# Morphological modification of Rh-C coatings upon low-energy Ar+ ion sputtering

Artem M Dmitriev, Moïse Gonda, Fabien Sanchez, Laurent Marot, Roland

Steiner, Pierre-Olivier Renault, Ernst Meyer

► To cite this version:

Artem M Dmitriev, Moïse Gonda, Fabien Sanchez, Laurent Marot, Roland Steiner, et al.. Morphological modification of Rh-C coatings upon low-energy Ar+ ion sputtering. Journal of Nuclear Materials, 2025, 604, pp.155502. 10.1016/j.jnucmat.2024.155502. hal-04916941

HAL Id: hal-04916941

https://isae-ensma.hal.science/hal-04916941v1

Submitted on 28 Jan 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

# Morphological modification of Rh-C coatings upon low-energy Ar⁺ ion sputtering

Artem M. Dmitriev<sup>a,*</sup>, Moïse Gonda<sup>a</sup>, Fabien Sanchez<sup>a</sup>, Laurent Marot<sup>a</sup>, Roland Steiner<sup>a</sup>, Pierre-Olivier Renault<sup>b</sup>, Ernst Meyer<sup>a</sup>

## ARTICLE INFO

**Keywords:**

First mirror

Mirror cleaning

Deposition

Rhodium

Carbon co-deposition

## ABSTRACT

In ITER, the metallic first mirrors (FMs) will undergo erosion due to their proximity to the fusion plasma and deposition of materials of the first wall, leading to mirror reflectivity's decrease. In vacuo plasma cleaning is foreseen for restoration of the FMs' optical properties by means of ion sputtering. Previously, it was shown that cyclic cleaning of polished metallic mirrors can lead to the development of pits due to low carbon amounts in the bulk mirror. The pitting formation is detrimental to the mirror's optical properties. This study aims to investigate the influence of carbon concentration on mirror morphology changes due to cyclic low-temperature plasma irradiation. Five rhodium (Rh) and carbon (C) coatings with different amounts of C were deposited on a pure Rh film on top of polished stainless steel substrates. All the samples were prepared by magnetron sputtering using a single or dual magnetron. Prior to each cycle of the plasma cleaning, a 20 nm layer of Al₂O₃ was deposited on the Rh-C samples. The plasma discharge was created with argon gas using a 60 MHz radio frequency excitation and resulted in the complete removal of the alumina layer after each cycle. The surface morphology of the mirrors was characterized by employing scanning electron microscopy (SEM) and focused ion beam (FIB). After the cyclic cleaning, the coatings containing carbon have failed, showing either partial delamination, cracking, or total delamination. Additionally, all the mirrors demonstrated the formation of mounds on the surface, while 17 at.% of carbon in the film led to the development of pits. The mechanisms of coating failure and such morphological modification are discussed in the paper.

## 1. Introduction

In the International Thermonuclear Experimental Reactor (ITER), a number of diagnostics will be used to maintain and control the high-temperature fusion plasma parameters. Most of these diagnostics will be optical ones [1]. To prevent radioactive leakage from the machine, optical layouts of such diagnostics will be represented as labyrinths of mirrors guiding the light from plasma toward diagnostic equipment placed outside the reactor. The space around the mirrors is going to be filled with neutron shielding. The described approach of optical layout design implies the utilization of optical elements placed in the direct view of the thermonuclear plasma, called the First Mirrors (FMs). FMs are prone to erosion by charge-exchange particles and material deposition originating from the tokamak walls e.g. beryllium (Be), tungsten (W), carbon (C), etc. [2]. Previous studies of mirror exposure in the tokamak environments showed that deposition can prevail [3], hence

an appropriate mitigation technique should be used [4]. The current approach to deposition mitigation, so-called mirror cleaning, consists of exposing the mirror surface to the ion flux created by gas discharge and physical and/or chemical-assisted sputtering of the contaminants. This process should not degrade the mirrors' surface and ensure recovery of the pristine optical properties.

Over the past years, a wide comprehensive study of mirror cleaning has been performed by a number of research groups worldwide. In order to remove contaminant layers and restore initial parameters of the FM, several approaches have been investigated, such as pulsed DC [5] or radio-frequency (RF) [6–9] discharges with the FM used as a powered electrode. To avoid extensive work with beryllium, which is known to be toxic, aluminum (Al) was shown to be an appropriate proxy material [10]. Razdobarin et al. presented the successful removal of an Al layer from molybdenum (Mo) mirrors by RF neon (Ne) and deuterium (D₂) plasmas [11]. The energy of ions in this work was 220 and 300

<footnote><sup>a</sup> Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056, Basel, Switzerland</footnote>

<footnote><sup>b</sup> Institut Pprime, CNRS - Université de Poitiers - ENSMA, Bd Marie et Pierre Curie, 86962 Futuroscope Cedex, France</footnote>

<footnote>* Corresponding author.
E-mail address: artem.dmitriev@unibas.ch (A.M. Dmitriev).</footnote>
eV respectively. Rogov et al. performed cleaning experiments with Penning discharges using helium (He) plasma with 700 eV ions showing an efficient cleaning of Mo mirror from Al with a recovery of the optical properties of the mirror [5]. Moser et al. also reported the cleaning of Mo mirrors from Al₂O₃ films with argon (Ar) RF plasma [12]. Some studies were done with beryllium contaminates, confirming the data obtained using the proxy materials. Moser et al. presented the cleaning of mirrors exposed in the JET ITER-Like Wall experiment (JET-ILW) by Ar and He RF-discharges [7]. Irradiation of mirrors by ions with energy in the range of 100 - 630 eV demonstrated the removal of mixed layers and mirror reflectivity improved towards initial values. Dmitriev et al. performed measurements of beryllium oxide (BeO) sputtering rates in He and D₂ plasmas with ion energy of 150 eV and presented cleaning of the protective windows from the BeO deposits [13]. Summarizing, the aforementioned studies demonstrated that the optical properties of the FMs can be restored by plasma cleaning within a single cleaning step.

It should be nonetheless noted, that an Al₂O₃ coating deposited utilizing magnetron sputtering differs from the tokamak contaminant layers in terms of density and sputtering yield. For example the studies of the Be layers deposited in JET exhibited low density as presented in [14]. Additionally, it was demonstrated, that the tokamak-relevant coatings exhibit higher sputtering yield compared to the dense coatings [13,15]. Despite that, the use of Al₂O₃ was accepted for the mirror cleaning experiments, since it provides testing of the mirror cleaning as the “worst-case” scenario [1,10].

Recently, for ITER it has been decided to replace the beryllium wall with a full-tungsten (W) wall, which will require periodic deposition of boron (B) on the plasma-facing components. Consequently, the deposition of B/W layers on the first mirrors (FMs) is anticipated [16]. In that case, the use of Al₂O₃ can be justified since no other common model contamination layer has been chosen yet. In the case of Ar as a process gas of the mirror cleaning system, B exhibits a similar sputtering yield as Be. For the Ar⁺ ion with the energy of 200 eV, Be and B sputtering yields are equal 0.2 at/ion [17]. The sputtering yield of Al₂O₃ is 4 times lower for the same energy, which creates a considerable margin for the efficiency of the cleaning system. The definition of the model contamination for future work should be addressed in the dedicated paper since it is still unknown what the exact ratio between W and B in the coatings deposited on the first mirrors would be.

Additional studies showed that the long-term or cyclic treatment of mirrors by the low-temperature plasma could lead to modification of mirror morphology which can be detrimental to the mirrors' optical properties. Sanchez et al. [18] showed that several cycles of Al₂O₃ deposition and removal via Ar plasma cleaning can lead to the appearance of a so-called pitting effect on Rhodium (Rh) mirrors. Rh being one of the ITER FMs' candidate materials provides a good reflectivity (between 70-80%) in the visible range as well as near-infrared and infrared ranges (around 85% at 1 µm). Additionally, Rh is known to have low chemical reactivity, preventing oxide and carbide formation. The pitting effect only affected the single-crystal mirrors due to the incorporation of carbon during their polishing via diamond paste. Rogov et al. [19] observed a similar effect on the Mo mirrors under long-term exposition in Ar and He DC-plasma. In both studies, the formation of the pits was related to the blistering formation process activated by the accumulation of C in the surface region, which was deformed during the polishing process. Gorodetsky et al. [20] claimed that removing the deformed layer with excessive carbon concentration would suppress pitting. This assumption was successfully proved in [18], where a pre-etched mirror showed no pitting after the sequence of plasma cleaning cycles.

In the former studies, it has been shown that pitting is happening on the polished mirrors with 3 at.% of C in the subsurface layer embedded during the polishing. However, it is still unclear how changing the amount of C in the mirror will affect the mirror's morphology in response to cyclic cleaning. Additionally, it should be investigated if the carbon originating from sources other than the polishing process can induce the pitting formation. To answer those questions, a batch

<caption>**Table 1**</caption>

Sample numbers, values of C at. concentration, power of rhodium and carbon magnetrons, deposition rates of rhodium and carbon.

<table><thead><tr><th rowspan="2">Sample #</th><th rowspan="2">C at.%</th><th colspan="2">Magnetron power (W)</th><th colspan="2">Deposition rate (Å/s)</th></tr><tr><th>Rhodium</th><th>Carbon</th><th>Rhodium</th><th>Carbon</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>25</td><td>-</td><td>5</td><td>-</td></tr><tr><td>2</td><td>4</td><td>50</td><td>15</td><td>3.4</td><td>0.1</td></tr><tr><td>3</td><td>17</td><td>35</td><td>50</td><td>2.3</td><td>0.4</td></tr><tr><td>4</td><td>28</td><td>25</td><td>50</td><td>1.8</td><td>0.3</td></tr><tr><td>5</td><td>39</td><td>25</td><td>140</td><td>1.9</td><td>1</td></tr></tbody></table>

of nanocrystalline Rh films were co-deposited with different concentrations of carbon and subjected to cyclic plasma cleaning. Similarly to the former studies [18], Al₂O₃ was used as a contamination material, and Ar was used as a process gas of the cleaning discharge. The morphology and optical properties of the mirrors were studied after 5 cycles of plasma cleaning.

## 2. Material and methods

Rhodium-carbon (Rh-C) coatings were deposited in a high vacuum facility pumped down to a base pressure of at least 5 × 10⁻⁵ Pa. The Rh-C depositions were carried out on polished stainless steel (SS) substrates with an intermediate 300 nm pure Rh layer. The carbon content of the films was varied from 0 to 39 at% of C by modifying the power applied to the target of a dual-target magnetron [21]. The dual-target magnetron was constituted of an internal Rh target and an external target made of graphite. Both targets were driven simultaneously by two identical DC-power supply sources. The pure Rh film was deposited with another Rh magnetron. The magnetron discharge was ignited at the pressure of 1 Pa for an argon (Ar) flow of 20 sccm and a distance target/substrate equal to 10 cm. The conditions of deposition for each of the studied samples are summarized in Table 1.

The chemical composition of the Rh-C coatings was determined via in-situ X-ray Photoelectron spectroscopy (XPS). To do so, after the deposition the samples were transferred from the deposition chamber to the ultrahigh vacuum (UHV) XPS chamber without breaking the vacuum. The electron spectrometer was equipped with a hemispherical analyzer (Leybold EA10/100 MCD) and a non-monochromatized Mg Kα X-ray source (hν = 1253.6 eV) was used for core-level spectroscopy. Normal electron escape angle and a step size of 0.05 eV were used. The binding energy scale was calibrated using a clean gold sample and the position of the Au 4f7/2 line was set at 84.0 eV binding energy. It should be noted that all studied samples were conductive and no charging of the XPS spectra was recorded, i.e., no charged correction was applied.

Wide scan XPS spectra from -4 to 1060 eV exhibited the presence of Rh, O, and C. The fitting of the data was performed using Doniach-Sunjic functions [22], after a Shirley background subtraction [23] with the help of UNIFIT for Windows (Version 2016) software [24]. A convolution of Lorentzian and Gaussian line shapes were used to fit the individual peaks. Asymmetric peak shapes were used for metal lines. The Rh and C atomic concentrations were derived using Scofield sensitivity factors [25]. Fig. 1a) and 1b) display the Rh3d and the C1s core level spectra of all the Rh-C coatings.

For C1s line two components were revealed after deconvoluting with two Lorentzian-Gaussian curves performed following a Shirley background subtraction (not shown here). One line is associated to C-O for a binding energy of 286 eV [26] the percentage of this compound representing no more than 5% for all these samples. The second line is a pure amorphous carbon phase (a-C), with a binding energy of 284.6 eV for pure carbon deposition. The shift of the C1s toward lower binding energy for lower carbon content was also observed by Marot et al., close to 1 eV [21]. This was not identified as a new chemical compound as the films' XRD patterns do not clearly show a new phase. However, further analyses are required.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Rh3d (a) and C1s (b) core level spectra of samples 1-5. Vertical lines are an eye guide. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)</figcaption></figure>

On each coating, 5 cleaning cycles were performed. One cleaning cycle is composed of two stages. In the first stage, samples were deposited with the Al₂O₃ film. A rotating magnetron with an aluminum target was operated with a 100 W RF power (13.56 MHz). The deposition was operated at a pressure of 3 Pa and using a mixture of Ar (89%) and O₂ (11%) as working gas. The deposition rate of alumina was equal to 0.97 nm/min. The 20 minutes of deposition resulted in a 20 nm thick film. Such a coating thickness is typically chosen for mirror cleaning studies [11,12], as the deposition of a 10-20 nm thick layer can significantly impact the performance of the first mirrors (FMs), which then need to be restored [16]. In the second stage, a capacitively-coupled Ar plasma was generated with a 60 MHz generator at the pressure of 0.13 Pa, the sample holder being used as a driven electrode. The plasma potential was around 30 V and the self-bias was kept at the value of -280 V. Each step of plasma cleaning lasted for 60 minutes, resulting in the complete removal of the Al₂O₃ layer as it was verified by XPS. Typically, this cleaning cycle led to 60 nm thickness removal of the pure Rh film [18].

The morphology of the films was investigated by means of SEM (Hietachi S-4800 field emission at 5kV) and by cross-section Focused Ion Beam (FIB, Helios NanoLab 650) analysis. The total and diffuse reflectivities in the range of 250–2500 nm were measured using a Varian Cary 5 spectrophotometer. The specular reflectivity was directly obtained by subtracting the diffuse reflectivity from the total reflectivity.

X-rays diffractograms (XRD) were recorded using a SIEMENS D5000 instrument with Cu Kα radiation (40 kV and 30 mA) at a glancing incidence of 5°. A graphite secondary monochromator (no filter) was used and a width of 1° for the primary and secondary divergence slits was applied. All XRD patterns obtained with scan steps of 0.02° and with 8 s of acquisition time are presented in Fig. 2. As determined from the XRD data, the average grain size was 7 nm, which is classical for this type of nanocrystalline coatings [27].

Residual stress analyses were carried out on witness silicon sample deposited simultaneously as the steel substrate using a four-circle diffractometer (Seifert XRD 3003) operating at 40 kV and 30 mA, with a Cu X-ray tube ($\lambda$ = 0.154 nm) equipped with a 1 × 1 mm² point focus and an energy dispersive point detector (Meteor0D). This detector allows selecting a sufficiently low energy window to avoid the Cu kβ radiation and fluorescence. The residual stress state was calculated from the lattice strains assuming a planar equi-biaxial stress state [28]. The X-ray elastic constants 1/2S₂(hkl) and S₁(hkl) have been calculated using the Hill-Neerfeld model [28] from the Rh stiffnesses ($c_{11}$=408, $c_{12}$=187.5 and $c_{44}$=187 GPa estimated from the work of Maurer et al.

<figure><img src="image_5.png" /><figcaption>Fig. 2. XRD diffraction patterns of samples 1, 2, 3 and 5.</figcaption></figure>

[29]), e.g. for the diffraction peak (420), 1/2S₂ (420) = 3.42 x 10⁻⁶ and S₁ (420) = -7.14 x 10⁻⁶ MPa⁻¹.

### 3. Results

Fig. 3 presents the SEM (top view and tilted view) images of the samples before and after plasma cycling and the schematics of the final state of the samples' surfaces. The initial surface morphology of all samples exhibited a nanocrystalline structure typical for the Rh films deposited with a DC-magnetron [21,27]. Increasing the carbon content in the film caused a moderate change in the grain size and appearance of voids (Fig. 3-a, -d, -g, -j), as well as a substantial decrease of specular reflectivity (Figure S1) similar to one observed in [21]. The 5 cycles of the alumina deposition and subsequent RF-plasma cleaning changed the morphology and reflectivity of all studied mirrors. Table 2 summarizes the status of the Rh-C films and the surface observations.

Samples 1 and 2 (Fig. 3-b and -e) underwent the formation of mounds on their surface after the repetitive cleaning. The height of the mounds was found to be around 50 nm. Generally, mounds were randomly distributed over the surface, however, some of them tended to follow the direction of the polishing scratches as can be seen in Figure S2. On the sample 2 surface, delamination of the coating has occurred, and pits formed on the opened areas (Figs. 3-f and 4-a, -d). The pits showed an average diameter of 250 nm, some of the pits were merged forming elongated features with a micron-sized length.

On the sample 3 surface, a pattern of cracks 50 nm in width appeared (Fig. 3-i and Fig. 4-b) forming a “dried mud” ornament. Similar cracks were observed on the witness silicon sample which was stored in the air and was not subjected to plasma exposure. The cracks were found to propagate the entire Rh-C coating and stop at the interface between Rh-C and initial Rh films as presented in the FIB image (Fig. 4-e and Figure S3). In addition to cracks, 200 nm diameter pits were present on the surface of the film covering the areas in between the cracks (Fig. 3-h). Some pits were merged forming mounds with a height of ~100 nm.

Samples 4 and 5 underwent similar phenomena and in the following only sample 5 is reported. After the cyclic cleaning samples evidenced a complete delamination of Rh-C coating, revealing the initial pure 300 nm Rh film (Fig. 4-c). The surface of the samples underwent the formation of two kinds of patterns. The majority of the surface area of both samples was covered by mounds (Fig. 3-k). Additionally, some areas of
<figure><img src="image_6.png" /><figcaption>Fig. 3. Top SEM-images of the morphology of the sample 1, 2, 3 and 5 before cyclic cleaning and tilted (52°) SEM-images of the morphology of the samples 1, 2, 3 and 5 after cyclic cleaning. The corresponding schematics show the final state of the samples.</figcaption></figure>

<caption>**Table 2**</caption>

Sample numbers, values of C at. concentration, type of coating failure and type of coating's morphology evolution of the mirrors used in this work.

<table><thead><tr><td>Sample #</td><td>C at.%</td><td>Rh-C failure type</td><td>Mounds formed</td><td>Pits formed</td></tr></thead><tbody><tr><td>1</td><td>0</td><td>None</td><td>On Rh-C film</td><td>No</td></tr><tr><td>2</td><td>4</td><td>Cracks, Partial delamination</td><td>On Rh-C film</td><td>On Rh film</td></tr><tr><td>3</td><td>17</td><td>Cracks</td><td>On Rh-C film</td><td>On Rh-C film</td></tr><tr><td>4</td><td>28</td><td>Total delamination</td><td>On Rh film</td><td>On Rh film</td></tr><tr><td>5</td><td>39</td><td>Total delamination</td><td>On Rh film</td><td>On Rh film</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>Fig. 4. FIB-image of the morphology of the samples 2 (a, d), 3 (b, e), and 5 (c, f) after 5 cycles of plasma cleaning.</figcaption></figure>

the surface were covered by pits with diameters in the range of 100-300 nm (Fig. 3-l). The pitted surfaces smoothly transfer to the areas with mounds as can be seen in Fig. 4-f. Some of the mounds and pits were found to be agglomerated along the straight lines which likely represent the polishing scratches (Fig. 4-c). The appearance of the mounds led to a moderate decrease (4% at $\lambda$=500 nm) in the specular reflectivity of

sample 1 which was caused by the increase of diffuse reflectivity (Figure S1). The specular reflectivity of sample 2 increased after the cyclic cleaning from 36 to 57% (at $\lambda$=500 nm) while diffuse reflectivity increased only by 3% which is caused by the decrease of the void amount on the surface caused by the ion sputtering. Finally, the specular reflectivity of sample 3 decreased from 56 to 23% and the diffuse increased
by 30% (at $\lambda$ = 500 nm) due to the appearance of cracks and voids. The reflectivity of mirrors 4 and 5 was not measured as the Rh-C film was delaminated.

## 4. Discussion

All the studied samples exhibited modification of the morphology due to alumina deposition and Ar⁺ ions bombardment. The coatings containing carbon have failed showing either partial delamination (sample 2), cracking (sample 3), or total flaking (samples 4 and 5). Coating cracking and delaminating are commonly caused by residual stress coming from the deposition process [30,31]. The XRD diffraction pattern presented in Fig. 2 shows no texture for the pure Rh with a calculated lattice constant $a$=0.3795 nm close to the corresponding value of the database ($a$=0.3803) [32]. When carbon is co-deposited, another phase is observed especially for 17 at.%. This phase was not identified as no rhodium carbide was reported, and further investigation is needed. The Rh (111) peak moved clearly to a lower $2\theta$ angle for all Rh-C films, but the calculated strain-free lattice parameter for 17 at.% was $a$=0.3778 nm even with a 1° shift for the (111) peak. The reduction of the lattice parameter for 17 at.% revealed that we do not have a solid solution, but carbon is segregated in the film. As will be shown in the following, the shift of the (111) peak is due to a change in stress in the film.

The residual stress measurements performed for sample 1 (0% at. of C) using the plane (420) at $\theta$ = 129.4° showed a tensile residual stress of +1.75 GPa. This high tensile stress value was checked and confirmed by measurements on 3 other diffracting peaks (111), (200), and (331), giving an average of +1.72 GPa. For pure Rh, the deposition parameters were 0.9 Pa and a deposition rate of 0.5 nm/s (Table 1). As reported by Thornton et al. [33] and Hoffman [34], this is classical for tensile stress. For the Rh-C films, even if the deposition rate was below 0.34 nm/s, the carbon inclusions limit the Rh adatom's mobility, leading to either a higher tensile stress or a tensile-to-compressive stress transition depending on the carbon amount. For example, the appearance of voids between grains was seen in Fig. 3 -d and -j. This effect is classical and explained by Thornton et al. [33] for the case of an increase in background gas pressure during the deposition process, which leads to higher tensile stress. Increasing the pressure during deposition induced the appearance of voids and cracks network for Rh films [27], reducing the film's reflectivity (Figure S1). Residual stress measurements for sample 3 (17% at. of C) using the plane (420) give a compressive residual stress of -1.52 GPa (-2.02 GPa for (111) plane). Compressive stress induces delamination by buckling, especially during external loading [35], like during our plasma sputtering for samples 4 and 5. Tensile stress triggers film cracks, such as in sample 2 [36]. Sample 3 (Fig. 3-i) measured in compression, shows also cracks network after plasma cleaning or air storage on witness silicon sample, evidencing that the cracking and flaking were not caused by the plasma cleaning but by the intrinsic properties (stress) of the film. As shown in Fig. 2, two phases were observed, which overlap with the rhodium planes (200) and (331). However, typical X-ray stress measurements on these two peaks displayed a peak position shift to a lower angle, indicating that this phase is in a tensile stress state. Without knowing the elastic constants of the unknown phase, we cannot directly calculate the stress value. Two stress release modes are present for sample 3, as seen in Figs. 3 d-f.

Mounds appeared on the surfaces of all of the studied samples after repetitive cleaning. Samples 1, 2, and 5 exhibited mounds with similar heights and density. It is worth noting that on the delaminated areas, the mounds were similar to ones observed on samples with 0% and 5% of C. The mounds developed on the sample 3 appeared to have higher size in comparison to other samples. In our previous study, the patterns of mounds were as well observed on single-crystal and nano-crystalline rhodium surfaces after cyclic RF-plasma cleaning [18]. The patterning of metallic surfaces under ion irradiation is a common feature and was observed in various forms by many investigators within the incident ion energy range from hundreds eV to several keV [18,19,37–39]. The for-

mation of patterns is usually addressed to the shadowing of the ion beam by the surface curvature and the dependence of the sputtering yield on the local surface curvature. The modification of the surfaces varies as a function of the ion energy, ion flux, and the surface temperature due to a competition between the kinetic and thermodynamic processes. [39]. Recently, a molecular dynamic calculation study by Lopez-Cazalilla et al. [40] have shown that, formation of the ripple and mounds under 30 eV Ar ion irradiation can be additionally explained by processes of surface atom displacement and a pile-up effect.

In addition to mounds, pits were observed on all samples containing C. However, two different pitting phenomena can be distinguished. The first one occurs in sample 3 (17 at.% C), which displayed the formation of pits on the Rh-C coating. It is worth mentioning that pitting was not observed on other samples with Rh-C films. The second phenomenon is related to the appearance of pits on the pure Rh surfaces after Rh-C coating delamination (samples 4 and 5).

The pitting process was previously observed on the surfaces of single-crystal Rh and Mo mirrors after the plasma cleaning [18,19,41]. The development of pits on mirrors during plasma cleaning is a complex phenomenon. During polishing, submicron diamond abrasive particles are introduced into the surface of the mirror substrate. During the introduction of the reactive gasses ($O_2$, $N_2$, $D_2$, etc.) of the cleaning discharge, carbon inclusions incorporated into the surface get gasified and initiate the formation of blisters [20]. Continuation of plasma exposure leads to the evolution of mirror morphology from blisters to pits [18].

In the present study, pits developed on the surface without a polishing process. In [18], it was shown that the polishing process applied on single-crystal Rh mirrors led to a carbon-enriched layer (around 3 at.%) of a few hundred nanometers depth. During the cleaning cycles, the presence of carbon led to the formation of pits via the mechanisms described above. In the present study, however, no pitting was observed on the sample with 4 at.% of C. It implies that the carbon retention by the bulk and films is different. The carbon-rich layer needed to initiate the pitting effect can be formed in the co-deposited coatings due to the separation of carbon and metal during the film deposition [42,43]. Carbon-rich layers in the sub-surface layer of co-deposited Pt-C films was observed for coatings prepared by magnetron deposition technique with two separate targets (platinum and graphite) [44]. A multilayer film structure of alternately carbon-rich and metal-rich layers was found for Au-, Ni- and Cu-C coatings produced by reactive magnetron deposition with Ar and $CH_4$ mixture [45]. According to the literature [46,47], this process can also affect the residual stress of the film. Hereby, when the concentration of C in the coating is low (4 at.% in sample 2), C atoms are evenly distributed in the coating, and the pitting process does not occur. By increasing the carbon concentration to 17 at.%, the C distribution in the film changes and leads to the formation of clusters and pits. A further increase in the carbon concentration in the Rh-C films leads to its stress-induced delamination.

Steps of morphological changes of samples 4 and 5 under $Al_2O_3$ coating and ion bombardment are presented in Fig. 5. Initially, the SS substrates were polished using carbon pastes, and a carbon-rich deformed layer was formed on the surface [20]. Then, pure Rh films were deposited on the SS substrates before the deposition of the studied Rh-C coatings. After flaking off the thick Rh-C coating, the initial 300 nm film was subjected to ion-induced sputtering, heating, and material mixing. The combination of the given processes can enhance the diffusion of carbon from the polished surface of the stainless steel substrate towards the surface of the rhodium layer [48–50]. After reaching a sufficient value of carbon enrichment (in the range of 4 to 17 at%), the pitting process occurs and leads to the morphological changes presented in Figs. 3 and 4. By continuing the ion bombardment, pits extend and merged on the surface. The linear grooves on the surface of pure Rh coating, which can be seen in Fig. 3-l, are the result of a combination of a chain of individual pits created over the polishing scratches on the SS substrate, which has an increased amount of carbon compared to the rest of the SS substrate surface [19].
<figure><img src="image_8.png" /><figcaption>Fig. 5. Schematic of the surface morphology changes. a) initial state of the sample; b) coating failure due to residual stress; c) blistering on the delaminated areas; d) blistering on the shadowed areas; e) formation of mounds and pits.</figcaption></figure>

It is worth noting that the Rh-C film does not peel off completely at once. Some parts of the Rh-C coating stay longer on the pure Rh coating's surface and shadow the underneath regions from the sputtering, as shown in Figure S4. After a while, the remaining parts of Rh-C film detach and the previously shadowed region becomes subjected to alumina deposition and Ar⁺ ion bombardment. This process causes the appearance of surface areas with pits (Fig. 3-l) and mounds (Fig. 3-k) which are subjected to different exposure times.

## 5. Conclusions

The paper presents the results of a campaign of repetitive plasma cleaning from Al₂O₃ deposits that has been carried out on the mirrors coated with Rh-C films. The study aimed to establish a relationship between changes in the morphology of samples under cyclic plasma cleaning, depending on the atomic concentration of carbon in the films. Five mirrors with different carbon-to-rhodium ratios from 0 to 39 at.% were deposited and subject to five cleaning cycles.

After the cleaning campaign, the mirrors exhibited changes in morphology depending on their carbon amounts. Sample 1 with a pure Rh coating exhibited the formation of mounds, while both mounds and pits were formed on the surfaces of the samples containing carbon. Additionally, coatings having carbon have failed through cracking or delamination due to an increase in stress associated with carbon content.

In contradiction to polished single-crystal mirrors, the presence of low (≤ 4%) content of carbon in the coating does not lead to the pitting effect. Pits were observed on the surface of the sample having 17 at.% of carbon and on the pure Rh-coating after delamination of the Rh-C film.

The following mechanism of pitting was proposed for the coatings: i) in the coating with a low percentage of carbon, C atoms are evenly distributed in the film, and hence, no pitting is observed; ii) carbon concentration higher than 17 at.% possibly leads to the formation of carbon clusters in the films, which provoke the pitting process; iii) on the delaminated areas, pits were formed due to C diffusion in the form of clusters from the substrate surface, which content few at.% of carbon from its polishing. By increasing the time of plasma cleaning pits evolved into mounds.

These results suggest that the plasma cleaning procedure results in different surface morphologies between nanocrystalline Rh coatings and single-crystal mirrors, despite having similar carbon content. Unlike single-crystal Rh, the use of nanocrystalline Rh containing a few atomic percent (at.%) of carbon does not induce the pitting effect. This is likely because the carbon distribution and nanocrystalline structure of the films prevent carbon diffusion, thus inhibiting pit formation. Hence, concerning the ion-induced pitting effect, nanocrystalline Rh mirrors prepared by magnetron sputtering can be considered a more robust material for the first mirrors in ITER, compared to single-crystal materials.

## CRediT authorship contribution statement

**Artem M. Dmitriev:** Writing – review & editing, Writing – original draft, Supervision, Investigation, Conceptualization. **Moïse Gonda:**

Investigation. **Fabien Sanchez:** Writing – review & editing, Conceptualization. **Laurent Marot:** Writing – review & editing, Supervision, Project administration, Investigation, Conceptualization. **Roland Steiner:** Supervision, Investigation, Conceptualization. **Pierre-Olivier Renault:** Writing – review & editing, Methodology, Investigation. **Ernst Meyer:** Writing – review & editing, Project administration.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgement

This work was supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number 22.00424. The authors would like to thank the Swiss Nanoscience Institute, Switzerland, and the Federal Office for Education and Science, Switzerland for their Financial support.

## Appendix A. Supplementary material

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.jnucmat.2024.155502.

## Data availability

The raw/processed data that support the findings of this study are available on request from the corresponding author, A. Dmitriev.

## References

[1] A. Litnovsky, V. Voitsenya, R. Reichle, M. Walsh, A. Razdobarin, A. Dmitriev, N. Babinov, L. Marot, L. Moser, R. Yan, M. Rubel, A. Widdowson, S. Moon, S. Oh, Y. An, P. Shigin, I. Orlovskiy, K. Vukolov, E. Andreenko, A. Krimmer, V. Kotov, P. Mertens, Specialists Working Group on First Mirrors of the ITPA Topical Group on Diagnostics, Nucl. Fusion 59 (2019) 066029, ISSN 0029-5515, 1741-4326, https://iopscience.iop.org/article/10.1088/1741-4326/ab1446.

[2] D. Ivanova, M. Rubel, A. Widdowson, P. Petersson, J. Likonen, L. Marot, E. Alves, A. Garcia-Carrasco, G. Pintsuk, JET-EFDA Contributors, Phys. Scr. T 159 (2014) 014011, ISSN 0031-8949, 1402-4896, https://iopscience.iop.org/article/10.1088/0031-8949/2014/T159/014011.

[3] A. Garcia-Carrasco, P. Petersson, M. Rubel, A. Widdowson, E. Fortuna-Zalesna, S. Jachmich, M. Brix, L. Marot, Nucl. Mater. Energy 12 (2017) 506–512, ISSN 23521791, https://linkinghub.elsevier.com/retrieve/pii/S2352179116300503.

[4] P. Shigin, N. Babinov, G. De Temmerman, A. Danisi, A. Dmitriev, J. Larsen, R. Madsen, L. Marot, L. Moser, E. Mukhin, M. Kochergin, R. Ortiz, A. Razdobarin, R. Reichle, R. Pitts, D. Samsonov, M. Tsalas, V. Udintsev, G. Vayakis, M. Walsh, Fusion Eng. Des. 164 (2021) 112162, ISSN 09203796, https://linkinghub.elsevier.com/retrieve/pii/S0920379620307109.

[5] A.V. Rogov, Y.V. Kapustin, A.G. Alekseev, Instrum. Exp. Tech. 58 (2015) 161–166, ISSN 0020-4412, 1608-3180, http://link.springer.com/10.1134/S0020441214060104.

[6] R. Yan, L. Moser, B. Wang, J. Peng, C. Vorpahl, F. Leipold, R. Reichle, R. Ding, J. Chen, L. Mu, R. Steiner, E. Meyer, M. Zhao, J. Wu, L. Marot, Nucl. Fusion 58 (2018) 026008, ISSN 0029-5515, 1741-4326, https://iopscience.iop.org/article/10.1088/1741-4326/aa96b8.
[7] L. Moser, L. Marot, R. Steiner, M. Newman, A. Widdowson, D. Ivanova, J. Likonen, P. Petersson, G. Pintsuk, M. Rubel, E. Meyer, J. Contributors, Phys. Scr. T 167 (2016) 014069, ISSN 0031-8949, 1402-4896, https://iopscience.iop.org/article/10.1088/0031-8949/T167/I/014069.

[8] K. Soni, S. Iyyakkunnel, R. Steiner, R. Antunes, L. Moser, O. Bieri, L. Marot, E. Meyer, Nucl. Fusion 62 (2022) 126009, ISSN 0029-5515, 1741-4326, https://iopscience.iop.org/article/10.1088/1741-4326/ac8b20.

[9] A.M. Dmitriev, N.A. Babinov, A.N. Bazhenov, I.M. Bukreev, M.M. Kochergin, A.N. Koval, G.S. Kurskiev, A.E. Litvinov, S.V. Masyukevich, E.E. Mukhin, A.G. Razdobarin, D.S. Samsonov, V.V. Solokha, S.Y. Tolstyakov, P. Andrew, F. Leipold, P.A. Shigin, R. Reichle, V.L. Bukhovets, A.E. Gorodetsky, A.V. Markin, A.P. Zakharov, R.K. Zalavutdinov, A.P. Chernakov, A.P. Chernakov, P.V. Chernakov, T.V. Chernozumskaya, A.A. Kobelev, A.S. Smirnov, I.A. Marzinovsky, Phys. Scr. T 170 (2017) 014072, ISSN 0031-8949, 1402-4896, https://iopscience.iop.org/article/10.1088/1402-4896/aa95e5.

[10] L. Marot, C. Linsmeier, B. Eren, L. Moser, R. Steiner, E. Meyer, Fusion Eng. Des. 88 (2013) 1718-1721, ISSN 09203796, https://linkinghub.elsevier.com/retrieve/pii/S0920379613004201.

[11] A. Razdobarin, A. Dmitriev, A. Bazhenov, I. Bukreev, M. Kochergin, A. Koval, G. Kurskiev, A. Litvinov, S. Masyukevich, E. Mukhin, D. Samsonov, V. Semenov, S. Tolstyakov, P. Andrew, V. Bukhovets, A. Gorodetsky, A. Markin, A. Zakharov, R.Zalavutdinov, P. Chernakov, T. Chernozumskaya, A. Kobelev, I. Miroshnikov, A. Smirnov, Nucl. Fusion 55 (2015) 093022, ISSN 0029-5515, 1741-4326, http://stacks.iop.org/0029-5515/55/i=9/a=093022?key=crossref.1a2a04682d1c1e69f79e5c31c5411ed8.

[12] L. Moser, R. Steiner, F. Leipold, R. Reichle, L. Marot, E. Meyer, J. Nucl. Mater. 463 (2015) 940-943, ISSN 00223115, https://linkinghub.elsevier.com/retrieve/pii/S0022311514008915.

[13] A. Dmitriev, A. Razdobarin, L. Snigirev, D. Elets, I. Bukreev, N. Babinov, L. Varshavchik, E. Mukhin, D. Samsonov, S.Yu. Tolstyakov, A. Chernakov, D. Kovalenko, V. Pogkovyrov, A. Yaroshevskaya, V. Barsuk, I. Kupriyanov, V. Bukhovets, A. Gorodetsky, A. Markin, R. Zalavutdinov, I. Arkhipushkin, S. Krat, V. Polskij, A. Gurbich, Nucl. Mater. Energy 30 (2022) 101111, ISSN 23521791, https://linkinghub.elsevier.com/retrieve/pii/S2352179121001769.

[14] M. Rubel, S. Moon, P. Petersson, A. Garcia-Carrasco, A. Hallén, A. Krawczynska, W. Fortuna-Zalewska, M. Gilbert, T. Plociński, A. Widdowson, Contributors, Phys. Scr. 2017 (2017) 014061, https://dx.doi.org/10.1088/1402-4896/aa8e27.

[15] R. Doerner, I. Jepu, D. Nishijima, E. Safi, L. Bukonte, A. Lasa, K. Nordlund, T. Schwarz-Selinger, in: PLASMA-SURFACE INTERACTIONS 21, J. Nucl. Mater. (ISSN 0022-3115) 463 (2015) 777-780, https://www.sciencedirect.com/science/article/pii/S0022311514006035.

[16] A. Litnovsky, M. Matveeva, A. Herrmann, V. Rohde, M. Mayer, K. Sugiyama, K. Krieger, V. Voitsenya, G. Vayakis, A. Costley, R. Reichle, G. De Temmerman, S. Richter, U. Breuer, L. Buzi, S. Möller, V. Philipps, U. Samm, P. Wienhold, the ASDEX Upgrade Team, Nucl. Fusion 53 (2013) 073033, ISSN 0029-5515, 1741-4326, https://iopscience.iop.org/article/10.1088/0029-5515/53/7/073033.

[17] W. Eckstein, C. Garcia-Rosales, J. Roth, MPI-Garching Report, 1993.

[18] F. Sanchez, L. Marot, R. Steiner, D. Mathys, P. Hiret, K. Soni, R. Antunes, M. Kisiel, C. Romero-Muñiz, L. Moser, F. Le Guern, J. Piqueras Meseguer, E. Meyer, J. Nucl. Mater. 581 (2023) 154382, ISSN 00223115, https://linkinghub.elsevier.com/retrieve/pii/S0022311523001526.

[19] A.V. Rogov, Y.V. Kapustin, V.M. Gureev, A.G. Domantovskii, Surf. Invest.: X-Ray Synchrotron Neutron Tech. 15 (2021) 563-569, ISSN 1027-4510, 1819-7094, https://link.springer.com/10.1134/S1027451021030307.

[20] A.E. Gorodetsky, R.K. Zalavutdinov, V.L. Bukhovets, A.V. Markin, A.P. Zakharov, T.V. Rybkina, V.I. Zolotarevsky, E.E. Mukhin, A.G. Razdobarin, A.M. Dmitriev, Surf. Invest.: X-Ray Synchrotron Neutron Tech. 10 (2016) 1214-1225, ISSN 1027-4510, 1819-7094, http://link.springer.com/10.1134/S1027451016050736.

[21] L. Marot, R. Steiner, G. De Temmerman, P. Oelhafen, J. Nucl. Mater. 390-391 (2009) 1135-1137, ISSN 00223115, https://linkinghub.elsevier.com/retrieve/pii/S002231150900316X.

[22] S. Doniach, M. Sunjic, J. Phys. C, Solid State Phys. (ISSN 0022-3719) 3 (1970) 285-291, https://iopscience.iop.org/article/10.1088/0022-3719/3/2/010.

[23] D.A. Shirley, Phys. Rev. B (ISSN 0556-2805) 5 (1972) 4709-4714, https://link.aps.org/doi/10.1103/PhysRevB.5.4709.

[24] A. Tolia, R. Smiley, W. Delgass, C. Takoudis, M. Weaver, J. Catal. (ISSN 0021-9517) 150 (1994) 56-70, https://www.sciencedirect.com/science/article/pii/S0021951787413224.

[25] J. Scofield, J. Electron Spectrosc. Relat. Phenom. (ISSN 0368-2048) 8 (1976) 129-137, https://www.sciencedirect.com/science/article/pii/0368204876800151.

[26] H. Estrade-Szwarkopf, Carbon (ISSN 0008-6223) 42 (2004) 1713-1721, https://www.sciencedirect.com/science/article/pii/S0008622304001629.

[27] L. Marot, G. De Temmerman, V. Thommen, D. Mathys, P. Oelhafen, Surf. Coat. Technol. 202 (2008) 2837-2843, ISSN 02578972, https://linkinghub.elsevier.com/retrieve/pii/S0257897207010559.

[28] Structural and residual stress analysis by nondestructive methods: evaluation, application, assessment, https://api semanticscholar.org/CorpusID:136620629, 1997.

[29] D. Maurer, R. Heicheim, N. Lingg, V. Müller, K.H. Rieder, Phys. Status Solidi (a) 160 (1997) 403-411, eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/1521-396X%28199704%29160%3A2%3C403%3A%3AAID-PSSA403%3E3.0.CO%3B2-F, https://onlinelibrary.wiley.com/doi/abs/10.1002/1521-396X%28199704%29160%3A2%3C403%3A%3AAID-PSSA403%3E3.0.CO%3B2-F.

[30] G. Abadias, E. Chason, J. Keckes, M. Sebastiani, G.B. Thompson, E. Barthel, G.L. Doll, C.E. Murray, C.H. Stoessel, L. Martinu, J. Vac. Sci. Technol., A, Vac. Surf. Films 36 (2018) 020801, ISSN 0734-2101, 1520-8559, https://pubs.aip.org/jva/article/36/2/020801/246484/Review-Article-Stress-in-thin-films-and-coatings.

[31] M.D. Thouless, J. Vac. Sci. Technol., A, Vac. Surf. Films 9 (1991) 2510-2515, ISSN 0734-2101, 1520-8559, https://pubs.aip.org/jva/article/9/4/2510/462727/ Cracking-and-delamination-of-coatingsCracking-and.

[32] Powder diffraction file card no. 05-0685, Joint Committee on Powder Diffraction Standards, 1953.

[33] J.A. Thornton, J. Vac. Sci. Technol., A, Vac. Surf. Films 3 (1985) 576, ISSN 07342101, http://scitation.aip.org/content/avs/journal/jvsta/3/3/10.1116/1.572997.

[34] D.W. Hoffman, J. Vac. Sci. Technol., A, Vac. Surf. Films 12 (1994) 953, ISSN 07342101, http://scitation.aip.org/content/avs/journal/jvsta/12/4/10.1116/1.579073.

[35] L. Marot, G. De Temmerman, M. van den Berg, P.O. Renault, G. Covarel, M. Joanny, J. Travère, R. Steiner, D. Mathys, E. Meyer, Nucl. Fusion 56 (2016) 066015, ISSN 0029-5515, 1741-4326, http://stacks.iop.org/0029-5515/56/i=6/a=066015?key=crossref.0ae7bdc0dc06423420f9f15e16b45407.

[36] J. Chen, S.J. Bull, J. Phys. D, Appl. Phys. 44 (2011) 034001, ISSN 0022-3727, 1361-6463, https://iopscience.iop.org/article/10.1088/0022-3727/44/3/034001.

[37] U. Valbusa, C. Boragno, F.B.d. Mongeot, J. Phys. Condens. Matter (ISSN 0953-8984) 14 (2002) 8153-8175, https://iopscience.iop.org/article/10.1088/0953-8984/14/35/301.

[38] A. Molle, F. Buatier de Mongeot, F. Granone, R. Buzio, G. Firpo, C. Boragno, U. Valbusa, Nucl. Instrum. Methods Phys. Res., Sect. B, Beam Interact. Mater. Atoms 230 (2005) 555-559, ISSN 0168583X, https://linkinghub.elsevier.com/retrieve/pii/S0168583X04013849.

[39] A. Molle, F.B. De Mongeot, A. Molinari, F. Xiaerding, C. Boragno, U. Valbusa, Phys. Rev. Lett. 93 (2004) 256103, ISSN 0031-9007, 1079-7114, https://link.aps.org/doi/10.1103/PhysRevLett.93.256103.

[40] A. Lopez-Cazalilla, F. Djurabekova, A. Ilinov, C. Fridlund, K. Nordlund, Mater. Res. Lett. (ISSN 2166-3831) 8 (2020) 110-116, https://www.tandfonline.com/doi/full/10.1080/21663831.2019.1711458.

[41] A.E. Gorodetsky, A.V. Markin, V.L. Bukhovets, V.L. Voytitsky, T.V. Rybkina, R.K. Zalavutdinov, V.I. Zolotarevsky, A.P. Zakharov, I.A. Arkhipushkin, L.P. Kazansky, A.M. Dmitriev, A.G. Razdobarin, D.S. Samsonov, E.E. Mukhin, Surf. Invest.: X-Ray Synchrotron Neutron Tech. 14 (2020) 1003-1015, ISSN 1027-4510, 1819-7094, https://link.springer.com/10.1134/S10274510200502098.

[42] I. Gerhards, H. Stillrich, C. Ronning, H. Hofsäss, M. Seibt, Phys. Rev. B 70 (2004) 245418, ISSN 1098-0121, 1550-235X, https://link.aps.org/doi/10.1103/PhysRevB.70.245418.

[43] J.M. Ting, W.Y. Wu, Surf. Coat. Technol. 231 (2013) 2-5, ISSN 02578972, https://linkinghub.elsevier.com/retrieve/pii/S0257897212003830.

[44] M. Mougenot, P. Andreazza, C. Andreazza-Vignolle, R. Escalier, T. Sauvage, O. Lyon, P. Brault, J. Nanopart. Res. 14 (2012) 672, ISSN 1388-0764, 1572-896X, http://link.springer.com/10.1007/s11051-011-0672-9.

[45] C. Ronning, I. Gerhards, M. Seibt, H. Hofsäss, W.Y. Wu, J.M. Ting, Nucl. Instrum. Methods Phys. Res., Sect. B, Beam Interact. Mater. Atoms 242 (2006) 261-264, ISSN 0168583X, https://linkinghub.elsevier.com/retrieve/pii/S0168583X0501520X.

[46] I.K. Hannstein, Self-Organized Formation of Metal-Carbon Nanostructures by Hyperthermal Ion Deposition, Ph.D. thesis, Georg-August-University Göttingen, 2006, https://ediss.uni-goettingen.de/handle/11858/00-1735-0000-0006-B58E-F.

[47] W.y. Wu, J.m. Ting, Thin Solid Films 420-421 (2002) 166-171, ISSN 00406090, https://linkinghub.elsevier.com/retrieve/pii/S0040609002008040.

[48] K. Lu, C.F. Huo, Y. He, J. Yin, J. Liu, Q. Peng, W.P. Guo, Y. Yang, Y.W. Li, X.D. Wen, J. Phys. Chem. C 122 (2018) 23191-23199, ISSN 1932-7447, 1932-7455, https://pubs.acs.org/doi/10.1021/acs.jpcc.8b07650.

[49] Z. Pászti, G. Pető, Z. Horváth, O. Geszti, A. Karacs, L. Guczi, Appl. Phys. A, Mater. Sci. Process. 76 (2003) 577-587, ISSN 0947-8396, 1432-0630, http://link.springer.com/10.1007/s00339-002-1464-y.

[50] O.V. Yazyev, A. Pasquarello, Phys. Rev. Lett. 100 (2008) 156102, ISSN 0031-9007, 1079-7114, https://link.aps.org/doi/10.1103/PhysRevLett.100.156102.