Snow Crystals - Kenneth G

Snow Crystals - Kenneth G. Libbrecht -

Published 2019, by Kenneth G. Libbrecht

I wrote this book for purposes of research, scholarship, and education only. Regarding all materials herein that I did not create, I do not intend to derive any income from these materials, nor will I authorize their use in any derivative publications, products, or other activities. By my understanding, this means that the fair-use doctrine in copyright law allows me to reproduce published material without express permission from the copyright holder (because I am using the materials in a transformative manner that will not divert any income from its creators). To the best of my abilities, I have fully cited all images or other materials that I did not create. In most cases, these materials were already freely available on the internet.

You are welcome to reproduce (without express permission) any materials in this book that I created in any non-commercial pursuit of research, scholarship, or education. If you are interested in any images or other materials for commercial or other purposes, please contact me at [email protected].

Snow Crystals

Contents ...... 2

Forward ...... 11

1. Snow Crystal Science ...... 15 1.1 Complex Symmetry ...... 17 From Clouds to Crystals ...... 18 Faceting and Branching ...... 20 1.2 A Brief History of Snow-Crystal Science ...... 23 Early Observations ...... 24 Emerging Science ...... 25 Microscopic Snowflakes ...... 26 Snowflake Photography ...... 26 Crystallography ...... 28 Attachment Kinetics ...... 29 The Morphology Diagram ...... 30 Crystal Dendrites ...... 32 Quantitative Snow Crystals ...... 35 1.3 Twenty-First Century Snowflakes ...... 35 Reductionism to Holism ...... 36 The Road Ahead ...... 37 1.4 Why Study Snowflakes? ...... 40 1.5 No Two Alike? ...... 42

2. Ice Crystal Structure ...... 45 2.1 The Phase Diagram ...... 47 2.2 Ice Crystallography ...... 48 Hexagonal and Cubic Ice ...... 49 Lattice Projections ...... 51 Terrace Steps ...... 53

2.3 Surface Premelting ...... 54 2.4 Ice Energetics ...... 56 Bulk Energies ...... 56 Vapor Pressure and Related Quantities ...... 58 Surface Energies ...... 58 Terrace Step Energies ...... 59 A Correspondence near 0 C ...... 61 Surface Relaxation ...... 61 2.5 Gibbs-Thomson Effect ...... 63 2.6 Equilibrium Shape ...... 64 Approach to Equilibrium ...... 65 2.7 Twinning ...... 66 Columnar Twins ...... 66 Arrowhead Twins ...... 68 Crossed Plates ...... 72

3. Attachment Kinetics ...... 75 3.1 Ice Kinetics ...... 77 Molecular Processes ...... 78 Surface Characteristics ...... 79 Facet Formation ...... 80 3.2 Nucleation-Limited Attachment Kinetics ...... 81 2D Nucleation Theory ...... 81 Measured Facet Kinetics ...... 83 3.3 Basal Facet Growth ...... 84 Nucleation-Limited Growth ...... 84 Terrace Step Energies ...... 85 Correspondence with Ice Growth from Liquid Water ...... 86 A Comprehensive Model of Basal Attachment Kinetics ...... 87 3.4 Prism Facet Growth ...... 88 Attachment Kinetics on Ideal Facet Surfaces ...... 89 Prism Terrace Step Energies ...... 90 Pressure-Dependent Attachment Kinetics ...... 91 A Terrace-Erosion Model ...... 92 Structure Dependent Attachment Kinetics ...... 93 The Edge-Sharpening Instability ...... 96 Inter-Facet Transport ...... 98 3.5 Dislocation-Mediated Growth ...... 98 3.6 Chemically Modified Attachment Kinetics ...... 100 3.7 A Comprehensive Model of Snow Crystal Attachment Kinetics ...... 101 Prior Attempts ...... 101 Ideal Facet Surfaces ...... 103 Pressure-Dependent Attachment Kinetics ...... 103 Structure-Dependent Attachment Kinetics ...... 105 The Snow Crystal Morphology Diagram ...... 105

Next Generation Morphology Diagrams ...... 107 3D Modeling ...... 108 3.8 Molecular-Dynamics Simulations ...... 108 Step Energies ...... 109

4. Diffusion-Limited Growth ...... 111 4.1 Faceting and Branching ...... 115 Transition to Branching ...... 116 The Branching Instability ...... 117 Additional Snow Crystal Growth Instabilities ...... 120 4.2 Free Dendrites ...... 120 Fishbone Dendrites near -5 C ...... 121 Ice Dendrites Growing from Liquid Water ...... 122 A Brief Classification of Solidification Systems ...... 123 Sidebranch Competition ...... 126 Fractal Structure ...... 126 4.3 Diffusion Physics in Snow Crystal Growth ...... 127 Particle Diffusion ...... 127 Boundary Conditions ...... 128 Example: A Basic Ice-Growth Experiment ...... 130 Heat Diffusion ...... 131 4.4 The Spherical Solution ...... 132 Kinetics plus Diffusion ...... 132 Kinetics, Diffusion, and Heating ...... 133 Experimental Verification ...... 134 Kinetics, Diffusion, Heating, and Surface Energy ...... 135 Finite Outer Boundary ...... 136 Example: Growth-Chamber Supersaturation Estimation ...... 136 4.5 Additional Analytic Solutions ...... 137 Cylindrical Growth ...... 137 The Ivantsov Solution ...... 138 4.6 Solvability Theory ...... 139 The Selection Problem ...... 139 Snow Crystal Dendrites ...... 141 Ice Dendrites Growing from Liquid Water ...... 142 Anisotropy and Tip Splitting ...... 143 4.7 Snow Crystal Aerodynamics ...... 144 Drag and Terminal Velocity ...... 144 Horizontal Alignment ...... 145 The Ventilation Effect ...... 146 4.8 Growth Behaviors ...... 147 Aspect Ratios and Anisotropy ...... 147 Stellar Dendrites near -15 C ...... 148 Faceting and Anisotropy ...... 149 Hollow Columns and Needles near -5 C ...... 150 Bubbles in Columns ...... 151

Hollows & Bubbles in Plates ...... 153 Ridges and Sectored Plates ...... 154 Ridges with Grooves ...... 157 Ridges on Cones and Cups ...... 158 Step Bunching and Inwardly Propagating Rings ...... 159 Ribs on Plates ...... 161 Induced Sidebranching and Complex Symmetry ...... 163 Tridents and Triangular Snow Crystals ...... 164 Negative Snow Crystals ...... 168 Sublimation ...... 169

5. Computational Snow Crystals ...... 171 5.1 A Progression of Snow Crystal Models ...... 173 Packard Snowflakes ...... 173 Diffusion-Limited Aggregation ...... 174 Improving Physical Inputs ...... 175 Front-Tracking ...... 176 Phase-Field Snow Crystals ...... 177 Cellular Automata ...... 178 Physically Realistic Cellular Automata ...... 180 Comparing Different Computational Methods ...... 181 Facet-Dominated Growth ...... 183 5.2 Spherical Cellular Automata ...... 184 The Diffusion Equation ...... 185 Boundary Conditions ...... 186 Convergence Criterion ...... 186 Growth Steps ...... 186 Adaptive Boundary Matching ...... 187 5.3 Two Dimensional Cylindrically Symmetric Cellular Automata ...... 188 A Facet-Kink Model ...... 190 Boundary Conditions ...... 191 Growth Steps ...... 192 Numerical Anisotropy ...... 192 A Facet-Vicinal Model ...... 193 Monopole Matching ...... 195 Surface Diffusion and the FSD Approximation ...... 195 Concave Growth ...... 196 The Gibbs-Thomson Effect ...... 196 Minimum Feature Sizes ...... 198 Edge Sharpening Instability ...... 198 A Scaling Relation ...... 198 Comparison with Experiments ...... 199 The 2D Future ...... 201 5.4 Three-Dimensional Cellular Automata ...... 202 A 3D Hexagonal Grid ...... 202 Boundary Pixel Attributes ...... 203

Laplace Approximation ...... 205 Outer Boundary and Monopole Matching ...... 205 The Surface Boundary and Facet-Dominated Growth ...... 205 Growth Steps ...... 207 Attachment Coefficients on Faceted Surfaces ...... 207 Upper Terrace Effects ...... 208 Vicinal Surfaces and the FSD Approximation ...... 209 Quantitative Modeling ...... 210

6. Laboratory Snow Crystals ...... 211 Artificial versus Synthetic ...... 213 6.1 Building Blocks ...... 214 Refrigeration ...... 214 Insulation & Condensation ...... 216 Vacuum Technology ...... 217 Chemical Contamination ...... 218 Temperature Control ...... 218 Supersaturation ...... 219 Diffusion Modeling ...... 220 Nucleation ...... 221 Expansion Nucleator ...... 222 Oriented Ice Crystals ...... 223 Substrate Interactions ...... 224 Optical Microscopy ...... 225 Optical Interferometry ...... 226 Electron Microscopy ...... 228 Imaging Terrace Steps ...... 229 Snow Crystal Growth Chambers ...... 229 6.2 Free-Fall Chambers ...... 230 Terminal Velocities ...... 230 Cloud Chambers ...... 231 Convection Chambers ...... 232 A Seed-Crystal Generator ...... 234 High Cleanliness and High Throughput ...... 234 A Laminar Flow Chamber ...... 235 6.3 Diffusion Chambers ...... 236 Clam Shell Design ...... 238 Linear Gradient Diffusion Chamber ...... 238 6.4 Other Techniques ...... 239 Microparticle Ion Trapping ...... 239 Capillary Snow Crystals ...... 241 Expansion and Mixing ...... 242 Epitaxial Growth ...... 242 Negative Snow Crystals ...... 243 Targeted Experiments ...... 243

7. Simple Ice Prisms ...... 245 7.1 Analysis of a Basic Ice-Growth Experiment ...... 248 Crystal Crowding Effects ...... 248 The Monopole Approximation ...... 250 7.2 Ice Growth at Low Background Gas Pressure ...... 251 The VIG Experiment ...... 251 Data Analysis ...... 258 Attachment Coefficients ...... 263 Constrained A=1 Model ...... 264 The Superhydrophobic Future ...... 265 7.3 Ice Growth in Air ...... 266 Free-Fall Growth Data ...... 266 Diffusion Corrections in Air ...... 268 Anisotropy Analysis ...... 269 The “Well-Behaved-Basal” Model ...... 270 7.4 Analysis of a Free-Fall Ice-Growth Experiment ...... 271 Large-Scale Diffusion ...... 271 Crystal Crowding ...... 272 Small-Scale Diffusion ...... 273 Heating Effects ...... 273 Pressure-Dependent Attachment Kinetics ...... 274

8. Electric Ice Needles ...... 275 8.1 A Tool for Creating Isolated Single Crystals ...... 276 Advantages… ...... 279 … and Disadvantages ...... 281 Comparisons with Other Laboratory Methods ...... 282 8.2 E-needle Formation ...... 284 Basic Theory ...... 284 Polarizability Effects ...... 287 E-needle Crystal Orientation ...... 287 Some Remaining Questions ...... 289 A Serendipitous Discovery ...... 290 8.3 An E-needle Dual Diffusion Chamber ...... 291 Diffusion Chamber 1 ...... 291 Diffusion Chamber 2 ...... 295 The Manipulator Arm ...... 297 Optical Microscopy ...... 298 Turn-Key Operation ...... 298 8.4 The Morphology Diagram on E-needles ...... 298 Robust Features ...... 299 The Next Grand Challenge ...... 305 8.5 Simplest E-needle Cylindrical Growth ...... 306 Infinite Cylinders ...... 306 8.6 Thin Plates on E-needles near -15 C ...... 308

An In-Depth Example ...... 309 Varying the Supersaturation ...... 312 Near-Surface Supersaturation ...... 313 Lessons Learned ...... 314 8.7 Air-Dependent Attachment Kinetics Near -5C ...... 315 A Growth Transition ...... 315 Prism Attachment Kinetics in Air and Vacuum ...... 317 8.8 E-needle Vignettes ...... 318

9. Plate-on-Pedestal Snow Crystals ...... 325 9.1 The Plate-on-Pedestal Method ...... 325 PoP Hardware ...... 328 The Seed-Crystal Generator ...... 329 The Growth Chamber ...... 331 Optical Imaging ...... 333 Choosing a Seed Crystal ...... 334 9.2 Illumination and Image Post-Processing ...... 335 Uniform Illumination ...... 335 Dark-Field Illumination ...... 339 Rheinberg Illumination ...... 340 9.3 PoP Growth Behaviors ...... 341 Simple Hexagonal Plates ...... 341 Fog Droplets ...... 343 Branches, Wrinkles, & Spikes ...... 345 Induced Sidebranching ...... 347 Ridge Growth ...... 350 Induced Rib Structures ...... 351 Inwardly Propagating Rings ...... 353 Columnar Forms ...... 354 9.4 Identical-Twin Snow Crystals ...... 355 9.5 PoP Art ...... 358

10. A Field Guide to Snowflakes ...... 379 Hieroglyphs from the Sky ...... 380 10.1 Snowflake Watching ...... 381 Snow Crystal Classification ...... 382 Biased Sampling ...... 386 Simple Prisms ...... 389 Stellar Plates ...... 393 Sectored Plates ...... 401 Stellar Dendrites ...... 405 Fernlike Stellar Dendrites ...... 411 Hollow Columns ...... 417 Needles ...... 419 Capped Columns ...... 421

Double Plates ...... 425 Split Plates and Split Stars ...... 427 Hollow Plates ...... 429 Skeletal Forms ...... 431 Columns on Plates ...... 432 Triangular Crystals ...... 434 Bullet Rosettes ...... 435 Radiating Plates and Dendrites ...... 436 Sheaths and Cups ...... 437 Crystal Twins ...... 438 Twelve-Branched Snowflakes ...... 439

11. Snowflake Photography ...... 441 11.1 Finding Snowflakes ...... 443 Weather & Climate ...... 444 Location Matters ...... 445 Handling Snowflakes ...... 447 Granular Gems ...... 449 11.2 Optics and Lenses ...... 450 Macro and Micro Lenses ...... 452 The Diffraction Limit ...... 453 Focus Stacking ...... 455 Point-and-Shoot versus Stable Mounting ...... 457 11.3 Illumination Matters ...... 458 Side Illumination ...... 459 Specular Reflection ...... 464 Front Illumination ...... 468 Back Illumination ...... 469 Dark-Field ...... 471 Rheinberg Illumination ...... 473 The SnowMaster 9000 ...... 476

12. Ice from Liquid Water ...... 479 12.1 Basic Phenomenology ...... 481 12.2 Attachment Kinetics ...... 485 The Gibbs-Thomson Effect ...... 486 12.3 Diffusion-Limited Growth ...... 488 The Laplace Approximation ...... 488 Surface Boundary Conditions ...... 488 The Spherical Solution ...... 489 Dendrite Growth ...... 489 12.4 Chemically Mediated Growth ...... 492 Segregation Phenomena ...... 493 Ice Nucleation ...... 494 Growth Inhibition ...... 495

12.5 Constrained Growth ...... 496

Appendices ...... 498 A. List of Variables and Physical Constants ...... 498 B. Analytical Modeling of Snow Crystal Growth ...... 500 Growth from Water Vapor ...... 500 The 1D Spherical Solution ...... 504 The 1D Cylindrical Solution ...... 508 Parabolic Solutions ...... 509 The Equilibrium Crystal Shape ...... 512 Ice Growth from Liquid Water ...... 513 The Ivantsov Solution in the Laplace Approximation ...... 517

Bibliography ...... 522

Index ...... 538

Forward

Studying snow crystals is a somewhat unusual different crystal types, including thin plates, endeavor, so people often ask me what got me slender columns, and blocky prisms, all started on this path, and why I have kept at it branched, hollowed, faceted, and patterned to for the past two decades. The short answer is varying degrees, often exhibiting a baffling simply that I find the science both fascinating degree of complexity, symmetry, and and entirely worthy of attention. Snow crystal morphological diversity. How does all this growth involves the coordinated molecular work exactly? What forces result in such motions of water molecules undergoing a complex structures? Why do the crystals phase transition from vapor to ice, creating change so dramatically from one snowfall to elaborate structures in the process. There is still the next? No one yet knows how to answer a great deal about this process that we cannot these questions. When you drill down into the fully explain. details, the fundamental physical dynamics of One might imagine that the formation of snow crystal growth is both captivating and ice crystals from water vapor would be a solved mysterious. problem by now; it’s not neurobiology, after Another part of me feels that the physics all, just plain, ordinary ice. Nevertheless, it of crystal growth is something we ought to turns out that the physics underlying crystal know better. The manufacture of growth in general is quite a tough nut to crack, semiconductor crystals underlies the entire and ice is a particularly intriguing example. electronics industry, yet growing crystals is a bit Even now, well into the 21st century, our like growing carrots – knowing how to do it is fundamental understanding of why snow not the same as knowing how it works. I often crystals grow into the rich variety of structures think of snowflakes as a convenient case-study we see falling from the clouds is remarkably in the science of crystal growth; if we can figure primitive. out the molecular dynamics governing snow Part of me feels that the lowly snowflake crystal formation, maybe that knowledge will has become something of an embarrassment to have application in other areas. the scientific community. We can split the Although crystal growth is an important atom and sequence the human genome; but area in materials science and engineering, my explaining the growth of a snowflake remains studies are not motivated by practical beyond our abilities. Every winter we see these applications. My focus is instead on icy works of art simply appearing, fundamental questions regarding the molecular spontaneously, quite literally out of thin air. physics of crystal growth. Applied research can And yet we have no ready explanation as to certainly be highly rewarding; but why snowflakes look the way they do. contemplating the overarching scientific Examining the falling snow up close, one questions can be worthwhile also. History soon witnesses a remarkable menagerie of clearly teaches us that the knowledge gained

11 from basic scientific pursuits often ends up But it was mostly idle conversation that being quite beneficial, even if one cannot evening, and our attention was soon pulled always imagine right now how, when, or where back to projects we had underway in atomic those future benefits might arise. physics. On a related note, I always make a point of Nevertheless, over the next few days I telling people that I am not spending any tax began musing about exactly what crystals one dollars on this research. I have always might examine in an ion trap, and my attention considered my snow-crystal studies to be quickly turned to ice. If nothing else, it was something of a scientific hobby – interesting to certainly an inexpensive material to work with, me, but with no obvious financial payoff now with no unpleasant safety issues, and its or down the road. I figure with over seven freezing temperature was easily accessible as billion people on the planet, and vast resources well. As an experimental physicist thinking being spent on sports, entertainment, and all about the general subject of crystal growth, it manner of generally unnecessary activities, seemed reasonable to start with a relatively maybe a few of us can be spared to low-cost test case. contemplate the inner workings of a snowflake. My interest now being piqued, I started Although studying snowflakes is an doing a bit of online research to see what was unusual activity, I am certainly not the first to known about the science of snowflakes. The engage in it, and hopefully I will not be the last. internet was quite a new thing back then, and I Beginning with Johannes Kepler over four soon found that it was the perfect tool for centuries ago, numerous scientists have put learning about an unusual subject like snow serious effort into understanding the details of crystals. While most current scientific fields how ice forms from water vapor, and how involve well-defined communities of structures arise during the process. At any researchers who have regular meetings and given time during that long history, you could publish in established journals, studies about usually find a handful of people pushing the snowflakes have been relatively sporadic and field forward, bit by bit. It has never been a isolated, with articles appearing in widely varied popular area of research, and it has attracted forums. Scientific interest has waxed and little support from the usual funding sources. waned over several centuries, usually led by a But it seems there are always a few scientists few curious souls from here and there around willing to ponder the topic. My efforts build the globe. Locating many of the relevant upon what my predecessors have published scientific references was a nontrivial accomplished over the years, and my sincere challenge. hope is that this book will provide a starting The internet soon steered me toward an point for those wanting to continue studying extraordinary book entitled Snow Crystals, the science of snow crystals into the future. Natural and Artificial published in 1954 by My foray into snow crystals began in 1995 Japanese physicist Ukichiro Nakaya during a conversation with Stephen Ross, who [1954Nak]. It quickly became apparent that I I had recently hired as a post-doctoral had to have this book, and I then discovered researcher in my lab at Caltech. Stephen had that rare-book dealers were early adopters of been working with electrodynamic ion internet marketing, as they normally sold their trapping in his previous job, so one evening we wares to a widely dispersed clientele. It all were chatting about what new opportunities sounds ordinary now; but locating a copy of a might lie in that direction. We both thought it difficult-to-find, long-out-of-print book and might be worthwhile to study the growth of purchasing it from a small shop halfway around isolated single crystals that were levitated in an the world with a few clicks was a marvelous ion trap, as the physics of structure formation experience at the time. during crystal growth was not well understood.

When my new purchase arrived, I was soon additional snowflake photos, but overall the to board a flight with my wife and two young quality I was looking for was not to be found. children to North Dakota, visiting some family As a laboratory physicist, I was already there for Christmas, so I packed Snow Crystals experienced with optics and electronics, so I along for some atypical holiday reading. decided that I had to build a better snowflake Thumbing through the book on the plane, I photomicroscope. I experimented with saw my first photos of several capped columns, different optical hardware and lighting as Nakaya had photographic examples of many methods, using small alum crystals as surrogate uncommon snow crystal types. Although I snowflakes to work out the photographic grew up in North Dakota, and I had plenty of details. This soon led to a collaboration with first-hand experience with snow, I had never Patricia Rasmussen in Wisconsin, who put the witnessed anything like the exotic capped microscope to good use during the 2001-2 column. winter season, substantially raising the bar for As luck would have it, it began snowing a high-resolution snowflake photography. few days later, so I braved the cold and went Voyageur Press then worked with us to publish outside, magnifier in hand, to see what I could The Snowflake: Winter’s Secret Beauty in the fall find. And, lo and behold, there I found my first of 2003, just in time for Christmas. capped column! As I delved more deeply into Being the first-ever popular-science book Nakaya’s book, I soon decided that I had to set about snowflakes, adorned with colorful my sights on writing a popular-science book photographs that were considerably higher in about snowflakes. People who live in snowy quality than past efforts, The Snowflake became climates, as I had done for 18 years, ought to an immediate hit, selling over 100,000 copies. know more about these marvelous works of art Once winter arrived and snow started falling floating down from the clouds. around the country, the book received a great By the fall of 1998, I had created a website deal of publicity from dozens of newspapers, devoted to snowflakes, which eventually often in full-page Sunday articles featuring morphed into what is now SnowCrystals.com. I photos of different types of snowflakes. posted examples of snowflake photographs I Building on this initial success, I soon made had found here and there, accompanied by numerous improvements to my microscope, brief descriptions of the science and history of including fitting it into a rugged suitcase for snow-crystal research. As the internet was traveling, calling it the SnowMaster9000. rapidly picking up in popularity during those Although Southern California was my home, I days, and educational content was still scarce, decided it was time to take the plunge and my snowflake website received a fair bit of become a serious snowflake photographer. attention from all corners. This led to several expeditions to northern As my research continued, I soon found Ontario and central Alaska, including countless that little progress had been made in snowflake hours out in the cold photographing minute ice photography over the preceding 50 years. This crystals. These new photos formed the basis was problematic for me, as I could hardly for The Little Book of Snowflakes, which came contemplate writing a popular-science book out during the 2004 holiday season. This was a about snowflakes without including a smaller, inexpensive gift book, and again it did representative collection of photographs. quite well and sold over 100,000 copies. Wilson Bentley’s photos were something of a During the following several years, I standard, but they were over 100 years old, and continued photographing snowflakes around their quality was rather poor by modern the globe, and the subject remained quite standards. Nakaya’s photos were better, but popular in the media. Voyageur Press and I they too were black-and-white and somewhat produced a new book every year, including The grainy. A few other photographers had taken Art of the Snowflake, The Secret Life of a

Snowflake, Ken Libbrecht’s Field Guide to Lately I have begun to realize that snow crystals Snowflakes, The Magic of Snowflakes, are my new calling, so, starting around 2014, I Snowflakes, and The Snowflake: Winter’s Secret have been focusing nearly all my efforts in this Artistry. I made numerous appearances to talk area. It remains, at least to me, a continually about the books, including on the Martha fascinating scientific endeavor. Stewart show, and I supplied snowflake images I am fortunate to have worked with many for numerous newspapers and magazines. I talented undergraduate students from Caltech even had four snowflake photos on a set of and other universities on my snow-crystal U.S. first-class postage stamps (over 3 billion research, including Victoria Tanusheva, Mark sold!), followed by Austrian stamps, Swedish Rickerby, Nina Budaeva, Robert Bell, Hannah stamps, and then again on U.S. bulk-mail Arnold, Timothy Crosby, Molly Swanson, Han stamps. It was all quite a thrilling experience. Yu, Johanna Bible, Ryan Potter, Christopher After about a decade of snowflake Miller, Kevin Lui, Cameron Lemon, Sarah everything for me, the phenomenon slowly Thomas, Helen Morrison, and Benjamin quieted down and life got back to normal once Faber. Their determined efforts are much again. Happily, with an influx of revenue from appreciated. book royalties I was able to gear up my In the same vein, I have enjoyed countless snowflake lab, to the point that I could start enjoyable interactions with fellow snow/ice doing serious experimental research enthusiasts, colleagues and collaborators, investigating the science of snow-crystal including Walter Wick, David Griffeath, Janko growth. This led to better measurements of the Gravner, Don Komarechka, Alexey Kljatov, molecular attachment kinetics, studies using Patricia Rasmussen, Mary Ann White, Carol electric needle crystals, and making designer Norberg, Matthew Sturm, Ted Kinsman, Plate-on-Pedestal snow crystals, topics that are James Kelly, Joseph Shaw. My editors at discussed at some length in the chapters that Voyageur Press, Michael Dregni and Todd follow. Berger, were terrific to work with. My students and I made considerable I am much indebted to Caltech for hiring progress on several scientific fronts, but not yet me as a young professor and providing me as much as I had hoped. I dreamed that it gainful employment for what has been nearly might be possible to “solve” the problem of my entire adult life. Caltech has provided snowflake growth, or at least make a big step ample lab space while allowing me full rein to forward. Alas, the lowly snowflake presents a explore this atypical line of research. Without rather rich and deep challenge. Like an onion, Caltech’s constant support, none of this work as you peel away layers, you find more layers. would have been possible. Of course, I and others are still pushing Finally, my wife, Rachel Wing, and our two forward, so perhaps our big Eureka! moment is children, Max and Alanna, have been just around the corner. Science is generally enthusiastic participants throughout this more about steady, layer-by-layer progress than snowflake adventure, especially on our astonishing breakthroughs, but one never numerous snowflake-related vacations to such knows in this business. far-flung venues as northern Japan, Vermont, During much of this time, my work on northern Ontario, northern Sweden, Alaska, snow crystals was mostly a side project. My and the mountains of California, all during the scientific interests have drifted over several cold of winter. Thanks for the memories! decades from solar astrophysics to atomic/laser physics to gravitational physics Kenneth Libbrecht and the LIGO (Laser Interferometer Pasadena, California Gravitational-wave Observatory) project, and I August 30, 2019 dabbled with snowflakes when time permitted.