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Visualization of deuterium dead layer by atom probe tomography Ryota Gemma, a,b,Talaat Al-Kassab, b Reiner Kirchheim a and Astrid Pundt a a Institute of Materials Physics, University of Go ¨ ttingen, Friedrich-Hund-Platz 1, D-37077 Go ¨ ttingen, Germany b Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia Received 7 July 2012; revised 14 August 2012; accepted 21 August 2012 Available online 26 August 2012 The first direct observation, by atom probe tomography, of a deuterium dead layer is reported for Fe/V multilayered film loaded with D solute atoms. The thickness of the dead layers was measured to be 0.4–0.5 nm. The dead layers could be distinguished from chemically intermixed layers. The results suggest that the dead layer effect occurs even near the interface of the mixing layers, sup- porting an interpretation that the dead layer effect cannot be explained solely by electronic charge transfer but also involves a mod- ulation of rigidity. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Dead layer; Atom probe tomography; Hydrogen; Multilayer; Transition metals Heterointerfaces influence the properties of materials on the local scale due to lattice defects and charge transfer [1]. Hydrogen atoms are sensitive to such local environmental changes and are accommodated in the related crystal lattice. For multilayered metals, hydrogen-depleted zones (dead layers) at the metal interfaces have been suggested [2,3]. To date, however, no direct observation of these dead layers has been re- ported. Atom probe tomography (APT) analysis [4–7] has opened up direct access to atomic scale chemistry and enables analysis of hydrogen in materials. However, quantitative mapping of the 3-D distribution especially of hydrogen species remains a challenging task because of their high mobility [8]. Recent developments and opti- mization of APT analysis conditions now enable quanti- fication of hydrogen species [9–12]. Here, we report a direct proof of hydrogen dead layers in the vicinity of interfaces, as well as depleted zones in intermixed re- gions in Fe/V multilayered thin films. Recent studies on hydrogen storage materials have demonstrated the importance of nanoscale metal– hydrogen (M–H) interactions for modifying both the kinetics and thermodynamics [13–16]. Heterointerfaces often exist in nanosystems, and it has been noted that the local chemical modulation at these interfaces strongly influences the hydrogen distribution. Multilay- ered (ML) thin-film structures fabricated by thin-film deposition techniques provide a means to artificially achieve this kind of heterointerface. A Fe/V ML film, for instance, is an ideal system for the investigation of the hydrogen distribution at interfaces, since it is com- posed of V, an effective hydrogen absorber, and Fe, a poor hydrogen absorber. Therefore, hydrogen is ex- pected to be absorbed essentially only in the V layers. The ratio g of the hydrogen solubilities c H (p, T) in Fe and V, respectively, can be calculated using the heats of solution, at a given pressure and temperature. At 300 K and 1 bar this ratio is about g = c HinFe / c HinV 10 10 as a first approximation [17]. Hence, this large solubility difference is even ideal for observing the significant change in hydrogen distribution at such interfaces. Consequently, it is inferred that the hydrogen distribution at the Fe/V interface closely follows this sol- ubility difference. In reality, however, the hydrogen distribution is determined by several factors induced particularly by the local environment at interfaces. These factors are ex- plained by the following arguments: (i) chemical inter- mixing (local alloying effect) of the adjacent metals during film preparation, which results in a changed local chemical environment for the H atoms; (ii) biaxial in- plane stress that modifies the chemical potential for hydrogen in the metal; (iii) microstructural defects such 1359-6462/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2012.08.025 Corresponding author at: Physical Sciences and Engineering Divi- sion, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. Tel.: +966 (0)2 8084493; e-mail: [email protected] Available online at www.sciencedirect.com Scripta Materialia 67 (2012) 903–906 www.elsevier.com/locate/scriptamat
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Page 1: Visualization of deuterium dead layer by atom probe tomography

Available online at www.sciencedirect.com

Scripta Materialia 67 (2012) 903–906

www.elsevier.com/locate/scriptamat

Visualization of deuterium dead layer by atom probe tomography

Ryota Gemma,a,b,⇑ Talaat Al-Kassab,b Reiner Kirchheima and Astrid Pundta

aInstitute of Materials Physics, University of Gottingen, Friedrich-Hund-Platz 1, D-37077 Gottingen, GermanybPhysical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST),

Thuwal 23955-6900, Kingdom of Saudi Arabia

Received 7 July 2012; revised 14 August 2012; accepted 21 August 2012Available online 26 August 2012

The first direct observation, by atom probe tomography, of a deuterium dead layer is reported for Fe/V multilayered film loadedwith D solute atoms. The thickness of the dead layers was measured to be 0.4–0.5 nm. The dead layers could be distinguished fromchemically intermixed layers. The results suggest that the dead layer effect occurs even near the interface of the mixing layers, sup-porting an interpretation that the dead layer effect cannot be explained solely by electronic charge transfer but also involves a mod-ulation of rigidity.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Dead layer; Atom probe tomography; Hydrogen; Multilayer; Transition metals

Heterointerfaces influence the properties ofmaterials on the local scale due to lattice defects andcharge transfer [1]. Hydrogen atoms are sensitive to suchlocal environmental changes and are accommodated inthe related crystal lattice. For multilayered metals,hydrogen-depleted zones (“dead layers”) at the metalinterfaces have been suggested [2,3]. To date, however,no direct observation of these dead layers has been re-ported. Atom probe tomography (APT) analysis [4–7]has opened up direct access to atomic scale chemistryand enables analysis of hydrogen in materials. However,quantitative mapping of the 3-D distribution especiallyof hydrogen species remains a challenging task becauseof their high mobility [8]. Recent developments and opti-mization of APT analysis conditions now enable quanti-fication of hydrogen species [9–12]. Here, we report adirect proof of hydrogen dead layers in the vicinity ofinterfaces, as well as depleted zones in intermixed re-gions in Fe/V multilayered thin films.

Recent studies on hydrogen storage materials havedemonstrated the importance of nanoscale metal–hydrogen (M–H) interactions for modifying both thekinetics and thermodynamics [13–16]. Heterointerfaces

1359-6462/$ - see front matter � 2012 Acta Materialia Inc. Published by Elhttp://dx.doi.org/10.1016/j.scriptamat.2012.08.025

⇑Corresponding author at: Physical Sciences and Engineering Divi-sion, King Abdullah University of Science and Technology(KAUST), Thuwal 23955-6900, Kingdom of Saudi Arabia. Tel.:+966 (0)2 8084493; e-mail: [email protected]

often exist in nanosystems, and it has been noted thatthe local chemical modulation at these interfacesstrongly influences the hydrogen distribution. Multilay-ered (ML) thin-film structures fabricated by thin-filmdeposition techniques provide a means to artificiallyachieve this kind of heterointerface. A Fe/V ML film,for instance, is an ideal system for the investigation ofthe hydrogen distribution at interfaces, since it is com-posed of V, an effective hydrogen absorber, and Fe, apoor hydrogen absorber. Therefore, hydrogen is ex-pected to be absorbed essentially only in the V layers.The ratio g of the hydrogen solubilities cH(p, T) in Feand V, respectively, can be calculated using the heatsof solution, at a given pressure and temperature. At300 K and 1 bar this ratio is about g = cHinFe/cHinV � 10�10 as a first approximation [17]. Hence, thislarge solubility difference is even ideal for observingthe significant change in hydrogen distribution at suchinterfaces. Consequently, it is inferred that the hydrogendistribution at the Fe/V interface closely follows this sol-ubility difference.

In reality, however, the hydrogen distribution isdetermined by several factors induced particularly bythe local environment at interfaces. These factors are ex-plained by the following arguments: (i) chemical inter-mixing (local alloying effect) of the adjacent metalsduring film preparation, which results in a changed localchemical environment for the H atoms; (ii) biaxial in-plane stress that modifies the chemical potential forhydrogen in the metal; (iii) microstructural defects such

sevier Ltd. All rights reserved.

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as misfit dislocations that release interfacial stressresulting from lattice parameter differences and trapconsiderable amounts of hydrogen locally [15].

In addition to the above aspects, the pioneering workof Hjorvarsson et al. on hydrogen interaction with Mo/V [2] and Fe/V [3] (100) superlattice thin films hasbrought new insights into the local hydrogen solubilityat heterointerfaces. Hjorvarsson et al. discovered thatthe hydrogen solubility in the V layers decreases to al-most zero as the V layer thickness l decreases to�1 nm. They attributed the reduced hydrogen solubilityto the presence of the interfaces and named this locallayer of reduced solubility the “dead layer”. Experimen-tal studies on other ML hydrogen systems [18,19] havealso confirmed the presence of dead layers. In thesestudies, the thickness of the dead layer was determinedby combining the 15N-method, Rutherford backscatter-ing spectroscopy and X-ray reflectivity or neutron reflec-tivity measurements [2,3,18,19]. The 15N-method has atypical depth resolution of better than 8 nm dependingon the ion beam energy and the depth of penetration.Thus, the dead layer thickness of 0.45–0.49 nm (l/2)could only indirectly be deduced from extrapolation ofmeasured hydrogen concentrations in thicker V layers(Supplementary Fig. S1).

Hydrogen dead layers were first considered to origi-nate from electron transfer between Fe or Mo and V.Electron transfer is expected because of the differentFermi levels in the electronic density of states (DOS)of the adjacent metals. Transferred electrons locallyblock sites for hydrogen because its electron can nolonger be accommodated in the DOS. However, densityfunctional theory (DFT) calculations have showed thatthe dead layers should mainly arise from elastic interac-tions between the adjacent metal layers [20]. In the cal-culation, the presence of chemical intermixing layerswas not considered. Meanwhile, alloying of V with Feis known to decrease hydrogen solubility [21], i.e. theinterface mixing layer, if any, might mimic the deadlayer effect. Hence, it is not clear if the dead layer effectcan be explained by elastic interactions when intermix-ing layers exist. Both suggested explanations are basedon the presence of a heterogeneous interface. Thus, ahydrogen-depleted dead layer should exist at any inter-face of the Fe/V multilayer and not just at the interfacesof the thinnest layers.

APT analysis is based on time-of-flight analysis offield evaporated ions. Therefore, all elements, includingH, can in principle be detected. However, use of D in-stead of H is highly recommended so that D atomscan be differentiated from residual hydrogen in thechamber. The typical resolution of APT is 0.1 nm indepth and 0.5 nm laterally, which enables analysis ofdead layers with the suggested thicknesses of �0.49 nmwhen the interface is measured in the depth direction.A tungsten needle-shaped tip substrate was preparedfrom a tungsten wire (initial diameter d = 0.1 mm).The wire, 10–15 mm in length, was electrochemicallypolished in an electrolyte of 2 N NaOH solution. Thepolished substrate was further refined by field evapora-tion in a field ion microscope (FIM), with helium gasat 30 K. The intention was to obtain an atomically flatand clean surface, as well as a tip with the desired radius

of curvature of 30–50 nm. The wire axis was the [011]direction as determined by FIM.

The Fe 5 nm/V 5 nm ML film, capped with a thin Pdlayer, was prepared on the developed tungsten substrateby ion beam sputter deposition in an ultra-high-vacuum(UHV) system with a base pressure of 10�8 Pa. Thedeposition was carried out at an argon pressure of10�2 Pa and at 306 K. Following the (110) plane ofthe W substrate, the film was grown with (110)orientation.

The D2 gas loading of the film was performed in anexternal UHV chamber. To minimize oxygen and waterpartial pressure, the chamber was first baked-out at383 K for 12 h. After reaching a pressure better than1 � 10�5 Pa, D2 was introduced. The film was loadedfor 48 h at 294 K in a 0.2 Pa D2 atmosphere. The D-loaded film in the transfer rod was connected througha gate valve to the pre-evacuation chamber of theAPT system without breaking the D2 atmosphere.

The APT analysis was carried out with a tomo-graphic atom probe detector type [6] at 30 K, with2 kHz voltage pulse repetition rate and a pulse fractionof 20%. After the analysis, volume reconstruction wascarried out by using AVS software and algorithm mod-ules developed at the University of Rouen, France andthe University of Gottingen, Germany. The W (110)planar distance was used as a reference for fine scalingof the depth. Unlike in the case of 1 � D atom probe,a ladder diagram obtained from the whole volume inthe APT is erroneous unless a small volume of analysisis defined at the middle of tip. Hence, the ladder dia-grams used here were composed from concentrationprofiles in a cylinder volume and the number of atomscounted in the volume.

For APT analysis at higher temperatures above 20–30 K, D diffusion often interferes with the analysis be-cause of surface segregation and redistribution of D[8,9]. Below 30 K, suppression of D diffusion allows acorrect analysis of the local position of solute D in V[8,9,22]. Here, the D atoms can be regarded as frozenat their initial lattice positions during the time of mea-surement. Thus, the results shown here do not includeartifacts of D redistribution and surface segregation.

Figure 1a and b shows the reconstructed volume of aD-charged Fe/V ML reproduced from Ref. [9] and theisoconcentration map of D by APT analysis carriedout at 30 K, respectively. As expected, D atoms were ab-sorbed mainly in all three V layers. The clear cD maxi-mum in the middle of each V layer (marked in red inFig. 1b) verifies the absence of surface segregation ofD, which is confirmed by the detection of the expectedaverage concentration cD = 0.05 D/Me. The lateral dis-tribution of D in the V layers appears inhomogeneous.However, this is due to the small box size(2 nm � 2 nm � 0.3 nm) needed for the concentrationmapping. The distribution of all measured concentra-tions in the V layers clearly shows a Gaussian shape,and no deuteride phase was detected either in the vol-ume of in this specimen or in the mass spectrum (Fig. 2).

For bulk V–D, the D solubility limit of the a-phase iscD = 0.03 D/V. Further D uptake leads to the formationof the deuteride (b)-phase with high local concentrationof cD = 0.47 D/V [23,24]. A concentration histogram en-

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Figure 1. Reconstructed volume from the analysis of Fe/V ML at 30 K(16 nm � 16 nm � 50 nm), loaded with 0.2 Pa D2 at 294 K. The smallcube represents a 1 nm3 box. (a) The entire volume of reconstruction(gray, Pd; green, V; red, Fe; blue, W; light blue, D) reproduced fromdata in Ref. [9]. (b) Isoconcentration maps of D concentration(cD = 0.05 D/Me) from the same reconstruction as in (a). Almost all ofthe D atoms are found in the V layers. (For interpretation of thereferences to color in this figure legend, the reader is referred to theweb version of this article.)

Figure 2. APT mass spectra of pristine Fe/V and D-loaded Fe/V. Themass peak at m/e = 2 can clearly be ascribed to D.

Figure 3. Concentration histogram of D in the second V layerrevealing the average concentration cD = 0.05(2) D/Me. Slightly widerexperimental distribution than the binomial distribution suggests abroadening of site energy distribution.

Figure 4. Analysis volume and ladder diagrams. (a) Selected volumefrom Figure 1 for ladder diagrams. Four Fe/V interfaces in the volumeare numbered 1–4. Three cylinder volumes 5 nm in diameter are placedat each interface to construct ladder diagrams. Ladder diagrams areshown for the regions around (b) the first Fe/V interface, (c) the secondand the third Fe/V interface and (d) the fourth Fe/V interface. Slope ofeach curve indicates its chemical composition. In every case, D is notfound in Fe and FeV intermixing layers (defined as deviation from theaverage Fe content in the V layers) due to alloying effect. Nearby arethe dead layers DL (shaded region with gray), that are defined as cD

drop or D depletion. Fe atoms found in the V layers are of minorimportance here.

R. Gemma et al. / Scripta Materialia 67 (2012) 903–906 905

ables careful examination of cD more in detail. In thesecond V layer between two Fe layers, we placed foursampling cylinders to evaluate the concentration of cD

in the V layer, and the cD in each cylinder was summed.For statistical reasons, the size of each cylinder was ad-justed so as to include more than 100 atoms. The result-ing cD histogram in the second V layer with the averagecD was 0.05(2) D/Me, in good agreement with the ex-pected binomial distribution, which is a measure ofhomogeneity (Fig. 3). The D solubility here is largerthan that of bulk. However, experimental miscibilitygaps are narrowed for thin-film systems: for the a-phasethe hydrogen solubility is extended due to trapping atmicrostructural defects [15]. The measured extended Dsolubility can thus be explained by this microstructuralcontribution.

Locally, however, some of the datasets even reachcD = 10 at.% (0.11 D/Me), which clearly exceeds theaverage cD = 0.05(2) D/Me, as shown in Figure 3. Thishints at an additional broadening of the site energy dis-tribution. Such broadening can be induced by a varied

stress distribution in the V layers. As known from Pd–H thin films, mechanical stress gives rise to isothermsloping in the two-phase region corresponding to modi-fications in the thermodynamics of M–H nanosystems[25]. A sloped plateau was, in fact, also observed inthe pressure–composition isotherm measured for a sim-ilarly structured film [9].

The local D distribution at the Fe/V interfaces isshown in detail in Figure 4a–d. The number of D ionsand of Fe ions is plotted as a function of the numberof V ions detected simultaneously. Thus, the slope ofeach curve indicates the concentration with respect toV (Supplementary Figs. S2 and S3). For instance, themean slope of the number of D ions in the middle Vlayer gives 0.051 D/V. Furthermore, almost no D is de-tected in the FeV intermixing layers (denoted as FeVmix.) due to the alloying effect.

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In addition, D is also depleted in the pure V layer,close to the intermixed region (grayish regions denotedDL in Fig. 4). This region is, therefore, called the “deadlayer”. The chemically intermixed region is spatiallyclearly separated from this dead layer. This indicatesthat the presence of the dead layer cannot be attributedto any alloying effects. The intermixing layer thicknesswas found to be about 1.6 nm [9], which exceeds any me-tal/metal electronic exchange length. Thus, electrontransfer alone cannot explain the presence of a deadlayer. According to the depth scale implemented in thefigure (Fig. 4b–d), the thickness of the dead layers is0.4–0.5 nm, which corresponds to two monolayers(0.43 nm) of V(110).1 The previously reported DLthickness of (100) film was three monolayers(0.45 nm). This difference of one monolayer (0.21 nm)as a result of crystal orientation was found also in thecase of the Mo/V system at low hydrogen concentra-tions [26].

As discussed by Meded et al., the rigid layers, repre-sented here by the Fe layers, imply high energy costs forlattice expansion at the Fe/V interface [20]. This is truefor both (10 0) and (110) films given that the shear mod-ulus G of Fe or Mo surpasses that of V, taking elasticanisotropy into account (see Supplementary Figs. S4and S5). Since G of V1�xFex alloy (x = 0–0.17) doesnot differ greatly from that of the pure V [27], the�2 nm of intermixed FeV layers are considered to beas rigid as Fe layers. We assume that the elastic contri-bution by Fe layers to V layers effectively remains eventhough an intermixing layer is present. A similar argu-ment may be valid for the origin of the dead layer inthe systems of, for example, Nb/Fe [18] and Nb/Cu[19], assuming that an intermixing layer also exists.Our results therefore support the interpretation of elas-tic interactions between Fe and V causing the dead lay-ers in Fe/V. More importantly, the presence of deadlayer, in turn, hints at a possible utilization of hydrogenatoms as a probe to locally explore the materials’ inter-face properties by means of APT analysis.

To summarize, the dead layer effect in Fe/V ML wasdemonstrated via careful examination of APT analysisresults. Regardless of the chemical interface mixing ef-fect, this dead layer exists and is considered to originatefrom modulated rigidity rather than the charge-transfereffect in the Fe/V ML system. The thickness of the deadlayer was 0.4–0.5 nm near every Fe/V interface, whichcorresponds to two lattice planes of V (110). This is inan excellent agreement with the suggested hydrogendead layer thickness of the Fe/V ML system.

Financial support for this work is gratefullyacknowledged from the Deutsche Forschungsgemeins-chaft via SFB 602 and PU131-9/1, and the DeutscherAkademischer Austauschdienst (DAAD).

1 It should be considered that the depth scale shown at the upperabscissa of Figure 4b–d relates to the V layers, but not to the Felayers.

Supplementary data associated with this article canbe found, in the online version, at http://dx.doi.org/10.1016/j.scriptamat.2012.08.025.

[1] F. Leonard, A. Alec Talin, Nat. Nanotechnol. 6 (2011)773–783.

[2] B. Hjorvarsson, J. Ryden, E. Karlsson, J. Birch, J.-E.Sundgren, Phys. Rev. B 43 (1991) 6440.

[3] G. Andersson, B. Hjorvarsson, P. Isberg, Phys. Rev. B 55(1997) 1774.

[4] A. Cerezo, T.J. Godfrey, G.D.W. Smith, Rev. Sci.Instrum. 59 (1988) 862–866.

[5] D. Blavette, E. Cadel, A. Fraczkiewicz, A. Menand,Science 287 (1999) 2317–2319.

[6] T. Al-Kassab, H. Wollenberger, G. Schmitz, R. Kirch-heim, Tomography by atom probe, in: M. Ruhle, F. Ernst(Eds.), High Resolution Imaging and Spectroscopy ofMaterials, Springer Series in Materials Science, vol. 50,Springer-Verlag, Berlin, 2003, pp. 271–320.

[7] T.F. Kelly, M.K. Miller, Rev. Sci. Instrum. 78 (2007)031101.

[8] P. Kesten, A. Pundt, G. Schmitz, M. Weisheit, H.U.Krebs, R. Kirchheim, J. Alloys Compd. 330–332 (2002)225–228.

[9] R. Gemma, T. Al-Kassab, R. Kirchheim, A. Pundt,Ultramicroscopy 109 (2009) 631–636.

[10] D. Hudson, A. Cerezo, G.D.W. Smith, Ultramicroscopy109 (2009) 667–671.

[11] J. Takahashi, K. Kawakami, Y. Kobayashi, T. Tarui,Scripta Mater. 63 (2010) 261–264.

[12] H. Sepehri-Amin, T. Ohkubo, T. Nishiuchi, S. Hirosawa,K. Hono, Ultramicroscopy 111 (2011) 615–618.

[13] H. Iba, E. Akiba, J. Alloys Compd. 253–254 (1997) 21–24.[14] K. Higuchi, H. Kajioka, K. Toiyama, H. Fujii, S. Orimo,

Y. Kikuchi, J. Alloys Compd. 293–295 (1999) 484–489.[15] A. Pundt, Adv. Eng. Mater. 6 (2004) 11–21.[16] B. Sakintuna, F. Lamari-Darkrim, M. Hirscher, Int. J.

Hydrogen Energy 32 (2007) 1121–1140.[17] Y. Fukai, The Metal–Hydrogen System, 2nd ed.,

Springer-Verlag, Berlin, 2005, pp. 16.[18] D. Nagengast, J. Erxmeyer, F. Klose, Ch. Rehm, P.

Kuschnerus, G. Dortmann, A. Weidinger, J. AlloysCompd. 231 (1995) 307–309.

[19] S. Yamamoto, S.P. Goppelt-Langer, H. Naramoto, Y.Aoki, H. Takeshita, J. Alloys Compd. 231 (1995) 310–314.

[20] V. Meded, S. Mirbt, Phys. Rev. B 71 (2005) 024207.[21] T. Eguchi, S. Morozumi, J. Jpn. Inst. Metals 38 (1974)

1025–1030.[22] R. Gemma, T. Al-Kassab, R. Kirchheim, A. Pundt, J.

Alloys Compd. 509 (2011) S872–S876.[23] W. Pesch, T. Schober, H. Wenzl, Scripta Metall. 16 (1982)

307–312.[24] K. Papathanassopoulos, H. Wenzl, J. Phys. F 12 (1982)

1369–1381.[25] S. Wagner, A. Pundt, Appl. Phys. Lett. 92 (2008) 051914.[26] B. Hjorvarsson, J. Birch, F. Stillesjo, S. Olafsson, J.-E.

Sundgren, E.B. Karlsson, J. Phys.: Condens. Matter 9(1997) 73–85.

[27] J.J. Donegan Jr., J.R. Neighbours, Acta Metall. 21 (1974)821–828.


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