Introduction

To understand how impurities affect the mechanical behavior of ice is important since a number of impurities exist in natural ice. Dissolved impurities in ice can occur either as substitutional ions in the lattice, like F⁻ and NH₄ ⁺, or as interstitials, like SO₄ ²⁻ and NO₃ ⁻. Impurities in the lattice can, in principle, either act as obstacles to the movement of dislocations or aid in dislocation motion, and therefore influence their mechanical properties.

Reference GlenGlen (1968) pointed out that proton disorder in crystals of ice Ih presents the major obstacle to dislocation glide. Adjacent (1) glide planes are connected through randomly oriented hydrogen bonds. Therefore, in order for a dislocation to move, the hydrogen bonds have to be appropriately reoriented. This bond reorientation occurs by the movement of ions (H₃O⁺ and OH⁻) and Bjerrum defects (D type and L type). Reference Petrenko and SchulsonPetrenko and Schulson (1992) used an electrical technique to study the effect of point defects on dislocation mobility and found that ice becomes harder when point defects are extracted, suggesting that dislocation mobility was directly related to protonic rearrangement.

Following Glen’s model, it is evident that impurities that introduce additional point defects into ice should increase the mobility of dislocations. For example, each HF molecule introduces one L-defect, and the H₃O⁺ concentration also increases (Reference GränicherGränicher 1963). Thus, Reference JonesJones (1967) and Reference Jones and GlenJones and Glen (1969) demonstrated that very small amounts of dissolved impurities (HF and NH₃) could strongly affect the mechanical properties of ice single crystals. For example, at −70°C and a constant strain rate of 2.7 × 10 s⁻¹, 50 ppb of HF decreased the peak stress by one-third, and with 8 ppm of HF the peak stress was only about one-quarter that of pure ice. The HF reduced the subsequent steady-flow stress even more. Reference Jones and GlenJones and Glen (1969) argued that the additional point defects introduced by the HF increased the probability of bond reorientation, allowing the bonds to assume the correct orientation for a dislocation to pass. Therefore, the dislocations moved faster and the HF-doped ice crystals became softer.

Reference Jones and GlenJones and Glen (1969) demonstrated that the effect of HF was not due to the grown-in defects from the melt, through the following experiment. They strained pure ice and then unloaded it. They then doped the specimen with HF, and, upon retesting, a dramatically smaller stress was required to maintain the same strain rate. On the other hand, if the specimen was simply annealed without doping with HF, further plastic deformation continued at a stress close to that prior to the interruption. However, Jones and Glen did not show whether the introduction of HF increased the dislocation density. Later, using conventional X-ray topography, Reference Mai, Perez, Tatibouët and VassoilleMaï and others (1978) found that the velocity of dislocations in ice doped with 10 ppm HF was double that in pure ice. However, as pointed out by Reference Ahmad and WhitworthAhmad and Whitworth (1988), the results of Maï and others are ambiguous due to the long image-acquisition time during which dislocation recovery may have occurred. Therefore, it is still not clear whether the increase in dislocation density or the increase in dislocation mobility causes the softening effect from HF.

Reference Nakamura and JonesNakamura and Jones (1970, Reference Nakamura, Jones, Whalley, Jones and Gold1973) also demonstrated a softening effect in the temperature range −5° to −26°C by doping ice single crystals with 5–12 ppm HCl. Both Reference Jones and GilraJones and Gilra (1972, Reference Jones, Gilra, Whalley, Jones and Gold1973a, Reference Jones and Gilrab) and Reference Oguro and HigashiOguro (1988), using conventional X-ray topography, found that the addition of dopants (HF, HCl, NH₃) greatly increased the grown-in dislocation density in ice. Using synchrotron X-ray topography, Reference Shearwood and WhitworthShear-wood and Whitworth (1992) found that 0.036 ppm HCl had no effect on the dislocation velocity in ice single crystals between −30° and −55°C. But for this amount of dopant they found that the dielectric relaxation time was reduced by about an order of magnitude, with a lower activation energy. Later, Reference Hu, Jia, Liu, Baker and BlackHu and others (1995), also using synchrotron X-ray topography, confirmed that low concentrations of HCl (0.020 ppm) had little effect on dislocation velocity in ice. In contrast, a single measurement at −16°C on ice doped with 7 ppm HCl showed an increase in the dislocation velocity by almost an order of magnitude compared to pure ice. However, the large dislocation density present in the latter case could have affected the motion of individual dislocations.

Although work on HCl and HF is of interest in elucidating the mechanisms of dislocation motion in ice, these impurities do not generally occur in natural ice. In contrast, sulfuric acid is present in natural ice, arising from aerosols produced by volcanoes. It is known that sulfuric acid is present in ice at the triple junctions where three grains meet (Reference Mulvaney, Wolff and OatesMulvaney and others, 1988; Reference Wolff, Mulvaney and OatesWolff and others, 1988; Reference Fukazawa, Sugiyama, Mae, Narita and HondohFukazawa and others, 1998). A substantial concentration of sulfuric acid (>1 M in areas of 1 μm²) was found, using energy-dispersive spectroscopy in a scanning electron microscope as a solid phase at the triple junctions of ice from Dolleman Island held at −160°C (Reference Mulvaney, Wolff and OatesMulvaney and others, 1988). The presence of the sulfuric acid at the triple junctions could explain the electrical properties of Antarctic ice.

By introducing point defects into ice, sulfuric acid might also be expected to influence both dislocation nucleation and mobility and, concomitantly, affect the mechanical properties of ice crystals. The effects of H₂SO₄ on mechanical behavior, dislocation nucleation and dislocation mobility have not been reported for either polycrystalline or single crystal ice. The purpose of the research presented here is to show how sulfuric acid affects the mechanical properties of ice single crystals.

Experimental

Distilled water was mixed with sulfuric acid, and its acidity was measured using a pH meter. Large pucks (28 cm diameter, 13 cm high) of various concentrations of H₂SO₄-doped ice were grown using the same method as that used to grow undoped ice, as described elsewhere (Reference Trickett, Baker and PradhanTrickett and others, in press). Ice single crystals with various orientations were cut from the pucks. The concentrations of sulfuric acid in the ice single crystals were determined using the pH meter on the crystals which were melted after mechanical testing. Using polarized light, all the single crystals appeared to be of high quality.

Compression specimens, 60 mm high by 25 mm wide by 20 mm deep, were prepared from the single crystals as described elsewhere (Reference Trickett, Baker and PradhanTrickett and others, in press). The crystal specimens were prepared with the basal plane tilted at an angle from the top face of the crystal by θ = 3°, 25°, 33° or 80° ± 1° (see Reference Trickett, Baker and PradhanTrickett and others, in press) and with dopant levels of 0.1, 4.4, 6.8 or 11.5 ppm of H₂SO₄. Compression tests were performed at a constant axial strain rate of either 1 × 10⁻⁵ s⁻¹ at −20°C ± 0.5°C or 1 × 10⁻⁶ s⁻¹ at −10°C ± 0.5°C on a Materials Testing System located in a cold room. For purposes of comparison, similar undoped specimens were also produced and tested.

The dislocation structures in some of the doped ice single crystals were examined using white-radiation synchrotron X-ray topography at the National Synchrotron Light Source at Brookhaven National Laboratory for Nuclear Research, Long Island, NY, U.S.A. The specimen preparation and operating conditions for the X-ray topography have been described in detail elsewhere (Reference Liu and BakerLiu and Baker, 1993; Reference Liu, Baker and DudleyLiu and others, 1993).

Results and Discussion

Figure 1 shows typical engineering stress–strain curves obtained at −10°C at a constant strain rate of 1 × 10⁻⁶ s⁻¹ for two identically oriented (θ = 80°) ice single crystals, one containing 0.1 ppm H₂SO₄ and the other undoped. Both curves showed typical behavior for ice deforming by basal slip, i.e. a linearly rising stress with increasing strain, followed by a sharply declining stress after reaching a peak. With further strain, the sharp decline in stress slowed. Comparison of the two curves shows that even 0.1 ppm of H₂SO₄ decreases both the peak stress and the subsequent flow stress at −10°C. Interestingly, the two curves appear to be diverging with increasing strain.

Fig. 1. Engineering stress–strain curves for undoped and H₂SO₄-doped (0.1 ppm) ice single crystals with θ = 80° at −10°C and an axial strain rate of 1 x 10⁻⁶ s⁻¹.

Crystals with various concentrations of H₂SO₄ were strained in order to examine the relationship between the dopant level and the strength. Figure 2 shows the situation for θ = 3° where it is clear that the higher the dopant level, the softer is the doped ice. Also, note that both of the pure ice crystals fractured at or near the peak stress (fracture is indicated by a vertical arrow), whereas only two of the doped-ice crystals fractured during testing (at greater plastic strains than for undoped ice). Figure 3 shows data for crystals with θ = 33° both undoped and doped with 4.4 ppm H₂SO₄. For this orientation and dopant level the peak stresses are only slightly reduced by the dopant, although the subsequent flow stress is clearly reduced. It is evident that the acid has a less significant softening effect at θ = 33° than at θ = 3°, i.e. H₂SO₄ doping has a more pronounced influence on the flow of ice crystals with a hard rather than a soft orientation.

Fig. 2. Comparison between the engineering stress–strain curves for pure and H₂SO₄-doped ice single crystals of various concentration with θ = 3° at an axial strain rate of 1 × 10^{−5 −1} at −20°C.

Fig. 3. Comparison between the engineering stress–strain curves for pure and H₂SO₄-doped (4.4 ppm) ice single crystals with θ = 33° at an axial strain rate of 1 × 10⁻⁵ s⁻¹at −20°C. The curves are offset along the strain axis for clarity.

The difference between the peak critical resolved shear stress (CRSS) for undoped ice and that for H₂SO₄-doped ice, i.e. , at θ = 3°, normalized to a shear strain rate of 1 × 10⁻⁵ s⁻¹ (see later), is plotted as a function of the square root of the concentration of H₂SO₄ in Figure 4. Δσ increases linearly with the square root of the concentration of H₂SO₄ in ice up to 11.5 ppm. This suggests that even at 11.5 ppm, the H₂SO₄ is still in solution. Parabolic defect hardening in metals can often be described by Δσ = βµc ^1/2, where µ is the shear modulus, c is the concentration of solute and β defines the strength of the hardening (Reference FleischerFleischer, 1963). Typically β = 0.2 for interstitial hardening and 0.002 for substantial strengthening. Using a value of µ = 7 GPa for ice, Figure 4 yields a value of β = 0.014. This is less than that for interstitial strengthening, but much greater than that for substitutional strengthening in metals (β = 0.001). Although metals exhibit parabolic hardening from solutes, and ice shows parabolic softening, the mechanisms are quite different. Parabolic hardening in metals arises from the dislocation line being held up at solute atoms and having to bow out in the slip plane before the dislocation can break away. The solute softening in ice presumably arises from the additional L-defects and H₃O⁺ ions allowing more rapid hydrogen-bond reorientation, thus easing dislocation passage along a slip plane. The c ^1/2 dependence of the solute softening in ice presumably arises because the softening is inversely related to the separation of solute ions on the slip plane, which itself is inversely proportional to the square root of the solute atom concentration.

Fig. 4. Graph of the difference in CRSS (peak stress) between undoped ice and H₂SO₄-doped ice crystals at θ = 3° vs the square root of the concentration of H₂SO₄ for crystals compressed at −20° C normalized to a shear strain rate of 1 × 10⁻⁵ s⁻¹.

In an earlier paper (Reference Trickett, Baker and PradhanTrickett and others, in press), it was shown that the orientation dependence of the CRSS (peak stress) of high-purity ice single crystals obeyed Schmid’s law. Thus, H₂SO₄-doped ice single crystals with various orientations were tested to see whether Schmid’s law applies to doped ice. Figures 5 and 6 show typical resolved shear-stress–shear-strain curves for two different dopant levels at different orientations, while Figure 7 is an example of engineering stress–strain curves at the same orientation for 6.8 ppm H₂SO₄-doped ice and undoped ice. In order to make comparisons between the CRSS at different orientations, it is necessary to normalize the peak stresses measured at a constant compressive axial strain rate to a fixed shear strain rate (Reference Trickett, Baker and PradhanTrickett and others, in press). This was done by using a relationship between the shear stain rate, , and the CRSS, τ, of (Reference TrickettTrickett, 1999). The resolved shear stress–strain curves were thus normalized to a shear strain rate on the basal slip plane of 1 × 10⁻⁵ s⁻¹.

Fig. 5. Comparison between the resolved shear stress–strain curves for H₂SO₄-doped (4.4 ppm) ice single crystals with θ = 3° normalized to a shear strain rate of 1 × 10⁻⁵ s⁻¹ at −20°C.

Fig. 6. Comparison between the resolved shear stress–strain curves for H₂SO₄-doped (6.8 ppm) ice single crystals with θ = 3° and 25° normalized to a shear strain rate of 1 × 10⁻⁵ s⁻¹ at −20°C.

Fig. 7. Comparison between the engineering stress–stain curves at an axial strain of 1 × 10⁻⁵ s⁻¹ at −20 for pure and H₂SO₄-doped (6.8 ppm) ice single crystal with θ = 25.

The peak CRSS normalized to a shear strain rate of 1 × 10⁻⁵ s⁻¹ is plotted as a function of angle 6 in Figure 8. The peak CRSS of H₂SO₄-doped ice crystals, unlike that of undoped ice single crystals (Reference Trickett, Baker and PradhanTrickett and others, in press), depends on their crystallographic orientation, i.e. Schmid’s law is not obeyed (if it was, the CRSS would be independent of θ for a particular dopant level). It is also clear from Figure 8 that, as noted earlier, H₂SO₄ has a more significant softening effect at θ = 3° than at θ = 25° or 33°. This suggests that the dislocation nucleation and multiplication mechanisms are different in a hard orientation (when the applied stresses are very high) than in a soft orientation (when the applied stresses are very low). Exactly how the mechanisms differ is unclear.

Fig. 8. Graph of the peak CRSS for pure ice and for H₂SO₄-doped ice with various dopant levels (indicated) and orientations at −20°C normalized to a shear strain rate on the basal slip plane of 1 × 10⁻⁵ s⁻¹.

The softening mechanism of H₂SO₄ should be different from HF since SO₄ ²⁻ occurs as an interstitial ion in the lattice but F⁻ is present as a substitutional one. H₂SO₄ might increase the dislocation mobility due to the addition of two H⁺ ions from each H₂SO₄ molecule. It also might be expected (see Introduction) that the H₂SO₄ doping would change the dislocation density. The latter possibility was investigated briefly using synchrotron X-ray topography.

Although all the specimens for the X-ray topography study appeared to be good single crystals as determined under the polarized light, sub-grains were clearly present in the as-grown H₂SO₄-doped ice single crystals. Dislocations were observed only in the sub-grains that satisfy the operating diffraction conditions; other sub-grains appear black. If the diffraction conditions were changed, different sub-grains were in contrast. The dislocation density in these sub-grains was quite high (compared to previously observed dislocation structures in undoped crystals) at > 1 × 10¹⁰ m⁻² (see Fig. 9). This observation of a high dislocation density in H₂SO₄-doped ice is similar to the observations of a greatly increased dislocation density in NH₃ ⁻, HCl⁻ and HF-doped ice found by Reference Jones and GilraJones and Gilra (1972) and Reference Oguro and HigashiOguro (1988). Regarding this observed high dislocation density in doped ice, it is well to keep in mind that although our method for making X-ray topography specimens works well with pure ice, there is a possibility that the softening effects from acids (HF, HCl and H₂SO₄) make it easier for dislocations to be introduced into doped crystals during specimen preparation. However, it does appear that at least part of the softening effect from sulfuric-acid doping is due to the presence of a high dislocation density.

Fig. 9. X-ray topograph showing a sub-grain which satisfied the operating diffraction conditions in a specimen doped with 11 ppm of H₂SO₄. The dislocation density was estimated to be > 1 × 10¹⁰ m⁻².

Conclusions

Single crystals of ice of various orientations containing various concentrations of H₂SO₄ up to 11.5 ppm were strained under compression, and the following conclusions were derived:

1. 1. Both the CRSS (peak stress) and subsequent flow stress in ice single crystals are reduced by doping with sulfuric acid.

2. 2. The peak CRSS of H₂SO₄-doped ice decreases as the square root of the concentration of H₂SO₄ increases.

3. 3. The peak CRSS of H₂SO₄-doped ice single crystals depends on their crystallographic orientation, i.e. Schmid’s law is not obeyed.

4. 4. The addition of H₂SO₄ appears to increase the ductility of ice crystals.

5. 5. The solubility limit of H₂SO₄ in ice single crystals is at least 11.5 ppm.

6. 6. X-ray topography indicates that at least part of the softening effect from H₂SO₄ doping is due to a high grown-in dislocation density.