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Fractality of self-grown nanostructured tungsten by He plasma irradiation
Physics Letters A 378 (2014) 2533–2538
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Fractality of self-grown nanostructured tungsten by He plasma irradiation Shin Kajita a,∗ , Yoshiyuki Tsuji b , Noriyasu Ohno b a b
EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
a r t i c l e
i n f o
Article history: Received 24 May 2014 Accepted 20 June 2014 Available online 27 June 2014 Communicated by F. Porcelli Keywords: Nanostructure Helium plasma Fractality Fractal dimension
a b s t r a c t Fractal property of the helium irradiated nanostructured tungsten was investigated from the scanning electron microscope (SEM) micrographs, gas adsorption isotherms, and transmission electron microscope (TEM) micrographs. From the SEM micrographs, fractal dimension and the parameter dmin , which characterizes the SEM texture image, were deduced, and the fractal dimension was compared with the one obtained from the gas adsorption isotherms. It was revealed that the fractal dimension obtained from the top view SEM micrographs was significantly lower than that from the adsorption isotherms. From the cross sectional SEM micrographs, two power law relations were identified in two different scales, and the fractal dimension from the adsorption was in between the two fractal dimensions. From the TEM micrographs, it was found that the porosity distribution also has fractal relation with height of the nanostructures when the nanostructures were sufficiently grown. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the course of basic plasma material interaction experiments for nuclear fusion research, formation of tungsten (W) nanostructures by the exposure to helium (He) plasma has been found in mid 2000s [1–3]. Fiberform fine nanostructures are grown on W surface when sufficient He ions irradiate the W surface under certain conditions [3]. Since the nanostructure could be fragile for transient heat loads, the nanostructurization raises discussion that it can significantly change the plasma material interaction in fusion reactors [4,5]. At the same time, the application of the He plasma irradiated metals has been initiated. Plasma-assisted laser ablation can significantly decrease the ablation power threshold [6]. The He irradiated W can be a total solar absorber [7], may be used as large area field emission emitter [8], and can be used as photocatalytic material for decomposition of organic material [9] and water splitting [10]. It has been revealed that the nanostructurization also occurs on other metals such as molybdenum (Mo) [3,11], nickel [9], iron [9,12], and titanium [13]. It has been identified that self-growth of helium bubbles inside the metal plays a key role in development of the nanostructures [14]; the mechanisms of the growth of the nanostructure have yet to be fully understood. To investigate the detailed formation and growth mechanisms of the nanostructure, various simulation stud-
*
Corresponding author. E-mail address: [email protected] (S. Kajita).
http://dx.doi.org/10.1016/j.physleta.2014.06.033 0375-9601/© 2014 Elsevier B.V. All rights reserved.
ies have been conducted. A first principle simulation showed that multi He atoms can trap on a W vacancy [15]. Availability of noble gas clustering on bcc W has been investigated using first-principles investigation [16]. Viscoelastic model was developed to explain the nanostructure growth rate and temperature range [17]. Recently, molecular dynamic (MD) simulation presented bursting of He bubbles [18] and formation of foams and fuzz structures [19]. When comparing between simulations and experiments, quantitative comparison with some indices will be of importance. To characterize the morphology and shape of the structure, several important parameters can be deduced from the fractal analysis. Analysis of scanning electron microscope (SEM) micrographs has been developed and utilized widely [20,21]; fractal dimension, D and several parameters (d par and dmin ) can be inferred from the micrographs. Moreover, gas adsorption property was also used to deduce D [22,23]. At the moment, however, no analysis of the fractality has been reported for the He plasma induced nanostructures. In this paper, fractal analysis was applied for the W nanostructures formed by the He plasma irradiation. Using the SEM micrographs, D and dmin are inferred, and the obtained D is compared with the one obtained from the gas desorption property. In addition, from the analysis of the cross sectional transmission electron microscope (TEM) micrographs, fractality in the porosity will be shown. Section 2 provides a short description of the sample fabrication method the methods of fractal analysis used. Results and discussions are given in Section 3, and Section 4 concludes the paper.
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2. Preparations 2.1. Samples This study used the data that have already been published from our group: the SEM images [3], TEM images [14], and gas adsorption isotherms [24]. All the samples were prepared in the linear plasma device NAGDIS-II by the exposure to the He plasmas. High density He plasma was produced in steady state using a DC arc discharge. The sample temperature was varied by changing the He flux and the incident ion energy, and the temperature range used in this study was 1400–1700 K. The incident ion energy was approximately 50 eV. The He fluence was in the range of 1–20 × 1025 m−2 . The growth process of the nanostructures has been discussed from TEM micrographs of the cross section of the He irradiated samples [14]. Here, we briefly describe how the nanostructures grow by the He plasma irradiation; details can be found in elsewhere [3,14,7]. During the He plasma irradiation, first He bubbles are observed in approximately 100 nm range and protrusions are started to be observed on the surface. At the same time, pinholes are formed on the surface. When the He fluence exceeds 1–2 × 1025 m−2 , fine nanostructures cover the surface and the thickness of the nanostructured layer increases in proportional to the square root of the irradiation time [2]. 2.2. Fractality from image brightness SEM images have been utilized to characterize the surface texture. Frequency spectrum obtained by fast Fourier transformation can be used to obtain the fractal dimension [25]. Also, the variation of the brightness has been widely used for fractal analysis [21, 26], because the algorism of the analysis is simple. In this study, the variation of the brightness of images is used for the analysis. This method is based on the calculation of the variation of the brightness level of the sample surface. For the analysis, eight bit gray images were used. Total black and white correspond to 0 and 255, respectively. The variation is calculated as
2 1/2 z(l) = z(x, y ) − z(x0 , y 0 ) ,
(1)
where l is the distance between the positions (x, y ) and (x0 , y 0 ), and the brackets means the average. The position (x0 , y 0 ) is fixed and the position (x, y ) is changed while taking the average. For z < η , where η is the lateral correlation length, following relation is satisfied [27,21]:
z(l) = l H .
(2)
Here H is Hurst exponents, and the fractal dimension, D, can be obtained from the relation H = 3 − D. 2.3. Fractality from gas adsorption isotherm The behavior of gas adsorption can be utilized to infer the fractal dimension. Adsorption isotherm can be obtained by measuring adsorption volume, V , while changing the gas pressure P . There are two methods to infer the fractal dimension from the gas absorption behaviors: one is multi-probe method and the other is single probe method. Multi-probe method deduces the fractal dimension with using adsorption isotherms for various gas species with different gas (atom or molecule) sizes [28]. This method seems to be reliable; it requires adsorption isotherm with different gas species. Single probe method is simpler, which can infer fractal dimension from an adsorption isotherms for one gas species [29,30].
Fig. 1. Variance of the brightness level as a function of the distance.
For the single probe method, the relation between V and P / P 0 , where P 0 is the saturation pressure, fractal dimension can be obtained from the following relation:
V ∝ ln
P0 P
D −3 .
(3)
In this study, this single probe method was used to deduce the fractal dimension. Comparative study between the single probe method and other methods suggested that it can deduce reasonable surface fractal dimension [23]. 3. Results and discussion 3.1. From top SEM micrographs Fig. 1 shows the variance of the brightness level z(l) as a function of the distance l for the sample shown in the inset. The He plasma irradiation was conducted at the incident ion energy of 50 eV and the surface temperature of ∼1400 K, and the He fluence was 5.5 × 1025 m−2 . As seen from the SEM micrograph, the nanostructures fully cover the surface. We can obtain D from the slope of log–log plot, and dmin can be obtained from the knee of the slope. From Fig. 1, the fractal dimension was inferred to be 2.17 ± 0.03, and dmin was 40 nm. It is noted that the width of the structure seen in the inset was slightly narrower but close to dmin . In the scale larger than dmin , the slope was almost flat, indicating that the variance of the brightness saturated around dmin . Figs. 2(a) and (b) show the fractal dimension and dmin , respectively, as a function of the He fluence. The SEM micrographs are also shown in Fig. 2(a) except for the case of the He fluence of 5.5 × 1025 m−2 , which was presented in Fig. 1. The He fluence range was 0.6 to 5.5 × 1025 m−2 . When the He fluence was lower than 1–2 × 1025 m−2 , the protrusions and pinholes are seen on the surface, while the fine nanostructures are clearly seen on the surface when the fluence is greater than ∼2 × 1025 m−2 . Although the surface morphology significantly changed with the He fluence, the inferred D was almost constant at ∼2.2, and dmin was in the range of 30–45 nm. A clear He fluence dependence was not identified on both of the parameters. As shown later, the obtained D is significantly smaller than the values obtained from other methods; the difference is discussed later. 3.2. From cross sectional SEM micrograph In the previous section, SEM micrographs observed from the top of the surface were analyzed. In this section, a cross sectional
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Fig. 2. (a) Fractal dimension and (b) dmin as a function of the He fluence.
micrograph [3] is used for the fractal analysis. Fig. 3(a) shows the cross sectional SEM micrograph of a He irradiated tungsten sample. The helium ion energy was 50 eV, the surface temperature was 1700 K, and the helium ion fluence was ∼ 2 × 1026 m−2 . The irradiation condition satisfied the necessary condition for the nanostructure growth, and the nanostructures are sufficiently grown on the surface. Fig. 3(b) shows the variance of the brightness level as a function of the distance from reference point for the SEM micrograph shown in Fig. 3(a). The depth of the reference position was 400 nm from the top of the image, as shown in Fig. 3(a). The depth here does not necessary mean the absolute depth from the top of the surface. It is only used for the discussion of the depth dependence. Clear knee can be identified in Fig. 3(b); interestingly, in the scale larger than dmin , that the slope became flatter but still it also satisfied the power law. From both of the slopes, the fractal dimension can be deduced; here, we define the fractal dimension obtained in the scales below and above dmin as D 1 and D 2 , respectively. Fig. 4(a) shows the depth dependence of D 1 and D 2 . Although the fractal dimension D 1 and D 2 varied, no clear depth dependence was identified; D 1 was in the range of 2.3–2.6 and D 2 was in the range of 2.8–2.9. The value D 1 was not so different from those obtained from the top SEM micrographs, though still it was slightly greater. On the other hand, D 2 was much greater. Fig. 4(b) shows the depth dependence of dmin . Although dmin also varied from 10–45 nm by position, no clear depth dependence was identified. In average, it is likely that dmin corresponds to the width of the nanostructures.
Fig. 3. (a) A cross sectional SEM micrograph of the He irradiated tungsten sample and (b) the variance of the brightness level as a function of the distance.
3.3. Discussion of fractal dimension
Fig. 4. The depth dependence of (a) D 1 and D 2 and (b) dmin , respectively, obtained from the SEM micrograph shown in Fig. 3(a).
From the top SEM micrographs, the deduced D was ∼2.2, and the variance of the brightness level saturated in the scale greater than dmin , which was ∼40 nm. On the other hand, from the cross sectional SEM micrograph, the fractality was identified in different
scales smaller and larger than dmin and the fractal dimensions are in the range of 2.3–2.6 and 2.8–2.9, respectively. Fig. 5 shows the surface fractal analysis of the adsorption isotherms for the He irradiated sample. Krypton was used for the
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absorption gas. The irradiation conditions, i.e., the sample temperature, the incident ion energy, and the He fluence were 1550 K, 55 eV, and 2 × 1026 m−2 , respectively. Although the surface temperature was ∼150 K lower, the irradiation condition was almost the same as that for the cross section SEM sample used in Figs. 3 and 4 with the same He fluence. From the B.E.T. method, it was found that the effective surface area was increased by roughly twenty times after the He plasma irradiation [24]. Usually, the adsorption range to be used for this analysis has to be taken roughly in the partial pressure range 0.05 < P / P 0 < 0.3 and limited below
Fig. 5. Surface fractal analysis of the adsorption isotherms obtained for the He irradiated sample.
the Kelvin condensation step that corresponds to the pore filling [31]. In Fig. 5, fitting was conducted using the data in the range 0.1 < P / P 0 < 0.3, where the linear relationship can be well identified and the above condition is satisfied. From the fitting, D was obtained to be 2.68 ± 0.02, which is in between D 1 and D 2 obtained from the cross sectional SEM micrographs. It has been reported that this single probe gas analysis could have some ambiguity and deduce different value when gas species was changed [22]. However, the value of 2.68 is significantly greater than that from the SEM micrograph observed from the top at least. This indicates that SEM micrographs observed from the top cannot be used for the fractal analysis for the nanostructures. Also, this may be true even for different nanostructures that were grown with a directionality from the surface. Concerning the two fractal dimension values D 1 and D 2 obtained from the cross sectional image, it is likely that D 1 reflects the information of surface morphology of the structure itself, since dmin was 10–50 nm, which corresponds almost to the width of the nanostructure. In the same manner, it is likely that the D from the top SEM images also reflects the information of the morphology of the nanostructure fibers. Since the SEM micrograph only reflects the surface morphology and does not contain the information of the inner porous structure, the fractal dimension in the scale less than the fiber width could be close to two. If images that contain inner porous structure were used for the analysis, the fractal dimension can alter. The information of the fractality in larger scale than dmin was included only in the cross sectional SEM images. The SEM micrographs from top were not able to be used for the fractal analysis. One possibility to explain it is that the structure did not grow in all the three directions uniformly. Since the surface was irradiated with He ions from normal direction, the growth direction of the structures may be mainly in the vertical direction. If so,
Fig. 6. Brightness level of TEM micrograph plotted as a function of the height of the nanostructure. The He fluence was (a) 1.1 × 1025 , (b) 1.8 × 1025 , (c) 2.4 × 1025 , and (d) 5.5 × 1025 m−2 .
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the structure would have self-affine fractal feature rather than selfsimilar property, and the fractality could not be properly measured from the top view. In that sense, the cross sectional view shown in Fig. 3(a) can reflect 3D morphology more accurately compared with the one observed from the top. In this study, simple SEM images were used for the analysis. For future work, 3D observations with stereomicroscopy [32] will be useful for more accurate fractal analysis. For gas absorption, usage of multi-probe method is of interest. Furthermore, it is expected to compare the fractality assessed in this study with the ones inferred from the structures obtained from numerical simulations. 3.4. Fractality in porosity distribution Fractal property of the nanostructure can be identified in various points. Here, let us focus on the porosity of the nanostructure. Averaged porosity of the W nanostructures has been measured by the mass measurement [33]. It was found that porosity increased with the nanostructured layer thickness and was approximately ∼0.9 when the thickness of the layer is ∼1 μm. Also, porosity of helium irradiated tungsten was evaluated from the variation in brightness level of TEM micrographs [34,35]; it was shown that the porosity of the nanostructure increased gradually from the bulk part of tungsten [35]. In this section, fractal property of the nanostructures is discussed in terms of the porosity using cross sectional TEM micrographs. Figs. 6(a)–(d) show the brightness level of the TEM micrographs shown in the inset as a function of the height of the nanostructure. The TEM sample was prepared with FIB (focused ion beam) milling process, and the sample thickness was approximately 200 nm. Because the sample thickness is sufficiently thin, it is likely that the brightness level can reflect the changes in the porosity level. The He fluence in Figs. 6(a)–(d) was 1.1 × 1025 , 1.8 × 1025 , 2.4 × 1025 , and 5.5 × 1025 m−2 , respectively. The ground level of the structures is determined from the boundary where brightness level started to increase. When the He fluence is 1.1 × 1025 m−2 , since there are many bubbles just beneath the surface, a dip is seen in the brightness level and clear power law cannot be identified between the brightness level and the height. When the He fluence increases, however, the brightness level, which is proportional to the porosity, is on a clear power law to the height. It is shown that the porosity is not uniform in height, but its distribution also has a fractal property in height. Recently, thermal response of the nanostructure has been investigated using transient heat loads [5]. Interestingly, melting of nanostructures occurred with very weak transient heat load, which can only increase the temperature less than 100 K for bulk W. From the comparison with the temperature measurement using infrared radiation, it was concluded that the thermally isolated part existed on the surface and melted in response to the transients. The fractality in the porosity distribution indicated that the porosity of the top part of nanostructures could be much greater than the average value. If the porosity was greater than 0.95, the thermal conductivity could be dropped significantly by more than two to three orders of magnitude from the bulk material. Thus, the fractal feature of the porosity may influence the response of the transient heat load, which is important for plasma facing material in fusion reactor. 4. Conclusions In this study, using scanning electron microscope (SEM) micrographs, gas adsorption isotherms, and transmission electron microscope (TEM) micrographs, fractality of helium irradiated nanostructured tungsten was investigated. From top view SEM images,
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the fractal dimension, D, was obtained to be ∼2.2. In addition, the parameter dmin , which characterizes the SEM texture image, was evaluated. The value dmin shows the scale to which the power law was observed. The top view SEM images deduced that dmin was in the range of 30–45 nm. From the cross sectional SEM images of tungsten with the He fluence of 5.0 × 1025 m−2 , D was inferred in the two different scales smaller or greater than dmin of 10–50 nm. The fractal dimension was 2.3–2.6 for less than dmin , while it increased to 2.8–2.9 for greater scale than dmin . It is understandable that the fractal dimension is small in the scale less than 10–50 nm, because the dimension reflects the scale less than the one fiberform structure. Since the SEM micrograph only reflects the surface information without inner porous structure, the surface can be more or less flat. The fractal dimension of the nanostructured tungsten with same He fluence was also inferred from the gas adsorption isotherm of Krypton using single probe method. The assessed D was 2.68 ± 0.02, which was in between the two fractal dimensions obtained from the cross sectional SEM micrographs. Moreover, the reasons to cause the discrepancy in D between from the cross section and top view of the nanostructure were discussed. One of the reasons can be attributed to the fact that the nanostructures grew with a directionality, basically in normal direction. If the structure had a directionality, it would have selfaffine fractal nature; the fractality cannot be correctly obtained from image observed from the top. From the TEM micrographs, the relation between the porosity profile and the height of the structure was discussed. The porosity increased from the bottom to the top part gradually, and they were on a power law when the nanostructures were grown sufficiently. These fractal features will be useful when comparing with the results of the simulation in future. Acknowledgements Authors thank Ms. M. Yajima from Nagoya University and Prof. Y. Hatano from Toyama University for providing the gas adsorption isotherms and Dr. A. Taguchi for giving us useful comments about the analysis of the adsorption isotherms. This work was supported in part by a Grant-in-Aid for Young Scientists (A) 23686133 from the Japan Society for the Promotion of Science (JSPS). This work is supported by NIFS/NINS under the project of Formation of International Scientific Base and Network. References [1] S. Takamura, N. Ohno, D. Nishijima, S. Kajita, J. Plasma Fusion Res. 1 (2006) 051. [2] M. Baldwin, R. Doerner, Nucl. Fusion 48 (2008) 035001, 5 pp. [3] S. Kajita, W. Sakaguchi, N. Ohno, N. Yoshida, T. Saeki, Nucl. Fusion 49 (2009) 095005. [4] S. Takamura, T. Miyamoto, N. Ohno, Nucl. Fusion 52 (2012) 123001. [5] S. Kajita, G.D. Temmerman, T. Morgan, S. van Eden, T. de Kruif, N. Ohno, Nucl. Fusion 54 (2014) 033005. [6] S. Kajita, N. Ohno, S. Takamura, W. Sakaguchi, D. Nishijima, Appl. Phys. Lett. 91 (2007) 261501. [7] S. Kajita, T. Saeki, N. Yoshida, N. Ohno, A. Iwamae, Appl. Phys. Express 3 (2010) 085204. [8] S. Kajita, N. Ohno, Y. Hirahata, M. Hiramatsu, Fusion Eng. Des. 88 (2013) 2842. [9] S. Kajita, T. Yoshida, D. Kitaoka, R. Etoh, M. Yajima, N. Ohno, H. Yoshida, N. Yoshida, Y. Terao, J. Appl. Phys. 113 (2013) 134301. [10] M. de Respinis, G. De Temmerman, I. Tanyeli, M.C. van de Sanden, R.P. Doerner, M.J. Baldwin, R. van de Krol, ACS Appl. Mater. Interfaces 5 (2013) 7621. [11] G. De Temmerman, K. Bystrov, J.J. Zielinski, M. Balden, G. Matern, C. Arnas, L. Marot, J. Vac. Sci. Technol. 30 (2012). [12] I. Tanyeli, L. Marot, M.C.M. van de Sanden, G. De Temmerman, ACS Appl. Mater. Interfaces 6 (2014) 3462. [13] S. Kajita, D. Kitaoka, N. Ohno, R. Yoshihara, N. Yoshida, T. Yoshida, Appl. Surf. Sci. 303 (2014) 438. [14] S. Kajita, N. Yoshida, R. Yoshihara, N. Ohno, M. Yamagiwa, J. Nucl. Mater. 418 (2011) 152.
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Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Fractality of self-grown nanostructured tungsten by He plasma irradiation Shin Kajita a,∗ , Yoshiyuki Tsuji b , Noriyasu Ohno b a b
EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
a r t i c l e
i n f o
Article history: Received 24 May 2014 Accepted 20 June 2014 Available online 27 June 2014 Communicated by F. Porcelli Keywords: Nanostructure Helium plasma Fractality Fractal dimension
a b s t r a c t Fractal property of the helium irradiated nanostructured tungsten was investigated from the scanning electron microscope (SEM) micrographs, gas adsorption isotherms, and transmission electron microscope (TEM) micrographs. From the SEM micrographs, fractal dimension and the parameter dmin , which characterizes the SEM texture image, were deduced, and the fractal dimension was compared with the one obtained from the gas adsorption isotherms. It was revealed that the fractal dimension obtained from the top view SEM micrographs was significantly lower than that from the adsorption isotherms. From the cross sectional SEM micrographs, two power law relations were identified in two different scales, and the fractal dimension from the adsorption was in between the two fractal dimensions. From the TEM micrographs, it was found that the porosity distribution also has fractal relation with height of the nanostructures when the nanostructures were sufficiently grown. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the course of basic plasma material interaction experiments for nuclear fusion research, formation of tungsten (W) nanostructures by the exposure to helium (He) plasma has been found in mid 2000s [1–3]. Fiberform fine nanostructures are grown on W surface when sufficient He ions irradiate the W surface under certain conditions [3]. Since the nanostructure could be fragile for transient heat loads, the nanostructurization raises discussion that it can significantly change the plasma material interaction in fusion reactors [4,5]. At the same time, the application of the He plasma irradiated metals has been initiated. Plasma-assisted laser ablation can significantly decrease the ablation power threshold [6]. The He irradiated W can be a total solar absorber [7], may be used as large area field emission emitter [8], and can be used as photocatalytic material for decomposition of organic material [9] and water splitting [10]. It has been revealed that the nanostructurization also occurs on other metals such as molybdenum (Mo) [3,11], nickel [9], iron [9,12], and titanium [13]. It has been identified that self-growth of helium bubbles inside the metal plays a key role in development of the nanostructures [14]; the mechanisms of the growth of the nanostructure have yet to be fully understood. To investigate the detailed formation and growth mechanisms of the nanostructure, various simulation stud-
*
Corresponding author. E-mail address: [email protected] (S. Kajita).
http://dx.doi.org/10.1016/j.physleta.2014.06.033 0375-9601/© 2014 Elsevier B.V. All rights reserved.
ies have been conducted. A first principle simulation showed that multi He atoms can trap on a W vacancy [15]. Availability of noble gas clustering on bcc W has been investigated using first-principles investigation [16]. Viscoelastic model was developed to explain the nanostructure growth rate and temperature range [17]. Recently, molecular dynamic (MD) simulation presented bursting of He bubbles [18] and formation of foams and fuzz structures [19]. When comparing between simulations and experiments, quantitative comparison with some indices will be of importance. To characterize the morphology and shape of the structure, several important parameters can be deduced from the fractal analysis. Analysis of scanning electron microscope (SEM) micrographs has been developed and utilized widely [20,21]; fractal dimension, D and several parameters (d par and dmin ) can be inferred from the micrographs. Moreover, gas adsorption property was also used to deduce D [22,23]. At the moment, however, no analysis of the fractality has been reported for the He plasma induced nanostructures. In this paper, fractal analysis was applied for the W nanostructures formed by the He plasma irradiation. Using the SEM micrographs, D and dmin are inferred, and the obtained D is compared with the one obtained from the gas desorption property. In addition, from the analysis of the cross sectional transmission electron microscope (TEM) micrographs, fractality in the porosity will be shown. Section 2 provides a short description of the sample fabrication method the methods of fractal analysis used. Results and discussions are given in Section 3, and Section 4 concludes the paper.
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2. Preparations 2.1. Samples This study used the data that have already been published from our group: the SEM images [3], TEM images [14], and gas adsorption isotherms [24]. All the samples were prepared in the linear plasma device NAGDIS-II by the exposure to the He plasmas. High density He plasma was produced in steady state using a DC arc discharge. The sample temperature was varied by changing the He flux and the incident ion energy, and the temperature range used in this study was 1400–1700 K. The incident ion energy was approximately 50 eV. The He fluence was in the range of 1–20 × 1025 m−2 . The growth process of the nanostructures has been discussed from TEM micrographs of the cross section of the He irradiated samples [14]. Here, we briefly describe how the nanostructures grow by the He plasma irradiation; details can be found in elsewhere [3,14,7]. During the He plasma irradiation, first He bubbles are observed in approximately 100 nm range and protrusions are started to be observed on the surface. At the same time, pinholes are formed on the surface. When the He fluence exceeds 1–2 × 1025 m−2 , fine nanostructures cover the surface and the thickness of the nanostructured layer increases in proportional to the square root of the irradiation time [2]. 2.2. Fractality from image brightness SEM images have been utilized to characterize the surface texture. Frequency spectrum obtained by fast Fourier transformation can be used to obtain the fractal dimension [25]. Also, the variation of the brightness has been widely used for fractal analysis [21, 26], because the algorism of the analysis is simple. In this study, the variation of the brightness of images is used for the analysis. This method is based on the calculation of the variation of the brightness level of the sample surface. For the analysis, eight bit gray images were used. Total black and white correspond to 0 and 255, respectively. The variation is calculated as
2 1/2 z(l) = z(x, y ) − z(x0 , y 0 ) ,
(1)
where l is the distance between the positions (x, y ) and (x0 , y 0 ), and the brackets means the average. The position (x0 , y 0 ) is fixed and the position (x, y ) is changed while taking the average. For z < η , where η is the lateral correlation length, following relation is satisfied [27,21]:
z(l) = l H .
(2)
Here H is Hurst exponents, and the fractal dimension, D, can be obtained from the relation H = 3 − D. 2.3. Fractality from gas adsorption isotherm The behavior of gas adsorption can be utilized to infer the fractal dimension. Adsorption isotherm can be obtained by measuring adsorption volume, V , while changing the gas pressure P . There are two methods to infer the fractal dimension from the gas absorption behaviors: one is multi-probe method and the other is single probe method. Multi-probe method deduces the fractal dimension with using adsorption isotherms for various gas species with different gas (atom or molecule) sizes [28]. This method seems to be reliable; it requires adsorption isotherm with different gas species. Single probe method is simpler, which can infer fractal dimension from an adsorption isotherms for one gas species [29,30].
Fig. 1. Variance of the brightness level as a function of the distance.
For the single probe method, the relation between V and P / P 0 , where P 0 is the saturation pressure, fractal dimension can be obtained from the following relation:
V ∝ ln
P0 P
D −3 .
(3)
In this study, this single probe method was used to deduce the fractal dimension. Comparative study between the single probe method and other methods suggested that it can deduce reasonable surface fractal dimension [23]. 3. Results and discussion 3.1. From top SEM micrographs Fig. 1 shows the variance of the brightness level z(l) as a function of the distance l for the sample shown in the inset. The He plasma irradiation was conducted at the incident ion energy of 50 eV and the surface temperature of ∼1400 K, and the He fluence was 5.5 × 1025 m−2 . As seen from the SEM micrograph, the nanostructures fully cover the surface. We can obtain D from the slope of log–log plot, and dmin can be obtained from the knee of the slope. From Fig. 1, the fractal dimension was inferred to be 2.17 ± 0.03, and dmin was 40 nm. It is noted that the width of the structure seen in the inset was slightly narrower but close to dmin . In the scale larger than dmin , the slope was almost flat, indicating that the variance of the brightness saturated around dmin . Figs. 2(a) and (b) show the fractal dimension and dmin , respectively, as a function of the He fluence. The SEM micrographs are also shown in Fig. 2(a) except for the case of the He fluence of 5.5 × 1025 m−2 , which was presented in Fig. 1. The He fluence range was 0.6 to 5.5 × 1025 m−2 . When the He fluence was lower than 1–2 × 1025 m−2 , the protrusions and pinholes are seen on the surface, while the fine nanostructures are clearly seen on the surface when the fluence is greater than ∼2 × 1025 m−2 . Although the surface morphology significantly changed with the He fluence, the inferred D was almost constant at ∼2.2, and dmin was in the range of 30–45 nm. A clear He fluence dependence was not identified on both of the parameters. As shown later, the obtained D is significantly smaller than the values obtained from other methods; the difference is discussed later. 3.2. From cross sectional SEM micrograph In the previous section, SEM micrographs observed from the top of the surface were analyzed. In this section, a cross sectional
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Fig. 2. (a) Fractal dimension and (b) dmin as a function of the He fluence.
micrograph [3] is used for the fractal analysis. Fig. 3(a) shows the cross sectional SEM micrograph of a He irradiated tungsten sample. The helium ion energy was 50 eV, the surface temperature was 1700 K, and the helium ion fluence was ∼ 2 × 1026 m−2 . The irradiation condition satisfied the necessary condition for the nanostructure growth, and the nanostructures are sufficiently grown on the surface. Fig. 3(b) shows the variance of the brightness level as a function of the distance from reference point for the SEM micrograph shown in Fig. 3(a). The depth of the reference position was 400 nm from the top of the image, as shown in Fig. 3(a). The depth here does not necessary mean the absolute depth from the top of the surface. It is only used for the discussion of the depth dependence. Clear knee can be identified in Fig. 3(b); interestingly, in the scale larger than dmin , that the slope became flatter but still it also satisfied the power law. From both of the slopes, the fractal dimension can be deduced; here, we define the fractal dimension obtained in the scales below and above dmin as D 1 and D 2 , respectively. Fig. 4(a) shows the depth dependence of D 1 and D 2 . Although the fractal dimension D 1 and D 2 varied, no clear depth dependence was identified; D 1 was in the range of 2.3–2.6 and D 2 was in the range of 2.8–2.9. The value D 1 was not so different from those obtained from the top SEM micrographs, though still it was slightly greater. On the other hand, D 2 was much greater. Fig. 4(b) shows the depth dependence of dmin . Although dmin also varied from 10–45 nm by position, no clear depth dependence was identified. In average, it is likely that dmin corresponds to the width of the nanostructures.
Fig. 3. (a) A cross sectional SEM micrograph of the He irradiated tungsten sample and (b) the variance of the brightness level as a function of the distance.
3.3. Discussion of fractal dimension
Fig. 4. The depth dependence of (a) D 1 and D 2 and (b) dmin , respectively, obtained from the SEM micrograph shown in Fig. 3(a).
From the top SEM micrographs, the deduced D was ∼2.2, and the variance of the brightness level saturated in the scale greater than dmin , which was ∼40 nm. On the other hand, from the cross sectional SEM micrograph, the fractality was identified in different
scales smaller and larger than dmin and the fractal dimensions are in the range of 2.3–2.6 and 2.8–2.9, respectively. Fig. 5 shows the surface fractal analysis of the adsorption isotherms for the He irradiated sample. Krypton was used for the
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absorption gas. The irradiation conditions, i.e., the sample temperature, the incident ion energy, and the He fluence were 1550 K, 55 eV, and 2 × 1026 m−2 , respectively. Although the surface temperature was ∼150 K lower, the irradiation condition was almost the same as that for the cross section SEM sample used in Figs. 3 and 4 with the same He fluence. From the B.E.T. method, it was found that the effective surface area was increased by roughly twenty times after the He plasma irradiation [24]. Usually, the adsorption range to be used for this analysis has to be taken roughly in the partial pressure range 0.05 < P / P 0 < 0.3 and limited below
Fig. 5. Surface fractal analysis of the adsorption isotherms obtained for the He irradiated sample.
the Kelvin condensation step that corresponds to the pore filling [31]. In Fig. 5, fitting was conducted using the data in the range 0.1 < P / P 0 < 0.3, where the linear relationship can be well identified and the above condition is satisfied. From the fitting, D was obtained to be 2.68 ± 0.02, which is in between D 1 and D 2 obtained from the cross sectional SEM micrographs. It has been reported that this single probe gas analysis could have some ambiguity and deduce different value when gas species was changed [22]. However, the value of 2.68 is significantly greater than that from the SEM micrograph observed from the top at least. This indicates that SEM micrographs observed from the top cannot be used for the fractal analysis for the nanostructures. Also, this may be true even for different nanostructures that were grown with a directionality from the surface. Concerning the two fractal dimension values D 1 and D 2 obtained from the cross sectional image, it is likely that D 1 reflects the information of surface morphology of the structure itself, since dmin was 10–50 nm, which corresponds almost to the width of the nanostructure. In the same manner, it is likely that the D from the top SEM images also reflects the information of the morphology of the nanostructure fibers. Since the SEM micrograph only reflects the surface morphology and does not contain the information of the inner porous structure, the fractal dimension in the scale less than the fiber width could be close to two. If images that contain inner porous structure were used for the analysis, the fractal dimension can alter. The information of the fractality in larger scale than dmin was included only in the cross sectional SEM images. The SEM micrographs from top were not able to be used for the fractal analysis. One possibility to explain it is that the structure did not grow in all the three directions uniformly. Since the surface was irradiated with He ions from normal direction, the growth direction of the structures may be mainly in the vertical direction. If so,
Fig. 6. Brightness level of TEM micrograph plotted as a function of the height of the nanostructure. The He fluence was (a) 1.1 × 1025 , (b) 1.8 × 1025 , (c) 2.4 × 1025 , and (d) 5.5 × 1025 m−2 .
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the structure would have self-affine fractal feature rather than selfsimilar property, and the fractality could not be properly measured from the top view. In that sense, the cross sectional view shown in Fig. 3(a) can reflect 3D morphology more accurately compared with the one observed from the top. In this study, simple SEM images were used for the analysis. For future work, 3D observations with stereomicroscopy [32] will be useful for more accurate fractal analysis. For gas absorption, usage of multi-probe method is of interest. Furthermore, it is expected to compare the fractality assessed in this study with the ones inferred from the structures obtained from numerical simulations. 3.4. Fractality in porosity distribution Fractal property of the nanostructure can be identified in various points. Here, let us focus on the porosity of the nanostructure. Averaged porosity of the W nanostructures has been measured by the mass measurement [33]. It was found that porosity increased with the nanostructured layer thickness and was approximately ∼0.9 when the thickness of the layer is ∼1 μm. Also, porosity of helium irradiated tungsten was evaluated from the variation in brightness level of TEM micrographs [34,35]; it was shown that the porosity of the nanostructure increased gradually from the bulk part of tungsten [35]. In this section, fractal property of the nanostructures is discussed in terms of the porosity using cross sectional TEM micrographs. Figs. 6(a)–(d) show the brightness level of the TEM micrographs shown in the inset as a function of the height of the nanostructure. The TEM sample was prepared with FIB (focused ion beam) milling process, and the sample thickness was approximately 200 nm. Because the sample thickness is sufficiently thin, it is likely that the brightness level can reflect the changes in the porosity level. The He fluence in Figs. 6(a)–(d) was 1.1 × 1025 , 1.8 × 1025 , 2.4 × 1025 , and 5.5 × 1025 m−2 , respectively. The ground level of the structures is determined from the boundary where brightness level started to increase. When the He fluence is 1.1 × 1025 m−2 , since there are many bubbles just beneath the surface, a dip is seen in the brightness level and clear power law cannot be identified between the brightness level and the height. When the He fluence increases, however, the brightness level, which is proportional to the porosity, is on a clear power law to the height. It is shown that the porosity is not uniform in height, but its distribution also has a fractal property in height. Recently, thermal response of the nanostructure has been investigated using transient heat loads [5]. Interestingly, melting of nanostructures occurred with very weak transient heat load, which can only increase the temperature less than 100 K for bulk W. From the comparison with the temperature measurement using infrared radiation, it was concluded that the thermally isolated part existed on the surface and melted in response to the transients. The fractality in the porosity distribution indicated that the porosity of the top part of nanostructures could be much greater than the average value. If the porosity was greater than 0.95, the thermal conductivity could be dropped significantly by more than two to three orders of magnitude from the bulk material. Thus, the fractal feature of the porosity may influence the response of the transient heat load, which is important for plasma facing material in fusion reactor. 4. Conclusions In this study, using scanning electron microscope (SEM) micrographs, gas adsorption isotherms, and transmission electron microscope (TEM) micrographs, fractality of helium irradiated nanostructured tungsten was investigated. From top view SEM images,
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the fractal dimension, D, was obtained to be ∼2.2. In addition, the parameter dmin , which characterizes the SEM texture image, was evaluated. The value dmin shows the scale to which the power law was observed. The top view SEM images deduced that dmin was in the range of 30–45 nm. From the cross sectional SEM images of tungsten with the He fluence of 5.0 × 1025 m−2 , D was inferred in the two different scales smaller or greater than dmin of 10–50 nm. The fractal dimension was 2.3–2.6 for less than dmin , while it increased to 2.8–2.9 for greater scale than dmin . It is understandable that the fractal dimension is small in the scale less than 10–50 nm, because the dimension reflects the scale less than the one fiberform structure. Since the SEM micrograph only reflects the surface information without inner porous structure, the surface can be more or less flat. The fractal dimension of the nanostructured tungsten with same He fluence was also inferred from the gas adsorption isotherm of Krypton using single probe method. The assessed D was 2.68 ± 0.02, which was in between the two fractal dimensions obtained from the cross sectional SEM micrographs. Moreover, the reasons to cause the discrepancy in D between from the cross section and top view of the nanostructure were discussed. One of the reasons can be attributed to the fact that the nanostructures grew with a directionality, basically in normal direction. If the structure had a directionality, it would have selfaffine fractal nature; the fractality cannot be correctly obtained from image observed from the top. From the TEM micrographs, the relation between the porosity profile and the height of the structure was discussed. The porosity increased from the bottom to the top part gradually, and they were on a power law when the nanostructures were grown sufficiently. These fractal features will be useful when comparing with the results of the simulation in future. Acknowledgements Authors thank Ms. M. Yajima from Nagoya University and Prof. Y. Hatano from Toyama University for providing the gas adsorption isotherms and Dr. A. Taguchi for giving us useful comments about the analysis of the adsorption isotherms. This work was supported in part by a Grant-in-Aid for Young Scientists (A) 23686133 from the Japan Society for the Promotion of Science (JSPS). This work is supported by NIFS/NINS under the project of Formation of International Scientific Base and Network. References [1] S. Takamura, N. Ohno, D. Nishijima, S. Kajita, J. Plasma Fusion Res. 1 (2006) 051. [2] M. Baldwin, R. Doerner, Nucl. Fusion 48 (2008) 035001, 5 pp. [3] S. Kajita, W. Sakaguchi, N. Ohno, N. Yoshida, T. Saeki, Nucl. Fusion 49 (2009) 095005. [4] S. Takamura, T. Miyamoto, N. Ohno, Nucl. Fusion 52 (2012) 123001. [5] S. Kajita, G.D. Temmerman, T. Morgan, S. van Eden, T. de Kruif, N. Ohno, Nucl. Fusion 54 (2014) 033005. [6] S. Kajita, N. Ohno, S. Takamura, W. Sakaguchi, D. Nishijima, Appl. Phys. Lett. 91 (2007) 261501. [7] S. Kajita, T. Saeki, N. Yoshida, N. Ohno, A. Iwamae, Appl. Phys. Express 3 (2010) 085204. [8] S. Kajita, N. Ohno, Y. Hirahata, M. Hiramatsu, Fusion Eng. Des. 88 (2013) 2842. [9] S. Kajita, T. Yoshida, D. Kitaoka, R. Etoh, M. Yajima, N. Ohno, H. Yoshida, N. Yoshida, Y. Terao, J. Appl. Phys. 113 (2013) 134301. [10] M. de Respinis, G. De Temmerman, I. Tanyeli, M.C. van de Sanden, R.P. Doerner, M.J. Baldwin, R. van de Krol, ACS Appl. Mater. Interfaces 5 (2013) 7621. [11] G. De Temmerman, K. Bystrov, J.J. Zielinski, M. Balden, G. Matern, C. Arnas, L. Marot, J. Vac. Sci. Technol. 30 (2012). [12] I. Tanyeli, L. Marot, M.C.M. van de Sanden, G. De Temmerman, ACS Appl. Mater. Interfaces 6 (2014) 3462. [13] S. Kajita, D. Kitaoka, N. Ohno, R. Yoshihara, N. Yoshida, T. Yoshida, Appl. Surf. Sci. 303 (2014) 438. [14] S. Kajita, N. Yoshida, R. Yoshihara, N. Ohno, M. Yamagiwa, J. Nucl. Mater. 418 (2011) 152.
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