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Mineralogical ClassificationIs Ericaite Valid?
18th Apr 2005 15:35 UTCJolyon
If this is the case, photos showing Ericaite are actually pseudomorphs of Congolite after Ericaite ?
Should we change anything in the database - my understanding is that we don't list phases unstable at room temperature as valid minerals.
Jolyon
18th Apr 2005 16:40 UTCDavid Von Bargen
From IMA CNMMN website
"The use of special procedures
in the investigation does not preclude the acceptance
of a metastable substance as a mineral species if it can
be adequately characterized and if it meets the other
criteria for a mineral."
18th Apr 2005 17:35 UTCJolyon
(Fe2.18,Mg0.71,Mn0.11)B7O13Cl so there's certainly some managanese in there.
It's interesting that when you look at the phase diagrams for this it does tend to be a good example of what's wrong with the 50% rule for dividing species. There are four species listed, Boracite, Ericaite, Trembathite and Congolite.
In my mind, two of these (Trembathite and Ericaite) are unnecessary - there should be just two
Boracite (Mg,Fe)3B7O13Cl - 0-35% Fe content, Orthorhombic
Congolite (Fe,Mg)3B7)13Cl - 35-100% Fe content, Hexagonal
But of course this falls foul of the 50% rule as the Congolite could contain less than 50% Fe.
The whole picture is no doubt far more complicated when Mn is thrown into the mix, but it seems to me when there is a simple phase change in a series such as this, the dividing line between species should be the phase change point, not the 50% point.
Jolyon
18th Apr 2005 17:43 UTCJolyon
Presumably it's not metastable, it doesn't exist at room temperature. Isn't this the same as 'argentite', which we've classed on the site as a 'variety' of acanthite (variety in terms of pseudomorphic form).
Reference is Canadian Mineralogist 34: 881-892
18th Apr 2005 18:49 UTCDavid Von Bargen
If you use the criteria of stable at room temperature, you would eliminate ice as a mineral. At the very least you would want to have the mineral stability fields for the range of temperatures found on earth (and then you would also need to look at subsurface conditions - a lot hotter and higher pressure).
Actually argentite is classified as a synonym on mindat. I think that the loss of argentite as status for a mineral species has more to do with the relatively minor movement of atoms that are required to go between the cubic and monoclinic symmetry.
As an aside, you always see that argentite inverts to acanthite at 173 degrees C. This only is true in pure samples. If you substitute some copper for the silver, you can get the transition temperature down to around 100 degrees.
18th Apr 2005 20:21 UTCDavid Von Bargen
not be desirable to create a new species defining only a
very short compositional range"
The factor of the topology of the crystallographic structure is the determining factor if a mineral is classified as a different species and not just a polymorphic variety.
"However, if the crystal
structures of the polymorphs have essentially the
same topology, differing only in terms of a structural
distortion or in the order – disorder relationship
of some of the atoms comprising the structure, such
polymorphs are not regarded as separate species."
See for mineral rules (and source of quotes):
http://www.geo.vu.nl/users/ima-cnmmn/cnmmn98.pdf
18th Apr 2005 20:29 UTCJolyon Ralph
Jolyon
18th Apr 2005 21:29 UTCAlfredo
19th Apr 2005 20:18 UTCRob Woodside
"However, if the crystal
structures of the polymorphs have essentially the
same topology, differing only in terms of a structural
distortion or in the order – disorder relationship
of some of the atoms comprising the structure, such
polymorphs are not regarded as separate species."
First this only applies to the definition of new species, all else is grandfathered. So unless someone is proposing a redefinition for submission to the IMA, it is irrelevant to published species.
Second the use of the word topology is problematic. I think it is trying to get at the connectivity of the structure which is an honest topological property. However a 100% ionic structure is merely a pile of charged cannon balls with no bonds connecting the ions. Connectivity is then established by drawing lines between nearest neighbours. The fact that no structure is 100% ionic is balanced by the fact that no one looks for saddle points in the electron density between atoms that would establish the connectivty of a chemical bond. The result is that the topology is that of a ball and stick model rather than anything physical. In defence of this one argues that interatomic spacing is characteristic of chemical bonding, so one doesn't need to verify it directly. However distortion will change interatomic distances and may in fact be the result of a changed connectivity with the breaking of chemical bonds on distortion. Of course the ball and stick connectivity is not altered by distortion. The dismissal of ordering means that all balls in the ball and stick model are regarded as identical as far as the "topology" is concerned. I applaud almost any attempt to cut down on the number of new names and dismissal of ordering would go some ways towards that. However, others have said that ordering has not been dismissed and is a very important property, sufficient to define species. Do they not know of this rule or am I missing something?
19th Apr 2005 20:59 UTCJim Ferraiolo
An example of this is analcime.(If fact, I don't recall hearing of of any others, but there must be others. Otherwise why have a rule?) Anyway, the "topologically identical polymorphs caused by different degrees of order of Al and Si in the tetrahedral structural sites." There are cubic, tetragonal, orthorhombic and monoclinic analcimes reported. These sound like polytypes or polytypoids to me, rather than polymorphs, bringing up the age-old question of how big does a polytype have to be to be a polymorph?
20th Apr 2005 13:04 UTCErnst A.J. Burke
The cause for the problems is of course the name of the rule. The 50% criterion applies indeed only to binary solid solution series. If there is solid solution in ternary series, or in multicomponent series, quoting Nickel, Can. Mineral. 30 (1992), 231-234, "then different names can be given to isostructural or isotypic phases that have different elements DOMINANT (my emphasis, EAJB) in specified structural sites".
This rule for naming new minerals should thus have been called the 'predominance rule' to avoid unnecessary confusion.
In the question mentioned above about the four minerals boracite, ericaite, trembathite and congolite, all four minerals are valid minerals; also natural ericaite is stable at ambient temperature.
Boracite and ericaite form a series, both are orthorhombic, boracite is the Mg-dominant member, ericaite is the Fe-dominant member.
The series trembathite and congolite is dimorphous with boracite-ericaite; trembathite and congolite are trigonal (rhombohedral), trembathite is the Mg-dominant member, congolite the Fe-dominant one.
The fact that Mn is present does not change the nomenclature in these four minerals; it does, of course, when Mn becomes the dominant element in the site otherwise occupied by Mg and Fe, then the (orhtorhombic) mineral is called chambersite.
To avoid that you think that matters are easy, 'boracite', 'ericaite' and 'chambersite' also exist in a high-temperature form (cubic), these are not recognized as minerals.
Ernst Burke.
20th Apr 2005 14:12 UTCJolyon
Jolyon
20th Apr 2005 18:44 UTCErnst A.J. Burke
Ernst.
20th Apr 2005 22:30 UTCJolyon
That reference is cited in UK Journal of Mines and Minerals, but I don't have access to that issue of Canadian Mineralogist - if someone can let me have a look at a copy, or summarise it here, I'd be grateful.
Jolyon
21st Apr 2005 09:07 UTCMarco E. Ciriotti
Also:
Burns, P.C. & Carpenter, M.A. (1996): Phase transitions in the series boracite-trembathite-congolite: phase relations. Canadian Mineralogist, 34, 881-892.
Marco
21st Apr 2005 09:50 UTCErnst A.J. Burke
They did, however, not examine a single specimen of natural ericaite.
Pseudo-cubic samples of a boracite-like mineral of orthorhombic symmetry with Fe dominant over Mg and Mn have been described from the Boulby mine, Loftus, Saltburn, Cleveland, United Kingdom, by Milne et al. in Mineral. Mag. 41 (1977), 404-406. This mine has boracite (Mg dominant) and what the authors call 'iron-boracite' (with Fe dominant). The latter name is of course not recognized by the IMA, the right name is ericaite. The 1977 paper gives partial analyses for Boulby specimens ('small anhedral grains' = ericaite; 'large crystals' = boracite). But they also give a complete analysis for 'iron-boracite' from a nodule with only anhedral grains, leading to the empirical formula:
(Fe 1.50 Mg 1.31 Mn 0.24 Ca 0.02 Na 0.01)sum=3.08 (B 6.92 Si 0.04)sum=6.96 (O 13.07 Cl 0.93)sum=14 which is clearly an ericaite.
The Boulby deposit has also been described in Mineral. Record 27 (1996), 163-170; this paper cites even higher Fe values for ericaite.
Ernst Burke.
21st Apr 2005 11:14 UTCJolyon
It states "Brown blocky crystals which have been described in the literature as either iron-boracite or ericaite, are in fact the recently described mineral trembathite, or the rare iron borate colgolite, or mixtures of both trembathite and congolite".
Jolyon
21st Apr 2005 19:15 UTCRob Woodside
The long range ordering in minerals is truly amazing. I can see 2 or possibly 5 mechanisms.
If a spiral dislocation has a large step size and the step has a growth defect, this step size ordering will be repeated through the xl as it grows along the spiral dislocation. This is a polytype. If the growth defect is structural, say the mixing of cubic face centred structure and a hexagonally close packed structure (such as with the Elmwood "sphalerites") the the polytype is a polymorph, but a very special one arising from stacking faults. As such it is not considered a true polymorph, although it obeys the polymorph definition of the same types of atoms in a different structural arrangement. If the growth defect involves missing or extra atoms, the the stoichometry is wrecked and the result is called a polytypoid, which is not a polymorph.
The next mechanism for ordering would be thermodynamic. In different temperature regimes ordered or disordered may be favoured (lower Gibbs free energy), then if the conditions are changed it may take a long time for the new structure to come to equilibrium, if it can. Most metals probably crystallize as disordered alloys and as the temerature falls the atoms slowly diffuse into ordered postions of intermetallic compounds. With artificial aluminum -magnesium alloys the ordering can be on the order of tens of angstroms. With conductors and semiconductors, the defining thermodynamics can be in the electronic structure. There was an interesting paper on Tetrahedrites some years ago in the American Mineralogist arguing that the electronic structure required a certain chemistry. What they didn't talk about was that such structures would consequently have a certain ordering.
The incredibly large cells of the homologous sulfosalts (hundred or so Angstroms) may start life on a large template of something simple and if this is incorporated into a spiral step - voila. However finding such a needle in the haystack would be next to impossible.
27th Apr 2005 06:56 UTCandy christy
1. As Ernst implied (21 April, 13:04), the “50% rule” should be replaced with a “dominant end-member” rule. for solid solutions. Fe > Mg, Mn etc means that one of the iron-dominant names applies.
2. The complicatiosn in this group arise because both the rhombohedral (hence trigonal, NOT hexagonal outside of the USA) and orthorhombic polymorphs are different slight distortions of a cubic form that is only stable at high temperature. The orthorhombic and rhombohedral distortions may or may not have their own stability fields depending on composition, temperature, etc. It appears that the rhombohedral form is not stable for Mn rich compositions, although the orthorhombic one (chambersite) is. Hence, minor Mn may indeed stabilise the orthorhombic form even when another cation is dominant.
3. The nature if the structural change is that, in the cubic “ideal” structure, one oxygen of the formula unit is rattling about in an over-large cage, equidistant from four boron atoms. On cooling, the oxygen moves off-centre, thus getting closer to some B atoms and further from others, while lowering the symmetry in different ways depending on the direction in which it moves. This type of “displacive phase transition” does not invovle breaking any strong bonds, can occur very fast, and hence is likely to be “unquenchable” - in other words, the structure that you see at room temperature is likely to be the structure that is most stable at room temperature. Hence the cubic forms are unknown as minerals. Metastable persistence like that of diamond is unlikely. But as David von B, and Ernst have said, some Mn in solid solution could lower the transition temperature for the orthorhombic-rhombohedral transition to the point where the orthorhombic structure is stable with Fe > Mn, Mg. Hence, not-quite-end-member ericaite would indeed be viable. Conversely, Burns and Carpenter indicate that subordinate Fe is required to stabilise the Mg-dominant material as rhombohedral trembathite rather than the commoner boracite. Burns and Carpenter, in stating that ericaite cannot exist at room temperature, were considering only the binary system between Fe and Mg end-members. The same conclusion cannot be safely extended to natural systems in which additional components (Mn) can complicate matters. If the Mills (1977) paper cited by Ernst (April 21, 9:50) determied the orthorhombic symmetry unambiguously, then there definitely appears to be natural ericaite at Boulby. In Jolyon’s post quoting Dave Green (April 21, 11:14), I guess that what is meant by “pseudo-orthorhombic” is in fact “pseudo-cubic”, which all htese minerals are. The tiny orthorhombic and rhombohedral distortions can only be detected by accurate measurement. If the symmetry is in fact orthorhombic, then the corresponding mineral names (boracite-ericaite) apply. Does Dave provide evidence that the brown “trembathite-congolite” IS actually rhombohedral?
27th Apr 2005 06:57 UTCandy christy
Rob: “...the use of the word topology is problematic. I think it is trying to get at the connectivity of the structure which is an honest topological property. However a 100% ionic structure is merely a pile of charged cannon balls with no bonds connecting the ions.”
Careful. Most bonds in non-metallic compounds have distinct covalent character. Particularly in the case of cations of low coordination number (B in borates, Si in silicates), ab initio computer models of the structure will not reproduce physical properties correctly without not just explicit polarisation energy terms but also three-body terms, expressing a preference for particular bond angles, and hence directedness of bonds.
When bonds are strong and highly directed, then a framework with a particular topology can indeed be said to exist.
Rob: “The fact that no structure is 100% ionic is balanced by the fact that no one looks for saddle points in the electron density between atoms that would establish the connectivty of a chemical bond. The result is that the topology is that of a ball and stick model rather than anything physical”
This is out-of-date info, sorry. The best-quality structure refinements can and do map electron density, and do find saddle points along bonds. See Gibbs GV, Boisen MB, Hill FC, Tamada O, Downs RT (1998) “SiO and GeO bonded interactions as inferred from the bond critical point properties of electron density distributions”, Physics and Chemistry of Minerals 25, 574-584.
Rob: “However distortion will change interatomic distances and may in fact be the result of a changed connectivity with the breaking of chemical bonds on distortion. Of course the ball and stick connectivity is not altered by distortion.”
Bonds that are strong enough do not break and remake readily. Incremental change of coordination number with progressive slight distortion is well known in some intermetallic compounds and relatives, such as the Ni2In-Co2Si-Cl2Pb series (Hyde BG, OKeeffe M, Lyttle WM, Brese NE (1992) “Alternative descriptions of the C23 (PbCl2), C37 (Co2Si), B8(B) (Ni2In) and related structure types”, Acta Chemica Scandinavica, 46, 216-223), and also in other structures where replacing an atom with one of a slightly different size causes weak bonds to be established or broken, as in the rare-earth perovskites of Sasaki S, Prewitt CT, Liebermann RC (1983) “The crystal structure of CaGeO3 Perovskite and the crystal chemistry of the GdFeO3-type perovskites”, American Mineralogist 68, 1189-1198.
Rob: “The dismissal of ordering means that all balls in the ball and stick model are regarded as identical as far as the "topology" is concerned...However, others have said that ordering has not been dismissed and is a very important property, sufficient to define species. Do they not know of this rule or am I missing something?”
Some terminologies are grandfathered-in that would not be approved today.
Incidentally, “Ordering” does not just mean occupational order (ie multiple colours of balls on distinguishable sites) but also positional order, which can include very slight but symmetry-breaking collapses of high-symmetry structure. These are well-known in a lot of minerals once one considers their in-situ properties at elevated temperatures and/or pressures rathert than just room temperature. Examples include the hgih- and low-polymorphs of quartz (both polymorphic varieties of the mineral species quartz) and the successive P-bar-1, I-bar-1 and C-bar-1 polymorphs of anorthite feldspar. These would not get separate names even if a minor solid solution component stabilised them down to room temperature.
The rhombohedral and orthorhombic distortions of boracite certainly fall into this category, given the major structure/bonding change is the position of one out of 13 oxygens with respect to 4 nearby borons. This is a rare example where bonding between oxygen and a small cation is rather labile, and only happens because the size of the borate cage is just right. Out of the 7 borons in the formula unit, 3 are always tetrahedral and the other 4 (the cage borons) have three oxygen neighbours in a nearly planar triangle. These atoms altogether make up a nearly rigid, cubic or nearly cubic framework of composition . The 13th oxygen, in the middle of the cage, may bond to all 4 borons very weakly (cubic), 3 of them less weakly (rhombohedral) or 2 of them even stronger (orthorhombic).
Before I go on, I stress that the boracite-group structures are not polytypes: the unit cell is always roughly the same shape and volume, but one atom clicks into a slightly different position in each structure, and the rest of the structure distorts very slightly to accommodate the change.
Rob (second post): “If a spiral dislocation has a large step size and the step has a growth defect, this step size ordering will be repeated through the xl as it grows along the spiral dislocation. This is a polytype. If the growth defect is structural, say the mixing of cubic face centred structure and a hexagonally close packed structure (such as with the Elmwood "sphalerites") the the polytype is a polymorph, but a very special one arising from stacking faults. As such it is not considered a true polymorph, although it obeys the polymorph definition of the same types of atoms in a different structural arrangement.”
Polytypes are a special case of polymorphs. The whole business of classification and description of “modular structures” has expanded and become massively more sophisticated over the last 25 years. More or less any structures which can be made by sticking together slabs or blocks of the same composition in more than one different way are now regarded as polytypes, not just the long-period ones controlled by giant screw dislocations. If the composition remains constant, then sphalerite and wurtzite and any topotactic intergrowth are indeed “polytypes”. So are zoisite-clinozoisite, orthoenstatite-clinoenstatite-protoenstatite, and several polytypes of wollastonite and sapphirine (my pet baby back in the late 80’s) which do not have grandfathered-ion names. The most recent big review of all this is probably the European Mineralogical Union “Notes in Mineralogy” monograph on “Modular Structures”, which I think is 1997 vintage, is in print and is inexpensive. A couple of years earlier, I co-wrote with the late Boris Zvyagin the relevant chapter in the Springer-Verlag “Encyclopedia of Mineralogy”, which has a few different examples but is probably much more difficult to get hold of.
Rob: “If the growth defect involves missing or extra atoms, the the stoichometry is wrecked and the result is called a polytypoid, which is not a polymorph.”
Not quite. You may be thinking of “polysomes” (where more than one stoichiometry of building block intergrow). The International Union for Crystallography recommends “polytypoid” for a “polytype” where stability of the different structures requires change in a solid solution component (by 5 mole% or more, I think). This creates a huge grey area since many polytypes can coexist metastably at the same composition and temperature, pressure etc without actually being genuinely thermodynamically stable together.
NB - many complex and subtle factors can drive long-period ordering. Factors that you do not mention include slight changes in the phonon density of states due to unit cell size changes. In my PhD work, I found from twin-width statistics in sapphirine that elastic strain in a hard mineral produced a preference for particular twin-boundary spacings operating over tens to hundreds of Ångström. Electronic density-of-states effects can also produce remarkably big unit cells for compositionally simple alloys, as well as stabilising relatively simple structure types at particular electron counts, as in the tetrahedrites that you mention, pentlandites, and others.
Re. thermodynamics: If rearrangement of the structure involves long-distance diffusion or breaking and remaking of strong bonds, then it is unlikely that polytypic structures will fully equilibrate to their minimum free energy, since the energy differences between alternative structures are tiny relative to those where polymorphs show greater differences in bonding and structure. A lot of metastable structures may persist through mistakes during growth, through being able to grow faster than the stable alternative, or due to being frozen in mid-transformation from something else. Nevertheless, systematic study of natural polytypes can show that pressure, temperature, and minor elemental substitutions affect polytypic stability (eg, sapphirine-2M is favoured over sapphirine-1A by high temperature, low pressure, and/or the incorporation of Fe2+ and/or Be).
9th May 2005 04:48 UTCRob Woodside
I agree with your statement, "When bonds are strong and highly directed, then a framework with a particular topology can indeed be said to exist." It is when the bonds are not strong and not highly directed, that troubles me. In that case, such as pyrite and marcasite, the ball and stick connectivity may be illusory.
Thanks so much for the reference on saddle points, I'm glad this is being addressed.
I'm not sure I understand "positional" order. Instead of different coloured balls on distinguished sites, are you keeping the colours the same and moving some distinguished sites a little bit, but in a regular fashion? That could give rise to the very similar space groups you mention. (You are dealing with the ignorance of a sulfide collector here) If that's what is meant by positional ordering, then provided the bonds are the same, there is no difference in the connectivity between the unordered and "positionally" ordered structure and thankfully that would not give rise to new names. So is trembathite a "positionally" ordered Boracite or are there new bonds formed when "one atom clicks into a slightly different position" Presumably new bonds would indicate a new topology and merit two names, but positional ordering would require only one, if there were no grandfathering.
Thanks also for the reference on modular structures. These are really troubling from the point of view of xl growth. Are the modules knocking about in the melt and incorporated into the growing xls as large "molecules"? Surely smaller things would get in the way. How do things like potosiite and cylindrite form?
Thanks for the clarification on polytypoids and polysomes. I'm beginning to get the picture.
Phonons are a long way from macroscopic elastic strain, but a volume change certainly changes the density of phonon states. I'm a little confused about a chicken and egg problem here. The phonon spectra are the vibrational properties of a given structure. The structure causes the phonons. Are you saying that phonons can cause the structure? There is an argument that the vibrational modes in a growing snow flake determine the incredible long range ordering. Supposedly the water molecules deposit at the symmetric nodes and as the mass distribution changes with xl growth the symmetric nodes move around symmetrically, producing identical xl tips up to a cm away. I don't know how to test this. Phonons are a bulk property and surface effects are usually removed with periodic boundry conditions of a 3-torus. For xl growth it is precisely the surface that matters. Please elaborate.
11th May 2005 15:46 UTCandy christy
“Andy, thanks so much for your reply and references.”
You’re welcome, Rob!
”I agree with your statement, "When bonds are strong and highly directed, then a framework with a particular topology can indeed be said to exist." It is when the bonds are not strong and not highly directed, that troubles me. In that case, such as pyrite and marcasite, the ball and stick connectivity may be illusory.”
Bad example. The S atoms in those structures are only 4-coordinate (3Fe and one S near neighbours)and are directionally bonded, and the Fe only 6 coordinate. INTERESTINGLY, things become much more ambiguous in “isostructural” minerals with bigger, softer “anions”, such as the bismuthides and tellurides of the platinum metals. “Non-bonded” distances become much more closely comparable to sums of metallic radii there, and the same structure grades seamlessly from “covalent/low-coordination number” to “intermetallic/high coordination number” as additional metal-metal vectors become regarded as “bonds”.
Rob: “Thanks so much for the reference on saddle points, I'm glad this is being addressed.”
Oh yes. The worst problem with some of the new data (eg Gerry Gibb’s work on MgO) is tha sometimes weird fine details of electron density pop up (extra little maxima in that case) that just don’t have an analogue in the traditional bond picture. Oh well. That’s real life, I guess.
”I'm not sure I understand "positional" order. Instead of different coloured balls on distinguished sites, are you keeping the colours the same and moving some distinguished sites a little bit, but in a regular fashion? That could give rise to the very similar space groups you mention. (You are dealing with the ignorance of a sulfide collector here)”
J
The idea is that a given coloured ball does not sit on an “ideal” high-symmetry site, but just off from it. The displacement vector is likely to be one of a set of possibilities that are related by symmetry elements of the high-symmetry structure but are broken once the displacement happens. There are many ways in which displacements of successive atoms can be ordered: all the same, alternating, helically, etc in different systems. A simple example is the perovskite BaTiO3, which is not cubic except at high temperature because the ti does not like sitting in the middle of the octahedra of oxygens. In the best-known tetragonal distortion, all the Ti atoms move parallel to one cubic axis, so as to be very close to 1 oxygen, slightly less close to 4, and much further from the sixth. This generates a substantial ferroelectric polarisation.
“If that's what is meant by positional ordering, then provided the bonds are the same, there is no difference in the connectivity between the unordered and "positionally" ordered structure and thankfully that would not give rise to new names.”
?? The movement can certainly be large enough for connectivity to change, and is so in the boracite group.
Whether this topological change actually justifies a new name in the absence of grandfathering is a moot point, though. I’d be inclined just to use space group suffixes, as is done for differently occupationally-ordered varieties of cobaltite, etc.
”Thanks also for the reference on modular structures. These are really troubling from the point of view of xl growth. Are the modules knocking about in the melt and incorporated into the growing xls as large "molecules"? “
Many “modules” are actually effectively-infinite rodlike or sheetlike components, so I doubt that they exist as such in solution. In many cases, division of a 3-D structure into modules is not a statement about how it grew, but more an aid allowing description of a complex structure in terms of pieces of simpler, more familiar structures. When, in the late 80’s, the sapphirine structure(s) and the ambiguity that results in polytytpism in sapphirine was described simultaneously by myself/Andrew Putnis and by Bruce Hyde/Jacques Barbier as due to its being made of “pyroxene” and “spinel” modules alternating, there was no intent to suggest that sapphirine crystallises from little blocks of spinel and pyroxene that are floating about. It has its own structure, but parts of its big unit cell are strongly similar to the smaller nit cells of the other structures, and many of its properties are intermediate.
However, Paul Moore has occasionally floated the idea that the pre-existence in solution of some multinuclear but finite complexes may be important for nucleation of some minerals. I think he mentions that in the structure solutions of both hyalotekite and maricopaite in American Mineralogist – both lead minerals in which distinctive, finite clusters of a few Pb cations and associated O/OH can be picked out that may have existed as units in solution.
Rob:”Surely smaller things would get in the way.”
Well, yes. But FINITE complexes could play this role.
Rob:”How do things like potosiite and cylindrite form?”
1-D commensurate 1-D incommensurate regular interlayers? One can only speculate. Clearly, there is little energetic preference for a fully commensurate 3-D structure, but a very strong driving force for forming infinite 2-D modules AS SOLIDS. In fact, comparably strong forces driving formation of two types of such layer. And a tendency for them to alternate on the 2-layer-thicknesses scale, despite the forces at the interlayer interfaces being so weak that there is no need to be commensurate…
Rob:”Thanks for the clarification on polytypoids and polysomes. I'm beginning to get the picture.”
In which case, you have as much of the picture as anyone else does! J
Rob: “Phonons are a long way from macroscopic elastic strain,”
Not really, since a static strain can be formally decomposed into zero-velocity phonons ;-)
Rob: “but a volume change certainly changes the density of phonon states. I'm a little confused about a chicken and egg problem here. The phonon spectra are the vibrational properties of a given structure. The structure causes the phonons. Are you saying that phonons can cause the structure?”
No. Several hypothetical rival structures, with different phonon DoS, have slightly different energies, in part because of those DoS differences. Hence the DoS plays a role in determining the one that has lowest energy under a given set of pressure/temperature/compositional conditions.
Rob: “There is an argument that the vibrational modes in a growing snow flake determine the incredible long range ordering.”
That’s crystal morphology, which is quite different. Those of us who concentrate on properties of the bulk crystal may tend to neglect the subtle forces that determine the shape of the crystal surface, but small surface/volume ratio means that the surface forces are not very influential on the bulk until particle size is down at the colloidal/nanoparticle range.
Rob”…Phonons are a bulk property and surface effects are usually removed with periodic boundry conditions of a 3-torus. For xl growth it is precisely the surface that matters. Please elaborate.”
The finite size and shape of a crystal show up in reciprocal space (k-space) as quantisation of the possible frequencies. Whole-body resonances of the sort that I think you were invoking would be very low-frequency, low-energy acoustic modes, almost entirely decoupled from the higher-energy phenomena that determine crystal structure stability. But given that snowflakes form fast, by a diffusion-controlled mechanism, far out of equilibrium, the symmetry between arms is a bit of a conundrum…
The reason that toroidal boundary conditions are usually imposed on computer simulations of structures is that the model is usually so small that otherwise, the surface would constitute a significantly large proportion of it – the simulation would be not of a bulk crystal but of a nanoparticle with properties that are often very different (think luminescent silicon nanodots here).
The cubic unit cell of halite (sodium chloride) contains 4NaCl and is about 0.6 nm on edge. A model crystal with 100x100x100 unit cells would have 4 million NaCl, but 120000 of them would be at the surface – this is 3%, which is way too big for any calculated “bulk” properties to be trustworthy. A real salt crystal that is 0.6mm on edge would contain 1 million x 1 million x 1 million = 10^18 unit cells, 4x10^18 NaCl units, and only(!) 12x10^12 of these would be at the surface. That is 3 millionths of them, which shows how minor the influence of the surface on the bulk is becoming at that grain size.
So many important things in solid-state science rely on small differences between big numbers. Amazingly enough, empirical rules of thumb can still produce reliable predictions, be it relating to bond lengths, coordination number, or likely crystal habit (the old “reticular area” idea gives spookily accurate predictions for the different cubic space groups), but nature keeps springing these meso-scale complications like potosiite and highly symmetrical snowflakes…
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