We report the experimental observation of an increase in the elastic anisotropy of tungsten upon He-ion implantation, probed optically using transient grating spectroscopy. Surface acoustic wave (SAW) velocity measurements were performed on a (110) oriented tungsten single crystal as a function of in-plane propagation direction for unimplanted and implanted samples. Our measurements allow us to finely resolve the remarkably small elastic anisotropy of the samples investigated. SAW velocity calculations are used to interpret the experimental data and to extract the Zener anisotropy parameter η and the elastic constant C44. Upon ion implantation, we observe an increase in the quantity (η1) by a factor of 2.6. The surprising increase in elastic anisotropy agrees with previous theoretical predictions based on ab initio calculations of the effect of self-interstitial atoms and He-filled vacancy defects on the elastic properties of tungsten.

Single crystal materials, even high symmetry ones such as cubic crystals, generally exhibit a finite degree of elastic anisotropy.1–3 When damage is introduced into a perfect crystal lattice, most material systems show a corresponding decrease in anisotropy due to amorphization and other damage pathways.4,5 Tungsten is unique in that it is almost perfectly isotropic, with a Zener anisotropy factor η2C44/(C11C12) very close to unity; it is often cited as the least anisotropic crystal.6 In fact, from various sets of elastic constants found in the literature,7 the magnitude of the elastic anisotropy for single crystal tungsten at room temperature can hardly be established, with discrepancies in the value of (η1) on the order of 100%. However, as we will see below, the small elastic anisotropy of tungsten can be assessed with high accuracy.

The prospect of using tungsten and tungsten alloys for plasma-facing components in nuclear fusion energy applications has motivated much recent investigation of their mechanical properties under extreme conditions.8 A recent study9 predicted, based on ab initio calculations, that He-ion implantation (a technique frequently used to emulate particle bombardment in a fusion reactor environment) could have the surprising effect of increasing the elastic anisotropy (η1) due to the introduction of relatively anisotropic atomistic defects.

Since ion implantation only affects a thin sub-surface layer of material, the effect of ion implantation on the elastic anisotropy cannot be assessed using traditional ultrasonic methods based on bulk acoustic waves.10,11 A number of techniques based on surface acoustic waves (SAWs) have been developed for measuring near-surface elastic properties.12 Among them, a non-contact optical technique referred to as laser-induced transient grating (TG) spectroscopy has demonstrated excellent capabilities in measuring elastic properties of thin films.13 In addition to a high precision in the SAW velocity measurement (104) and a small measurement spot, this technique has the ability to control the depth of the measurement by tuning the SAW wavelength. Due to these advantages, TG has recently begun to see use in studies of ion-implanted materials systems.14,15

In this paper, we show that TG spectroscopy on tungsten is able to resolve remarkably small elastic anisotropy variations with high precision. We measure the angular dependence of surface acoustic wave (SAW) velocity in the (110) plane of single-crystal implanted and unimplanted tungsten samples, and from these data quantify the change in the elastic anisotropy due to He-ion implantation. Ion implantation is found to increase the elastic anisotropy relative to the perfect tungsten lattice more than twofold, in agreement with the aforementioned ab initio prediction.

The tungsten single crystal sample (99.99%) was aligned using electron backscatter diffraction (EBSD) and sectioned with a diamond saw to extract a {110} oriented 1 mm thick slice. The {110} surface was polished mechanically, finishing with a colloidal silica polishing step, to give a flat, defect-free finish with good optical quality. Misorientation of the surface normal with respect to the 110 direction was found to be less than 3° using synchrotron x-ray micro-beam Laue diffraction performed at beamline 34-ID-E, Advanced Photon Source, USA. Helium ion implantation was carried out at 298 K at the National Ion Beam Facility, UK. 13 ion energies from 0.05 to 2.0 MeV were used to achieve a near uniform calculated helium concentration of 3180 ± 220 appm within a 2.7 μm thick surface layer.16 The implantation profile, predicted using the Stopping Range of Ions in Matter (SRIM) code17 (68 eV displacement threshold18), is shown in Fig. 1. The calculated displacement damage at depths <2.7 μm is 0.21 ± 0.03 displacements per atom (dpa). Also shown in Fig. 1 are the relative displacement profiles of a SAW with a wavelength of 2.746 μm (used in this study), normalized to their respective maxima and scaled for comparison to the spatial extent of the implanted region. SAW propagation will be mostly sensitive to the mechanical properties of the He-ion damaged layer given that the displacement amplitudes are largely confined within it. Below we will show that the effect of the unimplanted “substrate” is small and can be accounted for.

FIG. 1.

Injected helium concentration and cascade damage, predicted using the SRIM software package, plotted as a function of depth in the sample. Relative horizontal (H) and vertical (V) SAW displacement amplitudes at a SAW wavelength of 2.746 μm are also shown (scaled for comparison to implantation and damage profiles), illustrating how the SAW is largely confined to the damaged region.

FIG. 1.

Injected helium concentration and cascade damage, predicted using the SRIM software package, plotted as a function of depth in the sample. Relative horizontal (H) and vertical (V) SAW displacement amplitudes at a SAW wavelength of 2.746 μm are also shown (scaled for comparison to implantation and damage profiles), illustrating how the SAW is largely confined to the damaged region.

Close modal

In TG spectroscopy,13 two short laser pump beams are crossed at the surface of the sample, where optical interference and subsequent absorption lead to the generation of a sinusoidal temperature profile. Counterpropagating SAWs with the same wavelength as the thermal grating period are generated due to rapid thermal expansion, and the time evolution of the resultant displacement profile is measured via diffraction of a probe laser beam.19 Using a pulsed pump laser beam (515 nm, 200 ps pulse duration, 1.75 μJ pulse energy, and 500 μm spot radius), the ±1 diffraction orders of a binary transmission diffraction grating (i.e., “phase mask”) were imaged onto the surface of the sample, generating the transient grating. The SAWs were detected with a quasi-continuous wave probe laser beam (532 nm, 10 mW power, and 80 μm spot radius). The diffraction signal was superposed with a reference beam generated from the same probe laser source, to allow heterodyned detection of the TG signal. TG measurements of SAW frequency were performed on implanted and unimplanted tungsten samples as a function of angle in the (110) plane. A transient grating period of 2.746 μm was used to ensure that the SAW amplitude was mostly confined to the implanted surface layer, as explained above. The transient grating period was calibrated by measuring the SAW frequency of (001) silicon along 100 and dividing by the SAW velocity in this direction. The SAW velocity was calculated from the reported values of the elastic constants Cij of silicon; a survey of the literature determined that these constants are known to within an accuracy on the order of 0.1%,20,21 and therefore the transient grating period is also known to within an error on the same order.

Time-domain TG data on unimplanted tungsten are shown in Fig. 2(a), where the thermal decay and oscillatory SAW signal are clearly visible. The inset in Fig. 2(a) illustrates the θ-dependence of the SAW frequency. SAW velocity V as a function of θ for the unimplanted sample is plotted in Fig. 2(b). The elastic anisotropy of tungsten, albeit very small, is directly visible in the angular dependence of the SAW velocity. As will be explained below, all three independent elastic constants, C11, C12, and C44, cannot be accurately determined from the SAW velocity data. However, a comparison between the TG data and calculated SAW velocities allows us to assess the accuracy of reported sets of tungsten elastic constants. θ-dependent SAW velocities have been calculated using a well-known method outlined, for example, in Ref. 12 using four sets of (unimplanted) tungsten elastic constants reported in the literature.10,11,22,23 The results of these calculations are plotted alongside the unimplanted TG data in Fig. 2(b). It is evident that the sets reported in Refs. 10 and 11 yield SAW velocity values relatively close to those obtained from the measurement, although Ref. 10 yields a significantly smaller SAW velocity anisotropy compared to the measured data. Reference 22 yields an angular dependence generally consistent with the measurements, but with a large velocity offset, whereas the values reported in Ref. 23 exhibit an inverted θ-dependence with respect to the TG data. For small values of (η1) subject to C11 and C44 remaining constant, the range of the angular variation of the SAW velocity V90°V0°(η1). Therefore, an inverted SAW velocity behavior between two sets of elastic constants is indicative of η values on opposite sides of unity. Indeed, the anisotropy parameter for Ref. 23 is 0.9974, whereas the anisotropy parameters for Refs. 10, 11, and 22 are 1.0085, 1.0038, and 1.0083, respectively. Since the SAW velocity maxima of the TG data correspond to θ values that also yield SAW velocity maxima for the Cij from Refs. 10, 11, and 22, we can say prior to any further analysis that the TG data from both samples correspond to η>1.

FIG. 2.

(a) Representative time-domain TG signal for unimplanted (110) tungsten. Inset: Frequency domain data for θ=0°,40°, and 90°. (b) V(θ) obtained from TG measurements on unimplanted tungsten, plotted alongside V(θ) curves calculated from four sets of literature elastic constants Cij. (c) Unimplanted and implanted TG data, and best fits obtained from V(θ) calculations and least squares regression of C44 and η.

FIG. 2.

(a) Representative time-domain TG signal for unimplanted (110) tungsten. Inset: Frequency domain data for θ=0°,40°, and 90°. (b) V(θ) obtained from TG measurements on unimplanted tungsten, plotted alongside V(θ) curves calculated from four sets of literature elastic constants Cij. (c) Unimplanted and implanted TG data, and best fits obtained from V(θ) calculations and least squares regression of C44 and η.

Close modal

The observed reduction in the SAW velocity in the implanted sample relative to the unimplanted sample is expected and consistent with previous measurements on polycrystalline samples.9 What is remarkable, however, is a large increase in the SAW velocity anisotropy (i.e., the quantity V90°V0°) in the implanted sample. Thus, prior to any quantitative analysis, we can conclude that He-ion implantation has resulted in an increase of the elastic anisotropy (i.e., the quantity |η1|) of tungsten. Given that the SAW velocity maxima for both unimplanted and implanted samples correspond to the same θ values, we can also conclude that implantation leads to an increase in η.

Let us now turn to the quantitative determination of η from the measured data. Ideally, one would prefer to fit the data to determine all three independent elastic constants of a cubic crystal material such as tungsten. However, the angular dependence of the SAW velocity in the (110) plane does not suffice to reliably determine all three constants. Indeed, the dependence is close to sinusoidal and can therefore be well characterized by two parameters—i.e., the average velocity and the magnitude of the velocity variation vs. angle. Consequently, the structure of the data does not allow us to determine three independent quantities. However, it is possible to determine two elastic constants if the value of the third constant is known. We choose to assume the value of C11 and fit the data to determine C44 and the Zener anisotropy parameter η. We found that an error in the assumed value of C11 leads to a very small error in η. For example, changing C11 by as much as 10% in the case of the unimplanted tungsten data changes the best fit value of C44 by 1%, while the best fit value of η only changes by 0.03%. We will see that the error in the determination of η due to uncertainty in C11 is thus small relative to the measured change in η due to the implantation procedure.

For unimplanted tungsten, we assumed a C11 value of 523.27 GPa (i.e., the C11 value from the set of tungsten elastic constants yielding the closest agreement to the measured SAW velocity data, reported in Ref. 10) and a density ρ of 19 265 kg/m3. The error in C11 was taken to be the range of C11 literature values.10,11,22,23 For the implanted sample, we assumed that the value of C11 would be somewhat lower due to the damage caused by He-ion implantation. We observe that the mean SAW velocity decreases by approximately 2% upon implantation. The percentage change in the elastic constants Cij upon implantation can then be roughly estimated as twice the percentage change in the mean SAW velocity since Vη1, yielding a decrease in Cij by approximately 4%–5% compared to the unimplanted case. Thus, the assumed value of C11 for the SAW velocity calculations for the implanted sample was taken to be 497.11 GPa, with a generous error bar of ±5%. In the calculations, the implanted sample was modeled as a bilayer, with an implanted layer thickness of 2.75 μm on top of an unimplanted semi-infinite half-space. Since the SAWs were mostly localized in the implanted layer, the effect of the unimplanted “substrate” was small: we found that the value of η obtained using a bilayer model differs only by 0.2% from the value obtained assuming an infinitely thick implanted layer.

The best fit curves obtained from the least-squares regression procedure are plotted alongside the TG data in Fig. 2(c) for both the implanted and unimplanted samples. Table I shows the best fit values of η and C44 for both samples along with the associated error estimates. Details of the error analysis can be found in the supplementary material. One can see that the total uncertainty in the anisotropy parameter is very small, while the uncertainty in C44 is significantly larger. The high accuracy in determining η stems from the fact that the SAW velocity anisotropy directly measured by the TG technique is mostly controlled by η and is affected to a much lesser degree by the assumed value of C11.

TABLE I.

Measured values of η and C44 and the associated uncertainties expressed in absolute terms (σ) and in percentage terms (σ̃). The last line presents percentage uncertainties in the quantity (η1).

UnimplantedImplanted
η(=1.0122)C44(=161.62GPa)η(=1.0315)C44(=157.89GPa)
ση/C44 4.897×104 0.9741GPa 3.513×104 1.219GPa 
σ̃η/C44 0.04838% 0.6027% 0.03405% 0.7719% 
σ̃η1 4.014% … 1.115% … 
UnimplantedImplanted
η(=1.0122)C44(=161.62GPa)η(=1.0315)C44(=157.89GPa)
ση/C44 4.897×104 0.9741GPa 3.513×104 1.219GPa 
σ̃η/C44 0.04838% 0.6027% 0.03405% 0.7719% 
σ̃η1 4.014% … 1.115% … 

It was found that the implantation procedure imparts an increase in the elastic anisotropy (η1) by a factor of approximately 2.6. A previous study by Hofmann et al.9 investigated a polycrystalline W-1% Re alloy exposed to identical implantation conditions. No He bubbles, dislocation loops, or other mesoscopic defects were observable via transmission electron microscopy (TEM) after implantation. The authors found via x-ray micro-diffraction measurements and density functional theory (DFT) calculations that the damage microstructure due to helium-implantation is dominated by Frenkel pair defects consisting of self-interstitial tungsten atoms (SIAs) and He2V (V for vacancy) clusters. A DFT study was undertaken to calculate the effect of these defects on the elastic constants of the alloy, but factors of Cij,unimpexp./Cij,unimpDFT, renormalizing each implanted Cij value, had to be introduced due to significant differences between DFT-obtained Cij values (Cij,unimpDFT) and experimental Cij values (Cij,unimpexp.) for the unimplanted alloy. The results of this DFT analysis predicted that a damage microstructure dominated by SIAs and He2V clusters due to the present implantation conditions would yield an increase in η from 1.01 to 1.02. The experimental result obtained in this study, an increase in η from 1.0122 to 1.0315 upon He-ion implantation, is in agreement with the predicted anisotropy increase. The fact that we experimentally observe an increase in the anisotropy upon implantation supports the notion that atomistic defects such as SIAs and He2V clusters with anisotropy larger than the perfect tungsten matrix are introduced by the implantation procedure.

In conclusion, we have measured the SAW velocity as a function of propagation direction in the (110) plane of both unimplanted and He-ion implanted tungsten single crystals. From these data, we were able to determine the Zener anisotropy factors η with an accuracy finer than 5×104. We observed an increase in (η1) upon ion implantation by a factor of 2.6, which is consistent with theoretical predictions based on DFT analysis of the defect microstructure in He-ion implanted tungsten characterized by equal concentrations of SIAs and helium-filled vacancies. The ability of the TG technique to resolve the remarkably small anisotropy of tungsten samples highlights the potential of this method for high-accuracy measurements of near-surface elastic properties.

See supplementary material for a detailed description of the error analysis methods.

We thank C. A. Dennett for assistance with numerical SAW velocity calculations and associated coding. R.A.D., A.A.M., J.K.E., and K.A.N. acknowledge support from the National Science Foundation (NSF) Grant No. CHE-1111557. A.V.-F. appreciates support from CINVESTAV and CONACYT through normal, mixed, and PNPC scholarships. A.G.E. acknowledges financial support from the South African National Research Foundation (NRF). This work has in part been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training program 2014–2018 under Grant Agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This research used beamline 34-ID-E at the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC-02-06-CH11357.

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Supplementary Material