,9] notable properties such as high hardness[9,10] and fatigue resistance[11] and its use as a properties defining medium-entropy matrix with a titanium solute.[12] Furthermore, the presence of a potential intermetallic σ-phase (Cr-rich) allows for the exploration of multiphase configurations[13] as opposed to a pure face-centered cubic (FCC) phase. The addition of titanium as the fifth element was motivated by literature[9,14‐16] suggesting that it enhances material hardness through solid-solution strengthening and precipitation. Additionally, the calculated electronegativity (Pauling) difference of the alloy, Δχpauling, value indicates the possibility of Laves phase formation.[17,18] Understanding the presence of intermetallic phases like the σ-phase in CrFeCoNi-based HEAs is crucial for predicting its behavior in various applications.
Pulsed magnetron sputtering differentiates itself from continuous sputtering processes by modulating the power applied to the target material. This modulation allows for precise control over the plasma characteristics and, consequently, the energy imparted to the sputtered atoms. The modulation frequency, in particular, is a critical parameter that affects the plasma density, ionization energy, and the deposition rate, influencing the microstructure[19,20] and properties of the deposited films. Previous studies have indicated that varying the PMS parameters, including modulation frequency, can significantly impact the synthesis and properties of thin films. However, a comprehensive understanding of how modulation frequency specifically influences the properties of HEA thin films remains underexplored.
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To address this gap, the present work introduces Shannon entropy[21] as a metric for evaluating the complexity and homogeneity of the synthesized high-entropy thin films, which was previously used in materials science and engineering field for detecting defects,[22,23] time-of-flight secondary ion mass spectrometry for the analysis of complex materials,[24] continuous impingement mixing process evaluation,[25] and for designing HEAs.[26] Shannon entropy, a concept borrowed from information theory, provides a quantitative measure of the disorder or randomness within a system. By applying this measure to the characterization of HEA thin films, the study aims to unveil new insights into the effect of modulation frequency on the material’s structure and properties. The use of Shannon entropy is particularly apt for HEAs, given their inherent compositional complexity and the potential for achieving a wide range of microstructures depending on the synthesis conditions.
The manuscript is structured to leverage the concepts of mixing entropy, enthalpy of mixing, and other thermodynamic parameters to predict the formation and stability of the TiCrFeCoNi alloy. Subsequent sections delve into the experimental methodology, detailing the synthesis of the target alloy, the setup of the pulsed magnetron sputtering system, and the comprehensive characterization of the synthesized films. This includes energy-dispersive X-ray spectroscopy (EDS) analysis, surface and cross-sectional analyses using scanning electron microscopy (SEM), and mechanical property assessments via nanoindentation. Through this meticulous approach, the study elucidates the significant role of modulation frequency in controlling the synthesis of high-entropy thin films, setting the stage for optimizing film properties for a variety of material applications.
2 Experimental
2.1 Material Design
For the initial characterization of the Ti0.5CrFeCoNi alloy, parameters listed in Table I were calculated using Eq. [1] to [6] as a reference point for comparisons with synthesized materials.
Table I
Parameter Names, Equations, and References; R—Gas Constant, ci, cj—Molar Fraction of ith and jth Element, \(\Delta H_{ij}^{{{\text{mix}}}}\)—Enthalpy of Mixing Between ith and jth Elements, ri, rj—Atomic Radii, Ti—Melting Point [K], V—Atomic Volume, E—Young’s Modulus
Table II contains all the necessary values for the calculations relevant to this study, including parameters such as elemental concentrations, lattice constants, and other properties pertinent to the Ti0.5CrFeCoNi HEA.
Table II
Physical and Chemical Properties of Elements Used in the Alloy
Based on comprehensive data in Tables I and II, Table III presents the calculated results of the parameters of the designed Ti0.5CrFeCoNi high-entropy alloy. The results offer detailed insights into the alloy’s thermodynamic properties. Together, these tables serve as initial references for the study, providing a clear overview of the alloy’s characteristics and properties based on experimental and calculated data.
Table III
Calculated Parameters for the Ti0.5CrFeCoNi (Ti0.12Cr0.22Fe0.22Co0.22Ni0.22) Alloy
ΔSmix (R)
ΔHmix [kJ/mol]
Tm [K]
Ω
δ [%]
VEC
Δχpauling
Ealloy [GPa]
1.58
− 11.42
1879
2.18
5.44
7.78
1.412
208
Comparing the results obtained from the experimental and calculated parameters with the guidelines mentioned in earlier literature, it is evident that the Ti0.5CrFeCoNi high-entropy alloy should form a solid solution. The VEC values obtained suggest a combination of face-centered cubic (FCC) and body-centered cubic (BCC) phases, which is further reinforced by the fact that the single-phase region defined by Zhang[38] as − 15 kJ/mol < ΔHmix < 5 kJ/ml and 0 < δ < 5 is not met as δ is outside the guideline region. These findings are consistent with the principles of high-entropy alloys, where the presence of multiple principal elements promotes the formation of a stable solid solution. The combination of Ti, Cr, Fe, Co, and Ni in the alloy contributes to high configurational entropy, which favors the formation of a single-phase solid solution with a mixed crystal structure. By aligning these results with existing literature guidelines, the study validates the successful synthesis of the high-entropy alloy and provides valuable insights into its structural characteristics, offering a foundation for further investigation and understanding of its properties.
2.2 Target Synthesis
The non-equimolar alloy (Ti0.5CrFeCoNi) was synthesized using a two-stage melting process in a reinforced alumina crucible under vacuum to ensure high purity and prevent contamination. The two-stage approach was used to avoid titanium reducing aluminum from the crucible.
In the first stage, 99.99 pct pure Ni, Co, Cr, and Fe were melted in a vacuum-purged crucible using direct induction heating in order of their melting points (Ni → Co → Cr → Fe). Rapid melting, achieved with a 7 kW power input, minimized interaction with the crucible walls, reducing contamination. Electromagnetic stirring ensured alloy homogeneity, and the spherical shape of the molten alloy reduced contact with the crucible. The alloy was then solidified under vacuum, forming a pre-alloy for the second stage.
In the second stage, the pre-alloy was melted with titanium in an argon-purged vacuum chamber to minimize titanium’s reaction with the crucible. The molten alloy was cast into a graphite mold (∅51 mm), which enabled rapid cooling. Carbon contamination from the mold was thus minimized and later removed mechanically from the ingot's surface. The choice of gravity casting for alloy targets impacts their microstructure as it promotes directional solidification, potentially leading to a more pronounced columnar grain structure in the target,[39‐41] that in turn affects sputtering efficiency and film uniformity. This structural characteristic is crucial for the sputtering process, as it can influence the sputtering yield and deposition rate, supporting the notion that columnar grains may provide more consistent erosion rates and steadier deposition flux.[42,43] This effect is pivotal for achieving uniform thin-film coatings, especially when synthesizing high-entropy alloys (HEAs) with complex compositions. Finally, we removed slag from the as-cast target's surface by belt-sanding, and then cut it with a wire saw to obtain a flat sputtering surface.
2.3 Sputtering System and Sample Synthesis
To ensure the quality of deposited films, the target underwent pre-sputtered in order to remove surface impurities, such as various oxides, before the main sputtering processes. The alloyed target was placed in a copper holder and installed in a WMK50 unbalanced magnetron (Z0 = 24 mm and r = 25 mm). The magnetron was powered by a DPS Power Supply to facilitate the sputtering process. The setup was situated within a dedicated vacuum chamber equipped with a low-vacuum rotary pump and a high-vacuum turbomolecular pump. The sputtering system is illustrated in Figure 1. The flowchart was created using Draw.io.[44]
Fig. 1
Schematic illustration of the sputtering system created with Draw.io with all major subsystems (pumping, gas delivery, sputtering) marked
Before commencing each sputtering process, the chamber underwent pumping to attain a base pressure of 5 × 10−5 [Pa], ensuring a suitable vacuum environment. During sputtering, process pressure of 5 × 10−3 [Pa] was maintained by using high-purity (5N) argon gas.
To fabricate the thin films, we used polished silicon wafers (Si (100)) fabricated by the Łukasiewicz Research Network—Institute of Electronic Materials Technology, Warsaw, Poland. These wafers were placed on a grounded metallic stage that featured an integrated heater. For each sample, a consistent power of 500 W was applied during the synthesis process. To investigate the effect of modulation frequency, the fmod parameter was varied across four settings: 1, 10, 100, and 1000 Hz. This allowed for the energy application to occur at different intervals, enabling a comprehensive analysis of the energy-time distribution during the PMS process.
Temperature recorded during sputtering varied slightly based on modulation frequency (fmod) in the range of 100 °C to 110 °C, which translates to homologous temperature (Th) of Th ≈ 0.2.
2.3.1 Current–Voltage Measurements, Power, and Energy Calculation
During synthesis, we recorded voltage (V(t)—voltage as a function of time) and current (I(t)—current as a function of time) waveforms. These were used to calculate power waveforms which were in turn used to calculate energy per discharge (pulse) packet according to Eq. [1]. in a manner consisted with previous research employing pulsed processes.[45,46]
where t0 is the beginning of the discharge packet, as visualized in Section IIIA, and Δt is the discharge duration.
This approach allows for a detailed understanding of the energy input into the system, crucial for controlling the microstructure and composition of the deposited films. Specifically, the modulation frequency’s effect on energy distribution directly influences ad-atom mobility and surface diffusion, key factors in forming coherent and homogenous films.
2.4 Process and Sample Characterization
Rigol 4024 oscilloscope, equipped with a RIGOL PVP2150 Passive Probe, was used for voltage measurements and a Aim I-prober 520 for current measurements. The passive probe was connected to a 3:1 voltage divider to protect the equipment from overvoltage. The oscilloscope recordings were pre-processed in Octave.[15]
Energy-dispersive X-ray spectroscopy (EDS) was carried out on a Zeiss EVO MA 10 Scanning Electron Microscopy (SEM) equipped with a secondary electron Bruker XFlash Detector 5010.
Surface roughness measurements were taken with Hommel Tester T 2000 profilometer (Hommelwerke GmbH, Germany).
X-ray diffraction was carried out using X’Pert Pro Alpha1 MPD Panalytical diffractometer equipped with an Cu X-ray tube, a primary beam Johansson (Ge 111) monochromator and a X'Celerator linear semiconductor position-sensitive detector.
Nanoindentation measurements were obtained at room temperature using a Berkovich-shaped diamond indenter in the load partial unload (LPU) mode. Oliver and Pharr model[47] was used to calculate Young’s modulus and nanohardness from load–displacement curves.
Calculations were made using a tool[48] created in Python employing scikit-image[49] for Shannon entropy calculations.
3 Results and Discussion
3.1 Plasma Discharge Waveform Analysis
Through detailed oscilloscope measurements of voltage and current, we calculated the power waveforms, which were instrumental in determining the study’s essential parameters: average voltage (Vavg), average current (Iavg), duty cycle, process time (tp), and sputter time (ton). These calculations, summarized in Table IV, formed the basis of our analysis. For consistency and to control experimental variables, we standardized the sputter time (ton) across all samples. Notably, for the sample subjected to a 1 Hz modulation frequency, we observed a necessity to reduce ton to prevent the layers decohesion during prolonged processing. This modification ensured the integrity and adherence of the thin films under these unique conditions.
Table IV
Current–Voltage Measurements and Calculations Results of Electrical Synthesis Parameters
fmod [Hz]
Vavg [V]
Iavg [A]
tp [s]
Discharge time [s]
Off Time [s]
Duty Cycle [pct]
\(t_{{{\text{on}}}}^{\sum }\) [s]
1
477
4.34
11111
0.027
0.975
2.7
300
10
471
4.07
6451
0.0089
0.0909
9.3
600
100
469
3.70
6741
0.0009
0.0091
8.9
600
1000
480
3.33
6593
0.00009
0.0009
9.1
600
Voltage values vary only slightly between different fmod settings (474 ± 5/1%) (Figure 2), while the variations in current are much more significant (3.86 ± 0.48/12%) (Fig. 3.1/1.) and inversely correlated with fmod. The average power for each discharge was 1920 ± 166/9 pct, with 1 Hz being the outlier. Furthermore, a noteworthy observation was made during the study, indicating that the voltage required to initiate each discharge changed as fmod increased. This trend is graphically depicted in Figure 2. This phenomenon underscores the impact of modulation frequency (fmod) on the plasma discharge initiation process, providing insights into the energy-time distribution dynamics and how the magnetron sputtering process responds to different modulation frequencies.
Fig. 2
Plasma discharge current and voltage spikes during various fmod regimes as registered during sample synthesis
The observed data reveal that the plasma discharge initiation voltage (Vmax) for the 1 and 10 Hz processes is identical, while the 100 and 1000 Hz processes require progressively lower voltage. This finding suggests that during the off-time (toff) period of the 1 and 10 Hz processes, conditions in the magnetron discharge region have enough time to return to an equilibrium neutral state, resulting in similar Vmax values for these frequencies (\(V_{\max }^{{100\,{\text{Hz}}}} \, = \,V_{\max }^{{10\,{\text{Hz}}}}\)). However, at higher modulation frequencies, 100 and 1000 Hz, this equilibrious neutral state is disrupted to varying degrees, with higher values of fmod leading to a more pronounced effect (\(V_{\max }^{{100\,{\text{Hz}}}} \, = \,V_{\max }^{{1000\,{\text{Hz}}}}\)). This voltage behavior is generally followed by decreasing current, but there is no point where two different fmod exhibit the same initiation current. This phenomenon may be attributed to secondary effects, such as heat-induced ionization, which influence the discharge behavior at different modulation frequencies. These observed trends[50] provide additional insights into the underlying dynamics of the magnetron sputtering process under different modulation conditions, helping to better understand the energy-time distribution and its implications for the synthesis of high-entropy alloy thin films.
Given the observed impact of fmod on plasma discharge and, consequently, on film composition and structure, future research could explore the optimization of these parameters to enhance specific properties of HEA films. Investigating the role of different fmod settings, adjusting the pulse duration or energy per discharge could provide deeper insights into the kinetics of film growth and its effects on films chemical composition and thus its properties such as hardness, thermal stability, or corrosion resistance. Additionally, extending this analysis to other HEA systems could reveal universal trends or material-specific behaviors, broadening the applicability of PMS in thin-film synthesis.
3.2 EDS Analysis: The Target
EDS analysis of the target has provided promising results (summarized in Table V), indicating that the alloying process, described in Section IIA, has successfully synthesized an alloy with nearly the exact chemical composition as originally designed for this study. This is crucial, as it ensures that the target used in subsequent sputtering processes closely matches the intended high-entropy alloy composition.
Table V
Chemical Composition of the Designed and Obtained Alloyed Target
Element
Molar Fraction [pctat]
Ti
Cr
Fe
Co
Ni
Designed
12
22
22
22
22
Obtained
11.65 ± 0.3
21.25 ± 0.4
20.49 ± 0.2
24.08 ± 0.2
22.53 ± 0.3
Change [pct]
+ 5.91
− 3.41
− 6.86
+ 9.45
+ 2.41
Additionally, approximately 5 pctat of carbon was detected in the target and, subsequently, in the later-stage samples. This contamination is likely attributable to the operation of SEM/EDS, as it is well established that carbon contamination is a common byproduct of these analytical techniques.[51]
In order to accurately reflect the composition of the alloy used for the target in subsequent sputtering processes, experimentally obtained values of atomic concentrations from the as-cast target were used to update calculated thermodynamic parameters from Table V. These updated values are presented in Table VI. This ensures that the subsequent sputtering processes were based on the correct alloy composition, providing more accurate and reliable data for the synthesis of the high-entropy alloy thin films.
Table VI
Recalculated (“Obtained”) Values of ΔSmix, ΔHmix, Tm, Ω, δ, VEC, and Ealloy for the As-cast Target of Ti0.12Cr0.21Fe0.2Co0.24Ni0.23 and the Percentage Change Between the Envisioned and Manufactured Values
ΔSmix
ΔHmix [kJ/mol]
Tm [K]
Ω
δ [pct]
VEC
Δχpauling
Ealloy [GPa]
Designed
1.581
− 11.42
1879
2.18
5.44
7.78
1.412
208
Obtained
1.585
− 12.17
1875
2.04
5.50
7.8
1.413
206
Change [pct]
+ 0.25
+ 6.57
− 0.21
− 6.42
+ 2.39
+ 0.26
+ 0.07
− 0.96
Among the various parameters investigated, the most notable one worth highlighting is the change in ΔHmix. A more negative ΔHmix suggests a higher tendency to form a solid-solution alloy, but the value itself deviates outside from the range suggested by Guo et al.[30]
3.3 Surface Analysis: The Samples
We conducted EDS mapping (×50000 magnification) of samples surfaces (Figure 3; only S1 is shown) to analyze distribution of alloy components across the thin films and analyzed the SEM images for surface complexity and variations by applying Shannon entropy in the analysis.
Fig. 3
Compilation of EDS maps and Shannon entropy heat maps for sample S1
Shannon entropy for sample surfaces was calculated on an image split into 2n segments for n = [0, 1, 2, 3, 4, 5, 6], where n = 0 is the whole image. The results are shown in Figure 4. Higher n values were calculated, but are not shown here as the values rapidly approach 0 and the analysis loses meaning.
Fig. 4
Change in average Shannon entropy and standard deviation for each segmentation level
While the initial hypothesis suggested that higher fmod leads to smoother (lower entropy) surfaces, S2 challenges this by demonstrating that an intermediate frequency can achieve a high-complexity surface with uniform characteristics. This contrasts with the smoother textures observed at very high frequencies (S4) and suggests an optimal modulation frequency region for maximizing surface texture complexity without sacrificing uniformity.
The EDS measurement results are summarized in Table VII. These measured values were then compared with the composition of the target, which served as the reference point for the analysis. By comparing the EDS data with the target composition, we were able to assess how well the synthesized thin films matched the intended high-entropy alloy composition. It is an important comparison for assessing the effectiveness of the PMS technique in achieving the designed alloy composition and the changes introduced by employing different modulation frequencies. Additionally, exploring alternative sputtering techniques, such as High Power Impulse Magnetron Sputtering (HiPIMS), Gas Injection Magnetron Sputtering (GIMS) or High Impulse Power Gas Injection Magnetron Sputtering (HiPGIMS), could offer finer or coarser control over elemental deposition rates, potentially mitigating the observed deviations in composition or, conversely, allowing for a broader range of possible compositions from a fixed target composition. This also could broaden the appeal of high-throughput methods (HTM), as varying fmod could add another dimension to possible control parameters, where HTM mostly relies on distance to target during co-sputtering.
Table VII
EDS Measured Compositions of Synthesized Samples
fmod
Ti
Cr
Fe
Co
Ni
1
16.01 ± 0.2
16.07 ± 0.1
22.20 ± 0.3
22.51 ± 0.4
23.21 ± 0.1
10
17.23 ± 0.4
14.96 ± 0.1
20.07 ± 0.2
25.18 ± 0.2
22.56 ± 0.2
100
17.30 ± 0.4
15.09 ± 0.3
20.02 ± 0.2
25.24 ± 0.3
22.35 ± 0.2
1000
17.47 ± 0.3
15.07 ± 0.2
20.25 ± 0.1
25.32 ± 0.1
21.88 ± 0.4
Based on these results for the synthesized films, thermodynamic parameters were recalculated and compared with the target composition as the reference point. These results are presented in Table VIII. By comparing these calculated parameters with the target composition, we can gain insights into how fmod influences the energy-time distribution during the pulsed magnetron sputtering process and its subsequent impact on the alloy’s properties and characteristics. This comprehensive analysis will aid in understanding the correlation between the synthesis conditions, the resulting thin films, and the desired high-entropy alloy composition.
Table VIII
Material Parameters of Samples S1, S2, S3, and S4
fmod
ΔSmix [R]
ΔHmix [kJ/mol]
Tm [K]
Ω
δ [pct]
VEC
Δχpauling
Ealloy [GPa]
1
1.596
− 14.200
1862
1.740
6.17
7.73
1.418
197
10
1.593
− 15.097
1859
1.631
6.33
7.71
1.415
195
100
1.593
− 15.121
1860
1.629
6.34
7.71
1.415
195
1000
1.594
− 15.164
1860
1.626
6.37
7.69
1.415
195
The EDS results indicate significant deviations from the target compositions of titanium and chromium across all synthesized samples. The titanium content increases from approximately 40 pct in sample S1 to around 50 pct in samples S2 to S4. Conversely, the chromium content decreases by approximately 25% in S1 and by about 29 pct in samples S2, S3, and S4. Variations in the concentrations of other elements (Fe, Co, Ni—the ferromagnetic ingredients) within the studied samples are consistently below 9 pct, with the highest variability observed in sample S1. This behavior mirrors trends previously documented in the synthesis of Fe–Cu alloy metallic layers.[51] Based on the results summarized in Table 3.2.2/5. the expected structure of the synthesized films will be amorphous, as dictated by ΔHmix values remaining close to − 15 and δ values exceeding 6 pct in conjunction of rapid cooling of the sputtered material, where during every discharge a given amount of energy and mass is delivered to the substrate.[30] This line of reasoning is proven true by X-ray diffraction results (Figure 5), as all synthesized samples exhibit wide diffraction peaks of an amorphous structure, regardless of synthesis conditions.
Fig. 5
Recorded XRD spectra of synthesized samples. All samples synthesized as amorphous on Si(100) substrates
The amorphous films underwent nanoindentation measurements under constant load of 0.3 mN/s and the results are summarized in Table IX, where the percentage difference between calculated and measured values of Young’s Modulus (ΔE), \(\frac{{H^{2} }}{{E^{2} }}\)[52]—resistance to plastic deformation, \(\frac{H}{E}\)\(\frac{{H}^{3}}{{E}^{2}}\)[53]—wear resistance, \(\frac{1}{{E^{2} H}}\)[54]—resistance to crack damage is listed for easy reference. Authors are aware that of potential issues with the use of some of these parameters.[55]
Table IX
Mechanical Parameters Measured (H, E) and Calculated (\(\frac{{H^{3} }}{{E^{2} }}\), \(\frac{H}{E}\), \(\frac{1}{{E^{2} H}}\)), Used in this Study
Sample Name
Hardness—H [GPa]
Young’s Modulus—E [GPa]
ΔE [pct]
(\(\frac{{H^{3} }}{{E^{2} }}\))
(\(\frac{H}{E}\))
(\(\frac{1}{{E^{2} H}}\))
S1
11.24 ± 0.36
205.07 ± 4.12
+ 4.1
0.0338
0.05483
2.1149E-6
S2
7.28 ± 0.56
180.38 ± 12.71
− 5.0
0.01186
0.04036
4.22174E-6
S3
8.34 ± 0.09
182.12 ± 5.10
− 6.6
0.01751
0.04581
3.61358E-6
S4
7.33 ± 0.27
178.18 ± 7.81
− 8.6
0.01239
0.04112
4.29836E-6
The increase in titanium and decrease in chromium content observed in the synthesized films may significantly influence their mechanical properties, such as hardness and tensile strength. Titanium, being lighter and having a higher strength-to-weight ratio compared to chromium, could potentially enhance the specific strength of the films.[56‐58] However, chromium’s reduced presence might impact the corrosion resistance negatively. This trade-off underscores how critical the initial target composition is, and how important synthesis conditions during PMS, especially fmod, are.
Shannon entropy analysis results (SEM images, 50k magnification) were conducted to qualitatively describe sample surfaces complexity and to correlate it with synthesis conditions (fmod) and are illustrated in Figure 6. In similar fashion to Figure 4, segmented analysis was employed.
Fig. 6
Surface complexity of synthesized samples, measured by Shannon entropy, as a function of modulation frequency
For an additional measure of surface complexity, surface roughness measurements were carried. These results are summarized in Table X and include total height variation (Rt), maximum Peak-to-Valley height (RMAX), average height of the peaks (PT`), and average depth of the valleys (WT`).
Table X
Surface Roughness Measurements Results
Sample name
Rt [nm]
RMAX [nm]
PT` [µm]
WT` [µm]
S1
120 ± 10
90 ± 7
7.83 ± 0.82
6.46 ± 0.07
S2
90 ± 8
90 ± 8
15.10 ± 11.55
12.58 ± 0.99
S3
60 ± 7
60 ± 6
0.9 ± 0.04
0.71 ± 0.02
S4
130 ± 11
70 ± 5
0.42 ± 0.09
0.31 ± 0.05
3.4 Cross-Sectional Analysis
Scanning electron microscopy (SEM) investigations of the synthesized samples cross sections reveal a pronounced columnar microstructure across all samples, as presented in Figure 7 (left). Notably, no evidence of decohesion or delamination is observed on any of the samples. The microstructure observed across all samples indicates a high degree of directional solidification, usually associated with rapid cooling rates, which are typical during magnetron sputtering process with only ambiance substrate heating. These results differ significantly from previously synthesized HEAs, where modulation frequency had a much more pronounced effect on samples structure, where 10 Hz samples (M2.S1 and M2.S3) and 1000 Hz samples (M2.S2 and M2.S4) had distinct structures, either columnar, uniform, or a mixture of both.[59] Such structures, as these obtained in this study, are known to influence mechanical properties, including hardness and wear resistance. By correlating the uniformity of this microstructure, by both visual analysis and Shannon entropy of whole and segmented images, with the modulation frequency used in the PMS technique, the possibility to deduce specific frequencies optimizes the cooling rate, thus enhancing the material's mechanical properties. Future studies could explore the direct impact of these microstructural features on the alloy’s hardness and resistance to wear, providing a clearer link between synthesis parameters and material performance.
Fig. 7
SEM images of cross sections and corresponding entropy heat maps of synthesized samples
On the other hand, the growth rates at 10 Hz and 1000 Hz were found to be nearly identical at 1.265 ± 0.015 nm/s. However, the variance of the growth rate is 1.35 ± 0.14 (≈ 10 pct), so the overall effect of energy delivery modulation (fmod) has only limited influence on deposition rate if considering total discharge time. In industrial applications, however, process time is the crucial parameter, and rate of growth of layers synthesized under 1 Hz, a third of the rate of 10, 100 and 1000 Hz, might pose a challenge. Furthermore, the comparison between the plots of tp (process time) and ton (sputter time) highlights the usefulness of using ton as the base for calculations. This choice is essential, as the tp varied significantly depending on fmod values employed.
These growth rate results are in stark contrast to the ones obtained with a mosaic target, where the difference between fmod = 10 Hz (samples M2.S1 and M2.S3) and fmod = 1000 Hz (samples M2.S2 and M2.S4) was an order of magnitude different.[59]
We have extended structural analysis to incorporate Shannon entropy (ES) in its description, to quantify the effect of PMS parameters on the structure of the films. The results are presented in Table XII. This approach is an attempt to quantitatively describe the morphology of the cross sections. The first step was to calculate the overall ES for each samples SEM image.
Table XII
Overall ES for Each Sample
Sample Name
Shannon Entropy
S1
5.79
S2
7.13
S3
7.37
S4
6.92
These results show a significant increase in ES between S1 (fmod = 1 [Hz]) and other samples (fmod = 10, 100, 1000 [Hz]) which, when correlated with discharge times for each fmod, clearly suggests that long active deposition times homogenize the structure potentially due to time availability for longer ranged atomic migration. Higher entropy in the other samples therefore can be attributed to faster deposition rates causing more disorder. However, there is discordance when visually comparing these results with SEM images (Figure 7 left), especially S1, where the lower reaches of the film show a simpler structure than what is deposited further in the process. To verify, the original images were segmented, and for each segment ES was calculated. Based on these results, heat maps were generated to better illustrate structural complexities (Figure 7 right).
The heat maps visualize the distributions of information content that correlate with structural characteristics, as observed in SEM images of cross sections. Sample S1 visibly exhibits the lowest overall entropy, and all samples appear to have lower entropies closer to the substrate. To gain a better understanding of how entropy changes as the films are deposited, linear entropy (ES) is calculated from the original images. Linear entropy calculates entropy for each row of the image. The results, depicted as a plot of entropy values as a function of distance from the substrate, are presented in Figure 8.
Fig. 8
Linear entropy variance of synthesized samples as a function of substrate distance. Position denotes the line (pixel line, bottom x-axis) and the distance (nanometers, top x-axis) from the samples substrate
These results show that every sample exhibits lower entropy the closer it is measured to the substrate, and a cut-off point is visible at the distance of about 100 pixels (about 140 [nm]) for samples S2, S3 and S4, and 200 pixels (about 280 [nm]) for S1. After that distance, ES value stabilizes. As was seen on the segmented heat map, initial ES values can vary significantly.
Utilizing a moving window (Figure 9) (10 pct of sample height) to evaluate the variation of ES reveals that samples S2, S3, and S4 consistently maintain ES values across their entire cross-section. However, Sample S1 exhibits distinct behavior, characterized by a continual increase in ES, particularly pronounced near the surface.
Fig. 9
Moving window entropy variance of synthesized samples as a function of substrate distance. Position denotes the center of the moving window (pixel line, bottom x-axis) and the distance (nanometers, top x-axis) from the samples substrate
This abrupt rise in ES, indicative of a sudden alteration in the film's cross-sectional complexity, may be attributed to the necessity of halving the synthesis time for S1 during sputtering. This adjustment was prompted by its tendency to either delaminate from the Si substrate if the cause was a gradual increase in overall temperature or by forming cracks at the surface, possibly caused by increased complexity.
4 Conclusion
Modulation frequency was found to have a substantial influence on the plasma discharge process, affecting the composition, microstructure, and mechanical properties of the high-entropy alloy (HEA) films. This underscores the critical role of PMS parameters, especially modulation frequency, in tailoring the synthesis of high-entropy thin films to optimize their properties for advanced material applications.
By employing Shannon entropy as a metric to evaluate the complexity and homogeneity of the synthesized films, the study provided new insights into the material's structure and properties. This approach highlighted the potential of Shannon entropy in understanding the intricate details of high-entropy alloys, paving the way for its application in further materials science research.
Surface and cross-sectional analyses revealed significant effects of modulation frequency on film morphology and structure. An intermediate frequency (10 Hz) achieved a high-complexity surface with uniform characteristics, contrasting with smoother textures at lower (1 Hz) and higher frequencies (100 and 1000 Hz). This suggests an optimal modulation frequency region for maximizing surface texture complexity without sacrificing uniformity.
This work not only contributes to the understanding of high-entropy alloys but also opens up new avenues for the application of Shannon entropy in materials characterization. It demonstrates the potential for optimizing the properties of high-entropy thin films for a variety of applications, including wear-resistant coatings, corrosion-resistant layers, and materials with enhanced mechanical strength.
Acknowledgments
M. Wilczopolska used equipment funded from the European Union Horizon 2020 Research and Innovation program under grant agreement no. 857470 and from the European Regional Development Fund via the Foundation for Polish Science International Research Agenda PLUS program grant no. MAB PLUS/2018/8.
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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