Mechanical Properties of Ceramics and Composites

temperature of 800–1200°C does not occur. Note that Al2O3-ZrO2 eutectics also show some opposite trends of work-to-fracture and strength. These strength–toughness differences in ZrO2 toughened systems again strongly suggest toughening mechanisms associated with the presence of ZrO2 other than just transformation, as is also shown for TZP and especially PSZ bodies (e.g. (Fig. 6.6). However, more generally, strength–toughness differences in the latter as well as other composite systems show, despite more limited data, both some similarities and some differences similar to those for monolithic ceramics. As with monolithic ceramics, the differences probably reflect significant differences in strain rate–crack velocity effects between various toughness and strength tests.

Both cases of composite hardness versus temperature indicate faster decreases of hardness than for E, i.e. at rates of 2–4% per 100°C for hardness. However, while the Al2O3-(WC+ Co) composite showed similar trends of hardness with temperature as the Al2O3 alone, this is not the case for the Al2O3-SiC composite. Whether the latter reflects differences in the temperature dependences of the two phases and the former similarities in the two is not certain, since data on one of the composite phases was not obtained.

Turning to the third trend, namely property decreases at higher temperatures, typically ≥1000°C, much of this must involve increasing influence of creep processes. Thus the merger of strengths of Al2O3-SiC whisker composite with 10 and 20 v/o whiskers at higher temperatures is consistent with creep being less sensitive to v/o whiskers once the percolation limit has been reached. However, much again remains to be more clearly understood and documented.

V.SUMMARY

The broadest messages to take from this chapter are first the overall similarities of the temperature dependence of mechanical properties of ceramic composites and monolithic ceramics and the need for much more documentation and understanding. The latter is even more critical for composites, but the need for both material systems is for more comprehensive study and evaluation. With regard to similarities, it is important to note that these exist at both lower and higher temperatures. Thus tests at moderate temperature are often neglected in both material systems, based on the (often incorrect) assumption that no significant changes occur in this temperature range. This is frequently not the case. Substantial changes were shown in some cases, and other lesser but still significant changes were shown and discussed at temperatures < 600°C. Another broad message is the frequent, and often significant, disparity of toughness due to effects of material, microstructure, temperature, and especially test method and parameters, which is still incompletely documented and understood.

Some other points to note are as follows. Thermal shock resistance can often be increased via composites, with large crack toughnesses generally correlating with retained strengths (but not necessarily with normal strengths). However, significant thermal shock resistance is generally accomplished by mechanisms that limit strength and thermal shock fatigue, which has been demonstrated and can be substantial, is likely to be wide-spread, and probably entails mechanical fatigue (e.g. in zero-tension tests, apparently due to mismatch stresses between grains and particles). Tensile strengths of composites typically decrease increasingly rapidly above 1000–1200°C similar to monolithic ceramics, with rheological creep models generally being good guides. However, composites can have greater resistance to such plastic flow, especially as the percolation limit of the added phase is reached, which occurs much more rapidly as the dispersed phase is elongated in one direction, i.e. whiskers are better. Hardness tests may be useful for probing high-temperature plasticity.

REFERENCES

1.V. Lavaste, J. Besson, M.-H. Berger, and A. R. Bunsell. Elastic and Creep Properties of Alumina-Based Single Fibers. J. Am. Cer. Soc. 78(11):3081–3087, 1995.

2.J. C. Romie. New High-Temperature Ceramic Fiber. Cer. Eng. Sci. Proc. 8(7- 8):755–765, 1987.

3.D. J. Pysher, K.C. Goretta, R. S. Hodder, Jr., and R. E. Tressler. Strengths of Ceramics Fibers at Elevated Temperatures. J. Am. Cer. Soc. 72(2):284–288, 1989.

4.S. Sakagushi, N. Murayama, Y. Kodama, and F. Wakai. The Poisson’s Ratio of Engineering Ceramics at Elevated Temperature. J. Mat. Sci. Lett. 10:282–284, 1991.

5.J. D. French, H. M. Chan, M. P. Harmer, and Gary A. Miller. High-Temperature Fracture Toughness of Duplex Microstructures. J. Am. Cer. Soc. 79(1):58–64, 1996.

6.K. Tsukuma, K. Ueda, K. Matsushita, and M. Shimada. High-Temperature Strength

and Fracture Toughness of Y2O3-Partially-Stabilized ZrO2/Al2O3 Composites. J. Am. Cer. Soc. 68(2):C-56–58, 1985.

7.K. P. Gadkaree. Whisker Reinforcement of Glass-Ceramics. J. Mat. Sci. 26:4845–4854, 1991.

8.W. J. Lee and E. D. Case. Cyclic Thermal Shock in SiC-Whisker-Reinforced Alumina Composite. Mat. Sci. Eng. A119:113–126, 1989.

9.K. S. Mazdiyasni and R. Ruh. High/Low Modulus Si3N4-BN Composite for Improved Electrical and Thermal Shock Behavior. J. Am. Cer. Soc. 64(7):415–419, 1981.

10.J. P. Northover and G. W. Groves. High-Temperature Mechanical Properties of LiO2-Al2O3-SiO2 (LAS) Glass Ceramics. J. Mat. Sci. 16:1881–1886, 1981.

11.R. K. Govila, K. R. Kinsman, and P. Beardmore. Fracture Phenomenology of a Lithium-Aluminum-Silicate Glass-Ceramic. J. Mat. Sci. 13:2081–2091, 1978.

12.B. S. Majumdar, T. Mah, and M. G. Mendiratta. Flaw Growth in a Polycrystalline Lithium-Aluminum-Silicate Glass Ceramic. J. Mat. Sci. 17:3129–3139, 1982.

13.G. H. Beall, K. Chyung, R. L. Stewart, K. Y. Donaldson, H. L. Lee, S. Baskaran, and D. P. H. Hasselman. Effect of Test Method and Crack Size on the Fracture Toughness of a Chain-Silicate Glass-Ceramic. J. Mat. Sci. 21:1365–1372, 1973.

14.G. Brandt, B. Johannesson, and R. Warren. Fracture Behavior of Selected Mixed-Ceramic Tool Materials up to 1200°C. Mat. Sci. Eng. A105/106:193–200, 1988.

15.G. Orange, G. Fantozzi, F. Cambier, C. LeBlud, M. R. Anseau, and A. Leriche. High Temperature Mechanical Properties of Reaction-Sintered Mullite/Zirconia and Mullite/Alumina/Zirconia Composites. J. Mat. Sci. 20:2533–2540, 1985.

16.C. H. Henager, Jr., and S. Wada. Processing and Properties of Ceramic Matrix Composites with In Situ Reinforcement. Handbook on Discontinuously Reinforced Ceramic Matrix Composites (K. J. Bowman, S. K. El-Rahaiby, and J. B. Wachtman, Jr., eds.). Am. Cer. Soc., Westerville, OH, 1995, pp. 139–223.

17.A. Leriche, P. Descamps, and F. Cambier. High Temperature Mechanical Behavior of Mullite-Zirconia Composites Obtained by Reaction-Sintered. Zirconia 88:Advances in Zirconia Science and Technology (S. Meriani and C. Palmonari, eds.). Elsevier, New York, 1989, pp. 137–151.

18.K. Niihara, A. Nakahira, T. Uchiyama. and T. Hirai. High-Temperature Mechanical

Properties of Al2O3-SiC Composites. Fracture Mechanics of Ceramics 7, Composites, Impact, Statistics, and High-Temperature Phenomena (R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange, eds.). Plenum Press, New York, 1986, pp. 103–116.

19.J. G. Baldoni, S. T. Buljan, and V. K. Sarin. Particulate Titanium Carbide-Ceramic Matrix Composites. Second Intl. Conf. Science Hard Materials (Rhodes, ed.). Inst. Phy. Conf. Ser. No. 75. Adam Hilger Ltd., Bristol, England, 1986, pp. 429–435.

20.W.-P. Tai and T. Watanabe. Elevated-Temperature Toughness and Hardness of a Hot-Pressed Al2O3-WC-Co Composite. J. Am. Cer. Soc. 81(1):257–259, 1998.

21.C. F. Cooper. Graphite Containing Refractories. Refractories J. Ref. Assn. Great Brit., No. 6. 1980, pp. 11–21.

22.R. C. Rossi. Thermal-Shock-Resistant Materials. Ceramics in Severe Environments (W. W. Kriegel and H. Palmour III, eds.). Plenum Press, New York, 1971, pp. 123–136.

23.C. J. Fairbanks, H. L. Lee, and D. P. H. Hasselman. Effect of Crystallites on Thermal Shock Resistance of Cordierite Glass-Ceramics. J. Am. Cer. Soc. 67(11):C- 236–237, 1984.

24.M. Oguma, K. Chyung, K. Y. Donaldson, and D. P. H. Hasselman. Effect of Crystallization on Thermal Shock Behavior of a Chain-Silicate Canasite Glass-Ceramic. J. Am. Cer. Soc. 70(1):C-2–3, 1987.

25.P. F. Becher. Transient Thermal Stress Behavior in ZrO2-Toughened Al2O3, J. Am. Cer. Soc. 64(1):37–39, 1978.

26.I. Thompson and R. D. Rawlings. Monitoring Thermal Shock of Alumina and Zir-

conia-Toughened Alumina by Acoustic Techniques. J. Mat. Sci. 26:4534–4540, 1991.

27.H. Tomaszewski. Effect of Sintering Atmosphere on Thermomechanical Properties of Al2O3-ZrO2 Ceramics. Cer. Intl. 15:141–146, 1989.

28.T. Sornakumar, V. E. Annamalai, R. Krishnamurthy, and C. V. Gokularthnam. Thermal Shock Resistance of Composites of Alumina and Partially Stabilized Zirconia. J. Mat. Sci. Lett. 12:1253–1254, 1993.

29.E. H. Lutz, M. V. Swain, and N. Claussen. Thermal Shock Behavior of Duplex Ceramics. J. Am. Cer. Soc. 74 (1):19–24, 1991.

30.Q.-M. Yuan, J.-Q. Tan, and Z.-G. Jin. Preparation and Properties of Zirconia-Tough- ened Mullite Ceramics. J. Am. Cer. Soc. 69(3): 265–267, 1986.

31.M. Ishitsuka, T. Sato, T. Endo, and M. Shimada. Sintering and Mechanical Proper-

ties of Yttria-Doped Tetragonal ZrO2 Polycrystal/Mullite Composites. J. Am. Cer. Soc. 70(11):C-342–346, 1987.

32.V. P. Dravid, M. R. Notis, and C. E. Lyman. Twinning and Microcracking Associated with Monoclinic Zirconia in the Eutectic System Zirconia-Mullite. J. Am. Cer. Soc. 71(4):C-219–221, 1988.

33.I.-S. Kim and I.-G. Kim. Thermal Shock Behavior of Al2O3-SiC Composites Made by Directed Melt Oxidation of Al-Alloy. J. Mat. Sci. Lett. 16:772–775, 1997.

34.M. Landon and F. Thevenot. The SiC-AlN System: Influence of Elaboration Routes on the Solid Solution Formation and Its Mechanical Properties. Cer. Intl. 17:97–110, 1991.

35.T. N. Tiegs and P. F. Becher. Thermal Shock Behavior of an Alumina-SiC Whisker Composite. J. Am. Cer. Soc. 70(5):C-109–111, 1987.

36.N. Sato and T. Kurauchi. Microcracking During a Thermal Cycle in Whisker-Rein- forced Ceramics Composites Detected by Acoustic Emission Measurement. J. Mat. Sci. Lett. 11:590–591, 1992.

37.C. F. Cooper, I. C. Alexander, and C. J. Hampson. The Role of Graphite in the Thermal Shock Resistance of Refractories. Brit. Cer. Trans. J. 84:57–62, 1985.

38.R. C. Rossi and R. D. Carnahan. Thermal Shock Resistant Ceramic Composite. US Patent 4,007,049, 2/8/1977.

39.D. Lewis, R. P. Ingel, W. J. McDonough, and R. W. Rice. Microstructure and Thermomechanical Properties in Aluminaand Mullite- Boron-Nitride Particulate Composites. Cer. Eng. Sci. Proc. 2(7-8):719–727, 1981.

40.R. W. Rice, W. J. McDonough, S. W. Freiman, and J. J. Mecholsky, Jr. Ablative-Re- sistant Dielectric Ceramic Articles. US Patent 4,304,870, 12/8/1981.

41.W. S. Coblenz and D. Lewis, III. In Situ Reaction of B2O3 with AlN and/or Si3N4 to Form BN-Toughened Composites. J. Am. Cer. Soc. 71(12):1080–1085, 1988.

42.R. W. Rice. Processing of Ceramic Composites. Advanced Ceramic Processing and Technology 1 (J. G. P. Binner, ed.). Noyes, Park Ridge, NJ, 1990, pp. 123–213.

43.D. Goeuriot-Launay, G. Brayet, and F. Thevenot. Boron Nitride Effect on the Thermal Shock Resistance of an Alumina-Based Ceramic Composite. J. Mat. Sci. Lett. 5:940–942, 1986.

44.P. G. Valentine, A. N. Palazotto, R. Ruh, and D. C. Larsen. Thermal Shock Resistance of SiC-BN Composites. Adv. Cer. Mat. 1(1):81–86, 1986.

45.D. Lewis and R. W. Rice. Thermal Shock Fatigue of Monolithic Ceramics and Ce- ramic-Ceramic Particulate Composites. Cer. Eng. Sci. Proc. 2(7-8):712–718, 1981.

46.D. Lewis and R. W. Rice. Comparison of Static, Cyclic, and Thermal Shock Fatigue in Ceramic. Cer. Eng. Sci. Proc. 3(7-8):714–721, 1982.

47.J. H. Schneibel, S. M. Sabol, J. Morrison, E. Ludeman, and C. A. Carmichael. Cyclic Thermal Shock Resistance of Several Advanced Ceramics and Ceramic Composites. J. Am. Cer. Soc. 81(7):1888–1892, 1998.

48.M. P. Borom. Dispersion-Strengthened Glass Matrices-Glass-Ceramics, A Case in Point. J. Am. Cer. Soc. 60(1- 2):17–21, 1977.

49.R. K. Govila. Strength Characterization of Yttria-Partially Stabilized Zirconia/Alumina Composite. J. Mat. Sci. 28:700–718, 1993.

50.D. E.-W. Shin, K. K. Orr, and H. Schubert. Microstructure-Mechanical Property Relations in Hot Isostatically Pressed Alumina and Zirconia-Toughened Alumina. J. Am. Cer. Soc. 73(5):1181–1188, 1990.

51.S. Lathabai, D. G. Hay, F. Wagner, and N. Claussen. Reaction-Bonded Mullite/Zirconia Composites. J. Am. Cer. Soc. 79(1):248–256, 1996

52.H. Endo, M. Ueki, and H. Kubo. Microstructure and Mechanical Properties of Hot Pressed SiC-TiC Composites. J. Mat. Sci. 26:3769–3774, 1991.

53.B.-W. Lin and T. Iseki. Effect of Thermal Residual Stress on Mechanical Properties of SiC/TiC Composites. Brit. Cer. Trans. 91:1–5, 1992.

54.B.-W. Lin and T. Iseki. Different Toughening Mechanisms in SiC/TiC Composites. Brit. Cer. Trans. 91:147–150, 1992.

55.C. H. McMurtry, W. D. G. Boecker, S. G. Seshadri, J. S. Zangil, and J. E. Garnier.

Microstructure and Material Properties of SiC-TiB2 Particulate Composites, Am. Cer. Soc. Bull. 66(2):325–329, 1987.

56.K. S. Mazidyasni, R. Ruh, and E. E. Hermes. Phase Characterization and Properties of AlN-BN Composites. Am. Cer. Soc. Bull. 64(8):1149–1154, 1983.

57.X.-N. Huang and P.S. Nicholson. Mechanical Properties and Fracture Toughness of

α-Al2O3-Platelet Reinforced Y-TZP Composites at Room and High Temperature. J. Am. Cer. Soc.76(5):1294–1301,1993.

58.P. F. Becher, T. N. Tiegs, J. C. Ogle, and W. H. Warwick. Toughening of Ceramics by Whisker Reinforcement. Fracture Mechanics of Ceramics 7, Composites, Impact, Statistics, and High-Temperature Phenomena (R. C. Bradt, A. G. Evans, D. P. H. Hasselman, and F. F. Lange, eds.). Plenum Press, New York, 1986, pp. 61–73.

59.R. K. Govila. Fracture of Hot-Pressed Alumina and SiC-Whisker-Reinforced Alumina Composite. J. Mat. Sci. 23:3782–3791, 1988.

60.M. Yang and R. Stevens. Microstructure and Properties of SiC Whisker Reinforced Ceramic Composites. J. Mat. Sci. 26:726–736, 1991.

61.K. P. Gadkaree. Whisker Reinforcement of Glass-Ceramics. J. Mat. Sci. 26:4845–4854, 1991.

62.T. Kumazawa, S. Ohta, H. Tabata, and S. Kanzaki. Mechanical Properties of Mul- lite-SiC Whisker Composite. J. Cer. Soc. Jpn., Intl. Ed. 97:880–888, 1989.

63.S. R. Choi and J. A. Salem. Strength, Toughness and R-Curve Behavior of SiC

Whisker-Reinforced Composite Si3N4 with Reference to Monolithic Si3N4, J. Mat. Sci. 27:1491–1498, 1992.

64.S. Zhu, M. Mizuno, Y. Nagano, Y. Kagawa, and M. Watanabe. Stress Rupture in Tension and Flexure of a SiC-Whisker-Reinforced Silicon Nitride Composite at Elevated Temperatures. J. Am. Cer. Soc. 79(10):2789–2791, 1996.

65.C. Olagnon, E. Bullock, and G. Fantozzi. Properties of Sintered SiC Whisker-Rein- forced Si3N4 Composites. J. Eur. Cer. Soc. 7:265–273, 1991.

66.J. Dusza and D. Sajgalik. Mechanical Properties of Si3N4 + β-Si3N4 Whisker Reinforced Ceramics. J. Eur. Cer. Soc. 9:9–17, 1992.

67.J. E. Moffatt, W. J. Plumbridge, and R. Herman. High temperature Crack Annealing Effects on Fracture Toughness of Alumina and Alumina-SiC Composites. Brit. Cer. Soc. Trans. 95(1):23–29, 1996.

68.D. R. Carroll and L. R. Dharani. Effect of Temperature on the Ultimate Strength and Modulus of Whisker-Reinforced Ceramics. J. Am. Cer. Soc. 75(4):786–794, 1992.

69.C. Hulse and J. Batt, The Effect of Eutectic Microstructures on the Mechanical Properties of Ceramic Oxides. United Aircraft Res. Lab. Report for ONR Contract N00014-69-C-0073, 5/1974.

70.F. L. Kennard, R. C. Bradt, and V. S. Stubican. Mechanical Properties of the Direc-

tionally Solidified MgO-MgAl2O4 Eutectic. J. Am. Cer. Soc. 59(3-4):160–163, 1976.

71.V. S. Stubican, R. C. Bradt, F. L. Kennard, W. J. Minford, and C. C. Sorell. Ceramic Eutectic Composites. Tailoring Multiphase and Composite Ceramics, Materials Science Research 20 (R. E. Tressler, G. L. Messing, C. G. Pantano, and R. E. Newnham, eds.). Plenum Press, New York, 1986, pp. 103–113.

72.T. Mah, A. Parthasarathy, and L. E. Matson. Processing and Mechanical Properties

of Al2O3/Y5Al5O12 (YAG) Eutectic Composites. Cer. Eng. Sci. Proc. 11(9-10): 1617–1627, 1990.

73.Y. Waku, N. Nakagawa, T. Wakamoto, H. Ohtsubo, K. Shimizu, and Y. Kohtoku. High-Temperature Strength and Thermal Stability of a Directionally Solidified Al2O3/YAG Eutectic Composite. J. Mat. Sci. 33:1217–1225, 1998.

74.T. I. Barry, L. A. Lay, and R. Morell. High Temperature Mechanical Properties of Cordierite Refractory Glass Ceramics. Proc. Brit. Cer. Soc. 25, Mechanical Properties of Ceramics (2) (R. W. Davidge, ed.):67–84, 1975.

75.K. James and K. H. G. Ashbee. Plasticity of Hot Glass-Ceramics. Prog. Mat. Sci. 21(1):3–59, 1975.

76.D. Wilkinson. Creep Mechanisms in Multiphase Ceramic Materials. J. Am. Cer. Soc. 81(2):275–299, 1998.

77.H.-T. Lin, K. B. Alexander, and P. F. Becher. Grain Size Effect on Creep Deformation of Alumina-Silicon Carbide Composites. J. Am. Cer. Soc. 79(6):1530–1536, 1996.

78.J. M. Desmarres, P. Goursat, J. L. Besson, P. Lespade, and B. Capdepuy. SiC

Whiskers Reinforced Si3N4 Matrix Composites:Oxidation Behavior and Mechanical Properties. J. Eur. Cer. Soc. 7:101–108, 1991.

79.Z. C. Jou, S.-Y. Kuo, and A. N. Virkar. Elevated-Temperature Creep of Silicon Car-

bide-Aluminum Nitride Ceramics:Role of Grain Size. J. Am. Cer. Soc. 69(11):C- 279–81, 1986.

80.C. A. May and A. K. U. Obi. Compressive Strength of Lithia-Silica Glass Ceramics. Proc. Brit. Cer. Soc. 25, Mechanical Properties of Ceramics (2) (R. W. Davidge, ed.):49–65, 1975.

81.T. A. Parthasarathy, T. Mah, and L. E. Matson. Creep Behavior of an Al2O3- Y3Al5O12 Eutectic Composite. Cer. Eng. Sci. Proc. 11(910):1628–1638, 1990.

82.A. R. B. Verma, V. S. R. Murthy, and G. S. Murty. Microstructure and Compressive Strength of SiC-Platelet-Reinforced Borosilicate Composites J. Am. Cer. Soc. 78(10):2732–2736, 1995.

II.MICROSTRUCTURAL DEPENDENCE OF OTHER PROPERTIES OF CERAMICS

A.Monolithic Ceramics

Chapters 2–7 clearly show that grain parameters, especially size, and in some cases shape, and orientation play key roles in basic mechanical properties of toughness, tensile and compressive strengths, as well as of hardness, wear, and related behavior. Elastic properties and thermal expansion normally do not depend on grain size unless there is microcracking, but both depend on grain orientation due to crystalline anisotropy of these properties (for essentially all crystalline materials for elastic properties, but only in noncubic materials for expansion) and hence some also on grain shape. Some other properties have varying dependences on grain size, shape, and orientation, and some materials may exhibit special property dependences on these parameters.

Consider first thermal conductivity, where there is no intrinsic grain size (G) dependence in cubic materials. However, there is an intrinsic dependence on grain size, shape, and orientation in noncubic materials, since these parameters determine the tortuosity of the preferred path for heat flow from grain to grain and how much the average conductivity changes from grain to grain due to differing conductivities along different crystal axes. Thermal conductivity anisotropy in noncubic ceramics ranges from very modest to substantial levels, e.g. at 22°C from 10 to 50, and 70% higher along the c- versus the a-axis in respectively sapphire, rutile, and quartz [1], and 30% estimated for BeO [2], while materials such as micas [3], graphite, and hexagonal BN are more extreme with conductivities in the a versus the c directions being respectively nearly 10, 100, and 20-fold (the latter two from manufacturers’ literature). The issue of averaging methods to obtain polycrystalline values from single crystal values was addressed by Kumar and Singh [1] showing similar levels of agreement and disagreement to those for other properties addressed in this book. While the issue of grain size effects has received little attention, Williams et al. [4] have shown data for dense, pure Al2O3 to increase thermal conductivity at 22°C from 30 to 32, then 33 W/m/K 10% as G increased from 1 to 6, then 16 m, consistent with theoretical predictions of relative changes. Such G dependence with modest anisotropy indicates greater G dependence in more anisotropic materials.

Electrical conductivity is also isotropic in cubic crystal structures, so there are no intrinsic effects of grain size, shape, or orientation on conductivity in such materials, but there is a basic dependence on these parameters in noncubic materials, i.e. as for thermal conductivity. However, electrical conductivities cover a much broader range of values and thus provide more opportunity for more pronounced anisotropies, as with the converse property, resistivity. For example, sapphire has greater anisotropy of electrical than of thermal conductivity, e.g.

having electrical conductivity 3.3-fold greater parallel versus perpendicular to the c-axis [5]. However, there are other materials with greater anisotropy for both ionic and electronic conduction; the 3 orders of magnitude higher conductivity normal versus parallel to the c-axis of graphite is an example of the latter. Beta aluminas are examples of the former, having very anisotropic conduction, i.e. about 100 fold greater normal versus parallel to the c-axis at 300°C, and thus they essentially show conduction only normal to the c-axis via the Na or other alkali metal containing planes [6,7]. However, this anisotropy in conductivity and the converse anisotropy in resistivity can be significantly mitigated in polycrystalline bodies, e.g. Virkar et al. [8] showed that increasing G by 50–100-fold from 1–2 to 100 m reduced resistivity by < 2-fold, from 4.8 to 2.8 Ω ·cm.

Turning to another electrical property, dielectric constant ( ), this is normally independent of grain size, unless some other grain-size-dependent effect such as microcracking or grain boundary concentration of second phases occurs. Thus recent tests showed for dense, pure alumina independent of grain size over the range tested, G 1–6 m [9]. However, in ferroelectric and related ceramics there can be substantial G dependence of , e.g. the maximum at the Curie point in doped BaTiO3 bodies ranged from 10,000 to 30,000 as G increased from 2.5 to 7 m [10], and at room temperature for PZT ranged from 700 to 1300 as G increased from 2 to 4.4 m [11]. Dielectric loss, though often entailing other mainly extrinsic mechanisms as a function of grain boundary character, is clearly an important factor in many applications along with . In the above Al2O3 study [9], dielectric loss increased with grain size only at the larger grain sizes, i.e. it was constant from G 1 to 3 m, and then rose substantially at G = 4–5 m and still more at G 6 m. Hsueh et al.’s PZT study [11] showed dielectric loss (% tan δ) with a similar behavior, i.e. it was constant at 0.5 from G = 2– to 3+ m and then increased to 1.3 at G = 3.5 m (for 1100 and 1200°C firings) and ranged from 1.2 at G 3.4 m to between 1.7 and 2.6 at G= 4.5 to 5 m for firing at 1300°C.

At least some of the dielectric constant increase is related to intrinsic increases in Curie temperature that occur as G decreases, e.g. from 125 to 140°C as G decreased in a PLZT from 4 to 1.5 m [12]. This and other significant changes in ferroelectric properties are related to domain structure–grain size effects, which can lead to complex behavior, since some properties increase, some decrease, and some are independent of G. Since there are similar domain–grain size interactions in ferromagnetic materials, they also show varying effects of grain size. Thus the initial permeability of Ni Zn ferrites was reported to increase4-fold as G increased from < 1 to 50 m, while the coercive field decreased ≥ 15-fold and the remnant magnetic flux remained unchanged [13].

Scattering of electromagnetic waves intrinsically occurs in noncubic polycrystalline dielectric materials, since the dielectric constant and hence the refractive index vary with crystal direction, resulting in varying changes of these