STM study of a curved Pt (111)
single crystal with kinked steps.
THESIS
submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in PHYSICS
Author : Jessika Pi ˜neiros
Student ID : 1848437
Supervisor : Prof.dr.ir. T.H. Oosterkamp
2ndcorrector : Dr. L.B.F. Juurlink
STM study of a curved Pt (111)
single crystal with kinked steps.
Jessika Pi ˜neiros
Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands
August 27, 2018
Abstract
Curved crystals provide the possibility to study different vicinal surfaces in a single crystal. In this thesis, we analyzed a curved Pt (111) single crystal with kinked steps under UHV conditions using STM images to
characterize the sample. We present and compare terrace width histograms of different images taken on the crystal.
Contents
1 Introduction 7
2 Theory 9
2.1 Crystals and surfaces 9
2.2 Terrace width and surface energy 11
2.3 Platinum 13
2.4 Scanning Tunneling Microscope 14
3 Methodology 17
3.1 Sample preparation 17
3.2 Image analysis 18
3.2.1 Terraces separation 19
3.2.2 Removing outliers by z values 19
3.2.3 Optimization of the border parameter 21
4 Results and Discussion 23
4.1 Gwyddion 23 4.2 TWD Histograms 23 4.2.1 Image A 24 4.2.2 Image B 27 4.2.3 Image C 31 4.2.4 Image D 34
5 Conclusions and Outlook 39
Chapter
1
Introduction
Catalysts are widely used in the chemical industry to reduce the energy barrier of chemical reactions. Hence, is crucial to fundamentally under-stand the processes occurring during catalytic reactions. In these reactions, the surface structure undergoes some structural transformations [1, 2].
Under ultrahigh vacuum (UHV) conditions the surface may suffer changes as well, such as step bunching or faceting. These transformations can be triggered by temperature, the presence of adsorbates and also by a mis-cut dependence. For instance, Ilyn et al., 2017 showed the influence of elastic interactions in step-doubling for A-type steps in a curved Ni(111) crystal [2].
Surface phenomena such as crystal growth, surface roughening, equi-librium shape of small crystallites and chemical reactions are influenced by steps [3, 4]. Steps and defects play an important role as active sites of catalysts, nucleation, and electron scattering centers. Additionally, cat-alytic reaction rates might be influenced by specific steps orientation [1, 5]. Vicinal surfaces are used in catalysis and surface science since these structures provide a dense array of steps [3, 5]. In this respect, curved crystals offer high and low-index vicinal regions on a single surface which can significantly reduce the experimental time and simplify the study of surface properties [6].
Surface atoms have different bonding forces than bulk atoms. They will react with each other or with foreign atoms, and contract toward the bulk (relaxation). A surface can go through reconstruction as well to max-imize their bonding requirements [7, 8].
Steps atoms exhibit different bonding forces than terrace atoms. There-fore a different chemical reactivity is expected as well [7], and due to the lower coordination number of steps atoms, these are preferred places
8 Introduction
for adsorption and nucleation, and also active sites for chemical reactions [2, 3]. Thus, understanding the influence of steps on surface properties un-der UHV conditions might contribute to unun-derstanding physical-chemical processes on crystal surfaces [3].
Single crystals fundamental studies are usually done under UHV con-ditions. Several surface analysis, such as Low Energy Electron Diffraction (LEED), Auger Electron Spectroscopy (AES) and Scanning Tunneling Mi-croscopy (STM) are done under UHV conditions [6].
Platinum single crystals have been widely studied. These structures have remarkable thermal stability. Hence, these crystals have been used to study surface catalyzed reactions for temperatures below 1500 K [9]. Pt (111) has also been extensively used to study CO chemisorption, although the role of steps in catalytic reactions is still being investigated [3].
Usually, a curved single crystal is cut in a way to display straight step edges, but it can also display kinked step edges [6].
The main goal of this project was to calculate the terrace width distribu-tion of a curved Platinum (111) single crystal with kinked steps, focusing on the influence of the kinks. For the analysis of the crystal surface under UHV conditions, we will use STM images to characterize the sample.
Chapter
2
Theory
The theoretical background information about crystals, as well as the tech-niques used for the crystal surface analysis are given in this chapter.
2.1
Crystals and surfaces
An ideal crystal is a highly ordered microscopic structure, described in terms of a lattice. Some of the common Bravais lattices (crystalline struc-tures) in metals are face-centred cubic (FCC), body-centred cubic (BCC) and hexagonal close-packed (HCP). Crystal planes are defined by the sur-face normal and are denoted by Miller indices, three integers: h,k,l en-closed in parentheses for a single plane e.g.,(0 0 1)or curly brackets for a set of related planes, e.g. {0 0 1}. Directions vectors are denoted by Miller indices enclosed in square brackets, e.g. [0 0 1][7, 10].
Besides flat single crystals, there are different shapes available, such as cylindrical crystals, dome-shaped crystals or curved single crystals with the approximate size and shape of a single flat crystal [6]. If the crystal is cut at a slightly deviated angle with respect to the [hkl] direction, (miscut angle α), vicinal surfaces appear. A vicinal surface is composed of terraces separated by steps, and it might also have kinks sites along the steps [7, 10]. Steps on fully kinked surfaces are prone to step meandering since fewer bonds are broken, compared to a closed packed step [5]. In Fig. 2.1 terraces, steps and kinks are shown.
Cutting a curved crystal with the steps running along the [1 1 0] direc-tion and towards either the[1 1 2]or [1 1 2] direction gives a close-packed symmetry with straight step edges [11], see Fig: 2.2(c). Curved crys-tals feature a smooth transition between different vicinal surfaces. For a
10 Theory
Figure 2.1: Representation of single FCC crystal surface with (111) terraces.The step is shown in a lighter color.
curved (111) single crystal, (111) terraces are separated by A and B-steps on each side of the crystal, which have {100} and {111}-like microfacets re-spectively [1, 2]. A schematic illustration of a curved crystal with straight step edges is shown in Fig. 2.2, where the difference between A and B steps can be seen more clearly. Whereas a vicinal surface with fully kinked step edges running along the[1 1 2]direction is shown in Fig: 2.3 [5].
(a)
(b)
(c)
Figure 2.2:a)Surface of a curved (111) crystal where two kind of steps are shown: A-steps to the left, B-steps to the right. (Adapted from Blomberg et al., 2017 Ref [1]). b) Schematic drawing of steps structures of a FCC (111) crystal. (Adapted from Corso et al., 2009 Ref [12]). c) Schematic of a curved crystal with straight step edges. (Adapted from Ortega et al., 2011 Ref [13])
crys-2.2 Terrace width and surface energy 11
(a)
(b)
Figure 2.3:a)Schematic of the Pt(111) curved crystal with kinked step edges along the [1 1 2] direction analyzed in this report. b)Schematic front view of kinked step edges where the A and B step types are highlighted in purple and yellow, respectively.
tal [6]. The variation of structure provided by curved crystals facilitate the study of surface chemistry and may be used to study surface states bands [12, 14]. The analysis of low and high Miller index surfaces can be achieved by using different flat single crystals, which might have different quality and will increase the experimental time considerably, or by using a designed single curved crystal [6].
2.2
Terrace width and surface energy
The terrace width d (average step-step distance) decreases inversely pro-portional to the miscut angle α as Eq.( 2.1), where h is the monoatomic step height [13]. The monoatomic step density (v 1/d) increases according to the miscut angle [6].
d= h
sin α (2.1)
The surface energy γ is defined as a function of α and the temperature T, as Eq.( 2.2), where γ0 is the surface energy of the terrace, β is the step formation energy, aqis the atomic distance parallel to the steps, and B(T) is
the step interaction, which includes both the entropic interaction g(T) and the step-step interaction [12, 13, 15]. The entropic interaction play a more significant role for low step-density (wide terraces) while the step-step in-teraction has a critical influence for high step density (narrow terraces). Step-step interactions are usually described as dipole elastic interactions (v1/d2) [3, 13].
12 Theory γ(α) =γ0+β|tan α| h + B(T) aqh3 |tan α|3 (2.2)
An exhaustive analysis of STM images from a curved single crystal al-lows detecting the transition from entropic to elastic step interactions in vicinal surfaces [3]. This transition can be visualized with a terrace width distribution (TWD) [2]. The distribution of the steps evolves from wide to narrow terraces as the repulsive (elastic) interactions between steps over-comes the entropic repulsion [3, 16] Walter et. al., (2015) [3] illustrated his-tograms of high and low step densities and also the transition from elastic to entropic regime on a Pt(111) single curved crystal. They found that for large d values the linear correlation between the mean terrace width ˜d and
σis lost for a critical value ˜dcof 42 ˚A, see Fig. 2.4 [3]
Figure 2.4: a)STM images taken at both sides of the crystal with their respective histograms of the terrace width distribution fitted with Gaussian distributions. b) σvs ˜d from the full set of STM images showing the elastic to entropic transition at ˜dc=42 ˚A.(Adapted from Walter et al., 2015 Ref [3])
In regard to curved crystals with kinked step edges, Ortega et al., (2018) reported that fully kinked Ag(111) vicinal surfaces display fast step fluc-tuations at 300 K. They observed a symmetric terrace width probability histogram for small d, while for d>3nm the maximum value starts to shift to the left and some fluctuations appear on the right side tail, see Fig. 2.5 [5].
2.3 Platinum 13
Figure 2.5:a)Normalized probability histograms [P(d/ ˜d)] of the curved Ag(111), fitted with GWS functions for different values of the terrace width. b) Normalized probability for large d, fitted with a single series of Gaussian functions, (Adapted from Ortega et al., 2018 Ref [5] ).
2.3
Platinum
Platinum is a transition metal with a close-packed structure (FCC), con-sidered a noble and inert metal [17]. The lattice constant of platinum is 392.42pm [18]. Platinum is a widely used solid catalyst that provides a surface where reactants can bind, this binding speeds up the rate of the chemical reaction [19]. Platinum surfaces have been extensively studied since early years. For instance, the splitting on LEED patterns in clean Platinum stepped surfaces was reported by Lang et al., 1972. This split-ting appears at certain voltages and as a function of ordered steps [9]. The adsorption and desorption of oxygen and CO on Pt has been extensively studied as well, for more than forty years [20].
Structural distortions such as step relaxations towards the bulk and in the terrace have been found on stepped Pt(111). These topmost planes distortions can vary in average as a function of d [3, 21].
14 Theory
2.4
Scanning Tunneling Microscope
In 1981, Gerd Binning and Heinrich Rohrer built a microscope based on the quantum tunneling process, capable of image surfaces at the atomic level. They were awarded with the Nobel prize in 1986 for the develop-ment of the Scanning Tunneling Microscope, which has been widely used for research since then [22].
As historical review, Binning et al., (1982) [23] described in one of their first articles the feasibility of vacuum tunneling even at room tem-perature and non ultrahigh vacuum conditions. Tersoff et al.,(1983) [24] presented the theory to support vacuum tunneling using a model for the tip and calculations for the surface to explain the first experimental STM results for Au(110) reported previously by Binning et al.,(1983) [25]. Be-sides, Gerd Binnig and Heinrich Rohrer in the article ”Scanning tunneling microscopy-from birth to adolescence” published in 1987 [26] presented a summary of the historical development of the STM, including some tech-nical aspects.
STM components are: a sharp metallic tip (attached to a piezodrive), a scanner (piezoelectric), feedback electronics and a computer system. Dur-ing the scan, the tip is approached to the surface but held a few ˚A apart. Thus, the electron wave functions of the closest tip atom and surface atoms electron overlap [10, 22].
In the imaging process, a sharp metallic tip is scanned across a con-ductive sample while applying a bias voltage [22]. The bias voltage will unbalance the Fermi levels, allowing the electrons tunneling between tip and sample [26]. The tunneling current flowing between the tip and the sample depends exponentially on the distance between them and on the local density of states of the sample (LDOS) (i.e., its electronic density of states); it also depends on the applied voltage [22].
In Fig. 2.6 the electron tunneling from occupied states of the tip into unoccupied states of the sample is shown. Where z is the surface normal direction, s is the tip-sample distance, the work functions and the Fermi levels of the tip and the sample are φT and φS, EFS and EFT, respectively [22]. In order to have a tunneling current, a bias voltage V should be applied. If a positive voltage is applied to the sample, its Fermi level is shifted by −eV and electrons tunnel from occupied states of the tip into unoccupied states of the sample. On the other side, if a negative voltage is applied to the sample, its Fermi level is shifted by eV and electrons tunnel from occupied states of the sample into unoccupied states of the tip [22].
2.4 Scanning Tunneling Microscope 15
Figure 2.6:Energy potential vs the surface normal direction for a positive sample voltage V. The tunneling probability decreases correspondingly with the decreas-ing of the thickness and length of the arrows. (Adapted from Encyclopedia of Nanotechnology, 2012 Ref [22]).
There are two main modes for STM imaging: constant current mode and constant height mode [10]. For the constant current mode the tunnel-ing current and the bias voltage are kept constant, while the height (z) is measured. To maintain a constant current the vertical tip position is ad-justed by the feedback voltage Vz applied on the z-piezoelectric driver. Changes in the work function are compensated by changes in the tip-sample distance [27]. On the other side, for the constant height mode z and the bias voltage are kept constant while the tunneling current is measured [10], see Fig. 2.7.
16 Theory
Figure 2.7: STM imaging: a)constant current mode, b) constant height mode. (Adapted from Binning et al., 1987 Ref [26]).
Chapter
3
Methodology
This chapter describes the Pt(111) surface analysis as well as the criteria used for the terrace width distribution analysis. The crystal can be pic-tured as a thin circular section of 8 mm in diameter, enclosing 31◦of cylin-drical azimuth, such that the apex is a (1 1 1) plane of the FCC structure of bulk Pt, and the kinked step edges run along the [1 1 2] direction, see Fig. 3.1.
Figure 3.1: Schematic a)top and b)front view of the curved Pt crystal analysed (dimensions in mm). (Adapted from Janlamool et. al., 2014 [14].)
3.1
Sample preparation
Sputtering-annealing cycles are commonly used to remove lattice defects and adsorbed impurities of surfaces [7]. Sputtering is a physical va-por deposition method where an amount of material is released from a
18 Methodology
solid target by bombardment with energetic ions that are generated in a glow discharge plasma, under vacuum conditions [22]. During sputtering monoatomic vacancies are created but it can cause also lattice damaging effects. A layer-by-layer removal can also be achieved [28].
Whereas annealing is a heat treatment that induces some physical changes to the material [22]. Annealing after sputtering helps to recrystallize the surface damaged during sputtering and also provides mobility to the steps to achieve thermodynamically stable steps [11].
Michely et al., (1991) [28] reported the temperature dependence of the sputtering morphology of Pt(111). They concluded that annealing to tem-peratures above 700 K implies interlayer mass transport related to diffus-ing species and that the highest temperature determines the ultimate mor-phology of the crystal [28].
The cleaning cycles were based on the process described in Walsh et al., 2016 [6]. Multiples sputtering-annealing cycles: Ar+sputtering (1x10−5mbar, 0.23 kV, 1 µA, 800 K, 5 min), followed by O2 treatment (3x10−8mbar, 900 K, 3 min) and in vacuo annealing (1200 K, 3 min).
The crystal is heated by radiative heating and electron bombardment, using a filament (W) and applying a positive bias to the crystal to achieve high temperatures (>600 K). The surface was checked with LEED images. Unfortunately, during the cleaning cycles, which can take several days, the sputter gun stopped working, and we couldn’t fix it on time. Thus, we refocused on the analysis of some images of our crystal taken some time before in the same STM.
3.2
Image analysis
For image analysis, a python code was written. This code is capable of rec-ognizing the steps, and then it saves the steps and terraces coordinates in new arrays to calculate the terrace width distribution. The code is adapt-able for different crystal surfaces after determining some critical values inherent to every crystal, in order to distinguish steps from terraces. We will refer to the analyzed images as Image A, Image B, Image C and Image D.
The image analysis has two main parts: first some defects such as hor-izontal scars are removed, and the terraces are leveled in Gwyddion, sec-ond, the data is imported in Python to separate the coordinates of different terraces and plot the terrace width histograms. After loading the data file in python to visualize the crystal surface in a 3D plot, the data is sorted
3.2 Image analysis 19
by z (ascending order, see Fig. 3.2(a)) to calculate the gradient on z and distinguish different terraces. Then, a Savitzky Golay filter is applied to smooth the noise fluctuations without distorting the data [29].
3.2.1
Terraces separation
On the gradient plot (z), see Fig. 3.2(b), we can see that each peak cor-responds to a new terrace. Thus, we need a criterion to separate terrace coordinates from step coordinates. The border parameter will be the first criterion used to separate those coordinates. On the gradient plot, we plot a horizontal line (border line) to judge the separation of terraces and steps coordinates by choosing a value that seems visually appropriate. In such a way that every point above the green line will be considered a step coor-dinate, and every point below the green line will be considered a terrace coordinate. The appropriate separation of coordinates is checked on the 3D plot. After that, the position of every terrace is found as the local max-ima in the gradient of the z values.
(a) (b)
Figure 3.2: a)Lateral view of the data sorted by z, where the z position (height) is plotted against the number of data points. b)Gradient of z coordinates, where the raw data, filtered data and border line are shown in blue, orange and green, respectively. (Image D)
3.2.2
Removing outliers by z values
Once the terraces are separated as different arrays, we remove the outliers per terrace. There are several ways to remove outliers, one of those is a box plot. The whiskers of the box plot can be defined as one or more standard
20 Methodology
deviation above and below the mean of the data. Another alternative is to use the quartiles to determine these whiskers [30].
For the first approach, we remove outliers based on Eq. 3.1 and Eq. 3.2 for every single terrace. Where µtis the mean per terrace, σtis the standard deviation per terrace, zposand zneg are the z values equal or bigger than µt plus n times σt and equal or smaller than n times σt subtracted from µt, respectively. Thus, the values that fulfill these conditions are removed from the array.
zpos ≥µt+nσt (3.1)
zneg ≤µt−nσt (3.2)
For this approach, we plot the variation in the mean µn and in the stan-dard deviation σn of the entire histogram (all the terraces) as a function of the σ used to remove outliers (σt), see Fig. 3.3. It is clear that that from n = 3 the curve becomes stable, there is not a significant change for the mean or the standard deviation of the entire histogram anymore.
(a) (b)
Figure 3.3:Outlayers criteria for image A. a) µnof the entire histogram vs
differ-ent values of σt used to remove outliers b) σnof the entire histogram vs different
values of σtused to remove outliers.
The second approach is more commonly used to remove outliers since it considers not only the mean and dispersion of the distribution but also its variability. Any value outside the intervals defined by Eq. 3.4 and Eq. 3.5 is considered an outlier. Where Q1, Q3, and IQR are the first quar-tile, third quartile and the inter-quartile range, respectively. IQR is calcu-lated as the first quartile subtracted from the third quartile. zpos2and zneg2 are the z values equal or bigger than Q3 plus 1.5 times IQR and equal or
3.2 Image analysis 21
smaller than 1.5 times IQR subtracted from Q1, respectively [30]. Thus, the values that fulfill these conditions are removed from the array.
IQR =Q3−Q1 (3.3)
zpos2 ≥Q3+1.5IQR (3.4)
zneg2 ≤ Q1−1.5IQR (3.5)
For further calculations we selected the IQR approach to remove the outliers. In Fig. 3.4 we see in blue the lateral view of the terraces after the border parameter applied, and on the left the terraces after removing the outliers on different colors .
Figure 3.4:Lateral view of the terraces after removing the outliers (Image D).
Finally, we sort the terraces arrays by y to find the terrace width (xt f -xti). Where xt f and xti are the x final and initial position of one terrace per y value, respectively. At this point, we have terraces and steps coordinates in different arrays.
3.2.3
Optimization of the border parameter
Once the terraces are separated, and the terrace width values are saved on one array per terrace, we calculate the average and standard deviation of the step height per step, for different values of the border parameter. Based on these values, we select the step with the mean value closer to the real value and the smaller standard deviation. Then, we calculate the global minimum variance of this step as a function of the border parameter to reduce the step height dispersion for the whole image. As an example, the minimum value in the variance of step 3 for image A, is reached for
22 Methodology
border = 0.75x10−14, see Fig. 3.5. Hence, that will be the selected border value for all the calculations on image A. The procedure is done on every image, every image has its own border parameter. After selecting the ulti-mate border value, we rerun the code to calculate the terrace width values. In that way, we are getting as much accurate information as possible from every single image.
Chapter
4
Results and Discussion
As mentioned before the image analysis can be divided in two main parts: image treatment in Gwyddion and data analysis in Python. The details are given below.
4.1
Gwyddion
Different images were checked in Gwyddion to determine the best images to work with. The data is exported as a txt file containing (x,y,z) coordi-nates of the crystal surface. Four images (A, B, C, D) were analyzed, see Fig. 4.1. Image A represents an area of 100 x 100 (nm) while B, C and D represent an area of 50 x 50 (nm). Image A, B and D are taken on one side of the crystal, while Image C is taken on the other side. Image A is closer to the center of the crystal than the other images.
4.2
TWD Histograms
In this section, 3D plots and histograms of the four images are shown. Image A, B, and D correspond to the left side of the crystal and image C corresponds to the right side of the crystal. The bins sizes for the his-tograms were selected based on the nearest neighbour distance (2.77 ˚A). The distance between two consecutive atoms along a kinked step edge and between two atoms on different rows is the nearest neighbour distance. Therefore, the center of the bins are multiple of this distance as well, and we can say that a terrace is n-atom wide.
24 Results and Discussion
(a)A (b)B
(c)C (d)D
Figure 4.1:Images A, B, C and D as seen in Gwyddion.
4.2.1
Image A
The criteria used for this image analysis was the IQR method to remove the outliers per terrace and a border line equal to 0.75x10−14. In Fig. 4.2(a) the crystal surface is plotted, the raw data in red, the terraces in cyan, and the step edges in purple. For this image, the first and last terraces are not considered for the TWD, since they are incomplete and missing points. Histograms of different terraces can be seen in Fig. 4.3.
4.2 TWD Histograms 25
(a) (b)Entire image A
Figure 4.2: a)3D plot of the crystal surface with terraces and step edges high-lighted. b)Histogram of all terrace widths in image A fitted with two Gaussian functions with different amplitudes.
(a)Terrace 1 (b)Terrace 2
26 Results and Discussion
(e)Terrace 5 (f)Terrace 6
(g)Terrace 7 (h)Terrace 8
(i)Terrace 9 (j)Terrace 10
Figure 4.3: Histograms showing the variation of width within one terrace over the width of the image.
4.2 TWD Histograms 27
This image seems to have a bimodal distribution, not only for the entire surface, Fig. 4.2(b) but it can also be seen on the histograms of terraces 1,2,4. Although the distribution is not entirely symmetric. The TWD has a wide range in this case, up until to 139.885. We have narrow and wide terraces, from a couple of atoms (on the narrower part of terrace 3) up untilv50 atoms terrace wide. Terraces 4 and 5 are the wider terraces. The kinked steps are not clearly seen given the big area of the image but we can see that these are not straight step edges. The histogram of all terrace widths shows several peaks.
4.2.2
Image B
The criteria used for this image analysis was the IQR method to remove the outliers per terrace and a border line equal to 1.3x10−14. In Fig. 4.4(a) the crystal surface is plotted, the raw data in red, the terraces in cyan, and the step edges in purple. Histograms of different terraces can be seen in Fig. 4.5.
(a) (b)
Figure 4.4:a)3D plot of the crystal surface (image B) with terraces and step edges highlighted. b)Step edges for the entire surface.
28 Results and Discussion
(a)Entire image B (b)Terrace 1
(c)Terrace 2 (d)Terrace 3
4.2 TWD Histograms 29
(g)Terrace 6 (h)Terrace 7
(i)Terrace 8 (j)Terrace 9
30 Results and Discussion
(m)Terrace 12 (n)Terrace 13
(o)Terrace 14 (p)Terrace 15
Figure 4.5: a)Histogram of all terrace widths in image B fitted with a Gaussian function. b) to o):Histograms showing the variation of width within one terrace over the width of the image.
In this case, the terrace width goes up until 45.705 nm, i.e., from a cou-ple of atoms up untilv16 atoms wide. The distribution is asymmetric, as we can see in Fig. 4.5(a), where we have two central peaks 2 atoms apart, which might represent the width of one predominant type of kink, where the kink crest and trough are two atoms apart. Terraces 5, 6 and 10 are the wider terraces. The kinked steps are clearly visualized in Fig. 4.4(b).
4.2 TWD Histograms 31
4.2.3
Image C
The criteria used for this image analysis was the IQR method to remove the outliers per terrace and a border line equal to 1.25x10−14. In Fig. 4.6(a) the crystal surface is plotted, the raw data in red, the terraces in cyan, and the step edges in purple. For this image the first and last terraces are not considered for the TWD, since they are incomplete and missing points. So, even though we have 15 visible terraces, we will work with the 13 terraces located between the extremes. in Fig. 4.6(a) Histograms of different terraces can be seen in Fig. 4.7.
(a)
(b)
Figure 4.6:a)3D plot of the crystal surface (image C) with terraces and step edges highlighted. b)Step edges for the entire surface.
32 Results and Discussion
(c)Terrace 2 (d)Terrace 3
(e)Terrace 4 (f)Terrace 5
4.2 TWD Histograms 33
(i)Terrace 8 (j)Terrace 9
(k)Terrace 10 (l)Terrace 11
(m)Terrace 12 (n)Terrace 13
Figure 4.7: a)Histogram of all terrace widths in image C fitted with a Gaussian function. b) to n):Histograms showing the variation of width within one terrace over the width of the image.
34 Results and Discussion
In this case, the terrace width goes up until 51.245 nm, i.e., from a cou-ple of atoms up untilv18 atoms wide. The distribution is less asymmetric than image B, as we can see in Fig. 4.5(a), where one trough separates the left and right part of the histogram. Terraces 1 and 8 are the wider terraces. The kinked steps are clearly visualized in Fig. 4.6(b).
4.2.4
Image D
The criteria used for this image analysis was the IQR method to remove the outliers per terrace and a border line equal to 8.5x10−15. In Fig. 4.8(a) the crystal surface is plotted, the raw data in red, the terraces in cyan, and the step edges in purple. Histograms of different terraces can be seen in Fig. 4.9.
(a) (b)
Figure 4.8:a)3D plot of the crystal surface (image D) with terraces and step edges highlighted. b)Step edges for the entire surface.
4.2 TWD Histograms 35
(a)Entire image D (b)Terrace 1
(c)Terrace 2 (d)Terrace 3
36 Results and Discussion
(g)Terrace 6 (h)Terrace 7
(i)Terrace 8 (j)Terrace 9
4.2 TWD Histograms 37
(m)Terrace 12 (n)Terrace 13
Figure 4.9: a)Histogram of all terrace widths in image D fitted with a Gaussian function. b) to n):Histograms showing the variation of width within one terrace over the width of the image.
In this case, the terrace width goes up until 51.245 nm, i.e., from a cou-ple of atoms up untilv18 atoms wide. The distribution is less asymmetric than image B, as we can see in Fig. 4.9(a), one trough separates the left and right part of the histogram. Terraces 3 and 13 are the wider terraces. The kinked steps are clearly visualized in Fig. 4.8(b).
The step-step interaction (v 1/d2) might explain why the terraces on image B, C, and D follow a ’trend’. Thus, for a high step density (narrow terraces) the elastic repulsion of the step-step interaction will explain the formation of crests and troughs in the same region for consecutive terraces, i.e., for a crest on terrace n, we might see a crest on terrace n+1 almost in the same region, the same for troughs. This effect is evident on a short range (consecutive terraces). If we focus on the histograms of each terrace the step fluctuations are evident in all the images.
In Fig. 4.10 we plot the standard deviation σ for all terrace width his-tograms against the mean terrace width ˜d. In Fig. 4.11 we plot the width of the distributions (histograms) at different mean terrace width ˜d against the terrace width.We mark with a dotted line the mean value of each his-togram. Unfortunately, we only have the information of four images, so we cannot see the transition from the elastic to the entropic regime, as Walter et. al., 2015 [3] reported. We would need more good quality STM images to be able to see such transition.
38 Results and Discussion
Figure 4.10:Sigma σ versus mean terrace width ˜d for all terrace width histograms.
Chapter
5
Conclusions and Outlook
We did not manage to fulfill all the initial goals of this project due to exper-imental difficulties. However, we made progress on giving maintenance to the STM and on writing an adaptable code to analyze the crystal surface, including recognizing the steps and terrace coordinates, and determining the terrace width distribution on different crystals.
Regarding the image analysis, we observed step fluctuations on ev-ery terrace of the four images analyzed and a general asymmetric terrace width distribution as a consequence of the kinked steps. The influence of the repulsive elastic interaction is mainly observed at a short range (con-secutive terraces). Kinks crests and troughs are in most of the cases two atoms apart.
We also gave maintenance to electronic and mechanical systems, such as one manipulator, sample holders, heating system, electronic controllers, and the sputter gun among others. Besides that, every time we had to take out the sputter gun or the manipulator to fix we had to vent the system which implied we had to bake the system out prior to imaging any sample. In this respect, a bake-out process takes around five days. All these diffi-culties made impossible for us to image the crystal with the STM. Hence, we focused on the image analysis for the last part of the project because there was not enough time to fix the sputter gun, do the cleaning cycles and image the crystal before the deadline.
As an outlook, the sputter gun needs to be fixed or replaced in order to perform the cleaning cycles prior to imaging any crystal. The python code can be improved as well, in order to shorten the time needed for every image analysis.
Finally, I acquired some of the skills needed with this kind of instru-ments as well on the images analysis, which will be helpful for the future
40 Conclusions and Outlook
41
Acknowledgement
First of all, I would like to thank Dr. L.B.F. Juurlink and Sabine Auras for his guidance and support, and all the Surface Science group members, who were always willing to help throughout the project.
Chapter
6
44 Appendix
45
46 Appendix
47
List of Figures
2.1 Representation of single FCC crystal surface with (111)
ter-races.The step is shown in a lighter color. 10
2.2 a)Surface of a curved (111) crystal where two kind of steps are shown: A-steps to the left, B-steps to the right. (Adapted from Blomberg et al., 2017 Ref [1]). b) Schematic drawing of steps structures of a FCC (111) crystal. (Adapted from Corso et al., 2009 Ref [12]). c) Schematic of a curved crystal with straight step edges. (Adapted from Ortega et al., 2011
Ref [13]) 10
2.3 a)Schematic of the Pt(111) curved crystal with kinked step
edges along the[1 1 2]direction analyzed in this report. b)Schematic front view of kinked step edges where the A and B step
types are highlighted in purple and yellow, respectively. 11 2.4 a)STM images taken at both sides of the crystal with their
respective histograms of the terrace width distribution fit-ted with Gaussian distributions. b) σ vs ˜d from the full set of STM images showing the elastic to entropic transition at
˜
dc=42 ˚A.(Adapted from Walter et al., 2015 Ref [3]) 12 2.5 a)Normalized probability histograms [P(d/ ˜d)] of the curved
Ag(111), fitted with GWS functions for different values of the terrace width. b) Normalized probability for large d, fitted with a single series of Gaussian functions, (Adapted
from Ortega et al., 2018 Ref [5] ). 13
2.6 Energy potential vs the surface normal direction for a pos-itive sample voltage V. The tunneling probability decreases correspondingly with the decreasing of the thickness and length of the arrows. (Adapted from Encyclopedia of
50 LIST OF FIGURES
2.7 STM imaging: a)constant current mode, b) constant height mode. (Adapted from Binning et al., 1987 Ref [26]). 16 3.1 Schematic a)top and b)front view of the curved Pt crystal
analysed (dimensions in mm). (Adapted from Janlamool et.
al., 2014 [14].) 17
3.2 a)Lateral view of the data sorted by z, where the z posi-tion (height) is plotted against the number of data points. b)Gradient of z coordinates, where the raw data, filtered data and border line are shown in blue, orange and green,
respectively. (Image D) 19
3.3 Outlayers criteria for image A. a) µn of the entire histogram vs different values of σt used to remove outliers b) σn of the entire histogram vs different values of σt used to remove
outliers. 20
3.4 Lateral view of the terraces after removing the outliers
(Im-age D). 21
3.5 Border criteria for one of the steps of image A. 22
4.1 Images A, B, C and D as seen in Gwyddion. 24
4.2 a)3D plot of the crystal surface with terraces and step edges highlighted. b)Histogram of all terrace widths in image A fitted with two Gaussian functions with different amplitudes. 25 4.3 Histograms showing the variation of width within one
ter-race over the width of the image. 26
4.4 a)3D plot of the crystal surface (image B) with terraces and step edges highlighted. b)Step edges for the entire surface. 27 4.5 a)Histogram of all terrace widths in image B fitted with a
Gaussian function. b) to o):Histograms showing the varia-tion of width within one terrace over the width of the image. 30 4.6 a)3D plot of the crystal surface (image C) with terraces and
step edges highlighted. b)Step edges for the entire surface. 31 4.7 a)Histogram of all terrace widths in image C fitted with a
Gaussian function. b) to n):Histograms showing the varia-tion of width within one terrace over the width of the image. 33 4.8 a)3D plot of the crystal surface (image D) with terraces and
step edges highlighted. b)Step edges for the entire surface. 34 4.9 a)Histogram of all terrace widths in image D fitted with a
Gaussian function. b) to n):Histograms showing the varia-tion of width within one terrace over the width of the image. 37
LIST OF FIGURES 51
4.10 Sigma σ versus mean terrace width ˜d for all terrace width
histograms. 38
4.11 Mean terrace width ˜d versus d for all terrace width histograms. 38 6.1 Histogram of the entire surface A (10 terraces). 44 6.2 Histogram of the entire surface B (15 terraces). 45 6.3 Histogram of the entire surface C (13 terraces). 46 6.4 Histogram of the entire surface D (13 terraces). 47
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