Table Of ContentStructural Mineralogy
An Introduction
Solid Earth Sciences Library
Volume 7
Structural Mineralogy
An Introduction
by
J. LIMA-DE-FARIA
Centro de Cristalografia e Mineralogia,
Instituto de Investigariio Cientifica Tropical, Lisbon, Portugal
Springer-Science+Business Media, B.Y.
Library of Congress Cataloging-in-Publication Data
Lima-de-Faria, J. (Jose), 1925-
Structural mineralogy an introduction I by J. Lima-de-Faria.
p. cm. -- (Sol id earth sciences 1 ibrary ; v. ])
Inc 1 udes bib 1 i ograph i ca 1 references and indexes.
1. Minerals--Classification. 2. Crystal structure. 1. Title.
II. Series: Solid earth sciences library; SESL 7.
QE388.L56 1994
549' . 12--dc20 94-10374
ISBN 978-90-481-4396-2 ISBN 978-94-015-8392-3 (eBook)
DOI 10.1007/978-94-015-8392-3
Printed on acid-free paper
Cover illustration: Olivine crystal structure, (Mg, Fe)" Sit[041h, (condensed model representation).
All Rights Reserved
© Springer Science+Business Media Dordrecht 1994
Originally published by Kluwer Academic Publishers in 1994.
Softcover reprint of the hardcover I st edition 1994
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
To Natacha and Arnaldo Silverio
In spite of the variety of the mineral crystalline
world, the whole 'mineralogical game' just
reduces to various modes off illing gaps in
uniform close packing with various corresponding
patterns.
N.V. Belova
The greatest pleasure in the study of science is
understanding.
Leopold Infeld b
a From 'Structure of Ionic Crystals and Metallic Phases'
(1947). Izd. Akad. Nauk SSSR. Moscow.
b From 'Albert Einstein. His work and its influences on our
world' (1950). Scribner Publishers, New York.
Contents
Foreword IX 4.3.1. Rules governing the polyhedral
Preface Xl constitution of inorganic crystal
Acknowledgements Xlll structures (Pauling rules) 34
4.3.2. The bond-valence rules
1. The structural classification of minerals (Brown rules) 35
1.1. A very brief history of mineralogical 4.3.3. Rules governing the layer
classifications 1 organization of inorganic
1.2. The structural classification of crystal structures 36
inorganic structures 3
1.3. The structural classification of 5. Structure and properties 38
minerals 6 5.1. Physical properties and crystal
1.3.1. General considerations 6 structure 38
1.3.2. Implications of the structural 5.2. The importance of crystal structure
classification of minerals in in phase transformations 40
the classification of silicates 8 5.2.1. Topotaxy 40
5.2.2. Transformation twins: packing
2. The anatomy of crystal structures 9 and interstitial twinning 43
2.1. What is a crystal structure? 9 5.2.3. The measure of symmetry in
2.2. The constitution of atoms 9 crystal structures and its
2.3. The bonds between atoms 11 application to phase
2.4. The size of atoms 14 transformations 44
2.5. The coordination of atoms 17
6. Representation of crystal structures 52
3. The architecture of crystal structures 21 6.1. Kinds of representation 52
3.1. The structural units and their 6.2. Layer description and the condensed
'polymerization' process 21 models of crystal structures 53
3.2. The packing of structural units 21 6.3. Computing programs for layer
3.2.1. Kinds of close packing of description 59
individual atoms 22 6.4. Representation of real structures
3.2.2. The packing of groups, chains by ideal structures: packing and
and sheets 31 symmetrical analogues of crystal
3.2.3. The connectivity in structures 59
frameworks 31
7. Nomenclature of crystal structures 63
4. The stability of crystal structures 33 7.1. Degrees of similarity among mineral
4.1. The general conditions of stability 33 structures. Concept of structure
4.2. The extension of Laves principles type 63
to minerals 33 7.2. Structural formulas 65
4.3. Stability rules 34 7.2.1. General considerations 65
vii
Vl11
7.2.2. Notation for the coordination 8.3. Final remarks 78
of atoms 66 8.4. Descriptive charts of mineral structure
7.2.3. Notation for the structural types 81
units and their packing 68 8.4.1. Close-packed structures 81
7.2.4. General scheme for the 8.4.2. Group structures 167
structural formulas 70 8.4.3. Chain structures 199
7.2.5. The importance of structural 8.4.4. Sheet structures 221
formulas for the relationship 8.4.5. Framework structures 251
of crystal structures 72 8.4.6. Structures not classified 301
7.3. Structure type symbolism 73
References 327
8. Systematics of minerals on structural Mineral index 335
grounds 76 Subject index 341
8.1. Choice and presentation of data 76 Author index 344
8.2. Ordering of the main categories
of mineral structure types 77
Foreword
Recently, many fine textbooks in mineralogy have notable early achievements in unravelling the crys
appeared. The great tradition of mineral science tal structures of minerals. I would include Zachari
continued for over 100 years in Dana's systems, as en and Belov as well, two other giants in crystal
textbooks, and manuals, replete with discussion on structure analysis. How many contributed in their
crystallographic characters, and short statements own way to our science? Ten? Fifty? One hundred?
on the mineral species as then known. The more re It depends on how you weight the count, but I
cent superb RamdohrlStrunz Klockmann's Lehr suspect it is closest to the biggest number just men
buch der Mineralogie is a mine of rich crystal tioned.
chemical information, perhaps the finest contem The explosive growth in information (Ger.:
porary pedagogic book of its kind. Within the past Fach) on crystal structures began about 1950, when
three years, a new and ambitious project - the the big computers and automated diffractometers
Handbook of Mineralogy by several keen mineralo were just emerging. It contributes mightily to our
gists - receives much assistance from up-to-date science (Ger.: Naturwissenschaft). Unfortunately,
computer technology and promises to be a very fine technological knowledge seems to come easily now,
series. The little Mineral Reference Manual by Nic and Fach appears to be outstripping Naturwissen
kel and Nichols is a handy means of quick access to schaft, a sorry state of affairs. Most practicing mi
the original literature on species and reference to neralogists today are Fachidioten and are hardly
crystal structure determination. Do we really need Naturwissenschafters. The science has become tedi
another book? For the Structural Mineralogy of Jo ous; it no longer dances with nimble feet as Nietz
se Lima-de-Faria, I say indeed we do! sche instructed us. Mineralogists don't know their
Mineralogy is one of the natural sciences, and minerals. Mineralogists don't go into the field any
about the oldest one at that. It antedated inorganic more. Crystal structures, the products of blood,
chemistry, crystallography, and so much geology. sweat, and tears at the diffractometers, computers,
Mineralogy is at the scientific root of mining, and pocket calculators are slipping into a grey
prospecting, mineral dressing, and a host of other gloom, abandoned orphans of science. What do we
utilities stimulated by our science. Minerals were do with all this information? Is structural knowl
practically the first crystalline materials to be in edge hortative, beyond mere confirmation or deter
vestigated after the demonstration by von Laue and mination of a correct formula, or a challenge to an
the Braggs of X-ray diffraction by crystals in 1912. old one?
The phenomenal growth of crystallography as a It seems to me that mineralogy today is far from
workhorse for structure and crystal analysis, from a dead science, although most mineralogists may
Patterson's Faltung to Hauptmann and Karle's di fall into that category. These are really exciting ti
rect methods through probabilities of structure mes! With so much gruelling and repetetitive data
semi-variants are in many respects the crowning ti already accumulated, and much structure solving
ara of 20th century science. After all, without Wat and information collating out of the way, it seems
son and Crick's unveiling of elusive DNA, where that mineralogy is about to blossom again. This is
would molecular biology and biochemistry stand in the greatest and most ambitious intellectual exer
today? Dr. Linus Pauling, arguably the greatest cise of them all: the link between crystal structure
thinker in chemistry of the century, made his most and mineral paragenesis. Certain more serious
ix
x
thinkers in mineralogy have felt, especially since that fundamental law of nature, closest-packing,
WW II, that structure types just don't pop up out of are misrepresented!
nowhere like mushrooms, but that structure type is lose Lima-de-Faria prefers to cast the closest
a kind of Rosetta Stone to a mineral's genesis. The packed representation as a sphere packing model. I
famous kyanite-andalusite-sillimanite trimorphs find that rather hard to perceive, as I happen to be
serve this point well, but isn't it a rather sparse a polyhedrist by inclination. Because the closest
example of such a structure-paragenesis link?! Af packed representation is the real goal of the study,
ter all, we have about 2000 structure types to ex I would even submit a table listing the transform
plain and understand more fully. ation matrices, the old and new cell, the old and
One of the big hindrances in understanding new transformed coordinates, the mean layer sep
structure is found in structure representation. Most aration h, and difference, t..A, or the coordinate dif
structure representations in the literature resist the ferences (expressed as 'interatomic' distance) be
reader's perception. Several projections should tween real and ideal (calculable) perfect closest
really be shown as structures, like plumbing as packed representation. Such a table is akin to the
semblies, have joints which relate to other structu table of structure factors so familiar to all crystallo
res in different directions. Of course, closest graphers, a certificate of sorts to see whether or not
packing with at least one h (= ABA) in the stac one is cheating or just misinterpreting the infor
king sequence has just one principal direction. In mation at hand. Such a transformed cell also makes
such a structure, once t* (the vector normal to the listing of shared polyhedral edges much easier to
c.-p. layers) is defined, layer-by-Iayer sequences find, visualize, and enumerate.
within the asymmetric unit of translation can be Be that as it may, 10s6's book covers the prob
shown. Some of these may be building blocks for lem of structure description, utility, classification,
other structures. Often, each layer tells a little sto and representation quite well, and it tries to place
ry by itself, and it may reveal a 'secret' to the rea some guidelines toward more uniformity in struc
der. If t* falls along general [hk~, then it is the task ture descriptions, most of which in the literature
of the investigator to transform the cell into a new are really quite shoddy.
more reducible representation, but one that opens Structural Mineralogy is really not an end in it
up the window of closest-packing. Fractional self. Rather, it is a rallying call to urge further clari
coordinates are transformed according to the fication, representation, and systematization of al
transpose of the inverse of the adjoint of the trans ready known structures. Committees cannot dele
formation matrix, that is A' = T(Adj A), where A is gate such notions as ephemeral and individual as
the transformation matrix from the old cell to the structure description. Much more airing, many mo
new (pseudo )-orthogonal cell with one axis parallel re new ways at looking at old crystal structures are
to t*. To make it easy, transform the inversion cen required. But 10s6's book we can admire in com
ters according to the same matrix. Projection along mon, criticize in common, comprehend in com
t* layer-by-Iayer through the asymmetric unit then mon.
finishes the job. Surprisingly, this approach has
had very few practitioners in the past, thus most Chicago Paul B. Moore
structures which are in fact based on principles of 5 February, 1994
