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tetrahedron having one bridging and three non-bridging oxygens: Si/O ratio = 1/3.5; charge of the dimer: [Si2O7]6-, (for example, rankinite Ca3Si2O7); 3) single chain silicates, each tetrahedron having two bridging and two non- bridging oxygens: Si/O ratio = 1/3; a chain with N links has a charge [SiO3]n 2n- (for example, enstatite MgSiO3); 4) double chain silicates, half of the tetrahedra with two bridging and two non- bridging oxygens (Si/O = 1/3) and other half three bridging and one non-bridging (Si/O = 1/(2.5): in total Si/O = 2/5.5 and the charge is [Si4O11]n 6n- (for example, anthophyllite Mg7Si8O22(OH)2, the OHs being independent of the tetrahedra); 5) silicates forming two dimensional layers, each tetrahedron with three bridging and one non-bridging oxygens: Si/O = 1/(2.5); charge of a layer [Si2O5]n 2n- (for example, minerals of clays and micas or talc: Mg6Si8O20 (OH)4, the OHs being here again independent of the tetrahedra); 6) lastly, silicates where the tetrahedra are linked at all their corners: four bridging oxygens per tetrahedron, Si/O = 1/2 (for example, quartz SiO2). Quartz is part, like diamond, of a covalent description where the molecule extends to the scale of the entire crystal, regularly in the three-dimensional space. In addition to this classification, we can observe that: – when Al substitutes Si in the tetrahedron, we must consider the (Al+Si)/O ratio: for example, plagioclase feldspars, which range from albite NaAlSi3O8 to anorthite CaAl2Si2O8, the (Al+Si)/O ratio always being 1/2; – Al is generally in a tetrahedral site, instead of Si, but can be in an octahedral site: for example, muscovite mica K2Al4 octa[Si6Al2O20](OH)4, where tetrahedral coordination group is the one located between brackets [ ]; – an important point for the structure of hydrous silicates is the fact that O2- and OH- have the same ionic radius: 1.40 Å. We must not be misled by the examples of MgO, BaTiO3 or diamond: most ceramics do not crystallize in a cubic group and this implies that the many physical properties that are described by a second order tensor are not isotropic [NYE 87]. Thermal expansion, optical index, electric and thermal conductivities, permittivity and permeability are at first view anisotropic, which can misinform some metallurgists, because the most common metals (iron, aluminum, copper) are cubic. An effect of the anisotropy of thermal expansion is to create residual stress at the grain boundaries of the polycrystals. Beyond the properties described by a second order tensor, low symmetries combine with the properties of iono-covalent bonds to make dislocations rare and relatively immobile, which explains the lack of ductility and the impossibility of plastic deformation. Ceramic Compounds: Ceramic Materials 23 1.5.2. Polymorphism: crystals and glasses Many compounds of ceramic interest can exist in various varieties. We can mention the polymorphism of zirconia ZrO2 – cubic at high temperatures, then quadratic (tetragonal) and finally monoclinic at decreasing temperatures – a polymorphism that was regarded for a long time as a disadvantage, then understood as an advantage when the possibilities that it offered for the development of high mechanical performance ceramics were discovered [HEU 81] (see Chapter 6). However, it is the polymorphism of silica SiO2 that is most frequently used in ceramic and glass industry. Sand is primarily made up of silica, often highly pure (more than 98%), SiO2 having been crystallized in the form of quartz α, also known as low quartz (point group 32, without center of symmetry). When heated to 573°C, quartz α transforms to quartz β (high quartz, point group 622, centrosymmetric). Higher treatment temperatures help distinguish two types of behavior, depending on whether thermodynamically stable phases are achieved or whether kinetic effects favor metastable phases. These effects depend on the relative ease with which the transformations occur: displacive transformations – which require only small atomic movements to change the structure of a phase and modify its symmetries – are easier than reconstructive transformations – which require the structure to be destroyed and then recomposed. Figure 1.2 schematizes the evolutions between the various possible phases: the transformations indicated by vertical arrows are fast and always happen; those indicated by horizontal arrows are slow and often require, in order to occur, the addition of impurities that play the role of mineralizers. Thus, the transformation of quartz into tridymite is generally not achieved in the temperature range in which it is predicted by the equilibrium diagram, because what is formed is cristobalite, which is metastable. High cristobalite melts at 1,723°C to produce an extremely viscous liquid (4 MPa.s). On cooling, this high viscosity generally prohibits crystallization, from which it maintains a super-molten liquid and then, below the glass transition temperature [ZAR 82], a silica glass (molten silica, often called, incorrectly, molten quartz or, even worse, quartz). Heated at a sufficiently high temperature to allow sufficient atomic mobility (for example, about 1,100°C), silica glass tends to devitrify to produce cristobalite. The crystallized varieties of silica have properties that are very different from silica glass: the former exhibits anisotropic characteristics in general, whereas glass is isotropic and they have remarkable expansion coefficients (in the order of 10-5K-1), whereas silica glass has exceptionally poor thermal expansion (about 0.5.10-6K-1). 24 Ceramic Materials High quartz Low quartz High tridymite Middle tridymite Low tridymite High cristobalite Low cristobalite , Figure 1.2. Main crystallized varieties of silica Figure 1.3 illustrates the difference between crystallized quartz, where the tetrahedra [SiO4]4- are linked at their four corners to form an architecture regular in its angles and its ranges (crystal = triperiodicity, i.e. long-range order), and silica glass, where a short-range order continues to exist, significantly similar to the one that exists in the crystal, but with dangling bonds and distortions in angles and variations in length that disorganize the structure. Figure 1.3. Illustration of the structure of quartz (on the right) and silica glass (on the left); this two-dimensional diagram must be imagined in three dimensions, the silicon atom (full circle) being at the center of a tetrahedron of four oxygen atoms (hollow circle), of which only three are represented here Ceramic Compounds: Ceramic Materials 25 1.5.3. Ceramic microstructures The microstructural aspects are discussed in detail in Chapter 3, but we must underline the decisive role that the ceramic microstructure plays in relation to their properties, particularly sensitive properties like mechanical resistance or electric conductivity. The performances of the other categories of materials also depend on their microstructure, but seldom to the same extent as in the case of ceramics. There are several reasons for this sensitivity of ceramics to microstructural parameters: – the material is processed whilst the object is manufactured, therefore the causes for any disparity in the material are multiplied by the disparity of the processes; – sintering is accompanied by considerable dilatometric effects, with strong variations in porosity: pores and defects due to differential expansions are inherent to ceramic microstructures; they are rarer in metals prepared by plastic deformation or machining; – the granular properties of ceramics are more often anisotropic than in the case of other categories of materials; – ceramics have poor toughness, with critical stress intensity factors (Kc) generally lower than 5 MPa.m1/2, i.e. an order of magnitude lower than that of most metals. However, as mechanical resistance to brittle fracture (σf) is proportional to Kc and inversely proportional to the square root of the equivalent size of the critical defect (ac), the defects must be, for a given value of σf, 100 times smaller in ceramics than they can be in metals. This is all the more difficult to control since the size of the grains of ceramics is often lower than that of metals: it is much more difficult to avoid 50 μm defects in a ceramic whose grains are 5 μm than notches of a centimeter in a metal whose grains are 100 μm. The absence of plasticity does not allow the relaxation of excessive stresses; – the iono-covalent bond is less receptive to impurities than the metallic bond, and therefore segregations are more frequent in ceramics than in metals; given that electric conductivity can vary by more than 20 orders of magnitude between a conductor and an insulator, we understand that the presence of a insulating film at the grain boundaries of a material expected to be a conductor, or that of a conducting phase interlinked in a matrix expected to be insulating, can destroy the expected functionalities; – the frequency of the polymorphism of ceramic phases and the ability of a number of silicate phases to be crystallized or vitreous introduce additional variables into the complexity of ceramic microstructures. Despite the small number of really useful ceramic compounds, the variety of microstructures makes a very large number of different applications possible. We will limit ourselves to two examples: a ceramic prosthesis in alumina must be dense and fine-grained – to optimize mechanical resistance and tribological properties – 26 Ceramic Materials whereas an alumina refractory material must be porous and coarse-grained – to optimize resistance to thermal shocks and creep strength. Controlling the properties of ceramics requires controlling their microstructures. 1.6. Specificity of ceramics The variety of ceramics is such that they do not exhibit uniform characteristics, but there are common features that give them an undeniable specificity. Most of these common features have already been mentioned, but it is useful to recapitulate the overall physiognomy: – the iono-covalent bonds confer properties of electric insulation and transparency in the visible range, even if some semiconducting compounds and those that have a partially metallic nature are an exception to this rule; – the thermal conductivity of ceramics is often poor, because electrons do not, or hardly take part in it, but conduction by network vibrations (phonons) can be considerable: it is diamond, a non-metal, that is the best thermal conductor at ambient temperature and certain ceramics (AlN, BeO, SiC) perform better than copper in this respect; – strong and directed, subject to electrostatic restrictions, the iono-covalent bonds of ceramics do not allow the movement of the dislocations, i.e. linear defects in atomic stacking that are the reason for the plasticity of metals; hence their brittleness. On the other hand, ceramics offer a high degree of hardness and high moduli of elasticity; their mechanical resistance can be remarkable; they are light; their melting point is generally high; – most ceramics exhibit good resistance to chemical aggressions. As regards oxidation, we must distinguish oxides (stable in an oxidizing atmosphere, which helps us to take advantage of their refractoriness) from non-oxides, which can oxidize at relatively low temperatures and whose use at high temperatures requires protective, neutral or reducing atmospheres. Graphites and carbons are thus ultrarefractory (sublimation beyond 3,500°C), but they can be used only in protective gas. Among non-oxides, silicon compounds (silicon carbide SiC, silicon nitride Si3N4, molybdenum disilicide MoSi2) exhibit the remarkable ability of self- protection from oxidation thanks to a tight and overlapping silica layer SiO2 (until about 1,800°C for MoSi2). It is erroneous to identify refractoriness with a high melting point because a high melting point is a necessary but insufficient condition: chemical compatibility with the environment and sufficient thermomechanical performances (sufficiently low creep rate, in particular) are also necessary. Ceramic Compounds: Ceramic Materials 27 1.7. Bibliography [BAR 96] BARON J. (ed.), Les bétons; bases et données pour leur formulation, Eyrolles, 1996. [BED 86] BEDNORZ J.G. and MÜLLER K.A., “Possible high-Tc superconductivity in the Ba-La-Cu-o systems”, Z. Phys., UB 64, p. 189-193, 1986. [BRO 91] BROOK R.J. (ed.), Concise Encyclopedia of Advanced Ceramic Materials, Pergamon Press, 1991. [BUR 90] BURNS G. and GLAZER A.M., Space Groups for Solid State Scientists, Academic Press, 1990. [CAS 90] CASTEL A., Les alumines et leurs applications, Nathan, 1990. [CHE 89] CHERMANT J.L., Les céramiques thermomécaniques, Presses du CNRS, 1989. [COL 99] COLLECTIVE WORK, Ceramics Monographs, Handbook of Ceramics, updated by Interceram, Verlag Schmidt (since 1982), 1999. [EMS 95] EMSLEY J., The Elements, Clarendon Press, 1995. [GER 96] GERMAN R.M., Sintering Theory and Practice, John Wiley, 1996. [GIA 85] GIACOVAZZO C. (ed.), Fundamentals of Crystallography, Oxford Science Publications, 1985. [HAH 89] HAHN T. (ed.), International Tables for Crystallography, Vol. A, Kluwer Academic Publ., 1989. [HEU 81] HEUER A.H. and HOBBS L.W. (eds), Advances in Ceramics, vol. 3, American Ceramic Society, 1981. [JAF 88] JAFFE H.W., Introduction to Crystal Chemistry, Cambridge University Press, 1988. [KIN 76] KINGERY W.D., BOWEN H.K. and UHLMANN D.R., Introduction to Ceramics, 2nd ed., John Wiley & Sons, 1976. [KIN 84] KINGERY W.D. (ed.), Structure and Properties of MgO and Al2O3 Ceramics, American Ceramic Society, 1984. [KIT 98] KITTEL C., Physique de l’état solide, Dunod, 1998. [LEG 92] LEGENDRE A., Le matériau carbone, Eyrolles, 1992. [MCC 83] MCCOLM I.J., Ceramic Science for Materials Technologists, Leonard Hill, 1983. [NYE 87] NYE J.F., Physical Properties of Crystals, Oxford Science Publications, 1987. [OBA 84] O’BANNON L.S., Dictionary of Ceramic Science and Engineering, Plenum Press, 1984. [PUT 92] PUTNIS A., Introduction to Mineral Sciences, Cambridge University Press, 1992. [RIN 96] RING T., Fundamentals of Ceramic Powder Processing and Synthesis, Academic Press, 1996. 28 Ceramic Materials [TAY 97] TAYLOR H.F.W., Cement Chemistry, Academic Press, 1997. [WEL 84] WELLS A.F., Structural Inorganic Chemistry, Oxford University Press, 1984. [WES 90] WEST A.R., Solid State Chemistry and its Applications, John Wiley, 1990. [ZAR 82] ZARZYCKI J., Les verres et l’état vitreux, Masson