Small changes in crystal temperature can have large effects on ice crystal shape. Near liquid-water saturation, a few ∘C change near -8 ∘C changes long columns into thin tabular crystal forms . At low supersaturations, small temperature changes may significantly affect facet-normal growth rates since this rate can depend exponentially on the vapor-source temperature TVS (via its control of supersaturation) when the face is free of new-layer-generating defects (i.e., perfect faces, which were commonly found in CC1).

The stability of two temperatures, that of the experimental chamber TEC and that of the ambient air surrounding the crystal Ta, is important. The temperature stability of the EC is set by (1) the cryogenic refrigerant temperature control from a Neslab ULT-80 bath-circulator unit (temperature stability exceeds 0.1 ∘C over a 3 h period), (2) the room temperature stability, and (3) the large thermal mass of the EC (which smooths short-term temperature fluctuations via its roughly 15 min response time). Specifically, the EC was milled from a single block of tellurium copper and then nickel plated on the outside and gold plated inside for surface uniformity and to reduce the potential for oxide formation and contamination. Temperature variations in Ta will be due to temperature fluctuations and gradients in the internal walls of the GC. A time-series measurement of the 12 thermistors buried in the walls of the EC shows that the maximum fluctuation of the EC block is less than 50 mK over a 1 d period. We worried that the TECs might induce small gradients in the EC temperature but find no measurable additional thermal gradient in the GC when the TEC current ITEC<0.5 A – a value much larger than is needed for growth or sublimation conditions in a cold cloud. For a typical 11 h period, the maximum gradient across the EC block was less than 10 mK. So we are comfortable assuming that TEC=Ta to within a few millikelvin.

While chamber temperature is relatively straightforward to measure and control, precise supersaturation measurement within a chamber along with measurement and control near the surface of a growing crystal is much more difficult. In any experiment we are concerned with both spatial and temporal gradients in the growth chamber supersaturation SGC. The gold standard for crystal-growth experiments involves two parts: a stable, controlled, and gradient-free SGC within the experimental chamber, and the measurement of the supersaturation near the surface of the growing (or sublimating) crystal, Sa, at the same time the crystals are growing (or sublimating). No ice crystal growth rate experiment to date satisfies these two conditions, but the method used in CC2, although not yet at the gold standard level, has enhanced thermal stability and a relative gradient-free nature that is a large improvement over previous methods.

Within CC2 all crystals grow simultaneously within an approximately 1 cm3 volume near the center of the GC. Simultaneous growth in a chamber without gradients means all crystals experience the same thermodynamic conditions. Sequential growth experiments cannot claim all crystals experienced the same thermodynamic conditions without a direct, local measurement of Sa. Previous experiments have assumed gradient-free conditions and in this case the ambient supersaturation at the crystal surface given in percent by 1Sa=Neq(TVS)-Neq(Ta)Neq(Ta)×100, where Neq is the equilibrium vapor density in molecules per cubic meter (molecules m-3) and Ta is the temperature at the crystal surface. It is possible that other factors affect Sa, so in future experiments we will test the use of this equation. Other than the effect of thermal gradients within the EC (which are minimal as discussed above), the possible gradients in SGC within the GC can come from three potential sources: (a) thermal instability of TVS, (b) gradients within the VS itself, and (c) the presence of other ice crystals within the EC. a.

Thermal stability of TVS. The numerator in Eq. (1) is to first order proportional to the ice surface-temperature elevation ΔT=TVS-Ta. Thus, the relative uncertainty in supersaturation δSa/Sa=δΔT/ΔT. With feedback TEC temperature control the VS temperature standard deviation ΔT is typically about 3 mK (the variation observed over several hours). This gives an estimated uncertainty in Sa of about 0.03 %. To understand the meaning of 0.03 % supersaturation, consider that an ice crystal growing at the maximum possible rate at -30 ∘C at this supersaturation is about 60 µm h-1 in a pure vapor (from the Hertz–Knudsen equation, e.g., Eq. 1, of ; this equation assumes a rough surface, or α=1), then we expect the uncertainty to add about 0.2 µm h-1 additional growth to a 100 µm diameter spherical crystal in an atmosphere of air (Maxwell's expression or Hertz–Knudsen divided by the vapor-diffusion impedance). This uncertainty is less than the measurement resolution over several hours growth.

Frost can form on chamber walls and, if the area is large, can uptake a significant fraction of the source vapor. A highly controlled vapor-source supersaturation, SVS, does not necessarily set the ambient supersaturation, Sa, at the center of the chamber where the crystals are growing if there is frost or condensate growing on the wall. Such frost is a particular problem when growing crystals sequentially because any measured difference in their rate or habit may not be inherent but instead be due to their being affected more or less by frost. To reduce this issue, the CC2 windows allow observation of all surfaces inside the GC and VSC. But it is possible that this ice is so thin as to make it nearly invisible to the eye. An important factor is the relative surface area of the frost versus that of the VS ice. If their areas and thicknesses are the same, then the vapor density in the EC would be midway between the equilibrium values for the VS ice and the chamber walls. However, the effect in practice would likely be worse because the frost layers would likely be much thinner than the VS ice, pushing the vapor density closer to the equilibrium value for the walls due to the temperature-gradient effect in Sect. 3.1.2 above.

The windows on the sides of the VSC provide for easy detection of large frost crystals and, once noticed, that chamber can be immediately sealed off. In practice, we find that when frost crystals first appear, they are in the VSC, relatively close to the source ice. For the experiments described here, the VSC and GC internal walls were continuously monitored for frost. If frost began to form in the attached VSC, then the sliding valve was changed to disconnect the VSC from the GC, and the TEC in the other VSC was set to maintain the desired humidity in the GC. The ability to isolate one VSC from the GC when frost first occurs and to switch to a frost-free VSC allows us to continue to grow the crystals for long periods at near-constant Sa conditions. To clear the frost off the walls of a VSC, we first evacuate the VSC and set its TVS to at least 10 ∘C below Ta. The frost typically left the walls within about 30 min under these conditions. For the conditions of the experiments described here, typically no frost was observed on VSC walls for at least 6 h. The data set here was collected before frost started to form in the GC walls.

In a future paper, , we report results from droplet evaporation measurements done simultaneous with the crystal growth measurements. Measuring the evaporation rate of pure water droplets during crystal growth does give a direct and independent measure of Sa near the growing crystals surface. For these experiments one capillary is used to hold the evaporating droplet while the other two hold the growing or sublimating crystals. Results from these experiments demonstrate that accurately predicting Sa at a chamber center requires careful calibration. For the results reported here we are concerned with facet-normal growth rate differences for crystals growing simultaneously under the same thermodynamic conditions. In these experiments the ice crystal surface area is small compared with that of the VS and no wall ice was present. We continuously measure TGC and TVS and the enhanced thermal stability, and control within CC2 gives us confidence that, within the variations caused by the measured temperature gradient across the EC, Sa is to good approximation SVS within that 1 cm3 volume that contains the capillary tips. In future experiments, where a detailed comparison with crystal growth models is the goal, Sa calibration measurements will be made along with the growth rate measurements.

Radiative heating can occur in two places. First, consider thermal radiation between the VS surface and the VSC wall. The VS–GC temperature difference is typically less than 3.5 ∘C – the value needed to achieve liquid-water saturation at -40 ∘C. Due to the relatively small temperature differences involved, and also the very low emissivity of the gold plating of all interior walls, such a radiative heat transfer has a negligible influence on the VS surface temperature. Second, consider thermal radiation between the ice crystals and sources outside the windows. The ice crystals sit at Ta, but the thermal link is weak due to the crystal being surrounded by air. Considering the different materials viewed by the crystal (windows, walls, and circulating fluid), determining the influence of radiative heating on ice-crystal temperature is best handled as an experimental issue. We examine this issue by monitoring the crystals in the growth chamber under controlled conditions in which the windows are alternately exposed or covered with low-IR-emissive material. When we have tried this test, we observed no IR heating effects on the normal growth rates.

The capillary holds the crystal steady, allowing clear imaging and viewing from several angles. Also, as the crystal starts at the capillary tip (typical case), one can usually measure the advance of all parts of the crystal with respect to the fixed capillary tip. Although these features are advantages of the method, the capillary can promote growth on one, two, or three faces.

Consider the examples in Fig. 3. The images show two crystals nucleated and grown at the same time but on different capillaries – Fig. 3a and b show the front capillary Cf and Fig. 3c–f show the back capillary Cb. The crystal on the left (Fig. 3a and b) is nearly a hexagonal prism, but, by measuring the distance from the capillary tip along the surface normal, one finds that the top right prism face has grown about 25 % faster than the others. The capillary is seen exiting the crystal at the vertex between this face and the top left prism. Subsequent images (not shown here) show the crystal growing larger but the capillary remaining at this vertex. As the vertex stays at the capillary, these observations show that the capillary determines the relative normal growth rates of these two faces. The rotated view in Fig. 3b shows that the two basal faces have nearly equal normal growth rate, and neither is contacted by the capillary. Thus, the basal faces appear unaffected by the capillary. So, of the eight crystal faces, two are directly compromised by the capillary, but six are not directly influenced. In using data from this crystal, we must consider the influence that the faster growth on the top two prism faces has on the vapor-diffusion field near the other faces and the crystal temperature. In this way, the influence of the capillary may be overcome by crystal-growth modeling. The exact method will be described in a later publication.

The crystal on the back capillary, in Fig. 3c–f, shows further limitations and features. In this case, we cannot see the location of the capillary inside the crystal and must instead estimate its location by examining the growth sequence starting from nucleation (not shown). Nevertheless, the basal-side views in Fig. 3c and f show that the capillary does not contact the basal faces (except possibly from the ice interior), yet one basal face grew faster than the other. Moreover, the views in Fig. 3d and e show that this crystal has two opposite prism faces that are much larger in area and thus have much lower growth rates. The overall shape is similar to that proposed for crystals that generate the Parry arc .

Finally, consider the crystal in Fig. 4. In this case, the capillary exits at a corner, thus contacting one basal face and two prisms. As in other cases like this observed during both the CC2 and CC1 experiments, the crystal does not start this way, but once the corner reaches the capillary it always remains there (at least under constant conditions). Why does this occur? Clearly, the introduction of an interior glass-ice corner should promote new-layer nucleation. If such a site is the most active on a given face, then that site will increase the normal growth rate of the face. Moreover, if this capillary is tilted towards a neighboring face, then the relative increase in growth rate over that neighboring face will bring the edge between the two faces closer to the capillary. Once the edge reaches the capillary, it will stay there because the same promotion of layer nucleation will occur on the neighboring face. In three dimensions, if the capillary also tilts towards a third face, this process will bring that face to the capillary until the capillary exits at the common corner. However, if the layer-nucleation-promotion effect is relatively weak, then supersaturation gradients or a surface defect site may produce more rapid layer nucleation elsewhere, such as at a nearby crystal corner. Thus, there are cases where, despite such promotion of layer nucleation, the face growth is controlled by a more active site, making the capillary influence irrelevant. For example, if the capillary exits the crystal from near the face middle, it will likely lie at a lower-supersaturation region, with the more active step-generation site instead being at the corner. In such a case, the capillary may have a small local influence but not influence the normal growth rates of the faces. These considerations also apply to crystals grown not at the tip but midway along a capillary or any fiber. This explains why, for example, in previous high-supersaturation experiments, the rapid-growing parts of the crystal are away from the fiber (e.g., ).

Occasionally, we observe indications of different influences from the capillary. For example, the crystal can appear to avoid contact with the capillary. This appears to be a vapor-shielding effect because it only occurs when the crystal size is within a few diameters of the capillary tip and only occurs where the crystal contacts the capillary. Other parts of the crystal are unaffected, and the effect vanishes when the crystal grows larger. Another effect that can occur is rapid growth up the capillary in which the growth appears as smaller crystals of the same orientation. It is possible that this crystallization may be a result of thin-film crystallization on the glass capillary after a crystal nucleates at the tip. Both of these influences should be smaller with smaller-diameter capillaries and may also be reduced with suitable coatings. Finally, within the ice just adjacent to the capillary (within a few capillary diameters), the interface may create strain effects in the ice. To date, we have not seen evidence of such effects, but they remain a possibility.

Thus, the capillary influence on new-layer production can be irrelevant in some cases and may be overcome using modeling in other cases but should always be examined. Acknowledging this influence has two additional benefits. One, we may use it to study the nucleation process itself. Two, we can recognize the effect in other studies and realize that the resulting data may not be reliable. In future experiments, we plan to research these effects and develop strategies for quantifying their influence.