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Phase Identifiers.
- To: Multiple recipients of list <phase-identifiers@iucr.org>
- Subject: Phase Identifiers.
- From: "I. David Brown" <idbrown@mcmail.cis.mcmaster.ca>
- Date: Wed, 3 Apr 2002 17:34:04 +0100 (BST)
Dear colleagues, First let me thank you for agreeing to serve on the Working Group of the Commission on Crystallographic Nomenclature of the IUCr devoted to finding a crystallographic phase identifier, and let me welcome you to the opening of our email discussion. The Working Group has now been given formal approval and, by way of starting off the discussion, I have attached a position paper to this email. The paper is an .rtf file which you should be able to read into your favourite word processor. If you have any problems, let me know and I will send you the document in the format of your choice. This document provides some of the background and the formal material you will need (e.g. terms of reference) as well as a discussion of the rather formidable problems that face us. No doubt we all have ideas on the subject of phase identifiers and I would suggest that we share these through email. You should copy the email addresses at the head of this message to create an email list for the group on your own mail server, or you can reply to all recipients of this message. Since this topic has many dimensions, we need to share our thoughts and ideas before starting to chart a course leading to our goal. I look forward to hearing from each of you. I will try to moderate the discussion to prevent us from getting sidetracked, but at this stage no holds are barred! Best wishes David Brown Chair ***************************************************** Dr.I.David Brown, Professor Emeritus Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada Tel: 1-(905)-525-9140 ext 24710 Fax: 1-(905)-521-2773 idbrown@mcmaster.ca *****************************************************
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{\plain CRYSTALLOGRAPHIC PHASE IDENTIFIERS. \par
}{\plain A position paper prepared for the Working Group of the IUCr Commission on
Crystallographic Nomenclature to advise on Crystallographic Phase Identifiers.\par
}{\plain \par
}{\plain Prepared by I.David Brown\par
}{\plain \par
}{\plain \ul CONTENTS}{\plain \par
}{\plain 1. Background\par
}{\plain 2. Terms of reference\par
}{\plain 3. Membership\par
}{\plain 4. Assignment of unique phase identifiers \par
}{\plain 5. Structural chemical considerations\par
}{\plain 6. Problems of identifying inorganic compounds\par
}{\plain 7. Questions the group might consider\par
}{\plain Appendix: Pearson symbols for SiO}{\plain \sub 2}{\plain \par
}{\plain \par
}{\plain \ul 1. Background}{\plain \par
}\pard \sl0
{\plain \tab In October 2001, Howard Flack drew the attention of the Commission on
Crystallographic Nomenclature (CCN) to the IUCOSPED/IUCODIX project (International
Union of chemistry and COdata Standard Properties Electronic Database?) sponsored by
IUPAC, CODATA and ICSTI. This project aims to provide a standardized format for the
reporting of numerical chemical information such as thermodynamic measurements, etc. The
Standard ELectronic File (SELF), a fixed format structure, has been adopted for this purpose,
but plans are underway in discussions with Peter Murray-Rust to develop an XML version,
SELF-ML. Details of the project are described at http://www.fiz-karlsruhe.de/dataexplorer.\par
}{\plain \par
}{\plain \tab Each SELF entry starts with four descriptors, the first giving the file name, the second
the literature reference, the third a code indicating the property being reported and the fourth a
code identifying the material being studied. The suggestion has been made that the material be
identified by its Chemical Abstract Service (CAS) number, but this does not, in general,
indicate the state of the material (gas, liquid, solid), only its composition. The state can be
identified by adding 'gas', 'liquid' or 'solid' to the CAS number, but many materials exist in
more than one solid phase. In an attempt to find a way of identifying the solid phase, they
turned to the IUCr Commission on Crystallographic Nomenclature which has recently adopted
a notation for phase transitions which provides a description for each phase. This notation is,
however, unsatisfactory since it is not unique, that is, the same phase may be described in
different ways, depending on the interests and observations of the experimenter. \par
}{\plain \par
}{\plain \tab A vigorous email discussion ensued as a result of which Sidney Abrahams, the chair of
the Commission on Crystallographic Nomenclature, invited David Brown to head a Working
Group to propose a way of uniquely identifying a given crystallographic phase in an electronic
database. This group was approved by the CCN on 20 March 2002.\par
}{\plain \par
}{\plain \ul 2. Terms of reference of the Working Group}{\plain \par
}{\plain \tab Terms of reference of the Working Group on Crystal Phase Identifiers.\par
}{\plain \par
}{\plain The group will recommend to the IUCr Commission on Crystallographic Nomenclature(CCN)\par
}{\plain \par
}{\plain 1. The best method of defining a crystalline phase identifier that uniquely and unambiguously
identifies each crystalline phase in a way which would allow it to be used to link the same
material appearing in different electronic databases.\par
}{\plain \par
}{\plain 2. To recommend the best way in which this identifier can be implemented, including its
incorporation in the CCN recommended phase transition nomenclature.\par
}{\plain \par
}{\plain Keeping in mind that the primary purpose of the crystal phase identifier is to allow the
properties of a given material to be located in different databases, the working group should
consult with appropriate crystallographic databases to ensure that the proposed identifier will
be acceptable. \par
}{\plain \par
}{\plain \ul 3. Membership}{\plain \par
}{\plain \tab David Brown (chair)\par
}{\plain \tab Sidney Abrahams (chair of CCN ex officio)\par
}{\plain \tab John Faber (ICDD)\par
}{\plain \tab Vicky Karen (NIST and ICSD)\par
}{\plain \tab Sam Motherwell (CCDC)\par
}{\plain \tab Jean-Claude Toledano (Chair, CCN working group on phase transition nomenclature)\par
}{\plain \tab Brian McMahon (IUCr, consultant)\par
}{\plain \par
}{\plain \ul 4. Assignment of unique phase identifiers}{\plain \par
}{\plain \tab Phase or composition identifiers can be of two kinds. }{\plain \i Internal identifiers }{\plain are based on
the observed properties of the phases such as the space group or cell constants (for example,
the phase transition nomenclature recently adopted by the Commission). }{\plain \i External identifiers
}{\plain are arbitrarily assigned by some recognized authority (e.g. registry numbers assigned by the
Chemical Abstracts Service and mineral names assigned by the International Mineralogical
Association). Internal identifiers can only be assigned if the requisite properties have been
measured and if these are sufficient (perhaps in conjunction with a composition identifier) to
uniquely define the phase. External identifiers require a recognized competent authority that
can adjudicate in ambiguous cases and keep a public register of assigned identifiers. Both
identifiers have obvious advantages and disadvantages.\par
}{\plain \par
}{\plain \ul 4.1 External identifiers}{\plain \par
}{\plain \tab The obvious advantage of an external identifier is that, being assigned by a
knowledgeable human, it can be unique and unambiguous, and can be assigned in a way that
takes into account all that is known about the phase. The disadvantages include the cost of
providing a service which assigns phase identifiers on demand. The assignment must be made
by a person or group of people knowledgeable in the field, capable of recognizing a new and
distinct phase. Further, a register of identifiers together with sufficient information to
characterize the phase needs to be maintained in a form accessible to the public. To protect the
identifiers from misuse, they must be copyright raising the question of whether access to the
register might at some point be restricted. The legal issues involved are not trivial and add to
the expense of maintaining the register. As experience with the assignment of mineral names
shows, an assigned identifier may have to be dropped if two phases are subsequently found to
be the same.\par
}{\plain \par
}{\plain \ul 4.2 Internal identifiers}{\plain \par
}{\plain \tab The advantage of the internal identifier is that it can be assigned strictly from a
knowledge of the properties of the phase and requires no external agency. The problem is to
find an assignment that is both unique (everyone would assign the same identifier) and
unambiguous (different phases would be guaranteed to have different indentifiers).\par
}{\plain \par
}{\plain \ul 4.3 A review of some existing identifiers}{\plain \par
}{\plain \tab Chemical Abstract Service (CAS) Registry numbers are assigned on demand by
Chemical Abstracts, but ownership is vested in Chemical Abstracts and access to the registry
could possibly in the future be restricted. CAS numbers work well for organic molecules, but
are less successful for inorganic materials. Generic MgSO}{\plain \sub 4}{\plain may be assigned a number that can
be used when the material is in aqueous solution, perhaps in combination with other salts, but
this compound crystallizes as MgSO}{\plain \sub 4}{\plain .7H}{\plain \sub 2}{\plain O (or more correctly Mg(H}{\plain \sub 2}{\plain O)}{\plain \sub 6}{\plain SO}{\plain \sub 4}{\plain .H}{\plain \sub 2}{\plain O) and several
other hydrates are known each of which may have a different CAS number. A separate
number should be assigned for anhydrous solid MgSO}{\plain \sub 4. }{\plain CAS numbers are based on
composition (or molecular structure) and are not intended to distinguish between different
phases of the same composition.\par
}{\plain \par
}{\plain \tab The Cambridge Crystallographic Data Centre assigns a six letter refcode for each
crystalline composition (typically representing a single molecule) and, although this is
supplemented by a two digit number which is different for different phases, this number is
keyed to the structure determination and is not unique for a given phase. The problem for
inorganic compounds is more complex which is why the identifiers (collection numbers) used
in the Inorganic Crystal Structure Database are keyed only to the paper describing the structure
determination. No attempt is made to link different determinations of the same phase. \par
}{\plain \par
}{\plain \tab The phase identifiers developed by the Commission on Crystallographic Nomenclature
of the IUCr to describe phase transtions are internal identifiers which adequately identify the
phase to other workers (insofar as the phase has been characterized), but they are not unique,
the authors opting for a flexible informal format rather than one that could be used to link
databases. There is, furthermore, no guarantee that they are unambiguous since there is no
mechanism to ensure that two different phases (e.g., of different composition) generate
different identifiers.\par
}{\plain \par
}{\plain \tab The International Mineralogical Association has a committee which assigns mineral
names as an external identifier. They have developed a series of rules for deciding when two
minerals are sufficiently different to warrant different names. These names are unique and
unambiguous (even if not consistently used be people outside the mineralogical community),
but they are limited to materials formed naturally in the earth and do not apply to any material
synthesized in the laboratory.\par
}{\plain \par
}{\plain \tab Perhaps the simplest and most successful internal identifier for crystalline solids is the
Pearson symbol composed of three elements, a lower-case letter identifying the crystal system
(a=triclinic, m=monoclinic, o=orthorhombic, h=hexagonal and trigonal, t=tetragonal, and
c=cubic), an upper case letter indicating the centring of the unit cell (P=primitive, C=one
face centred, F=all faces centred, R=rhombohedral and I=body centred) and a number
indicating the total number of atoms in the unit cell. This information is not difficult to obtain
since a full structure determination is not needed and the symbol serves both to bring together
compounds of different composition having the same structure as well as to differentiate
between different structures of the same composition. Although originally developed for
metals, it can be used for any crystalline material. It is a unique identifier (providing the phase
is well enough characterized to allow the symbol to be assigned), but it can be ambiguous: two
different phases of the same compound can have the same Pearson symbol. For example the
208 structures of SiO}{\plain \sub 2}{\plain reported in the Inorganic Crystal Structure Database appear to represent
52 different phases (listed in the Appendix which discusses some of the practical difficulties of
assigning Pearson symbols). In some cases, such as the hi- and lo-quartz, two different phases
share the same Pearson symbol (hP9) but have different space groups. \par
}{\plain \par
}{\plain \tab The Pearson symbol comes closest to meeting the criteria of a unique and unambiguous
identifier. Its robustness arises from two properties of the items from which it is constructed:
they can be determined relatively simply (a full structure determination is not needed) and they
are not subject to experimental uncertainty as would be the case for properties such as the
density, melting point or unit cell volume. Any value that carries an experimental uncertainty
will inevitably be assigned slightly different values by different experimenters, thus destroying
the uniqueness of the identifier.\par
}{\plain \par
}{\plain \par
}{\plain \ul 5. Structural Chemical Considerations}{\plain \par
}{\plain \tab {\*\bkmkstart BM_1_}{\*\bkmkend BM_1_}Not least among the problems of assigning phase identifiers is the problem of deciding
what constitutes a phase. The solid state properties and structures of organic and inorganic
crystals are very different and require different treatments which is the reason why information
on crystal structures are stored in different databases. Organic compounds are found in the
Cambridge Crystallographic Database (CSD) and the Protein Data Bank (PDB), inorganic
compounds in the Inorganic Crystal Structure Database (ICSD) and the Metals Data File
(MDF). Organic compounds are usually found in the form of well-defined molecules
characterized by having strong internal (non-polar) bonding but weak external (van der Waals)
bonds. Such a molecule retains its integrity on melting (usually at relatively low temperatures)
and on dissolution in solvents. Its composition is therefore determined by its molecular
structure which can be identified by a structural chemical formula or a unique identifier, such
as the CAS number, keyed to this formula. Since organic compounds tend to form pure
crystals, this identifier is frequently all that is needed, but it can, if necessary, be followed by a
phase designator such as 'liquid', 'solute', 'crystal-1', 'crystal-2', etc. There is generally little
problem in identifying the different solid phases adopted by an organic molecule. Occasionally
a molecule will co-crystallize with a different molecule, typically a molecule of the solvent
from which it was grown, but even these crystals tend to be well characterized and the
molecular components appear in stoichiometric proportions. The nomenclature of cocrystals is
the subject of a separate proposed CCN Working Group with which we should keep in touch.\par
}{\plain \par
}{\plain \ul 6. Problems of indentifying inorganic compounds.\par
}{\plain \tab Defining the phases of inorganic compounds presents some challenging problems. The
bonding between the atoms is polar and the bonding network is usually infinite in extent. As a
result, inorganic compounds generally have high melting points. When the crystals are melted
or dissolved, most of the bonds are broken, though some components, such CO}{\plain \sub 3}{\plain \super 2-}{\plain and H}{\plain \sub 2}{\plain O,
may retain their integrity. Consequently, when inorganic solids are liquified, the individual
components (the ions) are dispersed, and the compound loses its identity. For example,
dissolving NaCl and CaCO}{\plain \sub 3}{\plain in the same solution gives rise to four solute components, Na}{\plain \super +}{\plain ,
Ca}{\plain \super 2+}{\plain , C}{\plain l}{\plain \super -}{\plain and CO}{\plain \sub 3}{\plain \super 2-}{\plain . The Na}{\plain \super +}{\plain ions are not associated with particular Cl}{\plain \super -}{\plain or CO}{\plain \sub 3}{\plain \super 2-}{\plain anions and
there is no requirement that the concentration of Na}{\plain \super +}{\plain be equal to the concentration of C}{\plain l}{\plain \super -}{\plain
provided that electroneutrality is satisfied among all the ions present. It is a fiction to describe
the composition of the solute in terms of NaCl and CaCO}{\plain \sub 3}{\plain , rather than Na}{\plain \super +}{\plain , Ca}{\plain \super 2+}{\plain , Cl}{\plain \super -}{\plain and
CO}{\plain \sub 3}{\plain \super 2-}{\plain . It is a fiction that is often used, but one should be cautious about using fictitious
descriptions because they can lead to problems and contradictions.\par
}{\plain \par
}{\plain \tab The composition of the crystals formed when a polar solid crystallizes from a melt or
solution is determined by how well the atoms can be arranged in a way that satisfies both the
chemical constraints (the charges and sizes of the ions) and the spatial constraints (the
requirements of continuous bonding). A useful heuristic in such cases is the principle of
maximum symmetry which can be justified from energy considerations. It states that a crystal
will have the highest symmetry consistent with the constraints (chemical and spatial) acting on
it. One implication of this principle is that crystals will have the smallest possible unit cell
since this allows the atoms of given species to adopt the smallest number of different
environments, frequently only one. This in turn imposes severe constraints on which
compounds can be formed. In contrast to organic compounds which are defined by their
molecular structure and can (in principle) exist in liquid, solid and gaseous form, an inorganic
compound only exists as a solid and its properties are entirely defined by its crystal structure.\par
}{\plain \par
}{\plain \tab A solid with a given composition sometimes appears in different crystalline forms
which may be able to coexist (as in diamond and graphite) if there is no ready mechanism of
transformation between them. The key descriptor of inorganic solids is the arrangement (or
topology) of the atom sites (the structure type) and in this sense crystals with the same
composition but different topology should be considered as distinct. No rational description
based on observed properties would place diamond and graphite in the same class. The
symmetry operations of the space group (including the translational symmetry of the lattice)
transform each atomic site found in the asymmetric unit into an infinite set of equivalent sites,
which may be occupied by one or more different (though chemically similar) elements (e.g.,
Na}{\plain \super +}{\plain and K}{\plain \super +}{\plain ) or by vacancies. However, the space group is not, in general, a good indicator
of the topology since two topologically similar crystals may adopt different space groups under
different conditions of temperature, pressure or composition. Chemical composition and
symmetry are both secondary factors in the classification of inorganic solids, the topology of
the crystal being primary.\par
}{\plain \par
}{\plain \tab Metals, alloys and intermetallic compounds where the bonding is not localized present a
different set of problems. Although not discussed here they still fall within the responsibility
of this committee.\par
}{\plain \par
}{\plain \ul 7. Questions that the group might consider}{\plain \par
}{\plain 7.1 Should the composition be part of the identifier (e.g., via the CAS number or Refcode)?
How should one handle solids of variable composition?\par
}{\plain \par
}{\plain 7.2 Is an external or internal identifier to be preferred?\par
}{\plain \par
}{\plain 7.3 Who would assign an external identifier? Should a new agency be set up, say under IUCr
sponsorship, or could an existing organization such as ICDD perform this task (assuming it
were willing)? Could the task be distributed between different organizations, each crystal
structure database each assigning identifiers in its own area?\par
}{\plain \par
}{\plain 7.4 Can the Pearson symbol be extended to make it unambiguous? If so in what way?\par
}{\plain \par
}{\plain 7.5 Is a hybrid system possible, for example the Pearson symbol with an additional external
identifier added in cases of non-uniqueness?\par
}{\plain \par
}{\plain 7.6 Are there other models that might be helpful?\par
}{\plain \par
}{\plain \ul Appendix: Pearson symbols for SiO}{\plain \ul\sub 2}{\plain \ul appearing in the Inorganic Crystal Structure Database.}{\plain \par
}{\plain \par
}{\plain The following list of structures of SiO}{\plain \sub 2}{\plain extracted from the ICSD shows some of the pitfalls in
assigning Pearson symbols. Early structure determinations assigned the space group with the
minimum compatible symmetry (e.g. P6}{\plain \sub 3}{\plain 22 for tridymite) whereas current practice assigns the
space group with the maximum compatible symmetry (P6}{\plain \sub 3}{\plain /mmc). Some space groups are
enantiomorphs of others but otherwise equivalent. In both these cases the Pearson symbol can
be correctly assigned from a knowledge of the space group. This is not, however, the case if
a non-standard space group settings results in a different Hermann-Mauguin symbol. A
simplistic generation of the Pearson symbol gives rise to the incorrect symbols mB48 for
coesite (ICSD collection number 24259, should be mC48) and the inadmissible aF960 for a
triclinic crystal (1440, should be aP240). Uncertainty about the correct space group can give
rise to different Pearson symbols, e.g., aP9 for 39830 and hP9 for 63532. Variations in the
occupation number of O in quartz result in different Pearson symbols for essentially the same
structure (hP8 for 9482 and hP9 for 26431, both hi-quartz). On the other hand hi- and lo-quartz have different space groups but the same Pearson symbol (hP9).\par
}{\plain \f1\fs20 \par
}{\plain \f1\fs20 COL # PRS HMS RVAL \par
}{\plain \f1\fs20 {\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}{\f2 \'34}\par
}{\plain \f1\fs20 1440 {\f2 \'2a} aF960 {\f2 \'2a} F1 {\f2 \'2a} 0.064 \par
}{\plain \f1\fs20 39830 {\f2 \'2a} aP9 {\f2 \'2a} P1 {\f2 \'2a} 0.046 alpha, quartz doped with Fe\par
}{\plain \f1\fs20 75670 {\f2 \'2a} aP12 {\f2 \'2a} P1 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 35536 {\f2 \'2a} cF24 {\f2 \'2a} F4132 {\f2 \'2a} Hi\_cristobalite |\par
}{\plain \f1\fs20 31073 {\f2 \'2a} cF24 {\f2 \'2a} Fd-3m {\f2 \'2a} Hi\_cristobalite |same structure\par
}{\plain \f1\fs20 201182 {\f2 \'2a} cF408 {\f2 \'2a} Fd-3m {\f2 \'2a} ZSM\_39 |\par
}{\plain \f1\fs20 48154 {\f2 \'2a} cF408 {\f2 \'2a} Fd-3 {\f2 \'2a} 0.064 Dodecasil 3C | same structure \par
}{\plain \f1\fs20 70016 {\f2 \'2a} cP12 {\f2 \'2a} Pa-3 {\f2 \'2a} * alpha, quartz! \par
}{\plain \f1\fs20 24587 {\f2 \'2a} cP24 {\f2 \'2a} P213 {\f2 \'2a} Hi\_cristobalite (1932) \par
}{\plain \f1\fs20 9482 {\f2 \'2a} hP8 {\f2 \'2a} P6222 {\f2 \'2a} Quartz (occ. # = 0.88) \par
}{\plain \f1\fs20 26431 {\f2 \'2a} hP9 {\f2 \'2a} P6222 {\f2 \'2a} 0.035 Hi\_quartz\par
}{\plain \f1\fs20 79637 {\f2 \'2a} hP9 {\f2 \'2a} P3121 {\f2 \'2a} 0.038 Lo\_quartz |\par
}{\plain \f1\fs20 63532 {\f2 \'2a} hP9 {\f2 \'2a} P3221 {\f2 \'2a} 0.016 Lo\_quartz |(enatiomorphic space groups) \par
}{\plain \f1\fs20 200479 {\f2 \'2a} hP12 {\f2 \'2a} P63/mmc {\f2 \'2a} 0.053 Tridimyte |(Kihari see also oC24) \par
}{\plain \f1\fs20 29343 {\f2 \'2a} hP12 {\f2 \'2a} P6322 {\f2 \'2a} 0.167 Tridymite | same structure \par
}{\plain \f1\fs20 48153 {\f2 \'2a} hP102 {\f2 \'2a} P6/mmm {\f2 \'2a} 0.056 \par
}{\plain \f1\fs20 75659 {\f2 \'2a} mC24 {\f2 \'2a} C121 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 24259 {\f2 \'2a} mB48 {\f2 \'2a} B112/b {\f2 \'2a} 0.169 Coesite |\par
}{\plain \f1\fs20 65371 {\f2 \'2a} mC48 {\f2 \'2a} C12/c1 {\f2 \'2a} 0.011 Coesite |\par
}{\plain \f1\fs20 49813 {\f2 \'2a} mC48 {\f2 \'2a} C2/c {\f2 \'2a} 0.027 Coesite |(different SG labels) \par
}{\plain \f1\fs20 62582 {\f2 \'2a} mC84 {\f2 \'2a} C12/m1 {\f2 \'2a} ZSM\_12 \par
}{\plain \f1\fs20 34867 {\f2 \'2a} mC144 {\f2 \'2a} C1C1 {\f2 \'2a} 0.069 \par
}{\plain \f1\fs20 67669 {\f2 \'2a} mI36 {\f2 \'2a} I12/a1 {\f2 \'2a} 0.035 Moganite \par
}{\plain \f1\fs20 75669 {\f2 \'2a} mP12 {\f2 \'2a} P121 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 75668 {\f2 \'2a} mP12 {\f2 \'2a} P1c1 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 75665 {\f2 \'2a} mP12 {\f2 \'2a} P1m1 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 100279 {\f2 \'2a} mP48 {\f2 \'2a} P121/a1 {\f2 \'2a} 0.096 \par
}{\plain \f1\fs20 15321 {\f2 \'2a} oC24 {\f2 \'2a} C2221 {\f2 \'2a} 0.086 Tridymite (Kihari see also hP12)\par
}{\plain \f1\fs20 30795 {\f2 \'2a} oC24 {\f2 \'2a} Cc2m {\f2 \'2a} Tridymite (from meteor) \par
}{\plain \f1\fs20 69114 {\f2 \'2a} oC72 {\f2 \'2a} Cmc21 {\f2 \'2a} 0.080 Theta\_1 |\par
}{\plain \f1\fs20 62581 {\f2 \'2a} oC72 {\f2 \'2a} Cmcm {\f2 \'2a} ZSM\_22 | (same structure)\par
}{\plain \f1\fs20 62584 {\f2 \'2a} oC144 {\f2 \'2a} Cmcm {\f2 \'2a} \par
}{\plain \f1\fs20 65551 {\f2 \'2a} oC336 {\f2 \'2a} Cmma {\f2 \'2a} \par
}{\plain \f1\fs20 38252 {\f2 \'2a} oI12 {\f2 \'2a} Icma {\f2 \'2a} \par
}{\plain \f1\fs20 75664 {\f2 \'2a} oI24 {\f2 \'2a} I212121 {\f2 \'2a} * Theoretical \par
}{\plain \f1\fs20 75652 {\f2 \'2a} oI24 {\f2 \'2a} Ima2 {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 65497 {\f2 \'2a} oI108 {\f2 \'2a} Immm {\f2 \'2a} 0.106 \par
}{\plain \f1\fs20 62585 {\f2 \'2a} oI144 {\f2 \'2a} Imma {\f2 \'2a} \par
}{\plain \f1\fs20 75649 {\f2 \'2a} oP12 {\f2 \'2a} Pna21 {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 100199 {\f2 \'2a} oP72 {\f2 \'2a} P212121 {\f2 \'2a} 0.082 \par
}{\plain \f1\fs20 75475 {\f2 \'2a} oP108 {\f2 \'2a} Pmnn {\f2 \'2a} 0.069 \par
}{\plain \f1\fs20 34370 {\f2 \'2a} oP288 {\f2 \'2a} Pn21a {\f2 \'2a} 0.160 \par
}{\plain \f1\fs20 75648 {\f2 \'2a} tI12 {\f2 \'2a} I-42d {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 75647 {\f2 \'2a} tI24 {\f2 \'2a} I-4 {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 65354 {\f2 \'2a} tI288 {\f2 \'2a} I-4m2 {\f2 \'2a} 0.105 \par
}{\plain \f1\fs20 10078 {\f2 \'2a} tP6 {\f2 \'2a} P42/mnm {\f2 \'2a} 0.015 \par
}{\plain \f1\fs20 75650 {\f2 \'2a} tP12 {\f2 \'2a} P41212 {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 75651 {\f2 \'2a} tP12 {\f2 \'2a} P43212 {\f2 \'2a} * Theoretical}{\plain \f1\fs20 \par
}{\plain \f1\fs20 34889 {\f2 \'2a} tP36 {\f2 \'2a} P43212 {\f2 \'2a} 0.098 \par
}{\plain \f1\fs20 Near silica structures\par
}{\plain \f1\fs20 COL # FORMULA PRS HMS RFAC \par
}{\plain \f1\fs20 73930 {\f2 \'2a} Si0.98 O2 {\f2 \'2a} cF572 {\f2 \'2a} Fd-3m {\f2 \'2a} 0.022 \par
}{\plain \f1\fs20 69667 {\f2 \'2a} Si O2.267 {\f2 \'2a} hP78 {\f2 \'2a} P6/mcc {\f2 \'2a} 0.036 \par
}{\plain \f1\fs20 69668 {\f2 \'2a} Si O2.717 {\f2 \'2a} hP89 {\f2 \'2a} P6/mcc {\f2 \'2a} 0.035 \par
}{\plain \f1\fs20 \par
}{\plain \f1\fs20 COL # = ICSD Collection number\par
}{\plain \f1\fs20 PRS = Pearson Symbol\par
}{\plain \f1\fs20 HMS = Hermann-Mauguin Symbol \par
}{\plain \f1\fs20 RFAC = Crystallographic R factor\par
}{\plain \f1\fs20 * Structure calculated theoretically by Boison Gibbs et al. 1994\par
}{\plain \f1\fs20 \par
}{\plain \f1\fs20 204 = Total number of SiO}{\plain \sub\f1\fs20 2}{\plain \f1\fs20 entries in ICSD\par
}\pard \fi-3600\li3600\sl0\tx720\tx1440\tx2160\tx2880\tx3600
{\plain \f1\fs20 52 = Number in above list\tab (entries with same Pearson and Hermann-Mauguin
symbol have been removed)\par
}\pard \sl0
{\plain \f1\fs20 49 = Number listed as SiO2 in above list\par
}{\plain \f1\fs20 36 = Number of distinct Pearson symbols\par
}{\plain \f1\fs20 13 = Number of theoretical structures (*)\par
}{\plain \f1\fs20 26 = Probable number of different observed structures \par
}}
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