# Geometric properties of platelet ice crystals **Authors:** D.E. Dempsey, P.J. Langhorne **Published in:** Cold Regions Science and Technology (2012) **DOI (version of record):** https://doi.org/10.1016/j.coldregions.2012.03.002 **This copy:** Accepted manuscript (peer-reviewed, author's version). Text extracted from the PDF at https://ddempsey.github.io/papers/2012-dempsey-geometric-properties-platelet-ice-crystals/dempsey2012-geometric-properties-platelet.pdf; equations, tables and figure placement may be imperfect, so cite the DOI. **Notice:** Accepted manuscript. © 2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. The version of record is available at https://doi.org/10.1016/j.coldregions.2012.03.002 **Licence:** CC BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/ --- 1 # **Geometric properties of platelet ice crystals** 2 D.E. Dempsey_∗_ , P.J. Langhorne 3 Department of Physics, University of Otago, Dunedin, New Zealand - 4 _∗_ Corresponding author at: Department of Engineering Science, University of Auckland, Private - 5 Bag 92019, Auckland Mail Centre, Auckland, New Zealand. Tel.: +64 9 373 7599x87061; fax: +64 6 9 373 7468. - 7 E-mail addresses: `d.dempsey@auckland.ac.nz` (D.E. Dempsey), `patricia.langhorne@otago.ac.` 8 `nz` (P.J. Langhorne). ### 9 # **Abstract** - 10 Sea ice that forms in McMurdo Sound, Antarctica, which is adjacent to the McMurdo and Ross Ice 11 Shelves, exhibits the uncommon ice fabric, incorporated platelet ice. This ice fabric is the subject of 12 a high resolution thin sectioning study, consisting of ten closely spaced horizontal sections bounded 13 above and below by vertical sections. From these we investigate the crystallographic and geometric - 14 properties of the ice grains and find a relationship between c-axis orientation and the minor axis - 15 of an ellipse fitted to a crystal’s grain boundary. Although accuracy is dependent upon the size 16 and shape of the crystal, the technique provides a means of extracting crystallographic information 17 from historical datasets for which only thin section photographs remain. Identification of common 18 grains in multiple, 2-D sections allows us to reconstruct an approximation of the original 3-D crys19 tal structures. These structures exhibit a variety of growth interactions, including upward directed - 20 crystal growth and intertwining crystals. We also construct hypothetical crystal grain boundaries 21 that might be observed for a variety of vertical thin section orientations. These indicate that grain - 22 shape can depend on thin section orientation and illustrates some of the limitations of 2-D repre23 sentations of 3-D crystals. Serrated grain boundaries are identified between neighboring crystals in 24 several vertical sections. Geometric arguments and crystallographic observations lead us to propose - 25 a mechanism of layer nucleation within grain boundary grooves that occurs as supercooling exceeds - 26 a threshold value. 1 27 **Keywords:** Platelet ice; Sea ice; Thin section; Crystal; Ice shelf; Grain boundary ### 28 # **1. Introduction** - 29 Annual sea ice growth in Antarctic waters yields changes in surface cover from a minimum of 30 3 _×_ 106 km2 to 20 _×_ 106 km2 (Gordon, 1981). The variable climatic and oceanographic conditions 31 around the continent combine to produce significant variability in the sea ice properties, both 32 spatially and temporally. The study of sea ice texture and crystallography is used to elucidate 33 aspects of the conditions in which the ice grows. - 34 Previous workers have measured crystallographic properties (e.g., c-axis orientations) to assess 35 prevailing current directions (Gow et al., 1998; Jeffries et al., 1993; Langhorne and Robinson, 1986; 36 Weeks and Gow, 1978); bulk properties (e.g., salinity, stable-isotope) to assess growth rates (Eicken, 37 1992, 1998; Souchez et al., 1988); and textural classifications to determine growth mechanisms (for 38 example Tison et al. (1998), Weeks and Ackley (1982)). - 39 The existence of platelet ice in the sea ice cover close to an ice shelf is a striking example of 40 the modification to the crystallography by environmental factors. Platelet ice is the name given to 41 an open-textured, random array of dendritic crystals, which may individually have a planar area 42 of tens of centimeters (e.g., Gow et al., 1998; Paige, 1966). Under some conditions these form 43 a loosely-bound, porous layer at the ice–water interface, called the sub-ice platelet layer, which 44 may be meters thick (e.g., Crocker and Wahhams (2004), Dempsey et al. (2010)). The study of 45 the incorporation of these crystals into the sea ice cover, which produces incorporated platelet ice, 46 provides insight into the growth mechanisms and crystal interactions that prevail during sea ice 47 formation. - 48 The aim of this study is to develop and test methods for interrogating sea ice at a macroscopic - 49 crystal scale. In particular, we are interested in the grain boundaries between crystals, their 3- 50 D structure and 2-D projections, and the extent to which these are linked to the kinetics of ice 51 growth and environmental conditions present during their formation. Furthermore, by quantifying 52 the contribution of ice growth kinetics to grain geometry, we establish the accuracy of the reverse 53 method, i.e., inferring crystal orientation from the geometric properties of grains. This provides - 54 an opportunity to analyze historical datasets for which only a photographic record remains. The 2 - 55 study also allows us to evaluate the ability of 2-D thin sections to represent 3-D crystal structures, - 56 thereby identifying potential sources of error and opportunities for textural misclassification. - 57 # **2. Sea ice growth and texture** - 58 The development of incorporated platelet ice is a multi-step process. Ice–ocean interaction at the - 59 base of an ice shelf initiates an ice pump (Lewis and Perkin, 1986), which delivers supercooled water, - 60 laden with small ice crystals called frazil, to the underside of the adjacent sea ice cover (Foldvik - 61 and Kvinge, 1974; Lewis and Perkin, 1986). Buoyancy forces cause thin disks of frazil, or platelets, - 62 to rise and settle beneath the underside of the sea ice cover and, provided the flux of loose crystals - 63 is large enough (Dempsey et al., 2010), a sub-ice platelet layer develops. The upper portion of this - 64 layer is incorporated into the overlying sea ice cover by freezing in the interstices (Jeffries et al., - 65 1993; Smith et al., 2001). Fig. 1: Conceptual model for a grain produced from 2-dimensional sampling of 3-dimensional ice crystal with c-axis, **c** , using a horizontal thin section. **z** ˆ is a unit vector in the _z_ direction. _−_ **x** ˆ corresponds to the direction of north. _ϕ_ = c-axis tilt: the angle between the c-axis and vertical. _θ_ = c-axis azimuth: the angle between the horizontal projection of the c-axis and north. In our analysis _z_ is positive downward and _z_ = 0 corresponds to the surface. > 66 Incorporated platelet ice presents a variety of crystallographic fabrics when viewed in thin sec67 tion, and for our purposes it is useful to distinguish three sub-categories; bladed, in which the 3 - 68 boundaries between grains are sharp and angular (Fig. 2(a); Eicken and Lange (1989), Gow et al. - 69 (1998), Tison et al. (1998)); draped, in which grain boundaries exhibit millimeter scale serrations - 70 (Fig. 2(b); Tison et al. (1998)); or resumed columnar, where large grains exhibit the lamellar tex- - 71 ture characteristic of columnar ice (Fig. 2(c); Dempsey et al. (2010)). Resumed columnar texture - 72 develops as the supply of platelets from the ocean is reduced and sea ice growth proceeds subject to - 73 geometric selection again. Growth of crystals oriented with c-axes (optic axes) close to the horizon- - 74 tal is favored due to the reduced growth rate parallel to the c-axis (Hillig, 1959). This “resumed” - 75 columnar ice type is distinguished from “traditional” columnar ice, which is produced by geometric - 76 selection amongst granular ice crystals, typically at shallow depths in the sea ice cover. Fig. 2: Comparison of platelet ice fabrics. (a) Bladed and (b) draped platelet ice are shown in vertical thin sections. (c) Resumed columnar ice is shown in a horizontal section. All thin sections share the same scale. ### 77 ## **2.1. Study area** - 78 Sea ice samples investigated in this work were collected during a survey of McMurdo Sound, Antarc- - 79 tica conducted during the austral summer of 2007. Ice cores were extracted from six locations along - 80 an east–west transect that traversed the annual sea ice across a distance of 25 km. A detailed - 81 treatment of the textural variability observed in the ice collected by this survey is presented in 82 Dempsey et al. (2010). - 83 Previous surveys of the Sound (Gow et al., 1998; Jeffries et al., 1993; Jones and Hill, 2001; 4 - 84 Leonard et al., 2006; Paige, 1966) have yielded multiple observations of incorporated platelet ice, - 85 which comprised up to 50% of the sea ice thickness in some locations. Platelet ice is also a feature - 86 of other regions of Antarctica (e.g., the Weddell Sea (Eicken and Lange, 1989), Hells Gate Ice - 87 Shelf (Tison et al., 1998)). In this work we examine the growth of incorporated platelet ice by the - 88 preparation of a series of horizontal thin sections in close vertical proximity. This is complemented - 89 by observations of platelet clusters grown on cables hanging in the water column (see Fig. 3), which - 90 illustrate some of the 3-dimensional growth forms observed in the 2007 ice cores. Several features of 91 the growth of platelets attached to cables are similar to ice crystal growth within the sub-ice platelet - 92 layer prior to its consolidation by the overlying ice cover. For instance, in both environments a 93 supply of supercooled water acts as a heat sink for further growth of existing crystals (Leonard - 94 et al., 2011). Further, while crystal growth attached to the submerged cable are likely to be less 95 constrained by the presence of neighboring platelets, crystal–crystal growth interactions evidently - 96 occur (Fig. 3). # 97 **3. Method** - 98 **3.1. Sample preparation** - 99 Prior to their extraction, handheld GPS devices were used to mark ice cores with a true north - 100 reference direction. Following the removal of a core in several pieces, this reference mark was - 101 transferred along the length of the core. At our chosen sample location two cores were extracted - 102 in this manner and returned to a cold lab at New Zealand’s Scott Base for further preparation and 103 analysis. 5 Fig. 3: Intersections of two platelets grown at an angle to one another. (a) Original photo and (b) intersecting platelets highlighted. We propose this as a 3-dimensional representation of the crystals R and G reconstructed in Fig. 9. Photo courtesy of Dr. Craig Stevens, NIWA, New Zealand. 104 The first core was cut lengthwise to produce a series of vertical sections, approximately 10– 105 20 mm thick. In transmitted light these thick sections provide an indication of the distribution of 106 granular, columnar and incorporated platelet ice, although it is not possible to distinguish between 107 the three platelet sub-categories from these samples. At a selection of depths vertical thin sections 108 were produced by reducing the thickness of the thick sections to less than 1 mm on a microtome. 109 Such thin sections, when viewed between crossed polarizers on a universal stage (Langway, 1958), 110 provide a 2-D projection of individual ice crystals (see Fig. 1). A series of horizontal thin sections, 111 spaced approximately 9 mm vertically, was prepared from the second core. These were photographed 112 between crossed polarizers on a universal stage. ## 113 **3.2. C-axis measurement** 114 Ice grains in horizontal thin sections are distinguished from their neighbors by the orientation of 115 their c-axes. Following Langway (1958) we measure for each crystal; (i) the c-axis azimuth, _θ_ , 116 defined as the angle of the c-axis projected in the horizontal plane and measured clockwise from the 117 north reference mark; and (ii) tilt, _ϕ_ , defined as the angle between the c-axis and the vertical axis. 6 - 118 In this study we have measured c-axis parameters for all grains with an area greater than 20 mm2 - 119 (see Fig. 8(b), section 10 for the smallest grain used in this experiment). While grains below this 120 threshold are more frequently encountered, they seldom belong to crystals with a vertical extent - 121 greater than 9 mm and therefore do not appear in adjacent sections. Further, these small crystals, - 122 while numerous, comprise only a small proportion of the total sea ice volume. Fig. 4: Construction of vertical thin section. (a) Grain boundaries for crystal G, observed in sections 2–10. Intersections of a vertical plane rotated 10_◦_ from crystal c-axis (dashed line) with the grain boundary (solid outline) are marked. The depth of each horizontal thin section is marked. (b) Grain boundary intersections with depth. Note, _x_ = 0 corresponds to the core axis. (c) Spline interpolation through grain boundary intersections. 123 A single crystal of ice, providing it is large enough, may end up sampled by two or more horizontal 124 sections. Grains from adjacent thin sections are judged to have originated from the same ice crystal 125 based on similarity of c-axis orientation and spatial position. Langway (1958) estimates errors in 7 126 measuring _θ_ and _ϕ_ on a universal stage as _±_ 5_◦_ , which provides a useful bound in judging c-axis 127 agreement between vertically adjacent grains. 128 **3.3. Digital analysis** 129 Digitization of thin section images is a necessary step in the reconstruction of a 3-dimensional volume 130 of ice. In previous studies digitized images have been processed to obtain brine feature shape and 131 size (Cole et al., 2004), and automated image analysis of thin sections has been used to provide 132 grain-boundary density and grain cross-sectional area (Durand et al., 2006; Eicken, 1993; Eicken et 133 al., 1994; Gough et al., 2012; Wilen et al., 2003). Digitization also facilitates the calculation of grain 134 parameters and implementation of various least squares fitting methods (Eicken, 1993). Grains are 135 rarely blemish-free and often display brine inclusions, such that care must be taken in designing 136 grain boundary edge detection algorithms. In this study grain boundaries were digitized manually. Fig. 5: Evidence for nucleation of discrete layers on the basal plane of platelet crystals grown attached to submerged cables. (a) Original image is presented along with (b) highlighted layer boundaries. The crystal of interest is a multi-layered disk roughly in the plane of the picture. Photo courtesy of Dr. Craig Stevens, NIWA, New Zealand. 8 Fig. 6: Demonstration of ellipse fitting to two sample grains. Solid contours mark outline of grain boundaries. Dashed outline shows the ellipse fitted through the grain boundary that minimizes the least squares error between the digitized boundary and approximated shape. Solid and dashed arrows are respectively measured and fitted projections of c-axis directions onto the horizontal plane. 137 We build a partial reconstruction of a 3-dimensional ice crystal by tracking its presence in a 138 series of adjacent horizontal thin sections. From this reconstruction we derive particular aspects of 139 its growth and interaction with neighboring crystals. 140 In Fig. 4 we consider the intersection of a reconstructed crystal with a hypothetical vertical 141 observation plane, oriented at some angle from the crystal’s c-axis. This process is analogous to the 142 extraction of a vertical thin section of ice along the same orientation. Due to the coarse nature of 143 this thin section study, grain boundaries cannot be resolved vertically to an accuracy better than 144 9 mm. Spline interpolation between the available points produces a first order approximation to 9 145 the vertical grain boundary. 146 If ice growth was unconstrained, discoid crystals would result because growth in the basal plane is 147 kinetically favored relative to growth parallel to the c-axis (for example see Fig. 5). These crystals are 148 approximated as ellipsoids in numerical modeling studies of platelet ice fabrics (Dempsey, 2008). The 149 intersection of a discoid crystal with a horizontal plane, for instance during thin section sampling, 150 yields grains that are approximately elliptical in shape. This simplified crystal shape does not 151 account for dendritic growth perturbations (such as shown in Fig. 5) or interactions with adjacent 152 crystals, however we expect an ellipse to provide a useful, first-order fit to a grain outline. In Fig. 6 153 we show the process by which an ellipse is fitted to the outlines of two grains in a digitized thin 154 section image. This process uses an algorithm that minimizes the least squares error between pixels 155 comprising the grain boundary and the equation of the fitted ellipse. The minor axis of the ellipse 156 approximates the horizontal projection of the c-axis, and is thus a measure of _θ_ . The major axis of 157 the ellipse lies approximately within the basal plane, along which ice growth is kinetically favored. 158 The concept of a grain’s minor axis closely corresponding to the horizontal projection of its 159 c-axis is not novel. In fact, a common approach when making c-axis measurements on a universal 160 stage is to initially align a grain as if its c-axis was perpendicular to its long dimension, i.e., its 161 major axis. Our method attempts to formalize this process to estimate c-axis orientations directly 162 from a thin section photograph. We also investigate the error associated with ellipse fitting, as a 163 function of grain size and shape, to establish the utility of this technique. ### 164 # **4. Results and discussion** 165 ## **4.1. Overview and selection of core for high resolution study** 166 In this work we study platelet fabrics that are typical of the sea ice on the eastern side of McMurdo 167 Sound (Dempsey et al., 2010; Gough et al., 2012; Leonard et al., 2006). Samples were extracted from 168 a site (coordinates: [165_◦_ 06.678 E, 77_◦_ 40.070 S]) in November and December of 2007 (Dempsey 169 et al., 2010). An initial inspection of the first core from the site indicated that the ice fabric was 170 primarily columnar for the top meter, punctuated at 0.5 m by a small length of incorporated platelet 171 ice (see Fig. 7). From 1 m depth draped platelet fabric is observed and continues to a depth of 172 1.6 m. Bladed platelet fabric is observed at the base of the 2.1 m core and no sub-ice platelet layer 10 - 173 was encountered at the time of sampling (1 December 2007). However, the absence of a sub-ice 174 platelet layer at the time of sampling does not preclude its presence at previous times during the 175 winter. The appearance of large platelet crystals incorporated into the ice cover indicates in situ 176 growth of these crystals. Gough et al. (2012) have demonstrated that when there is no sub-ice - 177 platelet layer smaller crystals disrupt geometric selection, while the presence of this layer results in - 178 larger platelet ice crystals in the sea ice fabric. Fig. 7: Sea ice composition at 165_◦_ 56.784 E, 77_◦_ 39.500 S, adapted from Dempsey et al. (2010). The lower left vertical section, marked _α_ , was chosen for further study by high resolution thin sectioning. 179 Serrated grain boundaries, a term we use here to describe millimeter scale perturbations along 11 180 a grain boundary, is observed in a vertical section of draped platelet ice at a depth of 1.6 m. As 181 a partial 3-dimensional crystal structure might illuminate the growth of draped platelet fabric and 182 serration along the grain boundaries, this depth interval was chosen for detailed study. We note 183 that a high resolution thin section study might also be applied at a depth of _∼_ 1.2 m, as the vertical 184 section at this depth (Fig. 7) indicates serrated grain boundaries at least as pronounced as those 185 at 1.6 m. However, grains at 1.6 m show greater vertical extent, and thus horizontal sectioning at 186 this depth is likely to image the 3-D crystal forms in greater detail. 187 ## **4.2. Reconstructions and insights** 188 Ten horizontal thin sections, numbered 1 to 10 with increasing depth, were prepared from the 189 second core at a depth of 1.55 to 1.63 m. Vertical thin sections were prepared immediately above 190 and below the horizontal sections and were cut along a plane that includes the north–south axis. 191 These sections were imaged between crossed polarizers and are presented in Fig. 8(a–b). 12 Fig. 8: (a) Upper bounding vertical section and upper five horizontal sections of the high resolution thin sectioning study. Note grains in adjacent thin sections belonging to the same 3-dimensional crystals are not required to be in the same color. Dashed line in horizontal section 1 marks the axis of the upper bounding vertical section. North is marked on each horizontal section by a solid dash. Grid is 1 cm _×_ 1 cm and has not been aligned along the North azimuth. (b) Lower five horizontal sections and lower bounding vertical section of the high resolution thin sectioning study. Dashed line in horizontal section 10 marks the axis of the lower bounding vertical section. Dashed circle in horizontal section 10 indicates the smallest crystal digitized in this study. Several grains have been marked in the lower horizontal and vertical section and are referred to in the text. 192 From the horizontal sections we observe that the ice structure is dominated by several large 193 crystals containing evenly spaced rows of brine pockets. Many of these crystals have planar areas 194 greater than 10 cm2 , and present in all ten horizontal sections and have been identified in the upper 195 and lower vertical sections on the basis of relative position. These crystals, which occur below the 196 onset of incorporated platelet ice, have c-axes that lie close to the horizontal plane and, along with 197 observations of their lamellar texture, we classify them as resumed columnar (Dempsey et al., 2010). 198 In addition, a number of isolated crystals are observed, with a variety of c-axis tilts, which suggests 199 that crystals originating in the water column are attaching themselves at random orientations to 13 200 the base of the sea ice. 201 C-axis measurements made on grains from the thin sections identify 108 separate crystals in the 202 400 cm3 volume of core. These were sampled 249 times by the ten thin sections (which includes only 203 those grains with area larger than 20 mm2 ). Thin sections were photographed and grain boundaries 204 digitized as outlined in Section 3.3. 205 Reconstructions of several extensive crystals raise interesting questions regarding the nature of 206 growth in the sub-ice platelet layer. Three reconstructed crystals are presented in Fig. 9, referred to 207 here by their shading red (xtitR), green ( _G_ ) and blue ( _B_ ). _G_ is laterally extensive, well established 208 in section 1, and is a dominant feature through to section 10. _B_ is extensive in section 1 and trends 209 eastward with depth such that it is nearly absent from section 6. _R_ first appears in section 2 and 210 persists to section 10, at which depth it is a prominent feature of the ice. 211 Of particular interest in this reconstruction is the initial appearance of crystals _B_ and _R_ . Rather 212 than appearing as a single grain, which is typical of the majority of crystals in this study, each crystal 213 initially appears in two disconnected locations, i.e., the grain is not continuous. In the sections below 214 these initial appearances (one below for _B_ and two for _R_ ) the disconnected grains merge, suggesting 215 that the upper surface of the crystal is characterized by two ‘prongs’. Furthermore, having become 216 continuous in section 4, _R_ becomes disconnected once more in section 6 and again in sections 9 and 217 10. 218 We identify three possible scenarios for the appearance of such a pronged crystal structure 219 (see Fig. 10(a)–(c)). First (Fig. 10(a)), two platelet crystals are independently advected to the 220 underside of the sea ice where they settle with identical c-axis orientations. Growth of these two 221 crystals downward and laterally causes their surfaces to meet and fuse into a single larger crystal. 222 However, the likelihood of two platelets settling with imperceptibly different c-axis orientations is 223 considered negligible and this scenario is rejected. 224 Alternatively, the crystal may have originated within the water column with the pronged struc225 ture already grown. Advection to the sub-ice platelet layer and subsequent consolidation of ice 226 around the crystal would produce the observed structure. However, observations of platelets in the 227 water column do not indicate the presence of such structures at the required magnitude, i.e., prongs 228 that extend 10–20 mm from the body of the crystal. - 229 Instead, we favor a third scenario involving advection of a crystal into the sub-ice platelet layer 14 - 230 and subsequent in situ growth. Once the crystal is settled, in addition to ice growth directed 231 downward, we postulate growth upward into two pre-existing voids produced naturally by the 232 porous ice matrix (see Fig. 10(g)–(i)). Such voids might originate as grain boundary grooves, in 233 which the basal planes of two ice crystals diverge downward and a gap is created between them. 234 The exposed surfaces within the groove are crystallographically flat and the void is thus stable until 235 a supercooling of _≈_ 0.03 K is achieved (Hillig, 1959). The advected crystal then acquires a pronged 236 shape through upward directed growth along its basal plane, for which the required supercooling is 237 less than that for growth on the groove walls. While we have not extracted sufficient information 238 from the ice to establish the validity of such a scenario, the case for upward directed growth is - 239 compelling. Video images of the sub-ice platelet layer (Smith et al., 2001) suggest a sufficient 240 proportion of void space and platelet complexity to accommodate such growth. 15 Fig. 9: Three-dimensional reconstructions. Three extensive resumed columnar crystals are labeled ( _R_ ), ( _G_ ) and ( _B_ ). The core boundary is marked by solid circles and has been oriented with north along the dashed line. The vertical axis has been scaled by a factor of three for clarity. C-axis azimuths measured on the universal stage — _G_ = 353_◦_ , _B_ = 122_◦_ , _R_ = 342_◦_ . 241 The reconstruction presented in Fig. 9 also shows an unusual interaction between crystals _G_ 242 and _R_ , which appear to have grown competitively, the growth of one impinging on and intersecting 243 the other. However, rather than consistent dominance of one crystal over the other, roles are 16 - 244 interchanged at different depths, i.e. _G_ intersects _R_ in sections 2, 3 and 4, then _R_ briefly intersects - 245 _G_ in section 5, before _G_ once more regains dominance in sections 6 and 7. Finally, for the remaining 246 sections 8, 9 and 10 _R_ is once more dominant and intersects _G_ . Complementing this observation, we 247 present photographic evidence from platelet clusters grown on submerged cables. Fig. 3 shows two 248 platelets intersecting at _≈_ 30_◦_ to each other. Thin sections prepared in the plane of this photograph 249 would sample this intersecting behavior and yield grain structures similar to those observed for _G_ 250 and _R_ , although there is no suggestion of interchanging dominance here. These observations provide 251 further testimony of platelet growth within an environment constrained by adjacent crystals. 252 ## **4.3. Dependence of grain shape on sample plane** 253 Following Section 3.3, reconstructions of vertical thin sections were prepared for three prominent 254 crystals, _R_ , _G_ and _B_ , for sample planes oriented at 0, 45 and 90_◦_ from the crystal’s c-axis (Fig. 11). 255 For crystal _R_ sampling at orientations between 0 and 70_◦_ ? yields a narrow outline that is stretched 256 in the vertical dimension. This form is qualitatively similar to several grains ( _G2_ and _G3_ ) in the 257 lower vertical section of Fig. 8(b), identified as resumed columnar. At higher angles of sampling the 258 outline thickens laterally as the intersecting plane cuts the crystal sub-parallel to the basal plane. 259 The resulting form is now more similar in shape to grain _G1_ in the lower vertical section of Fig. 8(b) 260 and the grains in section _α_ in Fig. 7, identified as a draped platelet fabric. 261 Crystal _G_ shows similar behavior to _R_ such that for a thin section oriented perpendicular to 262 the c-axis, the grain occupies the width of the section. However, there are several grain boundaries 263 within the larger outline (data points within the interpolated grain boundary), which suggests the 264 grain is not continuous throughout. These results suggest that grain shape and boundary features 265 may be related to the plane of observation, particularly when it is oriented close to the basal plane. 266 Consequently, care must be exercised in textural analysis of grain forms in vertical sections as a 267 wide variety of 2-D fabrics may be derived from a set of similar 3-D crystal structures. For instance, 268 in this work we have distinguished between grains of draped platelet and resumed columnar ice. 269 However Fig. 4.3 indicates that these differences may be superficial and largely a product of the 270 particular plane of observation. 17 Fig. 10: Three proposed mechanisms for development of a pronged crystal structure. All three involve an initial advection step followed by growth of the interface, marked by a gray solid line, and growth of the crystal, marked by a black solid line. In the final step of each mechanism the outline of the interface and crystal prior to growth is marked by a dashed outline. 271 ## **4.4. Fit of ellipses** 272 In Section 3.3 we proposed that a discoid ice crystal sampled by a horizontal thin section would yield 273 a grain whose boundary, to a first approximation, could be described by an ellipse (see Fig. 6). For 274 each of the 249 grains in this study, an ellipse of eccentricity, _e_ , was fitted to its boundary, and the 275 angle between the minor axis and north, _θ__′_ , obtained. Our conceptual model for discoid ice crystals 276 predicts the minor axis to be oriented along the c-axis azimuth, _θ_ , and consequently we define 277 the deviation between the fitted and observed azimuth, ∆ _θ_ = _θ − θ__′_ . Using bootstrap sampling 278 methods (Efron and Tibshirani, 1986) the mean and standard deviation of this distribution of _θ_ 279 were calculated and bounded by 95% confidence intervals. These are, respectively, _−_ 2 _._ 0_◦_ within 18 280 an interval of [ _−_ 4 _._ 6 2.6] and 28.9_◦_ within an interval of [24.9_◦_ 34.1_◦_ ]. As ellipse fitting does not 281 provide a measure of c-axis tilt, _ϕ_ , no distinction can be made between a grain of _θ_ or _θ_ + 180_◦_ . 282 Consequently, _θ_ lies in the range _−_ 90 to 90_◦_ . 283 The accuracy of this method depends on the extent to which a given grain expresses its crystal284 lographic properties in its geometric features. For instance, greater confidence would be expected 285 for an ellipse fitted to a grain of particularly pronounced elongation (parameterized by the eccen286 tricity, _e_ ). Similarly, for larger grains an ellipse fit will be less influenced by small deviations to the 287 boundary, e.g., random growth perturbations or crystal impingements. These ideas are quantified 288 in Fig. 12(a–b), which shows the error of the ellipse fitting method as thresholds based on grain 289 area (Fig. 12(a)) and eccentricity (Fig. 12(b)) are applied to the sample. Discarding smaller grains 290 results in a reduction in error (see Fig. 12(a)), although a sample size anomaly causes an increase 291 for a threshold between 120 and 280 mm2 . Imposing a threshold on grain elongation also improves 292 the accuracy of the method. 293 Fig. 12(c–d) demonstrates reduction in error that can be achieved by applying arbitrary thresh294 olds of area greater than 300 mm2 and eccentricity greater than 0.87. From the original sample of 295 249 grains, 47 exceed the chosen thresholds, and the error of the ellipse fitting method is now 6.0_◦_ , 296 within 95% confidence bounds of [4.7_◦_ 8.6_◦_ ]. 297 Fig. 12(c) plots the unfiltered sample of observed c-axis azimuths, _θ_ , versus the values predicted 298 by the ellipse fitting method, _θ__′_ . The raw data exhibits considerable scatter about the 45_◦_ line, 299 which represents a perfect match between _θ_ and _θ__′_ . However, in applying thresholds we observe 300 that the less accurate data points are removed and the prediction improved for the remaining 301 grains (Fig. 12(d)). These two datasets, unfiltered versus strongly filtered, demonstrate the implicit 302 trade-off associated with this method; error reduction is achieved at the expense of data exclusion. 19 Fig. 11: Vertical single crystal reconstructions from horizontal thin sections. Crystals _R_ , _G_ , and _B_ are reconstructed for vertical planes oriented 0_◦_ , 45_◦_ and 90_◦_ from crystal’s c-axis. Black dots indicate grain boundary intersections, which are interpolated using splines to produce a grain boundary for the vertical section. In some instances there are more than two grain boundary crossings for a plane through a single section and these are represented as black dots internal to the grain boundary interpolation. 20 Fig. 12: Accuracy of the ellipse fitting method as threshold values are imposed to (a) area and (b) eccentricity. The error (solid line) and a 95% confidence bounds (dotted line) are superimposed on histograms of relative frequency distributions to provide an indication of the sample proportion above and below a chosen threshold. (c) Observed c-axis azimuth plotted against the value yielded by the ellipse fitting method. The distance of each point from the 45_◦_ line (dashed) indicates the error of the fit. The full sample of 249 crystals is presented in (c) and the reduced sample of 91 grains with thresholds of A _≥_ 300 mm and _e ≥_ 0 _._ 87 is presented in (d). 303 Although this method does not match the accuracy of direct measures of the c-axis azimuth 304 performed on a universal stage ( _±_ 5_◦_ in Langway (1958)), its principle advantage is its low cost and 305 hands off qualities. The method requires only a digital photograph of the thin section and a means 306 of identifying grain boundaries. Machines that measure c-axis orientations automatically, while 307 available (Eicken, 1993; Yun and Azuma, 1999), are expensive, while the method presented offers 308 a first order measure of c-axis azimuth with increased confidence in accuracy for large, elongated 309 grains. The technique is also useful in circumstances where original ice cores are unavailable, 310 but sufficient documentation of the ice remains. For example, it would be possible to undertake a 311 retrospective analysis of historical datasets providing that photographic images of core thin sections 21 can be obtained. 312 ### 313 ## **4.5. Grain boundary serration** 314 Serrated grain boundaries are a common feature of incorporated platelet ice (Dempsey et al., 2010; 315 Gow et al., 1998; Jeffries et al., 1993) and are defined here as millimeter scale perturbations along 316 the grain boundary. Serration is observed on grains of draped platelet fabric in vertical sections 317 in Fig. 8(a–b). One grain boundary in particular is identified from the lower vertical section of 318 Fig. 8(b), exhibiting seven such perturbations (see Fig. 13). Crystals _G2_ and _G3_ are co-identified 319 in horizontal section 10 and the lower vertical section (Fig. 8(b)), due to the near proximity of these 320 sections. The lower vertical thin section was cut along the north–south axis, while the c-axes of _G2_ 321 and _G3_ lie close to the north–south plane. Consequently, interpretation of the grain boundary is 322 likely to be simplified because the c-axes of _G2_ and _G3_ lie approximately in the plane of Fig. 13. 323 The distortion of grain shape caused by sampling along a plane close to the basal plane, as described 324 in Section 4.3, is therefore minimized. 22 Fig. 13: Serrated grain boundary observed between crystals _G2_ ( _θ_ = 359_◦_ , _ϕ_ = 82_◦_ ) and _G3_ ( _θ_ = 350_◦_ , _ϕ_ = 70_◦_ ). Dashed lines indicate the average trend of seven serrated segments and the overall trend of the grain boundary and angles are measured clockwise from the horizontal. Grid is 1 cm _×_ 1 cm. Orientations of the basal planes and c-axes for _G2_ and _G3_ are also shown. 325 The c-axis tilts of grains _G2_ and _G3_ were measured using the universal stage and are _ϕ_ = 82_◦_ 326 and _ϕ_ = 70_◦_ , respectively. The mean angle of the grain boundary, measured clockwise from the 327 horizontal, is 71_◦_ (see Fig. 13), while the steeper segments between the serrations have an average 328 angle of 81_◦_ to the horizontal. We note a close correspondence between these observed angles and 329 the c-axis tilts, _ϕ_ , in other words, serrations develop their long axes along the direction of the basal 330 plane. Based on this observation we propose a mechanism of growth by layer nucleation within 331 grain boundary grooves (see Fig. 14). 332 Where two crystals grow adjacent to one another such that their basal planes diverge downwards, 333 a grain boundary groove forms comprising a steeply dipping surface (grain _G2_ ) and an opposing 334 overhanging surface (grain _G3_ ). The exposed surfaces are crystallographically flat and no growth 335 can occur on them until a supercooling of _≈_ 0.03 K is achieved (Hillig, 1959). As the ice–water 336 interface advances and the groove deepens, the temperature at the root of the groove lowers in 337 thermodynamic equilibrium with the sea ice temperature gradient (Wilen and Dash, 1995). When 23 338 the root is supercooled to _≈_ 0.03 K, a growth perturbation develops on the basal plane of the 339 steeper crystal. The data here are not sufficient to establish cause for the perturbation to form 340 on this crystal, as opposed to the overhanging one; however, the steeper temperature gradient in 341 _G2_ , compared with _G3_ , might favor basal growth on the steeper crystal. Alternatively, the non342 symmetric geometry of the groove might favor more efficient convective removal of salt from the 343 basal surface of the steeper crystal. Regardless, the growth perturbation seeds a new layer that 344 grows rapidly toward the ice–water interface. At the root of the groove some growth occurs on 345 the overhanging crystal and a serration is formed. Thus, the grain boundary groove is filled by a 346 series of stacked layers, each tilted at the angle of the steep face, but stacked such that the crystal 347 they comprise trends at the angle of the overhanging face. The method described has features in 348 common with dendritic growth in metallic alloys discussed by Rappaz and Gandin (1993), although 349 we emphasize that the mechanism, as presented here, is specific to serration on boundaries between 350 crystals that are crosscut approximately perpendicular to the basal plane. Where crystals are 351 crosscut much closer to the basal plane, a 3-D extension of the mechanism in Fig. 14 would be 352 required to account for grain boundary serration. 353 Evidence for layer nucleation is observed in photographs of platelets grown attached to sub354 merged cables in supercooled water (see Fig. 5). The broad platelet occupying the bottom left of 355 the photograph shows several concentric boundaries on the basal plane that follow the approximate 356 contour of the platelet edge. We suggest that these are layers of discrete thickness growing on the 357 smooth basal surface, and that a new layer seeds each time the required supercooling is achieved 358 on the basal plane. In McMurdo Sound, such supercooling persists in the upper meters of the 359 water column through much of the year (Leonard et al., 2011; Mahoney et al., 2011). Cable-grown 360 platelets are shown in an observation plane approximately perpendicular to the basal plane in Fig. 3; 361 stacks of several discrete platelets are evident in this image. 24 Fig. 14: Proposed mechanism for growth of serrated grain boundaries. (a) A groove develops through divergent growth of crystals _G2_ and _G3_ with c-axes and tilt angles shown. Supercooling within the groove is below the threshold, _Tnuc_ , required for nucleation of a new layer on _G2_ . (b) Supercooling within the groove increases with further growth until a new layer is nucleated. (c) The new layer grows rapidly along its basal plane. (d) Growth on _G3_ fills the void created between the new layer and the root of the groove. (e) Growth of _G2_ and _G3_ continue until supercooling once more reaches the threshold for nucleation of a new layer. (f) A serrated grain boundary develops through repeated cycles of steps (a)–(e). 25 - 362 Grain boundary serration is directly observed in vertical thin sections but its presence can also 363 be inferred in horizontal sections. In Fig. 15 we show that a serration is characterized by three 364 grain boundary intersections when considering a horizontal transect through the perturbation. A 365 single intersection is observed for transects elsewhere along the grain boundary. The presence of 366 grain boundary serration is thus inferred in horizontal sections by identifying similar sets of three 367 adjacent boundary intersections. Several such instances have been identified in the ten horizontal 368 sections in Fig. 8(a–b), of which two are presented in Fig. 15. These take the form of small, isolated 369 satellite grains embedded in a neighboring crystal. These inclusions are typically elongated with a 370 long axis parallel to the main grain boundary and their limited lateral extent provides some insight 371 into the 3-dimensional character of grain boundary serration. 26 Fig. 15: Demonstration of the characteristic grain sequence for serrated sections in vertical and horizontal thin sections. The upper panel identifies such a sequence for grains a and b in a vertical section. The image is magnified (note the color of b has been artificially modified to contrast with a) and a thin slice shows the ice that would be sampled by a horizontal thin section at this depth. In the lower panel, a similar grain sequence between grains a_′_ and b_′_ is identified within a horizontal section, and the ice that would be sampled by a vertical section chosen at a fortuitous location is shown. On the far right is shown the grain sequence sampled by the intersecting horizontal and vertical thin sections, for both the upper and lower panels. Note that grains a and b, and a_′_ and b_′_ , do not correspond to each other. 372 The proposed growth mechanism for grain boundary serration requires that grain boundary 373 grooves, once formed, are not impinged upon by other ice crystals, i.e., the grooves remain open. 374 The serration identified between crystals _G2_ and _G3_ demonstrates this behavior over an ice depth 375 of 60 mm. For late-season ice growth rates of 10 mm/day (Purdie et al., 2006) this suggests several 376 days of continuous growth within the groove, uninterrupted by the advection of new ice crystals. The 27 377 inferred presence of grain boundary serration throughout the entire high resolution thin sectioning 378 study, representing an ice depth of 150 mm, suggests that either the flux of ice crystals from the 379 ocean was small enough to have little crystallographic influence during the period that this ice grew, 380 or that a sub-ice platelet layer existed below the groove and blocking ice crystals originating in the 381 ocean from entering the groove. ### 382 # **5. Summary of results** 383 A high resolution thin sectioning study was used to gather geometrical and crystallographic data of 384 an assemblage of incorporate platelet ice crystals. From these data we have reconstructed individual 385 crystals, and applied geometric fitting techniques based on ice growth kinetics and expected crystal 386 forms. 387 As a method of measuring c-axis azimuth orientation, _θ_ , ellipse fitting has demonstrated tolerable 388 error providing it is applied to a restricted set of crystals. For instance, for crystal grains with area 389 greater than 300 mm2 and eccentricity greater than 0.87, the method is accurate to a standard 390 deviation (parameterizing the error) of 6_◦_ , with decreasing confidence for predictions made for 391 smaller, less elongated grains. 392 Reconstruction of vertical sections oriented along several planes illustrate the variety in grain 393 shapes derived from the same crystal, all of which are valid 2-D representations of the 3-D structure. 394 Where the angle between the basal plane and thin section plane is small the grain produced is broad 395 and exhibits minimal elongation. Increasing the angle permits the thin section to sample more of the 396 c-axis/basal plane growth anisotropy and consequently the grain appears elongated in the vertical 397 direction. 398 3-dimensional crystal reconstructions, produced by stacking grain images vertically, are a useful 399 tool for visualizing individual growth forms and crystal interactions within the sub-ice platelet 400 layer. From these reconstructions we have observed pronged shaped crystals, which suggest an 401 upward directed growth, presumably driven by heat conduction to the atmosphere. In addition, 402 we observe two crystals whose growth impinges upon and intersects one another, which has been 403 further correlated with observations of platelets growing freely on a cable. 404 Serrated grain boundaries have been identified along grains of resumed columnar ice in vertical 28 - 405 thin sections and their presence inferred in several of the horizontal sections. Applying geometrical - 406 arguments to the angles along these boundaries, and furnished by measurements of their c-axes, we - 407 have proposed a method of growth by layer nucleation in grain boundary grooves. This mechanism - 408 is consistent with concentric layer structures observed in images of freely growing platelets. Unin- - 409 terrupted action of this mechanism over a depth in excess of 100 mm suggests that the platelet flux - 410 supplied by the ocean is significantly reduced during the period this ice grew, or that a protective - 411 sub-ice platelet layer was in place. ### 412 # **6. Conclusion** 413 The preparation of thin sections of sea ice is a common method for interrogating ice structure and 414 making inferences on the conditions of its growth. However, this mode of sampling is inherently 415 restricted to providing a 2-dimensional slice of 3-dimensional crystal structures. 416 The thin sectioning study presented here therefore serves several purposes. First, production of 417 3-D grain boundary data has permitted a direct examination of the interactions between adjacent 418 crystal surfaces in a sub-ice platelet layer environment. For example, the data demonstrate compet419 itive growth between two large crystals intersecting one another over a depth of several centimeters. 420 It has also enabled us to propose a layer nucleation mechanism for the production of serrated grain 421 boundaries, which is present in both horizontal vertical sections. 422 Second, comment can be offered on the accuracy of thin section interpretation in the context of 423 the 3-D crystal structure. For instance, we have shown that the dimensional properties of grains 424 and grain boundaries vary as a function of vertical thin section orientation. Such limitations are a 425 natural consequence for a 2-D rendering of 3-D data. This underscores the importance of a cautious 426 approach to thin section analysis if misinterpretation is to be avoided. 427 Finally, an inferred correlation between elongation and c-axis orientation has been shown to 428 be appropriate for large, established grains; but for smaller specimens direct measurement on a 429 universal stage or automatic fabric analyzer is the only accurate technique. However, in the absence 430 of the original ice samples, for instance, when analyzing historical datasets, the geometric technique 431 may offer the only avenue for extracting crystallographic information. 29 ### 432 # **Acknowledgments** - 433 This work was funded by the Foundation for Research, Science and Technology, New Zealand, a 434 New Zealand Post Antarctic Scholarship and a University of Otago Postgraduate Award. Logistical 435 support in the field was provided by Antarctica New Zealand and Johno Leitch. 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