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Phase Identifiers.

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

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
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{\field{\*\fldinst DATE \\@ "yyyy-MM-dd"}{\fldrslt }}{\plain \par

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}{\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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