ORIGINAL PAPER

Evolution of Surface Roughness During Electropolishing

Prashant Pendyala • M. S. Bobji • Giridhar Madras

Received: 26 December 2013 / Accepted: 10 April 2014 / Published online: 24 April 2014

� Springer Science+Business Media New York 2014

Abstract The characteristics of surface roughness span a

range of length scales determined by the nature of the

surface generation process. The mechanism by which

material is removed at a length scale determines the

roughness at that scale. Electropolishing preferentially

reduces the peaks of surface protuberances at sub-micron

length scales to produce smooth surfaces. The material

removal in electropolishing occurs by two different

mechanisms of anodic leveling and microsmoothing. Due

to insufficient lateral resolution, individual contribution of

these two mechanisms could not be measured by conven-

tional roughness measurement techniques and parameters.

In this work, we utilize the high lateral resolution offered

by Atomic force microscopy along with the power spectral

density method of characterization, to study the evolution

of roughness during electropolishing. The power spectral

density show two corner frequencies indicating the length

scales over which the two mechanisms operate. These

characteristic frequencies are found to be a function of the

electropolishing time and hence can be used to optimize

the electropolishing process.

Keywords Electropolishing � Surface roughness � Atomic

force microscopy � Power spectral density

1 Introduction

Surfaces consist of superposed protuberances of widely

differing scales of size [1–6]. When two surfaces come

close to each other, contacts are established at certain pro-

tuberances that can be referred to as asperities [7, 8]. With

the development of nano/micromachining leading toward

fabrication of devices at small scales, roughness needs to be

understood and characterized at the length scales smaller

than that of devices. Roughness characteristics over various

length scales of a given surface depend on the processes that

generated the surface. For example, mechanical metal

removal processes such as machining and abrasive polish-

ing affect roughness only above certain length scale that is

determined by the dimensions of the cutting element [3, 9,

10]. In an electrochemical metal removal process such as

electropolishing, the roughness generated is dependent on

the local charge densities and the mass transfer mechanisms

[11], resulting in surfaces with ‘mirror finish.’ Roughness of

such surfaces is very small and is typically comparable to

the resolution of the conventional roughness measurement

techniques. In this work, we study the evolution of rough-

ness at sub-micron length scales during electropolishing

using atomic force microscopy (AFM).

Electropolishing is an anodic dissolution phenomenon

resulting in a smooth and bright surface [11, 12]. It is

generally employed either to replace abrasive polishing

entirely or as a finishing treatment after abrasive polishing.

Electropolishing was first systematically investigated by

Jacquet [13–16]. The conditions and mechanism of elec-

tropolishing were later studied in detail by many authors

[17–19]. Electropolishing occurs by two main mechanisms

of ‘anodic leveling’ and ‘microsmoothing’ [17, 19, 20].

Anodic leveling is due to differential local charge distri-

bution [17–19] where peaks of surface protuberances are

P. Pendyala � M. S. Bobji (&)

Mechanical Engineering Department, Indian Institute of Science,

Bangalore 560012, India

e-mail: bobji@mecheng.iisc.ernet.in

P. Pendyala

e-mail: pendyala@mecheng.iisc.ernet.in

G. Madras

Chemical Engineering Department, Indian Institute of Science,

Bangalore 560012, India

e-mail: giridhar@chemeng.iisc.ernet.in

123

Tribol Lett (2014) 55:93–101

DOI 10.1007/s11249-014-0336-x

preferentially dissolved. Microsmoothing is smoothing

induced by suppression of influence of surface defects and

of crystallographic orientation on the dissolution process

[17, 19, 21]. This is due to the formation of a thin ionic salt

film near to the surface of the anode that makes the

material removal a diffusion controlled process [17, 19].

Removal of irregularities by anodic leveling and micros-

moothing is widely demonstrated, but the exact contribu-

tions of different mechanisms have remained elusive to

determine [11, 17, 22]. In this work, we utilize the high

lateral resolution offered by AFM to study the individual

contributions of the material removal mechanisms in

electropolishing to the overall smoothing of a surface.

Surface roughness is typically characterized by various

statistical parameters from a measured profile of surface

heights [9]. Whitehouse and Archard [23] proposed that

roughness profile can be completely defined by two param-

eters: an amplitude parameter—rms height (Rq) and a lateral

or texture parameter—correlation distance (b�). The relation

between the amplitude and texture variations can be brought

out through power spectral analysis [3, 9, 24] of rough sur-

faces. Sayles and Thomas [25] established that power spec-

tral densities of many rough surfaces approximate to

continuous power law behavior. Mandelbrot [26] proposed

that spectral analysis can be used to measure the fractal

dimension of the surfaces, while Majumdar and Bhushan [3]

determined the fractal characteristics of magnetic tape sur-

face and machined steel surfaces using power spectral den-

sity. Power spectral density has also been used to relate the

roughness created by conventional machining techniques

such as turning, grinding, milling and mechanical polishing

to the modes of damage prevalent in the respective

machining process and the tool topography [10, 27, 28].

Unlike the abrasive machining processes which cannot

affect roughness characteristics below certain frequencies

(or above a certain wavelength), electropolishing through

anodic leveling can control roughness at higher frequen-

cies. In this work, we qualitatively analyze the surface

image and quantitatively process the height variation using

power spectral density as a function of electropolishing

time. Length scales of roughness, affected by the two metal

removal mechanisms operating during electropolishing, are

identified by the two corner frequencies in the power

spectral density plot. We show that roughness amplitudes

over a large range of frequencies can be controlled using

mechanical polishing and electropolishing in tandem.

2 Experimental Details

To ensure the uniformity of surface roughness at the start

of experiment, all the samples were mechanically polished

prior to electropolishing. Directional mechanical polishing

was performed with emery paper of gradually decreasing

sizes of grits from 300 to 2,000 grit. At each stage, care

was taken to remove scratches from previous grit size.

Finishing was done with diamond paste of 1–2 lm grit size

with almost no external load. In the final stages of pol-

ishing, the sample was polished alternatively in perpen-

dicular directions, to ensure nearly identical roughness

among all the samples. The uniformity in roughness was

cross examined by measuring the surface roughness.

Electropolishing was carried out in perchloric acid–eth-

anol solution of 1:4 ratio by volume [29, 30]. Pure aluminum

(99.99 %) samples of 10 mm 9 10 mm were used as anode,

and a graphite electrode was used as cathode. A voltage of

10 V was applied across the electrodes while maintaining the

electrolyte at 20 �C. The distance between the electrodes

was maintained at about 50 mm. The current density mea-

sured as soon as the sample is immersed into the electrolyte

was 0.210 A/cm2. This dropped to about 0.07 A/cm2 by

60 s. After this drop, the current density remained nearly

constant. Samples taken out of the solution after electro-

polishing were rinsed in distilled water and dried under

nitrogen purge. They were placed in desiccator vacuum

before roughness measurement.

Surface roughness was measured in a Bruker Dimension-

Icon AFM. A sharp silicon tip attached to a cantilever of

stiffness 40 N/m was used in tapping mode. Values of the

feedback controls are known to affect the roughness mea-

sured [31]. We used 7, 1.5 V as P, I values for the feedback

controller. These values were determined after optimizing

the feedback parameters for all surfaces such that the

roughness measured was not affected by minor changes in

these parameters. Roughness height profile was obtained for

scan sizes of 90 lm 9 90 lm, 30 lm 9 30 lm and

10 lm 9 10 lm with 256 9 256 data points per scan size.

The fast scanning direction was always maintained per-

pendicular to the direction of mechanical polishing in the

finishing step. The measured profiles were corrected for

AFM scanner bow by fitting a quadratic trend to each line

profile of 256 data points [31].

Apart from conventional parameters, the measured

roughness height profile was characterized by power

spectral density method. Power spectral density is obtained

from the discrete Fourier transform of the height profile. If

yðnÞ is the measured discrete height profile at N equally

spaced intervals dx over a length L ¼ N dx. Then, the

discrete Fourier transform [32] is given by

ZðmÞ ¼ dxXN�1

n¼0

yðnÞ exp�i2pnm

N

� �ð1Þ

where, 0�m�N. If ZðmÞ are the values obtained from

standard FFT routines, then

94 Tribol Lett (2014) 55:93–101

123

ZðmÞ ¼ dx:ZðmÞ ð2Þ

and the power spectral density can be obtained as [32],

PðmÞ ¼ L

N2ZðmÞ� �2 ð3Þ

This method gives the two-sided power spectral density

[32] and arrives at the correct values of rms roughness as

the area under power spectral density, as per Parseval’s

theorem [33]. It should be noted that in the equations

above, ‘m’ is a number and the corresponding frequency is

given by fm ¼ m=L. And due to symmetry only one half of

power spectral density, that is, from f ¼ 0 to N=ð2LÞ are

shown in figures. Practical issues with using one-sided

power spectral density have been discussed in detail by

Elson and Benett [32].

To reduce the fluctuation in the measured spectra,

ensemble average of the power spectra density is usually

used [34]. In the present case, we have calculated power

spectral density for each of the 256 height profiles along

the fast scanning direction, and a mean power spectral

density is obtained.

3 Results

3.1 AFM Imaging of Surfaces

Figure 1 shows the AFM images of surfaces that were

mechanically polished and electropolished for different

durations. The size of these images is 90 lm 9 90 lm, and

the vertical height scales are indicated beside every image.

The roughness initially increases, as compared to the

starting mechanically polished surface, and decreases

gradually with electropolishing time. It can also be seen

that the features that can be distinguished in these images

gradually decrease in number, and there are hardly any

Fig. 1 AFM images of (a) mechanically polished only surface and

(b–f) are of electropolished surfaces for 15, 30, 60, 120, 180 s time

durations respectively. The scan size is 90 9 90 lm with 256 data

points per scan length. Linear grooves appear in the mechanically

polished surface in the direction of polishing. The darker regions in

the 15 s electropolished sample are craters created due to pitting of

the sample. After 60 s groove remains disappear. With most of the

surface roughness getting reduced by 120 s of electropolishing, grain

boundaries indicated as ‘g’ in the figure, become prominent

Fig. 2 Representative line profiles of mechanically polished sample

are compared with line profiles of samples electropolished for various

durations of time. All the line profiles have been obtained along the

fast scan direction of the AFM image

Tribol Lett (2014) 55:93–101 95

123

distinguishing physical features after 120 s of

electropolishing.

The mechanically polished sample (Fig. 1a) is charac-

terized by linear grooves along the polishing direction. These

grooves are formed by the plowing action of the abrasive

particles and hence should be dependent on the size of these

particles as well as the normal load applied on the sample

[28]. The width of the grooves seen in the AFM images

varied from 500 nm to about 2 lm, comparable to the size of

the diamond particles used for final stage of polishing.

The surface of the mechanically polished specimen has a

non-uniform oxide layer, and the sub surface is damaged

[35]. The presence of this passive non-homogeneous layer,

accompanied by the high applied potential, gives rise to

pitting of the surface as soon as the mechanically polished

sample is placed in the electropolishing solution [17, 19].

The rapid dissolution of metal begins, accompanied by

high current densities, forming crater like structures on the

surface. From AFM image (Fig 1b), it can be seen that at

15 s of electropolishing time, surface is completely covered

with small and large craters. The width of the larger craters

is up to 10 lm. However, leftover grooves from the

mechanical polishing could still be seen clearly. At this

stage, the surface looks brighter compared to mechanically

polished surface. From the representative single-line pro-

files in Fig. 2, it can be seen that 15 s of electropolishing

has removed the high-frequency roughness but increased

the general amplitudes of roughness. Individual craters can

be identified in the line profile, as indicated by arrows.

The surface looks smoother with increase in electro-

polishing time to 30 s (Fig. 1c). The larger craters have

increased in width due to merger with other craters

(Fig. 1c). As the circular craters merge, they become

ellipsoidal in the plan view. 3-D view of one such larger

crater identified in the AFM image (Fig. 1c) of 30 s elec-

tropolished sample is shown in Fig. 3. The crater measures

around 20 lm in width. The rim of this crater formed by

merging of smaller craters seen in (Fig. 1b), is not even and

consists of hills placed far apart.

The grooves left over from the mechanical polishing

completely disappear only after 60 s of electropolishing.

The line profiles (Fig. 2) show that the general amplitude

of roughness has decreased after 120 s of electropolishing

time. As the roughness decreases with the electropolishing

time, the grain boundaries start becoming prominent after

120 s (indicated by ‘g’ in the AFM image of Fig. 1e).

Typically, a step of 5–10 nm is formed across the grain

boundary. In between the grain boundaries, the surface is

smooth as can be seen from the AFM image (Fig. 1f) and

line profile (Fig. 2). With further increase in electropol-

ishing time to 180 s, the surface becomes more flat with

grain boundaries creating the only distinguishable feature

in the profile. Evolution of hydrogen gas seems to be

defining the macroscopic surface morphology for very long

durations of electropolishing exceeding an hour.

Various statistical roughness parameters [36] of

mechanically polished and electropolished surfaces,

obtained from AFM images for a sampling length of 90 lm,

are shown in Table 1. The mean roughness (Ra) for the

mechanically polished samples is around 19� 3 nm. It

increases to 45 nm for the 15 s electropolished sample

because of the craters produced on the surface. The Ra values

remain high till 60 s electropolishing. The value decreases to

around 20 nm at 120 s and it reduces to less than 10 nm at

180 s. Root-mean-square roughness (Rq) and peak-to-peak

roughness (Rz) follow similar trend. It can be seen in Table 1

for mechanically polished sample, the roughness height

parameters are very similar to 120 s electropolished sample.

However, the line profiles (Fig. 2) and the AFM images

(Fig. 1) show contrasting features bringing out clearly the

limitations in the conventional parameters.

The distribution of heights about the mean plane, for the

mechanically polished surface containing groove structures

is positively skewed. For 15 s electropolished sample, the

skewness has increased owing to the micropits formed on

the surface. With a further increase in time, skewness

decreases indicating that the surface becomes more evenly

distributed about the mean plane. Electropolishing being

field assisted dissolution process, preferentially attacks the

peaks, and the kurtosis value reduced from 3.6 of

mechanically polished surface to less than 3 for electro-

polished surface [36].

3.2 Power Spectral Density of Roughness Profiles

Power spectral density for wide range of roughness fre-

quencies has been obtained by varying the scan size and

Fig. 3 Surface plot of a pit formed on 30 s electropolished sample

shown from the region marked in Fig. 1c

96 Tribol Lett (2014) 55:93–101

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keeping the number of sampling points constant. The

power spectral density of mechanically polished surface

obtained by superposition of power spectral density from

scan sizes of 90, 30 and 10 lm is shown in Fig. 4. The

solid line shows the power law fit to the data and is used to

compare with that of electropolished surfaces. It has been

found that the power spectral density measured for the

surfaces slightly flattens off for the highest frequencies.

The scatter in the power spectral density shown is

obtained from five different samples polished and imaged

under identical conditions. All the samples produced a sharp

change in the slope of power spectral density at a corner

frequency (CF) of about f ¼ 3:1� 105 m�1 (Fig. 4). This

characteristic frequency [3] corresponds to a wavelength of

3.2 lm comparable to the width of linear grooves (observed

in Fig. 1a) created by the diamond grit particles used in final

stage of polishing. The power spectral density to the left of

CF is flattened, as lower roughness frequencies are affected

by polishing [10]. The spectra to the right of CF represent

the roughness characteristics of a fractured surface created

due to material removal by grits of abrasive. The slope of the

spectrum in this region, expressed as exponent(n) of the

power law relation P / f n [9, 25, 37] was found to be

n ¼ �2:5. This has been interpreted as the fractal charac-

teristics of the surface roughness [9, 24–26, 37]. If the

exponent ‘n’ lies between -1 and -3, then the surface

roughness can be said to posses fractal characteristics [3,

24]. The exponent ‘n’ will be equal to zero if the roughness

is random with no lateral correlation.

Figure 5 shows the power spectral density of the surface

electropolished, for 60 s obtained from three different scan

sizes of 90, 30 and 10 lm. It represents the typical power

spectral density plot obtained for electropolished surfaces.

Unlike the mechanically polished sample, the power

spectral density of electropolished surface has two promi-

nent corner frequencies CF1 and CF2 where there is defi-

nite change in the slope of power spectral density. First

corner frequency CF1 is found at a frequency of f ¼3:9� 105 m�1 and the second corner frequency CF2 at

f ¼ 5:5� 104 m�1. The presence of two corner frequencies

indicates that more than one mechanism of surface for-

mation is active in electropolishing [9, 37].

The power spectral density of 15, 60, 120 and 300 s

electropolished surfaces for the scan size of 90 lm, along

Table 1 Roughness parameters obtained for mechanically polished and electropolished samples

Time (s) Ra (nm) Rq (nm) Rz (nm) sk ku m0 ð�103Þ ðnm2Þ m2 ð�10�3Þ m4 ð�10�9Þ ðnm�2Þ

Mech. polish 19� 3:0 24 99 0.17 3.6 0.27 1.05 32

15 45� 7:5 55 270 0.35 2.9 2.80 1.80 33

30 35� 6:3 43 196 0.20 2.7 1.40 0.51 10

60 40� 7:9 49 207 0.10 2.6 2.40 0.67 13

120 18� 7:2 23 103 0.10 2.7 0.33 0.08 2.9

180 9� 2:7 11 52 0.01 2.9 0.12 0.19 7.2

Fig. 4 Mean power spectral density obtained from the power spectral

density of the five mechanically polished surfaces is plotted. Scatter

of the power spectral density calculated at different roughness

frequencies is shown

Fig. 5 Roughness power spectral density of 60 s electropolished

sample. The power spectra are divided into three regions by two

corner frequencies CF1 and CF2 appearing in the spectra

Tribol Lett (2014) 55:93–101 97

123

with that of mechanically polished surface is shown in

Fig. 6. Electropolished surfaces initially show increased

power spectral density at lower frequency region compared

to that of mechanically polished surface. With an increase

in electropolishing time, the power spectral density of the

surfaces gradually decreases at all frequencies. By 300 s of

electropolishing roughness frequencies higher than f ¼105 m�1 are reduced. The three distinct regions in the

power spectral density separated by two corner frequencies

(as shown in Fig. 5) can be noticed in almost all (except for

300 s) the electropolishing power spectral density curves in

Fig. 6. Each of the three regions can be studied individu-

ally to understand the characteristics of various material

removal mechanisms over time.

4 Discussion

When a mechanically polished surface is immersed into the

electrolyte solution, ordinary anodic dissolution of the non-

uniform passive oxide layer starts, resulting in crater for-

mation on the surface. The power spectral density of 15 s

electropolished surface shows the corner frequency CF1 at

around f ¼ 105 m�1, comparable to the size of the craters

observed in the AFM image (Fig. 1b). Anodic dissolution

increases the roughness at all frequencies. However, the

accompanying electropolishing seems to have an effect at

higher frequencies. This can be seen from the line profile of

15 s electropolished surface (Fig. 2), where the high-fre-

quency roughness is reduced, even though the overall

roughness has increased.

The roughness generated by electropolishing is con-

trolled by two different mechanisms of anodic leveling and

microsmoothing. In anodic leveling, due to the higher local

charge distribution, protuberances with smaller radii of

curvature dissolves faster. Hence, power spectral density

decreases faster at higher roughness frequencies. However,

when the amplitude of the protuberances becomes com-

parable to the thickness of the ionic salt film formed in the

electrolyte close to the surface, micropolishing becomes a

dominant mechanism. Micropolishing is diffusion con-

trolled process and possibly gives rise to a flatter power

spectral density. It can be seen from Figs. 5 and 6 that for

the roughness frequencies to the right of CF2 (region 3),

the power spectral density is nearly flat. Roughness fre-

quencies in between CF1 and CF2 represent the region

affected predominantly by anodic leveling (region 2).

Roughness wavelengths corresponding to the characteristic

frequencies CF1 and CF2 are plotted as a function of

electropolishing time in (Fig. 7a, b), respectively. Anodic

leveling moves both the corner frequencies to the left of the

power spectral density plot with time. For 15 s of elec-

tropolishing, frequencies corresponding to the roughness

wavelengths than 1 lm are affected by micropolishing and

roughness wavelengths between 1 and 10 lm are con-

trolled by anodic leveling.

Anodic leveling and microsmoothing decrease the

magnitude of power spectral density for all the frequencies

to the right of CF1 (region 2 and region 3). However, for

roughness frequencies to the left of CF1 (region1), the

magnitude remains nearly constant till about 60 s. This

increases the slope of power spectral density in the region

2. At 120 s, when magnitude of power spectral density for

region 1 reduces, the slope starts to increase (Fig. 8). By

300 s, most of the roughness frequencies were reduced, and

thus, the power spectral density plot appears flat. At this

stage, power spectral density shows only CF2 at the left

end of the spectrum, indicating that amplitudes of most of

the roughness frequencies have decreased to the value

comparable to that of thickness of the salt film.

Power and hence amplitudes at low-frequency rough-

ness are much higher than those at high frequencies. This

may result in the magnitude of statistical roughness height

parameters such as Ra and Rq being principally influenced

by smaller roughness frequencies (or higher wavelengths)

of the power spectral density curve. Hence, in the initial

stages of electropolishing, even though the high-frequency

roughness is reduced (as shown in the schematic in Fig. 9),

the pitting of the surface keeps the magnitude of roughness

height parameters (Table 1) high till about 60 s of elec-

tropolishing. Only at 120 s of electropolishing time, when

lower roughness frequencies are reduced due to anodic

leveling, magnitude of height parameters start decreasing.

At 180 s of electropolishing, the mean roughness of the

surface is reduced to less than 10 nm. The slope of the

power spectral density in region 2 is in between -1 and -3

(Fig. 8), showing that roughness frequencies at these length

Fig. 6 Power spectral density of electropolished surfaces for 15, 60,

120 and 300 s are compared along with power spectral density of

mechanically polished surface

98 Tribol Lett (2014) 55:93–101

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scales are fractal in nature. Anodic leveling is now random

and unbiased due to the previous mechanical polishing [3].

The surface seems to be completely controlled by

electropolishing, which is evident from the complete dis-

appearance of features from mechanical polishing in the

AFM image (Fig. 1f).

Electropolishing will have a greater effect on the rms

slope and curvature as the higher-frequency roughness is

removed predominantly. These parameters can be obtained

from the higher-order moments of the power spectral

density [38, 39]. The pth order spectral moment mp can be

obtained as [40],

mp ¼ð2pÞp

L

XN=2

m¼0

ðfmÞp PðmÞ ð4Þ

The values of zeroth(m0), second (m2) and fourth moments

(m4) of the power spectral density of surfaces are given in

the Table 1. Square root of these values gives the rms

values of height, slope and curvature, respectively [38, 40].

It can be seen that the electropolishing to about 180 s

reduces the second moment and the fourth moment by an

order of magnitude compared to the mechanically polished

surface. In contrast to this, zeroth moment, which is equal

to R2q , increases initially and after 180 s of electropolishing

reaches the values similar to those of the starting

mechanically polished surface. Thus, electropolishing

results in asperities having larger apex angles and larger

radius of the curvature.

At a given electropolishing time, anodic leveling redu-

ces the amplitudes of roughness frequencies between CF1

and CF2 and primarily contributes to the smoothening of

the surface. Roughness frequencies to the right of CF2

follow a flat spectral characteristic. Thus, CF2 can be taken

as a cutoff parameter to optimize the electropolishing

process. Surface of samples electropolished for prolonged

time may look wavy as the higher roughness frequencies

are removed leaving behind the smaller roughness fre-

quencies. Also, other phenomenon such as streaking due to

hydrogen gas evolution affects the roughness characteris-

tics at smaller frequencies. It is to be noted that mechanical

polishing reduces the amplitude of the surface protuber-

ances above a characteristic frequency and electropolishing

reduces amplitude of protuberances below a characteristic

Fig. 7 Roughness wavelengths

corresponding to characteristic

frequencies CF1 and CF2 are

plotted as a function of

electropolishing time.

Roughness wavelengths getting

reduced steadily increase with

time. CF2 can be taken as cutoff

for deciding the electropolishing

parameters

Fig. 8 Exponent of the power spectra in the region 2 from Figs. 5 and

6 is plotted as a function of time. Electropolished for 180 s has

exponent value in between -1 and -3 for the profiles measured. That

is, electropolishing is becomes random only after 180 s where

roughness produced from mechanical polishing does not create any

bias in electropolishing

Fig. 9 Schematic showing the smoothing of surface in electropol-

ishing over time

Tribol Lett (2014) 55:93–101 99

123

frequency. Using both the processes in tandem, it is pos-

sible to control the roughness characteristics at all the

frequencies. Subsequently, this ability can be used to tailor

roughness at nanoscales to control tribological properties

of miniature components.

5 Conclusion

Using the high lateral resolution offered by AFM and the

roughness power spectral density, we have qualitatively

and quantitatively estimated the evolution of surface

roughness during electropolishing over time over a range

of length scales. Mechanically polished surface owing to

the non-uniform nature of the oxide layer resulted in pitting

of the surface, in the initial stages of electropolishing. With

an increase in electropolishing time, the amplitude of the

craters is reduced and the surface becomes smoothened.

Roughness power spectral density of electropolished

surfaces shows two corner frequencies CF1 and CF2

indicating the different material removal mechanisms in

operation. Roughness frequencies between CF1 and CF2

could be related to anodic leveling, while roughness fre-

quencies to the right of CF2 are affected by microsmoo-

thing phenomenon. Individual contributions of anodic

leveling and microsmoothing are obtained from the pro-

gress of CF1 and CF2 over electropolishing time. Further

CF2 can be used as a parameter to optimize the electro-

polishing process.

Unlike the abrasive machining processes, in electro-

polishing, roughness frequencies reduced are a function of

time and smallest roughness features are reduced first.

Hence, prolonged electropolishing may give a wavy sur-

face. Using combination of electropolishing and various

abrasive polishing processes, roughness can be controlled

over a wide range of length scales, which is an ideal

requirement for micro/nanomachining process.

Acknowledgments Authors acknowledge Prof. Mark Robbins, The

Johns Hopkins University, for his suggestions on higher moments of

power spectra. Authors acknowledge CeNSE, IISc., Bangalore for

AFM imaging.

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