-
N!$r PUBLICATIONS REFERENCE AlllDt Et.flMTM
NISTIR 6853
Elastic Moduli Data for Polycrystalline Oxide Ceramics
R. G. Munro Ceramics Division Materials Science and Engineering Laboratory
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1 I I 1 1 i Volume Fraction of Porosity (
Temperature / °C
United States Department of Commerce NIST National Institute of Standards and Technology Gaithersburg, Maryland 20899
QC 100 .U56 #6853 2002
NISTIR 6853
Elastic Moduli Data for Polycrystalline Oxide Ceramics
R. G. Munro Ceramics Division Materials Science and Engineering Laboratory National Institute of Standards and Technology Gaithersburg, Maryland 20899
June 2002
U. S. Department of Commerce Donald L. Evans, Secretary
Technology Administration
Phillip J. Bond, Under Secretary of Commerce for Technology
National Institute of Standards and Technology
Arden L. Bement, Jr., Director Certain commercial equipment, instruments, or materials are identified in this document to specify adequately experimental procedures and conditions. Such identification does not imply recommendation or endorsement by the
National Institute of Standards and Technology, nor does it imply that the materials, software, or equipment identified are necessarily the best available for the purpose.
National Institute of Standards and Technology N1STIR 6853
Natl. Inst. Stand. Technol. NIST1R 6853 235 printed pages (June 2002) Elastic Moduli Data for Polycrystalline Oxide Ceramics R. G. Munro Ceramics Division, National Institute of Standards and Technology Gaithersburg, Maryland 20899
ABSTRACT
A compilation of elastic moduli data, including Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio, is presented for polycrystalline oxide ceramics. The data have been collected from the technical literature, either as reported in textual or tabular formats or as digitized from graphical formats. Special emphasis is placed on the dependence of the moduli on porosity and temperature. For each material having sufficient data, an analytical model describing the simultaneous porosity and temperature dependence is fit to the data to provide a succinct and useful representation of the combined data.
Key Words
bulk modulus, elastic modulus, oxide ceramics, Poisson’s ratio, porosity dependence, shear modulus, temperature dependence
Table of Contents
Page Section
1 Abstract
1 Table of Contents
2 1 . Introduction
3 2. Measurement methods and standards
5 3. Previous data reviews
6 4. Models
10 5. Overview of the compilation
11 6. Acknowledgments
11 7. References
25 8. Index of materials
26 9. Data: organization of tables
27 9. Data: symbols and abbreviations 1. Introduction The coefficient, G, is known variously as the
shear modulus. Coulomb’s modulus [4], the All solid materials can deform, torsion modulus, and the rigidity modulus. stretch, compress, bend, flex, shear, twist, or For isotropic polycrystalline materials, the otherwise deviate from their original two parameters, E and G, are sufficient to unstressed sizes and shapes when subjected describe the macroscopic elastic behavior to external forces or internal thermal completely. However, it is convenient to stresses. This propensity of materials to consider two alternate parameters, Poisson’s deform under exerted forces is a critically ratio and the bulk modulus, that describe important consideration in the design of any specific attributes of the elastic behavior of mechanical component whose operation isotropic materials. depends on its ability to sustain loads or to maintain dimensions within specified Poisson’s ratio, v, describes the tolerances. Especially important is the relation between axial and lateral strains. condition known as elastic deformation. For example, when a rod of uniform circular
cross section is elongated by a tensile stress The deformation produced by an along the rod axis, the cross section external force acting on a solid is said to be undergoes a decrease in diameter. The elastic when removing the external force negative of the ratio of the lateral and axial returns the solid to its original undeformed strains is Poisson’s ratio, state. [1] 'lateral v = (3 ) Quantitative results describing the 'axial relationship between the magnitude of the applied force and the amount of deformation were presented as early as the 1 660s by the For isotropic materials, it can be shown that English scientist, philosopher, inventor, E = - Robert Hooke [2]. For linearly elastic v 1 . 4 2G ( ) materials, the idealized relation bearing his name may be written as The bulk modulus, 5, describes the o=Ee (1) particular circumstance when stress is applied hydrostatically rather than in which o is the applied stress (force per uniaxial ly. The hydrostatic pressure, P, unit area), € is the strain (fractional applied to an isotropic solid, causes the elongation), and E is a proportionality volume, V, to decrease such that, constant known variously as the elastic dP_' = J modulus, Young’s modulus [3], the B -V 5 dV) ( ) coefficient of elasticity, the tensile modulus, T and diverse other names. A similar relation can be found for the case of a shear stress, t, that produces an angular deformation, y. where the subscript T denotes constant temperature. Taking into account Poisson’s ^ - Gy (2) ratio, the strain in the x-direction, e x , in a three dimensional material with Cartesian
- 2 - coordinates (x, y, z), is given by the greater than isothermal moduli, but the appropriate generalization of Eq. fl), difference, about 0.3 %, is negligible for the present data. The static type involves = £ v( < stress/strain measurements employing * |h" v v>] «>> Eqs. (1) and (2) directly, while the dynamic type consists of resonance techniques or
the direction, is velocity where, with respect to x o x sound measurements. Resonance the axial stress and o and o are laterial methods require the detection of a resonant y z stresses. Similar expressions apply to e and frequency, while the sound velocity y with in flight e z obvious permutations of indices techniques determine the time of of a Eq. (6). Under hydrostatic conditions, the sound wave over a known distance.
is volumetric strain simply 5V/V= e x +e
first in strains, I: +e z , to order the linear and Table ASTM standards for E and G the stresses are a = o = o = -P. x y z Standard Scope Consequently, from Eq. (5) and Eq. (6), E 111 stress/strain slope; metals
(7) 3(1 -2v) C 215 sonic resonance; concrete
C 469 longitudinal compression; for isotropic materials. Using Eq. in (4) concrete Eq. (7), B can be expressed alternatively in terms of E and G. C 674 static deflection in three-point EG bend; whitewares 5 = ( 8 ) 9G - 3E C 623 sonic resonance; glass and glass ceramics
C 769 sonic velocity; carbon and As a matter of practice, most of the graphite data found in this compilation are from reported determinations of E and G. The C 747 sonic resonance; carbon and parameters v and B are most commonly graphite calculated using Eq. (4) and Eq. (8), C 848 sonic resonance; whitewares respectively. C 885 sonic resonance; refractories
C 1198 sonic resonance; advanced 2. Measurement methods and standards ceramics
Measurement techniques commonly C 1259 sonic resonance, impulse used to determine elastic moduli may be excitation; advanced ceramics classified into two generic types, static (isothermal) and dynamic (adiabatic), and E 1875 sonic resonance; elastic the terms ‘static moduli’ and ‘dynamic materials moduli’ are sometimes used to distinguish E 1876 sonic resonance, impulse results from the two types of measurements. excitation; elastic materials Adiabatic elastic moduli theoretically are
-3 - Numerous ASTM standards, Table I, is noteworthy that the development of have been developed for measurements of E international standards for the measurement and G [5]. Standard E 1 1 1 , which uses the of elastic moduli are currently in progress. initial linear slope of the directly measured At the present time, the International stress vs. strain curve, is intended primarily Organization for Standardization is voting for metals. A static modulus is also on standard ISO 17561, Fine Ceramics obtained by Standard C 469, which is (Advanced Ceramics, Advanced Technical intended for concrete under longitudinal Ceramics)—Test Method for Elastic Moduli compression, and by Standard C 674, which of Monolithic Ceramics at Room is intended for ceramic whitewares and Temperature by Sonic Resonance. utilizes a three-point bend test to measure ISO 17561 is very similar to ASTM C 1198. the deflection of bars or rods under loading. Standard C 769 uses sonic velocity Studies, principally on metals, have measurements applied to carbon and been conducted to compare and assess the graphite. various methods [9-11]. In early studies [9], the average results from both static and The remaining standards pertain to dynamic methods were found to be dynamic moduli determined by resonating a reasonably consistent with the variance rod or bar at its resonant frequency. The among laboratories being more significant initial basis for this approach seems to have than the variance for a single laboratory’s been provided by a series of papers by results. In later studies, however, Timoshenko [1,193] which related the measurement uncertainties were found to be elastic properties to the resonant frequency, significantly larger for static methods than
1 mass, and physical dimensions of the bar. for dynamic methods. In one study [ 2], the This work was followed by a series of standard deviation of the static test results studies to refine the experimental technique was approximately 7 % of the mean, while and to refine the semiempirical equations for the dynamic methods, the relative relating E to frequency and bar dimensions. standard deviation was only 1 .5 %. Those Goens [194] and Forster [195] pioneered results were consistent with an earlier round work in Germany. Pickett [6] in the USA robin study of dynamic test methods [13] in refined the equations further in 1945. The which the standard deviation was found to application of these methods was then be 2 % of the mean. Interestingly, the latter advanced to their present utility by S. study identified measurement of the bulk Spinner and W. E. Tefft at the National density as being a significant factor
Bureau of Standards [7]. ASTM standard contributing to the interlaboratory variance C 623 relies heavily on their 1961 paper, of the dynamic measurement results. When while standards C 747, C 848, C 885, the moduli were reevaluated using the C 1198, and E 1875 adapt and extend common mean density, the relative standard standard C 623. Standards C 1259 and deviation of the moduli was reduced to
E 1876 address the most recent innovation 1 .6 %. This level of uncertainty is known as the impulse excitation method [8] consistent also with the analysis in the and add the resonance of disk specimens as Precision and Bias section of ASTM an option. C 1259. That study estimated a relative uncertainty of 1.7 % when the component
In addition to the ASTM standards, it measurement errors for frequency, mass, and
- 4 - dimensions were 0.1 %. However, it should the bulk density, p. From the known or be noted that this uncertainty is much larger nominal chemical composition of the
than the relative uncertainty pertaining to the material, it may be possible to calculate the instrument, density, for a theoretically precision of a single which can maximum p theo , be as much as an order of magnitude smaller nonporous single crystal of the material. In (0.2 % for a dynamic resonance technique that case, the total volume fraction of
[14] applied to an alumina reference porosity, (j), in the experimental specimen material). can be estimated from the simple relation,
= 1 --£ With respect to the present * - (9) compilation, we may take the round robin result (an uncertainty of 2 %) as a lower limit of the uncertainty to be anticipated for results derived from independent studies, for Of course, the presence of secondary glassy which materials are only nominally similar. phases, additives, or impurities can modify this relation. In the present compilation,
Measurements of elastic properties at compounds are considered in relatively pure elevated temperatures are most commonly forms, except where noted explicitly, and performed using the dynamic methods. porosity is always expressed in the context
ASTM standard C 623 and its derivative of Eq. (9). standards provide for the use of either a cryogenic cabinet (for measurements at low temperature, down to -195 °C) or a furnace 3. Previous data reviews (for measurements at high temperature, up to 1200 °C). Static methods are used Development of the class of infrequently for the high temperature materials now broadly known as advanced measurements and are considered to be less ceramics ( a.k.a ., fine ceramics and reliable, particularly when creep occurs. engineering ceramics) began only as recently as the middle of the twentieth century. The
An additional factor of considerable first substantial review of the elastic importance to the reliability of elastic properties of these materials appears to have moduli data is the determination of the been the very fine work of S. M. Lang in volume fraction of porosity present in the 1960 [16]. That paper presented the bulk material [15]. Unfortunately, the role of density and dynamic moduli at room porosity is often treated rather superficially temperature, determined for 20 different in the literature. It is extremely rare that materials consisting of oxides, carbides, studies of elastic moduli are accompanied by borides, cermets, and intermetal lie detailed analyses of pore shape and pore size compounds. Over approximately the distributions, and little effort seems to have following three decades, O. L. Anderson et been made towards distinguishing open, al. produced a series of papers [17-19] closed, and total porosity values, except in regarding the elastic properties of computer simulation studies. In the polycrystalline ceramics and minerals of experimental works, the status of the importance to geophysics. More recently, R. material densification is most commonly W. Rice has undertaken a series of reviews
(but not always!) represented by a value for of the physical properties of ceramics [15,
-5 - 20-22] with the particular interest of gaining 4.1 Dependent and independent variables
insight into the manner in which physical It has been discussed previously [24] properties are influenced by porosity. that material properties, such as fracture Beginning in the late 1980s, the discovery of toughness or elastic moduli, usually are not high temperature superconductivity led to a themselves independent variables describing whole new class of advanced ceramics for a material system. Rather, the values of the which property data began to appear rapidly. properties derive from the interactions Early reports of the elastic properties of among the constituents of the material. The these materials were reviewed by R. G. property values, therefore, are affected by Munro [23] as part of a general review of the such variables as the composition, the mechanical properties of high temperature binding strengths, and the microstructure. In superconductors, which were principally this regard, physical characteristics such as oxide ceramics. grain size, pore size, and the shapes of the grains and pores determine boundary 4. Models conditions that serve as constraints on the interacting constituents. Mathematically, the Compilations of property data serve values attained by the properties for a given two different purposes. For scientific material system are the particular solutions studies, they serve as relatively generic to the system of equations describing the collections of data providing the basis for interactions. Clearly, those values may be statistical and theoretical analyses of general affected strongly by the constraints on the property relations. For engineering interactions and particularly by the boundary applications, they serve as materials property conditions. databases providing specific values to be used in product design and manufacturing. Numerous studies have concluded In the latter applications, computer aided that the elastic moduli of ceramics may design and manufacturing techniques enable depend strongly on the phase composition of simulations of a product’s behavior under the material specimen, the presence of pores, varying conditions of stress and temperature, and the temperature, but do not exhibit any in both equilibrium and nonequilibrium significant dependence on grain size. In the conditions. For such purposes, it is present work, any reference to a material desirable to have a means of estimating the will be taken implicitly to mean a collection value of a property at an arbitrary point in of specimens having, at least, nominally the allowed range of the operating similar phase compositions. The conditions. While interpolation techniques dependence of the elastic moduli on can be used with tabulated data, such temperature and porosity will be treated approaches are relatively slow and explicitly. cumbersome and require extensive tables of data for every material condition of interest Towards the end of finding a simple, to the application. A more succinct and analytic representation of the elastic moduli, efficient approach is to use semiempirical we shall proceed heuristically, beginning analytical models that incorporate both with the assumption that a separation of material and environmental factors within variables may be applied to the dependence the model. In this section, we consider one of elastic moduli on temperature and such model for the elastic moduli data. porosity. For any modulus, M(T,([)), of a
- 6 - given composition, it is assumed that we Consequently, the uncertainty in the value of
is large for may consider the parameter, T0 , unacceptably most of the data in the present compilation. M{T$)=M+T)M^) (IQ) For the present purpose, therefore, it suffices to consider only the simplified linear model
M (T)=M (0)(\ -a T) such that our task is to find suitable 7 7 M (12) representations for M (7) and M^cj)). /
rewritten 4.2 Temperature dependence with the parameters as A/7 (0) and Empirically, the temperature for each modulus M. aK , dependence of Young's elastic modulus for
most ceramics is relatively simple, generally decreasing monotonically with increasing 4.3 Porosity dependence temperature. At very low temperature, the The porosity dependence of the slope of the modulus with respect to elastic properties of solids has been the temperature must approach zero. On the subject of extensive investigation for basis of lattice dynamics, Bom and Huang decades. Numerous studies have examined [25] estimated that the elastic constants the role of pores as the second component of should vary as V at low temperature. Above two-phase solid media [28-33]. Those room temperature, the moduli generally works generally involve an analysis of the decrease linearly with increasing strain field in the composite body under the temperature. To describe the behavior from application of an external stress.
low to high temperature, Wachtman et al. Alternatively, several studies [22,34-39] [26] suggested the empirical relation have observed that stress internally is transmitted only over the areas of contact EJJ)=E^bTz\Q(-TJT) (ii) between the constituent particles or grains.
As the body is densified, the contact area increases while the porosity decreases.
in which E0 is Young’s modulus at absolute Consequently, the porosity dependence of
zero, and b and T0 are parameters to be the elastic moduli should be governed by the determined numerically from the observed contact area. More recently, detailed data. Anderson [27] later provided a analyses of the effects of pore size and pore justification of an expression of this form for shape have begun to be performed in finite the bulk modulus and noted that the elastic element computer simulation calculations modulus would be approximately of the [40,41], same form if the temperature dependence of Poisson’s ratio could be ignored. In addition to these microstructural modeling efforts, many semiempirical Empirically, graphs of elastic moduli analytical models have been proposed to
data vs. temperature exhibit very little represent the general trend of elastic moduli curvature except at very low temperature. with porosity. Analytical models are of This lack of curvature causes numerical considerable interest because of their fitting routines to be rather insensitive to the potential use as smoothing and interpolation
exponential factor in Eq. (11). functions. Since these models only relate
- 7 - bulk elastic properties to the mean porosity, contiguity of the assembage of components they generally do not represent detailed becomes an important issue since the microstructural effects arising from varying integrity of an elastic medium is dependent pore shape, anisotropy, or nonuniformity. on the transitivity of forces between adjacent Their importance rests in their capacity to material components. Indeed, in studies provide highly effective descriptions of the applying percolation theory, analyses of trends of the mean properties and characteristics of porous media. An approximate chronology of the principal Table II: Approximate chronology of that proposed for empirical models the porosity models [42-5 1 ] have been for the elastic or Young’s modulus is given in dependence of Young 's elastic modulus
Table II, while numerous other studies[52- E - E (l - a 59] have explored their applicability to f) tp) [42] 2 various experimental results. E = E„ (1 - atp + btp ) [43] Empirically, a simple linear model E = E„ exp(-atp) [44] - [42] may be adequate at very small porosity, E = Ea (1 (P)/(l + a
P-,) in the volume fraction of porosity (([)). and other models focused on the stacking of
Budiansky’s selfconsistent model [52] is of geometric shapes, there arises the possibility this type results in pair critical at and a of coupled of a porosity, (j) c , which the moduli equations for the bulk and shear moduli. must vanish [22]. Such studies pertain to Those relations are explicitly linear in the very important issue of the validity of porosity and implicitly nonlinear through the interpreting such an assembly of material selfconsistent dependence on Poisson’s components as an elastic continuum. Phani ratio, v, which is itself dependent on and Niyogi [48] suggested that if we are to porosity. allow for a vanishing modulus, then
Young’s modulus, E, should be proportional
very porosity, other issues to (l-(])/({) At high a power of c ). must be considered in determining the influence of porosity on elastic moduli. It is In the present work, elasticity, as a essentially selfevident that the volume bulk concept, is taken to mean a priori that fraction of porosity of a solid material must the spatial connectivity is sufficient to allow be less than one (4> < 1 ) because the the bulk material to sustain an applied stress. condition (j) = 1 corresponds to no material For any such material, without exception, at all. As the limit <|) = 1 is approached, the the elastic modulus does not vanish.
- 8 - material, is Assuming material contiguity, Wagh volume of the M/p, where M the et al. [49] considered a model in which the molecular mass and p is the bulk density. material was assumed to be composed of a As a result, the mean interaction potential at network of material chains and interposed a site must be reduced because the mean with channels of open pores. For a one interparticle distance is increased. To dimensional system, they obtained the account for this relaxation in the model closed form expression system, the length scale was formally renormalized. The renormalized system was E = E then related to the porous physical system 0 {l-W ( 13 ) by imposing the consistency condition that the equilibrium volume of the renormalized where E is Young’s modulus, and E„ and n system be equal to the sum of the volume at are constants. They then used numerical zero porosity and the pore volume. The solutions to verify that the same expression result was the closed form expression should be valid also for a three dimensional system. That conclusion was consistent with B - B 1 a ( -
Among these various models, it may can be different from the exponent, n, found be noted that the suitability of the various in the similar expression, Eq. (13), for analytical forms is not sharply distinguished Young’s modulus. over the observed range of porosity for polycrystalline ceramics. No one model seems to have a stronger theoretical 4.4 The general model justification than the others, and the For isotropic materials, the elastic empirical fits to the data are not sharply properties are fully described by any two of different. Additionally, the general trends of the elastic moduli. Polycrystalline ceramics the elastic moduli data vs. porosity, for usually are very good approximations to polycrystalline ceramics, do not seem to isotropic materials because of the depend greatly on the nature of the porosity randomness of the grain orientations, even since results for specimens from multiple when the individual grains are anisotropic. sources conform to a single trend line. Except for textured materials in which the Motivated by such observations, Munro [60] microstructure has partially aligned grain derived a simple effective medium theory orientations, polycrystalline ceramics may for the porosity dependence of bulk moduli. be treated as isotropic materials. In that work, the classical model of an ionic solid [17] was taken as an idealized, pore Upon viewing the dependence on free, reference system. That choice had the temperature and porosity separately, we have particular virtue of providing a closed form seen that the temperature dependence may expression for the bulk modulus. It was be represented effectively by Eq. (12). For noted that the introduction of porosity into the porosity dependence, there are several such a system must increase the molar alternatives, but only two of the models,
- 9 - Eq. (13) for the elastic modulus and Eq. (14) and depends directly on the ratio ( E/6B ). In for the bulk modulus, have been derived in Eqs. (15) and (16), the magnitudes of aT and closed form from theoretical models. bT are typically about 0.1 at 1000 °C.
Combining these models in the manner of Hence, the ratio ( E/B ) is approximately Eq. (10), we obtain the general model describing the simultaneous dependence of - |.^.( 1 [a -i]7l(l-*)- 21 B B ( ) E and B on the variables T and (}). Q
£(r,4.) = (l-ari(l-c|))" £0 (15) Consequently, Poisson’s ratio has a
dependence on T and cj) that reflects how the B(r,4» = elastic modulus and the bulk modulus differ B0 (l-67)(l-ct>r (16) in their dependence on those variables.
The shear modulus, G, may be 5. Overview of the compilation obtained from E and B as The data contained in this 3 BE (17) compilation were extracted from publicly 9 B-E accessible technical literature. Values reported numerically in the original papers but generally will not be of the same usually have been listed with the same analytical form as E and B. For ceramics, number of significant digits as originally the magnitude of E is typically on the order reported. An exception to this rule occurred of twice that of B. Consequently, the whenever the number of reported significant relation in Eq. (17) can be expanded as digits clearly was excessive compared to the number of digits that could reasonably be E V G = ~E 2 (18) expected for the observed measurement 3 ; =oV 9B, uncertainty.
Data reported graphically in the yielding original papers were extracted from the published figures using a mechanical 2 ' E ' ' E ' ••• digitization procedure. Since digitization is G*-E 1 + + + (19) 3 ,9 B 9 B, itself a measurement process, additional t , uncertainty must accrue to each individual point. To estimate this additional from which it is seen that G may have a uncertainty under worst case conditions, different functional dependence on T and 4>, replicate digitizations were performed on depending on the ratio (E/9B). figures containing both well resolved and poorly resolved data points. The relative
Poisson’s ratio, v, is given by expanded uncertainty for the digitization process using a coverage factor of two _E_ 20 (corresponding to a confidence level of 6 B ( ) approximately 95 %) was estimated to be
- 10 - 3 %. 3. T. Young, On the Equilibrium and Strength of Elastic Substances, While the goal has been to provide a Mathematical Elements ofNatural
it l 's comprehensive data set for each material, Philosophy, Vo II ofDr. Young
is recognized that such a goal usually is Lectures , Section IX, p. 46 ( 1 807). unattainable. Where a comprehensive set has 4. C. A. Coulomb, Theoretical and been unattainable, we have striven to Experimental Researches on the
provide at least a set representative of the Force of Torsion and on the available data. For some materials, phase or Elasticity of Metal Wires, Histoire
have affected the l 'Academie Year composition changes may de des Sciences ,
measurement results. Data for such cases 1784 , pp. 229-269(1787). (readily identified by their unusual behavior) 5. ASTM, American Society for are included to the extent available. In this Testing and Materials, West regard, we especially note the case of high Conshohocken, Pennsylvania. temperature superconductors (FITS). There 6. G. Pickett, Equations for Computing are many papers reporting anomalous results Elastic Constants from Flexural and for ultrasonic wave propagation in HTS Torsional Resonant Frequencies of materials at cryogenic temperatures [61-72]. Vibration of Prisms and Cylinders, Those papers often focus on the anomaly American Society for Testing and and usually have not reported the Materials, Proceedings, Vol. 45, quantitative behavior of the elastic moduli. pp. 846-865 (1945). While data appropriate to the present 7. S. Spinner and W. E. Tefft, A compilation, therefore, are not available in Method for Determining Mechanical
those papers, the results are still relevant to Resonance Frequencies and for understanding the limitations and behavior Calculating Elastic Moduli from of the elastic moduli of high temperature These Frequencies, American superconductors. Consequently, those papers Society for Testing and Materials, are cited here as additional references [61- Proceedings, Vol. 61, pp. 1221-1238 72] of potential use to the reader. (1961).
8. G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, and O. Van der 6. Acknowledgments Biest, Impulse Excitation Apparatus to Measure Resonant Frequencies, The author thanks G. D. Quinn for Elastic Moduli, and Internal Friction insightful discussions of measurement at Room and High Temperature, techniques and standards, and J. F. Harris Reviews of Scientific Instruments, for her able and diligent effort in digitizing Vol. 68, No. 12, pp. 4511-4515 data presented graphically in the literature. (1997).
9. J. T. Richards, An Evaluation of 7. References Several Static and Dynamic Methods for Determiing Elastic Moduli,
1 . S. Timoshenko, Theory of Elasticity , ASTM STP No. 129, American McGraw-Hill, New York (1934). Society for Testing Materials, 2. R. Hooke, De Potentia Restitutiva, Philadelphia, pp. 71-98 (1952). London (1678).
-11 - 10. S. Spinner and R. C. Vaiore, Jr., 15. R. W. Rice, Porosity of Ceramics, Comparison of Theoretical and Marcel Dekker, New York (1998). Empirical Relations Between the 16. S. M. Lang, Properties of High- Shear Modulus and Torsional Temperature Ceramics and Cermets, Resonance Frequencies for Bars of Elasticity and Density at Room
Rectangular Cross Section. Journal Temperature, Monograph 6, National of Research of the National Bureau Bureau of Standards, Washington,
of Standards, Vol. 60, No. 5, D.C. (1960). pp. 459-464 (1958). 17. O. L. Anderson, Determination and 11. S. Spinner, T. W. Reichard, and W. Some Uses of Isotropic Elastic E. Tefft, A Comparison of Constants of Polycrystalline Experimental and Theoretical Aggregates Using Single-Crystal Relations Between Young’s Modulus Data, Physical Acoustics, Vol. 3B, and the Flexural and Longitudinal pp. 43-95 (1965). Resonance Frequencies of Uniform 18. O. L. Anderson, E. Schreiber, and R. Bars, Journal of Research of the C. Liebermann, Some Elastic National Bureau of Standards, Constant Data on Minerals Relevant
Vol. 64A, No. 2, pp. 147-155 (1960). to Geophysics, Reviews of
12. J. S. Smith, M. D. Wyrick, and J. M. Geophysics, Vol. 6, No. 4, Poole, An Evaluation of Three pp. 491-524(1968). Techniques for Determining the 19. O. L. Anderson, D. Isaak, and H. Young’s Modulus of Mechanically Oda, High-Temperature Elastic Alloyed Materials, ASTM STP 1045, Constant Data on Minerals Relevant edited by A. Wolfenden, American to Geophysics, Reviews of
Society for Testing and Materials, Geophysics, Vol. 30, No. 1, Philadelphia, pp. 195-207 (1990). pp. 57-90(1992). 13. A. Wolfenden, M. R. Harmouche, G. 20. R. W. Rice, Relation of Tensile V. Blessing, Y. T. Chen, P. Strength-Porosity Effects in
Terranova, V. Dayal, V. K. Kinra, J. Ceramics to Porosity Dependence of
W. Lemmens, R. R. Phillips, J. S. Young’s Modulus and Fracture
Smith, P. Mahmoodi, and R. J. Energy, Porosity Character and Grain Wann, Dynamic Young’s Modulus Size, Materials Science and
Measurements in Metallic Materials: Engineering, Vol. A1 12, pp. 215-224 Results of an Interlaboratory Testing (1989). Program, Journal of Testing and 21. R. W. Rice, The Porosity
Evaluation, Vol. 17, No. 1, pp. 2-13 Dependence of Physical Properties of (1989). Materials: A Summary Review, Key
14. R. W. Dickson and J. B. Wachtman, Engineering Materials, Vol. 1 15, Jr., An Alumina Standard Reference pp. 1-20(1995). Material for Resonance Frequency 22. R. W. Rice, Evaluation and and Dynamic Elastic Moduli Extension of Physical Property-
Measurement, 1. For Use at 25 °C, Porosity Models Based on Minimum Journal of Research of the National Solid Area, Journal of Materials Bureau of Standards, Vol. 75A, No. Science, Vol. 31, pp. 102-1 18
3, pp. 155-162 (1971). (1996).
- 12 - 23. R. G. Munro, Mechanical Properties, Evaluation, Vol. 16, No. 4, Handbook ofSuperconductivity, pp. 187-192 (1997). edited by C. P. Poole, Academic 32. A. R. Boccaccini and Z. Fan, A New Press, New York, pp. 570-625 Approach for the Young’s Modulus- (1999). Porosity Correlation of Ceramic 24. R. G. Munro and S. W. Freiman, Materials, Ceramics International, Correlation of Fracture Toughness Vol. 23, pp. 239-245 (1997). and Strength, Journal of the 33. F. Wang, W. Gou, X. Zheng, and M. American Ceramic Society, Vol. 82, Lu, Effective Elastic Moduli of
No. 8, pp. 2246-2248 (1999). Ceramics with Pores, Journal of 25. M. Bom and K. Huang, Dynamical Materials Science and Technology,
Theory of Crystal Lattices , Oxford Vol. 14, pp. 286-288 (1998). University, New York (1954). 34. R. W. Rice, Comparison of Stress
26. J. B. Wachtman, Jr., W. E. Tefft, D. Concentration versus Minimum
G. Lam, Jr., and C. S. Apstein, Solid Area Based on Mechanical
Physical Review, Vol. 122, No. 6, Property-Porosity Relations, Journal pp. 1754-1759(1961). of Materials Science, Vol. 28, 27. O. L. Anderson, Derivation of pp. 2187-2190(1993). Wachtman' s Equation for the 35. R. W. Rice, Comparison of Physical Temperature Dependence of Elastic Property-Porosity Behaviour with Moduli of Oxide Compounds, Minimum Solid Area Models,
Physical Review, Vol. 144, No. 2, Journal of Materials Science, pp. 553-557 (1966). Vol. 31, pp. 1509-1528 (1996).
28. W. Kreher, J. Ranachowski, and F. 36. A. K. Mukhopadhyay and K. K. Rejmund, Ultrasonic Waves in Phani, Young’s Modulus-Porosity Porous Ceramics With Non- Relations: an Analysis Based on a Spherical Holes, Ultrasonics, Minimum Contact Area Model,
Vol. 15, No. 2, pp. 70-74 (1977). Journal of Materials Science, 29. E. A. Dean, Elastic Moduli of Porous Vol. 33, pp. 69-72 (1998). Sintered Materials as Modeled by a 37. A. K. Mukhopadhyay and K. K. Variable-Aspect-Ratio Self- Phani, Ultrasonic Velocity-Porosity Consistent Oblate-Spheroidal- Relations: An Analysis Based on a Inclusion Theory, Journal of the Minimum Contact Area Model, American Ceramic Society, Vol. 66, Journal of Materials Science Letters,
No. 12, pp. 847-854 (1983). Vol. 18, pp. 1759-1760(1999). 30. N. Ramakrishnan and V. S. 38. A. K. Mukhopadhyay and K. K. Arunachalam, Effective Elastic Phani, An Analysis of Moduli of Porous Solids, Journal of Microstructural Parameters in the Materials Science, Vol. 25, Minimum Contact Area Model for pp. 3930-3937 (1990). Ultrasonic Velocity-Porosity 31. D. N. Boccaccini and A. R. Relations, Journal of the European Boccaccini, Dependence of Ceramic Society, Vol. 20, pp. 29-38
Ultrasonic Velocity on Porosity and ( 2000 ). Pore Shape in Sintered Materials, 39. D. G. Bika, M. Gentzler, and J. N. Journal of Nondestructive Michaels, Mechanical Properties of
- 13 - Agglomerates, Powder Technology, Solids, Journal of Materials Science, Vol. 117, pp. 98-112 (2001). Vol. 22, pp. 257-263 (1987).
40. A. P. Roberts and E. J. Garboczi, 49. A. S. Wagh, R. B. Poeppel, and J. P. Elastic Properties of Model Porous Singh, Open Pore Description of Ceramics, Journal of the American Mechanical Properties of Ceramics, Ceramic Society, Vol. 83, No. 12, Journal of Materials Science, Vol. pp. 3041-3048 (2000). 26, pp. 3862-3868 (1991).
41. A. P. Roberts and E. J. Garboczi, 50. M. Kupkova, Porosity Dependence Elastic Moduli of Model Random of Material Elastic Moduli, Journal Three-Dimensional Closed-Cell of Materials Science, Vol. 28, Cellular Solids, Acta Materialia, pp. 5265-5268 (1993). Vol. 49, pp. 189-197 (2001). 51. A. R. Boccaccini, G. Ondracek, P.
42. J. M. Dewey, The Elastic Constants Mazilu, and D. Windelberg, On the of Materials Eoaded with Non-Rigid Effective Young's Modulus of Fillers, Journal of Applied Physics, Elasticity for Porous Materials: Vol. 18. pp. 578-581 (1947). Microstructure Modelling and
43. . J. K. Mackenzie, Elastic Constants of Comparison Between Calculated and a Solid Containing Spherical Holes, Experimental Values, Journal of the Proceedings of the Physical Society, Mechanical Behavior of Materials,
Section B, Vol. 63, pp. 2-1 1 (1950). Vol. 4, pp. 119-128 (1993). 44. R. M. Spriggs and T. Vasilos, Effect 52. B. Budiansky, On the Elastic Moduli of Grain Size and Porosity on the of Some Heterogeneous Materials, Transverse Bend Strength and Journal of the Mechanics and Elastic Modulus of Hot Pressed Physics of Solids, Vol. 13, pp. 223- Alumina and Magnesia, Journal of 227 (1965).
the American Ceramic Society, 53. E. A. Dean and J. A. Lopez,
Vol. 40, No. 4, pg. 187(1961). Empirical Dependence of Elastic 45. D. P. H. Hasselman, On the Porosity Moduli on Porosity for Ceramic Dependence of the Elastic Moduli of Materials, Journal of the American
Polycrystalline Refractory Materials, Ceramic Society, Vol. 66, No. 5, Journal of the American Ceramic pp. 366-370 (1983). Society, Vol. 45, pp. 452-453 (1962). 54. K. K. Phani, Young’s Modulus-
46. O. Ishai and L. J. Cohen, Elastic Porosity Relation in Gypsum Properties of Filled and Porous Systems, American Ceramic Society Epoxy Composites, International Bulletin, Vol. 65, No. 12, Journal of Mechanical Sciences, Vol. pp. 1584-1586(1986).
9, pp. 539-546 (1967). 55. K. K. Phani, Elastic-Constant-
47. J. C. Wang, Young’s Modulus of Porosity Relations for Polycrystalline
Porous Materials, Part 1 , Theoretical Thoria, Journal of Materials Science
Derivation of Modulus-Porosity Letters, Vol. 5, pp. 747-750 (1986). Correlation, Journal of Materials 56. K. K. Phani and S. K. Niyogi, Science, Vol. 19, pp. 801-808 Porosity Dependence of Ultrasonic (1984). Velocity and Elastic Modulus in 48. K. K. Phani and S. K. Niyogi, Sintered Uranium Dioxide, Journal
Young’s Modulus of Porous Brittle of Materials Science Letters, Vol. 5,
- 14 - pp. 427-430 (1986). Investigations on Superconducting
57. K. K. Phani and S. K. Niyogi, Elastic YBa2 Cu 3 0 7 _ 6 Samples of Different Modulus-Porosity Relation in Microstructure, Solid State
Polycrystalline Rare-Earth Oxides, Communications, Vol. 64, No. 8, Journal of the American Ceramic pp. 1153-1156 (1987).
Society, Vol. 70, No. 12, 65. Y. He, B. Zhang, S. Lin, J. Xiang, Y. pp. C-362 - C-366 (1987). Lou, and H. Chen, Ultrasonic 58. N. Ramakrishnan and V. S. Investigation of Lattice Instability Effective Elastic Superconductivity in Arunachalam, and High-T c Moduli of Porous Ceramic Materials, Systems, Journal of Physics F: Metal Journal of the American Ceramic Physics, Vol. 17, pp. L243-L248 Society, Vol. 76, pp. 2745-2752 (1987).
(1993). 66. S. Bhattacharya, M. J. Higgins, D. C.
59. L. J. Gibson and M. F. Ashby, The Johnston, A. J. Jacobson, J. P.
Mechanics of Three-Dimensional Stokes, D. P. Goshom, and J. T. Cellular Materials, Proceedings of Lewandowski, Elastic Anomalies Society Vol. Transitions in the Royal of London, and Phase High-Tc A382, pp. 43-59(1982). Superconductors, Physical Review 60. R. G. Munro, Effective Medium Letters, Vol. 60, No. 12, Theory of the Porosity Dependence pp. 1181-1184 (1988).
of Bulk Moduli, Journal of the 67. M. Suzuki, Y. Okuda, I. Iwasa, A. J. American Ceramic Society, Vol. 84, Ikushima, T. Takabatake, Y.
No. 5, pp. 1190-1192 (2001). Nakazawa, and M. Ishikawa, Sound 61. A. Migliori, T. Chen, B. Alavi, and Velocity and Attenuation in G. Griiner, Ultrasound Anomaly at YBa Cu O Japanese Journal of 2 3 y , T in YBa Cu O Solid State Applied Physics, Vol. 27, No. 3, c 2 3 y , Communications, Vol. 63, No. 9, pp. L308-L310 (1988).
pp. 827-829 (1987). 68. M. Saint-Paul, J. L. Tholence, P.
62. Y. Horie, Y. Terashi, H. Fukuda, T. Monceau, H. Noel, J. C. Levet, M.
Fukami, and S. Mase, Ultrasonic Potel, P. Gougeon, and J. J. Capponi, Studies the of High Tc Ultrasound Study of YBa2 Cu 3 0 7 . 6 Solid Single Crystals, Solid Superconductor Y 2 Ba4 Cu6 0 ]4 , State State Communications, Vol. 64, Communications, Vol. 66, No. 6, No. 4, pp. 501-504(1987). pp. 641-643 (1988).
63. G. Cannelli, R. Cantelli, F. Cordero, 69. S. Bhattacharya, M. J. Higgins, D. C.
G. A. Costa, M. Ferretti, and G. L. Johnston, A. J. Jacobson, J. P.
Olcese, Anelastic Relaxation in the Stokes, J. T. Lewandowski, and D. P. Ultrasound High-Tc Superconductor Goshom, Anomalous in YBa 2 Cu3 0 7. x , Physical Review B, Propagation High-Tc
Vol. 36, No' 16, 8907-8909 Superconductors: La, Sr Cu0 . pp. 8 0 2 4 y Physical (1987). and YBaXu 3 0 7 . 6 , Review 64. S. Ewert, S. Guo, P. Lemmens, F. B, Vol. 37, No. 10, pp. 5901-5904
Stellmach, J. Wynants, G. Arlt, D. (1988). Bonnenberg, H. Kliem, A. Comberg, 70. S. Hoen, L. C. Bourne, C. M. Kim, and H. Passing, Ultrasonic and A. Zettl, Elastic Response of
- 15 - Polycrystalline and Single-Crystal Mechanical Properties of Some Physical B, Commerical Alumina Ceramics, YBa^Cu 3 0 7 , Review Vol. 38, No. 16, pp. 11949-11951 Proceedings of the British Ceramic (1988). Society, Vol. 6, pp. 71-82 (1966). 71. X. D. Shi, R. C. Yu, Z. Z. Wang, N. 79. E. Schreiber and O.L. Anderson, P. Ong, and P. M. Chaikin, Sound Pressure Derivatives of the Sound Velocity and Attenuation in Single- Velocities of Polycrystalline Physical Journal the Crystal YBa2 Cu 3 0 7 _ 6 , Alumina, of American Review B, Vol. 39, No. 1, Ceramic Society, Vol. 49, pp. 827-830 (1989). pp. 184-190(1966). 72. P. K. Choi, H. Koizumi, K. Takagi, 80. N. Soga and O.L. Anderson, and T. Suzuki, Anomalies of High-Temperature Elastic Properties Velocity in Polycrystalline Ultrasonic High-Tc of MgO and A1 2 0 3 , Ceramics YBa Cu O and Journal of the American Ceramic 2 3 y BiSrCaCu Solid State Society, Vol. 49, No. 355-359 2 O v , 7, pp. Communications, Vol. 70, No. 12, (1966).
pp. 1175-1178 (1989). 8 1 . D.H. Chung and G. Simmons, 73. N.N. Ault and H.F.G. Ueltz, Sonic Pressure and Temperature Analysis for Solid Bodies, Journal of Dependences of the Isotropic Elastic the American Ceramic Society, Moduli of Polycrystalline Alumina,
Vol. 36, No. 6, pp. 199-203 (1953). Journal of Applied Physics, Vol. 39, 74. R.L. Coble and W.D. Kingery, Effect No. 11, pp. 5316-5326 (1968). of Porosity on Physical Properties of 82. A. Nagarajan, Ultrasonic Study of Sintered Alumina, Journal of the Elasticity-Porosity Relationship in American Ceramic Society, Vol. 39, Polycrystalline Alumina, Journal of No. 11, pp. 377-385 (1956). Applied Physics, Vol. 42, No. 10, 75. J.B. Wachtmanjr. and D.G. Lam,Jr., pp. 3693-3696(1971). Young's Modulus of Various 83. J.C. Wang, Young's Modulus of
Refractory Materials as a Function of Porous Materials, Part 2, Young's Temperature, Journal of the Modulus of Porous Alumina with American Ceramic Society, Vol. 42, Changing Pore Structure, Journal of
No. 5, pp. 254-260(1959). Materials Science, Vol. 19, 76. F.P. Knudsen, Effect of Porosity on pp. 809-814(1984). Young's Modulus of Alumina, 84. C.C. Wu and R.W. Rice, Porosity Journal of the American Ceramic Dependence of Wear and Other
Society, Vol. 45, No. 2, pp. 94-95 Mechanical Properties of Fine-Grain
(1962). A1 2 0 3 and B 4 C, Ceramic Engineering 77. R.M. Spriggs, J.B. Mitchell, and T. and Science Proceedings, Vol. 6, Vasilos, Mechanical Properties of pp. 977-993 (1985). Pure, Dense Aluminum Oxide as a 85. H. Hagiwara and D.J. Green, Elastic Function of Temperature and Grain Behavior of Open-Cell Alumina, Size, Journal of the American Journal of the American Ceramic
Ceramic Society, Vol. 47, No. 7, Society, Vol. 70, No. 1 1, pp. 323-327 (1964). pp. 811-815 (1987). 78. D.B. Binns and P. Popper, 86. T. Goto and O.L. Anderson, Elastic
- 16 - Constants of Corundum up to 1 825 Strength of Porous Alumina During K, Journal of Geophysical Research, Sintering, Journal of the European Vol. 94, No. B6, pp. 7588-7602 Ceramic Society, Vol. 20, pp. (1989). 2561-2568 (2000).
87. D.J. Green, C. Nader, and R. Brezny, 94. D. Dierickx, I. Houben. J. Lapin, F. The Elastic Behavior of Delannay, O. Van Der Biest, Dense
Partially-Sintered Alumina, Ceramic Polycrystalline BaZr0 3 Substrates
Transactions, Vol. 7, pp. 345-356 for YBa 2 Cu 3 0 7 _ x Melt Processing, (1990). Journal of Materials Science Letters,
88. J. Kubler, Weibull Characterization Vol. 15, pp. 1573-1576 (1996). of Four Hipped/Posthipped 95. K.C. Goretta, E.T. Park, R.E. Engineering Ceramics Between Koritala, M.M. Cuber, E.A. Pascual, Room Temperature and 1500 °C, N. Chen, A.R. de Arellano-Lopez, Report Number: EMPA-Nr. 129747, and J.L. Routbort, EMPA Swiss Federal Laboratories Thermomechanical Response of
for Materials Testing and Research, Polycrystalline BaZr0 3 , Physica C, pp. 1-88 (1992). Vol. 309, pp. 245-250(1998). 89. D.C. Lam, F.F. Lange, and A.G. 96. B. A. Chandler, E. C. Duderstadt,
Evans, Mechanical Properties of and J. F. White, Fabrication and Partially Dense Alumina Produced Properties of Extruded and Sintered from Powder Compacts, Journal of BeO, Journal of Nuclear Materials,
the American Ceramic Society, Vol. Vol. 8, No. 3, pp. 329-347 (1963).
77, No. 8, pp. 2113-2117 (1994). 97. R.E. Fryxell and B.A. Chandler,
90. J. Piekarczyk, J. Lis, and J. Creep, Strength, Expansion, and Bialoskorski, Elastic Properties, Elastic Moduli of Sintered BeO as a Hardness and Indentation Fracture Function of Grain Size, Porosity, and Toughness of P-Sialons, Key Grain Orientation, Journal of the Engineering Materials, Vol. 89, American Ceramic Society, Vol. 47,
pp. 541-546(1994). No. 6, pp. 283-291 (1964).
91 . K. S. Tan, P. Hing, and P. 98. Y. He, J. Xiang, S. Jin, A. He, and J. Ramalingam, The Elastic Moduli Zhang, Ultrasonic Investigation of and Diametrical Compressive the Layered Perovskite Ceramic Fracture Stress of Al 2 0 3 -Zr0 2 Superconducting Systems, Physica Ceramics, Journal of Physics D: B, Vol. 165&166, pp. 1283-1284 Applied Physics, Vol. 30, (1990). pp. 1029-1037(1997). 99. R. R. Reddy, M. Muralidhar, V. H. 92. A. Wolfenden, Measurement and Babu, and P. V. Reddy, The Analysis of Elastic and Anelastic Relationship Between the Porosity Properties of Alumina and Silicon and Elastic Moduli of the
Carbide, Journal of Materials Bi-Pb-2212 High-Tc Superconductor, Science, Vol. 32, pp. 2275-2282 Superconductor Science and
(1997). Technology, Vol. 8, pp. 101-107 93. B.D. Flinn, R.K. Borida, A. (1995).
Zimmermann, and J. Rodel, 100. M. Muralidhar, K.N. Kishore, Y. V. Evolution of Defect Size and Ramana, and V. H. Babu, Elastic and
- 17 - Plastic Behaviour of Lead and Silver American Ceramic Society, Vol. 52,
Doped Bi-Sr-Ca-Cu-Q No. 9, pp. 492-496(1969). Superconductors, Materials Science 107. A. A. Sharif, F. Chu, A. Mirsa, T. E.
and Engineering B, Vol. 13, Mitchell, and J. J. Petrovic, Elastic pp. 215-219(1992). Constants of Erbia Single Crystals, 101. S. Satyavathi, M. Muralidhar, V. H. Journal of the American Ceramic Babu, R. R. Reddy, and P. V. Reddy, Society, Vol. 83, No. 9, Elastic Behaviour of pp. 2246-2250 (2000).
Superconducting 108. J. A. Haglund and O. Hunterjr., Bi-Pb-Ag-Ca2 Cu0 3 Composite Materials, Journal of Elastic Properties of Polycrystalline
Alloys and Compounds, Vol. 209, Monoclinic Gd 2 0 3 , Journal of the pp. 329-335 (1994). American Ceramic Society, Vol. 56, 102. R J. Topare, K. Ganesh, N. K. No. 6, pp. 327-330 (1973).
Sahuji, S. S. Shah, and P. V. Reddy, 109. S. L. Dole, O. Hunterjr., and C. J. Elastic Anomalies in Bi-Pb-2223/Ag Wooge, Elastic Properties of Superconducting Composite Monoclinic Hafnium Oxide at Room Materials, Physica C, Vol. 253, Temperature, Journal of the pp. 89-96(1995). American Ceramic Society, Vol. 60, 103. O. O. Oduleye, S. J. Penn, and N. No. 11, pp. 488-490(1977). McN. Alford, The Mechanical 110. R. W. Scheidecker, O. Hunterjr., Properties of (Bi-Pb)SrCaCuO, and F. W. Calderwood, Elastic Superconductor Science and Properties of Partially-Stabilized
Technology, Vol. 1 1, pp. 858-865 HfO, Compositions, Journal of (1998). Materials Science, Vol. 14, 104. W. R. Manning, M. O. Marlowe, and pp. 2284-2288 (1979). D. R. Wilder, Temperature and 111. S. L. Dole, O. Hunter, Jr., and F. W. Porosity Dependence of Young's Calderwood, Elastic Properties of
Modulus of Polycrystalline Stabilized Hf0 2 Compositions, Dysprosium Oxide and Erbium Journal of the American Ceramic
Oxide, Journal of the American Society, Vol. 63, No. 3, pp. 136-139 Ceramic Society, Vol. 49, No. 4, (1980).
pp. 227-228 (1966). 112. S. L. Dole and O. Hunter, Jr., Elastic
105. W. R. Manning, O. Hunter, Jr., and Properties of Hafnium and
B. R. Powell, Jr., Elastic Properties Zirconium Oxides Stabilized with of Polycrystalline Yttrium Oxide, Praseodymium or Terbium Oxide, Dysprosium Oxide, Holmium Oxide, Journal of the American Ceramic
and Erbium Oxide: Room Society, Vol. 66, No. 3, pp. C-47- Temperature Measurements, Journal C-49 (1983).
of the American Ceramic Society, 113. G. W. Crabtree, J. W. Downey, B. K.
Vol. 52, No. 8, pp. 436-442 (1969). Flandermeyer, J. D. Jorgensen, T. E.
106. W. R. Manning and O. Hunter, Jr., Klippert, D. S. Kupperman, W. K.
Elastic Properties of Polycrystalline Kwok, D. J. Lam, A. W. Mitchell, A.
Yttrium Oxide, Holmium Oxide, and G. McKale, M. V. Nevitt, L. J. Erbium Oxide: High-Temperature Nowicki, A. P. Paulikas, R. B.
Measurements, Journal of the Poeppel, S. J. Rothman, J. L.
- 18 - Roubort. J. P. Singh, C. H. Sowers, Coarse-Grained, Transparent
J. at Elevated Temperatures, A. Umezawa, B. W. Veal, and E. MgAl 2 04 Baker, Fabrication, Mechanical Journal of the American Ceramic Properties, Heat Capacity, Oxygen Society, Vol. 75, No. 12, Diffusion, and the Effect of Alkali pp. 3440-3444(1992). R. Martinez, and P. Pena, Earth Ion Substitution on High T c 121. C. Baudin, Superconductors, Advanced Ceramic High-Temperature Mechanical
Materials, Vol. 2, No. 3B, Behavior of Stoichiometric pp. 444-456 (1987). Magnesium Spinel, Journal of the
114. A. J. Zaleski and J. Klamut, American Ceramic Society, Vol. 78,
Penetration Depth in Magnetically No. 7, pp. 1857-1862 (1995). Oriented, Ceramic, Ni- and 122. K. R. Janowski and R. C. Rossi, Elastic Behavior of Matrix Zn-doped La2 . x Srx Cu04 , Physica C, MgO Vol. 282. pp. 1463-1464 (1997). Composites, Journal of the American
115. W. R. Manning and O. Hunter, Jr., Ceramic Society, Vol. 50, No. 1 1, Elastic Properties of Polycrystalline pp. 599-603 (1967). Thulium Oxide and Lutetium Oxide 123. N. Soga and E. Schreiber, Porosity from 20 °C to 1000 °C, Journal of Dependence of Sound Velocity and the American Ceramic Society, Poisson's Ratio for Polycrystalline
Vol. 53, No. 5, pp. 279-280 (1970). MgO Determined by Resonant
116. O. Hunter, Jr. and G. E. Graddy, Jr., Sphere Method, Vol. 51, No. 8, Porosity Dependence of Elastic pp. 465-466(1968).
Properties of Polycrystalline Cubic 124. Y. Sumino, O. L. Anderson, and I. the Suzuki, Temperature Coefficients of Lu 2 0 3 , Journal of American
Ceramic Society, Vol. 59, No. 1, Elastic Constants of Single Crystal pp. 82-82 (1976). MgO between 80 K and 1300 K,
117. D. F. Porter, J. S. Reed, and D. Physics and Chemistry of Minerals,
Lewis, Elastic Moduli of Refractory Vol. 9, pp. 38-47 (1983). Spinels, Journal of the American 125. D. G. Isaak, O. L. Anderson, and T.
Ceramic Society, Vol. 60, No. 7, Goto, Measured Elastic Moduli of
pp. 345-349 (1977). Single-Crystal MgO up to 1 800 K, 118. R. L. Stewart and R. C. Bradt, Physics and Chemistry of Minerals, Vol. Fracture of Polycrystalline MgAl 2 04 , 16, pp. 704-713 (1989). Journal of the American Ceramic 126. R. A. Penty, D.P.H. Hasselman, and
Society, Vol. 63, No. 1 1, R. M. Spriggs, Young's Modulus of pp. 619-623 (1980). High-Density Polycrystalline 119. A. Ghosh, K. W. White, M. G. Mullite, Journal of the American
Jenkins, A. S. Kobayashi, and R. C. Ceramic Society, Vol. 55, No. 3, Bradt, Fracture Resistance of a pp. 169-170(1972). Transparent Magnesium Aluminate 127. K. S. Mazdiyasni and L. M. Brown, Spinel, Journal of the American Synthesis and Mechanical Properties
Ceramic Society, Vol. 74, No. 7, of Stoichiometric Aluminum Silicate pp. 1624-1630(1991). (Mullite), Journal of the American 120. K. W. White and G. P. Kelkar, Ceramic Society, Vol. 55, Fracture Mechanisms of a pp. 548-552 (1972).
- 19 - 128. B. L. Metcalfe and J. H. Sant, The Physics, Vol. 24, No. 8, pp. 988-997 Synthesis, Microstructure and (1953). Physical Properties of High Purity 136. S. Spinner, Journal of the American
Mullite, Transactions of the British Ceramic Society, Vol. 37, No. 5, Ceramic Society, Vol. 74, pp. 229-234 (1954). pp. 193-201 (1975). 137. S. Spinner, Elastic Moduli of Glasses 129. M.G.M.U. Ismail, Z. Nakai, and S. at Elevated Temperatures by a Somiya, Microstructure and Dynamic Method, Journal of the Mechanical Properties of Mullite American Ceramic Society, Vol. 39, Prepared by the Sol-Gel Method, pp. 113-118 (1956).
Journal of the American Ceramic 138. H. J. McSkimin, Measurement of
Society, Vol. 70, No. 1, pp. C-7-C-8 Ultrasonic Wave Velocities and (1987). Elastic Moduli for Small Solid
130. M. I. Osendi and C. Baudin, Specimens at High Temperatures, Mechanical Properties of Mullite Journal of the Acoustical Society of
Materials, Journal of the European America, Vol. 31, No. 3, pp. 287-295 Ceramic Society, Vol. 16, (1959). pp. 217-224(1996). 139. E. H. Camevale, L. C. Lynnworth, 131. C. Baudin, Fracture Mechanisms in a and G. S. Larson, Ultrasonic
Stoichiometric 3Al 2 0 3 -2Si0 2 Measurement of Elastic Moduli at Mullite, Journal of Materials Elevated Temperatures, using Science, Vol. 32, pp. 2077-2086 Momentary Contact, Journal of the (1997). Acoustical Society of America,
132. H. Ledbetter, S. Kim, D. Balzar, S. Vol. 36, No. 9, pp. 1678-1684 Crudele, and W. Kriven, Elastic (1964). Properties of Mullite, Journal of the 140. M. Fukuhara and A. Sanpei, High American Ceramic Society, Vol. 81, Temperature-Elastic Moduli and
No. 4, pp. 1025-1028 (1998). Internal Dilational and Shear 133. A. K. Yahya and R. Abd-Shukor, Frictions of Fused Quartz, Japanese Ultrasonic Velocity Measurements Journal of Applied Physics, Vol. 33,
on PrBa2 Cu3 0 7 .§ (6=0.1, 0.5), pp. 2890-2893 (1994). Physica B, Vol. 252, pp. 237-243 141. M. Fukuhara, A. Sanpei, and K. (1998). Shibuki, Low Temperature Elastic
134. S. L. Dole, O. Hunter, Jr., and F. W. Moduli, Debye Temperature and Calderwood, Elastic Properties of Internal Dilational and Shear Polycrytalline Scandium and Frictions of Fused Quartz, Journal of Thulium Sesquioxides, Journal of the Materials Science, Vol. 32, American Ceramic Society, Vol. 60, pp. 1207-1211 (1997).
No. 3, pp. 167-168 (1977). 142. S. Spinner, Temperature Dependence
135. H. J. McSkimin, Measurement of of Elastic Constants of Vitreous Elastic Constants at Low Silica, Journal of the American Temperatures by Means of Ceramic Society, Vol. 45, No. 8, Ultrasonic Waves - Data for Silicon pp. 394-397(1962).
and Germanium Single Crystals, and 143. O. Hunter, H. J. Korklan, and R. R. for Fused Silica, Journal of Applied Suchomel, Elastic Properties of
- 20 - Polycrystalline Monoclinic Sm 2 0 3 , pp. 835-836 (1984).
Journal of the American Ceramic 152. V. M. Baranov, Y. K. Bibilashvili, I.
Society, Vol. 57, No. 6, pp. 267-268 S. Golovnin, V. N. Kakurin, T. S. (1974). Men’shikova, Y. V. Miloserdin, and 144. S. Spinner, F. P. Knudsen, and L. A. V. Rimashevskii, In-Reactor Stone, Elastic Constant-Porosity Measurements of the Modulus of Relations for Polycrystalline Thoria, Elasticity of Uranium Dioxide, Journal of Research of the National Soviet Atomic Energy, Vol. 40, No. Bureau of Standards, Vol. 67C, No. l,pp. 37-39(1976).
1, pp. 39-46 (1963). 153. J. P. Panakkal, Use of Longitudinal 145. W. P. Minnear and R. C. Bradt, Ultrasonic Velocity as a Predictor of Elastic Properties of Polycrystalline Elastic Moduli and Density of Journal of the Sintered Dioxide, Ti0 2 . x , American Uranium IEEE Ceramic Society, Vol. 60, No. 9, Transactions on Ultrasonics, pp. 458-459(1977). Ferroelectrics, and Frequency
146. J. Li, S. Forberg, and L. Hermansson, Control, Vol. 38, No. 3, pp. 161-165 Evaluation of the Mechanical (1991). Properties of Hot Isostatically 154. V. Roque, B. Cros, D. Baron, and P. Pressed Titania and Titania-Calcium Dehaudt, Effects of the Porosity in Phosphate Composites, Biomaterials, Uranium Dioxide on Microacoustic
Vol. 12, pp. 438-440(1991). and Elastic Properties, Journal of 147. O. Anderson, C. R. Ottermann, R. Nuclear Materials, Vol. 277, Kuschnereit, P. Hess, and K. Bange, pp. 211-216 (2000). Density and Young's Modulus of 155. D. P. Almond, E. Lambson, G. A. Journal Thin Ti0 2 Films, Fresenius Saunders, and W. Hong, An of Analytical Chemistry, Vol. 358, Ultrasonic Study of the Elastic pp. 315-318 (1997). Properties of the Normal and
148. D. G. Isaak, J. D. Carnes, O. L. Superconducting States of Anderson. H. E. Hake, Journal of Physics F: Cynn, and YBa2 Cu 3 0 7 . 6 , Physics and Chemistry of Minerals, Metal Physics, Vol. 17, Vol. 26,31-43 (1998). pp. L221-L224 (1987).
149. J. B. Wachtman, Jr. and M. L. 1 56. N. McN. Alford, J. D. Birchall, W. J. Wheat, Elastic Constants of Single Clegg, M. A. Harmer, K. Kendall, Crystal at U0 2 25 °C, Journal of and D. H. Jones, Physical and Nuclear Materials, Vol. 16, pp. 39-41 Mechanical Properties of
(1965). YBa2 Cu 3 0 7 . 6 Superconductors,
1 50. A. Padel and Ch. de Novion, Journal of Materials Science, Constantes Elastiques des Carbures, Vol. 23, pp. 761-768 (1988).
Nitrures et Oxydes d’Uranium et de 157. M. Cankurtaran, G. A. Saunders, J. Plutonium, Journal of Nuclear R. Willis, A. Al-Kheffaji, and D. P. Materials, Vol. 33, pp. 40-51 (1969). Almond, Bulk Modulus and Its
151. J. P. J. Panakkal and K. Ghosh, Pressure Derivative of YBa2 Cu 3 0 7 . x , Ultrasonic Velocity in Sintered Physical Review B, Vol. 39, No. 4, Uranium Dioxide Pellets, Journal of pp^ 2872-2875 (1989).
Materials Science Letters, Vol. 3, 158. A. Al-Kheffaji, M. Cankurtaran, G.
-21 - A. Saunders, D. P. Almond, E. F. Properties of Fully Oxygenated
Lambson, and R. C. J. Draper, YBa2 Cu 3 0694 , Superconductor Elastic Behaviour under Pressure of Science and Technology, Vol. 7, Superconductors 4-9(1994). High-T c pp. = Y, and Eu), 165. P. V. Reddy, S. Shekar, and K. RBa 2 Cu 3 0 7 . x (R Gd Philosophical Magazine B, Vol. 59, Somaiah, Elasticity Studies of
No. 5, pp. 487-497 (1989). RE-Ba-Cu-O High-Tc
159. J. P. Singh, H. J. Leu, R. B. Poeppel, Superconductors, Materials Letters, E. Van Voorhees, G. T. Goudey, K. Vol. 21, pp. 21-29 (1994). Winsley, and D. Shi, Effect of Silver 166. H. Ledbetter, M. Lei, A. Hermann, and Silver Oxide Additions on the and Z. Sheng, Low-Temperature Elastic Mechanical and Superconducting Constants of Y,Ba 2 Cu 3 0 7 , Physica Vol. 397-403 Properties of YBa 2 Cu 3 0 7 . 6 C, 225, pp. Superconductors, Journal of Applied (1994).
Physics, Vol. 66, No. 7, 167. Z. Zhong, Y. Qianjin, T. Xinlu, Z. pp. 3154-3159 (1989). Lizhong, W. Qimin, and Z. Peiqiang, 160. B. Bridge and R. Round, Density The Dynamical Mechanical Dependence of the Ultrasonic Properties of YBCO Superconductor, Properties Sintered Vol. of High-T c Experimental Techniques, 18,
YBa2 Cu 3 0 7 _ x Superconductors, No. 4. pp. 25-27(1994). Journal of Materials Science Letters, 168. R. R. Reddy, O. M. Prakash, and R.
Vol. 8, pp. 691-694(1989). V. Reddy, The Effect of Porosity on 161. M. C. Bhardwaj and A. S. Bhalla, Elastic Moduli of YBa2 Cu 3 0 7 . 6 High Ultrasonic Characterization of Tc Superconductors, Applied Ceramic Superconductors, Journal of Superconductivity, Vol. 3, No. 4, Materials Science Letters, Vol. 10, pp. 215-222 (1995). pp. 210-213 (1991). 169. Q. Wang, G. A. Saunders, D. P. 162. M. Cankurtaran, G. A. Saunders, K. Almond, M. Cankurtaran, and K. C. C. Goretta, and R. B. Poeppel, Goretta, Elastic and Nonlinear Ultrasonic Determination of the Properties Acoustic of YBa 2 Cu 3 0 7 . x Elastic Properties and Their Pressure Ceramics with Different Oxygen and Temperature Dependences in Contents, Physical Review B, Very Dense YBa 2 Cu 3 0 7 . x , Physical Vol. 52, No. 5, pp. 3711-3726 Review B, Vol. 46, No. 2, (1995). pp. 1157-1165 (1992). 170. L. Masi, E. Borchi, and S. de 163. P. V. Reddy, R. R. Reddy, K. B. Gennaro, Porosity Behaviour of Reddy, and V. N. Mulay, Ulrasonic Ultrasonic Velocities in Anomalies in Y-Ba-Cu-0 High-Tc Polycrystalline Y-B-C-O, Journal of Superconducting Materials, Modem Physics F: Applied Physics, Vol. 29,
Physics Letters B, Vol. 7, No. 22, pp. 2015-2019(1996). pp. 1457-1465 (1993). 171. F. Yu, K. W. White, and R. Meng, 164. M. Cankurtaran, G. A. Saunders, and Mechanical Characterization of K. C. Goretta, Ultrasonic Study of Top-Seeded Melt-Textured the Pressure Crystal, Temperature and YBa 2 Cu3 0 7 _ 6 Single Dependences of the Elastic Physica C, Vol. 276, pp. 295-308,
- 22 - Y
91 (1997). Elastic Moduli of 2 0 3 + 9ThO,
172. F. Tancret, G. Desgardin, and F. from 25° to 1 100°C, Journal of the Osterstock, Influence of Porosity on American Ceramic Society, Vol. 51,
the mechanical Properties of Cold No. 4, pp. 233-234 (1968). Isostatically Pressed and Sintered 180. C. E. Holcombe, T. T. Meek, and N. Unusual Properties of YBa 2 Cu3 0 7 . x Superconductors, L. Dykes, Philosophical Magazine A, Vol. 75, Microwave-Sintered Yttria-2wt%
No. 2, pp. 505-523 (1997). Zirconia, Journal of Materials
1 73. P. V. Reddy and M. Murakami, Science Letters, Vol. 7, pp. 881-884 Elastic Behavior of Melt-Powder- (1988).
Melt-Growth Processed 181. B. R. Powell, Jr., O. Hunter, Jr., and Physics Elastic Properties YBa 2 Cu 3 0 7 _ 6 , Modem W. R. Manning, of Letters B, Vol. 13, No. 8, pp. Polycrystalline Ytterbium Oxide, 261-270(1999). Journal of the American Ceramic
174. R. Sreekumar, J. Isaac, J. Philip, K. Society, Vol. 54, No. 10, pp. V. Paulose, M. T. Sebastian, and A. 488-490(1971). D. Damodaran, Elastic and Thermal 182. L. P. Martin, D. Dadon, and M. Properties of Yttrium Barium Rosen, Evaluation of Ultrasonically
Zirconate, Physica Status Solidi (a), Determined Elasticity-Porosity Vol. 133, pp. 341-347(1992). Relations in Zinc Oxide, Journal of
1 75. M. O. Marlowe and D. R. Wilder, the American Ceramic Society,
Elasticity and Internal Friction of Vol. 79, No. 5, pp. 1281-1289 Polycrystalline Yttrium Oxide, (1996). Journal of the American Ceramic 183. A. K. Mukhopadhyay, M. R.
Society, Vol. 48, No. 5, pp. 227-233 Chaudhuri, A. Seal, S. K. Dalui, M. (1965). Banerjee, and K. K. Phani,
176. W. R. Manning and O. Blunter, Jr., Mechanical Characterization of Porosity Dependence of Young’s and Microwave Sintered Zinc Oxide, Shear Moduli of Polycrystalline Bulletin of Materials Science,
Yttrium Oxide, Journal of the Vol. 24, No. 2, pp. 125-128 (2001). American Ceramic Society, Vol. 51, 184. C. F. Smith and W. B. Crandall,
No. 9, pp. 537-538 (1968). Calculated High-Temperature Elastic 177. O. Yeheskel and O. Tevet, Elastic Constants for Zero Porosity Moduli of Transparent Yttria, Monoclinic Zirconia, Journal of the Journal of the American Ceramic American Ceramic Society, Vol. 47,
Society, Vol. 82, No. 1, pp. 136-144 No. 12, pp. 624-627(1964).
(1999). 185. J. W. Adams, R. Ruh, and K. S.
1 78. J. W. Palko, W. M. Kriven, S. V. Mazdiyasni, Young's Modulus,
Sinogeikin, J. D. Bass, and A. Sayir, Flexural Strength, and Fracture of
Elastic Constants of Yttria (Y 2 0 3 ) Yttria-Stabilized Zirconia versus Monocrystals to High Temperatures, Temperature, Journal of the Journal of Applied Physics, Vol. 89, American Ceramic Society, Vol. 80, No. 12, pp. 7791-7796 (2001). No. 4, pp. 903-908 (1997). 179. R. W. Dickson and R. C. Anderson, 186. M. A. Ewaida, A. A. Higazy, B. Temperature Dependence of the Bridge, and M. M. Abou Sekkina,
- 23 - Elastic Constants of the Iron Oxide References added in proof: Doped Yttria-Stabilized Zirconia, Journal of Materials Science, Vol. 193. S. P. Timoshenko, On the Correction 24, pp. 3660-3666 (1989). for Shear of the Differential Equation 187. Y. Kubota, M. Ashizuka, E. Ishida, for Transverse Vibrations of and T. Mitamura, Influence of Prismatic Bars, Philosophical Temperature on Elastic Modulus and Magazine, Vol. 41, Sixth Series, Strength of MgO-Partially Stabilized pp. 744-746(1921). Zirconia (Mg-PSZ), Journal of the 194. E. Goens, Uber die Bestimmung des Ceramic Society of Japan, Vol. 102, Elastizitatsmoduls von Staben mit
No. 8, pp. 708-712 (1994). Hilfe von Beigungsschwingungen,
188. W. J. Wei and Y. Lin, Mechanical Annalen der Physik, 5 Folge, Band
1 and Thermal Shock Properties of 1 , Reihe 403, Heft 6, 649-678 Size Graded MgO-PSZ Refractory, (1931). Journal of the European Ceramic 195. F. Forster, Ein neues Messverfahren
Society, Vol. 20, pp. 1 159-1 167 zur Bestimmung des (2000). Elastizitatsmoduls und Dampfung,
1 89. Y. Kubota, M. Ashizuka, and H. Zeitschrift fur Metallkunde, Vol. 29, Hokazono, Elastic Modulus and No. 4, pp. 109-115 (1937). - Fracture Toughness of Ce02 Containing Tetragonal Zirconia Polycrystals, Journal of the Ceramic
Society of Japan, Vol. 102, No. 2, pp. 175-179(1994). 190. G. A. Gogotsi, V. P. Zavada, and M. V. Swain, Mechanical Property Characterization of a 9 mol% Ce-
TZP Ceramic Material, I: Flexural Response, Journal of the European
Ceramic Society, Vol. 15, pp. 1185-1192 (1995). 191. Z. Zhang, D. Jin, L. Li, Z. Tu, L.
Zhao, P. Zhang, and J. Zhao, Fracture Strength and Dynamic Elastic Modulus of Ce- and Er-TZP at Low Temperature, Journal of the American Ceramic Society, Vol. 78,
No. 9, pp. 2548-2550(1995).
192. J. Luo and R. Stevens, Porosity-Dependence of Elastic Moduli and Hardness of 3Y-TZP Ceramics, Ceramics International, Vol. 25, pp. 281-286 (1999).
- 24 - 1
8. Index of materials
Section Material Designation Section Material Designation
9.1 AUOj { aluminum oxide } 9.28 Sc,0 3 { scandium oxide }
silica 9.2 Al 6 Si,0 13 { mullite } 9.29 SiO, { }
9.3 BaZrOj { barium zirconate } 9.30 SmBa 2 Cu 3 0 7 . x { Sm:123 }
9.4 BeO { beryllium oxide } 9.31 Sm,0 3 {samarium oxide }
9.5 Bi 2 Sr2 CaCu2 Og+x { Bi:22 1 2 } 9.32 Th0 2 { thorium dioxide }
Bi Sr titanium dioxide 9.6 2 . x Pb x 2 CaCu 2 0 8+v { Bi(Pb):2212 } 9.33 TiO, { }
9.7 Bi,. Pb Sr Ca Cu . Bi(Pb):2223 9.34 thulium oxide x x 2 2 3 O l0 y { } Tm 2 0 3 { }
9.8 Dy,0 3 { dysprosium oxide } 9.35 U0 2 {uranium dioxide }
9.9 Er erbium { 1 2 0 3 { oxide } 9.36 YBa2 Cu 3 0 7 . x Y: 23 }
9.10 Gd 2 0 3 { gadolinium oxide } 9.37 YBa2Zr06 {yttrium barium zirconate}
9.1 HfO, { monoclinic hafnia } 9.38 Y 2 0 3 { yttrium oxide }
9.12 HfO • xEr 0 partially stabilized hafnia 9.39 Y 0 • xThO, Th-doped yttria : 2 3 { } 2 3 { }
• partially stabilized • 9.13 HfO, xEu 2 0 3 { hafnia } 9.40 Y 2 0 3 xZrO, { Zr-doped yttria }
9.14 partially stabilized hafnia 9.41 Hf0 2 xY 2 0 3 { } Yb2 0 3 { ytterbium oxide }
9.15 • 9.42 HfO, xX 2 0 3 { partially stabilized hafnia } ZnO { zinc oxide }
9.16 • 9.43 HfO ; xEr2 0 3 { cubic hafnia } Zr0 2 {monoclinic zirconia }
9.17 cubic hafnia 9.44 • {partially HfO, xGd 2 0 3 { } ZrO, xMgO stabilized zirconia }
9.18 • • HfO, xPr2 0 3 { cubic hafnia } 9.45 ZrO, xCaO {cubic zirconia }
9.19 • • HfO ; xTb 2 0 3 { cubic hafnia } 9.46 Zr0 2 xPr2 0 3 {cubic zirconia }
9.20 • • Hf0 2 xY 2 0 3 { cubic hafnia } 9.47 Zr0 2 xTb 2 0 3 {cubic zirconia }
9.21 • 9.48 HfO, xX 2 0 3 { cubic hafnia } Zr0 2 xY 2 0 3 {cubic zirconia }
9.22 9.49 • • Ho 2 0 3 { holmium oxide } Zr0 2 xY 2 0 3 yFe 2 0 3 {cubic zirconia }
• 9.23 La . Sr Cu0 . La(Sr):21 9.50 Zr0 xX,0 {cubic zirconia 2 x x 4 y { } 2 3 }
9.24 Lu 2 0 3 { lutetium oxide } 9.51 ZrO ; xCe0 2 {tetragonal zirconia, TZP }
spinel • 9.25 MgAI 2 04 { magnesium aluminate } 9.52 Zr0 2 xEr2 0 3 {tetragonal zirconia, TZP }
9.26 • MgO { magnesium oxide } 9.53 Zr0 2 xY 2 0 3 {tetragonal zirconia, TZP }
9.27 Pr: PrBa 2 Cu 3 0 7 . x { 123 }
- 25 - .
9. Data
The data are organized alphabetically by the chemical formula of the material. Each material begins a new subsection. For example, the subsection for the first material, alumina, is oxide, labeled: 9.1 A1 2 0 3 { aluminum alumina }.
The first component of each subsection is an introductory page providing descriptive information, including the chemical formula, generic name(s), relative molecular mass M a.k.a r ( single density). molecular weight), and theoretical density p theo {a.k.a. crystal density and x-ray When sufficient data have been available, the parameters determined by fitting Eq. (15) and Eq. (16) to the data are also listed. Since the reported data actually pertain to E and G, the nonlinear fitting routine is applied to Eqs. (15) and (17) and using Eq. (16) for B. When the data are inadequate, it is sometimes possible to obtain useful estimates by combining data sets for similar materials (which might, for example, use different sintering aids or stabilizers). Values estimated in this manner are indicated by values in curly brackets, { }.
The second component of each subsection, contained also on the introductory page, is a collection of graphs showing, as available, the porosity dependence at room temperature, the temperature dependence at fixed porosity, and the fit of Eqs. (15) and (16). When the data set has been adequate for fitting the model, solid curves represent the fits to E and G and dashed curves for the derived quantities, B and v. When other noted approximations have been needed to estimate the parameters in the model, the results are shown as dashed curves.
The third and final component of the information set is a table of data giving the property values as extracted from the references. The data tables are labeled with the number of the subsection and the table page sequence number. For example, the pages in the data table for alumina are labeled from 9.1.1 through 9.1.16. Indicated in each table are the measurement method, the exhibit type (graph, table, or text), the exhibit number (figure number, table number, or page number), the value type (experimental, smoothed, or calculated), the measurement condition (temperature), the material condition (density or porosity), and the corresponding property value.
Further information regarding the composition and processing of individual specimens may be given in footnotes to the tables. Footnote numbers are cited in the column labeled Ft.Nt. in the data tables. Footnotes immediately follow the end of the table in which they are cited.
- 26 - Summary of the symbols used in the tables andfigures:
M : relative molecular mass ( a.k.a . molecular weight) x
: theoretical density {a.k.a. single crystal density, x-ray density) p theo
(15)*. , : parameters for Eq. E0 , a n
b, for Eq. (16)*. : parameters B0 , m ‘Values in {} are estimated with additional assumptions.
x : experimental data
s : smoothed values
c : calculated values
subscript is in figures to denote £bend : The “bend” used some a static modulus determined by means of a bend test.
n/a : not available (usually due to insufficient data)
3pt : three-point
4pt : four-point
flex. : flexure
meth : method
rec.par. : rectangular parallelepiped
res. : resonance
SAWS : surface acoustic wave spectroscopy
ult. : ultrasonic
Ref. Nbr. : reference number Ft. Nt. : foot note
Exh. Type : exhibit type Exh. Nbr. : exhibit number
Mtl. Nbr. : material number T : temperature
Vol. Frac. : volume fraction Long. : longitudinal
- 27 - 1
oxide, 9.1 A1 2 0 3 { aluminum alumina }
1 = M / mol' = 101.961 Temperature range / (°C) Oto 1000 r (g ) 3 = = Ptheo/(g cm" ) 3.984 Porosity range 0 to 0.9
= = E0 / (GPa) 393 BJ (GPa) 241 4o 4o a/(10 C) = 1.33 b / (10" C) = 0.84
77 = 3.06 m = 3.33
= o = A = 1 r- 0 00 [86] 0 01 [74] 0.37 [74] 1 0 0 0 500 1 ' 0 = 0.07 [75] V = 0.20 [74] 0 0=0.43 [74] Al,0, at 23 °C [16] © [83]
Modulus 100 !
0 1
1 . 1 . 1 i_ 1 J i 0.0 0.2 0.4 0.6 0.8 1.0
Volume Fraction of Porosity (
o 0 1
Modulus a
0 A
l i I i i
0.0 0.2 0.4 0.6 0.8 1.
Volume Fraction of Porosity ((j>) — —
— ” — T— t T T T— T— T“ T— 1 1 £ Nt.
CD
M" 0.17 0.254 0.221 0.236 CM 0.239 0.232 0.224 0.187
Ratio O Poisson's ! CO 53.3 264.5 212.9 241.5 234.9 228.9 o 157.9 123.5 Bulk Modulus GPa CM
00 r-- 97.7 47.9 CO 132.1 156.5 145.3 154.8 144.5 oco Shear Modulus GPa
1 CD o 287.2! 395.8 355.5 382.4 358.3 358.0 325.5 261.2 231.7 110.9 326.6 326.6 326.0 325.4 319.1 309.5 306.6 305.5 CM 300.9 298.6 296.9 295.2 294.6 294.0 292.9 292.9 290.6 288.3 288.3 T— O Elastic Modulus GPa CO CO
Shear Velocity km/s
Velocity km/s Long.
600
Vol.Frac. Porosity
o to r-. 3.64 E 3.942 3.904 3.902 3.824 3.825 3.714 3.335 2.850 Density 0 CO 01
CO T— CO CO CO 23 23 CO CO 23 o r- CM CO oo CO o CM CM CM CM CM CM CM co 105 152 210 305 342 CD CO 422 443 459 480 497 518 539 564 oo 597 o CM CO CO m 5 CD
Mtl. Nbr.
CM CO in CD r-'- CO O)
} of
resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance
Determination
Method alumina
resonance resonance resonance resonance resonance resonance resonance resonance resonance
sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic
oxide, aa> Value > t— X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
Nbr. aluminum Exh. CO CO CO CO CO CO CO CO CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM
{ Exh. Type Table Table Table Table Table Table Table Table Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 Q2 Ref. Nbr. CD CD CD CD CD CD CD CD CD CO CO 1 CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO AI | s 1^- I - r"- r-- r*- r^- | * T_ ’r r— T_ CM CM CM CM CM CM CM CM CM CM Ft. Nt.1
m CO CM 0.27 0.26 0.32 0.29 d O
Ratio Poisson's
Bulk Modulus GPa
Shear Modulus GPa
00 CT> CO 00
CO 283.2 283.2 283.2 283.2 281.4 d d 279.7 276.8 279.1 d 282.6 282.6 281.5 282.1 286.6 288.4 292.4 324.9 00 oo 00 YLLZ oo Elastic Modulus GPa eg CM CM CM
i
Shear Velocity km/s
Velocity km/s Long.
o CM CO o CM 0.4 SO 0.3 0.4 d d o d d -9.1.2-
Vol.Frac. Porosity
ro E Density Ol
CO OO CD in 24 m m 25 25 o o o 664 681 702 723 749 782 o CM 866 946 997 964 867 804 765 702 659 601 559 500 CM CM CM CM o 009 009 o 009 H o 00 00 CD C0
2 Nbr.
} of
resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance
Determination
Method alumina
bending bending bending bending bending bending bending bending bending bending bending sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic
oxide,
Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X w JQ aluminum Exh. 2 eg CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM
CD 1 X3 { Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Table Table Table Table Table Table Table Table Table (Table CD h- 3 — 02 Al Ref. Nbr. CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO co CO CO CO CO CO Tl" (h- 1^- h- h- 1^- 1^- I"- h- r*- h- h- I''- h-
| | 1 — — — —
. LL 2
Ratio Poisson's
Bulk Modulus GPa
Shear Modulus GPa
298.5 300.6 291.6 289.5 282.0 273.0 255.1 228.9 245.4 243.4 239.9 232.3 220.6 211.0
Elastic Modulus GPa
Shear Velocity km/s
Velocity km/s Long.
in o CM CO in o T CM CO in o CM CO in o o oT o o o oT oT CM CM CM CM CM CM o’ d O d o* o o O d d d d d d d o o d d d d d d d o d d d o o -9.1.3-
Vol.Frac. Porosity
CO E Density u O)
o o o O o o o o o o in o o o o o m o o o o o o o O o o o o o o CM o o o o o CM o o o o o 1000 1000 1000 1000 1000 1000 1200 1200 1200 1000 1100 1000 o CD oo 00 OO oo oo 00 CM CM CM CM •M- CO as CM CM M- CD oo T—
m Nbr.
} of
Determination
Method alumina
pending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending
oxide, 0) Q. Value >. 1- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
uminum Exh. Nbr. to to to m m in in m m in m m to m al
{ Exh. Type Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 02 hi Ref. £2 '3’ Al 1^- s- 2 r^- r- £ r^- r- r^. r-- I FtJ Nt.
Ratio Poisson's 1
Bulk Modulus GPa
Shear Modulus GPa
CO 00 °0 CD 00 M" 92.4 196.5 171.7 188.2 186.1 181.3 176.5 174.4 153.7 o 121.3 154.4 152.4 150.3 CD 142.0 131.7 120.6 102.7 144.1 d 139.9 136.5 124.8 111.0 113.1 111.7 108.9 108.9 102.7 O' CM O’ O' O' OO h- Elastic Modulus GPa
Shear Velocity km/s
Velocity km/s Long.
CM CM CO CO eo CO CO 00 oo 00 in in m in in in in in i^- f" r-- CO CO CO CO CO CO CO 00 CM CM CM CM CM CM CM CM CO CO CO to CO CO CO CO co co co co CO co CO M- O O -9.1.4- d O d d d o d d d d d d d d d d d d d d d d d o o o o o’ o o’ o
Vol.Frac. Porosity
CO E Density o O)
in O O o o in o o o o m o o o o m o o o o CM O O o o CM o o o o CM o o o o CM o o o o o 1100 1200 1000 1100 1200 1000 1100 1200 1000 1100 1000 1100 1200 o CM "•a- CO CO CM •o- CD oo CM o- CD oo CM CD oo
n s z
} of
Determination
Method alumina
bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending
oxide,
Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
aluminum Exh. z to CD vo VO LO vn VO VO VO m in VO VO VO VO VO VO VO VO VO VO VO VO VO VO VO VO vn VO VO VO VO m a0) { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph; 3 H 02 iJ, Ref. £i Al ''d* M- M- M- o- o- <*d- s- s- Z r-- r-- f^- h- r- 1^ r^. h- I I 4-* yu Nt.
Ratio Poisson's
Bulk Modulus GPa
CO CD CM o 00 6 CD r-~ 00 CD 99.3 94.4 79.3 84.8 132.4 129.6 126.8 120.6 117.2 o CO d in OO CM CM o OO o CD 99 OO 00 00 Shear Modulus GPa
oo m- 00 00 T— eg CNI m CM CO CO in CD 86.9 CD 82.0 o> CD CD CT> CD 00 D- CO 00 OO 00 Elastic Modulus GPa
Shear Velocity km/s
Velocity km/s Long.
m m in m in in in i-" r-- r^- c- 00 oo oo 00 oo oo 00 OO 00 00 M- - 0.45 m- m- M Tf 0.47 o o o o o o o O O O CM d d d d d d d d d d d d d d d d d d d d d 0.155 0.155 0.155 0.155 0.155 0.155 0.224 0.224 CM 0.224
Vol.Frac. Porosity O
CO E Density O)
in o o o o o in o o o o in o o o o m o o o o m o in o CM o o o o o CM o o o o CM o o o o CM o o o o CM m l>- o o 1000 1100 1000 1100 1200 1250 1275 1000 H o CM m- CO oo CM CM -if CD CO CO m r~- CD CO m CD CD co m
Mtj. Nbr.
} of
Determination
Method alumina
bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending
oxide,
Value Type
um X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
Exh. .Q alumin LT) s- z m m in in in in in in in in in in i-— r^- r-'- I I"'- r^* r~- r^- r- r- r"~ r-- r-- r-
{ Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 Q2 I Ref. n q,3- Xf s- 1^- r^- r^- A 2 I h- 1^ ir>- 1 Ft. Kit.
Ratio Poisson’sj
n
Bulk Modulus GPa
CO CD T 00 62 r^- CO co 53.1 CO 46.9 36.5 58.6 57.2 53.8 48.3 29.6 49.6 50.3 46.2 00 46.2 41.4 36.5 35.2 34.5 34.5 34.5 26.9 23.4 CO OO 71 'S' CO o oo 00 CO CD CD CNJ co CO Shear Modulus GPa
Elastic Modulus GPa
Shear Velocity km/s
Velocity km/s Long.
m Tj- CM 0.4 0.4 0.4 0.4 0.51 0.51 0.51 0.51 0.51 ISO 0.51 0.51 ISO 0.51 -9.1.6- 0.325 0.325 0.325 o O o 0.224 0.325 0.325 0.325 0.325 o 0.224 0.224 0.224 0.224 0.224 CO o
Vol.Frac. Porosity d
to E Density u o»
o in o o in o o in o o o 700 o CM 400 o 009 o CM o 500 o 950 CM 200 400 500 o o o o 1000 1100 1200 1250 1000 1100 1250 1000 1100 1200 1250 1000 1100 1250 i— O OO in OO CO 00 CO 00 CM
Mtl. Nbr.
} of
Determination
Method alumina
bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending bending
oxide,
Value Type
um X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
Exh. Nbr. alumin h- r-~- i-'- h- h» r- r^- i^- r-'- r- h- r^- h- h- r-~ r" r-- f- IT"- i-- r~- r-- r-- r- i"- {
Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph (Graph 3 Q2 Ref. Nbr. 1 AI ^ ^ 1 r- r- b — — —
CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO <*=* Ft. z
Ratio Poisson's 1 m Bulk Modulus Oa.
« Shear Modulus 0. 0
—
CD o- cr> CD CO h- uo x— CO CM CD o in CO CM CM oo o o h- h- CD CO in in •<3- CD oo uo CM CD 308.5 294.9 1 278.9 276.4 274.4 269.3 265.8 262.8 257.3 245.7 — m CO CO 00 Z'ZLZ CO co CO CO CO CO CM CM CN CM T CO CO Elastic Modulus 0a. CM CM
w
Shear Velocity E
(A
Velocity Long. E =j£
CD 00 S900 co oo T OO O T CO O o CO o CO CD CD co O CM CM O o o 2300 O T“ T— T“ 0.206 CM CO CO O 0.057
Vol.Frac. Porosity d d d O d d o o d d d o d
CO h- r^ E CO CO Density o O)
CO CO o O o o o o o o o o o o CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO o CM CM o O o o in o n o in o in o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM i- o it to i"- CO oo CD CD o o CM T nu 2 z T T— CM CM
} of
resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance
Determination
Method alumina
dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic O O
sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic ro TO w V)
oxide, 0) a. Value >. K X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X kJ
aluminum Exh. n z = CO CO CO CO CO co CO CO CO CO co co co — aa) { Exh. >» Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 Q2 Ref. a m n in in n in in in in in LO in in in CO CD CD CD CD CO CD CD CD CD CD CD CD CD CD CD CD AI 1-" z i"- r'- i-'- r» f'- r-' f- I''- r-- t"- h- D- r— r- r~- C'- h- I"- D- D- r» r- i-'- r-~- — — —
in in m in CO CD CO CO Ft. z
0.2363
Ratio Poisson's
248.7 231.8 252.06 251.92
Bulk Modulus GPa
CD
161.6 157.5 161.32 CO— 'i Shear Modulus GPa
CO CD 00 OO 7 275 236 224 h- 306 213 o 103 124 110 CXD 390 CD 369 375 7 CM CO CO 398.5 385.3 eg CO 398.86 Elastic Modulus GPa
1 OO
CO 6.15 €0 5.93 6.373 6.377 CD CO 9 Shear Velocity km/s
10.845 10.845
Velocity km/s Long.
1 o CO CM o o r"- 00 0.350' CD -9.1.8- OSO'O 0.094 0.111 0.142 0.209 o 0.205 0.217 0.343 0.285 CO o 0.029 O 0.074 o 0.0035 moo Vol.Frac. Porosity d d o d d o
i"- eo 3.98 3.94 3.87 00 3.941 E CO 3.972 3.972 3.974 Density u O)
CO CO CO CO CO CO CO CO CO CO CO CO CO O CO CO CO CO m m in m CO CO CO CO CO o CM CNJ CNJ CM CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNJ CNI CO CNJ CNJ CNJ CNJ CM CM CM CM CNJ CNJ CNJ CNJ CNJ H o
Nbr. CM CM CM CM CM CO CO CO CO CM CO 7“ CM
} of echo echo echo echo echo res.
res. res.
interferometry
Determination
Method bending alumina pulse pulse pulse pulse pulse
dynamic dynamic ultrasonic
static static static static static static static static static static static static static 4pt sonic sonic sonic sonic ult. ult. ult. ult. ult. ult.
oxide,
Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X
aluminum Exh. Nbr. 7— 7— v— 7— 7 7— 7— 1 7— CM 7“ 7“ = CO CO CO CO CO xz { Q.
Type CC Table Table Table Table Table Table Table Table Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph b— Graph Graph Graph Graph Graph Graph Graph 3 o 02 Ref. n Al CO CO CO CO CO CO CO CD CO CO CO CD CO i— 00 00 00 OO CD O o CM CM CNJ CM CM 2 h- I-" r-~ I"~ I"- h~ f- i"- h~ I-- i-- r«- 00 OO 00 00 OO OO OO OO — — —
Nt.1 ILL
Ratio Poisson’s
ra
Bulk Modulus a. CD
ra
Shear Modulus CL CD
CD T 00 iri CD f-’ n r- CD CD in Elastic Modulus cl — CD
CO O’ CM n CM CO o CD T o 00 r-- CO CD m CM T o CO CD vt CD in' in mi in in in in in in
Shear Velocity E
O O M- i"- CM CO CD M- h- OO CD CD M- o T— 00 oo CD o CO O CD m- 00 CM 00 CO CD V) a> d oi ai O) CD 00 CD 00 00 00 00 CD Velocity Long. E =S£
CO CM CO CM l"~ CO O M- in CM CD o o r- 00 o CD CD o CM ’M- o CD o CO in h- T CM CM CD CM CD O o o o -9.1.9- O 0.132 T“ CM CM CM 0.268 0.325 CO o O o O 0.102 CM CM CM 0.324 co 0.398 CM 0.228 CM 0.249 o’ o’ Vol.Frac. Porosity O d o O O o O d O o O d o d d d o d d d d o
rt E Density o O)
CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM h- o
&w 2 2 T— T—
} of echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo
velocity velocity velocity velocity Determination
Method alumina pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse pulse
sonic sonic sonic sonic ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult. ult.
oxide,
aluminum Exh. n z co CO CO CO CO CO CO CO CO CO CO CO M- M" ® a. { Exh. >« Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 (— Q2 u AI Ref. n eg CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CO CO CO CO z CO CO CO 00 oo CO CO CO oo 00 CO OO oo 00 00 CO CO OO oo oo 00 00 00 00 oo 00 oo 00 oo 00 00 00 | 1
Nt. Li.
Poisson'sl Ratio
£ 3 Modulus GPa ffi
Shear Modulus GPa
1 96 to 98.1 92.8 94.7 9'99 78.6 CM 350 342 322 212 155 96 1.02 2.95 333.1 d 150.9 150.9 214.1 219.6 200.4 189.4 136.3 132.3 — 128.6 376.8 197.6 200.4 118.9 127.4 t 0 Elastic Modulus GPa CO
Shear Velocity km/s
Velocity km/s Long.
1 r- 00 oo oo oo CD CM 0.31 co CM 00 o O 0.28 0.29 O 690 -9.1.10- 0.315 0.316 0.318 o CM 0.231 0.316 CO CM CM 0.205 0.281 0.292 0.047 0.052 0.201 0.279 0.283 0.032 0.077 0.259 0.354
Vol.Frac. Porosity d 0 d o d o O d
CO CO fO o CD E 0.393 CD Density o d O)
CO CO CO CO CO CO CO CO 23 23 23 23 23 23 23 CO CO CO CO CO CO CO CO CO CO CO CO o CM CM CM CM CM CM CM CM CM CM 23 23 CM CM 23 CM CM CM CM CM CM CM 23 CM s- o
Nbr, 2 T— CM CM CM CM CM CM CM CM CM CM CM CM CM CM
} of echo echo echo echo
resonance resonance resonance
velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Determination
Method bending bending bending bending bending bending bending bending bending bending bending alumina bending pulse pulse pulse pulse
sonic sonic sonic sonic 3pt 3pt 3pt 3pt 3pt 3pt sonic sonic sonic sonic sonic sonic sonic sonic 3pt 3pt 3pt 3pt 3pt 3pt sonic sonic sonic ult. ult. ult. ult.
oxide,
Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
aluminum Exh. Nbr. CO CO CO CO T— T- T— {
Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 — Q2 AI Ref. Nbr. CO CO CO CO CO CO CO CO S9 83 oo 83 83 83 OO 83 83 83 83 83 83 83 OO 83 83 83 83 OO 83 OO OO OO OO 84 84 84 84 85 85 2
i
1"- 1'- 1"- 1^ r^- r- h- h- i-- r~~ r- r- I r" r^- r- i-'- r~- r^~ LL z
CD m- O CD OO 0.24331 M- 0.2353 0.2362 0.2371 0.2378 0.2386 0.2391 0.2397 CM 0.2412 0.2419 0.2426 0.2443 0.2450 0.2456 CM 0.2472 0.2479 CM 0.2492 0.2499 0.2503 0.2513 0.2519 0.2533 0.2539 0.2550 Ratio Poisson's O O O
CD 240 231 230 253.7 253.3 252.6 251.8 250.9 249.7 248.6 247.7 CD 245.5 243.3 242.4 241.3 238.9 237.8 236.6 235.2 233.9 232.6 228.8 228.1 226.8 225.9
Bulk Modulus GPa CM CM
n 0 CO CD 2 O
CO 162.2 161.1 158.8 157.7 156.6 155.4 154.2 153.1 151.9 150.7 149.5 06 147.1 145.8 143.4 140.9 139.7 138.4 137.2 CD 134.8 133.5 132.3 142 CD 091- CO T Shear Modulus GPa
1 LO CO 00 O 1^- 0 OO CO 3.67 3.74 CO 400.9 398.5 396.0 393.5 390.8 389.3 385.6 382.8 380. 374.7 372.0 369.2 CD 363.5 0 357.9 CM 349.1 346.1 343.3 340.5 h- 334.9 CNJ CO co CO o YLLZ CD CD osse ID CO CO Elastic Modulus GPa CO co CO CO CO
Shear Velocity km/s
Velocity km/s Long.
-9.1.11
Vol.Frac. Porosity
CO E 0.682 0.682 0.721 0.717 0.714 3.982 Density 0 01
CO CO CO CO CO CO t"- r- 6771 CNJ CM CNJ CNJ CNJ CNJ 127 177 227 277 327 377 427 477 527 577 627 [LZL 777 CM 877 927 977 CM O 1027 1077 1127 1177 1227 1277 i- O CO co
Mtl. Nbr.
of ff=^l
(0 resonance resonance resonance resonance resonance
c Determination E Method 3 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance re sonic sonic sonic sonic sonic aT "O X 0) o Q. Value >. E h- 3 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X C E Exh. Nbr. 3 CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 15 a0) Exh. >» Graph Graph Graph Graph Graph Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table t- oCO CM Ref. Nbr. LO in in in in CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CO oo 00 00 00 OO OO OO CO OO oo OO 00 00 OO 86 00 OO OO OO OO 00 OO 00 OO 00 OO 00 OO 00 OO < 99l —
p- p- r^- 4-3 4=* UL Z 1
0.2558 0.2566 0.2577 0.2589 0.2594
Ratio Poisson’s
224.8 223.6 222.3 221.8 221.3
Bulk Modulus GPa
oo
131.2 130.0 128.7 127.5 CD CM
Shear Modulus GPa
°0 CD T— CD 123 130 123 160 1.62 3.19 CO 15.7 19.6 22.6 26.3 37.8 50.2 65.6 94.7 152 CO 190 194 210 221 244 240 249 315 329.5 326.6 CO 320.9 319.5 CM CO CO Elastic Modulus GPa CO
Shear Velocity km/s
Velocity km/s Long.
1 OO CD m 00 co T““ T o p- CO CO 0.28 960 -9.1.12- 0.411 0.412 0.414 0.412 0.411 0.406 M- 0.396 co CO 0.296 0.297 0.287 CM 0.251 0.248 0.221 0.201 0.201 0.196 0.175 0.155 ci o' Vol.Frac. Porosity d d d O o 0
CO E Density 0 01
p- CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO p- CM CM 23 CM CM 23 CM 23 CM CM CM CM CM CM CM CM CM 23 CM CM CM 23 CM CM CM 23 CM t- Do co 1427 1477 1527 1552
Nbr.
of
<0 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance
c Determination E Method 3 resonance resonance resonance resonance resonance re sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic
re" TJ x
o Value Type E 3 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X C E Exh. Nbr. 3 CM CM CM CM Exh. Type Table Table Table Table Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph oCO J ; 1 i 1 J j Ref. Nbr. p- p- p- p"- p- p- p- p» p^ CO CO 86 CD CO 1®Z 87 h- 87 r"- 87 87 87 r- 187 i"- 87 87 87 87 87 < CO oo CO CO 00 87 oo co 00 00 87 00 oo oo 00 00 00 00 oo — — U- Ratio Poisson's oo CO CM 1.58 3.26 CM 45.6 65.7 69.8 CO Bulk Modulus GPa CD CO 16.5 21.3 28.6 38.7 uo 58.6 64.7 71.5 89.3 o 105 105 132 130 133 uo 154 167 oo T Shear Modulus GPa o 322 CO 378 377 409 CO Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. CD CO CO CM i"- oo CO ct 00 9.1.13- o CM CD o 560 o M- 0.28 0.092 O o 0.042 o 0.411 0.405 0.395 0.378 CO 0.295 O CM 0.249 0.221 CM 0.174 0.163 0.154 0.092 o 0.047 0.042 o 0.412 0.411 0.405 0.396 00 co 0.299 Vol.Frac. Porosity O d d o d d 0 d o d o - CO E Density o o> CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO oo CO CO CO CO O CM 23 CM CM 23 23 CM CM 23 CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 23 23 CM h- o a 2 } of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method alumina sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, aa> Value >» I- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X w aluminum Exh. Q 2 CM CM C\J CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM a0) { Exh. >. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 I- 02 Ref. Nbr. !" Al r-'- i^- t"- r-- r- r- i-" r- i"- i"- f'- r" r- r- r- ir-- f'- h~ f'- r~- i"- r- r~- OO 00 oo oo 00 oo 00 00 CO oo 00 00 00 00 oo eo 00 oo oo oo oo OO 00 00 oo 00 00 oo OO 00 00 00 00 | — 1 — — — LL 2 CM CD CM CD 0.15 CD 0.147 0.156 0.158 0.161 0.169 0.142 0.137 0.179 0.171 0.165 0.172 0.166 -< 0.177 0.193 0.171 0.177 0.182 0 0.201 Ratio O 0 Poisson’s! ^ CO r^ CM OO 91.4 116 126 r» 198 198 209 JC 06 t— 3 Modulus GPa m Shear Modulus GPa Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. CM CD t'- CO CM CO T '' CM ID 00 O 1 CD 0.25 5690 960 -9.1.14- 0.265 CM 0.196 0.175 T 0.097 0 0.048 0 0.002 0.411 0.376 0.339 0.296 0.293 0.284 0.284 0.278 0.262 0.247 0.246 0.218 O 0.197 0.193 T— 0.152 0.091 CD Vol.Frac. Porosity O O 0 0 d O 0 CO E Density o> CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO O CM CM CM CM CM CM 23 CM 23 CM CM CM 23 23 CM CM 23 23 23 CM 23 CM CM CM CM 23 CM CM CM 23 CM CM 23 H O s Nbr. } of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method alumina sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, Value Type i X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X iuminum Exh. Nbr. CM CM CM CM CM CM CN) CM CM CM CM CO CO CO co CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO {a Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 Q2 Ref. Nbr. '- AI i"- i'- i'- i'- r- e'- 1 i'- i-" i'" e'- e'- e'- e'- e'- i'- e'- e'- e'- e'- e'- e'- e'- e'- e'- e' e'- e'- e'- e'- e'- e'- 00 £2100 00 00 00 en CO 00 00 CO en en en en en 00 en en en en en en en en en CD en en en en en en yu Nt. m- oo 0.19 oo 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.24 0.201 0.191 0.209 0.197 d 0.245 Ratio d Poisson's oo 00 CD SOS 34.3 92.9 115.2 CO o' 139.4 oo 00 CD Bulk Modulus GPa 159 158 Shear Modulus GPa OO 89 CD M" 398 100 CO 228 CD 120 184 276 393 ID 176 194 CO 402 00 379 380 377 363 357 CO CO Elastic Modulus GPa A A A A A A A A i 1 1 TO CO CO CO CO CO CO CO Shear Velocity km/s > > > > > > > > d d d d d d d d ro CO CO CO CO co CO CO o o o o o o o CJ Velocity km/s Long. S80 CM CO •M- CM CM M- 00 - o o o 0.29 0.15 o -M 0.15 O CM 0.20 0.0421 £00 0.22 SCO 0.27 -9.1.15- 0.046 o o o o O O d d Vol.Frac. Porosity 0 0 d o o d (O E 3.98 3.98 Density u CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO in T— 23 23 23 CD o o C\J CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 340 390 470 490 CD o h- o CO 00 nu 2 z of } meth. res. res. res. res. res. res. res. res. res. resonance resonance resonance resonance resonance resonance resonance velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Determination Method alumina ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X X Nbr. aluminum Exh. CM CO CO CO CO CO CO CO P4 CD Type Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 02 Al Ref. Nbr. h- h- i"- i"- h- oo cn cn CT) OJ cn cn o CM CM CM CM CM CM oo oo 00 00 oo 00 00 00 oo oo OO 00 89 00 89 oo cn oj cn cn OJ 92 OJ OJ OJ 92 OJ OJ *=< BJL 2 Ratio Poisson's Bulk Modulus GPa Shear Modulus GPa S. and - 'a CO 39 289 283 277 CO 256 251 Tf- 246 104 170 280 391 G CM CM Elastic Modulus GPa from calculated Shear Velocity km/s E data; Velocity km/s Long. crystal 9.1.16- Vol.Frac. Porosity single - of CO E Density a O) averaging CO CO CO CO 23 945 974 CNJ CNJ CNJ CNJ o 1020 1100 1140 1176 1190 1200 h- o i i i i Voight-Reuss-Hill Nbr. i i i i i i i i i i of i i } i res. res. res. res. res. res. res. res. i resonance resonance resonance resonance resonance i i via Determination e i Duckworth Method I Majumder Schofield alumina i i Spriggs i ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic i i obtained i sonic sonic sonic sonic sonic i i i to to to to i i oxide, i i i B i Value Type i i i Attributed Attributed Attributed Attributed and X X X X X X X X X X X X i Heating Cooling X t i i G i aluminum n Exh. i 1: 2: 3: 4: 5: 6: 7: 2 CO CO CO CO i CO > i i i Footnotes: i i Type Table Table Table Table Table Table Table Table Graph Graph Graph Graph Graph { Exh. i I 3 i 0 2 J Al Ref. Nbr. 92 CO 92 92 92 92 92 92 93 05 93 93 93 3 mullite, mullite(3:2), • 9.2 Al 6 Si 2 0, 3 { 3A1 2 0 3 2SiO, } mol' 1 = 426.052 Temperature range (°C) = 0 to 900 ATr / (g ) / 3 = = 0. 1 Pthe0 /(g cm' ) 3.17 Porosity range 0 to = 1 = E0 / (GPa) 229 B0 (GPa) 166 4o 4o fl/(10' C)= 1.17 Z>/(10' C)= {1.16} >7 = 3.33 m = 3.15 GPa / S) or (£,G, Modulus / Volume Fraction of Porosity ( “ CO CO CNJ 0.233 Ratio o Poisson's o 88.3 03 Bulk Modulus GPa | - 00 CO V) s- s- 3 I I 3 LO UO Shear •a GPa o S V) un o Is- CD CM s- 3 143 202 201 210 205 00 187 174 I 222 219 214 CM 196 193 CO CO 142.5 142.0 141.2 140.7 139.9 139.1 135.9 135.1 133.9 131.6 1382 ^ CM T— 3 M- CO Elastic •a GPa o S & o CO Shear o E >0) — .t o 1 0 km/s Long. >0) M" o CM o o s- s 6 CX) I T I - re 3920 CM CO 9190 0990 60Z00 0600 -cr O 'd- - m O 0.0305 o 0.0754 O 0.0091 0.0117 o 0.0466 o u. wQ 0 o o 0 0 o 0 o d o O -9.2.1 > a. 03 CO s- I 2.78 2.78 s- ILIZ E I Density o CM 03 CO CO CO CO CO CO CO CO CO o o o o 23 23 23 CO 23 23 23 CO 23 CO CN CN CM CM 100 200 300 400 500 o o 750 o 850 o CM CM CN CM CM CN CN CN o s- i- o CD I CO 03 Mtl. Nbr. X CM OCM C/3 «S of oCO oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator oscillator CM Determination aoueuosaj resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance < IVlethod CO N composite composite composite composite composite composite composite composite composite composite composite composite composite composite composite CO resonance resonance sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic 0) ojuos *-> 3 © a. E Value Sh o l— X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 Exh. Nbr. E CO CO -cr xr NT xr 'J- ’cr x x © CO a Exh. >* Table Table Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph G h- CM U) «o CD CD CD CD CD CD CD CD Ref. Nbr. CO CD to in m in in m m m in m in in m 126 CM CM CM CM 126 CM 126 126 126 126 CM 126 CM CM x s- s- s- < r- I I I T— — — —— —— — — " CM CM CM CM CM CM CM CM CM CM CO co co CO CO CO CO CO CO CO CO CO CO CO 4-i U. Nt. — CO CO o CM *3 d Poisson's re a. r^- LO re T Bulk Modulus O0. 3(A oo 3 re Shear o CL o O § (A Velocity Long. E CO CO CM CO o CD C- 00 OO *t— CO CD 6 CO o O CM CM CM CO CD 00 o 1-680 re £ 2690 CO oo 9960 0.042 0.120 0.120 O O o - 0.0755 0.0893 0.0873 o o O O O o (0 0.0612 O o 0.0874 LL. 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ILL, CO co Ratio ci Poisson's 150.62 Bulk Modulus GPa CD Shear Velocity km/s Velocity km/s Long. o CO CO 00 OO Z60 CD 00 CO CO CO 2S0 60 OO CO in - o 890 CD M- eoo 980 £ 0.029 o o O ZZO'O 0.114 0.123 0.167 0.175 0.189 0.032 o o (A o 0 Vol.Frac. © o o 0 0 d 0 d d 0 d o -9.8.2 oEa, CL CM CM CM CM CM CO CD CD CD CD CD 5.192 5.192 5.192 5.192 E in in in in Density o m O) CD CO CO CO CO CO CO CO CO CO CO 23 23 CO CO CO CO CO 23 CO 23 CO 23 23 CO CO 697 o 834 CD 884 889 913 CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 1045 i— Do CO CO 00 Mtl. Nbr. of .55 '35 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance o Determination k. Q. Method (A extrapolation >» T3 sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic — -Q 'x 0J o CL Value >. E 1- 3 X X X X X X X X X O X X X X X X X X X X X X X X X X X X X X X X '35 wo Exh. Nbr. = CL CM CM CM CM CM CnI CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM (0 >* ® sz T3 a a. Exh. H>» Graph Graph Graph Graph Graph Graph Graph Graph Graph Table m Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph L CD o CM ID in in in in in in in in in in in Ref. Nbr. >* O O O 104 104 104 104 104 104 105 O 105 o o 105 105 105 105 o o o 105 105 o o o 105 105 o o o X T— T T— x— X— T x X X Q M05 . — 4^ 4-S uu z Ratio Poisson's Bulk Modulus GPa CD 0O h- o o 3ca 55 55 29 53 m m 45 43 40 40 3 re Shear o a, © CD S 3(A 3 Elastic © GPa o 2 - £ o Shear © km/s >© >. o> (A C o o o E >m . 00 h- 00 oo CA CT> A- CM— CO oo CO CA CM o & in CO CO co CO a- o cn x O’ CO— 00 OO CA ‘5 o o o o o o o X a=> o O ILL. o o d o o o o O d o o o d O o -9.8.3- E= o O > £L co (0 E c o a© B) CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM h- Do . <*=>« £ § z c © 0) CD CD (D 1 = M /( mol = 382.516 Temperature range / (°C) Oto 1000 r g ) 3 = = Ptheo/(g cm' ) 8.651 Porosity range 0 to 0.2 = E0 / (GPa) 179 £0 /(GPa)= 160 4o 4o a/( 10‘ C)= 1.14 b / (10' C) = 1.14 n = 2.57 m - 3.08 GPa / 8) or G, (£, Modulus Volume Fraction of Porosity (<]>) — — — — Nt. ill. Ratio Poisson's 3(A 3 Bulk o GPa o 2 © 3 3 re Shear a. "D O 0 2 © CD ID <- o CO o CO CM oo CO T- CO h- CD CM CM CD or CO CM CD h~ o CO CM o CD ID CM oo O 3 CD ID CO CD CO oo CD oo CD T— CM CM T T— T— CD CD CD 00 00 OO re o d d d o or T O o o o CO 00 00 CD CD ID ID CO •O' O' or of or or CO CO CO 00 CO CO CO 3 = c- T— m °o o O LU s k. re o » o £ © (0 > & O) w c o o & £ © =s£ _i > . 00 00 CO 00 CD CD CO CD CD CO CD CM CM OO CD o 00 oo oo D- r- 00 00 ID ID OO OO O O - re o o V- CM CM CM CM CM CM co CO 9.1 u. 6 d o d d d o d d d O d d o d d 9. o © - > 0. ID D ID D D m ID ir> ID ID D ID ID IS) ID ID ID CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM E 00 OO 00 00 OO OO OO oo OO 00 CO 00 00 00 00 00 CO c o ID ID ID ID ID ID ID ID ID ID ID ID ID ID ID ID ID Q© » 00 CO CO CO CO CO CO CO CO CO CO CO CO CO CO O M" r- D CD OO CO O CO CO O O 00 f- CD f ^ CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM T“ •O' CD CO O CM T CO on D ID CD CO O ID T ”~ H O T— T CM CO CO CO or or ID CD r^- r- OO CD CD o Mtl. Nbr. e © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © © o O U O u u O o o o O O o a O o O o O o O O o u o O O o o O a O o o c c c c c tc c c cc C c c c c c c c: c c c c c c c c C tc cc CC c C iZ re to ro ro TO ro TO ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro "O c c cc c c c C c cc c. c c c cc c c c c c c c c c cc c c c cc cc cc C cc cc o o o o o o o o o o o o o o o o a o o o o o o o o o o o o o o o o «/) (/) (/> CO CO CO if) if) if) if) (/) if) if) if) if) if) if) if) if) if) if) if) if) if) if) £ fc « © © © © © © © © © © © © © © © © CD © © © © © © © © © © © © © © © © © © © © © © fc— fc— fc- fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc- fc— fc— i— fc- fc— fc— fc— fc— fc— 2 <1> o o a o o o o a o o a o o o a o o o a a a o o o o a o a o a o o S^=® m c c c c c c: c Cl c: c c c. a c c c cc c c c c c c c c c c c: c c c c re o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o W © if) © if) if) if) if) if) if) if) if) © © if) © © if) JQ © w © © w w w © © © w © © © © 0) © 3 Q. © re s > H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X K . o £ k. =e E X 3 Lii T— T— CN CN CM CN CN CN CN CN CN CN CN CN CN CN CN CN CN 5 . JC jc sz JC -C sz -C JC JC JC SI SI sz SI JC JC JC SI SZ JC JC SI sz SZ sz SZ JC SZ JC JC JC JC .C Cl CL Cl CL CL CL Cl al CL Q. Cl CL CL Cl CL Q. CL CL CL a. Q. Cl CL CL CL CL CL CL CL CL CL CL © X >s ro ro TO ro TO ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro m ro ro ro ro ro ro ro ro fc— fc— fc— l— fc— fc— fc- fc— fc- fc— fc— fc— fc— fc- 1— t— fc— fc— fc— fc— fc— fc— fc— fc- fc— fc— fc— fc— fc— fc— fc— in n h“ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oCO © or or or OT or or or or or M- •or or or or or or 5= Q£ o o o o O o o o o o O O o o O o o o o o o o o o o o o o o o o o yy 7 s— T“ M— ^r- T— T— ^ T— T- T- or- ^5— | — — — — 4-2 U. Nt. 0.292 Ratio Poisson's 1 CM O Bulk Modulus GPa O' 05 05 00 05 5 in 5 5 in in in 67.78 Shear Modulus GPa in CM o- o x— CM o CM CM d- CO oo T 3 37.6 37.5 157 in 154 LO in LO LO in in 144 O 143 127 125 o 107 o 05 o o> t T T 3 175.21 Elastic XJ GPa o § £ o Shear o km/s >a> £o o km/s Long. >3 o CM Z90 O' o- CM 9S0 CO 6Z0 CO 90 n CD 065 661. 9030 990 0.051 0.053 0.054 o 0.061 0.065 9900 o 0.092 0.123 0.143 0.154 0.171 0.187 0.191 0.195 0.198 o 0.054 0.061 o 0 0 -9.9.2- Vol.Frac. Porosity 0 o 0 0 o 0 o 0 o CO 825 E 5.825 5 Density o O) CO CO CO CO CO CO CO CO CO CO CO CO CO CO o 23 CO CO CO CO CO 23 CO CO CO CO 23 23 CO CO CO 00 CM CM CM CNI CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM O 1050 H- o o s Nbr. , of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method extrapolation } $onic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic — erbia 0) Q. Value S* H X X o X X X X X X X X X X X oxide, X X X X X X X X X X X X X X X X X X Exh. Nbr. — r\j CM d- d* d- d" d- d- d’ ’a* d- d- d- d" d- d- d- d- d- d- d" d- d- d- d“ d* d- d- d- d- d- erbium Type { Exh. Graph Graph Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 1 0 in CO in in in 2 Ref. Nbr. 105 Er 104 104 o 105 105 105 o 105 105 105 105 105 105 105 105 105 105 105 105 105 o 105 105 105 105 o 105 105 105 o — t— \ M05 — — — — — — — — y. z o ’•E Poisson’s re O' £ re 3 Modulus a. m o 00 l-- 1-'- in o CD in CNJ CM CO o CD CD CD O CD oo o CD oo o CD oo r- CD OO 00 h- CD h. in in in in CO CO CO m 00 oo D~ r-- r-^ CD CD CD CD id in in in re re re re (Q re CO CO CO co CO CO CO co CO CO co CO co co co CO co CO 0) Modulus fit. JZ CO 0 h- o CD CM •re- CD oo T o CO CD CO h- CD CM re- : r- r- CD CD in re re- CO CO CO CM d o CD CD CD oo re CD CD CD CD CD CD CD CD CD CD CD CD CD CD OO 00 00 CD Elastic Modulus oa, us Shear Velocity E o (A o Long. E >re oo co CD CO CD in CD CD CD CD CD CD CD CD CD CD CD CD CO 6Z0 00 00 CD CD & o O O o o O 903 O O O O O O -c — SOSO 9030 9030 o o 0.123 0.154 0.174 0.206 0.206 CM CM CM 0.206 CM CM CM CM CM CM CM 0.206 CM © o d 6 Voi.Frac. © o 0 o d d d d d d d o O d 0 d O d d d d k» © 6- 0. CO E Density _o O) CO 00 CO CO CO CO CO CO CO CO CO CO CO CO CD CM CO in in re- in CD r-~ CO CM o co o o CD CD CM o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CD cD o in CD in CD CO CD in o CO r-- I- o CM CM CO co CO re re in in CD h- i-'- 00 53 n1© s z of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic 5„2 k. Q> re Q. Value aT >» T3 H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X o JZ b X n E 3 UJ 2 re O’ O’ o- CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO JQ re k. si a, X >> Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph LU l- CO O bi Ft. Nt. Ratio Poisson's © 3 €1 3 CL 3 TJ CD O 0 s w LO oo CO T- o CD CM X o CM CM T- O CD oo T- o CD oo V- o CD CM x— CO in CD CD oo o CD oo k. 3 CO CD CD oo OO oo 00 id |d cd cd cd cd LO cd id td cd CD CD CO r- (d CO cd (0 ro co CO CO •^r in in If) in m in in in o 3 Q. £ "O O 0 (/) 5 s- (A CO CO 00 co oo o CO CD CM D- o CM ID CO CO 00 T— CO CD CM M- CD CM 00 T- I co co in o 3 00 r^- CO fd cd cd cd cd CM T— T— O) CD oo co fd cd id cd CM oo I'd id id cd CM T— T— re d 3 oo 00 00 CNI CM CM CM CM CM CM CM CM CM T— T T— T T T x— x— X x X— X in in in in in in in m LL 'r“ T_ X— X X— 'r“ T— T” X— x x °o iS o 0 yj s k» & ro o (0 £ o E © (/) > >> O) CA c o o o E © > . CO CO CO "nT Nf M" •'cr O' M- O' in in m in in in in in - o o o o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM o o o o o o o o "~ *” '5_ 4 AS CM CM CNJ T X T X— X— x T_ . k. «A o o o o d d o o 9 u. o o o o O o o O o o O O O O o O O d d d o o O o o O 9. o o - > £L & eo (A E C o a0) o> 00 CD LO CD o co CD o CD O CD r- CO CD oo CO CM LO h- T- CD 00 CO CM CO D- 00 CD in 00 CM oo CO OO CM CO CO CD CO CD lO CD lO CD CO 00 00 co co co co If CO O CO O' o o CM o M" — - i— O 00 CD CD X CM CM CO CO M M" LO CO co co r-'- oo 00 00 CD CD x T— CM CM co co Mtl. Nbr. e © © © © © © © © © © © 0} CD 0) 0) © © © © © © © © © © CD CD a) © © a) 0) a) 53= o o O o O o o O O o O O o O O o o o o o a o o O O O O O o a a o o o o c c c c c c c c c c c c c c c cz c C c c c c c c c c c c c c c c c « ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro "D c c c c c c c c c c c c c c tz c c c. c c c c c: c c c c c c c c c c c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o a o £ CO © CO © © CO © w © © (/) (/) if) if) CO CO CO CO CO CO CO © CO © CO CO CO CO CO w CO © CO <-• t k. © © © © © © © © © © © © © © © fl) © © © © © © © © © © © © © © © © © a> k_ L_ k_ l— L_ 1— k_ k_ L_ k_ w_ 1— k_ k— k_ k_ k_ k— k— k_ k_ k_ l— k_ k_ k_ l— k_ k_ s *» ul Nt. 0.338 Ratio Poisson’s © 183.6 3 Modulus CL 100' o © T o o> 00 T- o CD CM 1— o CO CM CM k 3 CO CO LO id id LO CO CO CO (TJ 3 CO LO LO LO lO LO LO lO lO LO LO LO lO CO £Q) © a= m © o s © T CO CO LO 00 1- CO CD oo O' D- CO o 3 o CD CD oo c- id O' sr CO CM T— D- 3 LO ^r •^r sj- xr •^r O' ' " ~ 'C~ T— r_ T- T— M r "C °S _ro o o HI s k» £• (O o m £ o E (0 >© S' ch © c o © o I >to . LO LO CO LO LO LO lO LO LO LO LO LO o o S' o o o o o o o o o o o o 0= o o d d w d o d d o d o d -9.9.5- LL o ^ O © > (no >» (A E C o © Q SJ CD CO •O' lO T— CO CT) o CO LO LO CO CM 00 CM CD CM LO CM CD ID oo CM (f > o •O' h- o 't LO LO CO CO 00 00 CO CT) a=^ -*=» £ s z c © © © © © © © © © © © © © H— © o o o o o o o o o o o o o © c c c c c c c c c c c c c CD to co TO CD CD CD CD CD CO CD CD CD "O © c c c c c c. c c c c c c c: o o o o o o o o o o o o o o (JO no (10 (/) no (JO £ fc © © © © © (0 m a= © © © © © © © © © © © © © 0) © k- k_ 1— k— k— L_ L_ u. l— i_ L_ k_ t— s <*=* o o o o o o o o o o o o o c. c c c a c c c c c c £= c ns o o o o o o o o o o o o o © (JO (/) (JO © (/) (/) JQ © © w w © © ok. © © 3 Q. 6 ffi 2 > t- X X X X X X X X X X X X X X m o £ k» X £ E 3 tU Z CO CO CO CO CO CO CO CO CO CO CO CO 5 „ 0 £ £ £ £ £ £ £ £ sz £ £ £ £ Cl CL CL CL Q. CL CL CL CL CL CL CL CL © X CD CD CD TO CD CD CD CD CD CD CD CD £ l_ L. k_ l— L_ L— k_ k_ L_ l— L_ k_ | Q j H G3 CD CD CD CD CD CD (D CD CD 0 0 0 1- o 6ft= ka css © £ CO CD CO CO CO co CO CO CO CO CO CO b- £g o o o o o o o o o o o o o ULI z 1 = M / mol' = 362.498 Temperature range / (°C) Oto 1400 x (g ) 3 = = Ptheo / (g cm' ) 8.348 Porosity range 0 to 0.37 = E0 / (GPa) 157 B0 / (GPa) =114 Ao 4o a/(\0 C) = 1.46 Z)/(10- C)= 1.47 n = 2.32 m = 2.19 GPa / B) or (E,G, Modulus Volume Fraction of Porosity (<(>) — — — — — — Ft. Nt. rx o ix o CO CM CD CO CO CO CO r- CO CO CD zoeo 0620 9920 CM CM CM CM CM CM 0.284 CM 0.267 0.269 0.270 0.258 0.262 CM Ratio o O O O o O O o Poisson's re Bulk Modulus 0CL CA CM CO Z o o 3 57.2 56.3 55.3 46.8 ib 45.7 35.0 34.9 34.3 22.1 21.8 21.0 21.0 22 3 O' CO CM CM Shear o GPa o S (A M- 0 U CD 2 CO CD 8 CO 3 53.0 148.0 143.5 140.9 121.0 116.6 115.9 CM cb 58 ib 9SQ CO 140.6 138.9 138.7 137.8 CD 135.8 134.9 133.0 132.8 131.9 130.9 129.1 128.9 127.9 126.9 3 CD 06 68 CO ID ID ID 89 CO Elastic o GPa o § £ o Shear o km/s >0) s? c © Velocity km/s =J '*3- Z9£ IX. rx - 6 CO CO 820 914 CM re 0.025 o 0.105 ’C 0.207 0.224 0.228 CM 0.351 0.360 0.361 0.364 0.370 0.370 co n %m 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 o o -9.10.1 UL Porosity 0 o 0 d O 0 o o >O CO E Density o O) CO T CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 89 o CO CD CsJ CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM T 158 201 261 CM CO CD 522 583 650 710 753 CM 893 o CO CO CD I- o 53 s , i of *»*» re resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance 'E Determination Method oo « O) sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic of o a> '5 a. Value o Hs* E X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X .3 ‘E Exh. Nbr. o T ’C ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro "O (0 a> O) a Exh. H Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph o CM CD "O Ref. Nbr. CO 00 108 108 108 108 108 108 o 108 108 108 108 o 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o T O M08 — — — — Ft. Nt. Ratio Poisson’s £ re 3 Modulus Q. m o Shear Modulus GPa CM •sj- CO CO to CO CO sr CM CO Shear Velocity km/s £ u> © km/s Long. >© i-'- D- Z622 r-. 6 2* CT) CD L6ZZ0 L6ZZ0 re 00347 co CM CM i. m 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 o CM CM -9.10.2- LL. o l- d d 0 d O o > Q. CO E Density o O) CO CO i"- T— CO CO CO o 910 965 o CD O tf) o 261 340 395 CD 528 h- 0S9 869 741 o 856 CM 972 CD CD 1020 1074 1117 1171 1238 1293 1329 1371 1014 1112 1148 o CM T T— CM to CO CT> i- o o s Nbr. } of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination gadolinia Method sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, re Q. Value >. I— X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Nbr. gadolinium Exh. CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO sz Q. Exh. Type CO { Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 o 02 Ref. Nbr. CO CO CO CO Gd 108 o 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o o 108 108 108 108 o t T T — — Ft. Nt. — w c o £© » re o a£ GL re 3 Modulus £L 00 CD CO o O' 'Sf O' re re in in in © Modulus Cu £ CD (0 CD CM r- 00 CD LO CO CO CO CT> 05 05 CO CD CD LO m O; CM CO CM o o CD 05 o — O CD CD CM T d d a> 00 CD CD CD LO ib O' O' CO CO cb CM CM d d h- f'- CD CD LO co in LO ID LO O' o '3- O’ O' O' O' o- O' O' O' O' O' O' O' O' Elastic Modulus GPa Shear Velocity km/s 05 <0 £ O Velocity E C'- D~ o o o o o o o o o O o o o O o o o O o o o o o o o o r^- h- CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O' o- O' eg CM CM CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CO co CO 0.2297 CM CM CM CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO o o o -9.10.3- Vol.Frac. Porosity O O O O d d d o d d d d o d O d d d d d d d d d d d d d d d d d CO E Density o 05 h~ o O' ID CD CM CO CM LO CM r^- oo LO O LO 05 00 CO oo CO CO CO in CD O' r" CO '='3' CO CM D- CM CD 5 CO c- CO oo LO o CD CO 05 o- 05 o- o in 5 05 in 05 CM r- m in O CO CO CO LO LO 05 05 x co CO h- o CM CM CO CM O CD CD 05 o o o CM CM £ a z of .5 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance E Determination o Method T3 re 05 sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oT T3 ® ® X 3 Q. O >» re H E > X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 £ sw E X £ ILI z oo CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO re fl> £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ 05 £ a Q. Q. CL CL Q. CL Q. CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL X >» CD CD CD CD CD CD CD CD CD CD CO CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD ID CD CD CD «-v' u. k_ k— u i_ i_ h k— k k— k— k_ k_ L k_ L. k_ UJ H CD CD CD CD o CD CD CD CD CD CD CD CD 6 CD CD CD CD CD CD CD CD CD CD CD CD CD CD 6 CD CD CD CD 6 sO CM ® £ 00 oo OO oo 00 oo oo 00 00 00 00 oo oo OO CO oo oo oo oo oo oo OO oo 00 00 oo 00 oo oo 00 00 00 00 T5 K Z o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o X — — uu Nt. Ratio Poisson's! Bulk Modulus GPa (0 o> co CD 8 8 9 o CO r~- m c- CM 53.7 53.5 53.3 52.1 51.2 SOS 49.4 49.2 49.1 47.6 s- 46.4 eee 32.3 32.2 32.9 31.9 31.5 31.3 30.3 3 co c\j O 48 CO h- h- I O 3 in in in 0S 90S 0S xr '3- co CO Shear a GPa o 2 3in 3 Elastic D GPa O 2 £ o in Shear o E >re Ja£ Velocity km/s Long. D- d ''T *3- re CO oo CO L6ZZ0 10.4- k_ 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 o 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 o o 0.0347 0.0347 0.0347 0.0347 0.2297 0.2297 0.2297 16ZZ0 0.2297 0.2297 0.2297 0.2297 0.2297 LL Porosity o o o -9 >O & CO (0 E c o are O) o CO CO co m- CM •sf 06 CO 253 00 454 515 CO 692 '3’ o 00 096 co CD m in cn 255 328 389 450 523 566 1009 1106 1167 1198 1234 1283 1320 O CO CO in 1"- CT) CO T— T— i- o co co CO o Mti. Nbr. of «*-» resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance .2 — c Determination Method Do re sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic OJ — 0) - TJ re 'x a O Value >* I- E X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 C Exh. Nbr. o CO CO CO CO CO CO CO CO CO CO CO CO CO co CO CO CO co CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO “D TO re O) Q. Exh. >. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph I- o” CM ef. Nbr. CO 00 CO CO CO CO OO 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 Gd,0 R o 108 o 108 o o O O — t T— T— T § M08 i — — — — — P Ft. Nt. Ratio Poisson's BuHIk Modulus GPa o 00 ID CM to CO M- co o 8 CT) CM 28.2 27.9 27.8 27.6 27.5 26.4 19.6 19.4 19.2 19.0 18.7 18.5 18.4 17.4 17.9 17.7 o CD 29.7 CT) 28.6 CD 00 LLZ co d d d o o 61 00 h- re co CM CM CM CM CM CM CM CM CM CM Shear Modulus o0- Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. D- Z622 e'- e'- h- o O o o o o o o o O o - CT> en en CT> CD CD CD CD CD CD CD CD CD CD CD L6ZZ0 CM CM CM CM 02297 CO CD CD CD CD CD 0998 CD CD CD CD CD 10.5 CM 0.2297 0.2297 0.2297 0.2297 CM CM 0.2297 0.2297 0.2297 CM 16ZZ0 0.2297 0.3660 CO CO 0.3660 CO 0.3660 CO CO CO CO 0.3660 CO CO CO 0.3660 CO VoS.Frae. Porosity O 0 d d d d d d d d o 0 d d d d d 9 - co E Density o OS CO CM 72 co M" CO 639 889 743 798 M- 914 896 133 164 231 304 CD 445 512 561 CO 00 744 792 847 902 957 Do 00 1011 1060 1103 1145 1188 1219 1273 1310 1353 CO CD CD — Mtl. Nbr. of .5 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance [E Determination Method Do re a> sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oT d o> x Q. Value o K>> E X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 E Exh. Nbr. o CO CO CO CO CO CO CO CO CO CO co CO CO CO CO CO CO CO CO CO CO CO CO CO co CO CO co co co co CO CO TO re a> O) CL Exh. >» Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph h- d CM CO GO 00 =o Ref. Nbr. CO CO CO 108 108 o 108 o 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 O 108 108 108 108 108 108 o 108 O 108 O T— X x x X o M08 1 Ft. Nt. Ratio Poisson's “1 L 6 Z 6 6 5 D- M- 5 M- CM 99.2 94.7 92.7 92.6 92.4 91.4 91.3 89.4 88.3 87.3 86.4 100.3 d CO O CD ro o 66 86 86 96 56 96 CD CD 88 CO 00 Bulk Modulus OCL (A in CO CN CO CD 3 16.8 17.2 15.8 h-— CD CD mi 3 T Shear 0 GPa O S 3(A 3 (O Elastic CL TJ O 0 s Shear Velocity km/s Velocity km/s Long. o o o o O r-- h- n- N- D- CD CD CD CD CD m- m- sr <0 CD CD CD CD co CO CO co CO 0.0347! 0.0347' co CO CO 0.3660 0.3660 0.3660 0.3660 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 CO CO CO CO CO o O o o O o o o -9.10.6- Vol.Frac. Porosity d O o d O d O d o O d d o co E Density o o> 95 o •'3' CM 158 195 262 323 377 456 524 578 un SOZ LTJ 815 CO 912 961 1177 1311 1119 i— Do 1012 1055 1098 1147 1219 1269 1354 T— CD CO 1016 1070 1167 1204 1228 1283 S Nbr. } of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination gadolinia Method sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, Value Type X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Nbr. gadolinium Exh. co CO CO co co CO co co co co co CO CO co CO CO CO co co co CO co CO CO CO co CO co co co co CO co Type { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 02 Ref. Nbr. CO 00 CO 00 Gd 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o 108 108 o o 5 t— i— T — — — — ILL z Ratio Poisson's x CO r-- M- o M- CD o CD CO CO 8 9 9 85.2 70.4 65.2 0'99 64.9 62.1 59.7 57.7 8'99 56.6 54.5 37.3 37.2 36.3 36.2 36.0 CD OO CD cb sr ob CM 609 d CD 89 8Z9 99 999 99 OO e^ CD CD CD CD CD CD CD ID Bulk Modulus GPa (B Shear Modulus OQ_ m 3 3 m Elastic DL 13 O 0 2 £ u (0 Shear Q E >m Velocity km/s Long. i t^- e'- e'- o o o o CD 05 05 CD en en CD CD CD CO & 0347 CM CM CM L6ZZ0 CM CM CM CD CD CD CD V) 0.0347 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.3660 CM CM CM CM CM CM CO CO CO CO -9.10.7- Vol.Frac. © 0 d d d d d d d d d d © EL co E Density o 05 CO T— CD CM M- 99 e^ o CO CD o 37 74 CO 1"- CD 164 199 CD 332 392 460 527 570 649 703 740 813 849 916 965 CD co CO CO o CO CO 1105 1147 1190 1220 1269 1317 co — h- O CM o O CM Mtl. Nbr. } of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination gadolinia Method sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oxide, a Value >* h" X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. £ Jjadellnium Z CO co CO co CO co co CO co CO CO CO CO CO CO CO co co CO CO co CO co CO CO co CO co CO CO CO CO CO Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 3 02 Ref. Nbr. CO CO OO Gd 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o 108 108 o 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o t t x — — — — Nt. ILL CD 00 00 CD 00 oo t^- 00 00 CD CD CD CD CD CD CD CD CD CD CD CD CD CD CM CM CM CM CM CM CM CM CM CM CM CM 3© O O O O d d d d d o d d Poisson's re O' OO co m CM CO CD D— CO CD to CO CM CM o CD 1"- CD in in to CO CO CO CM d d o CD CD d CD re co CO CO CO CO co co CO CO CO CO co CO CO co co CO CM CM CM CM 3 Modulus Q. CQ o re re £re Modulus QL CO o (A j3 3 re Elastic CL T3 O 0 s l. £ re o (A £re o E CO >re JC 2* d) o (A e o o XE _l >re o o o o o o o O O o o o O o o o O o o O r^- r— h- C'- r-- d CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD -3- •'3- O' O' M- M" M" O' •o M- re £ CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD co CO CO CO CO 00 CO CO CO co co (A CO CO CO CO CO CO CO CO CO CO CO 0.3660 CO CO CO CO CO CO CO CO 0.0347 £ o CO o o o o o O o o o o o -9.10.8- t_ o d o d o d d d d d d d d d d o d d d d o d d d d o d d d o d O o > CL CO E Density _o o> CD CM f'- h~ o o CO CO 00 CO to "O' f— o> CD LO sj- o 00 o CD CM CD CD 00 r-~. CD o CD ID o CD m- CD o O' o to to o M- 00 CM h- LO sr CD CO 00 in O 00 T— in co oo i- O CO CO to to CD CD CO CO CD CD o o CM CM co CO x CM CO CO in in CD CD o r n*1 S z of r .2 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance [E Determination o Method T5 ro OJ sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oT TJ re re ‘5 3 Q. o re >* E > l- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 £ hi C X £ O HI Z CO CO CO co CO CO CO CO CO co co CO CO CO co CO co co co CO co CO CO CO co CO co co co co co CO co TJ re re £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ O) £ Q. CL Q. Q. Q. CL CL Q. CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL X >* ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro CO ro ro ro ro s>< i i— k_ k_ k_ V— L_ k_ k_ l- i— UJ h- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 1*1 hi CM CO CO oo CO CO CO CO CO CO oo oo oo 00 oo oo 00 00 00 OO oo 00 oo oo 00 00 00 00 00 OO oo 00 CO oo T3 re £ a: Z o o— o— o o— o o o o o o o o o o o o o o o o o o o o o o o o o o o o o t T T T— T— T— — — — — — — Ft. Nt. h- 00 CD h- CD CO 05 CO CO CO CD CD CD CO 9930 683 683 CM CM 0.269 0.269 CM 0.267 0.266 0.266 0.266 0.267 CM CM CM 0.292 0.310 0.301 0.291 0.294 0.289 0.287 0.293 0.294 0.294 0.292 0.291 0.293 0.289 CM 0.290 0.289 Ratio O O O O O O O 0 0 Poisson's Bulk Modulus GPa Shear Modulus GPa Elastic Modulus GPa Shear Velocity I XL o o km/s Long. >© - r- f'- 1'- r~- N- Z6330 Z6330 r- -cr O" <}• 05 05 05 £ CO CO CO CO CO 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.0347 0.2297 CM 0.2297 0.2297 0.2297 0.2297 CM 0.2297 0.2297 CM 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 0.2297 (0 o o o o O CM CM CM 9.10.9 Vol.Frac. o o o o o o o O o o a. - CO E Density o OS CO o CD T 96 05 741 802 875 905 948 o CD LO "3- 197 252 324 385 452 520 568 641 069 738 799 847 915 957 1051 1106 1191 1228 1313 1355 1012 1054 O t h- O o CM s Nlbr. of re resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance c Determination o Method T3 (0 TO sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oT g to X Q. © Value H>* E X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 ;e Exh. Nbr. o CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO TO re =e 8) Type X Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph «=v» OJ d CM CO 00 CO CO 00 oo “O Ref. Nbr. o 108 108 108 108 108 o o 108 o 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 108 o 108 108 108 108 108 o 0 T— X T T— T T — — — Ft. Nt. — cr> o T o CM CM CO M- CO CO in M" in in M" M- CM o CO O' O’ CO CO co CM in in M- 00 CD CD CD CD CD CD co CO CD co CO CO CO CO co co CO CO CD CO CO CD CO CO CO CO CO CO CD CD co CD o CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM '5 O O d d d d d d d O O d O O d d d d d d d d O d d d d o d d d d d Poisson’s re CL re 3 Modulus 0. ffl o t. re re a> Modulus Q. JC (0 0 re Elastic Modulus 0Q. Shear Velocity E -X 05 (A e o Velocity E _i X N- ix |x |x ix ix |x o o O O o O o o o o o o o o o o o o o o o o o o o 6 CD CD CD CD CD CD CD CO CO CD CO CO CO CO co CD co CO CO co co CO co co co co CO CO co co co CO re CM CM CM CM CM CM CM CD CD CD CO CD co co CD CD co CO co co co CD CD co CO CO CD CO co CD CD co k_ CM CM CM CM CM CM CM CO CO CO CO CO CO CO co CO CO CO CO CO CO 0.3660 CO CO co CO CO CO CO co CO CO CO Li. Porosity d d d d d d d d O d d d o d d d d d d d d O d d d d d d d d d d >O CO E Density o O) ^r CO |x 00 't r- o CD CO oo h- co CD M" h- in o in CO oo o CD CM 00 m o o O) CD CO rx O co o "3- D- CO CO o CO M" o CO co 00 O’ CD O' o in o in CD M- IX. CM fx o Mr i- o O CM CM CO CO CM CO CO m m CO co h- 00 O) CD o o o T CM CM co CO o — T— hi 2 zS3 of .2 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance c Determination o Method T3 re o> sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic qT a Q> re '5 3 Q. o re >. E > X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 x: u C X n o Hi z co CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO "O CO re sz SI sz sz j= sz SZ sz sz .c sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz sz O) SZ Q. CL CL Cl Cl Cl CL CL Cl CL CL CL Cl CL CL Cl CL Cl CL Cl CL Cl Cl CL CL CL CL CL Cl CL CL CL CL CL X >* cd CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CO CD CD CD CD CD CD CD CD CD CD *v» k_ u_ k— k- 2 i_ l— i— b_ k. l. L_ LU 1- 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o iS CM 0) 00 oo 00 OO OO OO OO 00 00 00 OO 00 00 °o n 00 00 00 00 00 00 00 00 00 oo 00 00 00 00 oo oo 00 00 OO OO Gd,0 IT z o o o O o o o o o o o O o o o o o o o o o o o o o o o o o o o o o o T T 1 dioxide, hafnia, 9.1 Hf02 (monoclinic) { hafnium HfO, (m), monoclinic hafnia } 1 = = M / mol" ) 210.489 Temperature range / (°C) 23 to 23 r (g 3 Ptheo/(g cm" )= 10.113 Porosity range = 0 to 0.25 = = E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o a / (10' C) = n/a b / (10" C) = n/a n = n/a m = n/a Volume Fraction of Porosity () - 11.1 9. - } • (partially stabilized) hafnium dioxide, hafnia, Er-PSH, 9.12 Hf0 2 xEr2 0 3 { erbia partially stabilized hafnia } 1 = = M / mol ) 210.489 + 382.5 16x Temperature range / (°C) 0 to 1600 r (g 3 = = Ptheo / (g cm' ) n/a Porosity range 0 to 0.12 = = N.B.: {See also section 9.15 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o with all X-PSH data a / (10' C) = n/a b / (10' C) = n/a grouped together. n = na/ m = n/a 300 Hf0 (4 4 % Er 0 2 2 3 ) Q [110] = 0075 ro initial OQ. 250 S' Heating o CD 200 - o Ul w _3 3 T3 O 150 - o o o o @6 Cooling 100 400 800 1200 1600 Temperature / °C — — — — — — — — — — ' “ x““ X r“ X T CM CM CM CM CM CM CM CM CM CO co CO to CO 00 x x LL Nt. Ratio Poisson's Bulk Modulus GPa — CD cooling o 1 o 77.5 O' 72.3 re o h- Shear Modulus CL o On 3: CM o r-~ CO CD CM CM 252 221 192 CM o . CD 197 197 CO 193 177 CO 222.3 215.6 207.8 185.7 165.1 141.4 137.3 128.5 130.8 cri 00 00 168.5 CO CM CM CM CO N- N- N- CD Elastic Modulus GPa X x 1 .2 E >*- heating (0 Shear ~o Velocity km/s On 9) N 2: s (0 to Velocity km/s Long. "re r CO - re M CD CO CD 0 CD SS80 CD CD CM Q. OSOt CO SOZO'O CD 09600 06600 CO 0.0757 0.0764 0.0973 0.1127 LU re O O 0.0762 O o !5 Vol.Frac. Porosity d o 0 o 0 d 0) N; N- £ + CO CO 0. CM 1 o fc» E »*— Density LU o X o> Vp re c CO CO CO CO CD <4— CO 23 CO CO CO 23 23 23 CO G) CD o CD re CN CM CNJ CM CN CM CM CM CM x 132 CD 549 774 666 CO o LLL 442 CO CO O 1557 1558 1307 1030 cC i- O CO CM CD CD re cT •a 0 i i 4—* "S Mtl. Nbr. i o i a i ro i i E « 3 i re « i ’E i o <*- of i i E^ re i • resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance .c I *444 i c Determination i o i Method i i i i o re i Q_ N sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic i « i E i o o i i o re i *4 i -O (A i Value Type i re i _>* i c i o X X X X X X X X X X X X X X X X X X X X X X X X X X X X i i CL i i re E i Nbr. i or re Exh. i Q. — i . Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph i yy i o X I LL, CM u o Ref. .o o o o o o O o o o O O o o O O O o o «*=• 110 110 110 110 110 110 110 110 110 110 X z x x } / J • (partially stabilized) hafnium dioxide, hafnia, 9.13 Hf0 2 xEu2 0 3 { Eu-PSH, europia partially stabilized hafnia } 1 - = M / mol ) 21 0.489 + 351 .926x Temperature range / (°C) Oto 1600 r (g " 3 = = Ptheo / (g Cm ) ^ Porosity range 0 to 0. 12 = = N.B.: (See also section 9.15 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o with all X-PSH data a/( 10' C) = n/a b / (10' C) = n/a grouped together. w = na w = n/a 250 Hf0 (4.1 % Eu 0 2 2 3 ) d [11Q] PSH,^ = 0.11 ro ial o0- 200 5 E Cooling CQ ok_ / 0 O CD o o U w °° 3 c -=? 150 \ ° O <9 Heating 100 400 800 1200 160C Temperature / °C — — — —c —— — — —— — T CM CM CM CM CM CM CM CM CO CO CO CO co CO CO CO CO “ Nt T" T x T" X x ILL. (A o 05 L. ^3 o O re re r- h- (A in CM in T~ CO in in o o o in o o- CD O’ h- }, .a 3 05 CM CO 00 X— co h- in r^' 05 ih 05 CO +» ' ' 3 i"- CD in CM CM CM co co in in in CD 05 (A GPs x— 'r~ T_ X— T” re "O hafnia o LU s &- re o (A re stabilized £ o E (0 >re & C) o m partially c o o E _] >re . in in - o & 05 in 05 0 o CO o 13.1 europia &=> CL Eu-PSH, CO (A E c o Qre *5) hafnia, CO CO o in CO 00 h- in 00 CO 05 CM co in in CO CO o CM CM CM T— CO CM 05 XT in in O CO 05 O’ 00 CD CM 1- 9 X CM 05 m in in CO O OO OO CD CO CM oxide, bJ -4-J £ s z {hafnium c 05 re re re 03 re re re re re re re re re re re re re re O o a o o a o a o o o o o u CJ u o o o o o cz c c c c: c c c c c c c; c c c c c: c c re CD 03 03 03 03 03 0) 0) 0) 03 03 03 03 03 03 03 03 03 03 "O c c C c C C C c c c. c c c c c c c C c c o O o o o o o o a o O O o o o O o o o o £ E if) if) if) if) if) if) if) if) C/5 C/5 if) if) if) if) if) if) if) if) if) k. re re re re re re re re re re re re re re re re re re re 0 0 i— L— k_ k_ k_ L_ L_ k_ k— L_ k_ L_ L— L_ k. L— k— k_ i— +-* o o o o o a o a o o o o a o o o o CJ a s re c. c c c c c c c c c stabilized) c c c c c c c c c o o o o o o o o o o o o o o o o o o o a (A CO < o (partially > X X X X X X X X X X X X X X X X X X X o £ k c X £ O 3 LU Z T- X CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CN CO 02 . 0 £ £ £ £ £ J £ SZ sz £ £ £ £ £ £ sz £ £ £ £ Q, CL CL CL CL CL CL CL CL CL CL CL CL Q. Q. Q. Cl CL CL Cl X ro 03 03 03 03 03 03 CO ro 03 03 03 CO 03 03 03 03 03 CO xEu >, k_ L. L_ k_ k_ l— l— k_ L_ k_ L_ 1— U- k— LU h- 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 naJ o O o o O O O o o O O O O O o o O o o T— X X— X— X— X X x X— X— X— X— X— X— X— X— x X— X Hf0 OZ "~ ' ~~ ““ z T- T c X— T } • (partially stabilized) hafnium dioxide, hafnia, 9.14 HfCh xY 2 0 3 { Y-PSH, yttria partially stabilized hafnia } 1 = = M / mol ) 210.489 + 225.81 Ox Temperature range / (°C) Oto 1600 t (g 3 = = Ptheo / (g cnr ) n/a Porosity range 0 to 0.12 = = N.B.: {See also section 9.15 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o with all X-PSH data a / (10' C) = n/a b / (10' C) = n/a grouped together. n = na/ w = n/a 220 Hf0 (7.6 Y 2 % 20 3 ) o [110] pSH,4 = 0 10 m 200 nitial CL CD X 180 - Heating 00 L— / o = 3 CD 160 - O LU O O § 140 T3 O OD O <§> Oo S Q) 120 Cooling 100 0 400 800 1200 1600 Temperature / °C } — — — — — — — —— — T” CM CM CM CM CM CM CM CM CM CM CM CM CO CO co CO CO CO CO x x x Ft. Nt. — Ratio Poisson’s 1 Bulk Modulus GPa 75.1 Shear Modulus GPa CD CO O 0 CO O CM o 00 CO 159.7 142.5 129.7 CO 130.7 129.5 CO 118.5 112.0 123.2 128.7 129.8 O 129.9 150.6 167.9 CM CM CM CO CD 0GU Elastic Modulus GPa t hafnia Shear Velocity km/s zed 2 *»re o © km/s m Long. >© "ire — 3 - t 0 re £ 0779 2 0.0904 0.1013 Q. Y -9.14.1 Vol.Frac. re 2 0 % Z o C e. 7.6 >* + X CO 2 CO E Q. Density o 1 Hf0 > 0) % re CO CO CO CD CM o c CM CM CM CM 287 484 599 702 CO 982 879 715 508 259 CM 92.3 «*- T— 00 1274 1575 1279 1000 re Do CD JC oT w D m3 i ‘5 A i i fraction): s z i o i i i E i i i .3 i (mole i "E of i a*= . i re i i £ resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance i i Determination i i Method i i i i composition i © i i sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic N i i i i i re i <-> i i i V) Value heating cooling Type i >> i i Reported X X X X X X X X X X X X X X X X X X X X X i i i i On On i E i Nbr. re Exh. i i 1: 2: 3: a X CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM i i i co i © i Footnotes: i o a. i CM Exh. i >* Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph >- i l— i X i CM o o O O O O o o o O o o Ref. Nbr. 110 110 110 110 110 X— X 110 110 x 110 110 x x 110 X x X x 2 • (partially stabilized) hafnium dioxide, hafnia, 9.15 Hf0 2 xX 2 0 3 { X-PSH, partially stabilized hafnia } 1 = = M / mol' ) 210.489 + Af , ,x Temperature range / (°C) Oto 1600 r (g x 0 3 = = Ptheo / (g cm' ) n/a Porosity range 0 to 0. 1 N.B.: (All X-PSH data were E0 / (GPa) = {263} BJ (GPa) ={162} 4o 4o grouped together to a/(10' C)= {2.29} 6/(10' C) = {2.29} estimate the parameters} n= {3.47} m = {3.45} Volume Fraction of Porosity ( For data listings, see the separate listings for • (partially HfO, xX 2 0 3 stabilized), where X = Er, Eu, or Y. } • (cubic) hafnium dioxide, hafnia, Er-Hf0 (c), 9.16 Hf0 2 xEr2 0 3 { 2 erbia stabilized cubic hafnia } 1 = mol' = 210.489 + 382.516x Temperature range / (°C) Oto 1500 Mr / (g ) 3 - = Ptheo / (g cm' ) n/a Porosity range 0 to 0.08 = = N.B.: {See also section 9.21 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o all (c) (10' = b (10' = n/a with X-Hf0 2 a / C) n/a / C) data grouped together. n = na/ m = n/a Volume Fraction of Porosity (tf) — — — — — — — — — —— — —— — — —— —— — — — —— — — "“ "“ T- T T X— X X— X X T— re oEL CM CD co o o oo h- CO CM CD CD CM CO m CD r~- 03 o r-- 00 in oo CD CO oo oo oo oo CO CM oo in CM CD m M- co CM X o d oo h- CD m h- CD CD CD CD CD CD CD CD in in in in oCL CO o oo CM CD CD o CM h- oo O CM CD CD C- in CO o CD co co CO CM CM T— CD CD in — O in X CO in CM o 00 co Tt d D- CM oo re CsJ CM CM CN CM CM ' o o CD oo h- h- CD CD CD CD m in a. CM CM X X X x— X x x— x x X” x x— x— CD v> E } M. hafnia m E cubic - CO CD N- O T— in O X— CM in O O O o o o o O o o o o o o o o CM CO in 00 00 CD CD 00 00 00 oo oo 00 00 CO CO 00 00 00 oo 00 00 -9.16.1 O O o o o O o CM CO o o o o o o o o o o o o o o o LU stabilized o O o d d d d d d d d o d o d d d d d o d d d o o CM + 2? co CM erbia (A E o E _o 0 i Q o> sO CO CO CO CO CO CO CO CO CO CO in o o o o o o o o o o o o o o 00 Hf02(c), o CM CM CM CM CM CM CM CM CM CM co— CD oo o o o o o o o— o o o o o x CM co in CD 00 CD o X CM co in X— T— *“ X— c Er- 1 o 1 TO 1 03 1 hafnia, 1 TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO 1 TO a a TO O TO to <_> o o o o o a TO o o o O TO TO a O TO 1 o c c c: cz c c c C c c c c cz cz C cz c. c c= c c c c. C p ro TO TO TO TO TO TO TO ro RJ 03 0! 03 03 03 CD 03 03 03 03 CD 03 03 03 1 c C t= C c C c (Z cz cz c cz c c cz c c (Z C c c C CZ SZ 1 o o O o o o o O o a a o a o o o o o o o a o O o oxide, ia ia in in CA (A CA if) CA if) if) CA CO CA CA (A CA (A (A (A CA CA if) if) 1 to Q> TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO TO L_ L_ 4— 4_ 4_ 4_ k_ L_ l_ L— 4_ 4_ k_ l— W_ t_ 1 if) to o o o a O o O o o a a O O a o a O O O O a a TO 1 O c c c cz c c. c c c (Z c c £Z c cz c c c a c C c cz C o o o o o o o o o o o o O o o o o a o o o o o o 1 E hafnium (/) ia (A if) if) (A if) if) if) if) if) if) if) if) if) if) (A if) (A CA if) if) if) m 1 o TO 1 "O { TO t t 1 o X X X X X X X X X X X X X X X X X X X X X X X X 1 Q. 1 TO (cubic) 1 cc 1 1 if) T- T— X T- <- T- T- <«- T- CO CO CO CO co CO CO CO CO CO CO co CO CO CO 1 T- 1 a) 3 1 o jz JZ JZ x: jz SI JZ jz jz ,c JC. JZ sz JZ JZ JZ SZ sz JZ sz sz sz sz JZ 1 02 Cl CL CL Q. CL CL CL CL CL CL CL CL CL CL CL CL CL Cl CL CL CL Cl CL CL TO TO TO TO TO TO TO TO 03 03 03 03 03 03 03 03 CD 03 CD 03 03 m 03 03 1 o *=_ 4_ 4— 4=_ 4— 4— t— 4— 4— 4— k— l— 4— 4_ 4_ t— k_ 4— L_ k_ 4— xEr n cd CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD 1 lL •2 X X X X x— X™ X x— X X T— T~ X X X T— X X X x x x— x x— X X x— x— x— X X X HfQ ~* ~* "~ *“* X X 'r 'r T X — I } / 8 • dioxide, hafnia, (c), 9.17 Hf0 2 xGd 2 0 3 (cubic) { hafnium Gd-Hf0 2 gadolinia stabilized cubic hafnia } 1 M / mol' = 210.489 + 362.498x Temperature range / (°C) = 0 to 1 500 r (g ) 3 = = Ptheo / (g cm' ) n/a Porosity range 0. 1 6 to 0. 1 = = N.B.: {See also section 9.21 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o all (10' = (10' = with X-Hf02 (c) a / C) n/a b / C) n/a data grouped together. n = na w = n/a 200 1 1 0.25 Hf0 (20 % Gd 0 2 2 3 ) o [ill] Cubic, 23 °C 03 O 150 E a > S' o o u_ O ro DC CD 100 co c ui o CO co 3 O O G o o CL o 50 - 1 1 0.15 0.14 0.16 0.18 0.20 Volume Fraction of Porosity (0) — — 'C— X— LL, z Ratio Poisson's 3(A 3 Bulk 0 GPa 0 § CA h- LO 8= _3 m re ® 3 GPa £ T3 O <0 2 CD 138 CM Eiastic Modulus GPa .2 "E **= Shear Velocity km/s £ns O jS 3 O •a Velocity km/s Long. N - 3 s 0 17.1 re ci co 2 . re 0.184 Gd UL Porosity 0 - .2 % c O o > 20 T3 + (0 CO 2 OS E Density 0 Hf0 2 TO CM % O CO CO X H O CNJ CM 80 0 O "O ; o 1 1 1 Mti. Nbr. fraction): .2" 1 1 "E 1 1 «- 1 ns 1 1 £ 1 1 (mole 1 of 1 a 5 a a resonance resonance ‘x 1 1 Determination 0 1 1 Method 1 a 1 E composition a 3 a 1 'E sonic sonic l 1 1 re 1 1 — £, a a a 1 Value Type a 1 1 Reported O' a X X 1 [O » 0 3 1 l Exh. Nbr. a 1 : 1 « 1 1 1 O 1 CM l l Footnotes; "O 1 Exh. Type 1 Graph Graph l 0 a X a OCM Ref. Nbr. T X t 1 • (cubic) dioxide, hafnia, (c), 9. 8 Hf0 2 xPr2 0 3 { hafnium Pr-Hf0 2 praseodymia stabilized cubic hafnia } 1 - = M / mol' ) 210.489 + 329.814x Temperature range / (°C) Oto 1500 t (g 3 = = Ptheo / (g cm' ) n/a Porosity range 0 to 0.09 = = E0 / (GPa) 251 B0 / (GPa) 183 4o 4o a/(\0- C) = 1.21 6/(10- C)= {1.21} n = 2.86 m = 3.23 Volume Fraction of Porosity {) — — — —0 — — — — —— —— —— —— — — —z — — — —— — —— * — “" ~" -r_ T"” x T T X X T— T” T— Ft. z Ratio Poisson's 3re to 3 CL 3 •a m © CD 1 «o oo T~ 05 05 k. 3 CO CM O TO “ TO 05 00 OO h- 0 CL T3 .e O CD V) s 1- r^- 05 T- xT CO LC5 00 05 o h~ CM CO xr T- CM CO T- oo oo I— CM o x to CM 05 o to O w 3 cm rsi lO T— 05 r- co CO T— 03 h- to CM 05 LO oo d oo cri oo CM X— 05 00 X— h- +-» re — 3 CM o 00 CM CM x x X X x x O o o o O 05 05 05 05 05 OO oo oo OO oo r^- r-'- CO CO (0 £L CM CM CM X CM CM CM CM CM CM CM CM CM CM CM CM CM T“ x X X } to o CD LU s hafnia (/) 0re o -C o E (/5 re cubic > *=» 05 <0 S o o _o E stabilized _l >re 1- . X CM X oo CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM -9.18 o O 00 xT M- XT xT xT XT mt xr XT XT ’RJ" M- xr xf XT xf xj- xr Mr xr re o O o o O O O O O O o o o O O O o o O o O O O o O o o o O o o o u_ o o d o o O o d O d O o d d d d o o o d d d d d d d d o o d d o d a= o O praseodymia > 0. ** m E c o re (c), 05 2 Q X xj- X— x— x— CO co CO 00 OO CM o 05 r-- N- LO CO o o •‘st 05 CM— to CO r- 05 CO xr o . Q CM CM CM CM CM 00— CM 00 CO x CO CO x 00 CO CM 05 OO CD CM X x 00 CM CO o CM oo o CM r= o x X CM CM CO xT M" to CD CO OO 00 05 O x CM CO oo xr xt to CO to LCJ CD co Pr-Hf0 T“ T~ s z.o hafnia, r re re re re re re re re re re re re re re re re Q) (15 re re a) re re re re re re re re re re re n o o o o o o a CJ CJ CJ a a o CJ o o CJ a a o o o o o o o o o a o o o c c c c c c (Z c c c c: c c c c c C= c c c c c c c C c c c c c c c o CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD c C tz c c c C C c fZ c C c c c C C C c c c C c c re re { _3 a re >» > H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X (cubic) .c hi X & 111 z 3 T r- t- CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 0 . 0 sz sz sz SZ SZ SZ SZ -C -C SZ SZ SZ SZ SZ .C SZ SZ SZ SZ SZ SZ JZ SZ SZ SZ SZ SZ SZ SZ SC SZ SZ 2 £ CL Ql CL CL Cl CL CL Cl Q. CL Cl CL CL Cl CL CL Cl CL CL CL CL CL CL CL CL Q. CL CL CL CL CL CL CL X CD CD CD CD CD CD CD CD CD CD CD CD CO CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD t— fe_ t— k_ k_ l— L_ l— I— k- k_ k— k_ k_ k— k_ S— k_ k— k_ L_ k_ k_ k- k_ k_ k_ xPr yy IH CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD • 2 hi 0 CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM n * X X- T— X X T— x— x— X X— x— x x x-• x x— v— x X X— x— X x— x— x— x— x— T- x— xr- X— x Hf0 T- T— T" 'r~ ’r“ T” X“ 'r“ T“ T~ T“ x x X X— X— 1 » T“ T”’ T— Ft. Z Ratio Poisson's! m 3 Bulk 3 GPa “O o 2 (A3 3 re Shear a a. o O S 160.2 158.4 157.1 154.0 149.7 147.9 Elastic Modulus GPa JS t •*- re .c Shear o Velocity km/s 5 3 0 "O N0) Velocity km/s Long. 3 2 02 re *=> Pr (A CNI CN % -9.18.2- re NT Nf 0.042 0.042 O O 0.042 0.042 33.3 1 Vol.Frac. Porosity O o a>H o + re 2 in re co k- Hf0 Q. E Density o % D> «M 66.7 0 CO w- CN N- o 1659 1691 1723 1739 X t— o CO CD w1 i 0- i i i fraction): re" Mtl. Nbr. i ._ i i i »*» i re i i .c i (mole i i re" of i i o i resonance resonance resonance resonance resonance resonance i i K i O Determination i i Method i i E i composition i 3 i i sonic sonic sonic sonic sonic sonic 'E i « i re i i JC i re i **-» Q. i Value i >. i i 1— i Reported o' X X X X X X i i i 3 i 3 i i Exh. Nbr. U i CO i 1: i 0) CN C\l CN CN CN CN * i i o O i CSI i •4—c kc i i Exh. Type Graph Graph Graph Graph Graph Graph O 0= i i o X i u_ CM o CNI CNI CN CN CN Ref. Nbr. 112 X T— 8 • (cubic) hafnium dioxide, hafnia, Tb-HfO,(c), 9.19 Hf0 2 xTb 2 0 3 { terbia stabilized cubic hafnia } 1 = = M / mol' ) 210.489 + 365.849x Temperature range / (°C) Oto 1650 r (g 3 = = 0. 1 Piheo / (g cm' ) n/a Porosity range 0 to = = E0 / (GPa) 229 B0 / (GPa) 186 4o 4o a/( 10- C)= 1.41 Z? / (10- C) = {1.41} n= 1.78 m = 2.78 250 t 1 1 r 0 36 Hf0 (33.3 Tb 2 % 2 0 3 ) o [112] cubic, 50 0.26 0 300 600 900 1200 1500 1800 Volume Fraction of Porosity () Temperature / °C — — — — — —— —— —— — — . T_ T“ T X T~ T (A CD CM *- 3 T— O CO * 5 CO CD CD •a o CO ID CO M- 00 CM T~ in 00 O' in CO CO CO CO T- CM o h- h- CO CD 00 CM CM CM 00 CO CD h- CO CO T— 00 CO o in o CD o O CD 00 oo oo 00 r- h- r- i"- i"- c- CO CO CO CO in CM CM CM T T T— T— } hafnia - CO CO CO CO CO CD CO CO CO co CD CO CO co CO co CD co CO co 6 CO CM 1^ CO CD CO CO CO CO CO CO CO CO CO CO CO CO CO co CO co -9.19.1 cubic & ro i o *“ o O O o o o o o O o o o O o O o o o o o O d O o o o o o o o o o o o o O o d d d o stabilized terbia CO CO CO CO h- T T CM 00 M- r- CD CD M- CD CO o in CM o CM CM CM CM CO LO CO m CO T T CM CO M" CO in CM CO T CM CO M" in CO 00 oo CD o T— CM co m CO T“ ^ 1 1 1 1 1 1 Tb-Hf02(c), 1 1 CD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 o (_> O o o o o o o o o o o o O o O o o o o o 1 c cz c cz c c c c c c cz c c c c c c cz cz c cz cz 1 CD TO ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro CD 1 c C c c c c. c c c c cz cz c c c c c c c c cz CZ hafnia, o o o o o o o o o o o O o o o o o o o o o o co CO (0 0 0 0 0 0 0 CO 0 0 CO 0 CO CO CO CO CO 0 0 CO 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 l— 1— t_ i— t— k_ fc_ k_ k_ (=_ l_ 1— L— k_ k_ k_ k_ k— t— k_ k- 1 o o o o o o o o O o o o o o o o o o o o o o 1 c cz c cz c c c c c c c c c c c c c c CZ c c c 1 oxide, o o o o o o o o o o o o o o o o o o o o o o CO CO CO CO 0 CO CO 0 CO CO 0 CO CO CO CO 0 0 CO CO CO CO 0 i i I i i i i hafnium i X X X X X X X X X X X X X X X X X X X X X X i s 1 1 . 1 { 1 CO *— *“• 3 CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 1 0 1 o 0 X XI x xz XZ x: XZ sz xz XZ XZ XZ XZ X _cr X X X X JZ X X 1 2 Cl Cl CL Cl Cl Q_ Cl Cl CL CL Cl Cl CL Q. CL CL Cl CL Cl CL CL Cl CD TO ro ro CD CD CD ro ro CD CD ro CD CD CD ro CD ro ro CD CD ro 1 o xTb k_ k_ fc_ l_ k_ k_ k- k_ k— k_ k_ u. L— k_ k_ t— Q 0 0 0 CD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 lL •2 CM CM CM CM CM CM CM CM CM CM CM— CM CM CM CM CM CM CM CM CM CM CM T— 'c ^ T— ^ HfQ V — T T T— • (cubic) hafnium dioxide, hafnia, (c), 9.20 Hf0 2 xY 2 0 3 { Y-Hf0 2 yttria stabilized cubic hafnia } 1 = = M / mol' ) 210.489 + 225.810x Temperature range / (°C) Oto 1500 r (g ' 3 = = Ptheo / (g Cm ) Porosity range 0 to 0.38 = = N.B.: {See also section 9.21 E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o all (10' = n/a (10' = with X-Hf0 2 (c) a / C) b / C) n/a = - data grouped together. } n na/ m n/a 300 0.32 HfO (20 % Y 0 ) 2 2 3 [111] 250 - Cubic, 23 °C 200 QQ k_ o ro a: CD 150 0 0.26 0.00 0.05 0 10 0.15 0.20 0.25 Volume Fraction of Porosity () — —< y. z Ratio Poisson's 3V) re Bulk 3 a. "D O o 2 co 00 49 Shear Modulus GPa CD 127 CM Elastic Modulus GPa Shear Velocity km/s 2* o o km/s Long. .5 © - 'E > •*- CO re Z90 O -9.20.1 £ CM o 0.231 > !5 Vol.Frac. Porosity 0 3 o' O O CM T3 0) + N co CM E o s Density o re X <-> O) W o' re CO CO O 'C o CM CM 00 is t- o >e "S' i o i I -*—> i o CM Nbr. i i ro § i i_ o I M i i 0) X i a i i o >- i of i E i re i resonance resonance i i c 'E i Determination o ce- i •4— i Method re i i (/) £ i o i a CL re I sonic sonic "U i i E i o X i i o o i © i "O i a i © E Value i 3 i c i o £ X X i “E i Q. **- i i CO I Footnotes: © I o a i CM i Exh. Graph Graph >» i >- i X h- i CM 0 Ref. Nbr. - 1 x • (cubic) hafnium dioxide, hafnia, (c), 9.21 HfO : xX 2 0 3 { X-Hf0 2 X stabilized cubic hafnia } 1 = / mol' = 210.489 + M x Temperature range / (°C) Oto 1500 M ) x r (g 3 = Porosity = to Ptheo / (g cm' ) n/a range 0 0.38 N.B.: {All X-Hf02 (c) data EJ (GPa) ={256} B0 / (GPa) = {200} 4o 4o were grouped together to o/(10- C)= {1.52} 6/(10- C)= {1.70} estimate the parameters} n= {3.01} m = {4.09} 250 225 GPa O0. I B) ® 200 or o e> (£,G, ui * 175 3 Modulus TD O 5 150 125 0 400 800 1200 1600 Temperature / °C Volume Fraction of Porosity ( For data listings, see the separate listings for • (cubic), HfO, xX 2 0 3 where X = Er, Gd, Pr, Tb, or Y. 8 oxide, holmia 9.22 Ho 2 0 3 { holmium } 1 = = M / mol ) 377.859 Temperature range / (°C) Oto 1000 t (g 3 = = to 0. 1 Ptheo/Cg cm' ) 8.414 Porosity range 0 = = E0 / (GPa) 175 B0 / (GPa) 155 Ao = 4o a/(\0 C) 1.08 b / (10' C) = 0.98 n = 2.60 m = 3.43 1 1 1 1 . 1 1 1 . 180 i 1 1 r 1 r- o 0= 0.074 [106] 160 Ho2°3 v 0=0.133 [106] n ro E orco 0=0.182 [106] O MO S' 120 — o wwwv___ e> ioo UJ-^acQmc CCa3Qo_ UJ % 80 o 60 40 20 150C Temperature / °C — — — — <«** yu 2! 0.290; Ratio Poisson's 00 CD 3 Modulus GPa CO 00 CM ID CD CD 64 5 56 56 54 56 53 ID 65.54 Shear Modulus GPa CO CO in x CD CD CO CD 166 159 147 •'3- 140 143 139 136 137 134 CO 130 123 118 T O 105 169.4 X t Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. - o Z90 CO CD CD CM CD CO 9Z0 CD CO CO 0.02 ZSO CD zoo 9Z0 ezoo 980 960 860 ezoo -9.22.1 £ 0.013 0.015 0.019 0.045 o 0.071 0.073 O 0.107 0.123 0.157 0.174 0.014 O O O ezoo (A Vol.Frae. O 0 o 0 0 0 O 0 O O o O O 0 O 0 i_ O CL CO E Density o "5> CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO o 23 CM CM 23 CM 23 CM CM CM 23 CM CM 23 CM CM 23 23 CM CM CM CM CM CM CM 23 CM CM CM 23 23 CM 23 i- o s Nbr. 1 . — of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method m extrapolation E — o sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic £ . a> o. Value . X >. o t— o X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X £ 3 Exh. Nbr. — E CO co CO co CO CO co CO CO co co co CO CO CO co CO CO CO CO CO co co CO CO CO CO CO CO CO CO £o Exh. Type Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph o CSJ ID Ref. Nbr. ID ID 0 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 o O 105 105 105 105 105 105 105 105 105 105 o 1 T— t— <4=5 Nt. LL. Ratio Poisson's re 3 Modulus 0CL — CO CO CO CM X— X CD LO CO CO co CM CO CM o CD OO O CD OO CD 00 CD <3- LO LO LO in LO LO o o d O o CD CD CD CD OO OO OO OO [2 1^ CD CO CD re •O’ CO CO CO CO co CO co CO CO co CO CO co CO CO CO Shear Modulus 00. 00 CO CD 00 CM CM h- l''- CD OO CO in Shear © E >0) O) (A c Velocity E Jo X Z800 CD 00 CM CM CM CM CM CM CM CM CM CM d in OO 00 00 OO OO 00 OO 00 OO 00 OO 5600 660 -9.22.2- re 0.094 0.108 T— 0.122 0.133 0.174 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 T— i= u= Porosity 0 o o o d d d O O d o d o d >o ro E Density o OJ CO CO CO CO CO CO CO CO CO CO CO N" CO CD CD o CO o CM CD m CD CM CD CD in CD CD CM CN CNJ CN CM CM CM CM CM CM CN CN CD in CD x— CD in CD CO CD CM 00 CM CO CD O’ i- o o O o m O o CM CM CO CO O" m in CD CD h- r- OO 00 00 CD £ij 2 of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination m Method E dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic £o of Q> o. D Value '5 >. o H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E £ u 3 X £ UJ Z E CO CO CO CO CO CO CO CO CO CO CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM o CD £ £ £ a CL X >. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph CD Graph Graph Graph Graph Graph UJ h- 0 ! O i CN o a> £ in in in in in in in in in in in CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD tc. o o o o o o o o o o o o O o o O o O O O O o— O O o o O o o o— O o X Z T— T— T T X T— X n —V — — — — — — — — — — — — ; 4=5 4=5 LL Z — CA e o © CA re _CA a O' Bk MT CD CD r- O’ CD LO CO o CM co 03 o CO CM CM CD CD 03 T— 03 CD r- o CM 03 x— ko (A ©re O JC o 1 -X re ds (A c o o o E >© - . CO CO CO CO CO CO CO CO CO CO CO CO co CO CO CO CO CO CO CO O’ •^r M" *3- M O’ o -S’ CO CO CO CO CO 00 CO CO CO CO CO co co CO CO CO CO CO co CO i^- h~ r- r- c- r^- 1^- TO x— T— X— T“ x— x— X— X— X— X— X— X— X— x— X— X— X— x— X— -9.22.3- "m o o O o o o o o o o o o o LL. O o d d d d d o o d d d d d d d o d d d d d d d d d o o d d d o o d &= O o > 0. & CO CA E E o © Q O) *}- CO CD CM r— o CD X— I''- CO CD 00 co co f~- CM 00 OO CM LO T— in T— CO CO T— o M" 00 CM CM LO LO X— LO T LO CM CD 03 T“ CM CD T— CO CO 03 CM r— in T 00 CM 03 LO 1 o O' o o o "“ "‘ "_ P O T T CM CM CO CO M- O' LO in CO r~- C'- CD CD CD 03 03 T CM CM CM CO CO m in CD s Nbr. CD 0) B © SZ XI SZ XI sz xi x; JO JZ JO x: x: x: XI JZ x: sz JZ JO JO SO JO sz XI JZ sz XI JO JO SZ JZ JZ Pi- CL Q. CL CL CL Q. CL CL CL CL CL CL Q_ CL CL CL CL CL CL CL CL CL Cl CL CL CL CL CL CL CL CL CL CL 3»> 03 03 CD CD 03 03 03 CD CD CD 03 03 03 CD 0) 03 CD CO CD 03 CD CD ro CD 03 03 ro ro CD 03 CD ro CD { k— k- L— 1— k_ k_ fc_ L. L— f— k_ k_ l— L_ It— k_ fc_ k_ L_ k— l— U- k_ s_ k_ UJ |P= 3 0 0 0 o o O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 4=^ aJ © xs CD CO CO CD CO co CO CO CO CO CO CO co CD CD CD CO CO CD CD CD CD CO CD CD CD CD x> CD CD X) X) D Ho O' 7* O o o O o o o o CD o o o o O O O o o O O O O o O O O O o O O o o O 'l— " T TT- T- T v— 1 LL Nt. Ratio Poisson's re Bulk Modulus ft. CD IS 00 8 h- 03 51.71 49.7 k. LS o O) re in 0S LD 90S M" © Modulus GPa s. (0 CO T 135.6 135.6 CO 133.3 132.5 129.6 re CO CO CO Elastic Modulus 0. CD o Shear o km/s >© >. . O' M- o h- C'- t^- c- |X & -9.22.4- re o o o o o o O o Li- o o o o o o o o o “ k. O o > 0. & CO (A E C o © Q O) T— CO CD O’ CO CO 03 CO o CO in -o- o CO CD CM 03 O CD CD CO oo OO 03 03 k! S z.O oCD Q)o J^holmium . © _£Z sz sz SZ sz sz -C sz £ a. CL Cl CL CL Cl CL CL CL X >* CO CO 03 05 03 ro 03 03 L_ k_ 1— l_ t— k— 19 l r- 0^ cd CD CD CD CD CD CD CD 2 kl © .o oCD OCD OCD OCD CDO oCD OCD OCD Ho Q£ ~* “’ ,r~ T X— T V_ 0 9.23 La . Sr Cu0 _ La(Sr):21 2 x x 4 y { } 1 = - - = -256 M / mol' ) 405.355 51 ,286x 15.999y Temperature range / (°C) to 27 r (g 3 = Porosity = to 0. 1 Ptheo / (g cm' ) 6.94 range 0.06 for La, Sr Cu0 g5 0 , 5 4 = = E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o a / (10' C) = n/a b / (10~ C) = n/a n = n/a w = n/a 130 1 1 1 \ 1 1 ^wwvwvW^WVWWVWww^ 120 - ro Ol v O E v 00 ol— loory CD 60/ / UJ 3 3 50 - ^WWVWWVWW„^wwvwwvww vV TO O V7 - La2-xSrSr Cu0 40 2 . x x 4 . v [98] 30 1 1 l i i i 100 Volume Fraction of Porosity ($ 0 50 150 200 250 300 350 Temperature / °C 2- . 23 9. - lutetium oxide, lutetia 9.24 Lu 2 0 3 { } 1 = M / mol' = 397.932 Temperature range / (°C) Oto 1000 r (g ) 3 = = Ptheo / (g cm' ) 9.423 Porosity range 0 to 0.34 = =161 E0 / (GPa) 204 B0 / (GPa) 4o 4o fl/(10' C)= 1.03 b / (10' C) = 0.24 n = 3.12 m = 4.27 GPa / (v) S) Ratio or (£,G, Poisson's Modulus Temperature / °C — — — Nt.1 &JL O) 00 00 oo CD oo oo oo oo 00 00 00 8820 682 682 0.287 0.288 04 C\| 0.287 04 04 0.290 0.290 0.290 04 01 0.289 Ratio o o O o 0 o 0 o Poisson's! O in q 139.7 138.6 136.8 135.3 133.5 133.2 132.7 132.7 129.0 oo oo 126.3 125.8 CO CO CO 04 04 Bulk Modulus GPa T— T in r- CO S'S9 65.1 63.9 63.1 61.9 69.2 68.8 68.4 o-' to 66.3 64.7 62.7 62.7 61.9 CD to CD Shear Modulus GPa 'T 178.3 176.5 175.1 173.4 172.0 170.6 169.7 168.4 r»' 166.6 165.2 CO 162.5 161.2 160.3 158.9 CD CD Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. - -9.24.1 Vol.Frac. Porosity n E 9.022 9.022 Density u O! o 82 oo CO 20 04 o 04 146 227 o 372 435 517 584 625 700 783 837 CD 937 966 00 146 227 308 372 435 517 584 625 700 783 837 883 937 966 t- o CO 00 Mtl. Nbr. of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method 2 'P Q) *=» 3 sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic oT S 'x Value Type! © X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E 3 Nbr. °4S Exh. 0) T— T 3 0=^ Exh. Type Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table W I o i N m in m Poisson'sl Ratio Bulk Modulus GPa S T— 71.0 69.1 67.1 CO 67.2 65.3 58.6 58.6 52.9 42.4 36.7 cn 21.5 CD 09 CD CM Shear Modulus GPa 1 169.il O o O) see 52.6 181.7 180.7 172.9 174.9 162.4 155.7 157.6 CD CD CO 104.5 00 Elastic Modulus GPa T— Shear Velocity km/s Velocity km/s Long. o CO O CO m 00 CO CO >d- 05 o 00 00 CM -9.24.2- 0.057] o o 0.037 o 0.077 0.092 0.094 o 0.109 0.124 0.129 0.235 CM CO Vol.Frac. Porosity d d o d d o d d CO E Density u O) CO CO CO CO CO CO CO CO CO CO CO o 23 23 Mtl. Nbr. of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination #*** Method .2 0) *-* D sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic aT 0) D Q. '5 Value o >» h- X X X X X X X X X X X X X X X X X E 3 Nbr. ‘<£5 Exh. 0) s 0) Q. Exh. >. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 1- fO i ! j o u N CD CD CD CO co Ref. 116 116 116 3 n 116 116 116 116 116 116 116 116 116 _J z T“ 9.25 MgAl magnesium aluminate (spinel), MgOAl 0 : 04 { 2 3 } 1 = = M / mol' ) 1 42.266 Temperature range / (°C) 0 to 1200 r (g 3 = Porosity range = to 0.38 P.heo/lg cm' ) 3.572 0 = E0 / (GPa) 278 £0 /(GPa)=187 4o 4o fl/(10' C)= 1.98 b / (10' C) = 1.97 n = 3.20 m - 3.57 — “ ~ "” T“ T"“ T“ ,r 'r T — T uu Nt. Ratio Poisson's Biiik Modulus GPa Shear Modulus GPa r^- 9 CO 9 CO o o 9 9 CO 9 9 62.7 62.7 62.7 62.7 62.1 61.6 61.6 61.6 59.5 59.5 57.9 57.9 58.5 c\i 19 L9 o 909 909 909 o o 69 CD 069 CO CO CO co CD CO CO co 69 ID 89 89 Elastic Modulus GPa £ o Shear O km/s >03 Velocity km/s Long. - co C\l o -9.25.1 Vol.Frac. Porosity CO E Density o o> o r^ 00 in m CM CO T— CM CO o CM co in N- o 118 00 152 CO 198 220 237 258 279 296 313 339 360 CO 394 CO 454 479 492 552 590 T— 675 CD 735 K o CO M" CD CO I''- Mtl. Nbr. o c of Q. HI resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination £ Method 13 c E 3 sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic (0 E a> a. 3 Value >s ‘55 h- a> X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X c 05 (0 Exh. Nbr. E M- <3- •sr M- sr "cr sr M" "vT M" •M- ^r •^r ’cr Type O Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph < J o> Ref. Nbr. CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 73 CO CO CO CO 73 CO CO CO CO 73 CO CO CO CO 2 1^ r>- I-'- h- h- r^- } — — — — — X— CM CM CM CM CM CM CM CM CM CM CM CM CM I re Cu m o re O0. o CM CM CM CM CM CM OO CO CO O' 05 05 05 t- X CO CO CO ix CO o O o CD o 05 O' in CM |X 00 O O O O O X— x— CM CM CO CO CO x— x— o 05 00 rx ix |x (x fx CD CD CO X— OO CM m CD CD CD CD CD CD CD CD CD CD CD CD CD CO CO CO rx ix (X- IX. Ix |X (X |x fx fx IX rx CD CO O CM CM * w E S w E in x— CM o O -9.25.2- o O o O CO in in c o CM CM 05 o CO CD m OO r-~ in CM 05 o- 05 CD o CO CO o O o O o o O o O o o o o CO CO o CD T“ 05 |x in CO CO 05 |x in CO 05 m CM CM CM o O o O in o in o in o o O o CM CM rx rx CD CD CD CD m O' O' CO CM CM X CM CO O' O' in in CD CD |X OO 05 o X 0) CD CD CD CD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (spinel) o u O O o a o o o o o a O O o a o a o o o CJ o o o a o O <_> o a c c cz c c c c c c cz c c CZ c cz c CZ cz cz c c c c cz cz cz cz C cz c cz CD CD CD CD CD CD TO TO 0 ro CD CD 0 ro CD CD CD ro ro CD ro CD ro ro ro ro ro CD CD CD ro C c tz cz cz cz C c C cz c c c c c c CZ c c c c c c CZ CZ cz c C CZ c c: o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o CO 0 05 05 CO 05 C/) CO CO if) if) CO CO if) 0 0 0 0 0 CO CO if) CO 0 0 if) CO if) 0 0 0 CD CD CD CD CD 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 t- fc_ l— k— l— i_ L_ fc— 1— k— t— k_ l_ u_ fc— L_ l_ L- k_ L_ 1— L_ i— l— k_ w_ L_ l_ aluminate a o O O o a o o o o a a o o a o a o o o o o o o a o o a O o CJ c c c c c c c c cz c c c cz c c c c cz c cz cz c. c c cz c c c cz CZ c o o o o o o o o o o o o o o o o o o a O o o o o o o o o o o o 0 0 (/) if) CO CO (/) 05 05 CO CO CO if) CO (0 if) if) if) CO CO 0 if) CO if) CO CO CO CO 0 CO CO 0 magnesium X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X < < O' o- O' O' O' O' It O' O' O' O' O' O' O' O' O' O' •O' O' O' O' O' O' CO CO { jz jz JZ JC JZ JZ JZ sz sz JZ .c x: x: x: JZ JZ JZ JZ x: sz JZ JZ JZ JZ JZ JZ JZ JZ JZ JZ CL CL Cl Cl CL CL CL Cl CL CL CL CL Q. CL CL Cl Q. CL CL CL CL CL CL CL CL CL CL CL o. CL 4 CD CD CO ro CD ro CD cd CD cd CD cd ro CD JJ CD CD CD CD ro CD ro CD ro ro CD ro ro CD ro CD 0" CO 0" 0" 02 6 0 0 0 0 0 O 0 0 0 0 0 0 H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 MgAI fx |x CO r) CO o O CO CO CO CO CO co CO ro CO m m n n in in n n m in m in LO in in X x IX rx tx rx ix IX ix fx rx rx ix i-'- lx rx ix ix ix rx rx rx |X fx fx IX |x |x |x lx — — — CO co CO LL z Ratio Poisson's Bulk Modulus GPa CO 9 CO 94.5 ID 97.9 94.5 CO 74.5 72.4 53.8 CO 32.4 19.3 O CD 00 99 co Shear Modulus GPa 9 CO 6 CM CD 242 79.3 46.9 258 292 235.1 219.3 195.8 186.2 181.3 166.2 137.9 133.8 CD 254.4 237.9 180 CM 892 CO Elastic Modulus GPa CM Shear Velocity km/s Velocity km/s Long. CO O" 00 CD T h- CD CO M" 6Z0 o 068 CD h- CM 688 0.027 0.053 0.057 9900 0.119 0.125 0.128 0.137 0.161 0.198 0.312 0.319 0.045 0.049 0.135 2020 0.199 o o CM O O o CO co -9.25.3- Vol.Frac. Porosity o o 0 O 0 o O o d d d 0 co E Density o 03 CO CO CO CO CO CO CO CO CO CO CO CO CO 23 CO 23 CO CO 23 CO 23 CO CO CO CO CO CO CO CO CO CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 200 400 1- Oo Mtl. Nbr. "3 c a of i£. resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance ® Determination Method cre E sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic re E 3 Value Type 03 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X C/3 C/3 ca> 03 JZ X Nbr. 3A 3A 3A 3A 3A 3A 3A 3A 3A 3A < 3A 3A 3A 3B 3B 3B CD 3B 3B 3B 3B 3B 3B 3B 3B 620 620 620 E UJ ve VC CO ve CO a& Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph >* Text Text Text O i- CM < r- h- r^- CO 00 O) Ref. Nbr. — s 117 117 117 117 T 117 117 117 117 117 117 117 117 117 117 117 117 n T 118 } — ’ 1 CO CO CO CO Ft. Nt. Ratio Poisson's Bulk Modulus 0eu Shear Modulus GPa CT) CD O O CO CO CO 233 227 CM 258 275 275 CO CO ZQZ M- O 258 O 196 961- 189 CM CM CM CM CM CM CM Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. -9.25.4- Vol.Frac. Porosity i CO 89 E £ 3491 3.491 Density o o> O o O CO CO 23 O CO CO o o o O CM CM 400 o 800 CM CM o o 1000 1200 1400 1000 1200 1300 H o CO CO CM CO CO 1 Nbr„ l s 1 l 1 1 l 1 i 1 i l (spinel) of i method l (3-pt) (3-pt) (3-pt) (3-pt) (3-pt) (3-pt) (4-pt) (4-pt) (4-pt) (4-pt) (4-pt) i l l l resonance resonance resonance resonance resonance Determination l 3 Method 1 1 1 specimen 0 specimen 1 1 aluminate ultrasonic unknown 1 bending bending bending bending bending bending bending bending bending bending bending 1 sonic sonic sonic sonic sonic 1 1 1 1 1 1 1 1 heating Value Type 1 cooling Transparent 1 Translucent 1 1 if) if) if) magnesium CO X X X X X X X X X X X X X X 1 1 1 On On Nbr. o o o 1 Exh. C\l CM CM 1624 3441 1858 co 620 ! 0) 1: 2: 3: 4: co co co lO un cn in in un in un in LO m i i i o { © i i c a i i 4 Exh. X Graph Graph Graph Graph Graph Graph X Graph Graph Graph Graph Graph o Text Text Text Text Text i © CD i o 0 i 2 l- h- Li_ MgAI 00 CO 00 05 T— Ref. Nbr. — o o T T— 118 CM 120 120 CM 120 120 120 CNJ CM :m CM CNJ CNJ T— T— T 9.26 MgO { magnesium oxide, magnesia } 1 = M / mol' = 40.304 Temperature range / (°C) 0 to 2500 x (g ) 3 = = P.he0 /(g cm' ) 3.58 Porosity range 0 to 0.26 = = E0 / (GPa) 310 B0 / (GPa) 164 4o 4o a / (10' C) = 1.63 Z>/(10' C)= 1.23 n = 3.81 m = 2.64 (v) Ratio Poisson's — fUL z CO rx CO 00 CO CD CO 0 ™ d d d d Poisson's Kre 0- T O' CO M CO O CO M- zc re 10 — m CO 3 Modulus 0. 7 m O CO CM rx CO co 0 CO m CM rx S=B NT •^r d 0 0 0 CD co co m re re CM CM CM co CO CO CO— CM CM CM CM re Modulus a. t (0 O ix CO CM ix in CD CD CD CD CO 00 co co |X CM rx CM CM co CO rx co 0 CD T— 00 CD rx CD co CO CO IX |X 00 CD rx! •o- r- CM M- O' CD CD sr CM CD CD d d CD re CD 00 CO CD CD 00 rx r^ CD CO in in co CO CO CM CM CM 0 O 0 0 0 0 CD Elastic Modulus CM CM CM CM CM CM CM CM CM CM CM CM co CO co co CO CO OCL CM CM CM CM CM CM CM CM CM CM re m 0) JZ Velocity E V) j£ 6 * =SS co CD CO CO co CD CD - 0 O 0 0 0 0 O 0.02371 0 O 0 0 0 0 O -9.26.1 Vol.Frac. Porosity d d d d 0 d d CD CO CD 00 0 O CO O CO |x in in co E ID O' 'fr co in Density CO CO CO co CO CM CO O) CO co CO CO co co O O 0 0 O O 0 0 O O 0 0 0 in in O in in co M- co CM |x |x CM CM CM CNJ CM CM O O 0 0 O O 0 0 O O 0 in 0 CM |X O CM CM CO in fx CD CD CM H 0 CM CO M" in CD |x co CD O CM CM CM CO co CM 0 x 33 A s z of resonance resonance resonance resonance resonance resonance resonance .2 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance t/5 Determination CQ> Method O) resonance resonance resonance resonance TO dynamic dynamic dynamic dynamic dynamic dynamic dynamic E sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic 6 ~o re 'x 3 re o a re >> E > H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X GO X £ CD CD CD CD Q. CL CL CL CL CL Ol CL CL CL CL CL CL CL CL Q. CL CL CD CL Cl CL CL CL CL E X »> -Q .Q m -O .Q CD CD CD CD CD CD CD CD CD CD CD CD CO CD CD CD CD CD SZ CD CD CD CD CD CD i— u LU i_ TO CO CD CD CD CD I- 1- 1- H 1- O CD CD CD O O CD CD CD CD CD CD CD <5 CD CD CD O 1- CD CD CD CD CD CD o ij O) re a CD CO CD CO in in in in in in m in in in in in in in m in in in in O 0 0 0 0 0 0 s X 3! T— rx rx rx h~ rx IX. fx fx |X |x rx |x IX |x IX IX IX rx |X CO CO CO CD CO CD co — —— — — — — - — —— — Ft. Nt. o ‘5 Poisson's Kre O’ £ re CD 3 Modulus CL CD o s- s- CD 00 CD oo o m CNJ CNJ CD r^- CN oo CD o N" CN N" I I CD O CD CD O O O 00 OO s- s- O’ CO CN d CO CD LO csi CD O I d CD CO CD I CD CD CO in OO CD CD CD in CO o CD re CN CN CN x O CO CN CN CN CN CN CD 03 CD CD oo OO co CN . Shear Modulus QL T X X CD ^ s- s- s- in o CO O’ oo CN oo I CD I 00 CD O’ CN CN CD CO t^- CO CO CN 00 I CD CD in CD r-- CsJ s- r- CD CN CD CN oo CD co 00 CO 00 co CO oo r— d in OO oo co d in in CN CN I CN •^r X re s- s- s- s- s- s- CT> CO CT> 00 CO I i-- I CD CD O o o oo 00 CD 00 I I I I •N- N’ N- CD CD o O Elastic Modulus a. CN CN CN CN CN CN CN CN CN CN CN CO CO CO CN CN CN CN CN CN CN CN CN CN CN CN CN CN T co CO CD (A Shear Velocity E -X 03 (A c o Velocity E _l s- s- - ID CD CD CD CD CD CD CD CD CD CD in in in in in CN CD CD CO in in in in CD I OO in I CN o O O o O o O o o O O O’ O’ O’ O’ O’ O oo O CO CN co xr in »3’ N- N’ 00 co CO o O 2 o O o oO O o o o o o O o o o o o O o OCN OCN oCN oCN oCN oCN o O O OO’ o o O 9.26 Vol.Frac. Porosity o O o d O d d d d d d d d d d o d d d o d d o d d d d d d d d d - s I - CO CD E in Density o co OJ s- s-- o CN o k S zX2 of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance Determination Method resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic 0) Q. Value >. H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X l! Exh. A Z _ x x _ re A A A A x: A A x: A A x: A XI A x: A x: A A A A A A A A A A A A A A a CL CL CL Cl CL CL CL CL CL CL Q. C15 CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL Exh. >» 05 CD CD 03 CD CD CD co CD CD CD X3 CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD k. t_ k— L— k_ t u. k. h- CD CD CD CD CD CD CD CD CD CD CD CD 1- CD CD CD CD CD CD CD CD CD CD CD CD CD (5 CD CD CD CD CD CD k CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN MgO Ref. o o o o o o o o o o O O o o o o CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN z 00 00 00 00 CO 00 CO oo 00 oo 00 00 00 oo oo oo x— T T T— — . — — — — — — — — u. Nt. 5o Poisson's re VC - re Bulk Modulus 0a. T 8 97.2 97.1 998 87.3 128.1 126.4 124.2 122.4 119.5 121 116.7 114.1 115.8 112.3 110.5 96 Shear Modulus GPa 8 9 o CD CM 290.4 290.4 281.4 CO CO 273.6 275.2 270.1 CM 240.6 242.2 207.0 in 302 2434 862 CO 00 o Elastic Modulus GPa CM CM CM CM CO CD 6 5.901 9 5.818 5.818 6.026 6.023 6.019 5.945 5.948 5.936 in 5.932 5.928 5.897 5.845 5.802 Shear Velocity km/s Velocity km/s Long. CO CM in ^r 00 in t--- CO d O o O CM M- o co CO o 0019 zeoo re 0.021 0.023 0.024 SZO'O 0.109 0.112 991-0 0.034 o o CCOO'O 98000 o 0.0158 0.0163 0.0174 0.0192 ZZZO'O ZZZOO CM k. O o o o o 0.0204 0.0386 O o o o d -9.26.3- Li- Porosity O o o o o o o d 0 d >'S CO E Density o OS CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO 23 23 23 23 23 23 23 23 23 23 23 O CNJ CM CNJ CM CNJ CM CM CNJ CM CM CM CM CM CM CNJ CNJ CM CNJ CM CM CNJ h- O Mtl. Nbr. of sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere .2 ‘35 Determination a> Method e D) re resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance s resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant "O '5 o Value Type E X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 3 ‘35 Exh. Nbr. © — ^ — C 'i T _ T _ _ _ _ _ Ul re Type E Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph O _ CM CM CM CM CM CM CO CO CO CO CO CO CO CO CO CO CO D> Ref. Nbr. 122 CM 122 CM CM 122 122 CM 122 122 122 122 CM 122 122 CM 123 123 CNJ 123 CM CM 123 CM CM CM 123 CNJ CM CM CNJ CM s T T T X ^ T T— T— — — —— — ^ T x— uu Nt. CO 00 CO O’ co co LO o O CM ID CO O’ OO oo 00 oo OO CO CO CO CD CO CD 96 o O 0.183 0.181 0.182 0.182 0.183 0.185 0.188 0.185 0.189 0.187 0.187 0.183 061/0 0.192 L0 0.198 0.202 0.205 Ratio O o o o o d O d d d d Poisson's Bulk Modulus GPa CO CD CD CO 135.2 134.6 d 128.4 125.8 123.4 120.9 00 115.9 113.4 CD 103.9 CO O T Shear Modulus GPa h- 3 CO 319.1 r- 314.4 309.6 304.4 299.0 293.6 288.2 282.8 261.0 250.5 LLZ h/ Elastic Modulus GPa co CM co r- Shear Velocity km/s id Velocity km/s Long. co ID M- CO ^r CM O' [X- CD o CO CO O co h- CD o eoo CO CO co £ o o 6£00 8910 CM 3320 0.034 o CO 0.0437 O 0.0165 0.0222 0.0234 in o o o o O O O O -9.26.4- Vol.Frac. o O d >. o d 0 0 d o O O 0 d d o 0. CO CO o E CD 3.602 Density o cd o> CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO co CO CO CO CO i"- C'- CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM h- CM CM 227 327 427 527 627 727 927 -273 1127 H o T“ 1 O 1 s Nbr. of sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere sphere — .2 resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance <75 Determination cre Method O) re resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant resonant E sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic © "D '5 re Q. O Value >» E H X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X o 3 '<75 Nbr. 0) Exh. -Q X) -Q JD XJ _Q XI XI XJ XI c i CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM F~ £ i5 h- £ |x. r^- u> re © CL E Exh. >s Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Table Table Table Table Table Table Table Table Table Table Table Table Table h- O CO CO CO CO CO CO CO CO CO CO CO CO M- M- O' "3- M" D) Ref. Nbr. CM CM CM 123 CM 123 CM CM CM CM CM 123 123 CM CM 123 CM 123 123 CM CM CM CM 124 CM CM CM 124 124 CM CM CM s x— T T— T T— — — — T CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM LL Nt. 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Porosity CO CO 3.47 00 to E 3.486 3454 3.438 3.422 3.405 CO 3.371 CO Density 0 CO CO o> LZL 827 927 method 1027 1127 1227 1327 1427 1527 H Do Mtl. Nbr. 1 1 1 resonance 1 i 1 1 1 1 1 1 1 of l 1 1 a l l l Determination « 1 l 0) Method parallelepiped 1 specimen c 1 1 os l 1 A resonance resonance resonance resonance resonance resonance resonance resonance resonance 1 1 E l 1 1 oT l 1 crystal u 1 1 ‘5 0 1 1 a 1 Value 0 >. 1 Rectangular j h- 1 E X X X X X X X X X 1 Single 3 1 1 1 Nbr. 1 Exh. t/y ID ID ID ID ID ID ID ID ID 1 1 2 c 1 a) 1 0 1 b A a> 1 l c a 1 1 E Exh. >. Table Table Table Table Table Table Table Table Table 0 1 1 0 1 LL O os Ref Nbr. S 125 125 125 125 125 125 125 125 125 1 Pr:123 9.27 PrBa2 Cu 3 0 7_x { } 1 = 196-15. 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CL CL CL CL CL CL (X CL Cl CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL CL Cl CL CL CL >» TO to TO to ro 03 ro ro m ro ro ro ro ro CO ro ro ro ro ro ro m ro ro ro ro ro ro ro ro ro ro ro b— b_ l— l— b— t=_ b— b_ b_ b_ b_ b— v__ b_ i— b_ b_ b_ b^ b_ l— b^ b_ l— b_ b_ L— b_ { [I 3 CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD 0 CD 0 0 0 0 0 0 0 U 2 .Q -ct- m- •sr TT M- M- M- 'cr TT M- 'tf- Sc CO CO CO CO CO CO CO CO CO CO CO CO r) ro CO CO CO CO CO CO CO CO ro CO co co CO CO CO CO CO CO ro 2 ' “ , “* — •?— ' ~ — — N r 'I— c n T T" r T- T“ T_ — — — — — — —— —— — — — —— 4J UL z Ratio Poisson's V) 3 3 0. 3 T3 co O CD s (A O- CM o CD r- ID co CM o ID CO T— CD CO CD O’ CM CD 3 1^- 1^-' CO CD ID ID ID ^r CM CM CM CM X— d d d CD CO cd CD ID ID CD CD ID ID ID ID ID ID ID ID ID ID ID D or O’ 0) 3 Ob £ TJ O CD CO 2 (A o CO CD CO r— an CD CO T— CD CM o o 3 c- ID o CM an 00 D~ CO LD CM d 00 ‘-N 3 CO CO CO CO CO CM CM CM CM CM CM CM CM T v“ T "O (0 o CD 111 2 fc- re o (A £ o E =s£ (/) >re d> (A Sb u o O E _i >re Js£ . 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CO (0 E c o ® a o> CM CM CM m- O’ CO 00 o CD o o o o ID o CD co 00 T co co CO CO a> CD CD CM CD o CD o j o CD CD CO CD ID CO CM o r- ID CO o CM CD O' CD co O CD T“ oo ID CM CA CD CO M- o h- O M" ID CD CD D- CO 00 CD o o X CM CO o T— V— CM CO CO o O’ ID CD CD CO co CD o o X ^ T T r~ T s Nbr. c re re re re re re re re re re re re re re re CD re re re re re re re re re re re re re re a) an re o o o a o o u o u o o o a o o o a a o a o o o o o o o o o o o re a a o +* CZ c c c cz c c C c c c C c C c c c c cz cz c cz c c c cz c cz c cz c cz cz re cd cd cd CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD c c cz c c c cz C C C C c c c c c c c c c CZ c c c CZ CZ c CZ c c c CZ CZ CZ o o o o O o o o o o o o O o o o o o o o o o o o o o o o o O o o o o } £ if) C/D C/D (A (A CA CA (A CA CA CA CA C/D CA CA CA C/D C/D if) if) if) if) if) if) if) if) if) CA CA CA CA (A CA 4-4 fc fk= re re re re re re re re re re re re re re re re re re fl) re re re re re re re re re re re re re re o fc— fc— fc_ fc— fc— fc— fc— fc— k_ fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— fc— t— Jre s o o a o o a a o o a o o a o o a o a a o o o o a o c_> o o o o o a a scandia d) cz c c c c c c c c c cz c c c c c c c c C c c c c fZ c cz cz c cz cz c cz o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o a o o C/D C/D C/D if) (A if) C/D CA CA CA CA CA C/D CA CA if) if) if) if) if) if) if) CA if) if) if) CA if) if) CA CA CA if) re re 3 Q. oxide, re >% > I- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X £ kl X £ UJ z rvi rvj rvj rvj rvi r\j rvi cvi cvi rvi Cvl rvj rvj cvi rvj rvj o*j rvj rvj rvj rvj rvj CVJ rvj CVJ cvi cvj CVI . re £ XL £ SZ £ £ £ £ £ £ £ £ £ JC £ £ _C £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ r-^TJ Q. Cl CL CL Cl CL CL CL CL CL CL CL Q. CL a. CL CL CL CL CL Cl a. CL CL CL CL CL Cl GL CL CL CL CL GL >. re cd CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD { UJ L_ fc— fc— fc— i— fc— fc— t— fc_ fc— t— fc— fc— fc— fc— fc— fc— fc— fc- fc— fc— fc— fc- fc— fc— t— fc— fc— fc— fc— fc— fc— fc— 3 CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD O CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD CD 02 re £ M" OT vS- 0 or or OT or O" •^r O’ O' or or or O’ o O’ O’ Vt or or or or or 1 -9.28.4- } scandia oxide, scandium { 3 02 Sc silica, fused silica, fused quartz, vitreous silica 9.29 Si0 2 { silicon dioxide, } 1 = = M / mol ) 60.084 Temperature range / (°C) -200 to 1650 x (g 3 = = P.heo / (g cm’ ) n/a Porosity range n/a = = E0 / (GPa) n/a B0 / (GPa) n/a 4o 4o a / (10' C) = n/a b / (10- C) = n/a n = n/a m = n/a .28 .26 24 (v) .22 Ratio 20 18 Poisson's 16 14 .12 10 Temperature / °C 1 LL z Ratio Poisson's re Bulk Modulus o0. re Shear Modulus 0. 0 Elastic Modulus GPa CD CO 3.712 3.714 3.716 3.716 3.721 3.724 3.731 3.736 3.712 h- 3.737 3.745 3.757 Shear Velocity km/s co S98 co 5.8411 868 606 096 896 5.832 5.838 5.846 5.850 5.872 5.887 5.897 5.904 5.917 5.928 o> 5.949 5.970 Velocity km/s S S S in S S Long, - } 9.29.1 silica Vol.Frac. Porosity - CO vitreous E 2.203 Density 0 01 quartz, x— -79 CN 00 CD o 00 OJ -94 00 -73 CD -50 -34 CN i CN eg -99 00 -76 -76 -44 -196 -158 -150 -112 -197 -177 -162 -157 -135 -120 -195 o T— 1 0 i o w fused Mtl. n 2 silica, of Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic aa? Value >. dioxide, h= X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Nbr. Exh. r^* h- r- r~- r~- r'- o- o- on on on on on on on on on on on on on 04 CN 04 04 04 CN 04 CNJ 04 eg 04 04 rg CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN silicon a0) { Exh. H>. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 2 1 i I I ! ! UO ID un LD uo in uo 135 h35l 135 135 m 135 Ref. ]l\lbr. 135 135 135 135 135 Si0 135 135 135 135 135 135 CO 135 135 135 135 135 135 hssj CO 135 co CO CO CO CO CO — Ft. Nt. V) CN m o CD CO c CD CD r- oo o 0.162 0.165 0.175 Ratio O d d o d in o 0. Bulk Modulus GPa CD m r^- oo CD CO m °o 31.1 CO 32.2 32.6 30.39 30.65 30.75 30.98 31.23 31.35 31.39 31.35 o O o d CO CO CO Shear Modulus GPa CO CO co co CO 72 CD 70.521 LZL O 72.9 73.7 74.7 75.8 76.9 70.37 70.75 71.03 71.34 71.67 72.35 73.43 72.94 72.90 73.07 co Elastic Modulus GPa r- 3.766 Shear Velocity km/s Velocity km/s Long. - } 9.29.2 *>> CO silica Vol.Frac. o - u. o Cl CO vitreous 002 2.20 E 2.203 2.203 2.203 2.202 2.201 Density o 2 05 quartz, in in o o OS o o m OS CO CO CO CO o CO -75 -50 -25 CN C\l o -75 -50 -25 CN CM CM CM CM 100 200 o 400 -200 -175 -150 -125 -100 -200 -175 -150 o i CO i- o fused Mtl. Nbr. silica, of resonance resonance resonance resonance resonance resonance resonance resonance Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic Value Type dioxide, CO CO c/5 X 10 CO CO CO CO CO CO CO CO CO (O CO CO CO (n CO jCO CO CO X X X X X X X X Mbr. Exh. 28 29 CD 29 29 29 CD CD 29 CD 29 29 o o O o o o o o 30 30 30 CSJ CNJ C>J K'J ^7 d D CD CD CD o> CD silicon Type { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Table Table Table Graph Graph Graph Graph Graph 2 1 LO 36 CD CD 37 37 h- Ref. Nbr. 135 135 135 135 135 135 CO 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 CO CO 137 137 CO Si0 — T h hh T— — — IL Z y> 03 03 "c 0.189; o 0.185 0.193 0.197 w Ratio O tf) o 0. Bulk Modulus GPa CD o 32.9 33.1 33.3 CO CO CO Shear Modulus GPa 77.5 79.9 o 81.6 00 Elastic Modulus GPa Shear Velocity km/s o h- CM CO CM 886 o CD 060 660 5.968 5.970 5.974 o 6.013 6.019 O 6.031 6.037 6.054 O 6.062 6.072 6.070 6.097 6.109 6.119 6.133 6.135 6.141 6.145 6.149 6.154 s/ai>| Velocity S CO CO CD 9 9 CD Long. - } 9.29.3 silica Porosity Vol.Frac. - CO vitreous E 2.203 Density o OJ quartz, o o o CM in CM O 03 CD CD CD CD 00 o o 700 o 006 CM CM CO m 1"- CD 03 116 CM 130 162 1''- 198 222 246 03 239 263 273 CD 309 317 329 336 355 o CO CM CO I— o m CD fused Mtl. Nbr. silica, of resonance resonance resonance resonance resonance Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic Value Type dioxide, X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. Mbr. Type { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 2 r^* 00 00 00 00 CO 00 00 00 oo 00 OO 00 00 00 00 OO 00 00 00 OO 00 OO 00 00 00 OO OO Ref. Nbr. Si0 137 00 137 CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO T— T T T T" T v— T” T— V— T— T— - — ILL. z Ratio Poisson's Bulk Modulus GPa Shear Modulus GPa Elastic Modulus GPa 3.760 3.762 Shear Velocity km/s oo 00 o o "3- CD o M- CD CO 05 o 05 M- CO CD r-'- oo 00 00 00 o o o o CO r" 00 o — — 6.188 6.190 6.190 6.211 6.217 6.052 6.094 6.156 6.162 6.176 7 T 6.192 6.190 6.196 6.200 CM CM 6.207 CM CM CM O o O Velocity km/s CD CD CD CD CD CO CO CD CD CD CD CD CD CD CD CD Long. } 9.29.4- silica Vol.Frac. Porosity - CO vitreous E Density o Bi quartz, 00 CO CD CD oo m 365 367 00 392 394 416 423 420 CM CO 437 442 447 462 459 467 CD 466 474 479 00 496 05 135 157 CD 225 244 250 CM CO o CO CO T— I- o fused 2 Nbr. silica, of Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic 0) a, Value > dioxide, i- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X w Exh. n CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM 05 05 silicon V CL { Exh. >< Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 2 | 00 00 OO OO CO OO 00 OO 00 00 00 00 OO 00 00 00 OO 00 OO OO 00 00 00 00 138 Ref. Nbr. 138 138 138 138 138 138 Si0 CO CO CO CO CO CO CO 138 CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO r— T— M38 Ft. 2 — r CO CD CD 05 o CM CO CD e'- OO o e'- h- e'- e'- OO OO OO OO OO OO 00 en OO CD 0.172 t— 0.174 0.175 0.177 0.178 0.185 x— 0.163 Is.UOSSIOd Ratio er! o o er! en o o o o o o cd o cd cd CM OO CO CD cn CO 00 CM CD CD CO CD 00 CD o CM uo e- o CM uo e- 0 CM h- 05 T— o 40.63 40.85 41.28 41.49 £ CD e'- e-^ r- e'- OO 00 OO od 01 05 CD CD 05 o o 3 Modulus Q. en co CO en CO co CO CO CO CO CO CO co m 0 CD o OO 05 e'- CO in CD 31.14 31.26 31.38 31.59 31.80 31.89 31.99 32.07 32.16 32.24 32.39 32.46 32.52 32.64 32.74 CD CN CM CM Shear Modulus BL CO en CO co co o CO CM CD CO CD OO O CD 72.97 73.29 73.93 74.23 74.53 75.09 75.36 75.88 76.12 76.36 76.59 ZZLL 77.59 LLLL co •'3’ in CD r-^ e' Elastic Modulus 0. 0 e-- r- f' C'- e' e' un 05 CM CD 1'- e'- 00 cn o e'- r-- m o CD UO o OO CM CD CD CM in CD CD e-- r-- 00 en o o en h- OO oo o CM CN CO CO CO M" M- in m V) 1-- r- e-. e'- e'- OO OO CO 3.760 e'- r- e'- e'- 3.793 3.799 OO OO OO OO CO OO 00 OO OO 00 00 OO 00 Shear Velocity E 00 CO cd CO co en en CO CO CO en co en en co co CO cd CO CO CO CO CO CO CO cd cd uc r-- uo CD r-- e-- 00 OO 200 CD 690 o V) cn cn 6.017 6.032 6.047 O 6.075 6.102 6.127 6.140 6.152 6.163 6.175 6.196 CM 6.217 Velocity I in m 9 CD 9 CD CD CD Long. -X } u -9.29.5- CD k. silica LL. Porosity O > ro vitreous E 2.203 Density u O) quartz, CD CD e" CM CD e- CM 00 in m o in o in o in o in o in o in o uo o in o m o uo o uo CD t'- 00 CM CD T— CM CM in r-- o CM in e- o CM in I-- o CM in r-- o CM uo r- o CM o o CM CM CM CM CM CM CO co co co -'T in H o CM fused £ m 2 silica, of velocity velocity Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method ultrasonic ultrasonic silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic aa> Value >» dioxide, H X X X X X X X X X X CO if) if) if) if) CO if) if) CO if) if) if) if) if) if) if) if) if) if) if) X X £ X £ CD CD CD CD CD CD CD CD CD 05 05 05 05 05 05 05 05 05 05 UJ 2 Ratio O d d o d Poisson's oo 37.4 38.5 39.9 o 41.9 -M- Bulk Modulus GPa CT> 31.5 33.1 31.9 33.5 33.5 33.1 CO 33.9 33.9 33.9 34.3 33.9 31.4 32.0 32.5 32.8 33.1 CO Shear Modulus GPa co C"- CO CO CD CO CO 78.3 00 79.1 79.1 79.9 79.9 d co 75.1 CO 77.6 78.6 t"- 1-- oo I-- r" Elastic Modulus GPa Shear Velocity km/s Velocity km/s Long. } 9.29.6- silica Vol.Frac. Porosity - CO vitreous E Density o o> quartz, o o CO o o o o o 200 o 400 500 009 700 o 006 CM 100 200 o 400 500 550 570 o 700 720 o 006 920 930 o 450 o 750 900 h- Oo CO CO 1000 1050 CO CO oo 1000 1050 CO co fused Nbr. silica, of velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity fused Determination velocity velocity velocity velocity velocity Method ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic ultrasonic silica, sonic sonic sonic sonic sonic CD Q. Value >. dioxide, h- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. Nbr. m m id •D «D ID ID iD CD CD r- r^- r- r- r- r- r- r— CO CO CO CO CO silicon Type { Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph 1 I I 1 CN 1 CO u= Z V) CM o CO <3- oo CO 00 00 06 "c CD CD o 0.175 L0 0.190 0.193 0.195 0.197 0.149 0.152 0.153 0.156 0.160 191' 0.167 0.172 0.175 0.176 0.179 0.182 V) Ratio O o o o O O to o Q. 8 CD o 42.6 42 CO 44.2 44.8 33.5 33.9 34.3 34.6 un 35.4 35.8 CD 36.5 36.9 37.3 37.6 38.0 OO co CO CO Bulk Modulus GPa 9^ CO 0° o r^- oo o o o CD O CO CO 33.7 CO 30.6 30.6 30.7 30.7 o o 30.8 30.8 30.9 30. 30.9 O CO CO CO CO co CO CO CO CO Shear Modulus GPa CO CO CO 6 oo 79.3 80.3 81.5 70.3 70.5 71.0 71.? 71.5 71.7 71.9 ZZL 72.4 72.6 72.9 73.3 03 o CO 72.70 72.90 08 r- Elastic Modulus GPa 1 CM CO CO 1^- r^- h- 3.72 3.72 3.72 3.72 3.72 3.73 h- 3.74 3.74 3.74 CO CO co CO CO Shear Velocity km/s o T— ID oo 5.78 CO 00 5.83 5.84 OO CO 68 CD 5.93 5.94 96 86 uh in un in S in S S 66'S Velocity km/s Long. } 9.29.7- silica Porosity Vol.Frac. - ro vitreous E 2.2199 2.2012 2.2017 Density o CT quartz, O o o o o CO 00 CO 00 CO 00 CO oo CO CM CM CM CO CO O in o un o o r~- LO CM o uo CM 1 CM CD CM CM CM 1050 1200 1350 1500 1650 s 1050 1200 1350 1500 1650 o CO to I - CD C\| o i 1 1 u fused n 2 z silica, of resonance resonance Determination fused velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity velocity Method dynamic dynamic silica, sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic sonic 03 Q. Value >< dioxide, h- X X X X X X X X X X X X X X X X if) if) if) if) if) if) if) if) if) if) if) X if) X X Exh. £ — — CO CO CO CO CO ^3" -xtf- silicon a» sz xz .c Q. Cl Q. X >* Graph Graph Graph Graph Graph Graph Graph Graph CD Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph CD Graph Graph Graph Graph Graph Table Table 1 L. { lii 1- 0 o 2 tJ, O O O O O O O O o O O O CM CM a> n O O O Si0 ^S" tJ- Q£ z x X T— X X X x x x x x x — — — — — — — —— — ) — “ ~ "“ CM m CD T 7 T— T— -T— -r x x T x T CM CM CM CM CM CM LL Nt. Ratio Poisson's Bulk Modulus GPa 31.19 31.17 31.27 31.28 Shear Modulus GPa CO x— CM CD co oo •*3- O CM r~- 05 00 CM IV CD CO O OO CD 73.15 73.00 72.82 73.15 74.22 74.22 75.22 77.06 78.30 78.89 79.01 79.60 79.78 80.71 81.12 81.42 81.64 81.64 76.43 78.02 79.08 cm in CD OO d d CO CO 00 Elastic Modulus GPa r'- r"- LL C- oo 00 OO 1"- h- Shear Velocity km/s Velocity km/s Long. } -9.29.8- silica Vol.Frac. Porosity CO LZ vitreous E 2.2030 2.2026 2.2027 2.2030 Density o OZZ 9Z0ZZ O) 1 quartz, CO CO CO CO CO CM CO CO CM CM CN fused Mtl. Nbr. silica, of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance fused Determination Method dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic silica, 0) Q. Value dioxide, h- X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. Nbr. — = = = x x x X x x xr- silicon aa> Exh. >. Table Table Table Table Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph { r- 2 i CM CM CM CM CM CM CM CM CM CM 42 CM Ref. n 142 142 142 xJ" 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 Si0 z x X X Ll — — — — — 04 Ol 04 04 04 04 04 04 CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO ILL. 2 Ratio Poisson's Bulk Modulus GPa Shear Modulus GPa 0- h- CO CO CO S9 S9 CD o CO oo CO oo CD oo C"- r- 69 CD CD 69 79.37 79.49 79.91 80.3/ 80.78 81.42 72.70 74.92 76.89 76.95 78.46 78.57 78.86 79.21 79.79 80.42 72.90 74.59 75.18 co r--’ o O o O o Modulus 08 08 08 08 Elastic GPa 5 CO o- O' o- CO oo oo 00 oo Shear Velocity km/s Velocity km/s Long. - } 9.29.9 silica Porosity Vol.Frac. - 04 CO vitreous E 0 2.2017 Density u 01 O) 04 ^ quartz, CO T— T 96 o CO 706 CO 799 905 CM 172 203 405 418 513 o 607 663 701 819 901 CO 696 OO CM 165 209 o 1005 1105 1191 1259 1012 1024 1073 1097 1122 1116 h- o co a> 05 fused 2 Nfor. silica, of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance fused Determination Method dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic silica, Value Type dioxide, X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. & z T~ T“ ^ T— t T“ T— T— T— T— V— silicon a Exh. Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph { K— 2 | | ! 1 CM CM CM CM CM CM CM CM CM CM 142 142 142 142 S\Jbr. 142 Si0 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 DC T— ^ T— T— — ^1" N- m m in in m in in in in m m in in LL Nt. Ratio Poisson's Bulk Modulus GPa Shear Modulus GPa e'- t"- OO N- co in N- CD CD O' o en N" co O 06 OO O !'-• CO 77.98 79.42 80.12 81.03 74.13 76.29 77.40 79.55 80.24 80.53 72.82 76.05 ZZLL 77.58 77.98 78.51 78.75 79.39 80.72 76.23 77.28 OO OO CO ci CO O o 08 ci Elastic Modulus GPa OO OO OO I'- i"- OO r- r- OO OO Shear Velocity km/s Velocity km/s Long. } -9.29.10- silica Vol.Frac. Porosity CO vitreous E 2.2027 Density 0 01 1 quartz, o CO in CO CO CD o 317 418 500 CN 719 006 962 102 305 406 519 CN 726 814 CD CN r- 165 273 405 437 506 569 o 694 819 913 925 O CD 00 1036 1098 1134 CD OO 1079 i- o CD fused Mtl. Nbr. silica, of resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance resonance fused Determination Method dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic dynamic silica, Value Type dioxide, X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Exh. n T— T T— T“ silicon a> a. Exh. > Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph Graph { i- 2 1 L CN CN CN CN CN CM CN CN CN CN 142 42 Ref. n 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 142 Si0 2 h —— — — — — — — — — — — in CO CO in in m in in in in CD CD CD CD CD CD CD CD CD CD CD CD CD CD 1^- 4-* 4=* U_ z w re o © ca re .52 o a 0=