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Journal Reference: References Cited in NISTIR 6853

References are cited in the compilation by Reference Number (Nbr.). The complete list of references in NISTIR 6853 is given in the following table.

Nbr.	Reference Citation
1	S. Timoshenko, Theory of Elasticity, McGraw-Hill, New York (1934).
2	R. Hooke, De Potentia Restitutiva, London (1678).
3	T. Young, On the Equilibrium and Strength of Elastic Substances, Mathematical Elements of Natural Philosophy, Vol. II of Dr. Young's Lectures , Section IX, p. 46 (1807).
4	C. A. Coulomb, Theoretical and Experimental Researches on the Force of Torsion and on the Elasticity of Metal Wires, Histoire de l'Academie des Sciences, Year 1784 , pp. 229-269 (1787).
5	ASTM, American Society for Testing and Materials, West Conshohocken, Pennsylvania.
6	G. Pickett, Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders, American Society for Testing and Materials, Proceedings, Vol. 45, pp. 846-865 (1945).
7	S. Spinner and W. E. Tefft, A Method for Determining Mechanical Resonance Frequencies and for Calculating Elastic Moduli from These Frequencies, American Society for Testing and Materials, Proceedings, Vol. 61, pp. 1221-1238 (1961).
8	G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, and O. Van der Biest, Impulse Excitation Apparatus to Measure Resonant Frequencies, Elastic Moduli, and Internal Friction at Room and High Temperature, Reviews of Scientific Instruments, Vol. 68, No. 12, pp. 4511-4515 (1997).
9	J. T. Richards, An Evaluation of Several Static and Dynamic Methods for Determiing Elastic Moduli, ASTM STP No. 129, American Society for Testing Materials, Philadelphia, pp. 71-98 (1952).
10	S. Spinner and R. C. Valore, Jr., Comparison of Theoretical and Empirical Relations Between the Shear Modulus and Torsional Resonance Frequencies for Bars of Rectangular Cross Section, Journal of Research of the National Bureau of Standards, Vol. 60, No. 5, pp. 459-464 (1958).
11	S. Spinner, T. W. Reichard, and W. E. Tefft, A Comparison of Experimental and Theoretical Relations Between Young's Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars, Journal of Research of the National Bureau of Standards, Vol. 64A, No. 2, pp. 147-155 (1960).
12	J. S. Smith, M. D. Wyrick, and J. M. Poole, An Evaluation of Three Techniques for Determining the Young's Modulus of Mechanically Alloyed Materials, ASTM STP 1045, edited by A. Wolfenden, American Society for Testing and Materials, Philadelphia, pp. 195-207 (1990).
13	A. Wolfenden, M. R. Harmouche, G. V. Blessing, Y. T. Chen, P. Terranova, V. Dayal, V. K. Kinra, J. W. Lemmens, R. R. Phillips, J. S. Smith, P. Mahmoodi, and R. J. Wann, Dynamic Young's Modulus Measurements in Metallic Materials: Results of an Interlaboratory Testing Program, Journal of Testing and Evaluation, Vol. 17, No. 1, pp. 2-13 (1989).
14	R. W. Dickson and J. B. Wachtman, Jr., An Alumina Standard Reference Material for Resonance Frequency and Dynamic Elastic Moduli Measurement, I. For Use at 25 °C, Journal of Research of the National Bureau of Standards, Vol. 75A, No. 3, pp. 155-162 (1971).
15	R. W. Rice, Porosity of Ceramics, Marcel Dekker, New York (1998).
16	S. M. Lang, Properties of High-Temperature Ceramics and Cermets, Elasticity and Density at Room Temperature, Monograph 6, National Bureau of Standards, Washington, D.C. (1960).
17	O. L. Anderson, Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates Using Single-Crystal Data, Physical Acoustics, Vol. 3B, pp. 43-95 (1965).
18	O. L. Anderson, E. Schreiber, and R. C. Liebermann, Some Elastic Constant Data on Minerals Relevant to Geophysics, Reviews of Geophysics, Vol. 6, No. 4, pp. 491-524 (1968).
19	O. L. Anderson, D. Isaak, and H. Oda, High-Temperature Elastic Constant Data on Minerals Relevant to Geophysics, Reviews of Geophysics, Vol. 30, No. 1, pp. 57-90 (1992).
20	R. W. Rice, Relation of Tensile Strength-Porosity Effects in Ceramics to Porosity Dependence of Young's Modulus and Fracture Energy, Porosity Character and Grain Size, Materials Science and Engineering, Vol. A112, pp. 215-224 (1989).
21	R. W. Rice, The Porosity Dependence of Physical Properties of Materials: A Summary Review, Key Engineering Materials, Vol. 115, pp. 1-20 (1995).
22	R. W. Rice, Evaluation and Extension of Physical Property-Porosity Models Based on Minimum Solid Area, Journal of Materials Science, Vol. 31, pp. 102-118 (1996).
23	R. G. Munro, Mechanical Properties, Handbook of Superconductivity, edited by C. P. Poole, Academic Press, New York, pp. 570-625 (1999).
24	R. G. Munro and S. W. Freiman, Correlation of Fracture Toughness and Strength, Journal of the American Ceramic Society, Vol. 82, No. 8, pp. 2246-2248 (1999).
25	M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford University, New York (1954).
26	J. B. Wachtman, Jr., W. E. Tefft, D. G. Lam, Jr., and C. S. Apstein, Physical Review, Vol. 122, No. 6, pp. 1754-1759 (1961).
27	O. L. Anderson, Derivation of Wachtman's Equation for the Temperature Dependence of Elastic Moduli of Oxide Compounds, Physical Review, Vol. 144, No. 2, pp. 553-557 (1966).
28	W. Kreher, J. Ranachowski, and F. Rejmund, Ultrasonic Waves in Porous Ceramics With Non-Spherical Holes, Ultrasonics, Vol. 15, No. 2, pp. 70-74 (1977).
29	E. A. Dean, Elastic Moduli of Porous Sintered Materials as Modeled by a Variable-Aspect-Ratio Self-Consistent Oblate-Spheroidal-Inclusion Theory, Journal of the American Ceramic Society, Vol. 66, No. 12, pp. 847-854 (1983).
30	N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Solids, Journal of Materials Science, Vol. 25, pp. 3930-3937 (1990).
31	D. N. Boccaccini and A. R. Boccaccini, Dependence of Ultrasonic Velocity on Porosity and Pore Shape in Sintered Materials, Journal of Nondestructive Evaluation, Vol. 16, No. 4, pp. 187-192 (1997).
32	A. R. Boccaccini and Z. Fan, A New Approach for the Young's Modulus-Porosity Correlation of Ceramic Materials, Ceramics International, Vol. 23, pp. 239-245 (1997).
33	F. Wang, W. Gou, X. Zheng, and M. Lu, Effective Elastic Moduli of Ceramics with Pores, Journal of Materials Science and Technology, Vol. 14, pp. 286-288 (1998).
34	R. W. Rice, Comparison of Stress Concentration versus Minimum Solid Area Based on Mechanical Property-Porosity Relations, Journal of Materials Science, Vol. 28, pp. 2187-2190 (1993).
35	R. W. Rice, Comparison of Physical Property-Porosity Behaviour with Minimum Solid Area Models, Journal of Materials Science, Vol. 31, pp. 1509-1528 (1996).
36	A. K. Mukhopadhyay and K. K. Phani, Young's Modulus-Porosity Relations: an Analysis Based on a Minimum Contact Area Model, Journal of Materials Science, Vol. 33, pp. 69-72 (1998).
37	A. K. Mukhopadhyay and K. K. Phani, Ultrasonic Velocity-Porosity Relations: An Analysis Based on a Minimum Contact Area Model, Journal of Materials Science Letters, Vol. 18, pp. 1759-1760 (1999).
38	A. K. Mukhopadhyay and K. K. Phani, An Analysis of Microstructural Parameters in the Minimum Contact Area Model for Ultrasonic Velocity-Porosity Relations, Journal of the European Ceramic Society, Vol. 20, pp. 29-38 (2000).
39	D. G. Bika, M. Gentzler, and J. N. Michaels, Mechanical Properties of Agglomerates, Powder Technology, Vol. 117, pp. 98-112 (2001).
40	A. P. Roberts and E. J. Garboczi, Elastic Properties of Model Porous Ceramics, Journal of the American Ceramic Society, Vol. 83, No. 12, pp. 3041-3048 (2000).
41	A. P. Roberts and E. J. Garboczi, Elastic Moduli of Model Random Three-Dimensional Closed-Cell Cellular Solids, Acta Materialia, Vol. 49, pp. 189-197 (2001).
42	J. M. Dewey, The Elastic Constants of Materials Loaded with Non-Rigid Fillers, Journal of Applied Physics, Vol. 18, pp. 578-581 (1947).
43	J. K. Mackenzie, Elastic Constants of a Solid Containing Spherical Holes, Proceedings of the Physical Society, Section B, Vol. 63, pp. 2-11 (1950).
44	R. M. Spriggs and T. Vasilos, Effect of Grain Size and Porosity on the Transverse Bend Strength and Elastic Modulus of Hot Pressed Alumina and Magnesia, Journal of the American Ceramic Society, Vol. 40, No. 4, pg. 187 (1961).
45	D. P. H. Hasselman, On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials, Journal of the American Ceramic Society, Vol. 45, pp. 452-453 (1962).
46	O. Ishai and L. J. Cohen, Elastic Properties of Filled and Porous Epoxy Composites, International Journal of Mechanical Sciences, Vol. 9, pp. 539-546 (1967).
47	J. C. Wang, Young's Modulus of Porous Materials, Part 1, Theoretical Derivation of Modulus-Porosity Correlation, Journal of Materials Science, Vol. 19, pp. 801-808 (1984).
48	K. K. Phani and S. K. Niyogi, Young's Modulus of Porous Brittle Solids, Journal of Materials Science, Vol. 22, pp. 257-263 (1987).
49	A. S. Wagh, R. B. Poeppel, and J. P. Singh, Open Pore Description of Mechanical Properties of Ceramics, Journal of Materials Science, Vol. 26, pp. 3862-3868 (1991).
50	M. Kupkova, Porosity Dependence of Material Elastic Moduli, Journal of Materials Science, Vol. 28, pp. 5265-5268 (1993).
51	A. R. Boccaccini, G. Ondracek, P. Mazilu, and D. Windelberg, On the Effective Young's Modulus of Elasticity for Porous Materials: Microstructure Modelling and Comparison Between Calculated and Experimental Values, Journal of the Mechanical Behavior of Materials, Vol. 4, pp. 119-128 (1993).
52	B. Budiansky, On the Elastic Moduli of Some Heterogeneous Materials, Journal of the Mechanics and Physics of Solids, Vol. 13, pp. 223-227 (1965).
53	E. A. Dean and J. A. Lopez, Empirical Dependence of Elastic Moduli on Porosity for Ceramic Materials, Journal of the American Ceramic Society, Vol. 66, No. 5, pp. 366-370 (1983).
54	K. K. Phani, Young's Modulus- Porosity Relation in Gypsum Systems, American Ceramic Society Bulletin, Vol. 65, No. 12, pp. 1584-1586 (1986).
55	K. K. Phani, Elastic-Constant-Porosity Relations for Polycrystalline Thoria, Journal of Materials Science Letters, Vol. 5, pp. 747-750 (1986).
56	K. K. Phani and S. K. Niyogi, Porosity Dependence of Ultrasonic Velocity and Elastic Modulus in Sintered Uranium Dioxide, Journal of Materials Science Letters, Vol. 5, pp. 427-430 (1986).
57	K. K. Phani and S. K. Niyogi, Elastic Modulus-Porosity Relation in Polycrystalline Rare-Earth Oxides, Journal of the American Ceramic Society, Vol. 70, No. 12, pp. C-362 - C-366 (1987).
58	N. Ramakrishnan and V. S. Arunachalam, Effective Elastic Moduli of Porous Ceramic Materials, Journal of the American Ceramic Society, Vol. 76, pp. 2745-2752 (1993).
59	L. J. Gibson and M. F. Ashby, The Mechanics of Three-Dimensional Cellular Materials, Proceedings of the Royal Society of London, Vol. A382, pp. 43-59 (1982).
60	R. G. Munro, Effective Medium Theory of the Porosity Dependence of Bulk Moduli, Journal of the American Ceramic Society, Vol. 84, No. 5, pp. 1190-1192 (2001).
61	A. Migliori, T. Chen, B. Alavi, and G. Grüner, Ultrasound Anomaly at T_c in YBa₂Cu₃O_y , Solid State Communications, Vol. 63, No. 9, pp. 827-829 (1987).
62	Y. Horie, Y. Terashi, H. Fukuda, T. Fukami, and S. Mase, Ultrasonic Studies of the High T_c Superconductor Y₂Ba₄Cu₆O₁₄ , Solid State Communications, Vol. 64, No. 4, pp. 501-504 (1987).
63	G. Cannelli, R. Cantelli, F. Cordero, G. A. Costa, M. Ferretti, and G. L. Olcese, Anelastic Relaxation in the High-T_c Superconductor YBa₂Cu₃O_7-x , Physical Review B, Vol. 36, No. 16, pp. 8907-8909 (1987).
64	S. Ewert, S. Guo, P. Lemmens, F. Stellmach, J. Wynants, G. Arlt, D. Bonnenberg, H. Kliem, A. Comberg, and H. Passing, Ultrasonic Investigations on Superconducting YBa₂Cu₃O_7-(delta) Samples of Different Microstructure, Solid State Communications, Vol. 64, No. 8, pp. 1153-1156 (1987).
65	Y. He, B. Zhang, S. Lin, J. Xiang, Y. Lou, and H. Chen, Ultrasonic Investigation of Lattice Instability and Superconductivity in High-T_c Systems, Journal of Physics F: Metal Physics, Vol. 17, pp. L243-L248 (1987).
66	S. Bhattacharya, M. J. Higgins, D. C. Johnston, A. J. Jacobson, J. P. Stokes, D. P. Goshorn, and J. T. Lewandowski, Elastic Anomalies and Phase Transitions in High-T_c Superconductors, Physical Review Letters, Vol. 60, No. 12, pp. 1181-1184 (1988).
67	M. Suzuki, Y. Okuda, I. Iwasa, A. J. Ikushima, T. Takabatake, Y. Nakazawa, and M. Ishikawa, Sound Velocity and Attenuation in YBa₂Cu₃O_y , Japanese Journal of Applied Physics, Vol. 27, No. 3, pp. L308-L310 (1988).
68	M. Saint-Paul, J. L. Tholence, P. Monceau, H. Noel, J. C. Levet, M. Potel, P. Gougeon, and J. J. Capponi, Ultrasound Study of YBa₂Cu₃O_7-(delta) Single Crystals, Solid State Communications, Vol. 66, No. 6, pp. 641-643 (1988).
69	S. Bhattacharya, M. J. Higgins, D. C. Johnston, A. J. Jacobson, J. P. Stokes, J. T. Lewandowski, and D. P. Goshorn, Anomalous Ultrasound Propagation in High-T_c Superconductors: La_1.8Sr_0.2CuO_4-y and YBa₂Cu₃O_7-(delta), Physical Review B, Vol. 37, No. 10, pp. 5901-5904 (1988).
70	S. Hoen, L. C. Bourne, C. M. Kim, and A. Zettl, Elastic Response of Polycrystalline and Single-Crystal YBa₂Cu₃O₇, Physical Review B, Vol. 38, No. 16, pp. 11949-11951 (1988).
71	X. D. Shi, R. C. Yu, Z. Z. Wang, N. P. Ong, and P. M. Chaikin, Sound Velocity and Attenuation in Single-Crystal YBa₂Cu₃O_7-(delta), Physical Review B, Vol. 39, No. 1, pp. 827-830 (1989).
72	P. K. Choi, H. Koizumi, K. Takagi, and T. Suzuki, Anomalies of Ultrasonic Velocity in High-T_c Ceramics YBa₂Cu₃O_y and BiSrCaCu₂O_y , Solid State Communications, Vol. 70, No. 12, pp. 1175-1178 (1989).
73	N.N. Ault and H.F.G. Ueltz, Sonic Analysis for Solid Bodies, Journal of the American Ceramic Society, Vol. 36, No. 6, pp. 199-203 (1953).
74	R.L. Coble and W.D. Kingery, Effect of Porosity on Physical Properties of Sintered Alumina, Journal of the American Ceramic Society, Vol. 39, No. 11, pp. 377-385 (1956).
75	J.B. Wachtman,Jr. and D.G. Lam,Jr., Young's Modulus of Various Refractory Materials as a Function of Temperature, Journal of the American Ceramic Society, Vol. 42, No. 5, pp. 254-260 (1959).
76	F.P. Knudsen, Effect of Porosity on Young's Modulus of Alumina, Journal of the American Ceramic Society, Vol. 45, No. 2, pp. 94-95 (1962).
77	R.M. Spriggs, J.B. Mitchell, and T. Vasilos, Mechanical Properties of Pure, Dense Aluminum Oxide as a Function of Temperature and Grain Size, Journal of the American Ceramic Society, Vol. 47, No. 7, pp. 323-327 (1964).
78	D.B. Binns and P. Popper, Mechanical Properties of Some Commerical Alumina Ceramics, Proceedings of the British Ceramic Society, Vol. 6, pp. 71-82 (1966).
79	E. Schreiber and O.L. Anderson, Pressure Derivatives of the Sound Velocities of Polycrystalline Alumina, Journal of the American Ceramic Society, Vol. 49, pp. 184-190 (1966).
80	N. Soga and O.L. Anderson, High-Temperature Elastic Properties of Polycrystalline MgO and Al₂O₃, Journal of the American Ceramic Society, Vol. 49, No. 7, pp. 355-359 (1966).
81	D.H. Chung and G. Simmons, Pressure and Temperature Dependences of the Isotropic Elastic Moduli of Polycrystalline Alumina, Journal of Applied Physics, Vol. 39, No. 11, pp. 5316-5326 (1968).
82	A. Nagarajan, Ultrasonic Study of Elasticity-Porosity Relationship in Polycrystalline Alumina, Journal of Applied Physics, Vol. 42, No. 10, pp. 3693-3696 (1971).
83	J.C. Wang, Young's Modulus of Porous Materials, Part 2, Young's Modulus of Porous Alumina with Changing Pore Structure, Journal of Materials Science, Vol. 19, pp. 809-814 (1984).
84	C.C. Wu and R.W. Rice, Porosity Dependence of Wear and Other Mechanical Properties of Fine-Grain Al₂O₃ and B₄C, Ceramic Engineering and Science Proceedings, Vol. 6, pp. 977-993 (1985).
85	H. Hagiwara and D.J. Green, Elastic Behavior of Open-Cell Alumina, Journal of the American Ceramic Society, Vol. 70, No. 11, pp. 811-815 (1987).
86	T. Goto and O.L. Anderson, Elastic Constants of Corundum up to 1825 K, Journal of Geophysical Research, Vol. 94, No. B6, pp. 7588-7602 (1989).
87	D.J. Green, C. Nader, and R. Brezny, The Elastic Behavior of Partially-Sintered Alumina, Ceramic Transactions, Vol. 7, pp. 345-356 (1990).
88	J. Kubler, Weibull Characterization of Four Hipped/Posthipped Engineering Ceramics Between Room Temperature and 1500 °C, Report Number: EMPA-Nr. 129'747, EMPA Swiss Federal Laboratories for Materials Testing and Research, pp. 1-88 (1992).
89	D.C. Lam, F.F. Lange, and A.G. Evans, Mechanical Properties of Partially Dense Alumina Produced from Powder Compacts, Journal of the American Ceramic Society, Vol. 77, No. 8, pp. 2113-2117 (1994).
90	J. Piekarczyk, J. Lis, and J. Bialoskorski, Elastic Properties, Hardness and Indentation Fracture Toughness of (beta)-Sialons, Key Engineering Materials, Vol. 89, pp. 541-546 (1994).
91	K. S. Tan, P. Hing, and P. Ramalingam, The Elastic Moduli and Diametrical Compressive Fracture Stress of Al₂O₃-ZrO₂ Ceramics, Journal of Physics D: Applied Physics, Vol. 30, pp. 1029-1037 (1997).
92	A. Wolfenden, Measurement and Analysis of Elastic and Anelastic Properties of Alumina and Silicon Carbide, Journal of Materials Science, Vol. 32, pp. 2275-2282 (1997).
93	B.D. Flinn, R.K. Borida, A. Zimmermann, and J. Rodel, Evolution of Defect Size and Strength of Porous Alumina During Sintering, Journal of the European Ceramic Society, Vol. 20, pp. 2561-2568 (2000).
94	D. Dierickx, I. Houben, J. Lapin, F. Delannay, O. Van Der Biest, Dense Polycrystalline BaZrO₃ Substrates for YBa₂Cu₃O_7-x Melt Processing, Journal of Materials Science Letters, Vol. 15, pp. 1573-1576 (1996).
95	K.C. Goretta, E.T. Park, R.E. Koritala, M.M. Cuber, E.A. Pascual, N. Chen, A.R. de Arellano-Lopez, and J.L. Routbort, Thermomechanical Response of Polycrystalline BaZrO₃, Physica C, Vol. 309, pp. 245-250 (1998).
96	B. A. Chandler, E. C. Duderstadt, and J. F. White, Fabrication and Properties of Extruded and Sintered BeO, Journal of Nuclear Materials, Vol. 8, No. 3, pp. 329-347 (1963).
97	R.E. Fryxell and B.A. Chandler, Creep, Strength, Expansion, and Elastic Moduli of Sintered BeO as a Function of Grain Size, Porosity, and Grain Orientation, Journal of the American Ceramic Society, Vol. 47, No. 6, pp. 283-291 (1964).
98	Y. He, J. Xiang, S. Jin, A. He, and J. Zhang, Ultrasonic Investigation of the Layered Perovskite Ceramic Superconducting Systems, Physica B, Vol. 165&166, pp. 1283-1284 (1990).
99	R. R. Reddy, M. Muralidhar, V. H. Babu, and P. V. Reddy, The Relationship Between the Porosity and Elastic Moduli of the Bi-Pb-2212 High-T_c Superconductor, Superconductor Science and Technology, Vol. 8, pp. 101-107 (1995).
100	M. Muralidhar, K.N. Kishore, Y. V. Ramana, and V. H. Babu, Elastic and Plastic Behaviour of Lead and Silver Doped Bi-Sr-Ca-Cu-O Superconductors, Materials Science and Engineering B, Vol. 13, pp. 215-219 (1992).
101	S. Satyavathi, M. Muralidhar, V. H. Babu, R. R. Reddy, and P. V. Reddy, Elastic Behaviour of Bi-Pb-Ag-Ca₂CuO₃ Superconducting Composite Materials, Journal of Alloys and Compounds, Vol. 209, pp. 329-335 (1994).
102	R .J. Topare, K. Ganesh, N. K. Sahuji, S. S. Shah, and P. V. Reddy, Elastic Anomalies in Bi-Pb-2223/Ag Superconducting Composite Materials, Physica C, Vol. 253, pp. 89-96 (1995).
103	O. O. Oduleye, S. J. Penn, and N. McN. Alford, The Mechanical Properties of (Bi-Pb)SrCaCuO, Superconductor Science and Technology, Vol. 11, pp. 858-865 (1998).
104	W. R. Manning, M. O. Marlowe, and D. R. Wilder, Temperature and Porosity Dependence of Young's Modulus of Polycrystalline Dysprosium Oxide and Erbium Oxide, Journal of the American Ceramic Society, Vol. 49, No. 4, pp. 227-228 (1966).
105	W. R. Manning, O. Hunter, Jr., and B. R. Powell, Jr., Elastic Properties of Polycrystalline Yttrium Oxide, Dysprosium Oxide, Holmium Oxide, and Erbium Oxide: Room Temperature Measurements, Journal of the American Ceramic Society, Vol. 52, No. 8, pp. 436-442 (1969).
106	W. R. Manning and O. Hunter, Jr., Elastic Properties of Polycrystalline Yttrium Oxide, Holmium Oxide, and Erbium Oxide: High-Temperature Measurements, Journal of the American Ceramic Society, Vol. 52, No. 9, pp. 492-496 (1969).
107	A. A. Sharif, F. Chu, A. Mirsa, T. E. Mitchell, and J. J. Petrovic, Elastic Constants of Erbia Single Crystals, Journal of the American Ceramic Society, Vol. 83, No. 9, pp. 2246-2250 (2000).
108	J. A. Haglund and O. Hunter,Jr., Elastic Properties of Polycrystalline Monoclinic Gd₂O₃, Journal of the American Ceramic Society, Vol. 56, No. 6, pp. 327-330 (1973).
109	S. L. Dole, O. Hunter,Jr., and C. J. Wooge, Elastic Properties of Monoclinic Hafnium Oxide at Room Temperature, Journal of the American Ceramic Society, Vol. 60, No. 11, pp. 488-490 (1977).
110	R. W. Scheidecker, O. Hunter,Jr., and F. W. Calderwood, Elastic Properties of Partially-Stabilized HfO₂ Compositions, Journal of Materials Science, Vol. 14, pp. 2284-2288 (1979).
111	S. L. Dole, O. Hunter, Jr., and F. W. Calderwood, Elastic Properties of Stabilized HfO₂ Compositions, Journal of the American Ceramic Society, Vol. 63, No. 3, pp. 136-139 (1980).
112	S. L. Dole and O. Hunter, Jr., Elastic Properties of Hafnium and Zirconium Oxides Stabilized with Praseodymium or Terbium Oxide, Journal of the American Ceramic Society, Vol. 66, No. 3, pp. C-47-C-49 (1983).
113	G. W. Crabtree, J. W. Downey, B. K. Flandermeyer, J. D. Jorgensen, T. E. Klippert, D. S. Kupperman, W. K. Kwok, D. J. Lam, A. W. Mitchell, A. G. McKale, M. V. Nevitt, L. J. Nowicki, A. P. Paulikas, R. B. Poeppel, S. J. Rothman, J. L. Roubort, J. P. Singh, C. H. Sowers, A. Umezawa, B. W. Veal, and J. E. Baker, Fabrication, Mechanical Properties, Heat Capacity, Oxygen Diffusion, and the Effect of Alkali Earth Ion Substitution on High T_c Superconductors, Advanced Ceramic Materials, Vol. 2, No. 3B, pp. 444-456 (1987).
114	A. J. Zaleski and J. Klamut, Penetration Depth in Magnetically Oriented, Ceramic, Ni- and Zn-doped La_2-xSr_xCuO₄, Physica C, Vol. 282, pp. 1463-1464 (1997).
115	W. R. Manning and O. Hunter, Jr., Elastic Properties of Polycrystalline Thulium Oxide and Lutetium Oxide from 20 °C to 1000 °C, Journal of the American Ceramic Society, Vol. 53, No. 5, pp. 279-280 (1970).
116	O. Hunter, Jr. and G. E. Graddy, Jr., Porosity Dependence of Elastic Properties of Polycrystalline Cubic Lu₂O₃, Journal of the American Ceramic Society, Vol. 59, No. 1, pp. 82-82 (1976).
117	D. F. Porter, J. S. Reed, and D. Lewis, Elastic Moduli of Refractory Spinels, Journal of the American Ceramic Society, Vol. 60, No. 7, pp. 345-349 (1977).
118	R. L. Stewart and R. C. Bradt, Fracture of Polycrystalline MgAl₂O₄, Journal of the American Ceramic Society, Vol. 63, No. 11, pp. 619-623 (1980).
119	A. Ghosh, K. W. White, M. G. Jenkins, A. S. Kobayashi, and R. C. Bradt, Fracture Resistance of a Transparent Magnesium Aluminate Spinel, Journal of the American Ceramic Society, Vol. 74, No. 7, pp. 1624-1630 (1991).
120	K. W. White and G. P. Kelkar, Fracture Mechanisms of a Coarse-Grained, Transparent MgAl₂O₄ at Elevated Temperatures, Journal of the American Ceramic Society, Vol. 75, No. 12, pp. 3440-3444 (1992).
121	C. Baudin, R. Martinez, and P. Pena, High-Temperature Mechanical Behavior of Stoichiometric Magnesium Spinel, Journal of the American Ceramic Society, Vol. 78, No. 7, pp. 1857-1862 (1995).
122	K. R. Janowski and R. C. Rossi, Elastic Behavior of MgO Matrix Composites, Journal of the American Ceramic Society, Vol. 50, No. 11, pp. 599-603 (1967).
123	N. Soga and E. Schreiber, Porosity Dependence of Sound Velocity and Poisson's Ratio for Polycrystalline MgO Determined by Resonant Sphere Method, Vol. 51, No. 8, pp. 465-466 (1968).
124	Y. Sumino, O. L. Anderson, and I. Suzuki, Temperature Coefficients of Elastic Constants of Single Crystal MgO between 80 K and 1300 K, Physics and Chemistry of Minerals, Vol. 9, pp. 38-47 (1983).
125	D. G. Isaak, O. L. Anderson, and T. Goto, Measured Elastic Moduli of Single-Crystal MgO up to 1800 K, Physics and Chemistry of Minerals, Vol. 16, pp. 704-713 (1989).
126	R. A. Penty, D.P.H. Hasselman, and R. M. Spriggs, Young's Modulus of High-Density Polycrystalline Mullite, Journal of the American Ceramic Society, Vol. 55, No. 3, pp. 169-170 (1972).
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164	M. Cankurtaran, G. A. Saunders, and K. C. Goretta, Ultrasonic Study of the Temperature and Pressure Dependences of the Elastic Properties of Fully Oxygenated YBa₂Cu₃O_6.94, Superconductor Science and Technology, Vol. 7, pp. 4-9 (1994).
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168	R. R. Reddy, O. M. Prakash, and R. V. Reddy, The Effect of Porosity on Elastic Moduli of YBa₂Cu₃O_7-(delta) High T_c Superconductors, Applied Superconductivity, Vol. 3, No. 4, pp. 215-222 (1995).
169	Q. Wang, G. A. Saunders, D. P. Almond, M. Cankurtaran, and K. C. Goretta, Elastic and Nonlinear Acoustic Properties of YBa₂Cu₃O_7-x Ceramics with Different Oxygen Contents, Physical Review B, Vol. 52, No. 5, pp. 3711-3726 (1995).
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179	R. W. Dickson and R. C. Anderson, Temperature Dependence of the Elastic Moduli of 91Y₂O₃ + 9ThO₂ from 25° to 1100°C, Journal of the American Ceramic Society, Vol. 51, No. 4, pp. 233-234 (1968).
180	C. E. Holcombe, T. T. Meek, and N. L. Dykes, Unusual Properties of Microwave-Sintered Yttria-2wt% Zirconia, Journal of Materials Science Letters, Vol. 7, pp. 881-884 (1988).
181	B. R. Powell, Jr., O. Hunter, Jr., and W. R. Manning, Elastic Properties of Polycrystalline Ytterbium Oxide, Journal of the American Ceramic Society, Vol. 54, No. 10, pp. 488-490 (1971).
182	L. P. Martin, D. Dadon, and M. Rosen, Evaluation of Ultrasonically Determined Elasticity-Porosity Relations in Zinc Oxide, Journal of the American Ceramic Society, Vol. 79, No. 5, pp. 1281-1289 (1996).
183	A. K. Mukhopadhyay, M. R. Chaudhuri, A. Seal, S. K. Dalui, M. Banerjee, and K. K. Phani, Mechanical Characterization of Microwave Sintered Zinc Oxide, Bulletin of Materials Science, Vol. 24, No. 2, pp. 125-128 (2001).
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Elastic Moduli Data for Polycrystalline Ceramics

NIST Interagency/Internal Report (NISTIR) 6853

Database Reference: NIST Structural Ceramics Database, SRD Database Number 30

Journal Reference:

Elastic Moduli Data for Polycrystalline Ceramics, R. G. Munro, NISTIR 6853, (2002),
National Institute of Standards and Technology, Gaithersburg, Maryland 20899.

Other materials: Elastic Moduli Data

Other materials Properties: Property Data Summaries

Al₂O₃ { aluminum oxide, alumina }

Key to the Symbols: T = temperature, d = density, p = volume fraction of porosity, *V_L* = longitudinal sound velocity,
*V_S* = shear sound velocity, E = elastic modulus, G = shear modulus, B = bulk modulus, nu = Poisson's ratio.
Ref. Nbr.	Exhibit Type	Exhibit Number	Value Type	Measurement Method	Matl. Nbr.	T [°C]	d [g/cm³]	p [%]	V_L [km/s]	V_S [km/s]	E [GPa]	G [GPa]	B [GPa]	nu	Table Notes
16	Table	6	x	resonance	1	23	3.942				395.8	156.5	264.5	0.254
16	Table	6	x	resonance	2	23	3.904				355.5	145.3	212.9	0.221
16	Table	6	x	resonance	3	23	3.902				382.4	154.8	241.5	0.236
16	Table	6	x	resonance	4	23	3.824				358.3	143.8	234.9	0.246
16	Table	6	x	resonance	5	23	3.825				358	144.5	228.9	0.239
16	Table	6	x	resonance	6	23	3.714				325.5	132.1	201.8	0.232
16	Table	6	x	resonance	7	23	3.47				261.2	106.7	157.9	0.224
16	Table	6	x	resonance	8	23	3.335				231.7	97.7	123.5	0.187
16	Table	6	x	resonance	9	23	2.85				110.9	47.9	53.3	0.17

73	Graph	2	x	sonic resonance		20	3.64	0.09			326.6				1
73	Graph	2	x	sonic resonance		67					326.6				1
73	Graph	2	x	sonic resonance		105					326				1
73	Graph	2	x	sonic resonance		152					325.4				1
73	Graph	2	x	sonic resonance		210					319.1				1
73	Graph	2	x	sonic resonance		242					314.6				1
73	Graph	2	x	sonic resonance		305					309.5				1
73	Graph	2	x	sonic resonance		342					306.6				1
73	Graph	2	x	sonic resonance		363					305.5				1
73	Graph	2	x	sonic resonance		384					302				1
73	Graph	2	x	sonic resonance		422					300.9				1
73	Graph	2	x	sonic resonance		443					298.6				1
73	Graph	2	x	sonic resonance		459					296.9				1
73	Graph	2	x	sonic resonance		480					295.2				1
73	Graph	2	x	sonic resonance		497					294.6				1
73	Graph	2	x	sonic resonance		518					294				1
73	Graph	2	x	sonic resonance		539					292.9				1
73	Graph	2	x	sonic resonance		564					292.9				1
73	Graph	2	x	sonic resonance		581					290.6				1
73	Graph	2	x	sonic resonance		597					288.3				1
73	Graph	2	x	sonic resonance		618					288.3				1
73	Graph	2	x	sonic resonance		643					287.2				1
73	Graph	2	x	sonic resonance		664					283.8				1
73	Graph	2	x	sonic resonance		681					283.2				1
73	Graph	2	x	sonic resonance		702					283.2				1
73	Graph	2	x	sonic resonance		723					283.2				1
73	Graph	2	x	sonic resonance		749					283.2				1
73	Graph	2	x	sonic resonance		782					281.4				1
73	Graph	2	x	sonic resonance		803					280.9				1
73	Graph	2	x	sonic resonance		828					280.3				1
73	Graph	2	x	sonic resonance		866					279.7				1
73	Graph	2	x	sonic resonance		946					276.8				1
73	Graph	2	x	sonic resonance		997					277.4				1
73	Graph	2	x	sonic resonance		964					279.1				2
73	Graph	2	x	sonic resonance		867					280.8				2
73	Graph	2	x	sonic resonance		804					282.6				2
73	Graph	2	x	sonic resonance		765					282.6				2
73	Graph	2	x	sonic resonance		702					281.5				2
73	Graph	2	x	sonic resonance		659					282.1				2
73	Graph	2	x	sonic resonance		601					286.6				2
73	Graph	2	x	sonic resonance		559					288.4				2
73	Graph	2	x	sonic resonance		500					292.4				2
73	Graph	2	x	sonic resonance		24					324.9				2

74	Table	II	x	bending		25		0						0.27
74	Table	II	x	bending		25		0.1						0.26
74	Table	II	x	bending		25		0.2						0.32
74	Table	II	x	bending		25		0.3						0.29
74	Table	II	x	bending		25		0.4						0.25
74	Table	II	x	bending		25		0.5						0.13
74	Table	II	x	bending		600		0
74	Table	II	x	bending		600		0.1
74	Table	II	x	bending		600		0.2
74	Table	II	x	bending		600		0.3
74	Table	II	x	bending		600		0.4
74	Table	II	x	bending		600		0.5
74	Table	II	x	bending		800		0
74	Table	II	x	bending		800		0.1
74	Table	II	x	bending		800		0.2
74	Table	II	x	bending		800		0.3
74	Table	II	x	bending		800		0.4
74	Table	II	x	bending		800		0.5
74	Table	II	x	bending		1000		0
74	Table	II	x	bending		1000		0.1
74	Table	II	x	bending		1000		0.2
74	Table	II	x	bending		1000		0.3
74	Table	II	x	bending		1000		0.4
74	Table	II	x	bending		1000		0.5
74	Table	II	x	bending		1200		0
74	Table	II	x	bending		1200		0.1
74	Table	II	x	bending		1200		0.2
74	Table	II	x	bending		1200		0.3
74	Table	II	x	bending		1200		0.4
74	Table	II	x	bending		1200		0.5
74	Graph	5	x	bending		25		0.01			298.5
74	Graph	5	x	bending		200		0.01			300.6
74	Graph	5	x	bending		400		0.01			291.6
74	Graph	5	x	bending		600		0.01			289.5
74	Graph	5	x	bending		800		0.01			282
74	Graph	5	x	bending		1000		0.01			273
74	Graph	5	x	bending		1100		0.01			255.1
74	Graph	5	x	bending		1200		0.01			228.9
74	Graph	5	x	bending		25		0.2			245.4
74	Graph	5	x	bending		200		0.2			243.4
74	Graph	5	x	bending		400		0.2			239.9
74	Graph	5	x	bending		600		0.2			232.3
74	Graph	5	x	bending		800		0.2			220.6
74	Graph	5	x	bending		1000		0.2			211
74	Graph	5	x	bending		1100		0.2			196.5
74	Graph	5	x	bending		1200		0.2			171.7
74	Graph	5	x	bending		25		0.28			188.2
74	Graph	5	x	bending		200		0.28			186.1
74	Graph	5	x	bending		400		0.28			181.3
74	Graph	5	x	bending		600		0.28			176.5
74	Graph	5	x	bending		800		0.28			174.4
74	Graph	5	x	bending		1000		0.28			153.7
74	Graph	5	x	bending		1100		0.28			140.6
74	Graph	5	x	bending		1200		0.28			121.3
74	Graph	5	x	bending		25		0.35			154.4
74	Graph	5	x	bending		200		0.35			152.4
74	Graph	5	x	bending		400		0.35			150.3
74	Graph	5	x	bending		600		0.35			146.8
74	Graph	5	x	bending		800		0.35			142
74	Graph	5	x	bending		1000		0.35			131.7
74	Graph	5	x	bending		1100		0.35			120.6
74	Graph	5	x	bending		1200		0.35			102.7
74	Graph	5	x	bending		25		0.37			144.8
74	Graph	5	x	bending		200		0.37			144.1
74	Graph	5	x	bending		400		0.37			140.6
74	Graph	5	x	bending		600		0.37			139.9
74	Graph	5	x	bending		800		0.37			136.5
74	Graph	5	x	bending		1000		0.37			124.8
74	Graph	5	x	bending		1100		0.37			111
74	Graph	5	x	bending		25		0.43			113.1
74	Graph	5	x	bending		200		0.43			111.7
74	Graph	5	x	bending		400		0.43			108.9
74	Graph	5	x	bending		600		0.43			108.9
74	Graph	5	x	bending		800		0.43			102.7
74	Graph	5	x	bending		1000		0.43			92.4
74	Graph	5	x	bending		1100		0.43			84.8
74	Graph	5	x	bending		1200		0.43			72.4
74	Graph	5	x	bending		25		0.45			95.8
74	Graph	5	x	bending		200		0.45			92.4
74	Graph	5	x	bending		400		0.45			93.1
74	Graph	5	x	bending		600		0.45			93.8
74	Graph	5	x	bending		800		0.45			91.7
74	Graph	5	x	bending		1000		0.45			84.1
74	Graph	5	x	bending		1100		0.45			75.8
74	Graph	5	x	bending		1200		0.45			64.1
74	Graph	5	x	bending		25		0.47			86.2
74	Graph	5	x	bending		200		0.47			86.9
74	Graph	5	x	bending		400		0.47			86.2
74	Graph	5	x	bending		600		0.47			84.1
74	Graph	5	x	bending		800		0.47			82
74	Graph	7	x	bending		25		0.08				132.4
74	Graph	7	x	bending		300		0.08				129.6
74	Graph	7	x	bending		500		0.08				126.8
74	Graph	7	x	bending		700		0.08				120.6
74	Graph	7	x	bending		900		0.08				117.2
74	Graph	7	x	bending		1000		0.08				110.3
74	Graph	7	x	bending		1100		0.08				103.4
74	Graph	7	x	bending		1200		0.08				87.6
74	Graph	7	x	bending		1250		0.08				82
74	Graph	7	x	bending		1275		0.08				60
74	Graph	7	x	bending		25		0.155				100.7
74	Graph	7	x	bending		300		0.155				99.3
74	Graph	7	x	bending		500		0.155				95.8
74	Graph	7	x	bending		600		0.155				94.4
74	Graph	7	x	bending		900		0.155				86.9
74	Graph	7	x	bending		1000		0.155				79.3
74	Graph	7	x	bending		25		0.224				88.9
74	Graph	7	x	bending		350		0.224				82.7
74	Graph	7	x	bending		475		0.224				82.7
74	Graph	7	x	bending		500		0.224				84.8
74	Graph	7	x	bending		700		0.224				83.4
74	Graph	7	x	bending		800		0.224				78.6
74	Graph	7	x	bending		1000		0.224				71.7
74	Graph	7	x	bending		1100		0.224				64.8
74	Graph	7	x	bending		1200		0.224				46.9
74	Graph	7	x	bending		1250		0.224				36.5
74	Graph	7	x	bending		25		0.325				64.1
74	Graph	7	x	bending		400		0.325				63.4
74	Graph	7	x	bending		500		0.325				62
74	Graph	7	x	bending		600		0.325				58.6
74	Graph	7	x	bending		800		0.325				57.2
74	Graph	7	x	bending		1000		0.325				53.8
74	Graph	7	x	bending		1100		0.325				48.3
74	Graph	7	x	bending		1250		0.325				29.6
74	Graph	7	x	bending		25		0.4				53.1
74	Graph	7	x	bending		300		0.4				49.6
74	Graph	7	x	bending		500		0.4				50.3
74	Graph	7	x	bending		800		0.4				46.2
74	Graph	7	x	bending		950		0.4				48.3
74	Graph	7	x	bending		1000		0.4				46.2
74	Graph	7	x	bending		1100		0.4				41.4
74	Graph	7	x	bending		1200		0.4				31
74	Graph	7	x	bending		1250		0.4				24.1
74	Graph	7	x	bending		25		0.51				36.5
74	Graph	7	x	bending		200		0.51				35.2
74	Graph	7	x	bending		400		0.51				34.5
74	Graph	7	x	bending		500		0.51				34.5
74	Graph	7	x	bending		600		0.51				34.5
74	Graph	7	x	bending		800		0.51				31.7
74	Graph	7	x	bending		1000		0.51				30.3
74	Graph	7	x	bending		1100		0.51				26.9
74	Graph	7	x	bending		1200		0.51				23.4
74	Graph	7	x	bending		1250		0.51				18.6

75	Table	II	x	sonic resonance		23	3.71				309
75	Graph	3	x	sonic resonance		23	3.71				308.5
75	Graph	3	x	sonic resonance		400					294.9
75	Graph	3	x	sonic resonance		600					286.4
75	Graph	3	x	sonic resonance		700					281.9
75	Graph	3	x	sonic resonance		800					278.9
75	Graph	3	x	sonic resonance		850					276.4
75	Graph	3	x	sonic resonance		900					274.4
75	Graph	3	x	sonic resonance		950					272.3
75	Graph	3	x	sonic resonance		1000					269.3
75	Graph	3	x	sonic resonance		1050					265.8
75	Graph	3	x	sonic resonance		1100					262.8
75	Graph	3	x	sonic resonance		1150					257.3
75	Graph	3	x	sonic resonance		1200					245.7

76	Graph	1	x	dynamic	1	23		0.006			379				3
76	Graph	1	x	dynamic	1	23		0.008			374				3
76	Graph	1	x	dynamic	1	23		0.011			374				3
76	Graph	1	x	dynamic	1	23		0.022			363				3
76	Graph	1	x	dynamic	1	23		0.034			337				3
76	Graph	1	x	dynamic	1	23		0.065			315				3
76	Graph	1	x	dynamic	1	23		0.106			251				3
76	Graph	1	x	dynamic	1	23		0.118			253				3
76	Graph	1	x	dynamic	1	23		0.131			242				3
76	Graph	1	x	dynamic	1	23		0.161			219				3
76	Graph	1	x	dynamic	1	23		0.168			190				3
76	Graph	1	x	dynamic	1	23		0.206			185				3
76	Graph	1	x	dynamic	1	23		0.231			153				3
76	Graph	1	x	dynamic	1	23		0.3			122				3
76	Graph	1	x	dynamic	1	23		0.321			112				3
76	Graph	1	x	static	2	23		0.023			368				4
76	Graph	1	x	static	2	23		0.057			310				4
76	Graph	1	x	static	2	23		0.071			275				4
76	Graph	1	x	static	2	23		0.094			273				4
76	Graph	1	x	static	2	23		0.111			236				4
76	Graph	1	x	static	2	23		0.142			224				4
76	Graph	1	x	static	2	23		0.209			174				4
76	Graph	1	x	static	3	23		0.07			306				5
76	Graph	1	x	static	3	23		0.205			213				5
76	Graph	1	x	static	3	23		0.217			209				5
76	Graph	1	x	static	3	23		0.343			103				5
76	Graph	1	x	static	4	23		0.285			124				6
76	Graph	1	x	static	4	23		0.35			110				6
76	Graph	1	x	static	4	23		0.386			87.1				6
76	Graph	1	x	static	4	23		0.412			74.8				6

77	Graph	2	x	4pt bending		30					388

78	Table	1	x	sonic	1	23	3.98				390
78	Table	1	x	sonic	2	23	3.94				391
78	Table	1	x	sonic	3	23	3.87				369
78	Table	1	x	sonic	4	23	3.87				375

79	Table	III	x	ult. interferometry		25	3.972		10.845	6.373	398.86	161.32	252.06	0.2363

80	Table	I	x	dynamic res.	1	25	3.972	0.0035			398.5	161.6	248.7
80	Table	I	x	dynamic res.	2	25	3.941	0.0113			385.3	157.5	231.8

81	Table	I	x	ultrasonic res.		25	3.974		10.845	6.377		161.6	251.92

82	Graph	3	x	ult. pulse echo		23		0.01		6.31
82	Graph	3	x	ult. pulse echo		23		0.029		6.18
82	Graph	3	x	ult. pulse echo		23		0.05		6.15
82	Graph	3	x	ult. pulse echo		23		0.06		6.03
82	Graph	3	x	ult. pulse echo		23		0.074		5.93
82	Graph	3	x	ult. pulse echo		23		0.091		6.03
82	Graph	3	x	ult. pulse echo		23		0.108		5.84
82	Graph	3	x	ult. pulse echo		23		0.122		5.72
82	Graph	3	x	ult. pulse echo		23		0.132		5.85
82	Graph	3	x	ult. pulse echo		23		0.141		5.62
82	Graph	3	x	ult. pulse echo		23		0.201		5.54
82	Graph	3	x	ult. pulse echo		23		0.211		5.41
82	Graph	3	x	ult. pulse echo		23		0.244		5.29
82	Graph	3	x	ult. pulse echo		23		0.268		5.1
82	Graph	3	x	ult. pulse echo		23		0.325		5.01
82	Graph	3	x	ult. pulse echo		23		0.363		4.86
82	Graph	3	x	ult. pulse echo		23		0.402		4.61
82	Graph	4	x	ult. pulse echo		23		0.007	9.8
82	Graph	4	x	ult. pulse echo		23		0.033	9.8
82	Graph	4	x	ult. pulse echo		23		0.05	9.64
82	Graph	4	x	ult. pulse echo		23		0.074	9.17
82	Graph	4	x	ult. pulse echo		23		0.102	9.02
82	Graph	4	x	ult. pulse echo		23		0.105	9.33
82	Graph	4	x	ult. pulse echo		23		0.112	9.09
82	Graph	4	x	ult. pulse echo		23		0.121	8.94
82	Graph	4	x	ult. pulse echo		23		0.129	9.17
82	Graph	4	x	ult. pulse echo		23		0.14	8.78
82	Graph	4	x	ult. pulse echo		23		0.2	8.47
82	Graph	4	x	ult. pulse echo		23		0.207	8.86
82	Graph	4	x	ult. pulse echo		23		0.248	8.23
82	Graph	4	x	ult. pulse echo		23		0.324	7.84
82	Graph	4	x	ult. pulse echo		23		0.36	7.3
82	Graph	4	x	ult. pulse echo		23		0.398	6.91

83	Graph	4	x	sonic velocity	1	23		0.226			175.4
83	Graph	4	x	sonic velocity	1	23		0.228			166.9
83	Graph	4	x	sonic velocity	1	23		0.231			161.1
83	Graph	4	x	sonic velocity	1	23		0.249			157.8
83	Graph	4	x	sonic velocity	1	23		0.31			98.1
83	Graph	4	x	sonic velocity	1	23		0.315			92.8
83	Graph	4	x	sonic velocity	1	23		0.316			94.7
83	Graph	4	x	sonic velocity	1	23		0.318			96
83	Graph	4	x	3pt bending	1	23		0.067			333.1
83	Graph	4	x	3pt bending	1	23		0.069			310.6
83	Graph	4	x	3pt bending	1	23		0.228			150.9
83	Graph	4	x	3pt bending	1	23		0.231			150.9
83	Graph	4	x	3pt bending	1	23		0.316			88.6
83	Graph	4	x	3pt bending	1	23		0.318			78.6
83	Graph	4	x	sonic velocity	2	23		0.188			214.1
83	Graph	4	x	sonic velocity	2	23		0.208			219.6
83	Graph	4	x	sonic velocity	2	23		0.206			200.4
83	Graph	4	x	sonic velocity	2	23		0.205			189.4
83	Graph	4	x	sonic velocity	2	23		0.28			136.3
83	Graph	4	x	sonic velocity	2	23		0.281			132.3
83	Graph	4	x	sonic velocity	2	23		0.29			121
83	Graph	4	x	sonic velocity	2	23		0.292			128.6
83	Graph	4	x	3pt bending	2	23		0.047			376.8
83	Graph	4	x	3pt bending	2	23		0.052			350
83	Graph	4	x	3pt bending	2	23		0.192			197.6
83	Graph	4	x	3pt bending	2	23		0.201			200.4
83	Graph	4	x	3pt bending	2	23		0.279			118.9
83	Graph	4	x	3pt bending	2	23		0.283			127.4

84	Graph	13	x	ult. pulse echo		23		0.032			342
84	Graph	13	x	ult. pulse echo		23		0.077			322
84	Graph	13	x	ult. pulse echo		23		0.259			212
84	Graph	13	x	ult. pulse echo		23		0.354			155

85	Graph	4	x	sonic resonance		23	0.393				0.98
85	Graph	4	x	sonic resonance		23	0.403				1.02
85	Graph	4	x	sonic resonance		23	0.663				2.95
85	Graph	4	x	sonic resonance		23	0.682				3.35
85	Graph	4	x	sonic resonance		23	0.682				3.67
85	Graph	4	x	sonic resonance		23	0.721				3.74
85	Graph	4	x	sonic resonance		23	0.717				3.48
85	Graph	4	x	sonic resonance		23	0.714				3.18

86	Table	2	x	resonance		23	3.982				403	163.1	253.7	0.2353	7
86	Table	2	x	resonance		77					400.9	162.2	253.3	0.2362	7
86	Table	2	x	resonance		127					398.5	161.1	252.6	0.2371	7
86	Table	2	x	resonance		177					396	160	251.8	0.2378	7
86	Table	2	x	resonance		227					393.5	158.8	250.9	0.2386	7
86	Table	2	x	resonance		277					390.8	157.7	249.7	0.2391	7
86	Table	2	x	resonance		327					389.3	156.6	248.6	0.2397	7
86	Table	2	x	resonance		377					385.6	155.4	247.7	0.2406	7
86	Table	2	x	resonance		427					382.8	154.2	246.6	0.2412	7
86	Table	2	x	resonance		477					380.2	153.1	245.5	0.2419	7
86	Table	2	x	resonance		527					377.4	151.9	244.4	0.2426	7
86	Table	2	x	resonance		577					374.7	150.7	243.3	0.2433	7
86	Table	2	x	resonance		627					372	149.5	242.4	0.2443	7
86	Table	2	x	resonance		677					369.2	148.3	241.3	0.245	7
86	Table	2	x	resonance		727					366.4	147.1	240	0.2456	7
86	Table	2	x	resonance		777					363.5	145.8	238.9	0.2464	7
86	Table	2	x	resonance		827					360.7	144.6	237.8	0.2472	7
86	Table	2	x	resonance		877					357.9	143.4	236.6	0.2479	7
86	Table	2	x	resonance		927					355	142.2	235.2	0.2484	7
86	Table	2	x	resonance		977					352	140.9	233.9	0.2492	7
86	Table	2	x	resonance		1027					349.1	139.7	232.6	0.2499	7
86	Table	2	x	resonance		1077					346.1	138.4	231	0.2503	7
86	Table	2	x	resonance		1127					343.3	137.2	230	0.2513	7
86	Table	2	x	resonance		1177					340.5	136	228.8	0.2519	7
86	Table	2	x	resonance		1227					337.8	134.8	228.1	0.2533	7
86	Table	2	x	resonance		1277					334.9	133.5	226.8	0.2539	7
86	Table	2	x	resonance		1327					332.1	132.3	225.9	0.255	7
86	Table	2	x	resonance		1377					329.5	131.2	224.8	0.2558	7
86	Table	2	x	resonance		1427					326.6	130	223.6	0.2566	7
86	Table	2	x	resonance		1477					323.8	128.7	222.3	0.2577	7
86	Table	2	x	resonance		1527					320.9	127.5	221.8	0.2589	7
86	Table	2	x	resonance		1552					319.5	126.8	221.3	0.2594	7

87	Graph	2	x	sonic resonance		23		0.411			1.62
87	Graph	2	x	sonic resonance		23		0.418			3.19
87	Graph	2	x	sonic resonance		23		0.412			3.36
87	Graph	2	x	sonic resonance		23		0.416			15.7
87	Graph	2	x	sonic resonance		23		0.414			19.6
87	Graph	2	x	sonic resonance		23		0.412			22.6
87	Graph	2	x	sonic resonance		23		0.411			26.3
87	Graph	2	x	sonic resonance		23		0.406			31.1
87	Graph	2	x	sonic resonance		23		0.405			37.8
87	Graph	2	x	sonic resonance		23		0.396			50.2
87	Graph	2	x	sonic resonance		23		0.378			65.6
87	Graph	2	x	sonic resonance		23		0.341			94.7
87	Graph	2	x	sonic resonance		23		0.296			123
87	Graph	2	x	sonic resonance		23		0.297			130
87	Graph	2	x	sonic resonance		23		0.287			123
87	Graph	2	x	sonic resonance		23		0.28			141
87	Graph	2	x	sonic resonance		23		0.264			152
87	Graph	2	x	sonic resonance		23		0.251			160
87	Graph	2	x	sonic resonance		23		0.248			166
87	Graph	2	x	sonic resonance		23		0.221			190
87	Graph	2	x	sonic resonance		23		0.201			194
87	Graph	2	x	sonic resonance		23		0.201			210
87	Graph	2	x	sonic resonance		23		0.196			221
87	Graph	2	x	sonic resonance		23		0.175			244
87	Graph	2	x	sonic resonance		23		0.163			240
87	Graph	2	x	sonic resonance		23		0.155			249
87	Graph	2	x	sonic resonance		23		0.098			315
87	Graph	2	x	sonic resonance		23		0.092			322
87	Graph	2	x	sonic resonance		23		0.086			330
87	Graph	2	x	sonic resonance		23		0.046			378
87	Graph	2	x	sonic resonance		23		0.042			377
87	Graph	2	x	sonic resonance		23		0.001			409
87	Graph	2	x	sonic resonance		23		0.411				1.48
87	Graph	2	x	sonic resonance		23		0.405				16.5
87	Graph	2	x	sonic resonance		23		0.395				21.3
87	Graph	2	x	sonic resonance		23		0.378				28.6
87	Graph	2	x	sonic resonance		23		0.341				38.7
87	Graph	2	x	sonic resonance		23		0.295				53
87	Graph	2	x	sonic resonance		23		0.28				58.6
87	Graph	2	x	sonic resonance		23		0.262				64.7
87	Graph	2	x	sonic resonance		23		0.249				71.5
87	Graph	2	x	sonic resonance		23		0.221				84.1
87	Graph	2	x	sonic resonance		23		0.201				89.3
87	Graph	2	x	sonic resonance		23		0.174				101
87	Graph	2	x	sonic resonance		23		0.163				105
87	Graph	2	x	sonic resonance		23		0.154				105
87	Graph	2	x	sonic resonance		23		0.095				132
87	Graph	2	x	sonic resonance		23		0.092				130
87	Graph	2	x	sonic resonance		23		0.087				133
87	Graph	2	x	sonic resonance		23		0.047				154
87	Graph	2	x	sonic resonance		23		0.042				154
87	Graph	2	x	sonic resonance		23		0.001				167
87	Graph	2	x	sonic resonance		23		0.412					1.58
87	Graph	2	x	sonic resonance		23		0.411					3.26
87	Graph	2	x	sonic resonance		23		0.405					18
87	Graph	2	x	sonic resonance		23		0.396					23
87	Graph	2	x	sonic resonance		23		0.378					32.1
87	Graph	2	x	sonic resonance		23		0.341					45.6
87	Graph	2	x	sonic resonance		23		0.299					65.7
87	Graph	2	x	sonic resonance		23		0.28					69.8
87	Graph	2	x	sonic resonance		23		0.265					78.1
87	Graph	2	x	sonic resonance		23		0.25					83
87	Graph	2	x	sonic resonance		23		0.222					91.4
87	Graph	2	x	sonic resonance		23		0.196					116
87	Graph	2	x	sonic resonance		23		0.175					117
87	Graph	2	x	sonic resonance		23		0.156					126
87	Graph	2	x	sonic resonance		23		0.097					172
87	Graph	2	x	sonic resonance		23		0.087					171
87	Graph	2	x	sonic resonance		23		0.048					198
87	Graph	2	x	sonic resonance		23		0.043					198
87	Graph	2	x	sonic resonance		23		0.002					209
87	Graph	3	x	sonic resonance		23		0.411						0.147
87	Graph	3	x	sonic resonance		23		0.404						0.156
87	Graph	3	x	sonic resonance		23		0.395						0.158
87	Graph	3	x	sonic resonance		23		0.376						0.161
87	Graph	3	x	sonic resonance		23		0.339						0.169
87	Graph	3	x	sonic resonance		23		0.296						0.162
87	Graph	3	x	sonic resonance		23		0.293						0.15
87	Graph	3	x	sonic resonance		23		0.284						0.142
87	Graph	3	x	sonic resonance		23		0.284						0.137
87	Graph	3	x	sonic resonance		23		0.278						0.179
87	Graph	3	x	sonic resonance		23		0.262						0.171
87	Graph	3	x	sonic resonance		23		0.247						0.165
87	Graph	3	x	sonic resonance		23		0.246						0.172
87	Graph	3	x	sonic resonance		23		0.218						0.166
87	Graph	3	x	sonic resonance		23		0.2						0.166
87	Graph	3	x	sonic resonance		23		0.197						0.177
87	Graph	3	x	sonic resonance		23		0.193						0.193
87	Graph	3	x	sonic resonance		23		0.173						0.171
87	Graph	3	x	sonic resonance		23		0.161						0.177
87	Graph	3	x	sonic resonance		23		0.152						0.182
87	Graph	3	x	sonic resonance		23		0.096						0.2
87	Graph	3	x	sonic resonance		23		0.091						0.201
87	Graph	3	x	sonic resonance		23		0.085						0.19
87	Graph	3	x	sonic resonance		23		0.046						0.201
87	Graph	3	x	sonic resonance		23		0.042						0.191
87	Graph	3	x	sonic resonance		23		0.003						0.209
87	Graph	3	x	sonic resonance		23		0.002						0.197
87	Graph	3	x	sonic resonance		23		0.003						0.184
87	Graph	3	x	sonic resonance		23		0.001						0.18

88	Table	P4	x	ultrasonic meth.		23	3.98				398	159		0.245

89	Table	I	x	sonic velocity		23		0.29			100			0.17	8
89	Table	I	x	sonic velocity		23		0.22			168			0.17	8
89	Table	I	x	sonic velocity		23		0.15			228			0.17	8
89	Table	I	x	sonic velocity		23		0.04			364			0.17	8
89	Table	I	x	sonic velocity		23		0.42			68			0.17	8
89	Table	I	x	sonic velocity		23		0.35			120			0.17	8
89	Table	I	x	sonic velocity		23		0.27			184			0.17	8
89	Table	I	x	sonic velocity		23		0.15			276			0.17	8

90	Table	1,2	x	ultrasonic res.		23	3.98	0.002			393	158		0.24

91	Graph	9	x	sonic velocity		23		0.24			151
91	Graph	9	x	sonic velocity		23		0.2			176
91	Graph	9	x	sonic velocity		23		0.18			194

92	Table	I	x	ultrasonic res.		25					436

93	Graph	3	x	sonic resonance		23					39
93	Graph	3	x	sonic resonance		23					104
93	Graph	3	x	sonic resonance		23					170
93	Graph	3	x	sonic resonance		23					280
93	Graph	3	x	sonic resonance		23					391

           ===== Table Notes =====

           1: On heating.
           2: On cooling.
           3: Attributed to Spriggs.
           4: Attributed to Schofield.
           5: Attributed to Duckworth.
           6: Attributed to Majumder.
           7: G and B obtained via Voight-Reuss-Hill averaging of single crystal data; E calculated from G and B.
           8: E values were calculated from the reported relative values E/E_o using E_o = 400 GPa.

Elastic Moduli Data for Polycrystalline Ceramics

Al2O3 { aluminum oxide, alumina }

Al₂O₃ { aluminum oxide, alumina }