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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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159	J. P. Singh, H. J. Leu, R. B. Poeppel, E. Van Voorhees, G. T. Goudey, K. Winsley, and D. Shi, Effect of Silver and Silver Oxide Additions on the Mechanical and Superconducting Properties of YBa₂Cu₃O_7-(delta) Superconductors, Journal of Applied Physics, Vol. 66, No. 7, pp. 3154-3159 (1989).
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163	P. V. Reddy, R. R. Reddy, K. B. Reddy, and V. N. Mulay, Ulrasonic Anomalies in Y-Ba-Cu-O High-T_c Superconducting Materials, Modern Physics Letters B, Vol. 7, No. 22, pp. 1457-1465 (1993).
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).
165	P. V. Reddy, S. Shekar, and K. Somaiah, Elasticity Studies of RE-Ba-Cu-O High-T_c Superconductors, Materials Letters, Vol. 21, pp. 21-29 (1994).
166	H. Ledbetter, M. Lei, A. Hermann, and Z. Sheng, Low-Temperature Elastic Constants of Y₁Ba₂Cu₃O₇, Physica C, Vol. 225, pp. 397-403 (1994).
167	Z. Zhong, Y. Qianjin, T. Xinlu, Z. Lizhong, W. Qimin, and Z. Peiqiang, The Dynamical Mechanical Properties of YBCO Superconductor, Experimental Techniques, Vol. 18, No. 4, pp. 25-27 (1994).
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).
170	L. Masi, E. Borchi, and S. de Gennaro, Porosity Behaviour of Ultrasonic Velocities in Polycrystalline Y-B-C-O, Journal of Physics F: Applied Physics, Vol. 29, pp. 2015-2019 (1996).
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174	R. Sreekumar, J. Isaac, J. Philip, K. V. Paulose, M. T. Sebastian, and A. D. Damodaran, Elastic and Thermal Properties of Yttrium Barium Zirconate, Physica Status Solidi (a), Vol. 133, pp. 341-347 (1992).
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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).
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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

Ho₂O₃ { holmium oxide, holmia }

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	T [°C]	p [%]	E [GPa]	G [GPa]	B [GPa]	nu
105	Table	III	c	extrapolation	23	0	169.4	65.54	134.68	0.29
105	Graph	3	x	sonic resonance	23	0.013	163
105	Graph	3	x	sonic resonance	23	0.015	164
105	Graph	3	x	sonic resonance	23	0.019	166
105	Graph	3	x	sonic resonance	23	0.045	159
105	Graph	3	x	sonic resonance	23	0.057	147
105	Graph	3	x	sonic resonance	23	0.066	146
105	Graph	3	x	sonic resonance	23	0.071	141
105	Graph	3	x	sonic resonance	23	0.073	140
105	Graph	3	x	sonic resonance	23	0.073	145
105	Graph	3	x	sonic resonance	23	0.076	143
105	Graph	3	x	sonic resonance	23	0.085	139
105	Graph	3	x	sonic resonance	23	0.095	136
105	Graph	3	x	sonic resonance	23	0.096	137
105	Graph	3	x	sonic resonance	23	0.098	134
105	Graph	3	x	sonic resonance	23	0.107	131
105	Graph	3	x	sonic resonance	23	0.116	130
105	Graph	3	x	sonic resonance	23	0.123	123
105	Graph	3	x	sonic resonance	23	0.132	118
105	Graph	3	x	sonic resonance	23	0.157	116
105	Graph	3	x	sonic resonance	23	0.174	109
105	Graph	3	x	sonic resonance	23	0.181	105
105	Graph	3	x	sonic resonance	23	0.014		64
105	Graph	3	x	sonic resonance	23	0.014		62
105	Graph	3	x	sonic resonance	23	0.02		64
105	Graph	3	x	sonic resonance	23	0.044		61
105	Graph	3	x	sonic resonance	23	0.057		56
105	Graph	3	x	sonic resonance	23	0.066		56
105	Graph	3	x	sonic resonance	23	0.07		54
105	Graph	3	x	sonic resonance	23	0.073		56
105	Graph	3	x	sonic resonance	23	0.073		53
105	Graph	3	x	sonic resonance	23	0.076		55
105	Graph	3	x	sonic resonance	23	0.087		53
105	Graph	3	x	sonic resonance	23	0.094		53
105	Graph	3	x	sonic resonance	23	0.095		53
105	Graph	3	x	sonic resonance	23	0.099		52
105	Graph	3	x	sonic resonance	23	0.108		51
105	Graph	3	x	sonic resonance	23	0.116		51
105	Graph	3	x	sonic resonance	23	0.122		49
105	Graph	3	x	sonic resonance	23	0.133		47
105	Graph	3	x	sonic resonance	23	0.158		45
105	Graph	3	x	sonic resonance	23	0.174		43
105	Graph	3	x	sonic resonance	23	0.181		41

106	Graph	2	x	dynamic resonance	24	0.182	105.8	40.4
106	Graph	2	x	dynamic resonance	63	0.182	105.1	40.3
106	Graph	2	x	dynamic resonance	107	0.182	104.3	40.3
106	Graph	2	x	dynamic resonance	159	0.182	104.2	40.2
106	Graph	2	x	dynamic resonance	206	0.182	103.5	40.1
106	Graph	2	x	dynamic resonance	260	0.182	102.7	39.3
106	Graph	2	x	dynamic resonance	314	0.182	102.6	39.2
106	Graph	2	x	dynamic resonance	363	0.182	101.8	39.1
106	Graph	2	x	dynamic resonance	400	0.182	101.1	39
106	Graph	2	x	dynamic resonance	452	0.182	101	38.9
106	Graph	2	x	dynamic resonance	499	0.182	100.2	38.8
106	Graph	2	x	dynamic resonance	535	0.182	100.2	38.1
106	Graph	2	x	dynamic resonance	597	0.182	98.7	38
106	Graph	2	x	dynamic resonance	626	0.182	98.7	37.9
106	Graph	2	x	dynamic resonance	687	0.182	97.9	37.8
106	Graph	2	x	dynamic resonance	722	0.182	97.8	37.7
106	Graph	2	x	dynamic resonance	756	0.182	97.1	37.7
106	Graph	2	x	dynamic resonance	806	0.182	97	37.6
106	Graph	2	x	dynamic resonance	835	0.182	96.3	36.8
106	Graph	2	x	dynamic resonance	899	0.182	95.5	36.7
106	Graph	2	x	dynamic resonance	946	0.182	94.7	36.6
106	Graph	2	x	dynamic resonance	23	0.133	116.4	46.4
106	Graph	2	x	dynamic resonance	58	0.133	115.6	45.6
106	Graph	2	x	dynamic resonance	102	0.133	114.9	45.6
106	Graph	2	x	dynamic resonance	151	0.133	114.1	45.5
106	Graph	2	x	dynamic resonance	210	0.133	113.4	44.7
106	Graph	2	x	dynamic resonance	256	0.133	112.6	44.6
106	Graph	2	x	dynamic resonance	311	0.133	112.5	44.5
106	Graph	2	x	dynamic resonance	357	0.133	111.8	44.4
106	Graph	2	x	dynamic resonance	421	0.133	111	43.6
106	Graph	2	x	dynamic resonance	483	0.133	110.2	43.5
106	Graph	2	x	dynamic resonance	547	0.133	108.7	43.4
106	Graph	2	x	dynamic resonance	596	0.133	108.6	43.3
106	Graph	2	x	dynamic resonance	618	0.133	107.9	43.2
106	Graph	2	x	dynamic resonance	726	0.133	107	42.3
106	Graph	2	x	dynamic resonance	763	0.133	106.3	42.3
106	Graph	2	x	dynamic resonance	817	0.133	106.2	42.2
106	Graph	2	x	dynamic resonance	842	0.133	106.2	42.1
106	Graph	2	x	dynamic resonance	888	0.133	104.8	42
106	Graph	2	x	dynamic resonance	938	0.133	104.6	41.3
106	Graph	2	x	dynamic resonance	992	0.133	103.9	41.1
106	Graph	2	x	dynamic resonance	25	0.074	146.1	55
106	Graph	2	x	dynamic resonance	74	0.074	144.7	54.8
106	Graph	2	x	dynamic resonance	111	0.074	143.9	54.8
106	Graph	2	x	dynamic resonance	155	0.074	143.8	54.7
106	Graph	2	x	dynamic resonance	211	0.074	142.4	53.9
106	Graph	2	x	dynamic resonance	243	0.074	141.7	53.9
106	Graph	2	x	dynamic resonance	283	0.074	141	53.8
106	Graph	2	x	dynamic resonance	327	0.074	140.2	53.7
106	Graph	2	x	dynamic resonance	391	0.074	139.4	52.9
106	Graph	2	x	dynamic resonance	440	0.074	138.7	52.8
106	Graph	2	x	dynamic resonance	504	0.074	137.9	52.7
106	Graph	2	x	dynamic resonance	558	0.074	137.1	51.9
106	Graph	2	x	dynamic resonance	602	0.074	136.4	51.8
106	Graph	2	x	dynamic resonance	631	0.074	135.6	51.8
106	Graph	2	x	dynamic resonance	656	0.074	135.6	51.7
106	Graph	2	x	dynamic resonance	749	0.074	134.1	51.5
106	Graph	2	x	dynamic resonance	804	0.074	133.3	50.8
106	Graph	2	x	dynamic resonance	833	0.074	133.3	50.7
106	Graph	2	x	dynamic resonance	868	0.074	132.5	50.6
106	Graph	2	x	dynamic resonance	929	0.074	131.1	49.9
106	Graph	2	x	dynamic resonance	993	0.074	129.6	49.7

Elastic Moduli Data for Polycrystalline Ceramics

Ho2O3 { holmium oxide, holmia }

Ho₂O₃ { holmium oxide, holmia }