Fractal analysis with scanning probe microscopy

1992 ◽  
Vol 50 (2) ◽  
pp. 1046-1047
Author(s):  
Paul E. West ◽  
Sid Marchesse-Rugona ◽  
Zhuoning Li
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Physical Properties ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Optical Microscope ◽  
Two Dimensional ◽  
Atomic Force ◽  
Dimensional Measurements ◽  
Surface Profiles

Surface roughness determined qualitatively by direct visualization can be correlated to several physical properties. However, finding a suitable method of quantifying surface roughness, until recently, has been difficult. The concept of Fractal Dimension, recently popularized by Mandelbrot(1982) has been extremely successful in quantifying surface roughness and relating it to such measurable physical properties such as; cleanability, catalytic activity, rate of corrosion, and even flavor.Atomic Force Microscopes permit direct three dimensional measurements of surface microstructure. AFM images are obtained by measuring the motion of a sharp stylus as it is scanned across a surface. Because the AFM directly measures three dimensional topograms, it is ideally suited for two dimensional and three dimensional fractal analysis. Other microscope techniques such as the scanning electron or optical microscope give only two dimensional magnification and fractal measurements are not easily made.The Atomic Force Microscope enables us to obtain the fractal dimension of surface profiles as well as surface areas. For surface profiles we use a box counting method (Mandelbrot 1986, Chesters et al. 1989).

A Three-Dimensional Fractal Analysis Method for Ground Monocrystal Sapphire Surface

2014 ◽  
Vol 1017 ◽  
pp. 187-192
Author(s):  
Qiu Yan Wang ◽  
Zhi Qiang Liang ◽  
Xi Bin Wang ◽  
Wen Xiang Zhao ◽  
Yong Bo Wu ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Three Dimensional ◽  
Ground Surface ◽  
Surface Characteristics ◽  
Surface Phenomenon ◽  
Analysis Method ◽  
Characterization Methods ◽  
Box Counting

Conventional characterization methods of grinding surface using surface roughness parameters, e.g., Ra, depend on either the resolution of the measuring instrument or the length of the sample. But fractal dimension (FD) as a scale-independent fractal parameter is effective to evaluate the ground surface at any length scale and represent lots of surface phenomenon at its relevant length scales. In this paper, a three-dimensional (3D) box-counting fractal analysis method is used to investigate ground surface morphology of monocrystal sapphire by calculating 3D fractal dimension of the ground surface. The results obtained show that fractal dimension decreases with the increasing surface roughness. For the ground surface with higher fractal dimension, its microtopography is more exquisite with minor defects. Once the fractal dimension become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the ground surface obtained in ductile mode has much higher fractal dimension than that in brittle mode. Therefore, the fractal analysis method has the potential to reveal the ground surface characteristics of monocrystal sapphire.

A comparison of fractal methods for evaluation of hydraulic fracturing surface roughness

2020 ◽  
Vol 60 (1) ◽  
pp. 184 ◽  
Author(s):  
Abbas Movassagh ◽  
Xi Zhang ◽  
Elaheh Arjomand ◽  
Manouchehr Haghighi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Hydraulic Fracturing ◽  
Fractal Analysis ◽  
Roughness Length ◽  
Variation Method ◽  
Fracture Surfaces ◽  
Wide Range ◽  
Surface Profiles ◽  
Fractal Methods

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

scholarly journals Three-Dimensional Coordination Number from Two-Dimensional Measurements: A New Method

1986 ◽  
Vol 32 (112) ◽  
pp. 391-396 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Coordination Number ◽  
Three Dimensional ◽  
New Method ◽  
Two Dimensional ◽  
Shape Factors ◽  
Important Measure ◽  
Dimensional Measurements ◽  
Average Bond

AbstractThe average three-dimensional coordination number, n3, is an important measure of firn structure. The value of n3 can be estimated from n2, the average measured two-dimensional coordination number, and from a function, Γ, that depends only on the ratio of average bond radius to grain radius in the sample. This method is easy to apply and does not require the use of unknown shape factors or tunable parameters.

scholarly journals Tip-Based Nanomachining on Thin Films: A Mini Review

2021 ◽  
Author(s):  
Shunyu Chang ◽  
Yanquan Geng ◽  
Yongda Yan
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Data Storage ◽  
Three Dimensional ◽  
Maintenance Cost ◽  
Two Dimensional ◽  
Force Microscopy ◽  
Atomic Force ◽  
Current State ◽  
Two Dimensional Materials

AbstractAs one of the most widely used nanofabrication methods, the atomic force microscopy (AFM) tip-based nanomachining technique offers important advantages, including nanoscale manipulation accuracy, low maintenance cost, and flexible experimental operation. This technique has been applied to one-, two-, and even three-dimensional nanomachining patterns on thin films made of polymers, metals, and two-dimensional materials. These structures are widely used in the fields of nanooptics, nanoelectronics, data storage, super lubrication, and so forth. Moreover, they are believed to have a wide application in other fields, and their possible industrialization may be realized in the future. In this work, the current state of the research into the use of the AFM tip-based nanomachining method in thin-film machining is presented. First, the state of the structures machined on thin films is reviewed according to the type of thin-film materials (i.e., polymers, metals, and two-dimensional materials). Second, the related applications of tip-based nanomachining to film machining are presented. Finally, the current situation of this area and its potential development direction are discussed. This review is expected to enrich the understanding of the research status of the use of the tip-based nanomachining method in thin-film machining and ultimately broaden its application.

scholarly journals Study on the Physical Properties of a SiNW Biosensor to the Sensitivity of DNA Detection

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5716
Author(s):  
Siti Noorhaniah Yusoh ◽  
Khatijah Aisha Yaacob
Keyword(s):  
Surface Roughness ◽  
Physical Properties ◽  
Limit Of Detection ◽  
Silicon Nanowire ◽  
Volume Ratio ◽  
Silicon Nanowire Arrays ◽  
Atomic Force ◽  
Local Anodic Oxidation ◽  
Wet Chemical ◽  
Biosensor Device

SiNW (silicon nanowire) arrays consisting of 5- and 10-wires were fabricated by using an atomic force microscope—the local anodic oxidation (AFM-LAO) technique followed by wet chemical etching. Tetramethylammonium hydroxide (TMAH) and isopropyl alcohol (IPA) at various concentrations were used to etch SiNWs. The SiNWs produced were differed in dimension and surface roughness. The SiNWs were functionalized and used for the detection of deoxyribonucleic acid (DNA) dengue (DEN-1). SiNW-based biosensors show sensitive detection of dengue DNA due to certain factors. The physical properties of SiNWs, such as the number of wires, the dimensions of wires, and surface roughness, were found to influence the sensitivity of the biosensor device. The SiNW biosensor device with 10 wires, a larger surface-to-volume ratio, and a rough surface is the most sensitive device, with a 1.93 fM limit of detection (LOD).

scholarly journals Automated three-dimensional measurements of version, inclination, and subluxation

2019 ◽  
Vol 12 (1) ◽  
pp. 31-37
Author(s):  
Dave R Shukla ◽  
Richard J McLaughlin ◽  
Julia Lee ◽  
Ngoc Tram V Nguyen ◽  
Joaquin Sanchez-Sotelo
Keyword(s):  
Computed Tomography ◽  
Image Analysis ◽  
Three Dimensional ◽  
Automated Image Analysis ◽  
Two Dimensional ◽  
Analysis Software ◽  
Glenoid Version ◽  
Image Analysis Software ◽  
Planning Software ◽  
Dimensional Measurements

Background Preoperative planning software has been developed to measure glenoid version, glenoid inclination, and humeral head subluxation on computed tomography (CT) for shoulder arthroplasty. However, most studies analyzing the effect of glenoid positioning on outcome were done prior to the introduction of planning software. Thus, measurements obtained from the software can only be extrapolated to predict failure provided they are similar to classic measurements. The purpose of this study was to compare measurements obtained using classic manual measuring techniques and measurements generated from automated image analysis software. Methods Ninety-five two-dimensional computed tomography scans of shoulders with primary glenohumeral osteoarthritis were measured for version according to Friedman method, inclination according to Maurer method, and subluxation according to Walch method. DICOM files were loaded into an image analysis software (Blueprint, Wright Medical) and the output was compared with values obtained manually using a paired sample t-test. Results Average manual measurements included 13.8° version, 13.2° inclination, and 56.2% subluxation. Average image analysis software values included 17.4° version (3.5° difference, p < 0.0001), 9.2° inclination (3.9° difference, p < 0.001), and 74.2% for subluxation (18% difference, p < 0.0001). Conclusions Glenoid version and inclination values from the software and manual measurement on two-dimensional computed tomography were relatively similar, within approximately 4°. However, subluxation measurements differed by approximately 20%.

scholarly journals Multiscale three-dimensional surface reconstruction and surface roughness of porcine left anterior descending coronary arteries

2019 ◽  
Vol 6 (9) ◽  
pp. 190915 ◽  
Author(s):  
Hanna E. Burton ◽  
Rachael Cullinan ◽  
Kyle Jiang ◽  
Daniel M. Espino
Keyword(s):  
Surface Roughness ◽  
Coronary Arteries ◽  
Medical Devices ◽  
Ex Vivo ◽  
Three Dimensional ◽  
Force Microscopy ◽  
Optical Scanning ◽  
Atomic Force ◽  
Reconstructed Surface ◽  
Dimensional Surface

The aim of this study was to investigate the multiscale surface roughness characteristics of coronary arteries, to aid in the development of novel biomaterials and bioinspired medical devices. Porcine left anterior descending coronary arteries were dissected ex vivo , and specimens were chemically fixed and dehydrated for testing. Surface roughness was calculated from three-dimensional reconstructed surface images obtained by optical, scanning electron and atomic force microscopy, ranging in magnification from 10× to 5500×. Circumferential surface roughness decreased with magnification, and microscopy type was found to influence surface roughness values. Longitudinal surface roughness was not affected by magnification or microscopy types within the parameters of this study. This study found that coronary arteries exhibit multiscale characteristics. It also highlights the importance of ensuring consistent microscopy parameters to provide comparable surface roughness values.

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