Table Of ContentSNOW CRYSTALS
Snow Crystals
A Case Study in Spontaneous
Structure Formation
Kenneth G. Libbrecht
Prince ton University Press
Princet on & Oxford
Copyright © 2022 by Prince ton University Press
Prince ton University Press is committed to the protection of copyright
and the intellectual property our authors entrust to us. Copyright
promotes the pro gress and integrity of knowledge. Thank you for
supporting free speech and the global exchange of ideas by purchasing an
authorized edition of this book. If you wish to reproduce or distribute
any part of it in any form, please obtain permission.
Requests for permission to reproduce material from this work
should be sent to permissions@press . princeton . edu
Published by Prince ton University Press
41 William Street, Prince ton, New Jersey 08540
6 Oxford Street, Woodstock, Oxfordshire OX20 1TR
press . princeton . edu
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Names: Libbrecht, Kenneth, author.
Title: Snow crystals : a case study in spontaneous structure formation /
Kenneth G. Libbrecht.
Description: Princeton, NJ : Princeton University Press, [2022] |
Includes bibliographical references and index.
Identifiers: LCCN 2020057327 (print) | LCCN 2020057328 (ebook) |
ISBN 9780691200378 (hardback) | ISBN 9780691223629 (ebook)
Subjects: LCSH: Snowflakes.
Classification: LCC QC926.32 .L5295 2022 (print) | LCC QC926.32
(ebook) | DDC 548/.5—dc23
LC record available at https://lccn.loc.gov/2020057327
LC ebook record available at https://lccn.loc.gov/2020057328
British Library Cataloging- in- Publication Data is available
Editorial: Jessica Yao, Ingrid Gnerlich, Maria Garcia
Jacket Design: Layla Mac Rory
Production: Jacqueline Poirier
Publicity: Matthew Taylor, Amy Stewart
Jacket image courtesy of author
This book has been composed in Garamond Premier Pro
Printed on acid- free paper. ∞
Printed in the United States of Amer i ca
10 9 8 7 6 5 4 3 2 1
CONTENTS
preface vii
ONE FOUR
Snow Crystal Science Attachment Kinetics
Complex Symmetry 2 Ice Kinetics 112
A Brief History of Snow Crystal Science 6 Large- Facet Attachment Kinetics 116
Twenty- First- Century Snowflakes 17 Structure- Dependent Attachment Kinetics 123
No Two Alike? 24 Explaining the Nakaya Diagram 132
The Morphological Nexus at −5° C 135
TWO Snow Crystal Cartography 141
Dislocation- Mediated Growth 141
Ice Crystal Structure
Chemical Vapor Effects 143
Ice Crystallography 31
Surface Premelting 36
FIVE
Ice Energetics 37
Computational Snow Crystals
Molecular Dynamics Simulations 44
Surface Energy Considerations 45 A Progression of Snow Crystal Models 148
Snow Crystal Twinning 48 Spherical Cellular Automata 159
Cylindrically Symmetric Cellular Automata 163
THREE Three- Dimensional Cellular Automata 176
Diffusion- Limited Growth
SIX
Faceting and Branching 60
Laboratory Snow Crystals
Free Dendrites 64
Diffusion in Snow Crystal Growth 71 Free- Fall Snow Crystals 185
The Spherical Solution 74 Substrate Support 191
Additional Analytic Solutions 79 Levitation 196
Solvability Theory 80 Continuous Diffusion Chambers 198
Snow Crystal Aerodynamics 85 Snow Crystal Imaging 201
Order and Chaos 88
v
T
vi CONTENTS
SEVEN NINE
Simple Ice Prisms Designer Snow Crystals
Precision Ice Growth Mea sure ments 209 The Plate- on- Pedestal Method 278
A Tale of Two Experiments 214 Illumination and Postpro cessing 285
Simple- Prism Convergence 231 PoP Growth Be hav iors 291
Identical- Twin Snow Crystals 302
PoP Art 306
EIGHT
Electric Ice N eedles
TEN
Snowflake on a Stick 235
Natu ral Snowflakes
E- Needle Formation 240
An E- Needle Dual Diffusion Chamber 248 Snowflake Watching 330
The Nakaya Diagram on E- Needles 254
Simplest E- Needle Growth 262
ELEVEN
An Analy sis Example: E- Needles at −15° C 264
Snowflake Photography
E- Needle Vignettes 267
Finding Snowflakes 389
Optics and Lenses 397
Illumination Matters 405
appendix— list of variables and physical constants 423
bibliography 427
index 437
PREFACE
tudying snow crystals is a somewhat unusual The manufacture of semiconductor crystals underlies the
S
endeavor, so people often ask me what got me entire electronics industry, yet growing crystals is a bit
started on this path, and why I have kept at it like growing carrots— knowing how to do it is not the
for over two de cades. The short answer is sim- same as knowing how it works. Snowflakes can be a valu-
ply that I find the science both fascinating and entirely able case study in this regard; if we can figure out the
worthy of attention. The molecular dynamics of crystal detailed molecular dynamics governing snow crystal for-
growth is a knotty prob lem on many levels, and ice ex- mation, maybe that knowledge w ill be useful in other
hibits some especially curious be hav iors. Even now, well areas.
into the twenty- first century, our fundamental under- Although crystal growth is an impor tant area in ma-
standing of why snow crystals grow into the rich variety terials science and engineering, my studies have not
of structures we see falling from the clouds is remarkably been motivated by any specific practical applications. My
primitive. focus is instead on fundamental questions regarding the
Part of me feels that the humble snowflake has be- molecular physics of crystal growth. Applied research
come a bit of an embarrassment to the scientific commu- can certainly be rewarding, but contemplating the over-
nity. We can split the atom and sequence the human arching scientific questions has its merits as well. History
genome, but explaining the growth of a snowflake re- clearly teaches us that the knowledge gained from basic
mains beyond our abilities? Every winter we see these scientific pursuits often ends up being quite beneficial,
icy works of art simply appearing, spontaneously, quite even if one cannot always imagine right now how, when,
literally out of thin air. And yet we have no ready expla- or where t hose future benefits might arise.
nation as to why snowflakes look the way they do. On a related note, I always make a point of telling
Another part of me feels that the general physics of people that I have not spent any tax dollars on this re-
crystal growth is something we ought to know better. search. I have always considered my snow crystal studies
vii
T
viii PREFACE
to be something of a scientific hobby— in ter est ing to me, When The Snowflake did well, I made numerous im-
but with no obvious financial payoff now or down the provements to my microscope and mounted it in a rug-
road. I figure with over seven billion p eople on the planet ged suitcase for traveling, with the aim of becoming a se-
and vast resources being spent on sports, entertainment, rious snowflake photographer. This led to several
and all manner of generally unnecessary activities, per- expeditions to northern Ontario and central Alaska, in-
haps a few of us can be spared to contemplate the inner cluding countless hours out in the cold photographing
workings of a snowflake. minute ice crystals. These new photos formed the basis
My foray into snow crystals began in 1995 during an for The Little Book of Snowflakes, which came out dur-
idle conversation with Stephen Ross, whom I had re- ing the 2004 holiday season.
cently hired as a postdoctoral researcher in my lab at I continued photographing snowflakes around the
Caltech. It occurred to us that the basic physics of crys- globe for about a de cade, and the subject remained popu-
tal growth deserved more attention, and I soon realized lar in the media. Voyageur Press and I produced a new
that ice would be a good place to start. If nothing else, it book every year, including The Art of the Snowflake, The
was certainly an inexpensive material to work with, with Secret Life of a Snowflake, Ken Libbrecht’s Field Guide to
no onerous safety issues, and its freezing temperature was Snowflakes, The Magic of Snowflakes, Snowflakes, and The
easily accessible as well. Although our attention was Snowflake: Winter’s Frozen Artistry. These years were
quickly pulled back to ongoing proj ects in atomic phys- something of a whirlwind experience, highlighted by a
ics, I began researching what was known about the sci- set of snowflake photos on U.S. postage stamps (over 3
ence of snow crystals. By the fall of 1998, I had created a billion sold!) and even an appearance on the Martha Stu-
website devoted to the subject, which eventually morphed art show.
into what is now SnowCrystals . com. With an influx of revenue from book royalties, I was
Although I grew up in snowy North Dakota, I had able to gear up my snowflake lab to the point that I could
not r eally seen snowflakes u ntil I started digging through start d oing meaningful experimental research investigat-
the scientific lit er a ture. This wonderful story was simply ing the physics of snow crystal growth. This led to bet-
not being told outside that realm, so I set my sights on ter mea sure ments of the molecular attachment kinetics,
writing a popu lar science book on the subject, which, studies using electric needle crystals, and making de-
surprisingly, had never been done before. In search of signer Plate- on- Pedestal snow crystals, all topics that
suitable photo graphs, I found that Wilson Bentley’s pic- are discussed at some length in the chapters that follow.
tures were something of a standard, but they were more My students and I have made good pro gress on sev-
than 100 years old, and their quality was rather poor by eral scientific fronts, especially toward explaining the
modern standards. Newer snowflake photos were out Nakaya diagram, as I describe in detail in this book.
there, but the quality I wanted was not to be found. Why snow crystals switch back and forth between plate-
As a laboratory physicist, I was already experienced like and columnar forms with changing temperature
with optics and electronics, so I was soon building a bet- had been an outstanding puzzle for 75 years, and I feel
ter snowflake photomicroscope. This led to a collabora- now that it is fi nally beginning to make sense. Still, the
tion with Patricia Rasmussen in Wisconsin, who put the phenomenon of snow crystal growth is not a solved prob-
instrument to good use during the 2001–2002 winter lem by any means. Like an onion, as you peel away lay-
season, substantially raising the bar for high- resolution ers, you tend to find more layers, as this is the nature of
snowflake photography. Voyageur Press then worked scientific research. Many in ter est ing questions remain.
with us to publish The Snowflake: Winter’s Secret Beauty Until recently, my work on snow crystals was mostly a
in the fall of 2003, just in time for Christmas. side proj ect. My scientific focus has drifted over several
T
PREFACE ix
de cades from solar astrophysics to atomic/laser physics Dregni, Harald Garcke, Luis González MacDowell,
to gravitational physics and the LIGO ( Laser Interfer- Janko Gravner, David Griffeath, James Kelly, Ted Kins-
ometer Gravitational- wave Observatory) proj ect, and I man, Alexey Kljatov, Don Komarechka, Heiner Müller-
dabbled with snowflakes when time permitted. Recently Krumbhaar, Nathan Myhrvold, Carol Norberg, Joseph
I began to realize that snow crystals are my new calling, Shaw, Matthew Sturm, Walter Tape, and Mary Anne
so, starting around 2014, I have been focusing nearly all White.
my research efforts in this area. It remains, at least to me, I am especially indebted to Caltech for educating
a continually fascinating scientific venture. me, hiring me as a young professor, and providing me
gainful employment for most of my adult life. The uni-
I am fortunate to have worked with many talented un- versity has provided me with ample lab space while al-
dergraduate students from Caltech and other universi- lowing me the freedom to explore this aty pi cal line of
ties on my snow crystal research, including Hannah Ar- scientific research. Without Caltech’s support, none of
nold, Robert Bell, Johanna Bible, Nina Budaeva, this work would have been pos si ble.
Timothy Crosby, Benjamin Faber, Cameron Lemon, Fi nally, my wife, Rachel Wing, and our two c hildren,
Kevin Lui, Christopher Miller, Helen Morrison, Ryan Maxwell and Alanna, have been enthusiastic partici-
Potter, Mark Rickerby, Molly Swanson, Victoria Tanu- pants throughout this snowflake adventure, especially
sheva, Sarah Thomas, and Han Yu. Their determined ef- on our numerous snowflake- related vacations to such
forts are much appreciated. far- flung venues as northern Japan, Vermont, northern
In the same vein, I have enjoyed countless rewarding Ontario, northern Sweden, Alaska, and the mountains
interactions with fellow snow/ice enthusiasts, colleagues of California, all during the cold of winter. Thanks for
and collaborators, including Todd Berger, Michael the memories!
Kenneth Libbrecht
Pasadena, California
July 30, 2020
