American Mineralogist, Volume 81, pages 1021-1035, 1996
REVIEW
Effects of pressure on order-disorder reactions
ROBERT M. HAZENl ANDALEXANDRA NAVROTSKY2
'Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington, 5251 Broad Branch Road NW, Washington, DC 20015-1305, U.S.A. 2Department of Geological and Geophysical Sciences and Center for High Pressure Research, Princeton University, Princeton, New Jersey 08544, U.S.A.
ABSTRACT Order-disorder phenomena, which playa key role in the energetics, crystal chemistry, and physical properties of numerous solids, may be strongly affected by pressure. The effect of pressure on the state of cation order depends fundamentally on the volume of disordering, ~ Vdis= Vdisordered- Vordered'Although ~ Vdismay be positive or negative, it is usually positive for cation ordering in rock-forming minerals; pressure, therefore, tends to increase order in geological systems. Three structural mechanisms that contribute to ~ Vms are (1) positive ~ Vms(typically ~ 1%) associated with ordering of similar cations over two or more similar sites, (2) variable ~ Vdis(-1 % ~ ~ Vdis~ 1%) associated with AI-Si tetra- hedral ordering in framework minerals, and (3) large ~ Vms (up to 5%) associated with cation ordering involving mixed valence, mixed coordination, or both. Pressure alters order-disorder reaction rates by restricting cation motions or changing cation diffusion mechanisms. Influences of pressure on ordering in olivines, orthopyroxenes, high-pressure ferromagnesian silicates, spinels, garnets, perovskites, and rhombohedral carbonates are discussed. Several experiments are proposed to elucidate the phenomenon of high-pressure ordering in systems of mineralogical interest.
INTRODUCTION implies an important role for pressure in ordering phe- Order-disorder phenomena playa key role in the en- nomena. ergetics and crystal chemistry of numerous solids, includ- Pressure-induced ordering has implications for studies ing alloys, ferroelectric materials, fullerenes, high-tem- in materials science, geophysics, and solid-state physics. perature superconductors, and rock-forming minerals. In materials science, an understanding of pressure-in- Variations in degree of ordering result in changes in free duced ordering could lead to new techniques for tuning energy and, therefore, affect phase stability. Transitions the properties of synthetic materials such as ferroelectrics between disordered and ordered states, furthermore, can and cuprate superconductors. In geophysics, recognition alter crystal symmetry and cause significant changes in of high-pressure ordered states in the oxides, silicates, physical properties, including thermal and electrical con- and metal alloys that form much of the Earth's deep in- ductivity, vibrational spectra, and elastic moduli. terior is essential for developing realistic models of the Order-disorder behavior has traditionally been consid- transport properties and dynamic behavior of our planet. ered in terms of its temperature and compositional de- In solid-state physics, high-pressure order-disorder be- pendence. Recent studies, however, suggest that ordering havior may provide a sensitive indicator of relative in many crystals is strongly affected by pressure as well. changes in the nature of interatomic potentials. The ob- High-pressure synthetic crystals of olivine (Aikawa et al. jective of this review is to examine structural and ther- 1985), wadsleyite (Finger et al. 1993), garnets (Hazen et mochemical aspects of high-pressure ordering, to sum- al. 1994), and anhydrous phase B (Hazen et al. 1992), for marize existing high-pressure data on order-disorder example, display cation ordering to an extent that is not reactions, and to suggest needs and opportunities for fu- generally observed in analogous low-pressure phases. ture research. Other materials, including binary metal alloys (Owen and Liu 1947), spinels (O'Neill and Navrotsky 1983), frame- Types of crystallographic order-disorder transitions work silicates (Smith and Brown 1988), orthopyroxenes Each atom in an ideally ordered crystal occurs in a (Domeneghetti et al. 1995), and carbonates (Capobianco specific position and chemical environment-a crystal- et al. 198:7), experience significant variations in molar lographic site that repeats identically, essentially to infin- volume with changes in the state of order, behavior that ity. From a crystallographic point of view, four kinds of 0003-004X/96/091Q-I021$05.00 1021 ~_. --,
1022 HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE disorder phenomena that may affect the regularity of a tric crystals, which are defect structures with partial dis- stoichiometric crystal are commonly cited in the litera- order. Defects in these structures may occur as missing ture: positional disorder, rotational disorder, distortional atoms (vacancies), as in the case of wiistite Fe1_xO (Ha- disorder, and substitutional disorder. Note, however, that zen and Jeanloz 1984) and the oxide superconductor the distinctions between these phenomena in many cases YBa2Cu307_x (Hazen 1990). Alternatively, interstitial at- may be somewhat arbitrary. oms may occur, as observed in the excess a ofLa2Na04+X (1) Positional disorder: All atoms experience some dy- (e.g., Chaillout et al. 1989). namic positional disorder as a result of thermal vibra- tions. In addition, static positional disorder occurs in some Other types of order-disorder transitions crystals when an atom occupies slightly different mean Structural order-disorder reactions may also occur in positions in different unit cells. In the alkali feldspar al- materials that are not strictly crystalline, including quas- bite, NaAISi30g, for example, Na atoms adopt four dis- icrystals, liquid crystals, plastics, and amorphous phases tinct positions, depending on the local arrangement of Al (Venkataraman et al. 1989). In most cases these transi- and Si (Winter et al. 1977). tions are analogous to those in more regular crystals. (2) Rotational disorder: The closely related phenome- Of special interest are recently documented examples non of rotational disorder occurs in molecular crystals of molecular compounds in which pressure stabilizes such as high-pressure H2 (Mao and Hemley 1994) and highly ordered crystalline arrangements of dissimilar at- C60 (Fischer and Heiney 1993), in which the molecules oms or molecules-mixtures that form fluids at room have no fixed orientation but rotate more or less freely, temperature and lower pressures. Examples include van increasing the entropy of the phase. Rotational disorder der Waals compounds such as He(N2)11 (Vos et al. 1992), may also occur about a specific axis, as observed for C03 Xe(He)2 (Barrat and Vos 1992), Ne(He)2 (Loubeyre et al. groups in some rhombohedral carbonates (Ferrario et al. 1993), and Ar(H2)2 (Loubeyre et al. 1994), high-pressure 1994). clathrates such as those in the systems He-H20 (Londono (3) Distortional disorder: Distortional disorder, which et al. 1988) and H2-H20 (Vos et al. 1993), and molecular is also closely related to thermal disorder, may occur in compounds such as (02MH2)4 (Loubeyre and LeToullec structures like a-Si02, quartz, that can distort in more 1995) and phases in the H2-CH4 system (Somayazulu et than one equivalent way from a high-symmetry form (Ki- al. 1996). hara 1990). High-symmetry structures may thus repre- In addition to structural order-disorder, which in- sent a dynamic or static distortionally disordered aver- volves the positions of atoms, a variety of electronic and aging of unit cells that are, locally, in the low-symmetry magnetic order-disorder effects are known. Indeed, these configuration. This type of disorder abounds in perov- phenomena, which include the Verwey transition in Fe304 skite-type structures. and related spinels (see, for example, Kakol et al. 1992), (4) Substitutional disorder: Substitutional disorder, electron delocalization (for example, the insulator-to- which is the primary focus of this study, results from the metal transition in V02; Pintchovski et al. 1978), and interchange of different atoms over two or more sites. spin unpairing, as in C0304 and CaFe03 (O'Neill 1985; These sites are crystallographically distinct in the ordered Takano et al. 1991; Mocala et al. 1992), provide the focus phase but may be either distinct or equivalent (on the for most condensed matter research on ordering. Elec- average) in the disordered phase. In the classic example tronic and magnetic transitions have usually been studied of Cu-Au alloys (see, e.g., Hume-Rothery et al. 1969; as a function of temperature, though there have been some Rahman 1994), the disordered structure features a ran- high-pressure investigations (see, for example, Skelton et dom distribution of Cu and Au on a single symmetrically al. 1994; Harada et al. 1994; Kelso and Banerjee 1995). distinct site. Ordered forms, such as CuAu and Cu3Au, Because the change in electronic state involves a volume on the other hand, possess a lower symmetry, with at change, metallization and spin-pairing reactions may be- least two crystallographically distinct sites. Numerous come favorable at high pressure when .l V of ordering is rock-forming minerals, including ferromagnesian sili- positive (see below). cates, spinels, feldspars, and carbonates, exhibit this type of disorder, as discussed below. SIGNIFICANCE AND STRUCTURAL Any change in the degree of substitutional disorder re- ORIGINS OF 11Vdis quires atoms to move from one site to another in the The effect of pressure on the state of order depends structure, generally a distance of several angstroms. This fundamentally on the volume of disordering, .l Vdi"which situation contrasts with changes in positional and distor- may be defined as tional disorder, in which only a very small shift in atomic (1) coordinates is required (generally <0.5 A). As a result, an energy barrier must be overcome for intracrystalline Combining the first and second laws ofthermodynam- diffusion to occur and substitutional order to change. lCS, Consequently, order-disorder transitions of this kind are oG = -SoT + VoP. (2) often sluggish. Substitutional disorder also occurs in nonstoichiome- It follows that HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE 1023
TABLE 1. Volumes of disordering, A V.,S' for various minerals A V'" V", Structure Formula Sites Ions (ems/mol)" (ems/mol)" % change" References
Cu-Au alloy CusAu 12-fold Cu,Au 31.64 0.13 0.4 Owen and Liu (1947) CuAu 12-fold Cu,Au 17.4 0.15 0.8 Johansson and Linde (1936) and JCPDS card 25-1220 Olivine (MgFe)SiO. oct Mg,Fe 44.9 0.24 0.5 Akamatsu et al. (1993) (MgMn)SiO. oct Mg,Mn 46.2 -0.6 -1.3 Akamatsu et al. (1988) (MgNi)SiO. oct Mg,Ni 43.1 0.4 0.9 Ot1onello et al. (1989) Orthopyroxene (MgFe)Si,O. oct Mg,Fe 64.4 0.3 0.5 Domeneghetti et al. (1995) Spinel"" ZnAI,O. oct and tet Zn,AI 40.2 0.40 1.0 O'Neill and Dollase (1994) NiAI,O. oct and tet Ni,AI 39.1 0.36 0.9 O'Neill et al. (1991) MgFe,O. oct and tet Mg,Fe 44.7 0.54 1.2 O'Neill and Navrotsky (1983) and O'Neill et al. (1992) Mg,SiO. oct and tet Mg,Si 39.5 slightly + 0.1 Smith and Brown (1988) Pseudobrookite MgTi,Os oct Mg,Ti 55.0 0.3 0.5 Brown and Navrotsky (1989) (Mg,Fe)Ti,Os oct (Mg,Fe),Ti 55.4 0.4 0.6 Brown and Navrotsky (1989) Carbonates (CdMg)(COs), oct Cd,Mg 61.9 0.03 0.05 Capobianco et al. (1987) (CaFe)(COs), oct Ca,Fe 64.3 -0.3 -0.5 Davidson et al. (1993) and Chai and Navrotsky (1996) (CaMgXCOs), oct Ca,Mg 65.6 0.15 0.2 Reeder and Wenk (1983) Feldspar NaAISisO. tet SI,AI 100.5 0.5 0.5 Downs et al. (1994) and Winter et al. (1979) KAISisO. tet SI,AI 108.8 0.0 0.0 Smith and Brown (1988) RbAISisO. tet Si,AI 112.0 -0.3 -0.3 Pentinghaus and Henderson (1979) and Viswanathan (1971) Pentlandite M.S. oct and tet Ni,Fe 157.0 7.0 4.5 Tsukimura et al. (1992) "Estimated errors for molar volumes are typically <0.1%. Errors for AV.. are generally unknown, but they range from about 0.1% of molar volume for compounds in which end-member molar volumes for ordered and disordered states are well known (Le., albite), to >0.5% of molar volume for samples in which end-member volumes are extrapolated from intermediate states. Consequently, errors in percent change are large, In several cases as large as the estimated change itself. For both inverse and normal spinels, A where V.. corresponds to a spinel order parameter of x 0.67. "" V." = V~s- V""" =
and the pairs of octahedrally coordinated cations such as o!!..G diS =!!.. V (3) Mg, Fe, and Mn in olivines, orthopyroxenes, and carbon- oP T d>s' ( ) ates. In these cases, !!..VdiSis generally small and positive. Values for!!.. Vdishave been determined from X-ray dif- Cu-Au alloys provide a useful example of the volume fraction studies for a number of alloys, minerals, and oth- effects that may accompany ordering of two similar at- er materials (see Table 1). These volumes were obtained oms on two similar sites. All these Cu-Au alloy structures from differently ordered samples quenched to ambient possess a cubic close-packed (CCP) arrangement of metal conditions, with the exception of the Cu-Au alloys, which atoms, in which every Cu and Au is surrounded by 12 were examined as a function of temperature. In some neighbors. Owen and Liu (1947) documented the unit- instances, as in the case of orthopyroxenes and carbon- cell volumes of ordered and disordered Cu3Au, with mo- ates, the volume differences between fully ordered and lar volumes at room conditions, of 31.51 and 31.64 cm3/ disordered states were obtained by extrapolation from mol (extrapolated from a partially ordered state), respec- states of intermediate order, The relationship between tively. This change represents a density increase with or- molar volume and degree of disorder is not constrained dering of 0.4%. The disordered structure (space group to be linear, and few data are available to test linearity. Fm3m) has only one symmetrically distinct atom posi- In the exhaustively studied case of alkali feldspars, how- tion (see Fig. lA), whereas ordered Cu3Au adopts a prim- ever, near-linear behavior is observed (Kroll and Ribbe itive cubic structure (space group Pm3m), in which Au 1987; Smith and Brown 1988). is located at the origin and Cu occupies face-centered sites As evident from Table 1, !!..Vdismay be positive (i.e., (lh,1fz,O;see Fig. lB). the ordered form may be denser than the disordered form) The situation for CuAu is similar. Disordered CuAu or negative. A closer inspection of the materials involved (V ~ 17.45 cm3/mol; Johansson and Linde 1936), for reveals three structural trends that may be used to ra- example, has the same Fm3m structure as disordered tionalize the sign of!!..VdiSin most of these examples. Cu3Au (see Fig. 2A), whereas ordered CuAu (V = 17.3 cm3/mol; JCPDS card 25-1220) features alternating close- Ordering of two metal atoms between two similar packed layers of smaller Cu and larger Au atoms in a close-packed sites tetragonal structure (space group P4/mmm; see Fig. 2B). The easiest!!.. Vdisbehavior to rationalize involves or- The 0.8% density increase with ordering of CuAu can be dering of metal atoms of different sizes between two sim- understood in terms of the packing of spheres. In the ilar sites in a close-packed structure. Examples in Table ordered form, thicker layers of Au atoms alternate with 1 include the l2-fold coordinated atoms in Cu-Au alloys thinner layers of Cu atoms. The resulting molar volume ~
1024 HAZEN AND NA VROTSKY: ORDER-DISORDER AT HIGH PRESSURE
A B A B i'
() Random Cu 1AU1 2' 2' OCu O Cu .AU .Au FIGURE1. The structure ofCu,Au: (A) disordered form, space FIGURE2. The structure ofCuAu: (A) disordered form, space group Fm3m; (B) ordered form, space group P4/mmm. The group Fm3m; (B) ordered form, space group Pm3m. The fully fully ordered form is approximately 0.4% denser than the fully ordered form is approximately 0.8% denser than the fully dis- disordered form. ordered form. is identical to the sum of the molar volumes of pure cop- per (CCP; V = 7.1 cm3/mol) and pure gold (CCP; V = by the distribution of alkali and alkaline earth cations 10.2 cm3/mol). In the disordered phase of CuAu, how- that commonly occupy framework cavities. Different dis- ever, larger Au atoms are randomly interspersed with tributions of Al and Si in a tetrahedral framework, there- smaller Cu atoms in a less efficiently packed arrangement. fore, may result in significantly different molar volumes. Some Cu atoms occupy sites that are larger than in pure In these structures ordered arrangements do not neces- copper because of relatively long Au-Au contacts. Con- sarily display smaller molar volumes. Figure 3 presents sequently, the disordered forms of these alloys have a two-dimensional analog of this situation. The areas slightly greater molar volumes. bounded by two 90°- and two 120°-angle segments differ Similar reasoning may be applied to edge-sharing oc- by approximately 1%, depending on the arrangement of tahedral sites in biopyriboles, orthosilicates, carbonates, the four angles. and many other rock-forming minerals. In these struc- The systematics of .:lVdisfor framework aluminosili- tures two or more divalent cations of similar size may cates must be considered on a case-by-case basis. Con- order over two octahedral sites of similar size. Orthopy- sider, for example, the alkali feldspars (AAlSi30s; A = roxenes, olivines, and carbonates (Table 1), for example, Na, K, or Rb). The fully Al-Si-ordered Na end-member, display slightly greater densities, typically <0.5%, with low albite, has a molar volume of99.98 cm3/mol (Downs ordering of divalent octahedral cation pairs, including Mg, et al. 1994) in comparison with 100.45 cm3/mol for dis- Ca, Mn, Fe, Ni, and Cd. In each case, segregation of each ordered high albite (Winter et al. 1979). Thus, ordered cation into a distinct crystallographic site results in the sodium feldspar is approximately 0.5% denser than the most efficient packing of cation polyhedra. High-pressure disordered form. This difference may account for anec- geological environments, therefore, may favor phases with dotal evidence (H.S. Yoder, personal communication) that enhanced cation ordering. although disordered albite may be synthesized at atmo- These arguments, that ordered arrangements provide a spheric pressure, all albite synthesized at high pressure is more efficient volumetric packing of dissimilar units than ordered. disordered arrangements, also apply to high-pressure or- In rubidium feldspar (RbAlSi30s), on the other hand, dered molecular crystals, including van der Waals com- the ordered form (molar volume = 112.3 cm3/mo1; Pen- pounds and clathrates (Vos et al. 1992; Schouten 1995). tinghaus and Henderson 1979) is 0.3% less dense than the disordered form (molar volume = 112.0 cm3/mol; Tetrahedral site ordering in framework aluminosilicates Viswanathan 1971). In the case of potassium feldspar Feldspars and other framework aluminosilicates exhib- (KAlSi30s), with an alkali cation intermediate in size be- it a variety of Si-Al tetrahedral ordering patterns. Al- tween Na and Rb, ordered low microcline and disordered though Al and Si tetrahedra differ slightly in polyhedral high sanidine have been reported to have almost identical volumes, the molar volumes of framework structures are molar volumes (108.8 cm3/mol; Smith and Brown 1988). more closely tied to the magnitude and distribution of Examples of volume-dependent site ordering are to be T-O-T angles than to individual tetrahedral volumes. expected in other framework aluminosilicates, such as Average observed Si-O-Si, AI-O-Si, and AI-O-Al angles zeolites and feldspathoids, as well as alumino-phosphates are 145, 138, and 133°, respectively (Geisinger et al. 1985). and other tetrahedral framework compounds. A similar These angles, furthermore, may be significantly affected phenomenon may occur in perovskite-type phases in HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE 1025
2.20
~ 2.10 Co) ~ -< [J).~ ~ Q ~ 2.00 ~o I:Q o AREA = 4.316 AREA = 4.280 ~ FIGURE 3. Differentdistributionsof fixedanglesin a plane generally result in different enclosed areas. This situation is anal- 1.90 ogous to the volume dependence of framework aluminosilicates 1.75 1.85 1.95 2.05 on the distribution ofT-O-T angles. The areas (in arbitrary units) A-O BOND DISTANCE (~inA) of surfaces bounded by two 90°- and two 120°-angle segments, for example, differ by approximately I % depending on the ar- FIGURE4. The unit-cell edge a for cubic spinels is a function rangement of the four angles. of the octahedral (Ro) and tetrahedral (RT) bond distances. Points A, B, C, and D represent four ordered variants of C02Fe04 (see text). which multiple cations occupy the comer-linked octahe- dral framework [e.g., Pb(Zr,Ti)03' CaZCaU06, and CazFeTiOs.s; Hazen 1988]. In this binary oxide, both Fe and Co can adopt either + 2 or + 3 valence states in the octahedral site, whereas Fe2+, Ordering involving mixed valence or mixed coordination Fe3+, and Co3+ can adopt tetrahedral coordination. The largest known .:lVdiseffects arise in structures in O'Neill and Navrotsky (1983) documented the bond which two cations adopt different valence or coordination lengths, Ro and RT' for these spinels, as listed in Table 2 states. In the previous two examples, ordering does not and plotted in Figure 4. drastically change the volume contributions of constitu- From the points in Figure 4, it is evident that cubic ent cation polyhedra or T -0- T angles. Changes in valence cell edge a (and thus molar volume) ofCoFez04 depends or coordination, however, can significantly change the critically on the cation and valence ordering. The ordered volumes of structural building blocks. end-member (14IC02+)[[61Fe1+]04 (point A on Fig. 4), for Consider, for example, spinel-type oxides, which have example, has estimated RT and Ro bond distances of 1.96 the structural formula [4IAI6JBz04'This cubic structure and 2.025 A, respectively. The resultant molar volume is (space group Fd3m) has two symmetrically distinct cat- 44.77 cm3/mol. The disordered spinel (14IFe2+) ion sites: A, which is tetrahedrally coordinated at (lfs,lis,lis), [16JFe3+Co3+]04 (point B on Fig. 4), on the other hand, and B, which is octahedrally coordinated at (lfz,112,112).The has expected RT and Ro bond distances of 1.995 and 1.968 a atom also lies on the unit-cell diagonal, at (u,u,u), where A, respectively, and the observed molar volume is 43.06 u is approximately 1/4.The cubic unit-cell edge a is com- cm3/mol, approximately 4% denser than the ordered pletely determined by the tetrahedral A-a (RT) and oc- variant. This arrangement, with both Fe3+ and Co3+ in tahedral B-O (Ro) bond distances: octahedral coordination, results in the smallest possible octahedral volume for this composition. Intermediate 40RT + 8V33Rh - 8Ri molar volumes are expected for other partially ordered a= (4) 110 spinels of this composition, including (14JFe3+)
This variation of cubic a with RT and Ro is illustrated in Figure 4. Note that of the two sites, the larger octahedron TABLE2. Fe-O and Co-O bond distances in spinels as a (of which there are 16 per unit cell) plays a significantly function of valence and coordination number (after greater role than the tetrahedron (eight per unit cell) in O'Neill and Navrotsky 1983) determining unit cell a and thus molar volume. Ion Octahedral, Ro (A) Tetrahedral, RT (A) The order-disorder behavior of spinels is discussed at Fe"+ 2.12 1.995 length in a subsequent section, but the unusual spinel Fe3+ 2.025 1.865 CoFeZ04 provides a dramatic demonstration of the effects COH 2.10 1.96 of coordination and valence ordering on molar volume. Co"+ 1.91 1.83 .-----...------
1026 HAZEN AND NA VROTSKY: ORDER-DISORDER AT HIGH PRESSURE
[[6JC02+FeH ]04 and ([4JCOH )p6JFe2+FeH ]04 (shown in Fig. approaching a change in metallic character, spin state, 4 as points C and D, respectively). etc. Several other structures might be expected to display If energy and entropy of disorder vary with pressure, similar volume effects owing to valence and coordination then either of two situations may exist. The (OD.Edi.lOP)T ordering. Pentlandite [(Ni,Fe)9Ss], with both octahedral and the (MSdi.lOPh terms may fortuitously cancel each and tetrahedral Ni and Fe cations, displays a ~ Vdi, ~ other, in which case ~ Vdi, remains independent of pres- 4.5% (Tsukimura et al. 1992). Other likely candidates sure [i.e., (M Vdi.lOP)T= 0]. Alternatively, (OD.Edi.lOPhand include transition-metal binary oxides in the ilmenite (MSdi.lOP)T do not cancel, and ~ Vdj, is therefore a func- (FeTi03), ferberite (FeW04), and perovskite (CaTi03) tion of pressure. The point is that D.Edi" ~Sdi" and ~ Vdi, structures. High-pressure silicates with [6JSi, including cannot vary with pressure in arbitrary and independent silicate perovskites ([12JA[6JB03),silicate garnets ([SJA3- ways but are constrained as defined by Equation 7. [6JB2[4JSi3012),and phases related to [6JA,s[4JSi4024(Finger As shown in Equations 3 and 6, it is enough to know and Hazen 1991), should also display this behavior. ~ Vdi, as a function of pressure to calculate the pressure variation of the free energy of ordering at constant tem- Effects of pressure on .11Vdls perature, and therefore the ordering state. In practice, the Although few relevant data exist, there is no reason to volume change associated with disordering is known, at expect that ordered and disordered variants of a given best, only at atmospheric pressure for most systems of composition have identical equations of state. In most interest (as summarized in Table 1); no experimental data instances, therefore, ~ Vdj, is dependent on pressure. In on the variation of ~ Vdi,with pressure exist. Consequent- the case of anorthite, for example, Hackwell and Angel ly, the simplifying (and possibly erroneous) assumption (1992) proposed that increasing Al-Si disorder leads to is usually made that ~Vdj, is independent of pressure. On an increase in anorthite compressibility (see also review the basis of the above analysis, this assumption leads to by Angel 1994). On the other hand, Downs et al. (1994) a linear variation of ~Gdj, with pressure, as defined by suggested that disordered high albite should be less com- Equation 3. pressible than ordered low albite owing to the greater flexibility of AI-O-Si angles in comparison with Si-O-Si Kinetics of order-disorder angles. In both instances, if ordered and disordered var- It is well known that the rates of order-disorder reac- iants have different bulk moduli, then ~ Vdi, varies with tions depend strongly on temperature. At atmospheric pressure. Additional pressure-volume data for feldspars pressure, slow rates of divalent cation exchange in sili- are required to quantify these effects. cates and spinels generally preclude equilibration on a Factors influencing (o~ Vdi.lOPh may be identified by laboratory time scale below about 850 K, whereas very considering the difference in free energy of two compo- rapid equilibration prevents quenching of disordered states sitionally identical phases with different degrees of order: from above 1400-1500 K. These rates of equilibration, governed by diffusion rates, have been studied extensive- ly because of their potential applications as geospeedom- eters. Thus, for example, studies of ordering in Fe-Ni Differentiating Equation 5 in pressure at constant tem- alloys (Scorzelli et al. 1994) and pyroxenes (McCallister perature gives et al. 1975; Molin et al. 1991) are useful in documenting the thermal histories of meteorites. Similarly, ordering in O~Gdi' OD.Edi, _ o~Sdj' = T (Na,K)A1Si30s alkali feldspars (Megaw 1974; Ribbe 1983) ( OP )T ( oP )T ( oP )T and (Mg,Fe)Si03 orthopyroxene (Anovitz et al. 1988; Saxena et al. 1989; Domeneghetti and Steffan 1992; o~Vdj' + P + ~Vdj,' (6) Skogby 1992; Tribaudino and Talarico 1992) are widely (~ )T used in documenting the cooling rates of lunar and ter- This equation defines the pressure effect of disordering restrial rocks, even though those cooling events may oc- on G. Combining Equations 3 and 6 yields cur over time scales> lOs yr, whereas laboratory exper- iments occur in 10-4 to 10-1 yr. OD.E o~S o~V By contrast, few data exist on the effects of pressure on di' _ di' dj' T + P = O. (7) the kinetics of order-disorder reactions. Pressure confines ( oP )T ( oP )T ( oP )T atoms into a smaller volume and thus affects atomic mo- Equation 7 reveals that if the energy and entropy of tions, diffusion, and crystal-growth rates, which are be- disordering do not depend on pressure, then neither does haviors that can be modeled with a parameter such as the volume of disordering. Conversely, the energy and the activation volume (Fratello et al. 1980a, 1980b; Lu the entropy of disordering must vary with pressure ifthe et al. 1991a). Pressure imposes orientational order in H2 volume of disordering shows a pressure dependence. This (Mao and Hemley 1994), C60(Fischer and Heiney 1993), more complex behavior is likely if the nature of the and CH4 (Prager et al. 1982). Similarly, for a given crys- chemical bonding changes strongly with pressure, e.g., on talline phase, intracrystalline diffusion may be expected the steeply rising portion of a potential energy surface or to become more restricted as interatomic distances de- HAZEN AND NA VROTSKY: ORDER-DISORDER AT HIGH PRESSURE 1027 crease at high pressure. (This behavior does not generally 5 result, however, in high-pressure phase transitions in- T = 1500 K volving an increase in coordination number, in which case nearest-neighbor distances between some atoms may 4 increase.) Given the restricted motion of atoms in a com- --... pressed phase, it is possible that high-pressure ordered CI:I states of many minerals are more slowly achieved, and .D 3 more readily quenched once achieved, than those at low- :::.. 1.0 er pressure. -L' In spite of this prediction, Goldsmith and Jenkins 2 (1985) observed the opposite effect in albite, in which Al- ~c Si order-disorder reaction rates increase by orders of magnitude between atmospheric pressure and 1.8 GPa. They suggested that at higher pressures a new diffusion mechanism comes into play: Near the transition from albite to jadeite plus quartz, AI experiences transient states o of greater than fourfold coordination, during which Al-O o 1 0 20 bond breaking is facilitated. Pressure CGPa) Whatever the effects of pressure, it should be remem- FIGURE5. Equilibrium constant, KD, for Fe-Mg distribution bered that samples recovered at ambient conditions from in a ferromagnesian silicate varies as a function of pressure for high-pressure synthesis experiments generally have ex- different volumes of disordering (.1.Vdi,in cubic centimeters per perienced rapid temperature quenching (a few seconds) mole), as marked on each curve. Curves were calculated for a at high pressure, followed by slow pressure release (min- temperature of 1500 K. At lower temperatures the effect of pres- utes to hours). If the systematics above apply, then one sure on KD is somewhat larger for a given .1.Vdi' (see Eq. 10). cannot expect to recover the full extent of cation disorder of samples prepared above 1500 K in these studies. We conclude that 1500 K represents an upper temperature limit from which structural states are quenchable. This commonly possess similar MglFe, indicating no strong temperature is also reasonably representative of mantle tendency for these elements to segregate from each other conditions, under which many of the minerals discussed in the low-pressure environment. (3) Intracrystalline par- reach their limits of stability. Thus, below we give some titioning: In oxides and silicates with more than one crys- examples with 1500 K as a reference temperature, as il- tallographically distinct octahedral FeH and Mg site of lustrated in Figure 5. similar size and distortion, these cations tend to be dis- ordered. Ordering over two sites can be expressed as a distri- MINERALOGICAL EXAMPLES OF bution coefficient, KD: ORDERING AT PRESSURE (8) Numerous examples of cation ordering have been doc- umented in mineralogical systems. In the following sec- Given this definition, KD = 1 for complete disorder. Most tions we consider specific examples with regard to the low-pressure ferromagnesian minerals have KD < 2, possible influence of pressure. whereas four recent studies have suggested that the situ- Iron-magnesium silicates: General considerations ation at high pressure may be more complex. Note that, rigorously, the equilibrium constant should Iron-magnesium oxides and silicates have been studied be written as an activity ratio, not a concentration ratio: extensively because of their importance in understanding the Earth's deep interior. FeH and Mg behave as inter- (9) changeable ions in many low-pressure oxides and sili- cates. Divalent Fe and Mg have similar ionic radii (0.78 Because ~Gdi, = - RT In KD, the pressure effect on KD vs. 0.72 A, respectively; Shannon 1976) and electrone- can be written as gativities, and both tend to adopt octahedral environ- ments in oxides and silicates. These similarities have three important consequences: (1) Solid solution: Most com- mon rock-forming minerals, including olivines, pyrox- Figure 5 shows the pressure effect in KD by plotting enes, micas, amphiboles, garnets, spinels, and carbonates, KD(P)/KD (1 atm) for various values of ~Vdi' at 1500 K. display complete solid solution between FeH and Mg end- Note that in this figure and in subsequent discussions we members. (2) Intercrystalline partitioning: Coexisting pairs assume FeH /Fe3+ does not change. As noted above, of ferromagnesian minerals, such as olivine and clino- changes in Fe valence generally have a much larger effect pyroxene in a basalt or amphibole and mica in a granite, on molar volume than changes in Fe-Mg ordering. -~------
1028 HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE
Ferromagnesian olivine pendence on pressure and temperature has yet to be stud- Ferromagnesian olivines, a-(Mg,FeMi04, at low pres- ied. sure show little Fe-Mg ordering and generally display KD < 1.2. Aikawa et al. (1985), however, found that pressure Orthopyroxene enhances Fe-Mg ordering in olivines. Akamatsu et al. In (Mg,Fe)2Si206 orthopyroxene Fe orders preferen- (1993) equilibrated ferromagnesian olivines at pressures tially into the M2 site, which is both significantly larger to 10 GPa and found that KD increases significantly with and more distorted than MI. Distribution coefficients> 50 :::::0.02 GPa-1 and esti- pressure. They reported dKD/dP have been reported for slowly cooled natural orthopyrox- mated that the KD of olivine may exceed 2.0 in the Earth's enes (Tribaudino and Talarico 1992) and for samples an- mantle. On the basis of these experiments, Akamatsu and nealed at temperatures near 500 °C, whereas samples Kumazawa (1993) and Akamatsu et al. (1993) demon- equilibrated above 1000 °C and rapidly quenched more strated that above 1273 K, Mg-Fe ordering equilibrates typically have KD between 3 and 4 (Virgo and Hafner in less than a hundredth of a second. Thus, they conclud- 1969). These large KD values probably reflect strong dif- ed, quench experiments from higher temperatures cannot ferences in the degree of distortion of M1 and M2 sites, preserve the equilibrium cation distribution. with Fe2+ preferring the more distorted M2 environment. Akamatsu et al. (1993) presented a fairly complex five- Domeneghetti et al. (1985) investigated the effects of parameter model to account for the dependence of KD on Fe-Mg order on the structure of three orthopyroxenes with pressure, temperature, and composition, as well as non- different Fe/(Fe + Mg): 0.180, 0.462, and 0.755. In all ideal mixing on M1 and M2 sites. They noted that in the three samples, increased Fe-Mg disorder (induced by heat case of ferromagnesian olivine, because both the devia- treatment) caused an increase in unit-cell volume. In their tion from random Fe-Mg distribution and the volume sample with Fe/(Fe + Mg) = 0.462, for example, a de- change associated with order-disorder reactions are small, crease in KD from 49.2 to 7.3 is accompanied by an in- it is difficult to constrain the AVdisfrom crystallographic crease in unit-cell volume from 851.6 to 852.8 A3, or data alone. Using their thermodynamic model, Akamat- 0.14%. In a subsequent study Domeneghetti et al. (1995) su et al. (1993) obtained AVdis= 0.24 cm3/mol, a value performed multiple linear-regression analysis on composition about one-half of that cited in their earlier study (Aka- and structure information on > 200 orthopyroxenes. For matsu et al. 1988). The cation-distribution equilibrium (Mg,Fe)2Si206 orthopyroxenes they defined unit-ce~l vol- constant, KD, increases with pressure, reaching values near ume, V, as a linear function in terms of the fractIOn of 2.2 for olivines near the 400 km discontinuity in the Fe2+ in M 1 and M2: mantle in comparison with values of 0.9-1.2 near the surface. The variation of KD with pressure contains con- V = 26.20X~~,t + 17.67X~~? + 832.74 A3. (11) tributions from nonideality of the solid solutions and from Equation 11 can be used to predict unit-cell volumes the PA V term, because nonunity activity coefficients must for the extreme cases of complete disorder and complete be used to convert the experimental (concentration ratio) order with all Fe in M2. For a composition of KD to a thermodynamic (activity ratio) equilibrium con- (MgFe)Si206, volumes for ordered and disordered sam- stant (see, for example, Akamatsu et al. 1993). It should ples are predicted to be 850.41 and 854.68 A3, respec- be noted that f02 may playa significantrole in olivine tively. Thus, AVdis= 4.27 A3, or approximately 0.32 cm3/ Mg-Fe ordering (Will and Nover 1979, 1980), and these mol, which suggests that increased pressure favors Fe-Mg effects have not been taken explicitly into account in the order in orthopyroxene. Studies by Virgo and Hafner work of Akamatsu et al. (1988, 1993). (1969) on samples annealed at atmospheric pressure and Other transition metals, especially Mn, Co, and Ni, at 2 GPa, however, did not detect any significant effect also substitute into olivine, and cation distributions have - of pressure on ordering. Similarly, a synthetic orthopy- been studied as a function of temperature for Ni- and roxene sample with Fe/(Fe + Mg) 0.44, quenched from Mg-containing olivines (Rajamani et al. 1975; Ottonello = 1873 Kat 11 GPa (Hazen et al. 1993a), has KD = 3.9, et al. 1989) and as a function of both temperature and which is a relatively disordered value that is generally pressure for Mn- and Mg-containing olivines (Akamatsu consistent with the low-pressure results of Virgo and Haf- et al. 1988). Both of these systems show greater ordering ner (1969). Taking this last case, than ferromagnesian olivines, with Ni preferring Ml and Mn preferring M2. Although the ferromagnesian and Mg- AGdis(11 GPa) - AGdis(1 atm) and Ni-containing olivines show positive volumes of dis- = 11 x 104 x 0.32 = 3540J. (12) ordering, Akamatsu et al. (1988) reported a significant Assuming the samples preserved a cation distribution negative AVdisand pressure-induced disordering for Mg- characteristic of 1500 K, and Mn-containing olivine (see Table 1). No structural reasons for this unusual behavior have been proposed. RTln[KD(11 GPa)/KD(1 bar)] = 3540 Significant ordering has also been observed in several other or olivines, including those with Co-Mg, Ca-Mg, and Fe- Mn (Ghose and Wan 1974; Brown 1982), but their de- KD(11 GPa)/KD(1 bar) = 1.33. (13) HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE 1029
Thus, a KD of 3.9 at 11 GPa would imply a KD of 2.9 to suggest a greater difference in the crystal-chemical be- at 1 atm, within the range of the uncertainties for the havior of Fe and Mg in high-pressure phases than in low- data of Virgo and Hafner (1969) and subsequent work. pressure silicates. A similar conclusion was reached by Therefore, a fairly small pressure effect on KD is consis- Hazen (1993) in his study of the compressibilities of high- tent with both the volume data and the experimental KD pressure Fe-Mg silicate spinels. determinations. The above simple illustrative argument A cautionary note is in order, because it is extremely does not account for nonideal mixing; however, when difficult to ensure equilibrium states of order in high- comparing samples of the same composition, this effect pressure synthesis. The wadsleyite sample of composition is minor if the change in cation distribution is small over (MguFeo.s)Si04 described by Finger et al. (1993), for ex- the range considered. ample, is clearly a metastable product, because it crys- tallized well within the silicate spinel field. Even in the High-pressure ferromagnesian silicates synthesis of stable phases, reversals are rarely attempted, Wadsleyite, i3-(Mg,Fe)zSi04, is a high-pressure poly- much less achieved in high-pressure experiments. De- morph of olivine stable above about 13 GPa. Finger et grees of Mg-Fe order in the above examples, therefore, al. (1993) described the crystal chemistry of a series of are not presented as equilibrium states. Fe-bearing wadsleyite samples that were synthesized at approximately 15 GPa at temperatures> 1973 K. These Spinels wadsleyite crystals have three symmetrically distinct Fe- Oxide spinels encompass a large group of natural and Mg octahedra, all of similar size and distortion, yet Fe is synthetic compounds of the general form AB204, where significantly depleted in M2 relative to the other two sites, A and B are tetrahedrally and octahedrally coordinated with KD 2.7. Further systematic studies on the effects cations, respectively. As reviewed above, the cubic spinel "" of annealing and cooling rate on wadsleyite Fe-Mg order structure is fully defined by one 0 positional parameter are necessary to characterize fully this behavior. and the cubic cell edge. For a fully ordered "normal" Hazen et al. (1992) described single crystals of Fe- bear- spinel, A and B cation charges may be either + 2 and + 3, ing anhydrous phase B, (M&.ssFeo.d14Si50z4, that was or +4 and +2, respectively. If parentheses are used to synthesized at 24 GPa and 2073 K. This complex silicate designate A-site cations and brackets are used to desig- has six crystallographically distinct Mg-Fe octahedral sites, nate B-site cations, then a normal spinel has the struc- all of similar size and distortion. Nevertheless, Fe is sig- tural formula (A)[BzJ04' nificantly more concentrated in one of these sites (desig- In spite of the apparent simplicity of this structural nated M3) than the other five. Typical values of KD be- formula, spinels display complex patterns of disorder tween M3 and other octahedra range from 7 to 9, which (Navrotsky and Kleppa 1967; Lindsley 1976; O'Neill and are larger than in any comparable low-pressure phase. Navrotsky 1983, 1984). The mineral spinel, MgA1204, Observed Fe-Mg ordering in wadsleyite and anhydrous was the first stoichiometric compound found to incor- phase B is especially striking because the specimens were porate a disordered site (Barth and Posnjak 1931). The synthesized at temperatures above 1973 K and rapidly cation distribution has been found to vary from normal cooled at high pressure. Such extreme annealing temper- to about 30% inverse (Navrotsky and Kleppa 1967; atures usually produce relatively disordered Fe-Mg dis- Schmocker and Waldner 1976; Wood et al. 1986; Peter- tributions in low-pressure silicates. The large KD values son et al. 1991), depending on temperature. of these materials suggest that pressure could be a con- In MgAlz04 and many other spinels, the range 800- trolling factor in Fe-Mg ordering. However, the apparent 1400 K is accessible for equilibration and quenching ex- effect of pressure may result from several mechanisms. periments on cation distribution. A review of thermo- The most straightforward mechanism is that a large pos- dynamic models for the temperature dependence of cation itive ~ Vdi,enhances order by the thermodynamic argu- distribution is given by Navrotsky (1994). The most dis- ments above. If these studies capture distributions on ordered state for a spinel is the random cation distribu- quenching that are characteristic of 1500 K, then chang- tion (Ay,B"")[A;,,B,J, which both normal and inverse ing KD by about a factor of three implies a change in free spinels tend to approach at high temperature. For spinels energy of 13.7 kllmol. If this change is induced by a of the 2-3 charge type (e.g., MgAlzO., MgFez04), the in- pressure of about 20 GPa, then (MGdi,/OPh = 0.65 kll verse distribution generally has a smaller volume than GPa, or from Equation 7, ~Vdi, = 0.07 J/bar = 0.7 cm31 the normal (see Table 1). Thus, 2-3 spinels tend to be- mol. Similarly, an increase by a factor of five would imply come more inverse with increasing pressure at constant a ~ Vdi,of about 1 cm3/mol (see also Fig. 5). Such values temperature. Spinels that tend toward normal (e.g., of ~ Vdi" though large, are not physically impossible. Al- MgAlz04) at low temperature would become more dis- though the structures of these high-pressure phases may ordered with increasing pressure, whereas those that ap- also show large KD values at low pressures (where the proach the inverse distribution (e.g., MgFez04) a.t low phases would be metastable), there are no obvious crys- temperature would become more ordered with increasing tal-chemical reasons for strong Mg-Fe partitioning. The pressure. behavior ofwadsleyite and anhydrous phase B thus seems For spinels of the 2-4 charge type (e.g., Mg2Ti04, 1030 HAZEN AND NAVROTSKY: ORDER-DISORDER AT HIGH PRESSURE
-y-Mg2Si04), the situation is less clear. Both O'Neill and and Major 1971; Fujino et al. 1986), Ca3(CaGe)Ge3012 Navrotsky (1983) and Hazen et al. (l993b) suggested a (Ringwood and Major 1967; Prewitt and Sleight 1969), small positive volume of disordering for the normal spi- and Mg3(MgSi)Si3012 (Smith and Mason 1970; Angel et nel Mg2Si04. The effect of temperature probably out- al. 1989) have been synthesized. These garnets generally weighs that of pressure, and a small degree of disorder have tetragonal symmetry, and the divalent and tetra- (about 4%) has been suggested for Mg2Si04 spinel valent ions are ordered on two symmetrically distinct oc- quenched from 20 GPa and 1673 K but not for Fe-bear- tahedral sites. Such ordering may be more a consequence ing silicate spinels (Hazen et al. 1993b). of size and charge than of pressure, as borne out by the In spinels containing two or more cations of variable existence of tetragonal ordered garnets at atmospheric valence (e.g., in the case of C02Fe04 discussed above), pressure for compositions Y3(AIY)AI30'2 (YAG) and considerable volume differences have been predicted from Y3(FeY)Fe30'2 (YIG), with Y and Al or FeH, which are ionic radius arguments (O'Neill and Navrotsky 1983) for trivalent cations of quite different size, sharing octahedral different distributions of elements and charges among oc- sites. Nevertheless, for silicate and germanate garnets, the tahedral and tetrahedral sites. Thus, the site occupancies salient points are that pressure stabilizes garnets with and charge distributions may change significantly with mixed octahedral occupancies and that these high-pres- pressure, with the densest forms being favored at high sure phases are ordered. pressure. Hazen et al. (1994) characterized single crystals of a garnet with composition (Cao.49Mg2.s,)(MgSi)Si30'2 syn- High-pressure garnets thesized at 18.2 GPa and 2323 K. This sample is the first Materials that change symmetry upon ordering can be silicate garnet to display ordering on both octahedral and more complex than the examples considered above. A dodecahedral sites. This behavior may increase gamet's first-order phase transition may be involved, or a change compositional flexibility, affect element partitioning at from second- to first-order behavior (a tricritical point) high pressure, and stabilize the garnet structure in the may occur as a function of temperature, pressure, com- transition zone and upper portion of the lower mantle. position, and ordering state. Symmetry rules dictate Ca is concentrated in the D2 site, which has a refined whether a transition can be higher order; however, a tran- composition of CaO.32MgO.68, in comparison with sition that is allowed by symmetry to be second order can Cao.08M&.92for Dl. These site compositions may be ex- be first order. In many cases, the detailed nature of the pressed as a distribution coefficient: transition is poorly understood at atmospheric pressure and totally unknown at high pressure. Nevertheless, sev- KD = (Xg;/XB~)/(Xg~/XBD = 5.4. (14) eral relevant, mostly qualitative, observations have been made. The important cases of alkali feldspars and Cu-Au The reason for this unexpected degree of Ca-Mg or- alloys have been described previously, and additional ex- dering in calcic majorite garnet is not obvious. The two amples are summarized below. dodecahedral sites are not appreciably different in size or The garnet structure, first identified in common rock- distortion. One possibly significant difference between D 1 forming silicates, has been synthesized in a wide range of and D2 is the distribution of second-nearest-neighbor oxides and fluorides that incorporate at least 50 elements. cations. Distances between adjacent D 1 sites and between This compositional flexibility has led to a wide range of ap- Dl and D2 are relatively short: approximately 3.5 A. plications for gamet, including abrasives, lasers, waveguide Distances between closest D2 sites, on the other hand, components for microwave communications, low-con- are more than 5.7 A. Ordering of larger Ca atoms onto ductivity magnetic bubble-domain devices, and semipre- D2 minimizes Ca-Ca repulsion, which may in turn in- cious colored gemstones. Silicate garnets, furthermore, are crease .
--._- 1032 HAZEN AND NA VROTSKY: ORDER-DISORDER AT HIGH PRESSURE significant role in the order-disorder behavior of a variety dramatically affect cation mobility and thus the rate of of materials. Much additional research is needed, how- order-disorder reactions? Studies of pressure-induced or- ever, to document this phenomenon. Four types of stud- dering can provide answers to these kinetic questions. ies- high-pressure synthesis, controlled ordering experi- As noted above, increased pressure tends to confine ments, comparative compressibility measurements, and atoms and restrict their motions, except in unusual cir- theoretical modeling-would enhance our understanding cumstances such as proposed by Goldsmith and Jenkins of pressure-induced ordering. (1985) for albite. Thus, it is possible that high-pressure ordered states are more slowly achieved, and more readi- High-pressure synthesis and characterization of ly quenched, than those at lower pressure. (Note that ex- ordered states perimental protocol in multi-anvil experiments is to re- duce temperature while the sample is at pressure.) If For compounds with significant ~ is molar volume Vdi" pressure tends to increase cation order, then samples a linear function of the degree of order? What is the pres- quenched while at higher pressure are more likely to re- sure dependence of the degree of order? Our understand- tain their equilibrium ordered state than those quenched ing of pressure-induced ordering is severely limited by from the same temperature while at lower pressure. the lack of appropriate samples. Although numerous Until accurate in situ measurements of ordering can be minerals and synthetic compounds display varying de- made, these effects can be quantified by studying the cat- grees of order, it is difficult to find two compositionally ion distribution in a material such as ferromagnesian or- identical samples with markedly different ordered states. thopyroxene, in which the state of order is a sensitive The most basic experiments required to understand pres- function of temperature (Virgo and Hafner 1969; Yang sure-induced ordering, therefore, are systematic high- and Ghose 1994). Several experiments would equilibrate pressure synthesis and characterization of samples dis- both ordered and disordered samples of the same com- playing varying degrees of ordering. position, thus attempting to achieve equilibrium conver- Table 1 reveals several phases for which a range of gence, at a series of pressures and temperatures. In ad- ordered states are available. Additional investigations of dition, these samples could be quenched at different olivine, orthopyroxene, spinels, and feldspars are needed, cooling rates. All samples quenched rapidly from above whereas controlled synthesis studies of pseudo brookite- a certain critical temperature (perhaps 1500 K) should type MgTi205 and kutnahorite [CaMn(C03),] hold the - presumably display identical degrees of disorder. Sam- promise of providing complete suites of ordered inter- ples quenched from lower temperatures or at slower rates, mediates. however, should produce different degrees of order. Doc- Of special interest to the field of mineral physics would umentation of these ordered states can thus be used to be synthesis at several pressures (and the same temper- determine minimum rates of intracrystalline cation dif- ature) of samples of ferromagnesian silicates, including fusion, as well as equilibrium ordered states. A series of the minerals wadsleyite, anhydrous phase B, and ortho- such studies at different pressures, furthermore, could pyroxene described above. Multi-anvil devices, which can constrain the effect of pressure on cation diffusion. produce as much as 0.5 mm3 of sample at 25 GPa, pro- vide an ideal technique for these syntheses. X-ray anal- ysis, M6ssbauer spectroscopy, infrared spectroscopy, and Comparative compressibilities of ordered states other structural probes of the resulting samples would If a suite of crystals with varying degrees of order can reveal the extent of cation ordering and the corresponding be obtained, relative compressibilities of these different molar volumes, thus providing information on ~ Vdisas structural states could be determined by the method of well. Synthetic specimens could also be examined by vi- Hazen (1993). In this technique, several crystals are ar- brational spectroscopy or calorimetry to determine the ranged in the same diamond-anvil-cell mount and probed effect of ordering on heat capacities and to measure di- by X-ray diffraction. Small differences in compressibility rectly the energy of disordering. A suite of composition- can be detected because all crystals are at the same ally identical samples, which differ only in the pressure pressure. These differences in compressibilities can pro- of synthesis and degree of Fe-Mg ordering, would thus vide a direct measurement (or place an upper limit) on provide unambiguous evidence for the effect of pressure o~ Vdi,lOP. on order. In such a series, control and characterization of oxidation state (ideally all Fe as Fe2+ ) would also be im- First-principles calculations portant. The temperature chosen should be one at which Experimental studies are complemented by first-prin- cation distributions can be equilibrated in about an hour ciples calculations of the structure and energetics of dif- but are quenchable when a sample is cooled in seconds, ferent ordered states (see, e.g., Ducastelle 1991; Lu et al. i.e., probably in the range 1073-1173 K or below. 1991 b). These calculations may enhance understanding of the relative stabilities of ordered and disordered states Intracrystalline cation diffusion at high pressure and of states that are not attainable experimentally. First- How quickly do cation distributions equilibrate at high principles methods also facilitate modeling of the prop- temperature and high pressure? Is it possible to quench erties of known materials at extreme conditions of tem- states of order from extreme conditions? Does pressure perature and pressure. Most previous theoretical work HAZEN AND NA VROTSKY: ORDER-DISORDER AT HIGH PRESSURE 1033 has focused on ordering in alloy systems (see, e.g., Zunger Akamatsu, T., Kumazawa, M., Aikawa, N., and Takei, H. (1993) Pressure effect on the divalent cation distribution in nonideal solid solution of et al. 1988), but investigations of perovskite-type com- forsterite and fayalite. Physics and Chemistry of Minerals, 19,431- pounds by Burton and Cohen (1994, 1995) demonstrate 444. the applicability of these methods to mineralogical sys- Angel, R.I. (1994) Feldspars at high pressure. In 1. Parsons, Ed., Feldspars tems and support the proposition that high pressure often and their reactions, p. 271-312. Kluwer, Dordrecht, the Netherlands. stabilizes ordered states relative to disordered states. Angel, R.I., Finger, L.W., Hazen, RM., Kanzaki, M., Weidner, D.J., Liebermann, RC., and Veblen, D.R. (1989) Structure and twinning of single-crystal MgSiO, garnet synthesized at 17 GPa and 1800 "C. Amer- CONCLUSIONS ican Mineralogist, 74,509-512. Pressure plays a central role in the structure and ener- Anovitz, L.M., Essene, E.J., and Dunham, W.R. (1988) Order-disorder experiments on orthopyroxenes: Implications for the orthopyroxene getics of materials in the Earth's deep interior, and it geospeedometer. American Mineralogist, 73, 1060-1073. provides a powerful means of probing atomic interac- Barrat, J.L., and Vos, W.L. (1992) Stability of van der Waals compounds tions in solids. In a recurrent historical pattern, however, and investigation of the intermolecular potential in helium-xenon studies of phenomena at high pressure, which are often mixtures. Journal of Physical Chemistry, 97, 5707-5712. technically more difficult, usually follow detailed high- Barth, T.F.W., and Posnjak, E. (1931) The spinel structure: An example of variate atom equipoints. Journal of the Washington Academy of temperature investigations. The high-temperature decar- Sciences, 21, 255-258. bonation of limestone, for example, was well known to Bokov, A.A., Shonov, V.Y., Rayevsky, I.P., Gagarina, E.S., and Kupri- eighteenth-century neptunists, who used room-pressure yanov, M.F. (1993) Compositional ordering and phase transitions in data in their attempts to disprove the igneous origin of Pb(Yo.,Nbo,,)O,. Journal of Physics: Condensed Matter, 5, 5491-5504. Brown, G.E. (1982) Olivines and silicate spinels. In Mineralogical Society basalt in contact with limestone. Later, Sir James Hall of America Reviews in Mineralogy (2nd edition), 5, 275-392. demonstrated that pressure stabilizes carbonate at high Brown, N.E., and Navrotsky, A. (1989) Structural, thermodynamic, and temperature and thus supported the plutonist position kinetic aspects of disordering in the pseudobrookite-type compound (Hall, 1806). Almost two centuries later, data on mineral karrooite, MgTi,O,. American Mineralogist, 74, 902-912. and rock melting, rock mechanical properties, crystal Burton, B.P., and Cohen, R.E. (1994) Theoretical study of cation ordering in the system Pb(Sc_Ta")O,. Ferroelectrics, 151,331-336. structures, phase transitions, and many other mineral -(1995) Nonempirical calculation of the Pb(Sco.,Tao.,)O,-PbTiO, properties are often obtained at high temperatures long quasibinary phase diagram. Physical Review B, 52, 792-797. before high-pressure studies commence. Capobianco, c., Burton, B.B., Davidson, P.M., and Navrotsky, A. (1987) The situation is similar for order-disorder phenomena, Structural and calorimetric studies of order-disorder in CdMg(CO,J,. Journal of Solid State Chemistry, 71, 214-223. which have long been viewed as a key to understanding Chai, L., and Navrotsky, A. (1996) Synthesis, characterization, and en- the thermal history of rocks. Detailed studies of the ef- ergetics of solid solution along the dolomite-ankerite join, and impli- fects of temperature and composition on ordering have cation for the stability of ordered CaFe(CO,),. American Mineralogist, been conducted for most rock-forming minerals and for 81, 1141-1147. many metal alloys and other synthetic compounds. Ther- Chaillout, c., Cheong, S.W., Fisk, Z., Lehmann, M.S., Marezio, M., Mo- rosin, B., and Schirber, J.E. (1989) The crystal structure of supercon- mochemical models and kinetic parameters have been ducting La,CuO..o32 by neutron diffraction. Physica C, 158, 183-191. derived and are routinely used to estimate maximum Davidson, P.M., Symmes, G.H., Cohen, B.A., Reeder, R.I., and Lindsley, temperatures, cooling rates, and chemical environments D.H. (1993) Synthesis of the new compound CaFe(CO,), and experi- of igneous and metamorphic deposits, as well as mete- mental constraints on the (Ca,Fe)CO,join. Geochimica et Cosmochim- orites. As we attempt to understand the present state and ica Acta, 57, 5105-5109. Domeneghetti, M.C., Molin, G.M., and Tazzoli, v. (1985) Crystal-chem- dynamic behavior of our planet, the effects of pressure ical implications of the MgH_FeH distribution in orthopyroxenes. on order-disorder phenomena deserve closer scrutiny. American Mineralogist, 70, 987-995. Domeneghetti, M.C., and Steffen, G. (1992) MI, M2 site populations and ACKNOWLEDGMENTS distortion parameters in synthetic Mg-Fe orthopyroxenes from Moss- bauer spectra and X-ray structure refinements. Physics and Chemistry We thank Robert Downs, David Mao, and Charles Prewitt for their of Minerals, 19,298-306. stimulating discussions and thoughtful reviews during the preparation of Domeneghetti, M.C., Molin, G.M., and Tazzoli, V. (1995) A crystal- this study. We are also indebted to Ross Angel, Benjamin Burton, Ray- chemical model for Pbca orthopyroxene. American Mineralogist, 80, mond Jeanloz, and an anonymous reviewer, who provided detailed and 253-267. constructive reviews of the manuscript. This research was supported by Downs, RT., Hazen, R.M., and Finger, L.W. (1994) The high-pressure the NSF Center for High-Pressure Research, by NSF grant EAR-9218845, crystal chemistry of low albite and the origin of the pressure depen- and by the Carnegie Institution of Washington. dency of Al-Si ordering. American Mineralogist, 79, 1042-1052. Drazic, G., Trontel, M., and Kolar, D. (1993) TEM investigations in the PFN PFW PZN perovskite system. Journal of Materials Science, 28, REFERENCES CITED 4405-4411. Aikawa, N., Kumazawa, M., and Tokonami, M. (1985) Temperature de- Ducastelle, F. (1991) Order and phase stability in alloys, 500 p. North- pendence of intersite distribution of Mg and Fe in olivine and the Holland, New York. associated change oflattice parameters. Physics and Chemistry ofMin- Ferrario, M., Lyndenbell, RM., and McDonald, I.R. 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