1.11 Introduction to some more complex crystal structures Perovskite (CaTiO 3 ), barium titanate (BaTiO 3 ) and related structures

Transcription

1 1.11 Some more complex crystl structures 31 non-existence of identifible molecules in inorgnic ionic structures. Puling s rules lso determine, or limit, the wys in which the polyhedr cn be linked together. The octhedr nd cubeocthedr surrounding lrger nd weker ctions my shre corners, edges or even fces, but the tetrhedr surrounding the smller nd more highly positive ctions tend only to shre corners, such tht the ctions re s fr prt s possible. We hve lredy encountered this spect of Puling s rules in our discussion (Section 1.7) of the non-existence of hcp structures in which ll the tetrhedrl sites re filled; the sites occur in pirs with the tetrhedr rrnged fce-to-fce nd the ctions re too close to ensure stbility. This lso pplies to the (Si,l)O 4 tetrhedr which comprise the building blocks of the silicte minerls (see Section ), the tetrhedr re isolted or shre one, two, three or four corners, never edges or fces. However, this is not true of ll synthesized cermic mterils. The new nitrido-silictes nd silons re bsed on the linkge of (Si, l)(n, O) 4 (predominntly SiN 4 ) tetrhedr which shre edges s well s corners nd in ddition, Si is octhedrlly coordinted by N. Figure 1.23 shows the coordintion polyhedr in three simple crystl structures: () the edge-shring octhedr in sodium chloride, Nl; (b) the corner-shring tetrhedr in zinc blende, ZnS; nd (c) the corner-shring octhedr nd the centrl cubeocthedron in perovskite, TiO 3. The unit cell shown is the sme s tht in Fig. 1.17() Introduction to some more complex crystl structures Perovskite (TiO 3 ), brium titnte (TiO 3 ) nd relted structures Perovskite is n importnt type minerl (in the sme wy s sodium chloride, Nl) nd is the bsis of mny technologiclly importnt synthetic cermics in which the is replced by, Pb, K, Sr, L or o nd the Ti by Sn, Fe, Zr, T, e or Mn. The generl formul is O 3 (see Fig. 1.17), the ion being in the lrge cubeocthedrl sites nd the ion being in the smller octhedrl sites (Fig. 1.23(c)). In perovskite itself, is the divlent ion nd the tetrvlent ion. This however is not necessry restriction; trivlent ions cn, for exmple, occupy both nd sites; ll tht is needed is n ggregte vlency of six to ensure electricl neutrlity. It is, in short, working out of Puling s rules gin. Of much greter importnce re the sizes of these ions becuse they led, seprtely or in combintion, to different distortions of the cubic cell. In perovskite itself, the ction is too smll for the lrge cubeocthedrl site nd so the surrounding octhedr tilt, in opposite senses reltive to one nother, to reduce the size of the cubeoctohedrl site. This is shown digrmmticlly in Fig. 1.24(). The unit cell is now lrger, s outlined by the solid lines, the unit cell repet distnce now being between the similrly oriented octhedr (see Section 2.2). The symmetry is tetrgonl, rther thn cubic. The tilts re lso slightly out of the plne of the projection which further reduces the symmetry to orthorhombic (see hpter 3 for description of these non-cubic structures). In brium titnte, TiO 3, the Ti ction is too smll for the octhedrl site nd shifts slightly off-centre within the octhedron (Fig. 1.24(b)); the cubic unit cell is distorted to tetrgonl. These shifts my occur long ny of the three cube-edge directions such tht

2 32 rystls nd crystl structures () (b) Fig Two modifictions to the perovskite structure: () octhedr tilted in opposite senses, the cubic cell is outlined by dshed lines nd the tetrgonl cell by full lines; (b) displcements of the ctions from the centres of the octhedr resulting in distortion of the originl cubic cell to tetrgonl unit cell (full lines). (From n Introduction to Minerl Sciences byndrew Putnis, mbridge University Press, 1992.) Fig polrized-light microgrph (crossed polrs) of single crystl of brium titnte which revels the domins in ech of which the tetrgonl distortion is in different cube-edge direction. single crystl of TiO 3 my be divided into domins; within ech domin, the shift is in the sme direction (Fig. 1.25) (the ide of domins is discussed, with respect to ordered crystls, in Section 9.7). The consequence is tht within crystl (or within domin) there is net movement of chrge, resulting in structure with dipole moment, nd this spontneous electricl polriztion leds to the property of ferroelectricity which is of

3 1.11 Some more complex crystl structures 33 such gret importnce in mny electronic devices nd is the bsis of much reserch on the titntes some of which re ntiferroelectric (e.g. PbZrO 3 ), ferromgnetic (e.g. Lo.2 Mb.8 O 3 ) or ntiferromgnetic (e.g. LFeO 3 ). rium titnte itself undergoes further trnsformtions t lower tempertures (to orthorhombic nd rhombohedrl forms) which re, s with the tetrgonl form, ferroelectric. t higher tempertures (12 for brium titnte), due to the incresed therml movement of the toms, these structures revert to the cubic forms. This is n exmple of displcive trnsformtion: no bonds re broken. Such displcive trnsformtions lso chrcterize the high temperture (α) nd low temperture (β) forms of qurtz, tridymite nd cristoblite (see Section ) nd lso relte the polymorphous forms of mny orgnic compounds the structures only differing in the wy in which the molecules re pcked together under the influence of the wek vn der Wls forces Tetrhedrl nd octhedrl structures silicon crbide nd lumin onsider, for exmple, the crystl structures which consist of close-pcked or nerly close-pcked lyers of lrge toms or ions with the smller toms or ions occupying some or ll of the tetrhedrl interstitil sites. Zinc blende nd wurtzite re two such structures (Section 1.7) which re re-drwn in Fig so s to emphsize the 2 c = 2 c = 3 2 c = 4 2 c = 6 2 c = (2H) Wurtzite 3 (3) Zinc blende 5 (4H) rborundum III 6 (6H) rborundum II 7 (15R) rborundum I Fig Five common tetrhedrl structure types. The brcketed symbols refer to the number of lyers in the repet sequence nd the structure type: H (hexgonl), (cubic) nd R (rhombohedrl) (fter E. Prthe, rystl hemistry of Tetrhedrl Structures, Gordon nd rech, New York, 1964, reproduced from The Structure of Metls, 3rd edn,. S. rrett nd T.. Msslski, Pergmon, 198).

4 34 rystls nd crystl structures... Stcking of the Zn (or S) toms in zinc blende nd the... stcking of the Zn (or S) toms in wurtzite. Mny crbides, including silicon crbide, Si, lso possess such close-pcked structures with the crbon toms occupying the tetrhedrl sites nd the metl or metlloid toms stcked in vrious combintions of... nd... Figure 1.26 shows five structures or polytypes of silicon crbide (3 7) in which the silicon toms re represented s solid spheres nd the crbon toms s smll open spheres. The low-temperture form, β-si (3) hs the fcc structure, isomorphous with zinc blende. There re number of high-temperture polytypes known collectively s α-si, the simplest structure of which, 4, is isomorphous with wurtzite. The other polytypes of α-si, three of which (5, 6, 7) re shown in Fig. 1.26, hve more complex stcking sequences, resulting in longer unit cell repet distnces. For exmple, the stcking sequence in 5 (rborundum III) is (reding up) - giving four-lyer repet distnce. In the Frnk nottion this is represented s...i.e. by inversions in the stcking sequence every two lyers, rther thn every lyer s in 4, the wurtzite structure. Similrly, for 6 (rborundum II) the stcking sequence is giving six-lyer repet distnce which in the Frnk nottion is...i.e. n inversion every three lyers. Figure 1.27 shows n lterntive representtion of the polytypes of Si showing (for clrity) only the close-pcked lyers of the metlloid (Si)toms. The number below ech polytype refers to the number of lyers in the unit cell repet distnce nd the letter refers to the type of unit cell ( cubic; H hexgonl; R rhombohedrl). ll these polytypes of silicon crbide should not be thought of s distinct species, rther they should be regrded s interrelted s result of different sequences of stcking fults nd the trnsformtions β α Si pper, from electron microscopy evidence, to occur s the result of the pssge of prtil disloctions cross the close-pcked plnes in the sme wy s for the genertion of twinned crystl, s shown in Fig For exmple 6H, common form of α-si, my be regrded s microtwinned form of 3, the three-lyer thick twins being generted by the pssge of three prtil disloctions on successive close-pcked plnes s shown in Fig. 1.2(d). In luminium oxide, 1 2 O 3, the lrge oxygen nions occur in close-pcked or nerly close pcked lyers with the luminium ctions occupying two-thirds of the octhedrl interstitil sites. We now hve n dded complexity; not only my the oxygen nions be pcked in different sequences but lso the luminium ctions my be distributed differently throughout the interstitil sites i.e. there my be different distributions of the one-third empty sites. In the well-chrcterized form, α-l 2 O 3 (corundumisomorphous with α-fe 2 O 3 ), the oxygen nions re stcked in the hcp stcking sequence nd the luminium ctions between them re stcked in rhombohedrl sequence in exctly the sme pttern s the crbon toms in the rhombohedrl form of grphite (see Fig. 1.37(b)). Hence the structure of α-l 2 O 3 is rhombohedrl with six-lyer unit cell repet distnce of oxygen nions. The other polytypes of lumin, clled the trnsition lumins, re not so well chrcterized, prticulrly with respect to the distribution of the luminium ctions. common form, γ -l 2 O 3 is bsed on n (fcc) stcking of oxygen nions with distribution of luminium ctions which gives rise to mghemite structure, described in Section

5 1.11 Some more complex crystl structures 35 2H () 3 (b) (c) (d) 6H (e) 8H (f) 4H 15R Fig The crystl structures of six Si polytypes. 3 is β-si, the fcc low temperture form nd the others with 2, 4, 6 nd 8-lyer repet hexgonl cells or 15-lyer repet rhombohedrl cell re the α-si high temperture forms (from ermic Microstructures by W. E. Lee nd W. M. Rinforth, hpmn & Hll, 1994) The oxides nd oxy-hydroxides of iron Iron is remrkble for the rnge of oxides nd hydroxides which cn be formed nd is one of the few elements which form compounds intermedite between these two the oxy-hydroxides, the crystl structures of which re lso of interest, nd we will now describe them (s fr s we re ble) nd trce their interreltionships. We will begin with the simplest oxide, wustite, ferrous oxide, FeO nd consider the structurl chnges which tke plce in the progressive oxidtion of FeO to Fe 3 O 4 (ferroso-ferric oxide) nd Fe 2 O 3 (ferric oxide). FeO hs the Nl structure the Fe 2+ ions re situted in the octhedrl interstitil sites between the oxygen nions 3. However, FeO is rrely stoichiometric but hs vcnt Fe 2+ sites in the fce-centred cubic 3 The terms nion nd ction re used when we wnt to drw specific ttention to the chrge on the ionic species, otherwise the more generl term tom is used it being understood tht the term encompsses both neutrl nd chrged species.

6 36 rystls nd crystl structures structure, electricl neutrlity being preserved by the presence of equl numbers of Fe 3+ ions (some of which re situted in the tetrhedrl interstitil sites). The oxidtion of FeO to Fe 3 O 4 proceeds, not by the ddition of oxygen toms to the structure, but by the migrtion of Fe toms to the surfce (to combine with tmospheric oxygen there) to first pproximtion the close-pcked oxygen toms in the originl FeO structure remin undisturbed. Within the structure the Fe 2+ ions re progressively replced by Fe 3+ ions, hlf of which re situted in the tetrhedrl interstitil sites. The structure of Fe 3 O 4 (mgnetite) thus formed is tht of n inverse spinel with the generl formul 2 O 3 in which the tetrhedrl sites re occupied by Fe 3+ ions nd the octhedrl sites by equl numbers of Fe 3+ nd Fe 2+ ions. Fe 3 O 4 is therefore better represented by the formul Fe 3+ (Fe 3+ Fe 2+ )O 4. However, the occupncy of the interstitil sites is not rndom, but ordered such tht the unit cell of Fe 3 O 4 hs twice the side-edge (eight times the volume) of the originl FeO unit cell nd contins 32 O 2 ions, 8 Fe 2+ ions nd 16 Fe 3+ ions. The distinction between n inverse nd norml spinel (both bd nmes!) is simple: spinel is the minerl Mgl 2 O 4. The Mg 2+ ions occupy the tetrhedrl sites nd the l 3+ ions occupy the octhedrl sites with regrd to the sites only the inverse of Fe 3 O 4. gin, we see tht the occupncies of the interstitil sites re determined not simply by the vlencies of the ions but lso their sizes. Figure 1.28 shows projection, or crystl pln of the spinel structure (see Section 1.8), split into two hlves to mke the tom/ion positions more cler. s oxidtion proceeds further the remining eight Fe 2+ ions in the unit cell re replced by two-thirds of their number by Fe 3+ ions (i.e. to mintin electricl neutrlity) giving totl of / 3 = 21 1 / 3 Fe 3+ ions, 32 O 2 ions nd the overll composition Fe 2 O 3. Except for smll reduction in volume (on ccount of the incresed number of vcnt lttice sites) the lrge cubic unit cell is unchnged. The structure is clled mghemite, γ -Fe 2 O 3 nd is isostructurl with the γ -l 2 O 3 structure (see Section ) y x x y : ; : ; : X Fig Pln view of the unit cell of the cubic spinel structure 2 X 4 projected on to plne perpendiculr to cube xis. The heights of the toms re indicted in units of one-eighth the cubic cell edge length. For clrity, the upper nd lower hlves of the cell re shown seprtely nd only the tetrhedrl coordintion of the ions is indicted. (From rystl hemistry, 2nd Edn, by R.. Evns, mbridge University Press, 1966.)

7 1.11 Some more complex crystl structures 37 However, γ -Fe 2 O 3 (like γ -l 2 O 3 ) is not the stble structurl form nd its conversion to α-fe 2 O 3 (hemtite) occurs essentilly by the rerrngement of the oxygen toms from the fcc to the hcp stcking sequence. Similr reltionships exist in the oxy-hydroxides in which iron is in the Fe 3+ (ferric) form. The formule re best written FeO OH (rther thn Fe 2 O 3 H 2 O) to emphsize the replcement of oxygen ions by hydroxyl, (OH) groups rther thn the presence in the structure of discrete molecules of wter. In γ -FeO OH (lepidocrocite), the oxygen nd hydroxyl ions re pproximtely cubic close-pcked nd in α-feo OH (goethite), they re pproximtely hexgonl close-pcked. The devition from perfect close-pcking rises from the formtion of directed hydrogen bonds between the hydroxyl groups in different lyers; the structures re not cubic or hexgonl but hve orthorhombic symmetry (see hpter 3). On heting, these oxy-hydroxide structures dehydrte to γ -Fe 2 O 3 nd α-fe 2 O 3, respectively. Lepidocrocite nd goethite re not the only oxy-hydroxides which occur. Of perhps more biologicl or technologicl importnce is ferrihydrite, poorly crystllized minerl which is ubiquitous cross the Erth s surfce. It is common product of wethering of iron-bering minerls nd of the microbil oxidtion of ferrous ions nd doubtless of the rusting of iron itself. The determintion of its crystl structure nd composition is mtter of considerble difficulty becuse of the very smll crystllite size, typiclly in the rnge 2 1 nm. However, it ppers tht the oxygen-hydroxyl groups re rrnged in n hcp (2H, 4H or 6H) stcking sequence (see Fig. 1.27), i.e. closer to goethite thn lepidocrocite nd possibly isostructurl with nturl lumin hydrte phse, kdleite. The composition is commonly given s Fe 5 (OH) 8.4H 2 O but the wter content ppers to depend on prticle size. Ferrihydrite is n exmple of nturlly occuring nnocrystlline mteril upon which whole new science nd technology is now being built. Their importnce consists in the simple fct tht t these sizes lrge proportion of the toms or ions re t, or ner, the surfce nd the conditions for the stbility of the structures re found to be (s might be expected) quite different t the centres of the crystls nd t their surfces. Such nno-sized crystls of ferrihydrite lso pper to constitute the inorgnic core of the ferritin molecule the iron storge molecule tht occurs principlly within the liver. The core is enclosed within protein shell (Fig. 1.29) which hs cubic symmetry not found in ny inorgnic crystls (see hpter 4). The mechnisms by which iron leves nd enters the ferritin molecule, nd how it is tken up, nd relesed, from the ferrihydrite, re mtters of much reserch. ut undoubtedly the crystllogrphy the vlency nd distribution of iron ions cross the interstitil sites both t nd below the crystl surfces will emerge s fctors of gret importnce Silicte structures Silictes which constitute by fr the most importnt minerls in the erth s crust re bsed on the different wys in which SiO 4 tetrhedr 4 my be joined together, ech 4 The SiO 4 tetrhedr my be referred to more generlly s Si O tetrhedr since, s described in subsections () (g), the silicon oxygen rtio depends on how they re linked.