à ост Кристаллоь / Rost Kristallov / Growth of Crystals: Volume 11

387 Pages·1979·18.23 MB·English

by  N. V. Belov, A. A. Chernov (eds.), E. N. Belova (auth.)

POCT KPHCTAJlJlOB
ROST KRISTALLOV
GROWTH OF CRYSTALS
VOLUME 11
Growth of Crystals
Volume 11
Edited by
A. A. Chernov
Institute of Crystallography
Academy of Sciences of the USSR, Moscow
Translated by
J. E. S. Bradley
Senior Lecturer in Physics
University of London
@CO NSULTANTS BUREAU· NEW YORK AND LONDON
The Library of Congress cataloged the first volume of this title as follows:
Growth of crystals. v. [1]
New York, Consultants Bureau, 1958-
v. illus., diagrs. 28 cm.
Vols. 1,3- constitute reports of Ist- Conference on Crystal
Growth, 1956- v. 2 contains interim reports between the lst and
2d Conference on Crystal Growth, Institute of Crystallography,
Academy of Sciences, USSR.
"Authorized translation from the Russian" (varies slightly)
Editors: 1958- A. V.Shubnikov and N. N. Sheftal'.
1. Crystals - Growth. I. ~hubnikov, Aleksei Vasil'evich, ed. II.
Sheftal', N. N., ed. III. Consultants Bureau Enterprises, inc., New
York. IV. Soveshchanie po rostu kristallov. V. Akademiia nauk
SSSR. Institut kristallografii.
QD921.R633 548.5 58-1212
Library of Congress Catalog Card Number 58-1212
ISBN 978-1-4615-7115-5 ISBN 978-1-4615-7113-1 (eBook)
DOI 10.1007/978-1-4615-7113-1
The original Russian text, published for the Institute of Crystallography of the
Academy of Sciences of the USSR by Nauka Press in Moscow in 1975, has been
corrected by the editor for this edition.
© 1979 Consultants Bureau, New York
Softcover reprint of the hardcover 1st edition 1979
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
All rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
in any form or by any means, electronic, mechanical, photocopying, microfIlming,
recording, or otherwise, without written permission from the Publisher
PREFACE
The Growth of Crystals series was begun in 1957 by A. V. Shubnikov and .N. N. SheftaP
with the publication of the first volume. which contained the proceedings of the First All-Union
Conference on Crystal Growth. The initiative and considerable efforts of the principal editor
of the entire series. N. N. Sheftal', and his assistants led over the next 15 years to the publica-
tion of ten volumes which have assumed a leading position among the numerous books on crys-
tal growth. It has become traditional in this series to adopt a broad approach to crystal growth
problems, and this approach is continued in Volumes 11 and 12, which are composed mainly
of papers presented at the Fourth All-Union Conference on Crystal Growth in Tsakhkadzor.
September 17-22, 1972. These papers, presented by both Soviet and foreign workers, deal
with crystal growth processes. growth methods. and crystal perfection.
Many of the papers reflect the tendency for our knowledge of crystallization processes
to become increasingly more fundamental. with emphaSis on quantitative treatments. There
are some extremely difficult problems in this approach. especially when the requirements of
practical uses are envisaged. and many of these are discussed in various ways in these two
volumes. These topics include detailed theoretical and experimental analysis of cooperative
phenomena in crystallization. with emphasis not only on statistical thermodynamics but also
statistical kinetics. This approach involves research on the structure and properties of phase
boundaries. including the composition and structure of surface layers in liquids. the fre-
quencies and types of elementary acts at phase boundaries. impurity trapping. and the for mation
of metastable phases. Any ultimate solution in this field requires an enormously large body
of information on liquid structure. particularly for multi component liquids. and the topiCS are
of interest not only to physicists. but also to chemists and researchers in physical chemistry.
Another aspect. equally important but less researched. is the kinetics of electronic states in
elementary acts of crystallization and adsorption. together with the effects of external electri-
cal and magnetic fields. In addition. such fields affect the formation of crystals generally.
There are also major mathematical difficulties in analyzing macroscopic diffusion. convective
and radiation processes. and the stresses in growing crystals.
Quantitative experimental studies in these areas involve major difficulties. which arise
on account of the exceptional sensitivity of surface processes to the external conditions. Never-
theless. such researches are in hand. although they are concentrated mainly on macroscopic
processes. Quantitative research on elementary steps is at present possible only for crystalli-
zation from the vapor state. although in recent years it has proved possible to measure ex-
change ion currents at elementary stages in solutions. The prospects for research on surface
states in condensed phases are good. particularly when resonance methods and certain related
techniques are employed.
Systematic fundamental researches on crystallization will lead to further progress in
this area. but they would be inconceivable without a reasonably broad approach to the problems.
It is becoming steadily more difficult to maintain this broad approach with the ever-increasing
flow of information. The solution to this must be to take care not to reject what is of value in
v
vi PREFACE
the older lmowledge but to formulate fresh hypotheses providing deeper insights. In this way
we should be able to facilitate fresh discoveries. It has repeatedly been observed that consi-
derable assistance in maintaining a proper balanced viewpoint under conditions of super-
abundance of detailed information is derived from frequent reviews. Therefore, about one-third
of the papers in Volumes 11 and 12 of Growth of Crystals are devoted to reviews on various
aspects of crystal growth.
The reviews and the original papers are distributed by topic between the volumes.
Following tradition, the first papers in Volume 11 deal with nucleation at surfaces and in the
bulk; here much attention is given to molecular kinetics and the role of defects and inhomo-
geneities in the production of centers and critical nuclei.
The next section deals with layered growth, which presents researches on elementary
parameters and kinetic coefficients in crystallization, step interaction, and growth-surface
morphology .
The next section is a logical continuation and deals with the macroscopic consequences
of elementary surface processes such as crystal growth forms, stability in growth forms, and
heat and mass transport.
A considerable body of papers also deals with impurity trapping, with particular empha-
sis on the kinetic aspect of this problem.
The emphasis in Volume 12 will be on techniques of crystal growth and aspects of crys-
tal perfection in relation to growth conditions. These topics have become particularly compli-
cated and important on account of the enormous demand for large perfect single crystals for
use in solid state physics and chemistry, and especially in novel technologies. The production
of large Single crystals requires not only proper use of all the latest advances in research on
crystallization mechanisms but also a very detailed lmowledge of the causes of defects such
as inclusions, nonuniform impurity distributions, dislocations, blocks, internal stresses, etc.
Solutions here must come largely from new technological principles and equipment designs,
which allow one to provide closely controlled crystallization conditions. The very rigid cur-
rent specifications for crystal perfection have raised various complicated but important prob-
lems in equipment design. This applies particularly to the precision maintenance and measure-
ment of temperatures, including high temperatures, and the provision of appropriate tempera-
ture patterns, phySicochemical problems in crucible chOice, difficulties over reagent purity,
etc. The single-crystal industry is at present growing very rapidly, and this has made some
of these problems extremely acute. The specifications imposed in the production of large
single crystals have a close relationship also to the production of single-crystal films.
Volume 12 will contain papers on the growth of crystals by various methods from the
vapor state, from low-temperature solutions, from high-temperature solutions (including
hydrothermal ones), and from melts. The section on defect formation is dominated by papers
dealing with the formation of dislocations, the origin of internal stresses, and the causes of
impurity distribution.
The editorial board is indebted to many collaborators in the Institute of Crystallography
at the Academy of Sciences of the USSR and at Erevan State UniverSity, especially L. A. 8010-
mentsev, T. A. Lebedev, L. N. Obolenskaya .. S. A. Grinberg, A. M. Mel'nikov, L. V. Prikhod'ko,
N. A. Mekhed, V. I. Muratov, A. G. Nalbandyan, K. B. Seiranyan, and A. Kh. Eritsyan, who
have provided a great deal of assistance in preparing the manuscipts of both volumes. We are
also very much indebted for collaboration from numerous Soviet and foreign speCialists on
crystal growth in the early publication of these volumes.
A. A. Chernov
Kh. S. Bagdasarov
E. 1. Givargizov
R. O. Sharkhatunyan
CONTENTS
RUSS.
PAGE PAGE
Reaction Features of Silica. N. V. Belov and E. N. Belova ....•.. 1 6
I. NUCLEATION AND INITIAL GROWTH STAGES
Homogeneous Nucleation in a Liquid Metal.
D. E. Ovsienko ............................... . 9 11
Crystal Nucleation Kinetics in Small Volumes.
V. P. Skripov, V. P. Koverda, and G. T. Butorin •...•...•. 22 26
The Effects of Thermal Strains on the Activity of Nuclei
in Induced Crystallization in Glasses. I. Gutsov .•...•.•.• 26 29
High-Voltage Electron Microscopy Observation of
Nucleation and Growth of Precipitates on
Dislocations in AI-4 % Cu Alloy. N. Takahashi
and T. Taoka. . . 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 32 36
Dispersion of the New Phase in the Early stages of Mass
Crystallization. D. B. Kashchiev .•.•.•••.•.••••••••. 38 41
Crystallization as a Matrix Replication Process. G. I. Distler .••• 44 47
Elastic Interaction in Epitaxial Effects. V. L. Indenbom •••••.••• 57 62
Electron- Microscopic Investigations of Surface Diffusion
and Nucleation of Au on Ag (111). M. Klaua ••••••••.••..• 60 65
Nucleation, Growth Processes, and Electrical Properties
of Semiconductor Thin Films. R. Ueda •...••••••...••. 64 69
Distribution and Nature of Gold Crystallization Centers on
Single-Crystal Substrates. V. I. Trofimovand
E. Kh. Enikeev ••...•••.....•...•....•.•....... 67 71
Substrate-Induced Strain by Epitaxially Oriented Nuclei.
G. Le Lay, G. Quentel, A. Masson, and R. Kern ...•..•... 73 77
Migration of Polyatomic Groups in Crystal Growth from
a Vapor. L. I. Trusov .•.........••••••.......•.. 78 83
Selectivity and Growth Mechanisms for Stages of Growth from
a Vapor or Gas. V. F. Dorfman ....•.•........•.•.•. 82 87
Molecular-Beam Condensation and Accommodation: Sodium
Chloride on Tantalum. A. M. Zatselyapin, V. I. Mikhailov,
Yu. A. Gel'man, Yu. N. Lyubitov, and A. A. Chernov ••....• 89 93
Autoepitaxial Nucleation in Ionic Crystals. A. Smakula •••.•...• 97 100
Crystalline Growths on Object Points in Field-Emission
Microscopes. O. L. Golubev, B. M. Shanklin, and
V. N. Shrednik. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . 100 103
vii
viii CONTENTS
Structure and Desorption Energy for Monomolecular
Barium Oxide Films. T. A. Tumareva and T. S.
Ki rsanova. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 110
II. GROWTH KINETICS AND SURFACE MORPHOLOGY
Computer Modeling of Crystal Growth Processes. W. A. Jackson .• 115 116
Monatomic Layer Propagation Rate and The Electrolytic
Deposition Mechanism for Silver. V. Bostanov, R. Rusinova, and
E. Budevski ••••.........••..••........••..... 130 131
Determination of Kinetic Crystallization Coefficients in
Experiments with Whiskers. E. I. Givargizov ....•...•.. 136 138
Bulk and Interface Effects in Crystal Growth by the
Moving-Solvent Method. V. N. Lozovskii,
G. S. Konstantinova, V. Yu. Gershanov,
E. I. Kireev, and V. S. Zurnadzhyan •....•..•••••.•..• 146 147
Faces with High Indices on Ionic Crystals as a Consequence
of Layer Growth. P. Hartman .......••.•..••.•.•..• 152 154
Macroscopic Steps on Vicinal Growth Surfaces in Ger-
maniwn.. A. A. Tildlonova ........................ . 155 157
Simulation of Modes of Vibrations in Trains of Steps.
P. Bennema and R. van Rosmalen •..........•. 160 162
The Distortion Mechanism for Photolithographic Projec-
tions in the Epitaxy of Silicon. A. F. Volkov and
N. S. Papkov .•....••..•..•••••••.•.........•.. 166 168
Effects of Dopes on the Anisotropy in the Rate of Growth
of Germanium from the Vapor State. A. N. Stepanova .....• 172 174
Effects of Crystallization Conditions on Growth and Doping
Anisotropy for Epitaxial Germanium. L. G. Lavrent'eva,
I. S. Zakharov, I. V. Ivonin, and S. E. Toropov •••.......• 177 179
Effects of Foreign Particles on a Macroscopically Smooth
Surface on the Movement of Steps Due to Evaporation
and Condensation. Ya. E. Geguzin, V. V. Kalinin,
and Yu. S. Kaganovskii ..•....••......•••.••••...• 183 184
Estimation of the Mean Displacement of Adsorbed Molecules
from the Growth of Lochkeims. M. Kron •.•..••••.••.•• 191 192
Observation of the Kinematic Interaction of Surface Steps
During Evaporation of NaCl. K. W. Keller .•.•••••.••.•. 195 196
On the Shape of Growth and Evaporation Spirals.
T. Surek, J. P. Hirth, and G. M. Pound ••.....••..•.••. 202 203
Holographic Techniques in Crystal Growth. R. J. Schaefer,
J. A. Blodgett, and M. E. Glicksman ••••••••••....••.. 207 208
Concentration Inhomogeneity in a Solution during Crystal Growth
and Dissolution. I. N. Guseva, V. M. Ginzburg, and
v. A. Kramarenko ............................. . 215 216
III. GROWTH SHAPE STABILITY AND TRANSPORT PROCESSES
Stability of a Planar Growth Front for Anisotropic Surface
Kinetics. A. A. Chernov •.••.••..••••..••••••••••• 223 221
CONTENTS ix
Morphological Stability near a Grain Boundary Groove in a
Solid- Liquid Interface during Solidification of a Pure
Substance. S. R. Coriell and R. F. Sekerka ••..••••••••. 232 230
Morphological Stability near a Grai n Boundary Groove in a
Solid- Liquid Interface during Solidification of a Binary
Alloy. S. R. Coriell and R. F. Sekerka •••....•.••••••• 254 248
Size Behavior of Crystals Interacting by Diffusion During
Phase Transition. B. Ya. Lyubov and V. V.
Shevelev ................................... . 267 262
Supercooling for Growth Front Motion Limited by the Heat-
Transfer Rate. N. A. Avdonin ••••........••••••..•. 274 268
A Theoretical Study of the Effects of Various Factors on
Impurity Zoning in Crystals. B. I. Birman .••....••••.• 278 272
Steady-State Dendritic Growth. G. E. Nash and M. E. Glicksman ..• 284 278
Diffusion-Limited Growth of Zinc Single Crystals. C. N. Nanev
and D. G. Ivanov ........................ 0 ••••••• 290 284
Factors Governing Crystal Growth and Dissolution Shapes in
Molten Metals. L. M. Kolganova, A. M. Ovrutskii, 295 289
and E. V. Finagina • . • • • . . . • • • . . . . . . • • • . . • . • . . . . •
Growth of Naphthalene and p-Dibromobenzene Crystals in
Thin Films of Melt. A. M. Ovrutskii and V. V. 299 293
Podo linskii . . . . . . . . . . . . . . . . . . . . . . . • . • . • . . . . . . .
Effects of a MOving Magnetic Field on the Stability of a Crystalliza-
tion Front in a Melt. K. M. Rozin, V. V. Antipov, and N. V. 304 298
Isa}{ ova .......••. . . . . . . . . . . . . . . . . . . • . . . . • . . .
IV. IMPURITY TRAPPING
Trapping during Growth from Solution. I. V. Melikhov •.•••••••. 309 302
Trapping during Growth from a Melt. J. Barthel ••••.•.•..••.. 322 316
Aspects of High-Speed Solid-Solution Crystal Growth.
D. E. Temkin ................................ . 334 327
Formation of Metastable Phases in a Rapidly Cooled Melt.
I. S. Miroshnichenko .••••.••••.•..•....•...•..•. 344 337
Trends in the Formation of Supersaturated Solid Solutions
at High Crystal Growth Rates. A. I. Dukhin and
G. I. Miroshnichenko ...............•............ 355 348
The Distribution Constant in Hydrothermal Quartz Growth.
R. A. Laudise, E. D. Kolb, N. C. Lias, and E. E.
Grudenski ................................... . 359 352
Dope Uptake Factor in Relation to Growth Rate and Surface
Inclination. V. V. Voronkov ••••••••••••••.•••••••• 364 357
Impurity Trapping in the Movement of a Short Elementary
Step. S. S. Sfoyanov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 367
Growth Conditions and Structured Nitrogenous Inclusions
in Diamond. Yu. A. Klyuev, N. F. Kirova,
V. I. Nepsha, and V. M. Zubkov •••••.••••••••••••••• 379 371
Effects of Isomorphous Replacement on Some Properties
of Synthetic Diamonds. G. N. Bezrukov and V. P.
Butuzov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 374
REACTION FEATURES OF SILICA
N. V. Belov and E. N. Belova
Institute of Crystallography. Academy of Sciences of the USSR. Moscow
The history of the production of large synthetic quartz crystals goes back nearly 100
years; the problem involves considerable difficulties on account of the exceptionally low solu-
bulity of SiD:! and of silicates generally in ordinary solvents, together with the exceptional
difficulty of handling SiD:! in the form of silica in classical chemical analysis. A series of
studies about 15 years ago, including some of our own, repeatedly confirmed the view that
silicon is an extremely inert or immobile element, which as its oxide SiD:! is almost complete-
ly incapable of participating in reactions, particularly those utilized in classical analytical
chemistry. Some have sought to argue, in spite of the inertness, that silicon-oxygen patterns
are readily adapted to other details of silicate architecture, but in that case one is really
speaking of a form of chemical reaction. No conflict arises if we do not seek to equate reac-
tions in dilute fluids with those in condensed phases, especially solids, since in the latter we
find that silica can readily adapt not only to the cation framework but also to ephemeral rings
of water molecules and even large clusters of other structures such as zeolites, A and X mole-
cular sieves, etc. [1].
Undoubtedly, one of the major advances in mineralogy and silicate technology (e.g.,
cement and glass) has come from x-ray researches, which have shown that the basic unit in
nearly all silicates is the Si04 tetrahedron, which is either individualized, when the four °
atoms do not participate in the environment of adjacent Si atoms, or else the Si04 forms part
of some larger silicate radical, while still remaining a reasonably regular tetrahedron, al-
though some of the vertices, or perhaps all, participate in the environment of adjacent Si atoms,
or rather in adjacent equivalent Si04 tetrahedra. It is generally accepted to say that a diortho
group or pyro group Si20 7 is the result of condensation of two tetrahedra: 2Si04 = [Si20 7] + 0, .
with six Si04 condensing to a [SiS018] ring: [S4018] = 6Si04 - 60. Similar equations are readily
written for the unbounded radicals in pyroxenes, amphiboles, networks, and even frameworks,
but in every case they involve release of free oxygen, whose subsequent external fate is of no
particular interest. No search has been made for the reducing agent that would absorb this
oxygen, and there is none. An exception may perhaps be made for those few statements by
petrographers on the environment of amphibole formed after pyroxene, which contains grains
of magnetite, and which is due to oxidation of the FeO from the primary pyroxene.
A [Si0414- tetrahedron is itself a large cluster composed of four ° anions linked to the
highly charged Si4+, and during the last 40 years this has become accepted in mineralogy and
in earth sciences generally as capable as transferring as a whole from one compound or phase
to another. In particular, the present authors have discussed the position of femic com-
ponents from a differentiating magma and have written that the originally depositing MgO
takes up individual Si04 tetrahedra to produce olivine: 2MgO + Si04 = Mg2[Si04] + ~ (?),
although no question of the released oxygen was raised. A similar problem arises over Si20 7
groups and even over the change required to produce pyroxene and biotite from MgO.
1
2 N. V. BELOV AND E. N. BELOVA
In recent years it has repeatedly been stated [2] that the Si04 tetrahedron is undoubtedly
the basic static unit in any silicon-oxygen structure, i.e., is the silicate brick, but one which
is produced directly at the point of use and introduced into preexisting structures as single
mobile neutral Si~ molecules. Conversely, an entire Si04 brick cannot be released from a
complex silicate framework, since all four vertices are closely linked to four equivalent Si04
bricks, and the latter would thus be destroyed by the release of one Si04• Such a yield of only
20% would be too small for a solid-state reaction. Therefore, only Si~ molecules may be
considered as dynamic units, and they transport silica in living organisms (silicosis), in the
walls of furnaces, and in other such circumstances, e.g., in the formation of olivine, where the
neutral or basic MgO extracts neutral Si~ from the magma, although the mineralogist consi-
ders such molecules as acid (electronegative), and although when we write the equation
2MgO + SiC>:! = 2MgO. Si~ = Mg2Si04 we take oxygen from the first member and attach it on
papertotheSi,whichleadstospeakofthe [Si04]4- tetrahedron as a basic silicate brick in the
olivine building. As the magma cools, successive neutral batches of Si~ are detached, and the
Si04 tetrahedra are bound into pyroxene chains: Mg2[Si04] + Si~ = Mg2[Si06], the scheme being
0 0
I -
. Si .
As the silicification proceeds, i.e., as the pyroxenes are formed, new batches of Si~ are
taken up and result in silicon-oxygen networks oftalc-biotite type: [Si20 6]00 + 2Si~ = [Si40 10 ]0000
[2].
We have already noted above the special position taken by amphibole in this particular
sequence.
It is readily seen that if there are cations bearing their own oxygen (MgO, FeO, or Zr02) ,
one can get silicification in a pure Si~ framework (quartz, tridymite, cristobalite), Le., in a
three-dimensional network of Si tetrahedra, in which all vertices are shared with neighbors.
The pale (feldspar) constituents of rocks contain three-dimensional frameworks composed of
tetrahedra, and these are formed in situ, i.e., within the initial magmatic glass around large
cations such as Ca, Na, and K [2].
In the original studies on the formation of complex silicon-oxygen radicals in femic
minerals, nothing was said on the state of aggregation of the siliCifying Si~ molecule on the
path to the final pOSition, namely from the acid phase to the basic one; this was imagined as
being gaseous, although it is difficult to imagine a gaseous layer between the phases in a con-
densed system at very high pressures and therefore any long life for the Si~ molecule.
Ten years ago it was supposed [3] that, if the true basis of a silicate structure is to be
seen in the large cation polyhedra, with small Si atoms placed between the oxygen vertices
(with all the ° attached to these by tradition), then the small Si should readily migrate, and that
without any oxygen burden, thereby being able to jump from oxygen tetrahedron to another or
to an adjacent hole. The present writers for long viewed this possiblity at the very least skep-
tically since in our laboratory we obtained no evidence for such jumps from x-ray analysis of
hydrated Ca - Al sodalite [4].
To find an explanation we need to go back to the 1890s, when coordination concepts were
introduced into chemistry and mineralogy (by Werner and Vernadskii), when the coordination
prinCiple was received with considerable skeptiCism, and therefore the state, for instance, of
aluminum in the coordination octahedron was still described by means of three valency bonds