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Timeline of the project for numerical simulation of crystal growth.

by Dr. Leonid Sakharov

"A timeline of the project for numerical simulation of crystal growth has being conducted by Dr. Leonid Sakharov is outlined in form of memoir.

Looking back at amount of efforts and hopes invested into the project to understand how crystals are growing compare with fruits it brings in return anybody can make own judgment did it worth it. Lifetime effort ends with finding universal formulas for growth rate of crystal surface, its roughness and concentration of hole like defects. My life has been sun-setting too. It would be only fair, whatever this word "fair" means, that in exchange for revealing these finding humanity secures modest comfort for my winter years. I can only hope that outcome will not be punishment by poverty.

My childhood coincides with probably most respected time for science in human history. At sixties of last century in my birth country, USSR, science was declared to be an official ideology. Communist Party equals communist ideology to scientific conclusion of materialistic philosophy, rejected religions as fair tales for keeping population obedient and enjoyed products of nuclear physics to secure borders of country from any outside forces. Science was new religion and I was book-worming kid learning ideas through all sci-fi novels was able to obtain. My family has home library, neighbors did too with books for exchange and borrow plus there were public libraries. I was reading everything published in Russian including numerous translations of Jules Verne, Herbert Wells, Conan Doyle. I read all about science including popular and biographies books about atom age. My family subscribed to all popular science journals. But I wasn't just a nerdy kid. I loved sport, fighting and thee musketeers. Idea to serve science as monk in isolated from simple sensitive pleasures life can provide was not too attractive. One book hit my imagination with sample of prominent scientist life convinced me that life of scientist can be the same enjoyable as for actor or other celebrity like figure. It was popular in Russia translation of "Doctor Wood, modern wizard of the laboratory: the story of an American small boy who became the most daring and original experimental physicist of our day--but never grew up" by William Seabrook. By strange coincidence the city of Concord, Massachusetts that is the birthplace of Prof. Wood is now the destination of my regular bike trips to Walden Pond for summer swimming.

My father, German Sergeevich Sakharov, infected me with sin of ambition to be celebrated for first class achievement. He was unique for USSR person even by formal description: naval captain of first rank (colonel) nonsmoker, non-drinker, non-member of Communist party decorated by three major orders including The Order of Lenin. He was born ten years before 1917 turmoil that destroyed future of Russia Imperia in family of self-made railroad official. By family account my grandfather Sergei Illarionovich Sakharov as Vikzhel (All-Russian Executive Committee of the Union of Railwaymen) member was arrested by Bolsheviks just after their grabbing power. His wife Lubov Grigorievna contacted the famous writer Gorki and via him Felix Dzerzhinsky, that helped with release of my grandfather from jail. My granddad took assignment to deliver bread to hungered Petrograd, did it and has died from lung inflammation during that winter. An uncle of my farther was officer in headquarter of Trotsky during Russian Civil War. After Trotsky ousting from USSR it was important negative point in my father biography. During communist reign everybody had to submit auto-biography along application for any position of importance including student for higher education. My farther put all this info into his official auto-biography every time. In spite he found himself blacklisted for civil higher-education institutions (first by exams - out of list) the Red Army was sort of refuge because of desperate need to expand fast. Then season of repressions came in 1937. It is my family believe that the habit to report everything on himself safe my father from arrest and death because absent of anything hidden that was the proof of absent any conspiracy. He did survive communist epoch. He was not promoted to admiral but kept clean hands. In many ways he made outstanding career but not enough to be put into any history book how I think he did dream about himself. He wanted it for me.

It is always dubious idea to push hard your child into career success. If you think that life is constant competition for higher place in career stair to start earlier have perfect sense. I was six years young when my farther signed me in elementary school, one year younger than all my classmates. First years when in prime school was difficult to pass Russian grammar. Perfecting languages I always had problem with. Only later until period of activity in internet forums I was forced to understand importance of spelling as litmus test of intelligence to be taken serious. Later on school was relatively easy for me academically but socially in teenagers years all girls around were more mature. It is topic for autobiography novel, maybe. Yes, wunderkind can start career earlier but will he be he happier social? Looking back I have definite answer - it depends on luck: historical, friends, teachers, genetics. Nobody can foresee future with such precision to be sure that his influence on fate other person including his son will be positive. Maybe yes, maybe not. In any case my fascination with science stars since school years. I had formally recognizable successes then as well. In state TV show "Cognition continues" about Physics quiz I got diploma among other winners. My guess is that I was selected from thousand others because one answer - idea how to make air-air rocket to fire from firefighter tail back. Just a wild guess. Reading books about invention of atom bomb, quantum physics, theory of relativity together with numerous sci-fi stories I naturally want to be the inventor of Theory of Everything - that will finally explain how the reality is constructed. If you are learning fundamentals of physics any textbook starts with definitions these are axiomatically true. Many theories has its own set of true definitions. Can be one meta-theory? What is vacuum? Is it nothing between particles? If so what is field force? Is it mater? If so and fields like magnetic are always all around us is vacuum a matter? I wanted to became theoretical physicist to find answers on all such questions, to invent anti-gravitational engine and travel around space to discover other civilizations to meet space princes, charm her and instantly quest for next in infinite line of them living forever.

The University to train for Einstein like career was Moscow PhysTech. It was as I thought been sixteen high school graduate. I did not passed oral Physics exam there. It was painful but very useful for my future lesson how not to handle series of trick questions. I was naive in faith that examiner interested to find hidden genius in immature juvenile and answering as fast as I can. Mostly wrong if to dig dipper. Then I tried Physical department of Leningrad State University. Oral Physics exam I passed with highest mark thinking twice before saying a word but Math marks was not good enough. I landed in Chemistry Department in group oriented to be radiochemists. They needed males to be exposed to radioactivity (almost all girls wisely didn't wanted to). Years in University was spitted in my mind on nightmarishly difficult three semesters at start and comfortable relaxing smooth finish till graduation. Something happened when eighteen with my brain to step up at next level of intelligence. Who knew what it was - just genetic clock in growth, cosmic ray hit a switch or something in a water.

It was far not my very first encounter with crystals at course of crystal structure in Laboratory of Crystallography during my education at Chemistry Department of Leningrad (Saint Petersburg) State University. In the laboratory was opening for assistant of lecturer V.N. Markin to continue research of super-structure compounds of oxyfluoride vanadate of cobalt and cooper. I did shine among chemistry students in programming (we had in 1974 first course of algorithmic languages ALGOL and I was the star) and physics related disciplines. In diploma thesis works my best achievements was synthesis isomorphic analogous vanadate crystals and plus very special structure crystals of cooper vanadates. Its X-ray pictures of invert crystal structure was so strange that my adviser at first cannot accepted them to be for real. My diploma thesis was successfully defended although the atomic structure of compounds was not defined. Super-structure crystals are hard to handle and now I (looking at internet) suspect that there is no definite answer for positions of atoms in them like for liquid crystals are. It is not so hot topic to be easy financed and explored - just academic curiosity that society sometimes permit to perform for no particular reason like a sport often not enough for complete answer.

Being graduated in 1976 I have recommendation in graduate school of Geological Faculty of Saint Petersburg State University in Crystallography Department to learn soon that they only thought that position was for real. I had happen without place first time in my life but not last, unfortunately. That year after several months of just struggling with my shyness and wrong expectation that my family via social network would care for my future. I made obvious but brave move to walk into human resource department of Academy of Science. There I learned that sometime the best idea is just ask for help. A nice woman connected me with Institute of Silicate Chemistry where there were an open position in graduate school waited to be filled.

In some way it is the begin of timeline of this story of numerical simulation of crystal growth. The content before was about my physiological profile to explain mostly for myself how the scientific project can last forty years practically without real outside encouragement. My scientific advisor P.F. Rumynzev was in 1976 vice director of the Institute of Silicate Chemistry. His office was on second floor, my table in a floor higher in laboratory of structure transitions of silicates that was synonymous for science of cement. One day my adviser appeared and write on the small piece of paper: "Crystallization in eutectic systems of CaO-Al2O3-SiO2." It was preliminary title of for my doctorate graduate thesis. Several peoples before me refused to take this project as too difficult experimentally and not too actual. I was too young (21), fearless and trained to be subordinative. The project was based on experiment with high temperature microscope. It is an  accessory to long focus microscopy where hot platinum wire with drop of silicate sample is heated and cooled in controlled manner to observe crystal growth in situ. The experiment was sort of challenging but durable for me. Not too much researches on quantitative level has done in this area even up to now I can brag.

In my thesis research I was able to obtain Tamman temperature curves of crystal growth rate for dozens silicate melts. Classical scientific approach demanded to make interpretation of results on the base theoretical concepts and formulas. Experimental data of growth rate fit quite nicely to nonlinear formulas in whole temperature interval from 1600º to 900º degrees of Celsius. The problem was that fitting coefficients did not easily matched with theory or at least I thought so. Now I think that I felt into a trap of weighting specific numbers of fitting coefficients too heavy instead of just describing theoretically the whole picture with broad brush. In any way dissatisfaction with theoretical explanation of mechanism of crystal growth was seeded in my mind for future as constant irritator.

There were period in my career from 1986 to approximately 1993 when I was occupied with unrelated to theory of crystal growth problems. I moved into newly founded Institute of Mechanical Engineering of Academy of Science. There ware project of ceramic engine, plasma coating of turbine blades, plasma coating, temperature dependence of strength of high refractory materials, novel high temperature superconductive ceramics research in collaboration with Ioffe Physical -Technical Institute. I became Senior Scientist and got leadership of group of young scientists. Then Soviet Union was crashed and salaries in Academy of Science haven't paid in time at the background of hyperinflation and for me there was brand new child. Lines of destiny were sharply bent for many during these troubled days. I had many options to move on from science - into business, politics or maybe weather out bad times in science nevertheless. My best guess is I would try myself in politics and soon ended in grave as most of neophytes in Russia politics of nineties. Soros Foundation made effort to support scientific community of former Soviet Union or maybe to keep best minds from resistance to criminal reforms. There were grants in US dollars for authors of  publications in academic journals and then open competition for scientific projects. I has applied for grant project as group of one person to make numerical simulation of crystal growth.

Before writing down the proposal I already had preliminary algorithm ready. It was done on my very first sort of personal computer I was able to buy it selling some antic family staff. It was Sinclair ZX Spectrum for about $40 USD or so. It worked with portable TV and cassette audio recorder. Besides games there were software like PASCAL making possible to develop own programs. I was able to create fast algorithm to simulate processes on crystal surface to convince myself that it is perspective enough way to present as grant proposal.

I did win the Soros grant in 1994 just for myself. It was so big money on the scale of salaries of Academy of Science those years that I was able to buy real PC Computer for myself, feed with fresh fruits my family, made leadership of Institute so jealous that they retailed against me administratively making me practically without formal position. There were conflict, court lawsuit, firing and settlement later on. About one year I did software, made numerical experiment and tried to understand what I had on hand. I thought that I found approximation formulas these can be used for replacing numerical experiment for every set of parameters. In general the problem looked like to be solved in my hungry to round up the project eyes. The tension with administration was really bad. Situation in country developed even worse. I tried to report my findings at Material Research Society conference in Boston at 1995. My thesis of report were rejected but I received a letter that contained an invitation to attend.

Soros grant add three thousand dollars for second stage and I did decide to use these money to travel to MRS conference in Boston. Soros foundation helped to buy ticket. In Saint Petersburg USA consulate in spite that on question: "Do I going to work in America?" - I did answer: "Yes, I if I would be invited"  I did got visa in USA. At conference I did begged to show my presentation at night posters and was permitted to. I was quite close to find job position, at least I had two interview one of them with Harvard. After conference I had visa to stay for three month and return flight ticket in three month too. It was the time window to change my fate. For good or for bad. I was landed in Northeastern University as visiting scientist literally across Huntington avenue where I against all odds sublet a room from Russian speaking Georgia student. The professor Bill Giessen hired me to be used me for two projects simultaneously - magnetic alignment of high-temperature superconductors and for statistical support of his speculations on currency market. I did learn Visual C++ programming technique these several years working for him. He did threw me out like a squeezed lime even before my current contract expired just upon frustration I didn't want to play with my software as day-trader for half of my basic salary. Day trading is only gambling, believe me I did all analysis. Currency market is money pump only for whose who knows future for sure because they set price targets themselves and for internal use only. In between I did proposal to NASA for this crystal growth numerical simulation project. No luck then by many reasons.

I had happen to be in transition stage. Starting new career in America been close to fifty is not easy. I was landed in start-up Admetric BioChem as programmer for analysis mass-spectrometry experimental files. I did developed innovative algorithm for detecting peaks so good that firm indented to patent it. Everything was nice except this nice start-up business was liquidated and I was laid off. It was June of 2001. Then 9/11 had happened. Russian born scientist-programmer became imposable to get clearance and most research oriented businesses were closed or frozen. Then when I got US citizenship but aged too. When tried into clearance demanded position learned that citizenship is not enough now - was told I must be graduated in USA university as well. My idea to develop and sell my own software kept me occupied but provided no significant financial success.

Periodically I was been returning to crystal growth simulation project revising my software LeoCrystal developed primary as tutorial tool. It gives nice presentation of the crystal growth on the molecular level. Formulas for fitting numerical simulation experiment haven't satisfy me mostly from premonition that correct formulas must be mathematically beautiful. New function for random number generator for large numerical interval was incorporated in program then. It helped to get smoother performance but not enough to make me completely happy with results.

I did last, in my mind, desperate attempt to fulfill the project on the level to be proud for outcome without reservations. New attack coincide with bought of more productive computer in 2011. I revised the formulas to calculate probabilities for given value of time step for molecule to be incorporated into crystal and  be emitted from its surface into surrounding, incorporating sophisticate normalization methods; obtained on the base separate numerical experiment for one event of such elementary move. I run very big series of numerical experiments for broad set of parameters. My software for data analysis LeoDataAnalysis was advanced to fit of analytical formulas written in free form. I did add a feature to LeoCrystal to recognize situations of trapping hole like defects. I did also rename LeoCrystal into LeoMonteCrystal for the method of Monte Carlo it is based on.

I was almost on the edge to accept that only formal approximation by open ended series are possible. Essentially I considered to give up.

After many semi-successful  attempts to construct semi-analytical fitting functions is was a wonder time. As by wish of wizard every bricks of formulas have to start gathering into building with logical architecture. At first formulas had array of fitting coefficients with some unrelated to anything else values. To get one constant for my name could be nice but seven of them are too much for comfort. One by one I was able to replace fitting coefficients by by values of mathematical constants in these formulas. As by magic spell it was the success. All coefficients in fitting formulas with good agreement with result of numerical experiment had happened to be fundamental math constants.

It was the complete victory from my prospective. I was happily surprised that I did it. But with sort of bitter taste considering how late in my life the victory has come.

Now I am in stage to convert this knowledge into income. My present business strategy is to sell the software LeoMonteCrystal that incorporated fitting formulas keeping their analytical form confidential up to the point when I will feel secure financially if such moment will come at all someday.

 

, please.

Oct. 17, 2017; 17:49 EST

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