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 klibbrecht@gmail.com.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Studying snow crystals is a somewhat unusual endeavor, so people often ask me what got me started on this path, and why I have kept at it for the past two decades. The short answer is simply that I find the science both fascinating and entirely worthy of attention. Snow crystal growth involves the coordinated molecular motions of water molecules undergoing a phase transition from vapor to ice, creating elaborate structures in the process. There is still a great deal about this process that we cannot fully explain.

One might imagine that the formation of ice crystals from water vapor would be a solved problem by now; it’s not neurobiology, after all, just plain, ordinary ice. Nevertheless, it turns out that the physics underlying crystal growth in general is quite a tough nut to crack, and ice is a particularly intriguing example. Even now, well into the 21st century, our fundamental understanding of why snow crystals grow into the rich variety of structures we see falling from the clouds is remarkably primitive.

Part of me feels that the lowly snowflake has become something of an embarrassment to the scientific community. We can split the atom and sequence the human genome; but explaining the growth of a snowflake remains beyond our abilities. Every winter we see these icy works of art simply appearing, spontaneously, quite literally out of thin air. And yet we have no ready explanation as to why snowflakes look the way they do.

Examining the falling snow up close, one soon witnesses a remarkable menagerie of

different crystal types, including thin plates, slender columns, and blocky prisms, all branched, hollowed, faceted, and patterned to varying degrees, often exhibiting a baffling degree of complexity, symmetry, and morphological diversity. How does all this work exactly? What forces result in such complex structures? Why do the crystals change so dramatically from one snowfall to the next? No one yet knows how to answer these questions. When you drill down into the details, the fundamental physical dynamics of snow crystal growth is both captivating and mysterious.

Another part of me feels that the physics of crystal growth is something we ought to know better. The manufacture of semiconductor crystals underlies the entire electronics industry, yet growing crystals is a bit like growing carrots – knowing how to do it is not the same as knowing how it works. I often think of snowflakes as a convenient case-study in the science of crystal growth; if we can figure out the molecular dynamics governing snow crystal formation, maybe that knowledge will have application in other areas.

Although crystal growth is an important area in materials science and engineering, my studies are not motivated by practical applications. My focus is instead on fundamental questions regarding the molecular physics of crystal growth. Applied research can certainly be highly rewarding; but contemplating the overarching scientific questions can be worthwhile also. History clearly teaches us that the knowledge gained

Forward

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from basic scientific pursuits often ends up being quite beneficial, even if one cannot always imagine right now how, when, or where those future benefits might arise.

On a related note, I always make a point of telling people that I am not spending any tax dollars on this research. I have always considered my snow-crystal studies to be something of a scientific hobby – interesting to me, but with no obvious financial payoff now or down the road. I figure with over seven billion people on the planet, and vast resources being spent on sports, entertainment, and all manner of generally unnecessary activities, maybe a few of us can be spared to contemplate the inner workings of a snowflake.

Although studying snowflakes is an unusual activity, I am certainly not the first to engage in it, and hopefully I will not be the last. Beginning with Johannes Kepler over four centuries ago, numerous scientists have put serious effort into understanding the details of how ice forms from water vapor, and how structures arise during the process. At any given time during that long history, you could usually find a handful of people pushing the field forward, bit by bit. It has never been a popular area of research, and it has attracted little support from the usual funding sources. But it seems there are always a few scientists willing to ponder the topic. My efforts build upon what my predecessors have accomplished over the years, and my sincere hope is that this book will provide a starting point for those wanting to continue studying the science of snow crystals into the future.

My foray into snow crystals began in 1995 during a conversation with Stephen Ross, who I had recently hired as a post-doctoral researcher in my lab at Caltech. Stephen had been working with electrodynamic ion trapping in his previous job, so one evening we were chatting about what new opportunities might lie in that direction. We both thought it might be worthwhile to study the growth of isolated single crystals that were levitated in an ion trap, as the physics of structure formation during crystal growth was not well understood.

But it was mostly idle conversation that evening, and our attention was soon pulled back to projects we had underway in atomic physics.

Nevertheless, over the next few days I began musing about exactly what crystals one might examine in an ion trap, and my attention quickly turned to ice. If nothing else, it was certainly an inexpensive material to work with, with no unpleasant safety issues, and its freezing temperature was easily accessible as well. As an experimental physicist thinking about the general subject of crystal growth, it seemed reasonable to start with a relatively low-cost test case.

My interest now being piqued, I started doing a bit of online research to see what was known about the science of snowflakes. The internet was quite a new thing back then, and I soon found that it was the perfect tool for learning about an unusual subject like snow crystals. While most current scientific fields involve well-defined communities of researchers who have regular meetings and publish in established journals, studies about snowflakes have been relatively sporadic and isolated, with articles appearing in widely varied forums. Scientific interest has waxed and waned over several centuries, usually led by a few curious souls from here and there around the globe. Locating many of the relevant published scientific references was a nontrivial challenge.

The internet soon steered me toward an extraordinary book entitled Snow Crystals, Natural and Artificial published in 1954 by Japanese physicist Ukichiro Nakaya [1954Nak]. It quickly became apparent that I had to have this book, and I then discovered that rare-book dealers were early adopters of internet marketing, as they normally sold their wares to a widely dispersed clientele. It all sounds ordinary now; but locating a copy of a difficult-to-find, long-out-of-print book and purchasing it from a small shop halfway around the world with a few clicks was a marvelous experience at the time.

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When my new purchase arrived, I was soon to board a flight with my wife and two young children to North Dakota, visiting some family there for Christmas, so I packed Snow Crystals along for some atypical holiday reading. Thumbing through the book on the plane, I saw my first photos of several capped columns, as Nakaya had photographic examples of many uncommon snow crystal types. Although I grew up in North Dakota, and I had plenty of first-hand experience with snow, I had never witnessed anything like the exotic capped column.

As luck would have it, it began snowing a few days later, so I braved the cold and went outside, magnifier in hand, to see what I could find. And, lo and behold, there I found my first capped column! As I delved more deeply into Nakaya’s book, I soon decided that I had to set my sights on writing a popular-science book about snowflakes. People who live in snowy climates, as I had done for 18 years, ought to know more about these marvelous works of art floating down from the clouds.

By the fall of 1998, I had created a website devoted to snowflakes, which eventually morphed into what is now SnowCrystals.com. I posted examples of snowflake photographs I had found here and there, accompanied by brief descriptions of the science and history of snow-crystal research. As the internet was rapidly picking up in popularity during those days, and educational content was still scarce, my snowflake website received a fair bit of attention from all corners.

As my research continued, I soon found that little progress had been made in snowflake photography over the preceding 50 years. This was problematic for me, as I could hardly contemplate writing a popular-science book about snowflakes without including a representative collection of photographs. Wilson Bentley’s photos were something of a standard, but they were over 100 years old, and their quality was rather poor by modern standards. Nakaya’s photos were better, but they too were black-and-white and somewhat grainy. A few other photographers had taken

additional snowflake photos, but overall the quality I was looking for was not to be found.

As a laboratory physicist, I was already experienced with optics and electronics, so I decided that I had to build a better snowflake photomicroscope. I experimented with different optical hardware and lighting methods, using small alum crystals as surrogate snowflakes to work out the photographic details. This soon led to a collaboration with Patricia Rasmussen in Wisconsin, who put the microscope to good use during the 2001-2 winter season, substantially raising the bar for high-resolution snowflake photography. Voyageur Press then worked with us to publish The Snowflake: Winter’s Secret Beauty in the fall of 2003, just in time for Christmas.

Being the first-ever popular-science book about snowflakes, adorned with colorful photographs that were considerably higher in quality than past efforts, The Snowflake became an immediate hit, selling over 100,000 copies. Once winter arrived and snow started falling around the country, the book received a great deal of publicity from dozens of newspapers, often in full-page Sunday articles featuring photos of different types of snowflakes.

Building on this initial success, I soon made numerous improvements to my microscope, including fitting it into a rugged suitcase for traveling, calling it the SnowMaster9000. Although Southern California was my home, I decided it was time to take the plunge and become a serious snowflake photographer. This led to several expeditions to northern Ontario and central Alaska, including countless hours out in the cold photographing minute ice crystals. These new photos formed the basis for The Little Book of Snowflakes, which came out during the 2004 holiday season. This was a smaller, inexpensive gift book, and again it did quite well and sold over 100,000 copies.

During the following several years, I continued photographing snowflakes around the globe, and the subject remained quite popular in the media. Voyageur Press and I produced a new book every year, including The Art of the Snowflake, The Secret Life of a

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Snowflake, Ken Libbrecht’s Field Guide to Snowflakes, The Magic of Snowflakes, Snowflakes, and The Snowflake: Winter’s Secret Artistry. I made numerous appearances to talk about the books, including on the Martha Stewart show, and I supplied snowflake images for numerous newspapers and magazines. I even had four snowflake photos on a set of U.S. first-class postage stamps (over 3 billion sold!), followed by Austrian stamps, Swedish stamps, and then again on U.S. bulk-mail stamps. It was all quite a thrilling experience.

After about a decade of snowflake everything for me, the phenomenon slowly quieted down and life got back to normal once again. Happily, with an influx of revenue from book royalties I was able to gear up my snowflake lab, to the point that I could start doing serious experimental research investigating the science of snow-crystal growth. This led to better measurements of the molecular attachment kinetics, studies using electric needle crystals, and making designer Plate-on-Pedestal snow crystals, topics that are discussed at some length in the chapters that follow.

My students and I made considerable progress on several scientific fronts, but not yet as much as I had hoped. I dreamed that it might be possible to “solve” the problem of snowflake growth, or at least make a big step forward. Alas, the lowly snowflake presents a rather rich and deep challenge. Like an onion, as you peel away layers, you find more layers. Of course, I and others are still pushing forward, so perhaps our big Eureka! moment is just around the corner. Science is generally more about steady, layer-by-layer progress than astonishing breakthroughs, but one never knows in this business.

During much of this time, my work on snow crystals was mostly a side project. My scientific interests have drifted over several decades from solar astrophysics to atomic/laser physics to gravitational physics and the LIGO (Laser Interferometer Gravitational-wave Observatory) project, and I dabbled with snowflakes when time permitted.

Lately I have begun to realize that snow crystals are my new calling, so, starting around 2014, I have been focusing nearly all my efforts in this area. It remains, at least to me, a continually fascinating scientific endeavor.

I am fortunate to have worked with many talented undergraduate students from Caltech and other universities on my snow-crystal research, including Victoria Tanusheva, Mark Rickerby, Nina Budaeva, Robert Bell, Hannah Arnold, Timothy Crosby, Molly Swanson, Han Yu, Johanna Bible, Ryan Potter, Christopher Miller, Kevin Lui, Cameron Lemon, Sarah Thomas, Helen Morrison, and Benjamin Faber. Their determined efforts are much appreciated.

In the same vein, I have enjoyed countless enjoyable interactions with fellow snow/ice enthusiasts, colleagues and collaborators, including Walter Wick, David Griffeath, Janko Gravner, Don Komarechka, Alexey Kljatov, Patricia Rasmussen, Mary Ann White, Carol Norberg, Matthew Sturm, Ted Kinsman, James Kelly, Joseph Shaw. My editors at Voyageur Press, Michael Dregni and Todd Berger, were terrific to work with.

I am much indebted to Caltech for hiring me as a young professor and providing me gainful employment for what has been nearly my entire adult life. Caltech has provided ample lab space while allowing me full rein to explore this atypical line of research. Without Caltech’s constant support, none of this work would have been possible.

Finally, my wife, Rachel Wing, and our two children, Max and Alanna, have been enthusiastic participants throughout this snowflake adventure, especially on our numerous snowflake-related vacations to such far-flung venues as northern Japan, Vermont, northern Ontario, northern Sweden, Alaska, and the mountains of California, all during the cold of winter. Thanks for the memories!

Kenneth Libbrecht

Pasadena, California August 30, 2019

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