Fractal Dimension Df Research Articles

Predicting a Wide Range of Fractal Dimensions of Salt-Induced Aggregates in Water Using a Random Forest Model.

Salt-induced colloidal aggregates can significantly influence contaminant fate and transport in natural and engineered systems. These aggregates' fractal dimensions (df), ranging from 1.4 to 2.2, depend on various system variables. However, the quantitative relationship between these variables and df of aggregates has not been fully explored, especially in predicting a wide range of df. Here, we developed a random forest model capable of predicting the complete range of aggregate df using just four simple physical and chemical parameters of the aggregating system as inputs. The model accurately predicts the df of aggregates formed by colloids of different sizes, ranging from nano to micro sizes, after being trained and tested on appropriate data sets. Ionic strength (IS) has the most significant influence on the df of aggregates formed by microsized particles followed by the relative hydrodynamic radius of aggregates (Rh/Rp), particle concentration (Cp), and primary particle radius (Rp). For aggregates formed by both nano- and microsized particles, IS still has a strong influence on the df, with the significance of Rp increasing. All four inputs are negatively correlated with predicting the df of aggregates. The predictions align well with the physical interpretations.

Impact of surface-roughness and fractality on electrical conductivity of SnS thin films

Mono- and multi-fractal geometry have been used to explore the surface characteristics of scanning electron microscopy (SEM) micrographs of the SnS films with thicknesses of 100nm (SnS1) to 600nm (SnS4), respectively. For this investigation, the SnS thin films have been grown on fluorine-doped tin oxide (FTO)-coated glass substrate through the thermal evaporation route, and surface morphologies are captured by SEM. Two-dimensional multi-fractal detrended fluctuation analysis (MFDFA) based on the partition function is used to examine whether the surfaces have a multi-fractal nature or not. The partition function is applied to extract the generalized Hurst exponent from the segment size. It has been found that surfaces with higher surface roughness induce substantial nonlinearity and a wider width of the multi-fractal spectrum. The multi-fractal spectrum acquired from the analysis of the geometry and shape of the singularity spectrum is used to quantify the irregularity and complexity of surfaces. Minkowski functionals (MFs) parameters such as volume, boundary, and connectivity were measured for each thin film. Moreover, we tried to correlate the electrical conductivity with the mono- and multi-fractal parameters such as fractal dimension (Df), singularity strength function (Δα), singularity spectrum Δf(α), and it is observed that the conductivity of a thin film decreases with decreasing fractal dimension. The minimum (maximum) resistivity (conductivity) was observed for the surface having a larger fractal dimension. The present investigation suggests that such SnS surfaces, having minimal resistivity and maximum conductivity on the roughest surface, indicate enhanced light trapping capacity and can be utilized as active layers for advanced optoelectronics devices.

Neuro-evolutionary evidence for a universal fractal primate brain shape.

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of df = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future.

Neuro-evolutionary evidence for a universal fractal primate brain shape

The cerebral cortex displays a bewildering diversity of shapes and sizes across and within species. Despite this diversity, we present a universal multi-scale description of primate cortices. We show that all cortical shapes can be described as a set of nested folds of different sizes. As neighbouring folds are gradually merged, the cortices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps with over 70 other mammalian species. Our results indicate that all cerebral cortices are approximations of the same archetypal fractal shape with a fractal dimension of df = 2.5. Importantly, this new understanding enables a more precise quantification of brain morphology as a function of scale. To demonstrate the importance of this new understanding, we show a scale-dependent effect of ageing on brain morphology. We observe a more than fourfold increase in effect size (from two standard deviations to eight standard deviations) at a spatial scale of approximately 2 mm compared to standard morphological analyses. Our new understanding may, therefore, generate superior biomarkers for a range of conditions in the future.

Analysis of the effect of lactobacillus exopolysaccharide on the rheological properties of fermented soybean protein gel: Using acid-induced soybean protein as the model

In order to accurately describe the contribution of extracellular polysaccharide (EPS) to the rheological properties of the gel in the complex system induced by lactic acid bacteria fermentation, acid-induced soy protein isolate (SPI) was used as the model. The effect of exopolysaccharide produced by Lactobacillus casei (CEPS) on the macro rheological properties and microstructural changes of acid-induced SPI gel were analyzed by scaling model and image analyses. The estimated value of storage modulus (G′) at time infinity, gel point, G′ at 37 °C, enhancement effect of G′ during cooling (ΔG'), recovery rate, critical strain (γc) and fractal dimension (Df) exhibited strong CEPS concentration dependence. The addition of CEPS led to the formation of uniform and compact three-dimensional network, which was mainly represented by small voids and apertures. Therefore, by reducing the complexity of the fermentation gel system, this study explored the effect of CEPS on the rheological properties of fermented soy protein gels and the fermented soybean protein gel with good rheological properties can be selected by quantitative image analysis.

Combining functional and morphological retinal vascular characteristics achieves high-precision diagnosis of mild non-proliferative diabetic retinopathy

BackgroundTo explore the functional and morphological variations of retinal vessels in diabetes with no clinically detectable retinopathy (NDR) and mild non-proliferative diabetic retinopathy (NPDR) and to establish a high-performance mild NPDR diagnostic model.MethodsNormal subjects and type 2 diabetes patients with NDR and mild NPDR were recruited. Oxygen-saturation-related functional parameter (optical density ratio ODR) and morphological characteristics (fractal dimension Df, vessel area rate VAR, mean vascular diameter Dm, vessel tortuosity τ) of different vascular areas were extracted with single fundus photography and comprehensively analyzed among groups. An interpretable model combining marine predator algorithm (MPA) and support vector machine (SVM) based on characteristic selection was proposed for mild NPDR diagnosis.ResultsA total of 91 NDR subjects, 75 mild NPDR subjects, and 111 sex- and age-matched normal controls were analyzed. Increased main vessels ODR, while lower VAR of all areas except outer ring macula, lower Dm of all vessels and decreased τ of all areas were associate with NDR (e.g. main vessels ODR: OR [95%CI] 1.42[1.07–1.89], full macula τ:0.53[0.38–0.74]). Increased ODR of all areas, higher Dm of all areas except inner ring macula, increased inner ring macula τ, while decreased Df of full and inner ring macula, lower VAR of all areas were associate with mild NPDR (e.g. main vessels ODR:5.68[3.03–10.65], inner ring macula VAR: 0.48[0.33–0.69]). The MPA-SVM model with selected characteristics obtained the best diagnosis performance (AUC:0.940 ± 0.014; Accuracy:90.4 ± 3.9%; Sensitivity:89.2 ± 6.4%; Specificity:91.3 ± 6.4%).ConclusionsMore significant retinal vascular variations are associate with the incidence of mild NPDR than NDR. High-precision mild NPDR diagnosis is achieved combining the morphological and functional vascular characteristics based on characteristic selection.

Improving the predictions of black carbon (BC) optical properties at various aging stages using a machine-learning-based approach

Abstract. It is necessary to accurately determine the optical properties of highly absorbing black carbon (BC) aerosols to estimate their climate impact. In the past, there has been hesitation about using realistic fractal morphologies when simulating BC optical properties due to the complexity involved in the simulations and the cost of the computations. In this work, we demonstrate that, by using a benchmark machine learning (ML) algorithm, it is possible to make fast and highly accurate predictions of the optical properties for BC fractal aggregates. The mean absolute errors (MAEs) for the optical efficiencies ranged between 0.002 and 0.004, whereas they ranged between 0.003 and 0.004 for the asymmetry parameter. Unlike the computationally intensive simulations of complex scattering models, the ML-based approach accurately predicts optical properties in a fraction of a second. Physiochemical properties of BC, such as total particle size (number of primary particles (Npp), outer volume equivalent radius (ro), mobility diameter (Dm), outer primary particle size (ao), fractal dimension (Df), wavelength (λ), and fraction of coating (fcoating), were used as input parameters for the developed ML algorithm. An extensive evaluation procedure was carried out in this study while training the ML algorithms. The ML-based algorithm compared well with observations from laboratory-generated soot, demonstrating how realistic morphologies of BC can improve their optical properties. Predictions of optical properties like single-scattering albedo (ω) and mass absorption cross-section (MAC) were improved compared to the conventional Mie-based predictions. The results indicate that it is possible to generate optical properties in the visible spectrum using BC fractal aggregates with any desired physicochemical properties within the range of the training dataset, such as size, morphology, or organic coating. Based on these findings, climate models can improve their radiative forcing estimates using such comprehensive parameterizations for the optical properties of BC based on their aging stages.

Effects of Oxygen Concentration on Soot Formation in Ethylene and Ethane Fuel Laminar Diffusion Flames

In studying the effects of oxygen concentration and molecular structure on the morphologies of the soot particles produced by hydrocarbon fuels, ethylene and ethane were chosen as experimental fuels. With a Gülde laminar coaxial diffusion flame device, a soot particle device was used to sample soot particles at different oxygen concentrations (21%, 24%, 26%, 28%, and 31%) and at different heights above a burner (HABs = 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm). High-resolution transmission electron microscopy (HRTEM) was used to scrutinize and analyze the soot particles at varying oxygen concentrations. The findings suggest that at the same oxygen concentration, ethylene produces brighter and taller flames. With an increase in the oxygen concentration, ethylene flames and ethane flames gradually decrease in height and become brighter. With an increase in the HAB, the average primary soot particle diameter (Dp) increases initially and then decreases, the fractal dimension (Df) increases, and the aggregates transition from strips and chains to clusters. At the same flame height (HAB = 30 mm), the Dp decreases, the Df increases, the carbon layer torsion resistance (Tf) and the carbon layer spacing (Ds) increase, and the carbon layer changes from a parallel arrangement to a curved arrangement to form denser network aggregations.

Fractal Dimension (Df) Theory of Ismail’s Entropy (IE) with Potential Df Applications to Structural Engineering

As an ultimate generalisation to several kinds of generalised entropy in the literature, a novel entropy measure, namely, Ismail’s entropy, or (IE), is presented. This article spotlights the significance of fractal dimension, through highlighting several possible applications of fractal dimension to structural engineering. In addition to several difficult open problems and the next step of inquiry, the paper ends with some concluding observations

Morphology, aspect ratio, and surface elemental composition of primary aerosol particles at urban region of India.

The PM2.5 and PM10 particles were characterized in terms of morphology (size and shape) and surface elemental composition at two different (traffic and industrial) locations in urban region of India and further linked to different morphological defining parameters. The overall PM2.5 and PM10 showed significant daily variability indicating higher PM10 as compared to PM2.5. PM2.5/PM10 ratio was found to be 0.58 ± 0.10 indicating the abundance of PM2.5. Soot aggregates, aluminosilicates, and brochosomes particles were classified based on morphology, aspect ratio (AR), and surface elemental composition of single particles. The linear regression analysis indicates the significant correlation between area equivalent (Daeq) and feret diameter (Dfd) (R2 0.86-0.98). Higher aspect ratio (1.48 ± 0.87-1.43 ± 0.50) was noted at traffic site as compared to industrial site (1.33 ± 0.58-1.29 ± 0.30), while circularity showed the opposite trend. Fractal dimension (Df) of soot aggregates estimated by the soot parameters method (SPM) were found to be 1.70, 1.72, and 1.88, mainly attributed to vehicular emissions, biomass, and industrial emission/coal burning, respectively. This further inferred that freshly emitted soot particles exhibited lacey in nature with spherical shape (Df 1.70) at traffic site, while at industrial location, they were different with compact shapes (Df 1.88) due to particle aging processes. This study inferred the synoptic changes in mass, chemical characteristics, and morphology of aerosol particles which provide the new insights into individual atmospheric particle and their dynamic nature.

New Insights into the Formation of Aggregates of Bidisperse Nano- and Microplastics in Water Based on the Analysis of In Situ Microscopy and Molecular Simulation.

Microplastics (MPs) and nanoplastics (NPs) in water pose a global threat to human health and the environment. To develop efficient removal strategies, it is crucial to understand how these particles behave as they aggregate. However, our knowledge of the process of aggregate formation from primary particles of different sizes is limited. In this study, we analyzed the growth kinetics and structures of aggregates formed by polystyrene MPs in mono- and bidisperse systems using in situ microscopy and image analysis. Our findings show that the scaling behavior of aggregate growth remains unaffected by the primary particle size distribution, but it does delay the onset of rapid aggregation. We also performed a structural analysis that reveals the power law dependence of aggregate fractal dimension (df) in both mono- and bidisperse systems, with mean df consistent with diffusion-limited cluster aggregation (DLCA) aggregates. Our results also suggest that the df of aggregates is insensitive to the shape anisotropy. We simulated molecular forces driving aggregation of polystyrene NPs of different sizes under high ionic strength conditions. These conditions represent salt concentration in ocean water and wastewater, where the DLVO theory does not apply. Our simulation results show that the aggregation tendency of the NPs increases with the ionic strength. The increase in the aggregation is caused by the depletion of clusters of ions from the NPs surface.

A Fractal Model of Fracture Permeability Considering Morphology and Spatial Distribution

Summary In fractured reservoirs, the fracture system is considered to be the main channel for fluid flow. To better investigate the impacts of fracture morphology (tortuosity and roughness) and spatial distribution on the flow capacity, a fractal model of fracture permeability was developed. Based on micro-computed tomography (CT) images, the 3D structure of the fracture was reconstructed, and the fractal characteristics were systematically analyzed. Finally, the control of permeability by fracture morphology and spatial distribution in different fractured reservoirs was identified. The results demonstrate that the complexity of the fracture distribution in 2D slices can represent the nature of the fracture distribution in 3D space. The permeability fractal prediction model was developed based on porosity (φ), spatial distribution fractal dimension (Df), tortuosity fractal dimension (DT), and opening fractal dimension of the maximum width fracture (Db). The permeability prediction results of the fractal model for Samples L-01 (limestone), BD-01 (coal), BD-02 (coal), S-01 (sandstone), M-01 (mudstone), and C-01 (coal) are 0.011 md, 0.239 md, 0.134 md, 0.119 md, 1.429 md, and 27.444 md, respectively. For different types of rocks, the results predicted by the model show good agreement with numerical simulations (with an average relative error of 2.51%). The factors controlling the permeability of fractured reservoirs were analyzed through the application of the mathematical model. The permeability is positively exponentially correlated with the fractal dimension of spatial distribution and negatively exponentially correlated with the fractal dimension of morphology. When Df < 2.25, the fracture spatial structure is simple, and the morphology and spatial distribution jointly control the seepage capacity of fractured reservoirs. When Df > 2.25, the fracture spatial structure is complex, and the impact of morphology on seepage capacity can be disregarded. This work can effectively lay the foundation for the study of fluid permeability in fractured reservoirs by investigating the effects of fracture morphology (tortuosity and roughness) and spatial distribution on flow capacity.

A Fractal Adsorption Model on Methane in Coal with Temperature Effect Dependence

The traditional Langmuir equation displays drawback in accurately characterizing the methane adsorption behavior in coal, due to it assuming the uniform surface of coal pores. Additionally, the decay law of gas adsorption capacity with an increasing coal reservoir temperature remains unknown. In this study, the fractal adsorption model is proposed based on the fractal dimension (Df) of coal pores and the attenuation coefficient (n) of the adsorption capacity. The principles and methods of this fractal adsorption model are deduced and summarized in detail. The results show that the pore structures of the two coal samples exhibit obvious fractal characteristics, with the values of fractal dimensions (Df) being 2.6279 and 2.93. The values of adsorption capacity attenuation coefficients (n) are estimated as −0.006 and −0.004 by the adsorption experiments with different temperatures. The proposed fractal adsorption model presents a greater theoretical significance and higher accuracy than that of the Langmuir equation. The accuracy of the fractal adsorption model with temperature effect dependence is verified, establishing a prediction method for methane adsorption capacity in deep coal reservoirs. This study can serve as a theoretical foundation for coalbed methane exploration and development, as well as provide valuable insights for unconventional natural gas exploitation.

Retinal vascular morphological characteristics in diabetic retinopathy: an artificial intelligence study using a transfer learning system to analyze ultra-wide field images.

To investigate the morphological characteristics of retinal vessels in patients with different severity of diabetic retinopathy (DR) and in patients with or without diabetic macular edema (DME). The 239 eyes of DR patients and 100 eyes of healthy individuals were recruited for the study. The severity of DR patients was graded as mild, moderate and severe non-proliferative diabetic retinopathy (NPDR) according to the international clinical diabetic retinopathy (ICDR) disease severity scale classification, and retinal vascular morphology was quantitatively analyzed in ultra-wide field images using RU-net and transfer learning methods. The presence of DME was determined by optical coherence tomography (OCT), and differences in vascular morphological characteristics were compared between patients with and without DME. Retinal vessel segmentation using RU-net and transfer learning system had an accuracy of 99% and a Dice metric of 0.76. Compared with the healthy group, the DR group had smaller vessel angles (33.68±3.01 vs 37.78±1.60), smaller fractal dimension (Df) values (1.33±0.05 vs 1.41±0.03), less vessel density (1.12±0.44 vs 2.09±0.36) and fewer vascular branches (206.1±88.8 vs 396.5±91.3), all P<0.001. As the severity of DR increased, Df values decreased, P=0.031. No significant difference between the DME and non-DME groups were observed in vascular morphological characteristics. In this study, an artificial intelligence retinal vessel segmentation system is used with 99% accuracy, thus providing with relatively satisfactory performance in the evaluation of quantitative vascular morphology. DR patients have a tendency of vascular occlusion and dropout. The presence of DME does not compromise the integral retinal vascular pattern.

Fractal Dimension(Df )Theory of Ismail's Entropy(IE) with Potential Df Applications to Smart Cities

Ismail entropy (IE), my newly developed entropy measure, is a final generalisation to many generalised entropies found in the literature. This research identifies the fractal dimension of IE. Additionally, this study presents some possible uses of fractal dimension in smart city applications. Concluding thoughts are included at the end of the work along with several difficult outstanding problems and the direction of future research

Multifractal analysis of the perimeters of glaciers in the Svalbard Archipelago

The investigation of the evolution of glaciers largely relies on the characterisation of extensive quantities like their mass, area, and perimeter. In this work we use fractal and multifractal analysis to investigate the non-extensive structural properties of the perimeters of glaciers in the Svalbard Archipelago. We show that the perimeters of the glaciers exhibit a fractal structure with a fractal dimension Df≃1.25 , independently from the area of the glaciers. The investigation of the multifractal properties of the perimeters shows that small glaciers exhibit a more pronounced multifractal structure, as witnessed by the larger range of generalized dimensions Dq needed to characterise them. The range ΔD q of generalised dimensions required to characterise the multifractal perimeter of a glacier exhibits a power-law dependence with exponent −1.2 from the area, and represents a non-extensive parameter able to grab effectively the dependence of the multifractal structure of the perimeters on the size of glaciers. The comparison with similar results obtained in a previous study performed on glaciers in the Lombardy region of the Italian Alps confirms the robustness of the analysis performed, which does not appear to be affected by the morphology of the substrate or by climate conditions.

Clay Tailings Flocculated in Seawater and Industrial Water: Analysis of Aggregates, Sedimentation, and Supernatant Quality.

High-molecular-weight anionic polyacrylamide was used to analyze the effect of kaolin on the structure of particle aggregates formed in freshwater and seawater. Batch flocculation experiments were performed to determine the size of the flocculated aggregates over time by using focused beam reflectance measurements. Sedimentation tests were performed to analyze the settling rate of the solid-liquid interface and the turbidity of the supernatant. Subsequently, a model that relates the hindered settling rate to the aggregate size was used to determine the mass fractal dimension (Df). Flocculation kinetics revealed that greater amounts of kaolin generated larger aggregates because of its lamellar morphology. The maximum size was between 10 and 20 s of flocculation under all conditions. However, the presence of kaolin reduced the settling rate. The fractal dimension decreased with the increase in the kaolin content, resulting in the formation of irregular and porous aggregates. By contrast, factors such as the flocculation time, water quality, and quartz size had limited influences on the fractal dimension. Seawater produced a clearer supernatant because of its higher ionic strength and precoagulation of particles. Notably, the harmful effect of clays in seawater was reduced.

Study on the gelling properties of egg white/surfactant system by different heating intensities

The aim of this study was to elucidate the different effects and difference mechanism of gelling properties among egg white (EW) treated with different heating intensities and the composite addition of rhamnolipid and soybean lecithin. Particle size analyzer, potentiometric analyzer, surface hydrophobicity method, and Fourier transform infrared spectroscopy techniques were used to determine the physicochemical properties and molecular structure, respectively. Low-field nuclear magnetic resonance, magnetic resonance imaging, texture profile analysis, and scanning electron microscopy techniques were used to analyze the gelling properties and gel structure, respectively. And we illuminate the different mechanisms in the gelling properties of the EW with various treatments and key internal factors that play important roles in improving gelling properties by establishing the link between the gelling properties and relevant characteristics by mixed effects model and visual network analysis. The results indicate raising the content of rhamnolipid decreased the migration of immobilized water in the EW gel and the free water content. At the heating intensities of 55 °C/3.5, 65 °C/2.5, and 67 °C/1.5 min, with an increase in rhamnolipid, the gel's cohesiveness, gumminess, and chewiness gradually increased. The mixed effects model indicated that heating intensities and composite ratios have a 2-way interaction on zeta potential, the relaxation time of bound water (T21), the content of bound water (P21), the content of immobilized water (P22), and fractal dimension (df) attributes (P < 0.05). The visual network analysis showed that the protein solubility, the relaxation time of immobilized water (T22), surface hydrophobicity, zeta potential, average particle size (d43) and the relaxation time of free water (T23) are critical contributors to the different gelling properties of EW subjected to various treatments and the improvement of gelling properties. This study will provide theoretical guidance for the development of egg white products and the expansion of egg white's application scope in the egg product processing industry.

The investigation of thickness-dependent mono-fractal, optical and optoelectronics properties of sputtered silver thin film for silicon solar cell

Here we report, the room temperature deposition of silver (Ag) thin films on silicon, glass and silicon solar cell substrates by magnetron sputtering. The effect of thickness on the deposited thin films and their morphological, fractal, optical and solar cell parameters have been extensively investigated. AFM results show that the Ag thin films are composed of different-size of nano-grains and the grain size increases with increasing thickness. Mono-fractal parameters, namely fractal dimension (Df) and Hurst exponent (H), were determined from the power spectral density function. X-ray photoelectron spectroscopy studies indicate that the deposited samples exhibit the presence of oxidation state of Ag (0) in thin films, confirming the stable structure. The optical analysis shows that the transmittance of the deposited thin films decreases with increasing thickness, on the other hand, the silver thin film with thickness of 20 nm shows surface Plasmon resonance (SPR) at 436 nm. Current-voltage (I–V) curves were measured in dark and under illumination mode at standard testing conditions, i.e., 300K, 1000 W/m2 and 1.5 AM global using a solar simulator. These measurement studies indicate that thicknesses are effectively impacts on photovoltaic performance. The calculated values of change in solar efficiency (Δη) are 0.26, −0.20, −0.76 and −6.88 % for thin films with nominal thickness 0.5, 1, 2 and 20 nm respectively.

Nanostructuring, fractal characterization and wettability of ion irradiated Au thin films and their thickness effect

This study proposes a method for modifying the wettability of Au thin films of thicknesses 5 nm and 10 nm on Si substrates using 8 keV Ne ion beam irradiation at different fluences, thereby enabling surface wettability adjustment at the nano-scale and its thickness dependence. This advancement would be highly beneficial for applications such as high-resolution printing and nano-biotechnology. The contact angle of the irradiated region for the 5 nm thin film changed from hydrophobic to hydrophilic with increasing ion dosage, whereas for the 10 nm thin film, it changed from hydrophilic to hydrophobic under the same conditions. Fractal analysis was performed on pristine and ion beam modified surfaces to investigate the underlying nano-structuring process, with reported values for average roughness (Ra), Hurst exponent (H), fractal dimension (Df), contact angle (CA), and wettability at different ion dosages. Atomic Force Microscopy and Rutherford Backscattering Spectroscopy were used to examine surface roughness and depth profile. The process of sputtering becomes crucial when the ion range approaches the thickness of thin films, with the sputter yield showing dependence on the thickness of thin films at different ion fluence levels. Monte Carlo simulations SRIM/TRIM and TRIDYN were used for comparison with the experimental results, with TRIDYN taking into account dynamic changes in the target's morphology and composition.