John F. G. Hicks Department of Ceramic Engineering Ohio Stote University Columbus, 43210
I Formation and Crystal Structure
The question of what constitutes glass has interested numerous workers for some time and various points of view have been emphasized in the literature. In a recent book, Bartenev (I) categorizes hypotheses about glass structure under the following headings: 1) Crystallite, 2) Short Range Order, 3) Aggregate, 4) Crystal Chemical, 5) Polymeric, and 6 ) Micro-heterogeneous. Data can he cited to support each concept, and each has served to illuminate some aspect of a complicated problem. These viewpoints have come about largely from looking closely a t the finished product a t room temperature. It is helpful in putting these different ideas into perspective to remember how glasses are made, that they once were liquids, and that the forces tending to crystallize them as they are cooled are what make them set up. We can define " elasses as that class of liauids which become rigid without crystallizing as they are cooled. These liauids are viscous (of the order of ~ o i s e s )a t least a few degrees above their melting or liquidus temperatures and they set up some degrees lower. Cooling too slowly through the upper transformation (2) range can cause devitrification: but cooling without devitrification can produce any number of configurations depending upon dwell-times a t different temperatures. Discussion Viscosity, or the resistance to flow, in a liquid can he thought of as being governed by two factors: One is the number of chemical bonds which must be broken in order to permit the flow units to migrate; and the other is the available space (3) into which these clusters can move. The stronger the bonds to be broken, the higher the liquidus or melting temperature; and the larger the clusters which move, the higher the viscosity. The concept of a cluster as a static assemblaee of atoms is useful as an instantaneous picture; but, oicourse, bonds, both inside as well as outside of the cluster, are continuallv being broken and remade according to some function of the;atio of thermal energy to bond energy. As solid glass is heated, thermal expansion eventually provides the free volume required for flow. We assume that the decrease in viscositv with rise in temperature is due both to increasing free voiume and to the decreasing size of the flowing clusters. A liquid can be viewed as the remnants (4) of the crystal in equilibrium a t the melting temperature, where the long range structure has failed. The regular array of atoms forming the crystal fails because it has accumulated too many defects for the structure to support itself against the thermal motion of its constituent atoms and groups of atoms. These defects in the solid can be misplaced atoms of the pure substance, impurity atoms, or both. All defects accumulate to cause the structure to fail at a temperature lower than the melting point of the undefective structure. The temperature of melting is a structure characteristic first, a chemical characteristic second. When a structure fails, the residue consists of clusters of varying sizes and shapes made up of its elementary building blocks. The distribution of these sizes and s h a ~ e s depends on the relative strengths of the bonds linking the various atoms together. While long- range - order d i s a ~ ~ e a r s when a crystal melts, short range order remains, as bb the 28
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long range forces which form crystalline arrays; hut these forces are not strong enough a t melting temperatures to maintain rigidity against the disrupting thermal motion. However, below the strain point ( 5 ) , they are. If we assume that small numbers of atoms in a cluster characterize low resistance to flow or low viscosity, and large clusters, high viscosity, we should be able to obtain some idea of bow much the liquid elements of a given substance retard flow from the distribution of weak bonds and holes in the crystal structure. Structures with strong directional, or covalent bonds are the best glass formers ( 6 ) . Tetrahedral coordination favors large atomic groupings in the liquid, especially when extended in three directions. If extended in only one or two directions, chains or sheets, rather than clumps form. On the other hand, higher coordination numbers and ionic binding tend to leave smaller groups after melting, giving low viscosity. However, even with small groups, competition for preferred coordination increases the time required to sort out proper environments, and gives rise to viscosity. Examples
Silica occupies a unique position as a glass former. The structure of its stable high temperature form, beta cristobalite (7) can he described as two interpenetrating lattices of Si atoms. Half of the Si atoms form one lattice in face centered cubic array and the other half in the second lattice occupy half the tetrahedral sites of the first lattice. Each pair of nearest Si atoms is separated by an 0 atom, makine 0 tetrahedrallv dis~osed about Si. The SiOa tetrahedra all share all cornek and these linkages extend in 3 dimensions as interconnected -Si-O-Si-Ochains forming hexagonal rings (Fig. 1). This is not a close packed structure. It is an expanded lattice with holes in half the tetrahedral positions, and this combination of
Figure 1. Cr~stobaiile.The small silicon atoms (not shown1 are at the Center of the tetrahedron of oxygen atoms [spheres). Part of the 0 a t D m ~have been omitted to show the manner in which Si atoms are linked in the same kind of network as in silicon. The expanding of the Si lattice to admit 0 enlarges the holes at the unoccupied tetrahedral positions and permits mobility of Si04 groups or parts thereof as the lattice is further expanded by heating.
tightly bonded Si04 tetrahedra and holes already present for them to move into as additional free vdume is acquired, which puts SiOa a t the head of the list of glass formers. Where the bonds break in pure crystalline SiOz would appear to he largely a matter of chance. All Si-0 bonds being alike in the pure, perfectly ordered crystal, weak points are induced by thermal motion only, i.e., by stretching and bending these honds. The breaks will occur where more strain energy has accumulated, and the probability of broken honds increases with the numher of atoms composing the assemblage. Large clusters are therefore to he expected in silica and hence its high viscosity. But the size of the clusters is very sensitive indeed to impurities such as H20, NazO, and CaO. These and other mono- and divalent oxides are very effective in breaking Si-0-Si bonds, with a resultant lowering in melting temperature. Less than 30 mole percent of these Si-0 hond breakers can lower the iso-viscous temperature more than 1000°C below that of "pure" silica, making these systems important technologically. On the other hand, A1203 which melts some 300°C above SiOz is very fluid at its melting point. The Al atom is in six-fold coordination in corundum (81, and its structure can be described as an hexagonal close packed array of oxygen atoms with aluminum atoms occupying twothirds of the octrahedral sites as in Figure 2. When this structure fails the residual long range forces cannot hold large clusters together a t the mp as they do in silica. The atoms are too far apart. There are no built-in holes for A1-0 groups to move into and the bonds are strongly ionic. A close packed octahedron of 0 atoms requires more space than a tetrahedron. The A-0 distance, or hond length, in A1203 is greater than the Si-0 hond length in SiOz. The Si-0 bond is more directional (covalent) than the A I L 0 bond. Therefore SiO4 tetrahedra can
Figure 2. Corundum. The larger spheres are 0 atoms.
Figure 3 Peravskle. The iargest spheres are 0 atoms, the nexf Ca. and thesmallest TI.
change positions with strong honds holding some individual tktrahedra together. The Aloe octrahedra cannot do this. They break up first. Acquisition of free volume by the lattice does not ~ r o v i d emaces into which clusters can move, but instead stretches'the bonds to the breaking point. Clusters containing onlv a few atoms result and the melt is fluid. However, ~ i z 0 boes 3 form glasses as a minor additive in alkali silicates. There the A1 atom takes on tetrahedral coordination with 0 atoms, because of the presence of monovalent ions, and these tetrahedral groups share corners with SiOa tetrahedra. Ferric iron behaves similarly. Titania behaves somewhat similarly to alumina. In the pewoskite (9a) structure (Fig. 3) oxygen atoms together with calcium atoms in the ratio 3:l form a close packed cubic array with titanium atoms occupying one-quarter of the octahedral sites. The Ti coordinate six 0 atoms and the Ca 12. It is a highly ionic structure consisting of the oxides, and is not a titanate in the same sense that the pyroxenes (10) (e.g., MgSiOa) are silicates. There is not only no tetrahedral goordination in pervoskites, but the structure lacks holes for a group to move into as free volume is acquired on heating. When melting occurs, the bonds have been stretched throughout, so that a large number of them fail a t once and no substantial clusters persist in the liquid. These compounds are fluid at their melting points and poor glass formers. However, in small concentrations, Ti can coordinate four 0 atoms and these Ti01 tetrahedra share comers with the SiO4 tetrahedra in a stable glass structure (96). The borates are notable glass formers, both as major constituents and as minor ones in silicate melts. The structures of B203 (11).H3B03 and the tetraborates show that B links with 0 as Boa and BO4 groups and these linkages persist in the melts. H3B03 contains planar sheets of B o a triangles, the sheets being held together by hydrogen bonds. Hydrogen bonds, being much weaker than the B-0 honds, determine the melting point of boric acid and give pieces-of-sheet structure to the melt. To crystallize, these pieces must become untangled. The associated relaxation time provides the viscosity required for boric acid (either H3B03 or, with loss of water, HB02) to form stable glasses. Anhydrous boric oxide also has a sheet structure with the bonding holding the sheets together much weaker than that holding the B03 triangles in sheets. It therefore has a low melting point. However, replacement of H by alkali or alkaline earth ions links BOs sheets with ionic bonds which are stronger than the H bonds, and raises liquidus temperatures. In particular, the liquidus temperatures of the alkaline earth borates vary inversely with atomic numher (12). This is to be expected with the smaller divalent ion pulling the 0 atoms of neighboring sheets closer together. As more mono- and divalent oxides are added to B203. more B's take on tetrahedral coordination (13) with 0 atoms. These tetrahedra share corners and can form disordered arrays, or glasses, in the same way Si04 tetrahedra do; and, of course can incorporate into these silica structures. This property of the boron atom of being able to coordinate three or four oxygen atoms a t ordinary pressures gives it special glass forming properties. It imparts another factor in the sorting process required for crystallization and introduces weak points in the network. It probably accounts for the graininess of these glasses and promotes phase separation, heat treatment being required for the diffusion which furthers the process. The borate-rich disperse phase is glassy because the separation occurs above its liquidus and the phase, itself, is viscous. Thus, at low alkali concentrations, the fluxing of SiOz by Bz03 would appear to be due to the strains introduced into the SiOa tetrahedral network by the plane Boa groups. This strain energy provides a suhstantial part of Volume 51, Number
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the energy required to hreak Si-0 honds and lowers the melting teniperature. Phosphorus pentoxide (14) contains P atoms in tetrahedral array with 0 atoms in between P atoms. Three crystalline forms exist: one containing discrete P4010 molecules held together by van der Waals forces; a second consisting of rings of ten PO1 tetrahedra in three dimensional array; and the third made u p of sheets containing six membered rings of Po4 tetrahedra. These last two structures form the basis for the extensive glass forming properties of the phosphates. The more volatile nature of the first modification points up the lower strength of van der Waals honding compared to the P-0 bonds. A notahle difference between PzOs and SiOz is that only three 0 atoms in the tetrahedra are bridging (common to two tetrahedra), the fourth non-bridging 0 heing considerably closer to the P atom. With only three instead of four network formine bonds. lower meltine temveratures are to be expected. As in the horates. additions of monovalent and divalent oxides (the so-called network modifiers), such as NazO and CaO, substitute ionic bonds in the network, and these are stronger than those previously holding the sheets together. Accordingly, they raise the liquidus temperature. By linking pieces of sheet together, large clumps are formed and the viscosity at corresponding temperatures is increased. But as the alkali and alkaline earth oxide concentrations increase, weaker ionic honds replace the stronger covalent P-0 bonds and more non-bridging 0 atoms result. We obtain smaller groupings and more ions. NOWcrystallization becomes very much easier. The compounds As203 (15), AS& (16). Vz06 (17)- for example, likewise owe their glass forming properties to sheet structures, but as atomic weight increases, so does atomic size, with a gain in tendency for increased coordination number or lessening of covalency. In other words, the elements become more metallic and tend to f o m ions or smaller clusters. Hence they are not so strong glass formers. Two more notahle and strong glass formers have the SiOz structure; they are BeF2 (18)and GeOz (19). Two divalent oxides which readily incorporate in silica and boric oxide lattices and are important glass stabilizers are Zn and Ph. Their property of vitrification probably is due to their taking on tetrahedral coordination in linking disparate groups. A number of substances, such as S (20), and Se (21) owe their glass forming properties to chain structures. Certain organic compounds form glasses by virtue of hydrogen bonding between molecules (22). The alcohols, es~eciallvdvcerol. are well known for this tendencv. The hidragen LoLding with oxygen permits three dimensional disordered arravs when the liauid is cooled ranidlv. Water (23) can behave the same way, pointing up i s simctural similarity to silica. In addition, glasses (22) can be formed in molecular liquids having no chains and no hydrogen honding, with only van der Waals forces keeping them from volatilizing. Toluene and other aromatic hydrocarbons having molecular force fields lacking spherical symmetry are examples. Glass formation depends on removing heat faster than the liquid structural elements can rearrange for crystal formation and the dissymmetry of these molecules demands sorting time to arrange them in crystalline order. Heat can he removed faster than this can he accomplished. Areon. " . of course. is no class former: neither is mamesium metal. The nhenomenon of elass formation (24) in mixed C ~ ( N O & - K N O ~melts presents an interesting case in point. Neither of the components is a ready glass former, both heing ionic crystals composed of cations and nitrate
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Figure 4. Cubic close packing of the larger spheres with the smaller in half the tetrahedrai sites and forming the central atom of the tetrahedral grouping. There are no holes big enough for these la move "to as groups as the lattice expands. if all atoms ware of equal sire, this would depict silicon.
ions. Molten KN03 is very fluid at its mp, as presumably is Ca(NO&, hut it is difficult to obtain pure molten Ca(NO& because of loss of NOz and Oz a t these temperatures. However, the 50:50 molar mixture forms a eutectic a t 146% with C a ( N 0 3 ) ~melting at 561°C and KN03 at 337°C. The glass transition temperature of this mixture is given as 56°C where its viscosity is 10'3 P. The driving force to crystallize at the transition temperature is very strong, hut in order to do so, CaZ+must he surrounded by eight NOS- in a distorted fluorite structure and K + by six NOa- in an aragonite array. This sorting process provides a notential harrier to c~stallizationwhich imoarts viscosity and the mixture sets up as a glass on cooling. Finallv. havine emnhasized the snecial elass formine from tetrahedral coordination, we should a& why silicon and diamond (Fig. 4) are not glass formers. The answer is, I believe, that these structures with atoms all of the same size have 4:4 coordination. There is not the preferential tendency for four atoms about a central atom to maintain coordination as free volume is added and honds rupture. As the honds are extended they essentially all hreak at once. The clusters in the liquid consist largely of single atoms. In contrast, the introduction of oxygen into the silicon lattice adds honds much stronger than the Si-Si honds (25). The smaller silicon atom holds the oxygen tetrahedra tightly as discrete structural units joined only by sharing comers (26). These same structural units persist throughout silicate crystals, not only in quartz, tridymite, cristohalite, and in the feldsvars where the three dimensional network is maintained, but in sheet arrangements in kaolinite, chain structures in the amnhiholes and wroxenes. three rine structures in beryl, double tetrahedia in he&imorphitey and finally single tetrahedra in olivine (27). This multitide of crystal habits gives silicates an extremely large number of possibilities for disorder when the liquids are under-cooled. Oxygen-carbon bonds completely destroy the diamond lattice. Summary It has been emphasized that the forces tending to set up liquids are crystalline in nature. Viscosity is the harrier preventing fulfillment of their function. As the structure accumulates thermal energy, these forces fail in maintaining rigidity in order of increasing bond strength. The
chemical bonding in the crystal determines the melting temperature and the size of the clusters which will be formed in the melt. In order of increasing strength, the honds can be classified as van der Waals, hydrogen, ionic (octahedral coordination), and covalent (tetrahedral coordination) (28). The time required for sorting these clusters into crystallizable atomic groupings imparts viscosity to the liquid and this leads to glass formation under the driving force of temperatures lower than the melting or liquidus. Thermal energies, i.e., kT,of a few percent of the weakest bond energy are generally sufficient to cause the long range structure to fail. The unique position of silica as a glass former is attributed to two things: tetrahedral coordination of the small Si atom by the larger 0 atoms, and the built-in holes in the cristobalite (quartz) structure. In this structure there is only one kind of bond to fail on melting. It is a strong bond so that the melting point of silica is high. The bondbreaks are statistically distributed, implying large numbers of atoms in the clusters formed in melting. These account for the high viscosity at the melting point. Next to the silicates, the borates are important glass formers. Here, three kinds of bonds must be considered, and the weak hydrogen bonds holding sheets of the stronger B-0 honds in triangular coordination account for the low melting point and glass forming properties of boric acid. The third kind of bonding occurs in B01 tetrahedra with alkali and alkaline earth ions making this coordination possible. The phosphates show tetrahedral coordination also, with the glass formers being restricted to no more than sheet structures, since only three of the four oxygen atoms share corners. Close packed structures are not good glass formers, whether or not they comprise more than one kind of atom. The relative glass forming capacity, or inversely, the rate of crystallization from the melt, can be obtained from the distribution of the different kinds of bonds in the crystal. The weakest bonds establish the temperature region of melting and the remaining ones, the size of the clusters which can persist in the liquid. Thus we can characterize the crystals whose melts lead to glass formation as follows: Either they have built-in holes into which groups can move as the lattice expands and finally melts, as in silica which has only one kind of bond; or they have some bonds much weaker than others and which break on melting, leaving the stronger ones to hold the clusters together in the liquid, as in borax or in sulfur. The glass forming capacity of a substance depends upon how fast its melt
has to he cooled in order to avoid crystallization. From considerations of the crystal structures of the following, we would expect them to be increasingly better glass formers as listed from left to right: Mg, Si, MgzSiOl, MgSiOa, SiOz. Literature Cited (11 BaMnnl, G. M., in "The Structure and Mechanical Ploperti~sof Inorganic Glasses." (l'mio~lolon:Jarsy, P. and Jaray. F. F.), Waltera-Naordhoff Publishing Dmningm. 1970, p. 70. ScealsoTumbull, D., Contemp. Phya., 10.413 (1369). (21 h k d e f f , A. A,. Re". Opfiyur. 5, 1 (1926): Tammann, G.. Gloatrch. Be,., 7, 445 (19301; Winter. A,. J. Amor Cemm. Soc.. 26, 189 (19431: Keurmann. W.. Chem. Re". 43. 219 (1948): Jones. G. 0.. m "Glas," revised edition by S. Park.. ChapmanHsll. 1 9 7 1 , ~4.. (31 Batschinski, A. J., 2. Phyr. Chem., 84, 644 (19131; Eyring, H., and Marehi, R. P., J. CHEM. EDUC., 40.562 (1963); Barker, J. A., in "LattiecTheorieaof the Liquid State." Tho Macmillan Company. N m York. 19G. p. 96-103. Eckstrin. B..Phys. Status Solidi, 20.83 (1967). (41 Randall. J . T., Rmkeshy, H. P., and Cooper, B.S.. 2. Kriatdlom. 75, 196 (1930). Obcriies, F., and Diet-I. A,. Gloateeh. B e , 30. 37 119571 sh-ed fmm X-ray data that silica glass retained structural elements that muid not be far removed from t h a e in eristobalite. (See Hicks. J. F. G., Science 155. 439 ((19671far a emsequence of this obrervation.1 It may be noted st thls point that the opposite of glans formation, namdy, lack of melting of nystals while b i n s hold for long pc" d s above their melting temporaturn, has been ohrewed. The rilineral albite is a notable example: Schairer. J. F., in "Phase Transformatio~in Solids." (EdiLon: Smolueholuaki, R.. Mayer. J. E.. and Wryl, W.I. John Wiby & Sam, New York. 1948: Diet.. E. D.. Baak, T., and Blau, H. H., 2. KRstollogr, 132, 340 (19701. (51 Hutchins III, J. R.. and Harringtm. R. V., in '"GI=. Kirk-Othmer, Encyclopedia of Chemiesl Techooiagy." 2nd Edition Volume 10. John Wiley & Sons. he.. Nev Ynrk 1. 9.. 6,C -. n LR? ~~~~, . .... (61 Zacharisacn, W. H.. J A m e r C k m . Soe.. 59.3841 (1932). (71 Wclls, A. F.. in "Structural Inorganic Chemistry;' 3rd Edition. Oxford Univeraify Press, NsraYork, 1962, p. 787. (81 Wclls. A. F.. oo. . cit.. o. 464. (91 (alWells, A. F., op.
