Clustered field evaporation of metallic glasses in atom probe tomography

Ultramicroscopy 162 (2016) 35–41

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Clustered field evaporation of metallic glasses in atom probe tomography J. Zemp a, S.S.A. Gerstl b, J.F. Löffler a, B. Schönfeld a,n a b

Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland Scientific Center for Optical and Electron Microscopy, ETH Zurich, 8093 Zurich, Switzerland

art ic l e i nf o

a b s t r a c t

Article history: Received 23 July 2015 Received in revised form 23 November 2015 Accepted 28 November 2015 Available online 1 December 2015

Field evaporation of metallic glasses is a stochastic process combined with spatially and temporally correlated events, which are referred to as clustered evaporation (CE). This phenomenon is investigated by studying the distance between consecutive detector hits. CE is found to be a strongly localized phenomenon (up to 3 nm in range) which also depends on the type of evaporating ions. While a similar effect in crystals is attributed to the evaporation of crystalline layers, CE of metallic glasses presumably has a different – as yet unknown – physical origin. The present work provides new perspectives on quantification methods for atom probe tomography of metallic glasses. & 2015 Elsevier B.V. All rights reserved.

Keywords: Atom probe tomography Metallic glasses Clustered evaporation Correlated evaporation

1. Introduction Atom probe tomography (APT) is a powerful tool for the characterization of nanometer-sized features such as grain boundaries [1–3], precipitates [4,5], thin films [6,7], or solute distributions [8]. In metallic glasses (MGs), APT can provide information on structural features in the range of a few nanometers, e.g., in phaseseparated MGs [9–12] or MG composites [13,14]. Oh et al. [10] studied phase separation of Cu43Zr43Al7Ag7 MGs and were able to observe the separation into Ag-rich and Ag-depleted phases on a length scale of 10 nm. For crystalline materials, APT offers a depth resolution well below 1 nm [15], capable of imaging single atomic layers, with a slightly lower lateral resolution. The good depth resolution is a direct consequence of the layer-by-layer field evaporation which is observed around crystallographic poles. In regions between crystallographic poles the depth resolution is less accurately defined as the atomic layers are indistinct. In MGs the radial distribution function (RDF) calculated from APT data does not show features due to short-range or mediumrange order, in contrast to the RDF determined from x-ray or neutron data [16]. Shariq et al. [17] correlated the separation distances in nearest-neighbor histograms of amorphous Pd55Cu23P22 to the atomic distances in the RDFs of Pd52Ni32P16 MG [18] determined via neutron diffraction. However, this approach does not take into account the fact that Cu and Ni can behave differently in n

Corresponding author. E-mail address: [email protected] (B. Schönfeld).

http://dx.doi.org/10.1016/j.ultramic.2015.11.014 0304-3991/& 2015 Elsevier B.V. All rights reserved.

MGs [19,20] and that the compositions of the glasses differ. Of course, the results also depend on the reconstruction parameters applied, which – for MGs in particular – are difficult to be determined precisely. In a random solid solution the average nearestneighbor distance of solute atoms is only a function of detection efficiency and concentration [21]. The nearest-neighbor distance of the solute species (e.g. P in Pd55Cu23P22) is thus expected to be shifted to somewhat larger values than might be expected from scattering experiments. In current reconstruction algorithms [22–24] the atomic positions are reconstructed using a back-projection onto a hemisphere, the location of which is lowered by a depth increment for each detector hit. The hemisphere assumption might appear to be more realistic for MGs than for crystals, for which the surface is nonhemispherical due to crystallographic faceting. Thus, the depth resolution in MGs might be similar or even better than the one for crystals away from crystallographic poles. In crystalline materials, a strong dependence of the spatial resolution on the field evaporation sequence is observed. In MGs, field evaporation is expected to be close to random due to the absence of crystallographic layers. However, an effect referred to as clustered evaporation (CE) was described by Haley et al. [16], which manifested itself in a heterogeneous distribution of a few hundred consecutive detector events. Possible reasons for CE are manifold: pores, local density variations, and surface roughness are just some candidates which might either change the local electric field or the susceptibility to field-evaporate atoms. A similar phenomenon, the correlated evaporation, is known from

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crystalline materials: because of the non-uniform distribution of the electric field due to crystallographic faceting, atoms are evaporated spatially and temporally correlated [25]. Correlations in crystalline material were previously investigated by considering simultaneously detected ions (multiple hits) [25–27]. De Geuser et al. [25] employed Al and constructed a histogram of their separation distance that shows a strong deviation from a random evaporation sequence. Yao et al. [26] employed microalloyed steel and introduced a visual approach to the spatial correlations, which showed a non-random behavior and also different correlations among the various atomic species. In this work, CE of MGs is addressed by analyzing the raw detector data of amorphous Cu45Zr45Ag10 and comparing it to a random evaporation sequence; additionally, field evaporation of crystalline Al is measured. It is highly advantageous to apply the analysis to the raw data rather than to the reconstructed data since reconstruction artefacts and uncertainties due to unknown reconstruction parameters can be excluded. The key element is the analysis of spatial and temporal correlations in the evaporation sequence by a technique called consecutive hit analysis (CHA), which is an extension to previous work on crystalline material [25–28]: instead of looking at multiple hits, the CHA focuses on consecutive hits separated by n detector hits, to follow the spatial and chemical correlations as function of time. The CHA is a technique that can be quantitatively compared to a random evaporation sequence, a property that allows the fraction of non-random detector hits to be calculated directly. An understanding of the field evaporation of MGs is crucial for the future development of advanced reconstruction protocols and for a better understanding of the capabilities and limitations of APT with respect to spatial resolution in amorphous materials.

2. Consecutive hit analysis For crystalline materials the evaporation sequence is a fairly ordered process: atoms at kink and ledge sites usually experience the highest local electric field and are thus most prone to field evaporation. In MGs no kink or ledge sites exist and the evaporation sequence consists of two contributions, stochastic and clustered evaporation. The CHA is a simple algorithm, which analyzes the detection sequence during an APT experiment. Fig. 1 shows a schematic illustration of the CHA: the i-th ion of type A is detected at position r iA = (XD , YD ), referred to as initial hit, where XD and YD are the coordinates on the detector. The separation distance riA, n− B between the initial and a consecutive hit of ion type

Fig. 1. Schematic drawing for the CHA. The consecutive hit histogram represents the abundance of the distance between an initial hit (turquois circle) of ion type A at position r iA and a consecutive hit (red circle) of ion type B at position r iB+ n , which occurred n hits after the primary hit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

p (r ) =

2π Δr r, AD

(2)

where AD is the total area of the detector (ignoring boundary effects due to the finite detector size) [25]. In the case of MGs, where the consecutive hit histogram is a combination of stochastic and clustered evaporation, the slope of p(r) is marginally reduced based on the fraction of CE, which is considered in peff(r). The consecutive hit histogram can be corrected for the stochastic contribution by subtracting peff(r) using a linear fit. Under the assumption that the contribution to hnA − B (rm ) due to CE vanishes at r 4 rmax (otherwise the detector size must be taken into account), the fraction of CE is given by M

fc =

∑

⎡ h A − B (r ) − p (r ) ⎤, m ⎣ n eff m ⎦

m=1

(3)

where M is the total number of bins.

B at position r iB+ n is defined as

riA, n− B = r iB+ n − r iA ,

(1)

where n ¼1, 2, and 3, etc. is the separation of the two detector hits. The nth-consecutive hit histogram hnA − B (rm ) for bin m of width Δr is given by the number of riA, n− B between rm − Δr/2 and rm + Δr/2 and is normalized by the total number of initial hits N of type A. To reduce the influence of the finite detector size, only initial hits within the distance rs from the detector center are used in the calculation (all detector events are, however, considered as consecutive hits). The histogram is then unaffected by the detector size up to rmax ¼ rD − rs. For example, h1Cu-Zr(r) is the 1st-consecutive hit histogram with Cu as initial and Zr as consecutive hits. The ion species do not necessarily need to be differentiated; in this case A and B are just labeled as “X”. If initial and consecutive hits are fully uncorrelated, i.e. the field evaporation is stochastic, then the consecutive hit histogram is given by

3. Experimental High-purity Cu45Zr45Ag10 (Cu: 99.995%, PRAXAIR Electronics, USA; Zr: 99.9% Alfa Aesar GmbH & KG, Germany; Ag: 99.9%, UBS, Switzerland) pre-alloys were prepared by arc melting under Ar (99.9999%) atmosphere. The pre-alloy was re-melted and overturned several times to ensure a homogeneous mixture. Amorphous plates (0.5 mm in thickness) were produced by suction casting and the amorphous character was checked using x-ray diffraction. The plates were then ground and polished to a thickness of 250 μm and cut into bars of the size 0.25  0.25  15 mm3 using a wire-saw. Next, the samples were electropolished with an ElectroPointer (Simplex Scientific, USA) using a 9 wt% nitric acid in 2:1 methanol:2-butoxyethanol electrolyte and a DC voltage of 8 V at room temperature. Finally, a FIB-milling step using a Helios 600i (FEI, USA) instrument with a Ga-ion beam at 30 kV acceleration voltage in the beginning and 5 kV in the end was applied to ensure

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Fig. 2. Mass spectra of Cu45Zr45Ag10 at 20 K, 80 K, and 140 K. The number of counts is normalized by the height of the background increases drastically, which reduces the signal-to-noise ratio. Table 1 Composition normalized to cCu þ cZr þ cAg ¼1 for the three measurements. T (K)

20 80 140

Composition(%) Cu

Zr

Ag

45.8 44.0 45.4

44.4 46.0 44.9

9.8 10.0 9.7

37

Cu þ peak. With increasing temperature the

63

a circular cross-section of the tip. The FIB-milling resulted in a final tip radius of about 50 nm. The APT experiments on Cu45Zr45Ag10 were carried out on a LEAP™ 4000X HR (Cameca, USA) instrument in laser pulsing mode (wavelength 355 nm; pulse frequency 250 kHz; specimen temperature 20, 80, and 140 K; laser energy 75 pJ; detection rate 1.2%). These parameters resulted in charge-state ratios of Zr3 þ /2 þ ¼0.03–0.05 and Cu2 þ / þ ¼0.009–0.015. For comparison, voltage pulsing mode was also employed using a pulse fraction of 10–20%,

Fig. 3. Two-dimensional detector event histogram (bin size of 0.5  0.5 mm2) for a total number of 5000 consecutive ion detections for (a) Cu45Zr45Ag10 at 20 K, (b) Cu45Zr45Ag10 at 140 K, (c) pure Al, and (d) a modeled random detection sequence for comparison. (a)–(c) show heterogeneous evaporation, which changes dynamically in location during the measurement for Cu45Zr45Ag10, but is fixed to the crystallographic poles (indicated by white arrows) for Al.

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Table 2 Fraction of 1st-consecutive hits, fc, due to CE as function of specimen temperature. T (K)

20 80 140

fc Cu–X

Zr–X

Ag–X

0.043 0.039 0.029

0.088 0.080 0.031

0.034 0.031 0.022

Data analysis was performed on data away from Ga implantation regions generated by FIB processing. Epos-files were created from the raw hit files using IVAS software (Cameca, USA) and then processed using custom-made MATLAB routines. For the calculation of the consecutive hit histogram a bin size of Δr ¼0.025 mm and rs ¼12 mm were used. To study spatial and temporal correlations the discussion is based on single-hit events (i.e. events where only one ion is detected per pulse), which present  93% of all ions detected.

4. Results 4.1. Mass spectra and composition A single Cu45Zr45Ag10 sample was measured at 20, 80, and 140 K. The corresponding mass spectra as normalized to the counts of the 63Cu þ peak are shown in Fig. 2. When increasing the temperature from 20 to 140 K, the background increases by roughly an order of magnitude. Consequently, the signal-to-noise ratio is strongly reduced when the measurement temperature is increased, in agreement with the literature [30]. Nevertheless, the nominal composition of Cu45Zr45Ag10 is reproduced well by the APT measurements for all temperatures, although Zr frequently forms hydrides and oxides. Table 1 lists the compositions measured at the three temperatures and normalized to cCu þcZr þcAg ¼1. In Ref. [31] the present alloy system was reported to show atomic-scale heterogeneity, but none of the reconstructed atom maps showed indications of such and neither did a comparison of the frequency distribution with the corresponding binomial distribution (data not shown). 4.2. Detector hitmaps

Fig. 4. (a) 1st-consecutive hit histograms h1A − X (r ) for A ¼ Zr, Cu, and Ag at 20 K. X−X (r ) at (b) 1st-consecutive hit histogram h1X − X (r ) and multiple-hit diagram hmulti 20 K. (c) nth-consecutive hit histograms hnZr-X(r) for n¼1, 10, 100, and 1000. The linear behavior of stochastic field evaporation (solid line) is obtained for nE1000. The random contribution is calculated using Eq. (2), with Δr ¼0.025 mm and AD ¼ 943 mm2.

a detection rate of 1.0%, and specimen temperatures 4 80 K. In laser pulsing mode the samples were less prone to fracture and yielded up to 50 million atoms, while in voltage mode specimen fracture [29] typically occurred before 1 million ions were registered, especially if temperatures were below 100 K. Parameter space investigations [30] were completed to ensure that laser pulsing would not introduce thermally induced artifacts.

Fig. 3 shows the two-dimensional histograms of detector events (detector hitmap) using a bin size of 0.5  0.5 mm2 for Cu45Zr45Ag10 at 20 K, Cu45Zr45Ag10 at 140 K, pure Al, and a modeled random hitmap over a total of 5000 consecutive hits. The hitmaps of Cu45Zr45Ag10 [Fig. 3(a) and (b)] are heterogeneous, which is characteristic of the field evaporation of MGs and known as CE. Al, too, evaporates non-uniformly [Fig. 3(c)], but this detection pattern is linked to the crystallographic poles. For comparison a modeled random detection sequence is shown in Fig. 3 (d), which is clearly distinguishable from the experimental data and much more homogeneous. By eye no significant differences are observable among the hitmaps of Cu45Zr45Ag10 at 20 K and 140 K [Fig. 3(a) and (b)]. Measurements of Cu45Zr45Ag10 were performed in both laser and voltage pulsing modes, and CE was observed in both modes, thereby excluding the laser beam as primary source of CE. Due to low specimen yield and the lower signal-to-noise ratio in voltage pulsing mode, only data using laser pulsing mode are presented here.

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Fig. 5. 1st-consecutive hit histograms for Zr–B (top row), Cu–B (middle row), and Ag–B (bottom row) with B¼Zr, Cu, or Ag for T ¼20 K (left column), 80 K (middle column), and 140 K (right column).

4.3. Consecutive hit histograms

Fig. 6. 1st-consecutive hit histograms for amorphous Cu45Zr45Ag10 [ h1Zr − X (r ) ] and crystalline Al.

The 1st-consecutive hit histograms h1A − X (rm ) with A ¼Zr, Cu, or Ag are shown in Fig. 4(a). A well-resolved peak ranging up to a detector hit distance of  2 mm is observed, which is attributed to CE. At larger separation distances evaporation continues linearly, in good agreement with Eq. (2). Table 2 lists the degree of CE as calculated with Eq. (3): it is highest for Zr, followed by Cu, and is lowest for Ag. These variations among the different species follow the same tendency as the fraction of multiple hits (data not shown). The separation-distance histogram of multiple hits, X−X hmulti (rm ), is very similar to the one of consecutive hits, h1X − X (rm ) [Fig. 4(b)]. As expected, the peak in the histogram is higher with multiple hits and located at similar separation distance rm [cf. Fig. 4(c)]. Thus, it is reasonable to assume that spatial correlations of multiple and consecutive hits are closely related. Fig. 4(c) shows the nth-consecutive hit histograms hnZr − X (rm ) for n ¼1, 10, 100, and 1000. Up to a few hundred consecutive hits the CE peak remains visible until it disappears and only the stochastic contribution

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Fig. 7. Two-dimensional histograms of initial hits (bin size 0.25  0.25 mm2) which have a 1st-consecutive hit with a separation distance o2 mm for (a) amorphous Cu45Zr45Ag10 over a total number of 9.2  106 hits and (b) crystalline Al over a total number of 7.7  106 hits. A slight gradient is seen for Cu45Zr45Ag10, possibly due to the reflectron ion optics or the laser beam.

[25], there is no straightforward explanation for the differences in the amount of CE among the various species in MGs: it is neither correlated with the evaporation fields of the pure elements (Fe,Cu 4 Fe,Zr 4 Fe,Ag) nor with their radii (rZr 4rAg 4 rCu). Topological variations such as those known for binary Cu–Zr [32,33] may explain the appearance of local radius variations (see also Gerstl et al. [34]), which in turn lead to a change in the electric field. 4.4. Comparison to crystalline Al

Fig. 8. 1st-consecutive hit histograms calculated using the reconstructed coordinates x and y of Zr–X (red circles; kf ¼ 3.3, ξ¼ 1.65, and Fe ¼ 28 V/nm) and Al (green triangles; kf ¼ 3.3, ξ ¼1.15, and Fe ¼ 19 V/nm). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

remains at n ¼1000. Thus, the study of consecutive hits in addition to multiple hits provides further information on temporal correlations during field evaporation. In Figs. 5 and 6, the histograms are always plotted after subtraction of the stochastic contribution peff(r), which was obtained by fitting the data in the linear regime, i.e. between r ¼2 and 5 mm. Note that the histograms are normalized before subtracting peff(r) which is why the sums of the data points in Figs. 5 and 6 are o1. Fig. 5 shows the 1st-consecutive hit histograms h1A − B (r ) for 20, 80, and 140 K and A, B ¼Cu, Zr, and Ag. CE is observed for all combinations of initial and consecutive hits. One notes that the degree of CE depends on the ion type of the initial and consecutive hit. In general, CE is strongest if A ¼B and slightly decreases with increasing temperature (see also Table 2). Consequently, CE is not thermally activated and the decrease might simply be the result of the smaller signal-to-noise ratio, which is present at higher temperature. Although the crystalline counterpart to CE, the correlative evaporation, was attributed to changes in the local electric field

Fig. 6 shows the consecutive hit histograms for Zr–X in Cu45Zr45Ag10 and Al–Al in crystalline Al, which both show a peak at low separation distances. The reason for these peaks differs, however, as seen in Fig. 7. There, all initial hits during the entire APT experiment are summed up that have a consecutive hit separated by less than 2 mm. For the MG sample [Fig. 7(a)] these hits are homogenously distributed all across the detector (a slight gradient is observed, though, possibly due to the reflectron geometry [35]). CE thus occurs on the entire sample surface. For the crystalline Al sample [Fig. 7(b)], however, CE is restricted to major crystallographic poles and zone lines, which also agrees with simulations by De Geuser et al. [25]. In the detector regions between crystallographic poles CE is not observed. From Fig. 6 one might conclude that, due to the location of the histogram maximum, correlated evaporation from Al takes place on a shorter length scale than for Cu45Zr45Ag10. However, a comparison of length scales in the detector space of two samples is meaningless because the magnification that is experienced by the evaporating ions depends on the sample geometry and the reconstruction parameters, which are not being considered at this stage. 4.5. Comparison to reconstruction A major and ongoing question in APT is the reliability of reconstructing raw data into three-dimensional atom maps. Today's reconstruction protocols require the knowledge of sample- and device-specific input parameters, namely the image compression factor ξ, the field factor kf, and the evaporation field Fe. In crystalline material, ξ, kf, and Fe can be determined from crystallographic features, such as pole structure, crystallographic

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terraces, and interplanar spacings [15]. For the present Al data the interplanar spacing of the (0 0 2) layers (¼2.02 Å) is reproduced using ξ ¼1.15, kf ¼3.3, and Fe ¼19 V/nm. Fig. 8 shows the consecutive hit histogram of Al using the reconstructed coordinates x and y, which has a maximum at rrecon E1 nm. This value is well beyond the nearest-neighbor distance value. Because the reconstruction parameters define the magnification in an APT experiment, the peak position of the reconstructed consecutive hit histogram is inversely proportional to the factor kfFe/ξ. To force the maximum of the consecutive hit histogram into the range of the nearest-neighbor distances, unrealistic reconstruction parameters must be employed that would lead to incorrect interplanar spacings. Thus, the characteristic length scale of correlated evaporation in Al is in the range of a few nanometers, which agrees with the results from simulated field evaporation [25], where atoms evaporate as groups of tens of atoms. Under the assumption that correlative evaporation in crystals and CE in MGs take place on a comparable length scale, the Cu45Zr45Ag10 data were reconstructed to have the maximum of the consecutive hit histogram for the reconstructed coordinates at rrecon E1 nm as shown in Fig. 8 for Zr–X. The histogram is obtained for kf ¼3.3, ξ ¼1.65 (note that these values happen to coincide with the IVAS default values [36]), and Fe ¼ 28 V/nm. The values of the reconstruction parameters are plausible as the field factor kf corresponds to an applied voltage of 5 kV and a tip radius of 50 nm as present in the investigation. The value of the image compression factor ξ – its value has to be between 1 and 2 – may also vary between 1.5 and 1.8 without shifting the location at the maximum in Fig. 8 by more than 10%. Thus, the finding that consecutive hits originate from a range up to about 3 nm off the initial hit in CE is reasonable.

5. Conclusions Field evaporation of metallic glasses such as Cu45Zr45Ag10 is characterized by an effect referred to as clustered evaporation. The evaporation of a surface atom leads to a cascade of spatially and temporally correlated field evaporation events on top of a stochastic contribution, which can be calculated analytically. Using the consecutive hit analysis clustered evaporation can be studied and the spatial correlation is observed up to roughly 1000 consecutively detected ions. The amount of CE depends on the type of the evaporating ions and is highest for Zr and lowest for Ag. For a fixed initial hit the self-correlation, i.e. Zr–Zr, Cu–Cu, and Ag–Ag, is strongest. With increasing temperature CE decreases, probably due to the lower signal-to-noise ratio at higher temperatures. Whether the varying extent of CE is solely due to the different field evaporation behavior of the different elements or whether information on chemical and topological short-range order is hidden in the CE data remains an open question. Consecutive hit analysis is limited neither to MGs nor to raw detector data, but can also be used for crystalline materials and to optimize reconstructed coordinates. If CE in MGs occurs on a length scale comparable to that of crystalline metals, the information can be employed to calibrate and improve the reconstruction of MGs.

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Acknowledgments Support by the Swiss National Science Foundation (SNF Grant No. 200020-153103) is gratefully acknowledged.

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