Coexisting Structures in Vitreous Silica CLARENCE L. BABCOCK AND STEPHEN W. BARBER General Research Division, Owens-Illinois Glass Co., Toledo, Ohio
KASIMIR FAJANS, Department of Chemistry, Lniversity of Michigan, Ann Arbor, Mich.
The unusual behavior of vitreous silica indicates that its structure may involve two or more distinctly different atomic arrangements coexisting in a homogeneous equilibrium in ratios that vary with temperature and pressure. The very small expansion coefficient can be explained if, under given conditions, the “structures” dominant at low temperatures have a larger volume than the others. The exceptional behavior of both, the compressibility and the elastic properties of the glass, are consistent with this assumption. Low temperature heat capacity, as well as infrared and Raman spectra, indicate the coexistence of relatively weak and strong forces, or of large and small vibrating masses, or both. The fact that the unusual behavior of vitreous silica is observable during measurements at moderate temperatures shows that the assumed mutual conversions of the coexisting structures are rapid and reversible. Besides these structures, one has to distinguish various relatively stable “states” which the glass assumes depending on thermal history. Knowledge of the structure of glass, and especially of atomic positions, should promote its widespread use as an engineering material.
S
ILICA is the major constituent in a wide variety of commer-
cial glasses and exerts controlling influence upon their characteristics. The excessively high temperatures required to convert quartz into vitreous silica limit its commercial use. Pure silica is otherwise an ideal glass-making material, in that it can easily be brought down to room temperature as glass. The properties of vitreous silica change with time in the range of temperatures covered in its manufacture. The time required to attain an equilibrium value of a property, such as density, increases very rapidly as the temperature is lowered. This suggests that the high viscosity of vitreous silica not only prevents crystallization but retards other structural changes. Examination of the effects of thermal history on the properties of vitreous silica should therefore give important information on its structure. A great variety of commercial silicate glasses can be obtained by melting quartz in combination with other inorganic materials. The properties of these glasses, like those of vitreous silica, are dependent upon thermal history but are strongly influenced by their Bpecific oxide compositions. Their equilibrium properties, at a given temperature, approach more and more those of vitreous silica as the silica content increases. It is desirable that the factors controlling the properties of silicate glasses be known with sufficient precision to allow the most favorable adjustment of end-usage specifications and of the various stages of manufacture. Experimental studies on the effects of oxide composition and thermal history have furnished the glass technologist with empirical information which can be used in the formulation of glasses for specific applications. Such information, however, is generally useful only within the limited field of compositions studied. Knowledge of the structure of glass, especially of the atomic positions in it, should further promote the widespread use of glass as an engineering material. January 1954
Zachariasen (58) assumed that the ions in oxide glasses are linked together by forces essentially the same as in their crystalline counterparts and that both form three-dimensional networks of a type designated as coordinative. On the basis of x-ray diffraction studies on vitreous silica, Warren et al. ( 5 6 ) concluded that each silicon is tetrahedrally bonded to four oxygens, each of which is shared by two silicons, the average Si-0 distance being close to 1.62 A. In a later summary ( S 5 , page 258) of his work on simple silicate glasses, Warren states “that the x-ray study of a glass gives information only on average quantities; it tells nothing about the fine details of the structure and the possibility of small variations in the structure . , The x-ray studies of glass might be said to establish the first-order approximation to a picture of the structure, and the fine details must be filled in from other kinds of measurements.” In spite of this cautious remark, the impression prevails that the x-ray work confirmed the presence in silica glass of only one s-0 distance between adjacent ions and that the randomness of the network is limited to the orientation of the SiOatetrahedra with respect to each other. Much of the research work on silicate glasses during the past few years has been directed toward the relations existing between their properties and structures (33). The use of the randomnetwork theory, employing a single Si-0 distance, has in general been unsuccessful in interpreting the properties of silicate glasses, although Huggins (19) has used i t to give a reasonable explanation of glass densities. Many studies on glass properties, especially as affected by thermal history, have been interpreted as showingthat glass has a structure morecomplex than that indicated by the random-network theory. Turner (34),Lillie (bS), Preston (36), Dietzel (I@, and Tool (33) have used such terms as “complex molecules,” “aggregates,” “complex anions,” “mixed ion and atom lattice,” and “two-component glasses’’ (two networks) to describe the nature of glass.
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This rather uncertain situation with respect to silicate glalseg recalls in some respects that in the field of borate glasses. Until recently boron oxide glass was considered to be a typical example of a random-network structure (38)and was assumed to have one B-0 distance between adjacent ions (56). Fajans and Barber (16), from the consideration of several properties of crystalline,
EQUILIBRIUM TEMPERATURE, “C.
Figure 1. Effect of Equilibrium Temperature from Which Vitreous Silica Was Quenched on Molar Volume at Room Temperature According to Douglas and IBard (14)
vitreous, and liquid boron oxide, concluded that at normal temperature more than one B-0 distance existed and that the structure was more complex than that of a three- or two-dimensional coordinative network. New powder x-ray photographs of crystalline boron oxide ( 4 ) support the conclusion that it cannot have a coordinative network involving only one B-0 distance.
approximately 1 month at 1000” C., and would be of the order of many thousands of years at normal temperature. Therefore, property data obtained at normal temperatures, such as thermal expansion and compressibility, are characteristic of a given frosenin state, and the relatively fast measurements leave the state unchanged. Figure 1, obtained from the density data of Douglas and Isard, shows that the higher the temperature at which the quenched state was in equilibrium, the smaller its volume at room tempera ture. These authors were led to suggest the coexistence of an “open structure due to directed bonds” and “Si02 molecules” in order to explain their data. PECULIARITY OF THERMAL EXPASSION AT NORMAL PRESSURE. In Figure 2 the thermal expansion coefficients of vitreous silica ( 3 1 ) are compared with those of diamond (21),sapphire ( I ) , and quartz (31). Both the magnitude and temperature dependence of the expansion coefficientsof diamond and sapphire show a behavior expected for the coordinative structures of these substances. However, of the two modifications of silica, the less dense glass has a much smaller expansion coefficient than even diamond, The very small and nearly constant coefficient of vitreous silica between 300’ and 1250’ K. and the fact that it becomes negative below 200’ K. are unique among homogeneou~~ solid substances. A minimum at 200” K. occurs not only for the volume but also for the dielectric constant ( I S ) of vitreous silica. No satisfactory explanation of these facts has been offered, and they cannot be understood from the viewpoint of a single continuous network which, with increasing temperature, would show merely the effects of the anharmonicity of atomic vibrations.
In the detailed publication ( 3 ) of these powder diagrams, seven different B-0 distances in the range 1.31 to 2.145 A. are given. This wide range is in accord with the definite information obtained (16)concerning the coexistence of weak and strong interactions within the boron oxide crystal as well as glass. However, measurements on single crystals will be necessary in order to decide whether the extreme differences in distances are due to the presence of B406 molecules suggested as a possibility (15) or to deviations from the ideal coordinative network of the kind proposed in (3). The fact that a glass built, for instance, from AskOBmolecules does not transform easily into the crystal, which also contains these molecules, is due to the nonspherical symmetry of the force field around them (see IS, page 112).
It is believed that a correlation of all available data on properties of vitreous silica is necessary for the elucidation of its detailed structure. This paper outlines selected parts of such studies now in progress. I t deals briefly with conclusions derived from the effects of thermal history, temperature, and pressure on volume; from the dependence of elastic properties on temperature; and from vibrational frequencies revealed by the heat capacity as well as by the infrared and Raman spectra. DEPENDENCE OF VOLUME ON THERMAL HISTORY, TEMPERATURE, AND PRESSURE
ABSOLUTEVOLUMEAND THERMAL HISTORY. Volume ( 9 7 ) and other properties of vitreous silica at a given temperature are determined by the “state” which it acquires, owing to thermal history imposed by the manufacturing process. Douglas and Isard (14) observed substantial differences in density at room temperature caused by quenching the glass from temperatures that varied between 1000’ and 1500” C. At each temperature the equilibrium state was established before the quench. As this temperature, called below and in Figures 1 and 3 “equilibrium temperature,” decreases, the time necessary to attain equilibrium states increases exponentially. I t is a few seconds a t 1500’ C.,
162
TEMPERATURE,
OK.
Figure 2. Thermal Expansion Coefficients us. Temperature for Vitreous Silica, Diamond, Sapphire, and Quartz Points for vitreous silica and q u a r t z represent true coe5cient6. For sapphire and diamond mean w e 5 c i e n t s apply to temperature intervals indicated by length of horizontal linea
STRUCTURAL CHANGESIN A HOMOGENEOUS PHASE.T h e negative expansion coefficient which supercooled and stable liquid water has up to 4’ C. has been explained (6) by a change from a‘ structure of larger volume to one of smaller volume which occurBq on heating and overcompensates the “true” thermal expansion. Similarly, a structural change is the most plausible explanation also in the case of the unusual behavior of vitreous silica with re spect to expansibility, compressibility (see below), and other properties. Because these peculiarities show up during measurements, which are very fast compared with the changes of state observed by Douglas and Isard, they must be due to structural changes of a character different from that of the latter. T h i ~ differentiation with respect to rate is analogous to that between the a -+ p transformation for cristobalite, which occurs in secondB
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and Glass-
-Ceramics a t 270' C. and the 0-tridymite + p-cristobalite transformation which is only two thirds completed after 16 hours a t 1480' C. (97). On the other hand, while both these transformations involve phase changes, the two kinds of conversions considered for vitreous silica are assumed to take place in a homogeneous phase.
to be positive and of the usual order of magnitude, but are nearly balanced by the negative volume change due to conversion I -P I1 caused by the increase of temperature. Negative coefficients occur at low temperatures, where the true positive expansions due to both structures are small and can be overcompensated by the negative effect due to the conversion. In order to estimate the order of magnitude of the volume difference VI-VII which fits this interpretation, one may assume 1.5 X 10-6 deg.-' and that a t 200' K., where a = 0, a1 UII that the glass consists predominantly of I-i.e., VI N 27 cc. per mole. Furthermore, as the postulated conversion I + I1 extends over the whole temperature ran5e of Figure 2, about X mole of I changes to I1 when At = 1 . Hence, 1.5 X 27 (VI-VII), and VI-VII 0.4 cc. per mole, a reasonable result. N
-
EQUILIBRIUM TEMPERATURE, "C.
Figure 3. Effect of Equilibrium Temperature from Which Vitreous Silica Was Quenched to Room Temperature on Mean Expansion Coefficients between 300" and 700" C. Derived from data of Douglaa and Isard ( 1 4 )
As t o the nature of the changes in atomic arrangements which take place in these various cases, whole layers of Si++"+ and 0-- ions are displaced with respect to each other in the slow tridymite + cristobalite transformation, while mainly the SiOSi-angle and to a minor degree the internuclear distances are involved in the fast a + p transformation. Similarly, the fast reversible changes assumed to take place on heating or compressing vitreous silica might consist merely in changes of angles and distances. However, in specifying the character of these changes, one will have to take into account that the structure more stable at the higher temperature has the larger volume in the a + p transformations, but the smaller volume in the changes assumed here for vitreous silica. Although the magnitude of these structural changes appears to vary continuously with temperature or pressure, they could be continuous or discontinuous, depending on which of the two following possibilities is correct: 1. Throughout the phase, angles and distances change more or less continuously. c
2. Two (or more) well-defined ionic arrangements, "structures" I and 11, coexist within the glass, each of which behaves "normally," but their relative amounts, which are in equilibrium with each other within the homogeneous phase, change continuously with temperature and pressure. The data presented in this article do not allow a clear-cut decision oetween these two possibilities. Only an indication, which seems to favor possibility 2, is mentioned in the section on spectra. In any case it appears to be simpler and more fruitful to consider, a8 was done in the case of boron oxide ( 1 4 , the coexistence of only two definite structures, I and 11. INTERPRETATION OF SMALLTHERMAL EXPANSIBILITY. The facts and assumptions presented in the last two sections can be correlated if the following conditions are fulfilled: 1. At a given temperature, the specific volume of I is greater than that of 11. 2. Increase of temperature shifts the equilibrium from I toward 11-Le., the conversion I + I1 is endothermic. 3. Interconversion of I and I1 is rapid and reversible even at low temperatures.
The thermal expansion coefficients of both I and I1 are assumed January 1954
N
-
Conditions 1 to 3 were applied above to the expansion of vitreous silica in a given state. Douglas and Isard also compared the expansibility of the glass in the various states it acquired by quenching from different high temperatures to room temperature. The mean expansion coefficients between 300" and 700" C., derived from the data of these authors, are plotted in Figure 3. It shows that the expansibility increases distinctly with the temperature a t which the glass attained equilibrium with respect to the slow changes of state before being quenched, Nevertheless, even the highest values are unusually small, and one has to assume that the fast conversion I -+ I1 is involved in temperature changes in all of the states formed in the experiments of Douglas and Isard.
TEMPERATURE, "C.
Figure 4. Mean Compressibilities of Vitreous Silica us. Temperature for Various Pressure Intervals Calculated from Birch and Dow (7) Pressure intervals, kg. crn.-s X 10-3 a. 8-10 d. 2-4 b . 6-8 e. 0-2 c. 4-6
The increase of the thermal expansion coefficients with increasing equilibrium tem erature might be interpreted to mean that the magnitude of t i e conversion I + I1 due to a given temperature increase is the smaller the higher the equilibrium temperature from which the glass has been quenched. However, this conclusion is not certain, since the states, the transformation of which occurs slowly, cannot differ merely with respect to the relative amounts of the structures I and 11,the interconversion of which is rapid. COMPRESSIBILITY A K D THERMAL EXPANSION AT INCREASED PRESSURES. From condition 1 thermodynamics leads to condition 4:
4. Increased pressure shifts the equilibrium from I toward 11. Figure 4 shows that the mean compressibility of vitreous silica, calculated from measurements of Birch and Dow (7), increases with increasing pressure and decreases with increasing temperature. This is opposite in both resperts to the behavior of the
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compressibility of all other solids, in which no phase transformation occurs due to the compression. Bridgman (8)found that the compressibility (in lor6 kg.-l omsz)of vitreous silica at room temperature increases with pressure to a maximum value of 3.50 for 30 to 35 ( X 108 kg. and then decreases to 2.69 for 40 to 50 ( X 103 kg. cm.-2).
800" C. could not be explained by surface imperfections but must involve the atomic positions in the glass. The strengthening of cohesive forces between room temperature and about 800' C., indicated by all these results, in combination with condition 2 mean8 that structure I1 is stronger than I. This is analogous to the behavior of vitreous boron oxide, which changes with increasing temperature towards a stronger structure (16). HEAT CAPACITY AND SPECTRA
The frequencies of vibration of the constituent parts of a solid are related to its heat capacity. Certain of these frequencies reveal their presence in Raman and infrared spectra. A given vibrational frequency depends upon the vibrating mass (or reduced mass) and the corresponding force constant. They are related by the equation: F
~=
L 2s
PRESSURE, I O '
KG. C M - 8
Figure 5. Mean Thermal Expansion Coefficients of Vitreous Silica between 11' and 390' C. us. Pressure Calculated from Birch and Dow (7)
The Birch and Dow ('7) data have also been used to calculate the mean thermal expansion coefficient plotted in Figure 5 as a function of pressure. The increase of this coefficient with increasing pressure is also opposite to the known behavior of solids, the structure of which is not changed by pressure (6,9). The exceptional pressure dependence of expansibility and temperature dependence of compressibility of vitreous silica can be interpreted in terms of the conversion I -.c 11, The small expansibility of the glass was explained above according to conditions 1,2, and 3 by the negative volume change in the conversion I 4 11. However, at increased pressure, structure I1 is favored according to condition 4; therefore, the extent of this conversion, owing to a given increase of temperature, will be smaller and the measured thermal expansion will be closer to a normal value. According to conditions 4 and 1, the coefficient of compressibility can be expected to be relatively large because the conversion I + I1 causes contraction; and, in fact, it is 8 times that for sapphire (6) and 5.6 times that for rutile (6) at normal temperature. At increased temperatures structure I1 is favored, according to condition 2. Therefore, the high pressure applied during the measurement of compressibility at elevated temperature causes smaller amounts of the conversion I + 11 and therefore a diminution of the apparent compressibility. The diminution of the room temperature compressibility a t pressures above 35 x l o 3 kg. cm.-2 can be interpreted in a similar way. More difficult to explain is the increase of compressibility with increase of pressure up to this value, I t means, if no other structural change is amumed, that the conversion I + 11,owing to compression of the glass by not too high pressures, is the more favored the higher the pressure. ELASTIC MODULI AND TENSILE STRENGTH
Young's modulus (20,81, 85) and the modulus of rigidity (18) of vitreous silica unexpectedly increase with temperature in the range from room temperature to 700" C., and both attain maxima between 700" and 950' C. This might be related to the minimum in the expansion coefficient shown in Figure 2 between 900' and llOOo K. Dawihl and Rix (11) measured the tensile strength of vitreous silica rods in the temperature range -60' to 800' C. and found a minimum near room temperature. They concluded that the unusual increase of strength between room temperature and 164
4
~force constant ~ mass
~
~
Thus an examination of these frequencies can give information about the individual masses and the forces involved in the structure of the solid. HEATCAPACITY. In Figure 6 the temperature dependence of the heat capacity per gram-atom of vitreous silica and cristobalite (crist., Si02) ($1) are compared with those of crysAlzOa) and boron oxide ( ' / 5 BZO,) talline aluminum oxide according to measurements of H. L. Johnson et al. (see 15). Sapphire can be considered as an ionic solid with one AI-0 distance between the nearest ions. In common with other solids of this type, its heat capacity can be represented approximately by a single Debye function with a characteristic temperature 0 950°, corresponding to a frequency of 660 cm.-l =i
TEMPERATURE,
OK.
Figure 6. Heat Capacities per Gram-Atom of Vitreous Silica ( l / a SiOn), Cristobalite (1/3 Sios), Sapphire (I/& AlZOs), and Crystalline Boron Oxide ( ' / E BnOs) us. Temperature
The mass of Si++++is a little larger than that of AI+++, and the interionic forces between Si++++and 0 - - can be expected to be a little stronger than those between AI+++, and O - - , as the charge of the cation is larger and its size is a little smaller. Therefore, in the case of one interionic Si-0 distance one would expect, according to Equation 1, the frequency of interionic vibrations in silica and its heat capacity per gram-atom in the whole temperature range to be close to the corresponding values for sapphire. On the contrary, the curves for sapphire and vitreous silica cross at 226' K., and below this temperature the values for silica are the larger-e.g., 2 times at 104', 6 times at 54' K. It follows that the heat capacity of silica cannot be represented by a single Debye function.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 1
~
~
and Glass
-Ceramics This situation is in some respects similar to that encountered in the comparison (15) of sapphire with crystalline boron oxide, the curve for which is also shown in Figure 6. In vitreous and crystalline boron oxide the consideration of various properties has shown the coexistence of relatively strong and weak forces. For instance, the high heat capacity of boron oxide, compared to sapphire, a t low temperatures was ascribed to low frequencies due to the vibration of polyatomic units held by weak forces. On the other hand, above about 200' K. a considerable part of the heat capacity must be due to high-frequency vibrations of B + + +and O--., In the case of the heat capacity of '/a SiOt, which is still higher BzOs,one has to consider, according to condition than that of 2, whether the endothermic conversion I + I1 contributes appreciably to the apparent values. The order of magnitude of the heat of conversion can be expected to be 100 cal. per mole, and the total conversion I -.c I1 has to be distributed over a range of about 1000". Hence, the contribution of this effect pe? 1" is of the order of magnitude of 0.1 cal. per mole of SiOn-i.e., 0.03 cal. per gram-atom. This is not sufficient to explain the difference in Figure 6 between vitreous silica and the other materials a t low temperatures. In such cases as boron oxide and silica, it is appropriate to calculate apparent Debye frequencies which are plotted as a function of temperature in Figure 7 . The curve for sapphire shows variations of the apparent frequencies only within 10%. However, the values for crystalline boron oxide range from 386 cm.-' a t 20' K. to 825 cm.-1 a t 300" K. Similarly, the curve for vitreous silica rises from 200 cm.-l a t 20' K. to 800 crn.-' at 500" K. The unusual decrease of the apparent frequency between 500" and 825" K. would be significant if it is real, but it requires an experimental verification The calculated apparent frequencies average real frequencies, the extremes of which for silica must therefore be still lower than 200 ern.-' and higher than 800 cnx-1. The highest frequencies could arise from vibrational motions of atom-ions, S i + + + +and 0--, but the lowest frequencies imply larger masses or weaker forces than those acting between nearest atom-ions and probably both. This means that more than one Si-0 distance between adjacent ions is present in at least one of the structures I and I1 assumed on the basis of the volume properties of the glass. In any case, the near coincidence of the curves for vitreous silica and cristobalite (Figure 6 ) indicates that the peculiarities of the heat capacity of vitreous silica cannot be due entirely to the randomness of its vitreous state. It appears advisable to postpone more specific interpretations
TEMPERATURE,
Figure 7'.
"K,
Apparent Debye Frequencies
Corresponding to 3R limit of heat capacities per gram-atom of vitreous silica, sapphire, and crystalline boron oxide us. temperature. For sapphire above 300' K . curve is dashed because experimental data (6) and Cz - C u correction are uncertain. Re arding this correction below 300' K. see (15). For vitreous silica Ce is negligibly small.
&-
January 1954
TABLE I. FREQUENCIES I N INFRARED d N D RAMAN SPECTRA OF VITREOUS SILICAAT ROOMTEMPERATURE^ Infrared Freq., c m . 3
Ref.
Raman . _Freq., cm.-1
< 76
213 (1) b
472 685
500 625 670 740 790-850 1000-1080 1150-1235
Ref.
85 116 372
800 950 Broad) 1100 {sharp) 1190 (Broad)
5 Values from (90)are from reflection measurements corrected to real frequencies (88). Infrared maxima 372 472,and 685 cm.-1 are not corrected. b Questioned (1) because of close sikilarity to quartz frequencies.
until the investigations of heat capacity and x-ray diffraction on silica modifications at still lower temperatures are concluded. SPECTRA.In Table I are listed the frequencies revealed by the Raman and infrared spectra of vitreous silica. The wide range of these frequencies (from
