Surface Topography Research Articles

Surface roughness measurement in the notch area for estimating dynamic component load bearing capacity

The surface of a part can have an essential influence on its dynamic load bearing capacity as grooves and scratches act as more or less significant imperfections or additional micro-notches, depending on the interpretation. In order to accurately predict the fatigue strength, detailed knowledge of the surface structure in critical areas is essential but cannot always be established due to geometric constraints. To overcome these restrictions, a method utilizing impressions and a laser scanning microscope to take surface topography measurements in critical notch areas is used in this work. It enables precise and reproducible measurements to be taken. The method is used to conduct surface roughness measurements on fatigue strength specimens made of four different materials. Several roughness influence factors are calculated based on the results and their influence on the result of a recalculation using a fatigue strength assessment is shown as example. The calculated fatigue limit is compared against experimental results. The comparison shows significant scatter in prediction accuracy and no optimal surface influence factor can be recommended so far. It has to be noted that only a small sample of specimens, which were not designed for researching surface roughness influence in particular, were available for this work. The effects of roughness in the notch may not be completely captured by the available roughness influence factors. Furthermore, issues arise in the correct implementation of stress concentration factor based roughness influence factors. Further research is required to provide a more comprehensive understanding of the effects of surface roughness on the fatigue limit.

Impact of Glow-Discharge Nitriding Technology on the Properties of 3D-Printed Grade 2 Titanium Alloy

This study presents a comparative analysis of the corrosion resistance of nitrided layers on conventional Grade 2 titanium alloy and those produced by direct metal laser sintering (DMLS). Low-temperature glow-discharge nitriding of the tested materials was carried out using conventional glow-discharge nitriding (so-called nitriding at the cathode potential—TiN/CP) and with the use of an “active screen” (nitriding at the plasma potential—TiN/PP). The TiN + Ti2N + Ti(N) layers were characterized by their microstructure, nanohardness profile distribution, surface topography, and corrosion resistance. The reduction in the cathodic sputtering phenomenon in the process using the active screen allowed the creation of surface layers that retained the topography of the base material. The parameters of the glow-discharge treatment led to grain growth in the printed substrates. This did not adversely affect corrosion resistance. The corrosion resistance of nitrided layers on the printed titanium alloy is only slightly lower than that of layers on the conventional Grade 2 alloy. Iron precipitates at grain boundaries facilitate increased nitrogen diffusion, resulting in reduced nitrogen concentration in the surface layer, slight changes in corrosion potential values, and increased nitrogen concentration in the Ti(N) diffusion layer.

Navigating Complex Process and Design Challenges in Hybrid Bonding for Advanced Semiconductor Integration: A Comprehensive Analysis

Abstract In advanced electronic systems, achieving top-tier interconnect interfaces with fine-pitch integration is of paramount importance. Among interconnect options, hybrid bonding is the preeminent choice given its exceptional capacity for accommodating a high input/output (I/O) count, which facilitates high-density memory integration, increased power delivery, and enhanced signal speed. One key technique for ensuring utmost quality in hybrid bonding involves embedding Cu interconnects within the dielectric layer. Equally pivotal is surface planarization, accomplished through chemical mechanical polishing (CMP), which encompasses a meticulous two-step procedure, commencing with copper bulk CMP and culminating in barrier CMP. The latter step is particularly critical, yielding the indispensable surface finish required for a successful hybrid bonding process. Several crucial surface properties significantly influence overall bond yield, including a copper recess (“dishing”) in the vias, erosion and roughness of the dielectric layer, and surface topography changes from high-density to low-density copper vias. To optimize these parameters, a comprehensive understanding of the interconnect layer's design is essential. Here, we delve into the ramifications of via scaling, ranging from 5 to 1 µm, on dishing and roll-off, and the effects of copper via density variation, spanning from 16% to 13%, on topography. Furthermore, we explore how incorporation of dummy vias impacts the final surface finish, potentially leading to improved bond yie

Calibration of the spherical tip radius of Rockwell hardness diamond indenters using a confocal laser scanning microscope

Abstract The precise form of an indenter is an essential part of hardness testing methods. It is therefore incumbent upon a user to ensure that the indenter geometry is calibrated before performing a hardness test. A geometric change of the tip radius by ±5 μm can cause a change of approximately 0.6 units of Rockwell hardness C scale (HRC) in a material with a hardness of 65 HRC. Keeping in mind that the measurement uncertainty is typically of the order of 0.3 HRC, it is critical to know the true value of the tip radius. Typically, tactile methods are used to determine the tip radius of a Rockwell hardness diamond indenter from the measured surface topography. Two main drawbacks of tactile measurements are the long duration of measurement and the limitation in capturing surface features of sizes smaller than the probe tip radius of 2 μm. Both could be overcome by using an optical 3D measurement. Confocal laser scanning microscopes (CLSM) allow a fast contactless 3D-mapping of the surface of Rockwell hardness diamond indenters and can be used to obtain geometric information such as the tip radius. The accuracy of these 3D measurements is still under question. Within this work, some of the influencing factors for fast 3D surface measurement are investigated. Using a CLSM with a 50x objective lens and a numerical aperture of 0.95, typical shape deviations of Rockwell diamond indenters are shown. Furthermore, an improved 3D based point cloud method for the evaluation of the indenter radius is presented. The aim of this paper is to explore the capabilities and limits of CLSM to obtain the 3D surface of a Rockwell hardness diamond indenter in order to calibrate the tip radius and compare their results with measurements from traceable stylus instruments.

Reshaping and enzymatic activity may allow viruses to move through the mucus.

Filamentous viruses like influenza and torovirus often display systematic bends and arcs of mysterious physical origin. We propose that such viruses undergo an instability from a cylindrically symmetric to a toroidally curved state. This "toro-elastic" state emerges via spontaneous symmetry breaking under prestress due to short range spike protein interactions magnified by surface topography. Once surface stresses are sufficiently large, the filament buckles and the curved state constitutes a soft mode that can potentially propagate through the filament's material frame around a Mexican-hat-type potential. In the mucus of our airways, which constitutes a soft, porous 3D network, glycan chains are omnipresent and influenza's spike proteins are known to efficiently bind and cut them. We next show that such a non-equilibrium enzymatic reaction can induce spontaneous rotation of the curved state, leading to a whole body reshaping propulsion similar to - but different from - eukaryotic flagella and spirochetes.

The Impact of Modeling Liquids on Surface Roughness and Color Properties of Bulkfill Resin Composites After Simulated Tooth Brushing: An in Vitro Study. Part I.

To evaluate the effect of different modeling agents on color changes, surface roughness, and translucency parameters over time in Bulkfill resin composites. Sixty specimens were prepared using three Bulkfill resin composites (Tetric N-Ceram Bulkfill, Filtek One Bulkfill and Opus Bulkfill) and three modeling agents (Wetting Resin, Optibond FL and Ambar APS). All specimens were subjected to a simulated tooth-brushing (Baseline, 50.000 cycles, 100.000 cycles), and surface roughness was measured at each interval. Surface topography was evaluated. The translucency parameter and color changes were assessed after 24-h, 7-, 14- and 30-day immersion in water, wine, and coffee. Data was analyzed using ANOVA and Bonferroni test. All specimens increased roughness after simulated tooth-brushing (p < 0.05). Wetting Resin decreased roughness on Tetric N-Ceram Bulkfill (p < 0.05). The translucency parameter remained unaltered for all groups. All groups changed color after 30-days of immersion in wine and coffee (p < 0.05). Ambar APS and Wetting Resin on Tetric N-Ceram Bulkfill showed higher color changes when immersed in coffee (p < 0.05). The use of modeling agents does not jeopardize translucency properties but may affect surface roughness and color properties of Bulkfill resin composites depending on their composition. The findings of this study suggest that surface roughness and color properties are affected by the differences in the composition between modeling agents and Bulkfill resins composites.

Design and Technological Aspects of Integrating Multi-Blade Machining and Surface Hardening on a Single Machine Base

Modern mechanical engineering faces high competition in global markets, which requires manufacturers of process equipment to significantly reduce production costs while ensuring high product quality and maximum productivity. Metalworking occupies a significant part of industrial production and consumes a significant share of the world’s energy and natural resources. Improving the technology of manufacturing parts with an emphasis on more efficient use of metalworking machines is necessary to maintain the competitiveness of the domestic machine tool industry. Hybrid metalworking systems based on the principles of multi-purpose integration eliminate the disadvantages of monotechnologies and increase efficiency by reducing time losses and intermediate operations. The purpose of this work is to develop and implement a hybrid machine tool system and an appropriate combined technology for manufacturing machine parts. Theory and methods. Studies of the possible structural composition and layout of hybrid equipment at integration of mechanical and surface-thermal processes were carried out, taking into account the basic provisions of structural synthesis and componentization of metalworking systems. Theoretical studies were carried out using the basic provisions of system analysis, geometric theory of surface formation, design of metalworking machines, methods of finite elements, and mathematical and computer modeling. The mathematical modeling of thermal fields and structural-phase transformations during HEH HFC was carried out in ANSYS (version 19.1) and SYSWELD (version 2010) software packages using numerical methods of solving differential equations of unsteady heat conduction (Fourier equation), carbon diffusion (2nd Fick’s law) and elastic–plastic behavior of the material. The verification of the modeling results was carried out using in situ experiments employing the following: optical and scanning microscopy; and mechanical and X-ray methods of residual stress determination. Formtracer SV-C4500 profilograph profilometer was used in the study for simultaneous measurement of shape deviations and surface roughness. Surface topography was assessed using a Walter UHL VMM 150 V instrumental microscope. The microhardness of the hardened surface layer of the parts was evaluated on a Wolpert Group 402MVD. Results and discussion. The original methodology of structural and kinematic analysis for pre-design studies of hybrid metalworking equipment is presented. Methodological recommendations for the modernization of multi-purpose metal-cutting machine tool are developed, the implementation of which will make it possible to implement high-energy heating with high-frequency currents (HEH HFC) on a standard machine tool system and provide the formation of knowledge-intensive technological equipment with extended functionality. The innovative moment of this work is the development of hybrid metalworking equipment with numerical control and writing a unique postprocessor to it, which allows to realize all functional possibilities of this machine system and the technology of combined processing as a whole. Special tooling and tools providing all the necessary requirements for the process of surface hardening of HEH HFC were designed and manufactured. The conducted complex of works and approbation of the technology of integrated processing in real conditions in comparison with traditional methods of construction of technological process of parts manufacturing allowed to obtain the following results: increase in the productivity of processing by 1.9 times; exclusion of possibility of scrap occurrence at finishing grinding; reduction in auxiliary and preparatory-tasking time; and reduction in inter-operational parts backlogs.

Influence of RE2O3 (Dy2O3, Yb2O3, and Lu2O3) buffer layers on the structural and ferroelectric characteristics of BiFeO3 thin films

Abstract This study investigates the impact of RE2O3 (Dy2O3, Yb2O3, and Lu2O3) buffer layers on the structural and ferroelectric properties of BiFeO3 thin films grown using a spin-coating method. BiFeO3 thin films with various RE2O3 buffer layers were analyzed using X-ray diffraction, atomic force microscopy, secondary ion mass spectrometry, and X-ray photoelectron spectroscopy to determine their crystalline structures, surface topographies, depth profiles, and chemical compositions, respectively. The RE2O3-buffered BiFeO3 film showed better electrical properties compared to the control BiFeO3 film. The buffer layer composed of Yb2O3 showed the lowest leakage current of 6.82×10-6 A/cm2, highest remnant polarization of 44.1 C/cm2, and smallest coercive field of 189 kV/cm because of the incorporation of Yb3+ ions into the BiFeO3 film, high degree of (110) preferred orientation, high Fe3+ content, low surface roughness, reduction of Fe3+ valence fluctuation to Fe2+ ions, and decrease in oxygen vacancies. Such BiFeO3 thin films with various RE2O3 buffer layers using spin-coating method pave a pathway toward practical applications of spintronic, sensor and memory.

Active illumination mode with checkerboard pattern in focus variation microscopy: Analysis and application

Optical measurement methods for surface topography offer the advantages of high accuracy, rapid measurement, and non-destructiveness. Each method has its own suitable application scenarios. Among them, focus variation microscopy is extensively employed in precision manufacturing, aerospace, and medical industries due to its ability to measure rough and large slopes surfaces. However, since the measurement depends on local grayscale differences between focused and blurred images, it cannot measure surfaces with low reflectivity or insufficient texture information. In this work, we propose an active illumination mode for focus variation method that utilizes a digital micromirror device (DMD) to generate a checkerboard pattern. This method introduces additional texture information, resulting in a usable local gradient of image grayscale. Additionally, we analyze the selection criteria for the checkerboard pattern parameters, including the period and light-dark ratio. Furthermore, measurements of two standard steps with different heights demonstrate that the measurement repeatability of the proposed method can reach the nanometer level, rendering it suitable for high-precision measurements. More importantly, the measurement noise results indicate significantly superior performance of active illumination mode compared to the uniform illumination mode. Finally, we reconstruct the surface topography of the microchannels in a microfluidic chip through the encapsulation layer, demonstrating the feasibility of the proposed method.

Evaluation of antibacterial activity on nanoline-array surfaces with different spacing

Extensive research has been conducted on anti-biofouling or antibacterial surfaces, with nanostructured surfaces that mimic cicada and dragonfly wings emerging as promising candidates for mechano-bactericidal applications. These biomimetic nanostructured surfaces are capable of exerting a bactericidal effect by directly damaging the membranes of bacteria attached to nanostructures. Although research on bactericidal effect using various nanostructures have been conducted, no specific studies have yet reported on the antibacterial efficiency of the surface having nanoline array, especially regarding the spacing between nanolines. This study details the fabrication of nanoline array via ultraviolet (UV) molding with polyurethane acrylate (PUA), noted for its UV sensitivity and rapid curing, enabling the fabrication of precise and scalable nanoscale structures. Investigation into the nanoline array’s antibacterial effects against Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) reveals that nanoline spacing critically influences bacterial adherence and viability, with specific spacings enhancing antibacterial properties. Scanning electron microscopy (SEM) and confocal microscopy analyses show that surface topography significantly affects bacterial behavior, with specific spacings leading to varied bacterial responses, including membrane damage and altered attachment patterns. The study highlights the potential of nanoline array in fabricating surfaces with tailored antibacterial properties, emphasizing the importance of nanoscale design in influencing bacterial interaction and viability. We also confirm the relative mechanical rigidity of the nanoline array, which exhibits antibacterial effects, through both experimental observations and numerical analysis. This indicates our proposed nanoline-array surface could have potential future applications in mechanical anti-bacterial functions that require such structural robustness.

Effect of peroxide-free and peroxide-based in-office bleaching on the surface and mechanical properties of CAD/CAM esthetic restorative materials.

The study aimed to investigate the influence of H2O2-based and H2O2-free in-office bleaching on the surface and mechanical attributes of CAD/CAM composite blocks. CAD/CAM composite blocks from five different composite materials (CC1, CC2, CC3, CC4, and CC5) were randomly divided into two groups according to bleaching application (H2O2-based and H2O2-free). The surface topography, morphology, nanohardness, elastic modulus, flexural strength, and fracture toughness were measured. A paired and unpaired sample t-tests gauged the effect of pre- and post-bleaching on the substrates. The estimated mean differences (before-after bleaching) suggested an increase in surface roughness for two materials CC2 and CC4, and a significant decrease in nanohardness for material CC4 and in elastic modulus for materials CC2 and CC4 with H2O2-based bleaching, whereas H2O2-free bleaching resulted in changes compatible with no change in these properties. Flexural strength and fracture toughness showed no evidence of changes, irrespective of the bleaching gel used. Scanning electron microscopic analysis revealed erosive effects and micropore formation due to H2O2-based bleaching. H2O2-based bleaching deteriorates the surface of CAD/CAM composite materials while H2O2-free bleaching gel had an insignificant effect on both surface and bulk properties. The clinician should carefully evaluate the potential effects of H2O2-based bleaching on the surface properties of CAD/CAM composites.

Dilatational rheological studies on the surface micelles of Poly(styrene)-[formula omitted]-Poly(4-vinyl pyridine) block copolymer at the air-water interface

A thin film of an amphiphilic block copolymer, poly(styrene)-b-poly(4-vinyl pyridine), is investigated at the air–water interface. The surface pressure - area per molecule isotherm and the static compressional modulus provide evidence of two phases, assigned as L1 and L2, respectively. The surface topography and the phase images of these phases obtained using atomic force microscope reveal the presence of surface micelles of different sizes and densities. The dilatational rheology of these phases was investigated using the oscillatory barrier method for different strain amplitudes (1−5%) and qualitatively assessed using Lissajous–Bowditch curves. It points out the emergence of nonlinearity (asymmetric shape and distorted ellipse) with an increase in strain amplitude. Using a fast Fourier transform, the amplitudes and the phases of different harmonics of the stress–strain curves were extracted, and the total harmonic distortion was determined. In contrast to L1 phase, the total harmonic distortion for the L2 phase increases monotonically with strain amplitude. Fixing the strain amplitude at 1% (small amplitude regime), the temperature as well as frequency dependence studies of the dilatational moduli were carried out. The dynamic storage moduli of the L1 phase is found to be insensitive to temperature while it decreases for the L2 phase suggesting softening. Further, evidence for solid-like viscoelastic response emerges (explained using the Kelvin–Voigt model) for the L1 phase, whereas the L2 phase show a cross-over behaviour.

Surface Topography Analysis of BK7 with Different Roughness Nozzles Using an Abrasive Water Jet

Surface Topography Analysis of BK7 with Different Roughness Nozzles Using an Abrasive Water Jet

The Influence of Electro Less Ni-P Coating Comprising of Nano Additive on Surface Topography of Mg Alloy

The Influence of Electro Less Ni-P Coating Comprising of Nano Additive on Surface Topography of Mg Alloy

The effect of semi-curing on neat resin mode I fracture properties

The sensitivity of fracture toughness to the cure path of a high-performance hot infusion epoxy resin (EP2410) is assessed in this study through single-edge notch bend testing of neat resin specimens. The specimens were prepared using a two-stage semi-curing process. In the initial stage, the partial degree of cure and the semi-cure temperature were varied. In the second stage, samples were heated to 180 °C for a secondary post-cure. These samples were compared to two baseline samples produced using the manufacturer's recommended cure cycle of 180 °C, and a modified isothermal cure at a lower cure temperature of 140 °C. The results show that the semi-curing path has no statistically significant influence on the mode I fracture toughness of the material studied here. Sample similarity was confirmed through SEM examination of the fracture surface, which showed minimal variation in surface topography. These findings open new possibilities to use this type of material for novel manufacturing processes involving semi-curing steps.

Roughness measurement results evaluation of 6082 aluminium alloy specimens after fatigue bending tests

In this paper, the topography of 6082 aluminium alloy specimens after fatigue bending tests was studied with a comprehensive evaluation of measurement noise caused by vibration. Roughness results were acquired by contactless Focus Variation Microscopy (FVM). Studied data were pre-processed, removing the non-measured points and outliers with regular methods, respectively, and high-frequency noise was considered. The variations in ISO 25178 roughness parameters were studied. Based on the previous studies, it was found that surfaces after fatigue bending tests can be difficult to consider when analyzing the measurement noise in a selected bandwidth. Some advantages of profile data extraction in selected directions, like horizontal, vertical or crack, were found deficient, even in studies by various functions, like autocorrelation, power spectral density, or texture direction ratio. When noise suppression methods depend on the details studied, boundary areas were extracted to compare and highlight the presence of high-frequency data characteristics. The proposed method was validated when contrasting standardised Gaussian or median filtering techniques with the spline filtering approach. A proper filter for the reduction of vibrational noise from the results of FVM topography measurements was suggested based on the proposed procedure. Finally, it was proposed how use the new method for reducing errors caused by high-frequency measurement noise in the surface topography of specimens after fatigue bending tests.

PH-dependent self-assembly of an acid derivative of cholesterol at interfaces

Understanding and control over the self-assembly of molecules is desirable in many physico-chemical processes. Functional groups responsive to a pH change offer immense scope in driving selective molecular self-assembly. pH-dependent self-assembly of an aromatic acid derivative of cholesterol, 4-(6-(cholest-5-ene-3-yloxy)-5-(oxopentyloxy)) benzoic acid, ChBA, is investigated at the air-aqueous interface and characterized using different interface-sensitive techniques. Evidence for the presence of unstable films of ChBA at the air-water interface or for pH < 10 emerges from the surface pressure – area per molecule isotherm, surface pressure relaxation, and Brewster angle microscopy studies. In contrast, for pH > 10.6, ChBA forms a relatively stable film with a higher magnitude of the collapse pressure (45 mN/m). The compressional moduli and the textures obtained using Brewster angle microscopy reveal the presence of two phases (L1 and L2), which are also highly stable with temperature. The surface topography of ChBA films transferred from the air-water interface reveals the presence of multilayers of different thicknesses, for film transferred at pH 11 reveals primarily a uniform and homogenous monolayer. Based on the dependence of the collapse pressure with pH, the surface pKa of ChBA is estimated to be about 10.6. Our studies show that the undissociated ChBA spontaneously forms multilayers, whereas partially or fully dissociated ChBA forms distinct and ordered monolayer phases, highlighting the role of electrostatic interactions.

Polyvinyl alcohol-chitosan based oleanolic acid nanofibers against bacterial infection: In vitro studies and in vivo evaluation by optical and laser Doppler imaging modalities

The present work focuses on the fabrication of polyvinyl alcohol-chitosan-loaded oleanolic acid-nanofibers (PVA-CS-OLA-NFs) for bacterial infection. The prepared PVA-CS-OLA-NFs were characterized for contact angle, SEM, AFM, XRD, FTIR, and TGA. The solid-state characterization and in vitro performance evaluation of nanofibers reveal consistent interconnection and diameters ranging from 102 ± 9.5 to 386 ± 11.6 nm. The nanofibers have a flat surface topography and exhibit efficient drug entrapment. Moreover, the in vitro release profile of PVA-CS-OLA-NFs was found to be 51.82 ± 1.49 % at 24 h. Furthermore, the hemocompatibility study showed that the developed PVA-CS-OLA-NFs are non-hemolytic to human blood. The PVA-CS-OLA-NFs demonstrate remarkable antibacterial capabilities, as evidenced by their MBC and MIC values, which range from 128 and 32 μg/mL, against the strains of S. aureus. The in-vivo fluorescence optical imaging showed the sustained PVA-CS-OLA-NFs release at the wound site infected with S. aureus for a longer duration of time. Moreover, the PVA-CS-OLA-NFs showed superior wound healing performance against S. aureus infected wounds compared to the marketed formulation. Further, the laser Doppler imaging system improved oxygen saturation, blood supply, and wound healing by providing real-time blood flow and oxygen saturation information.

Enhancing Photoswitchable Wetting Properties of Hydrophobic Porous Spiropyran Copolymer Surfaces Through Surface Roughness Engineering

AbstractSurfaces with photoswitchable wettability are of great interest for various applications such as smart coatings or liquid condensation. The photochromic ring opening reaction of spiropyran (SP) to merocyanine (MC) implies a high dipole moment change, making it interesting for photo‐controlled wetting properties. In addition to the material chemistry, surface wettability is influenced by the surface topography. Porous SP copolymers with various micro‐/nanostructures, that is, different submicron roughness, are fabricated via polymerization‐induced phase separation. The influence of the surface topography on the photoswitchable wetting properties is studied. Surfaces with arithmetic mean roughness (Sa) below 150 nm exhibited a maximum static contact angle (SCA) photoswitch up to 16° from 124 ± 6° to 108 ± 4° upon UV exposure. While superhydrophobic surfaces with higher Sa (157 – 608 nm) showed an insignificant SCA switch. The latter surfaces have a SCA above 150° and low CA hysteresis indicating small and insufficient contact with SP/MC surface asperities for the switch. With the optimized surfaces, photo‐controlled water condensation is studied on microscale and showed that the condensate droplets merged faster, and formed larger droplets pinned to the original contact lines on surfaces switched to the less hydrophobic state.

An overset-grid finite-difference algorithm for seismic wavefield propagations modelling in the polar coordinate system with a complex free-surface topography

Summary Nowadays, finite-difference method has been widely applied to simulate seismic wavefield propagation in a local seismic model with a complex topography by utilizing curvilinear grids and traction image method in Cartesian coordinates system. For a global seismic model in polar coordinate system, it is still a challenge for the conventional finite-difference method to deal with the grid singularity at the center and the topographic free surface at the top. In this study, we develop a finite-difference method in polar coordinates for seismic wavefield propagation in the 2D global model. In the proposed finite-difference method, the overset-grid algorithm is used to handle the grid singularity at the center, and the curvilinear grid technique as well as the traction image method are applied to implement free-surface boundary condition on the complex topography. The proposed finite-difference method is validated in flat and topographic free-surface models by comparing synthetic waveforms with reference solutions. The seismic wavefield propagation in a realistic Mars profile is computed by the proposed finite-difference method. The proposed finite-difference method is an efficient and accurate method for seismic wave modeling in the polar coordinate system with a complex free-surface topography.