Topic 5 : Crystal chemistry

Transcription

1 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 1/16 GEOL360 Topic 5 : Crystal chemistry (read p ; ) 5.1 Introduction what is a crystal? Lecture #1 A crystal is a homogeneous, solid body of a chemical element, compound, or isomorphous mixture, having a regularly repeating atomic arrangement that may be outwardly expressed by plane faces. The main feature of crystals is their long-range order, i.e. atoms or molecules) repeating at regular intervals along parallel lines. In contrast, liquids have only short-range order (as do glasses and other amorphous solids). 5.2 Crystallization (i) From a liquid or gas, the crystal either forms a nucleus of its own composition (e.g. crystallization of a magma), or adds material to a foreign particle (seed crystal, e.g. CaCO 3 deposition on a shell fragment in the ocean). Crystal nuclei have large surface area to volume ratios, and hence nucleation often does not occur until the solution is supersaturated to some degree: G Crystal nucleus (high S/V) Critical size crystal supersaturated solution Large crystal (low S/V) (ii) From a solid, crystals form by recrystallization (e.g. metamorphic recrystallization to produce a schist from a mudstone). This requires an activation energy, which for nucleation of phase A in a matrix of phase B is given by: G r = G A-B + G surface + G strain where G A-B = difference in free energy between phases A and B G surface = surface energy (particularly important for small crystals) G strain = strain energy required to make space for nucleation

2 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 2/16 If G r is negative, crystal nucleation and growth will occur (if kinetic effects allow). Reaction overstepping and / or defects in crystal B promote nucleation of phase A. 5.3 Unit cells and bonding A unit cell is the smallest volume or parallelepiped within the threedimensional repetitive pattern of a crystal that contains a complete sample of the atomic or molecular groups that compose this pattern, and that displays the symmetry present in the crystal structure. In other words, the unit cell is the smallest representative unit of a crystal, from which all its crystallographic properties can be derived. Atoms and ions are arranged in the unit cell and held there by chemical bonds. There are several types, the two main end-members are: Ionic bonds: bonding forces due to attraction of oppositely charged ions, e.g. halite NaCl Covalent bonds: bonding forces due to mutual interaction of equally shared electrons, e.g. sulfur S 8 There are also van der Waals bonds: between neutral atoms or molecules, e.g. graphite. These bonds are only about 1% of the strength of ionic or covalent bonds metallic bonds: a special case of covalent bonding, where positive ions are surrounded by a freely moving sea of shared electrons Most real bonds are somewhere between the ionic and covalent end-members. The % ionic character of a bond can be related to the electronegativity difference between the atoms involved, where electronegativity is a measure of the attraction of an atom for electrons (when that atom is bonded in a molecule or crystal; c.f. electron affinity is a measure of the attraction of an isolated gaseous atom for electrons) Table 5.1, Pauling electronegativities: large atoms have a larger screening effect, diminishing the attraction between the nucleus and the outer electron shell, leading to smaller electronegativities. Atoms which nearly have a full outer electron shell (e.g. halogens) have larger electronegativities. (For comparison, H has an electronegativity of 2.2). Useful web site: Bonds between atoms with similar electronegativities will be very covalent in character (e.g. bonds between atoms of the same element, like S-S and C-C) Bonds between atoms with different electronegativities will be very ionic in character (e.g. Na, 0.9, and Cl, 3.0. The greatest difference in electronegativity is between Cs, 0.7, and F, 4.0).

3 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 3/16 As we mentioned before, most bonds are intermediate in character between ionic and covalent. Consider quartz (SiO 2 ): - no discrete molecules, and a high melting point, suggest bonding is ionic - insolubility in solvents of high dielectric constant (e.g. water), and electrical insulator when molten, suggest covalent bonding In fact in silicate minerals, Si-O bonds are 40% ionic (60% covalent) Al-O bonds are 60-75% ionic (25-40% covalent) In terms of bond strength: covalent > ionic > metallic > hydrogen bond > van der Waals bond (weakest) Hydrogen bonds are about 5% as strong as covalent bonds Bond strength is proportional to bond length (shorter bonds are stronger): For ionic bonds, strength F of electrostatic bond between cations and anions is inversely proportional to the square of the bond length: F = e 1 e 2 /r 2 where e 1 and e 2 are charges, r is bond length. Bond length leads to the idea of ionic and atomic radii (next section). 5.4 Covalent and Ionic Radii Bond length is the distance between the centers of adjacent atoms. This can be investigated with XRD, (Bragg s Law, nλ = 2d sinθ), where dspacing is the distance between adjacent planes of atoms. X-rays have wavelengths of the order of m (0.1 nm or 1 Å), which happens to be about the same as typical ionic and covalent bond lengths. Bond length may also be thought of as the sum of two ionic / atomic / covalent radii. Which type depends on the substance; atomic radius covalent radius.

4 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 4/16 e.g. bond length in diamond is 1.54 Å, so the atomic radius (or covalent radius) of carbon in diamond is about 0.77 Å. Ionic radii are more useful for minerals, but more difficult to resolve. They are generally calculated by comparing interatomic distances with the ionic radius of O 2- which is approximately 1.32 Å. In detail, ionic radius depends on coordination number, particularly for cations: Coordination number: (tetrahedral) (octahedral) Ionic radius (O 2- ): 1.30 Å 1.32 Å 1.34 Å Ionic radius (Si 4+ ): 0.34 Å 0.48 Å Also note that the entire concept of ionic radii is only approximate because the locations of electrons are only known approximately (Heisenberg), and because electron densities are not spherical about the site of nuclei (overhead). Table of ionic radii for common ions: Ionic radius of anion > atomic radius Ionic radius of cation < atomic radius In general, radii decrease to the right (increasing nuclear charge, same number of electron shells)

5 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 5/16 In general, radii increase down the periodic table (addition of new electron shells from period to period). Questions: Why is ionic radius of Fe 3+ > ionic radius of Fe 2+? (has lost an extra electron) Why is ionic radius of Mg 2+ < ionic radius of Na +? (same number of electrons but Mg has higher nuclear charge which pulls electrons closer and also pulls surrounding anions closer) Why is ionic radius of F - < ionic radius of O 2-? (same number of electrons but F has higher nuclear charge which pulls electrons closer and also pulls surrounding anions closer) Why are Lanthanides all 3+ and all approximately same ionic radius? (with increasing atomic number and nuclear charge, electrons are added to the third shell which is crowded and cannot contract very much) Why does Pb 2+ have a much larger radius than Tl 3+? (Pb 2+ has a complete 6s subshell; Tl 3+ has no electrons in shell 6) Now we can understand why some elements readily substitute for others in certain sites in certain minerals. 5.5 Goldschmidt s rules of substitution Lecture #2 1. The ions of one element can substantially replace those of another in ionic crystals if their radii differ by less than about 15%. 2. Ions whose charges differ by one unit substitute readily for one another provided electrical neutrality of the crystal is maintained (requiring a coupled substitution (e.g. Ca 2+ Al 3+ = Na + Si 4+ ). If the charges of the ions differ by more than one unit, substitution is generally slight. 3. When two different ions can occupy a particular position in a lattice, the ion with the higher ionic potential forms a stronger bond with the anions surrounding the site (ionic potential = charge/radius ratio). 4. Substitution may be limited, even when size and charge criteria are satisfied, when competing ions have different electronegativities and form bonds of different ionic character. [this rule added by Ringwood in 1955: e.g. Cu + should substitute very easily for Na + in sodium minerals, but it does not because copper has a higher electronegativity (Cu = 1.9, Na = 0.93).] Three types of substitution: (i) Camouflage occurs when the minor element has the same charge and a similar ionic radius as the minor element it is replacing. e.g. Hafnium, Hf 4+ (0.79Å) frequently substitutes for zirconium, Zr 4+ (0.80 Å) in the mineral zircon, ZrSiO 4. Hafnium does not form its own minerals because it is only about 1 to 3% as abundant as zirconium I moat rocks, but it can substitute for zirconium very easily.

6 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 6/16 (ii) Capture occurs when a minor element enters a crystal preferentially because it has a higher ionic potential than the ions of the major element. e.g. Ba 2+ (1.44 Å) and Sr 2+ (1.21 Å) can substitute for K + (1.46 Å) in feldspars because they have higher ionic potential. This requires a couple substitution of Al 3+ for Si 4+ in order to preserve electrical neutrality of the crystal lattice. (iii) Admission involves the entry of a foreign ion that has a lower ionic potential than the major ion because it has either a lower charge or a larger radius, or both. e.g., Rb + (1.57 Å) has a lower ionic potential than K + (1.46 Å), and so Rb can substitute for K + in feldspars. Rb will have a harder time substituting for Na, since the Na ionic radius (1.10 Å) is substantially smaller than Rb +. Likewise, Sr 2+ (1.21 Å) will substitute for Ca 2+ (1.08 Å) very easily, but will not easily substitute for Mg 2+ (0.80 Å). Question: A commonly used accessory phase in U-Pb dating is zircon, ZrSiO 4. How bad do you think is the assumption that zircon contains no initial Pb (i.e,. all Pb found in the zircon formed from the decay of thorium and uranium)? Question: Why is potassium an incompatible element, enriched in the Earth s crust and depleted in the earth s core and mantle? (Recall definition of compatible and incompatible elements!) The reason that K is an incompatible element in the mantle is that the mantle is predominantly composed of pyroxenes and olivine (and garnet, and perovskite, and spinel ) The main cations in pyroxenes and olivine are Mg 2+ and Fe 2+. Compare the ionic radii of Mg 2+ and Fe 2+ (and Mn 2+ ). Now look at Ca 2+, which is considerably larger, but still manages to fit in some pyroxenes. K + is incompatible in pyroxenes because its ionic radius is substantially bigger (and it has an ionic charge of only 1+, which would require balancing by inclusion of some 3+ ions). However, K + is clearly compatible in granitic rocks because of the presence of K-feldspar. Because it substitutes for K, Rb is also compatible in granitic rocks. So the terms compatible and incompatible must be used with caution, and always bearing in mind the sort of crystal phases that may be present. To investigate (in)compatibility further, we must learn about crystal structures:

7 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 7/ Crystal Structures Basic structure of a crystal is the unit cell, which contains one or more formula units. e.g. halite has the chemical formula NaCl, while the unit cell of halite contains 4 Na atoms and 4 Cl atoms, i.e. 4 formula units OH: Brownlow Fig. 5-11: halite unit cell Note that this is actually: 1 Na (in center of unit cell) + (12 Na on edges shared by 4 unit cells) = 1 + (12/4) = 4 Na (6 Cl on faces shared by two unit cells) + (8 Cl on corners shared by 8) = 3 + (8/8) = 4 Cl Minerals can be classified by: Formula Bond type Chemistry e.g. AX, AX 2, etc e.g. ionic, covalent e.g. element, oxide, silicate, etc. (i) Ionic structures: Anion size (usually O 2-, sometimes OH - ) is very important (N.B. O 2- and OH - have similar size because H + is tiny, but charge is different) Cations sit in interstices between much larger anions. Pauling s rules (p. 259) Rule 1: Number of anions in coordination polyhedron depends to some extent on r CATION / r ANION : in general there will be more anions around large cations OH: Brownlow Fig. 5-11: halite unit cell e.g. halite, Na + is octahedrally coordinated (each Na + is surrounded by 8 Cl - ) Rule 2: Crystals are electrostatically neutral (e.g. each of the six Cl- anions may be considered to have an effective charge of 1/6, giving a total effective charge of 1 to balance the single Na+) Rule 3: Cations tend to be as far apart as possible due to mutual repulsion Bond strengths are important for the physical properties of a mineral, e.g. cleavage usually occurs along planes that pass through longer (weaker) bonds.

8 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 8/16 (ii) Covalent structures: e.g. sulfides: pyrite FeS 2 has a similar crystal structure to halite, with Cl replaced by S 2 groups. The S 2 groups are covalently bonded, strong bonds with a bond length of 2.10 Å (c.f. twice ionic radius of tetrahedral S 2- would be ~3.12 Å). The bonds between Fe and S are an example of hybrid bonding, where FeS 6 octahedra share faces with other octahedra (c.f. in halite, all 12 edges are shared between NaCl 6 octahedra, but faces are not shared) There may also be some metallic bonding between Fe atoms in pyrite. e.g. organic molecules, covalent bonding between C and other atoms, with weak van der Waals or hydrogen bonds between molecules. Structures of organic solids are determined by the shapes of constituent molecules (usually irregular). (iii) Combined ionic and covalent structures: e.g. calcite CaCO 3, composed of a cation (Ca 2+ ) and a complex anion (CO 3 2- ). On this level calcite is ionic, with carbonate ions occurring in 6 coordination around each calcium ion. Carbonate anion is a planar group of 3 oxygens around a carbon atom, which are covalently bonded together (stronger than ionic bonding).if calcite dissolves in water, CO 3 2- ions continue to exist as a group. Compare perovskite CaTiO 3 and calcite CaCO 3 : Electronegativities: Ca 1.0, Ti 1.5, C 2.5, O 3.5 So Ti-O bonds are predominantly ionic (~60% ionic), while C-O bonds are much more covalent (~80% covalent). [Fig. 5-2 % ionic vs. electronegativity] e.g. silicates silicate tetrahedron, SiO 4 4- : Si 1.8, O 3.5, = 1.7, bonding is 60% covalent and 40% ionic in character In some minerals, silica tetrahedra are isolated and may be thought of as SiO 4 4- anions coordinated by cations. e.g. olivine (forsterite), Mg 2 SiO 4 is an example of a nesosilicate In others, silica tetrahedra share one or more corners. Pyroxenes, e.g. diopside CaMgSi 2 O 6 are infinite chains of tetrahedral sharing two corners (inosilicate). Amphiboles, e.g. cummingtonite (Fe,Mg) 7 Si 8 O 22 (OH) 2 are infinite double chains sharing alternately two and three corners (inosilicate) Micas, e.g. muscovite K 2 Al 6 Si 6 O 20 (OH) 4 are sheet silicates, with infinite planes of tetrahedral (phyllosilicate) Quartz (SiO 2 ) and feldspars are examples of tectosilicates, which consist of an unbounded framework of tetrahedral sharing all four corners.

9 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 9/16 OH: Brownlow Fig. 5-16: silicate classification OH: Brownlow Table 5-3: silicate classification No mineral is known to have silicate tetrahedral sharing edges or faces (Pauling s third rule: cations are mutually repulsive) At high P, bonds become shorter and mineral structures change. (Another sort of perovskite with composition (Mg,Fe)SiO 3 is probably the most abundant mineral in the Earth as it is stable over the whole pressure range of the lower mantle.) Increases in both P and T often offset higher T leads to longer ionic bonds, and higher P to shorter ionic bonds. Remember the effects of compressibility and expansivity, from thermodynamics! More covalent bonds (e.g. Si-O) are affected less by changes in P and T. Crystal structures, and how they change with P and T, are investigated by X-ray diffraction (not discussed here, but recall Bragg s Law (nλ = 2d sinθ, see p. 4) 5.7 Solid Solutions Solid solution = a single crystalline phase that may be varied in composition within finite limits without the appearance of an additional phase. At this point we digress briefly to discuss some mineral terminology: Isotypes = minerals with identical structures, e.g. halite (NaCl) & galena (PbS) Isostructural minerals have similar structures, but not necessarily a one-to-one relationship between their atoms, e.g. coesite (SiO 2 ) & albite (NaAlSi 3 O 8 ) are both framework minerals consisting of silicate tetrahedra. Isomorphism = general similarity of mineral structures, e.g. pyroxenes in general (although some are orthopyroxene and some are clinopyroxene, all are single chain silicates, a form of inosilicate) There are three important types of solid solution: Substitutional solid solution: consider a mineral A-silicate, where A is a metal cation. If cation B has the same charge and similar ionic radius to A, it will likely substitute for A. This is a form of substitutional solid solution, which may be written (A, B)-silicate. An example would be the olivine series, where there is complete solid solution between forsterite (Fo, or Mg 2 SiO 4 ) and fayalite (Fa, or Fe 2 SiO 4 ). We can express any intermediate composition as a combination of forsterite and fayalite end-members. For example, Mg 1.6 Fe 0.4 SiO 4 is Fo 80 Fa 20. Another example is the potassium feldspar series, with end-members orthoclase (KAlSi 3 O 8 ) and albite (NaAlSi 3 O 8 ). At high temperatures, above about 700 C, there is nearly complete solid solution. At low temperatures, only limited

10 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 10/16 substitutional solid solution is possible, so that there will often be an albitic feldspar (Ab >90 Or <10 ) and a potassic feldspar (Or >85 Ab <15 ) which occur as separate phases. Plagioclase feldspar exhibits solid solution between the sodium end-member albite (NaAlSi 3 O 8 ) and the calcium end-member anorthite (CaAl 2 Si 2 O 8 ), which involves a substitution of (Na + Si 4+ ) for (Ca 2+ Al 3+ ), to maintain charge balance. Interstitial solid solution occurs when foreign atoms or ions occur between the usual lattice sites. For example, sometimes small amounts of Al 3+ will substitute for Si 4+ in the crystal structure of tridymite (SiO 2 ). In order to conserve charge balance, Al 3+ cations are accompanied by Na + cations which are accommodated in interstitial areas of the framework structure. Omission solid solution occurs when some ions are missing from their regular sites in the crysta structure. For example, in pyrrhotite (Fe 1-x S), as many as one in five Fe sites may be vacant (i.e. compositions range from FeS to Fe 0.8 S). The charge deficit is compensated by having some Fe 3+ cations as well as Fe 2+. For those of you who have done Structural Geology, you may recall different types of crystal defect, including dislocations as well as substitution, interstitial and omission defects. All have an effect on the free energy of the mineral (any change from the regular stucture of the pure end-member mineral requires some strain energy in the lattice). Dislocations have no effect on the chemistry of the material. We now consider the thermodynamics of solid solutions: Lecture #3 (i) ideal solutions (we already discussed these in topic 3) For an ideal solution, chemical potentials obey the following equation: µ = µ * +RT ln N (ideal solutions) i i i where µ i is the chemical potential of component i in the solution N i is the mole fraction of component i in the solution µ i * is the chemical potential of pure component i at standard P, T Recall that the activity, a i = N i when dealing with ideal solutions. In the ideal case, the physical properties of the solid solution are linear interpolations of the properties of the end-members e.g. the volume of a mixture of two materials A and B, in the ratio A 40 B 60, is given by V AB = (60/100) V B + (40/100) V A. An additional requirement is that the enthalpy of formation of an ideal solid solution, starting with its end-members, is zero. i.e. for the reaction A-silicate + B-silicate = 2 (A, B)-silicate, H = 0

11 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 11/16 This is only possible if the structures of A-silicate and B-silicate are identical (including all bond angles, bond lengths, unit cell properties, etc). Clearly this is never achieved in the real world, although substitution between two cations of identical charge and very similar radius is more ideal than substitution between two cations of different charge and radius. The entropy of formation of a solid solution can never be zero, even in the hypothetical ideal case. Starting with pure A-silicate and pure B-silicate, and mixing them together randomly, we end up with a disordered (A, B)-silicate. We have increased the amount of disorder relative to the pure end-members, and so increased the entropy. This is the entropy of mixing. Recall G = H T S, so G of formation of a solid solution from its endmembers will be more negative (more favourable) at higher temperatures. Olivines show near-ideal behaviour, with the properties of the solid solution being well predicted by simple interpolation of the properties of the endmembers. E.g. the calculated liquidii and solidii (fig. 5-18, in handout) Recall that olivine is a solution between Mg 2 SiO 4 and Fe 2 SiO 4. Mg 2+ has an ionic radius of 0.80 Å (octahedral coordination) Fe 2+ has an ionic radius of 0.86 Å (octahedral coordination, high-spin state) 0.69 Å (octahedral coordination, low-spin state) So there is little strain induced by substituting Mg 2+ for Fe 2+ (c.f. Ca 2+, r = 1.08 Å) (ii) non-ideal solutions (also discussed in topic 3) For non-ideal solutions, µ = µ * +RT ln a (real solutions) i i i where µ i is the chemical potential of component i in the solution a i is the activity of component i in the solution µ i * is the chemical potential of pure component i at standard P, T Recall that the activity, a i = γ N i when dealing with non-ideal solutions. The activity coefficient γ can be thought of as a correction factor to account for non-ideal behaviour recall activities are effective concentrations Alkali feldspars show distinctly non-ideal behaviour, with non-linear V and H as a function of composition. O/H: Fig We can summarise different solid solutions into three basic types of behaviour

12 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 12/16 (i) Raoult s Law (ideal behaviour) states that a i = N i. e.g. olivine (almost) (ii) Henry s Law states that a i = h i N i, where h i is a constant that depends only on P and T. This applies when component i is a solute, present at low concentrations, for example trace elements such as nickel in olivine. (iii) non-ideal behavior requires the use of a i = γ N i, where γ has to be experimentally determined and will depend on composition (other components present in the solution) as well as P and T. e.g. alkali feldspars These types of behaviour are summarized in fig. 5-20a (OH): µ vs. N and in fig. 5-20b (OH): a vs. N Example: application to geothermobarometry (Also mentioned in topic 3)

13 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 13/16 If we know the compositions of coexisting phases, we can calculate the distribution coefficient, K D : For the reaction: 1/3 Mg 3 Al 2 Si 3 O 12 + CaFeSi 2 O 6 = 1/3 Fe 3 Al 2 Si 3 O 12 + CaMgSi 2 O 6 pyrope garnet + hedenbergite = almandine + diopside K D = 2+ ( Fe Mg) 2+ Fe Mg ( ) 13 garnet clinopyroxene For ideal solutions (obeying Raoult s Law), at constant P, it can be shown that ln K D = A + B / T where A and B are constants and T is temperature So we can relate composition to T (i.e. this exchange reaction can be used as a geothermometer, because the value of K D depends a lot on temperature but very little on pressure). Other reactions which may be very sensitive to P but depend little on T are called geobarometers 5.8 Exsolution and the solvus In some minerals, solid solution may be stable at high temperatures but unstable at lower temperatures (as we mentioned earlier, feldspars show considerable solid solution at high T but form two separate phases at lower temperatures). We now look at why this occurs. Recall, G = H T S: In this diagram (F1) we can see the enthalpy of mixing for an ideal solid solution. Since G = H TS, we may expect solid solutions to have higher Gibbs free energies than separate endmembers and be thermodynamically unfavourable. However, the entropy of mixing provides a contribution in favour of solid solutions. At low temperatures this is not sufficient to overcome the enthalpy of mixing, which discourages solid solution formation (F2):

14 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 14/16 H mix Enthalpy H H A H mix Composition X B H B 0 G mix x 1 x composition -T S mix H mix Gmix Composition X B A G composition x 1 x 2 Fig. 1 Fig. 2 B Because of the shapes of the H and T S curves, solid solutions are least thermodynamically favourable for intermediate compositions (which require the most distortion of the crystal structure of either A or B). In the example shown above, two near-endmember phases will form, one dominated by component A (composition X 1 ), and the other dominated by component B (composition X 2 ). Because of the temperature term (-T S), the shapes of the resulting G curves will vary dramatically with temperature, and solid solutions are much more favourable at high temperatures:

15 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 15/16 A Composition X B B G mix 0 T 2 Temperature T 3 T 4 T S Chemical solvus T 5 A Composition X B B G mix = H mix - T S mix On cooling, the bulk composition will often move from a situation where solid solution is favoured to a situation where separate phases are more favoured. Exsolution is the process whereby a solid solution begins to unmix into separate phases. Here we see that solid solution is favoured for high temperatures (T > Ts). Exsolution is favoured for intermediate bulk compositions at temperature T3, and at most bulk compositions at temperature T4 or cooler. The line dividing regions where solid solution is thermodynamically favoured from regions where it is not favoured, in a temperature-composition diagram, is called the solvus. (Strictly, this is the chemical solvus, but we don t need to worry about the difference between this and the coherent solvus for now.) On cooling of a solid mixture of phases A and B, a solid solution should form when the solvus is reached. In the example below, this is at T3, where two different solid solutions will form (C0 and C1). On further cooling these compositions will tend to diverge, through coexisting C2 and C3, to C4 and C5,

16 GEOL360 LECTURE NOTES: T5 : CRYSTAL CHEMISTRY 16/16 and so on. Note that the two phases will rarely, if ever, reach pure (stoichiometric) endmember compositions. Temperature T 2 T 3 T 4 C 0 Solvus C 0 C 1 C 2 C 3 T 5 A C 4 C Composition X B B The above discussion applies where thermodynamics is the only factor governing the behaviour of the system. In the real world, kinetics plays a similarly important role, and a substantial nucleation energy may be required to begin formation of separate phases from a homogeneous solid solution. This is particularly true where one of the phases which is trying to nucleate has a substantially different crystal structure to the solid solution. That is a topic for a more advanced course, however 5.8 Summary (i) Bonding: covalent, ionic, metallic, van der Waals. Electronegativity. (ii) Crystal structures and substitutions; ionic charge and radius (iii) Solid solution types (substitution, interstitial, omission) and exsolution