Silicon Nitride Ceramics

Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

The widespread interest in silicon nitride ceramics stems from their desirable physical and mechanical properties in many high temperature and pressure applications [1, 2, 3, 4, 5]. Good resistance to oxidation and corrosive environments, low coefficient of friction and thermal expansion, negligible creep, and high decomposition temperature are some of these important properties. Because of these, silicon nitride (especially its polymorph) is widely used in gas turbines, engine parts, bearings, dental drills and gauges, and cutting tools. In addition, thin films and coatings have been studied in relation to high-speed memory devices [6, 7, 8, 9, 10] and optical waveguide applications [11].

Keywords

Porosity Crystallization Brittleness Hexagonal Nitride 

References

  1. 1.
    Chen, I.W., Becher, P.F., Mitomo, M., Petzow, G., Yen, T.S.: Silicon nitride ceramics scientific and technological advances. Mater. Res. Soc. (MRS Proc.) 287, 147–158 (1993)Google Scholar
  2. 2.
    Hoffmann, M.J.: Analysis of microstructural development and mechanical properties of \(\hbox{Si}_3\hbox{N}_4\) ceramics. In: Hoffmann, M.J., Petzow G. (eds.) Tailoring of Mechanical Properties of \(\hbox{Si}_3\hbox{N}_4\) Ceramics, pp. 59–72. Kluwer Academic Publishers, Dordrecht (1994)Google Scholar
  3. 3.
    Cahn, R.W., Hassen, P., Kramer, J.: Materials Science and Technology, Structure and Properties of Ceramics. Wiley, Weinheim (1994)Google Scholar
  4. 4.
    Richerson, D.W.: The Magic of Ceramics. The American Ceramics Society, Westerville (2000)Google Scholar
  5. 5.
    Riley, F.L.: Silicon nitride and related materials. J. Am. Ceram. Soc. 83(2), 245–265 (2000)CrossRefGoogle Scholar
  6. 6.
    Liu, L., Xu, J.P., Chen, L.L., Lai, P.: A study on the improved programming characteristics of flash memory with \(\hbox{Si}_3\hbox{N}_4/\hbox{SiO}_2\) stacked tunneling dielectric. Microelectron. Reliab. 49, 912–915 (2009)CrossRefGoogle Scholar
  7. 7.
    Saraf, M., Akhvlediani, R., Edrei, R., Shima, R., Roizin, Y., Hoffman, A.: Low thermal budget \(\hbox{SiO}_2/\hbox{Si}_3\hbox{N}_4/\hbox{SiO}_2\) stacks for advanced SONOS memories. J. Appl. Phys. 102, 054512 (2007)CrossRefGoogle Scholar
  8. 8.
    Berberich, S., Godignon, P., Morvan, E., Fonseca, L., Millan, J., Hartnagel, H.L.: Electrical characterisation of \(\hbox{Si}_3\hbox{N}_4/\hbox{SiO}_2\) double layers on p-type 6H-SiC. Microelectron. Reliab. 40, 833–836 (2000)CrossRefGoogle Scholar
  9. 9.
    Wang, Y.Q., Hwang, W.S., Zhang, G., Yeo, Y.C.: Electrical characteristics of memory devices with a high-\(k\) \(\hbox{HfO}_{2}\) trapping layer and dual \(\hbox{SiO}_2/\hbox{Si}_3\hbox{N}_4\) tunneling layer. IEEE Trans. Electron Devices 54(10), 2699–2705 (2007)CrossRefGoogle Scholar
  10. 10.
    Santussi, S., Lozzi, L., Passacantando, M., Phani, A.R., Palumbo, E., Bracchitta, G., De Tommasis, R., Alfonsetti, R., Moccia, G.: Properties of stacked dielectric films composed of \(\hbox{SiO}_2/\hbox{Si}_3\hbox{N}_4/\hbox{SiO}_2\) tunneling layer. J. Non-Cryst. Solids 245, 224–231 (1999)CrossRefGoogle Scholar
  11. 11.
    Kazmierczak, A., Dortu, F., Schrevens, O., Giannone, D., Vivien, L., Marris-Morini, D., Bouville, D., Cassan, E., Gylfason, K.B., Sohlstrom, H., Sanchez, B., Griol, A., Hill, D.: Light coupling and distribution for \(\hbox{Si}_3\hbox{N}_4/\hbox{SiO}_2\) integrated mutichannel single-mode sensing system. Opt. Eng. 48(1), 014401 (2009)CrossRefGoogle Scholar
  12. 12.
    Kijima, K., Shirasaki, S.I.: Nitrogen self-diffusion in silicon nitride. J. Chem. Phys. 65(7), 2668–2671 (1976)CrossRefGoogle Scholar
  13. 13.
    Lange, F.: The sophistication of ceramic science through silicon nitride studies. J. Ceram. Soc. Jpn. 114(11), 873–879 (2006)CrossRefGoogle Scholar
  14. 14.
    Dutta, S., Buzek, B.: Microstructure, strength, and oxidation of a 10 wt% zyttrite-\(\hbox{Si}_3\hbox{N}_4\) ceramic. J. Am. Ceram. Soc. 67(2), 89–92 (1984)CrossRefGoogle Scholar
  15. 15.
    Pezzotti, G.: \(\hbox{Si}_3\hbox{N}_4\)/SiC-platelet composite without sintering aids: a candidate for gas turbine engines. J. Am. Ceram. Soc. 76, 1313–1320 (1993)CrossRefGoogle Scholar
  16. 16.
    Li, H., Komeya, K., Tatami, J., Meguro, T., Chiba, Y., Komatsu, M.: Effect of \(\hbox{HfO}_2\) addition on sintering of \(\hbox{Si}_3\hbox{N}_4\). J. Am. Ceram. Soc. Jpn. 109, 342–346 (2001)Google Scholar
  17. 17.
    Campbell, G.H., Rühle, M., Dalgleish, B.J., Evans, A.G.: Whisker toughening: a comparison between aluminum oxide and silicon nitride toughened with silicon carbide. J. Am. Ceram. Soc. Jpn. 73, 521–530 (1990)CrossRefGoogle Scholar
  18. 18.
    Becher, P.F., Ferber, M.K.: Temperature-dependent viscosity of SiREAl-based classes as a function of N:O and RE:Al ratios (RE = La, Gd, Y, and Lu). J. Am. Ceram. Soc. 87, 1274–1279 (2004)CrossRefGoogle Scholar
  19. 19.
    Park, H., Kim, H.E., Niihara, K.: Microstructural evolution and mechanical properties of \(\hbox{Si}_3\hbox{N}_4\) with \(\hbox{Yb}_2\hbox{O}_3\) as a sintering additive. J. Am. Ceram. Soc. 80, 750–756 (1995)CrossRefGoogle Scholar
  20. 20.
    Hong, Z.L., Yoshida, H., Ikahara, Y., Sakuma, T., Mishimura, T., Mitomo, M.: The effect of additives on sintering behavior and strength retention in silicon nitride with RE-disilicate. J. Eur. Ceram. Soc. 22, 527–534 (1997)CrossRefGoogle Scholar
  21. 21.
    Guo, S.Q., Hirosaki, N., Yamamoto, Y., Nishimura, T., Mitomo, M.: Strength retention in hot-pressed \(\hbox{Si}_3\hbox{N}_4\) ceramics with \(\hbox{Lu}_2\hbox{O}_3\) additives after oxidation exposure in air at 1500 degrees C. J. Am. Ceram. Soc. 85, 1607–1609 (2002)CrossRefGoogle Scholar
  22. 22.
    Guo, S.Q., Hirosaki, N., Yamamoto, Y., Nishimura, T., Mitomo, M.: Hot-pressed silicon nitride ceramics with \(\hbox{Lu}_2\hbox{O}_3\) additives: elastic moduli and fracture toughness. J. Eur. Ceram. Soc. 23, 537–545 (2003)CrossRefGoogle Scholar
  23. 23.
    Satet, R.L., Hoffmann, M.J.: Influence of the rare-earth element on the mechanical properties of RE-Mg-bearing silicon nitride. J. Am. Ceram. Soc. 88(9), 2485–2490 (2005)CrossRefGoogle Scholar
  24. 24.
    German, R.M.: Liquid Phase Sintering. Plenum Press, New York (1985)Google Scholar
  25. 25.
    Clarke, D.R.: On the equilibrium thickness of intergranular glass phases in ceramic materials. J. Am. Ceram. Soc. 70(1), 15–22 (1987)CrossRefGoogle Scholar
  26. 26.
    Kleebe, H.J., Hoffmann, M.J., Rühle, M.: Influence of secondary phase chemistry on grain boundary film thickness in silicon nitride. Zeitschrift fur Metallkunde 83(8), 610–617 (1992)Google Scholar
  27. 27.
    Kleebe, H.J., Cinibulk, M.K., Cannon, R.M., Rühle, M.: Statistical analysis of the intergranular film thickness in silicon nitride ceramics. J. Am. Ceram. Soc. 76, 1969 (1993)Google Scholar
  28. 28.
    Clarke, D.R., Shaw, T.M., Philipse, A.P., Horn, R.G.: Possible electrical double-layer contribution to the equilibrium thickeness of intergranular glass films in polycrystalline ceramics. J. Am. Ceram. Soc. 76, 1201 (1993)Google Scholar
  29. 29.
    Tanaka, I., Kleebe, H.J., Cinibulk, M.K., Bruley, J., Clarke, D.R., Rühle, M.: Calcium concentration dependence of the intergranular film thickness in silicon nitride. J. Am. Ceram. Soc. 77, 911 (1994)Google Scholar
  30. 30.
    Wang, C., Pan, X., Hoffmann, M.J., Rühle, M.: Grain boundary films in rare-earth-glass-based silicon nitride. J. Am. Ceram. Soc. 79, 788 (1996)Google Scholar
  31. 31.
    Subramaniam, A., Koch, C.T., Cannon, R.M., Rühle, M.: Intergranular glassy films: an overview. Mater. Sci. Eng. A 422(1–2), 3–18 (2006)Google Scholar
  32. 32.
    Sanders, W.A., Miekowski, D.M.: Strength and microstructure of sintered \(\hbox{Si}_3\hbox{N}_4\) with rare-earth-oxide additions. J. Am. Ceram. Soc. 64, 304–309 (1985)Google Scholar
  33. 33.
    Sun, E.Y., Becher, P.F., Plucknett, K.P., Hsueh, C.H., Alexander, K.B., Waters, S.B., Hirao, K., Brito, M.E.: Microstructural design of silicon nitride with improved fracture toughness: II, effects of yttria and alumina additives. J. Am. Ceram. Soc. 81, 2831–2840 (1998)CrossRefGoogle Scholar
  34. 34.
    Satet, R.L., Hoffmann, M.J.: Grain growth anisotropy of \(\beta\)-silicon nitride in rare-earth doped -oxynitride glasses. J. Eur. Ceram. Soc. 24, 3437–3445 (2004)CrossRefGoogle Scholar
  35. 35.
    Choi, D.J., Scott, W.D.: Devitrification and delayed crazing of SiO\(_2\) on single-crystal silicon and chemically vapor-deposited silicon nitride. J. Am. Ceram. Soc. 70, 269–272 (1987)CrossRefGoogle Scholar
  36. 36.
    Part, J.Y., Kim, J.R., Kim, C.H.: Effects of free silicon on the \(\alpha\) to \(\beta\) phase transformation in silicon nitride. J. Am. Ceram. Soc. 70, 240–242 (1987)Google Scholar
  37. 37.
    Burns, G.T., Chandra, G.: Pyrolysis of preceramic polymers in ammonia: preparation of silicon nitride powders. J. Am. Ceram. Soc. 72, 333–337 (1989)CrossRefGoogle Scholar
  38. 38.
    Choi, D.J., Fishbach, D.B., Scott, W.D.: Oxidation of chemically-vapor-deposited silicon nitride and single-crystal silicon. J. Am. Ceram. Soc. 72, 1118–1123 (1989)CrossRefGoogle Scholar
  39. 39.
    Kleebe, H.J., Ziegler, G.: Influence of crystalline secondary phases on the densification behavior of reaction-bonded silicon nitride during postsintering under increased nitrogen pressures. J. Eur. Ceram. Soc. 72, 2314–2317 (1989)CrossRefGoogle Scholar
  40. 40.
    Tanaka, I., Pezzotti, G., Okamoto, T., Miyamoto, Y., Koizumim, M.: Hot isostatic press sintering and properties of silicon nitride without additives. J. Am. Ceram. Soc. 72, 1656–1660 (1989)CrossRefGoogle Scholar
  41. 41.
    Mitomo, M., Tsutsumi, M., Tanaka, H., Uenosono, S., Saito, F.: Grain growth during gas-pressure sintering of \(\beta\)-silicon nitride. J. Eur. Ceram. Soc. 73, 2441–2445 (1990)CrossRefGoogle Scholar
  42. 42.
    Mitomo, M., Uenosono, S.: Microstructural development during gas-pressure sintering of \(\alpha\)-silicon nitride. J. Eur. Ceram. Soc. 75, 103–108 (1992)CrossRefGoogle Scholar
  43. 43.
    Watari, K., Hirao, K., Toriyama, M., Ishizaki, K.: Effect of grain size on the thermal conductivity of \(\hbox{Si}_3\hbox{N}_4\). J. Am. Ceram. Soc. 82, 777–779 (1999)CrossRefGoogle Scholar
  44. 44.
    Kitayama, M., Hirao, K., Tsuge, A., Watari, K., Toriyama, M., Kanzaki, S.: Thermal conductivity of beta-Si\(_3\)N\(_4\): II, effect of lattice oxygen. J. Am. Ceram. Soc. 83, 1985–1992 (2000)CrossRefGoogle Scholar
  45. 45.
    Shen, J.Z., Zhao, Z., Peng, H., Nygren, M.: Formation of tough interlocking microstructures in silicon nitride ceramics by dynamic ripening. Nature (London) 417, 266–269 (2002)CrossRefGoogle Scholar
  46. 46.
    Cinibulk, M.K., Thomas, G., Johnson, S.M.: Strength and creep behavior of rare-earth disilicate-silicon nitride ceramics. J. Am. Ceram. Soc. 75, 2050–2055 (1992)CrossRefGoogle Scholar
  47. 47.
    Hoffmann, M.J., Gu, H., Cannon, R.M.: Interfacial engineering for optimized properties II. In: Hall, E.L., Carter, C.B., Briant, C.L. (eds.) MRS Proceedings, p. 65. Pittsburgh, Pennsylvania, Mater. Res. Soc. (2000)Google Scholar
  48. 48.
    Satet, R.L., Hoffmann, M.J., Cannon, R.M.: Experimental evidence of the impact of rare-earth elements on particle growth and mechanical behaviour of silicon nitride. Mater. Sci. Eng. A 422, 66–76 (2006)CrossRefGoogle Scholar
  49. 49.
    Tanaka, I., Pezzotti, G., Matsushuta, K.I., Miyamoto, Y., Okamoto, T.: Impurity-enhanced intergranular cavity formation in silicon nitride at high temperatures. J. Am. Ceram. Soc. 73, 752–759 (1990)Google Scholar
  50. 50.
    Ohji, T., Hirao, K., Kanzaki, S.: Fracture resistance behavior of highly anisotropic silicon nitride. J. Am. Ceram. Soc. 78, 3125–3128 (1995)CrossRefGoogle Scholar
  51. 51.
    Becher, P.F., Sun, E.Y., Plucknett, K.P., Alexander, K.B., Hsueh, C.H., Lin, H.T., Waters, S.B., Westmoreland, C.G., Kang, E.S., Hirao, K., Brito, M.E.: Microstructural design of silicon nitride with improved fracture toughness: I, effects of grain shape and size. J. Am. Ceram. Soc. 81, 2821–2830 (1998)CrossRefGoogle Scholar
  52. 52.
    Tajima, Y.: Development of high-performance silicon nitride ceramics and their applications. In: Chen, I.W. (ed.) Silicon Nitride Scientific and Technological Advances, p. 189. Pittsburgh, USA, journal = Mater. Res. Soc. (MRS Proc.) (1993)Google Scholar
  53. 53.
    Hoffmann, M.J.: Relationship between microstructure and mechanical properties of silicon nitride ceramics. Pure Appl. Chem. 67(6), 939–946 (1995)CrossRefGoogle Scholar
  54. 54.
    Becher, P.F., Painter, G.S., Shibata, N., Satet, R.L., Hoffmann, M.J., Pennycook, S.J.: Influence of additives on anisotropic grain growth in silicon nitride ceramics. Mater. Sci. Eng. A 422, 85–91 (2006)CrossRefGoogle Scholar
  55. 55.
    Becher, P.F., Painter, G.S., Shibata, N., Water, S.B., Lin, H.T.: Effect of rare-earth (RE) intergranular adsopriton on the phase transformation, microstructure evolution, and mechanical properties in silicon nitride with \(\hbox{RE}_2\hbox{O}_3\) + MgO additives: RE = La, Gd, and Lu. J. Am. Ceram. Soc. 91(7), 2328–2336 (2008)CrossRefGoogle Scholar
  56. 56.
    Bonnell, D.A., Tien, T.Y., Rühle, M.: Controlled crystallization of the amorphous phase in silicon nitride ceramics. J. Am. Ceram. Soc. 70, 460–465 (1987)CrossRefGoogle Scholar
  57. 57.
    Lee, W.W., Hilmas, G.E.: Microstructural changes in \(\beta\)-silicon nitride grains upon crystallizing the grain-boundary glass. J. Am. Ceram. Soc. 72, 1931–1937 (1989)CrossRefGoogle Scholar
  58. 58.
    Greil, P.: Analysis of Microstructural Development and Mechanical Properties of \(\hbox{Si}_3\hbox{N}_4\) Ceramics. In: Taylor, D. (ed.) High-Temperature Strengthening of Silicon Nitride Ceramics, p. 645. Stoke-on-Trent, Canterbury (1987)Google Scholar
  59. 59.
    Bergström, L., Pugh, R.J.: Interfacial characterization of silicon nitride powders. J. Am. Ceram. Soc. 72, 103–109 (1989)CrossRefGoogle Scholar
  60. 60.
    Keeble, H.J.: Structure and chemistry of interfaces in \(\hbox{Si}_3\hbox{N}_4\) ceramics studied by transmission electron microscopy. J. Ceram. Soc. Jpn. 105, 453–475 (1997)Google Scholar
  61. 61.
    Shibata, N., Pennycook, S.J., Gosnell, T.R., Painter, G.S., Shelton, W.A., Becher, P.F.: Observation of rare-earth segregation in silicon nitride ceramics at subnanometre dimensions. Nature 428(6984), 730–733 (2004)CrossRefGoogle Scholar
  62. 62.
    Benco, L.: Chemical bonding at grain boundaries: MgO on \(\beta\)-\(\hbox{Si}_3\hbox{N}_4\). Surf. Sci. 327, 274–284 (1995)Google Scholar
  63. 63.
    Liu, A.Y., Cohen, M.L.: Structural properties and electronic structure of low-compressibility materials: \(\beta-\hbox{Si}_3\hbox{N}_4\) and hypothetical \(\beta-\hbox{C}_3\hbox{N}_4\). Phys. Rev. B 41, 10727 (1990)CrossRefGoogle Scholar
  64. 64.
    Nakayasu, T., Yamada, T., Tanaka, I., Adachi, H.: Local chemical bonding around rare-earth ions in \(\alpha-\) and \(\beta-\hbox{Si}_3\hbox{N}_4\). J. Am. Ceram. Soc. 80, 2525–2532 (1997)CrossRefGoogle Scholar
  65. 65.
    Nakayasu, T., Yamada, T., Tanaka, I., Adachi, H.: Calculation of grain-boundary bonding in rare-earth-doped \(\beta-\hbox{Si}_3\hbox{N}_4\). J. Am. Ceram. Soc. 81, 565–570 (1998)CrossRefGoogle Scholar
  66. 66.
    Dudesek, P., Benco L.: Cation-aided joining of surfaces of \(\beta\)-silicon nitride: structural and electronic aspects. J. Am. Ceram. Soc. 81, 1248–1254 (1998)CrossRefGoogle Scholar
  67. 67.
    Bermudez, V.M.: Theoretical study of the electronic structure of the \(\hbox{Si}_3\hbox{N}_4\)(0001) surface. Surf. Sci. 579(1), 11–20 (2005)CrossRefGoogle Scholar
  68. 68.
    Wang, L., Wang, X., Tan, Y., Wang, H., Zhang, C.: Study of oxygen adsorption on beta-\(\hbox{Si}_3\hbox{N}_4\)(0001) by the density functional theory. Chem. Phys. 331(1), 92–95 (2006)CrossRefGoogle Scholar
  69. 69.
    Belkada, R., Shibayanagi, T., Naka, M.: Ab initio calculations of the atomic and electronic structure of \(\beta\)-silicon nitride. J. Am. Ceram. Soc. 83, 2449 (2000)CrossRefGoogle Scholar
  70. 70.
    Matsugana, K., Iwamoto, Y.: Ab initio molecular dynamics study of atomic structure and diffusion behavior in amorphous silicon nitride containing boron. J. Ceram. Soc. Jpn. 84, 2213–2219 (2001)Google Scholar
  71. 71.
    Pezzzotti, G., Painter, G.S.: Mechanisms of dopant-induced changes in intergranular \(\hbox{SiO}_2\) viscosity in polycrystalline silicon nitride. J. Am. Ceram. Soc. 85, 91–96 (2002)CrossRefGoogle Scholar
  72. 72.
    Painter, G.S., Averill, F.W., Becher, P.F., Shibata, N., Van Benthem, K., Pennycook, S.J.: First-principles study of rare earth adsorption at beta-\(\hbox{Si}_3\hbox{N}_4\) interfaces. Phy. Rev. B 78, 214206 (2008)CrossRefGoogle Scholar
  73. 73.
    Painter, G.S., Becher, P.F.: Bond energetics at intergranular interfaces in alumina-doped silicon nitride. J. Am. Ceram. Soc. 85, 65–67 (2002)CrossRefGoogle Scholar
  74. 74.
    Yoshiya, M., Tatsumi, K., Tanaka, I., Adachi, H.: Theoretical study on the chemistry of intergranular glassy film in \(\hbox{Si}_3\hbox{N}_4\)-\(\hbox{SiO}_2\) ceramics. J. Am. Ceram. Soc. 85, 109–112 (2002)CrossRefGoogle Scholar
  75. 75.
    Painter, G.S., Becher, P.F., Shelton, W.A., Satet, R.L., Hoffmann, M.J.: Theoretical study on the chemistry of intergranular glassy film in \(\hbox{Si}_3\hbox{N}_4\)-\(\hbox{SiO}_2\) ceramics. Phys. Rev. B 70, 144108 (2004)CrossRefGoogle Scholar
  76. 76.
    Rulis, P., Chen, J., Ouyang, L., Ching, W.Y., Su, X., Garofalini, S.H.: Electronic structure and bonding of intergranular glassy films in polycrystalline \(\hbox{Si}_3\hbox{N}_4\): ab initio studies and classical molecular dynamics simulations. Phys. Rev. B 71, 235317 (2005)CrossRefGoogle Scholar
  77. 77.
    Pennycook, S.J., Jesson, D.E.: High-resolution incoherent imaging of crystals. Phys. Rev. Lett. 64, 938–941 (1990)Google Scholar
  78. 78.
    Nellist, P.D., Pennycook, S.J.: The principles and interpretation of annular dark-field Z-contrast imaging. Adv. Imag. Elect. Phys. 113, 147–203 (2000)Google Scholar
  79. 79.
    Shibata, N., Painter, G.S., Becher, P.F., Pennycook, S.J.: Atomic ordering at an amorphous/crystal interface. Appl. Phys. Lett. 89(5), 051908 (2006)CrossRefGoogle Scholar
  80. 80.
    Ziegler, A., Idrobo, J.C., Cinibulk, M.K., Kisielowski, C., Browning, N.D., Ritchie, R.O.: Interface structure and atomic bonding characteristics in silicon nitride ceramics. Science 306, 1768–1770 (2004)Google Scholar
  81. 81.
    Ziegler, A., Idrobo, J.C., Cinibulk, M.K., Kisielowski, C., Browning, N.D., Ritchie, R.O.: Atomic-resolution observations of semicrystalline intergranular thin films in silicon nitride. Appl. Phys. Lett. 88(4), 041919 (2006)CrossRefGoogle Scholar
  82. 82.
    Van Benthem, K., Painter, G.S., Averill, F.W., Pennycook, S., Becher, P.F.: Experimental probe of adsorbate binding energies at internal crystalline/amorphous interfaces in Gd-doped \(\hbox{Si}_3\hbox{N}_4\). Appl. Phys. Lett. 92, 163110 (2008)Google Scholar
  83. 83.
    Winkelman, G.B., Dwyer, C., Marsh, C., Hudson, T.S., Nguyen-Manh, D., Döblinger, M., Cockayne, J.H.: The crystal/glass interface in doped \(\hbox{Si}_3\hbox{N}_4\). Mater. Sci. Eng. A 422, 77–84 (2006)Google Scholar
  84. 84.
    Winkelman, G.B., Dwyer, C., Hudson, T.S., Nguyen-Manh, D., Döblinger, M., Satet, R.L., Hoffmann, M.J., Cockayne, J.H.: Arrangement of rare-earth elements at prismatic grain boundaries in silicon nitride. Philos. Mag. Lett. 84, 755–762 (2004)Google Scholar
  85. 85.
    Walkosz, W., Klie, R.F., Öğüt, S., Borisevish, A., Becher, P.F., Pennycook, S.J., Idrobo, J.C.: Atomic resolution study of the interfacial bonding at \(\hbox{Si}_3\hbox{N}_4/\hbox{CeO}_{2-\delta}\) grain boundaries. Appl. Phys. Lett. 93, 053104 (2008)Google Scholar
  86. 86.
    Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136(3B), B864–B871 (1964)CrossRefGoogle Scholar
  87. 87.
    Payne, M.C., Teter, M.P., Allan, D.C., Arias, T., Joannopoulos, J.D.: Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64(9), 30–35 (1992)Google Scholar
  88. 88.
    Kohn, W., Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(A4), A1133–A1138 (1965)CrossRefGoogle Scholar
  89. 89.
    Muller, D.A.: Structure and bonding at the atomic scale by scanning transmission electron microscopy. Nat. Mater. 8, 263–270 (2009)Google Scholar
  90. 90.
    Pennycook, S.J.: Structure determination through Z-contrast microscopy. In: Merli, P.G., Vittor-Antisari, M. (eds.) Advances in Imaging and Electron Physics, vol. 123, p. 173. Academic Press, New York (2002)Google Scholar
  91. 91.
    Pennycook, S.J.: Z-contrast imaging in the scanning transmission electron microscope. In: Zhang, Z.F., Zhang, Z. (eds.) Progress in Transmission Electron Microscope 1: Concepts and Techniques, pp. 81–111. Springer, Tsinghyua (2001)Google Scholar
  92. 92.
    Egerton, R.F.: Applications of energy-loss spectroscopy. In: Electron Energy-Loss Spectrosocy in the Electron Microscopy 2nd edn., pp. 59–72. Plenum Press, New York (1996)Google Scholar
  93. 93.
    Idrobo, J.C., Öğüt, S., Yildirim, T., Klie, R.F., Browning, N.D.: Electronic and superconducting properties of oxygen-ordered \(\hbox{MgB}_2\) compounds of the form \(\hbox{Mg}_2\hbox{B}_3\hbox{O}_x\). Phys. Rev. B 70, 172503 (2004)Google Scholar
  94. 94.
    Bernholc, J.: Computational materials science: the era of applied quantum mechanics. Phys. Today 52(9), 30–35 (1999)CrossRefGoogle Scholar
  95. 95.
    He, H., Sekine, T., Kobayashi, T., Hirosaki, H., Suzuki, I.: Shock-induced phase transition of \(\beta\)-\(\hbox{Si}_3\hbox{N}_4\) to \(c\)-\(\hbox{Si}_3\hbox{N}_4\). Phys. Rev. B 62(17), 11412–11417 (2000)Google Scholar
  96. 96.
    Ching, W.Y., Ouyang, L., Gale, J.D.: Full ab initio geometry optimization of all known crystalline phases of \(\hbox{Si}_3\hbox{N}_4\). Phys. Rev. B 61, 13 (2000)Google Scholar
  97. 97.
    Hao, S., Delley, B., Veprek, S., Stampfl, C.: Superhard nitride-based nanocomposites: role of interfaces and effect of impurities. Phys. Rev. Lett. 97, 086102 (2006)Google Scholar
  98. 98.
    Mo, S.D., Ouyang, L., Ching, W.Y., Tanaka, I., Koyama, Y., Riedel, R.: Interesting physical properties of the new spinel phase of \(\hbox{Si}_3\hbox{N}_4\) and \(\hbox{C}_3\hbox{N}_4\). Phys. Rev. Lett. 83(24), 5046–5049 (1999)Google Scholar
  99. 99.
    Kuwabara, A., Matsunaga, K., Tanaka, I.: Lattice dynamics and thermodynamical properties of silicon nitride polymorphs. Phys. Rev. B 78, 064104 (2008)Google Scholar
  100. 100.
    Paszkowicz, W., Minikayev, R., Piszora, P., Knapp, M., Bähtz, C., Recio, J.M., Marques, M., Mori-Sanchez, P., Gerward, L., Jiang, J.Z.: Thermal expansion of spinel-type \(\hbox{Si}_3\hbox{N}_4\). Phys. Rev. B 69, 052103 (2004)Google Scholar
  101. 101.
    Idrobo, J., Iddir, H., Öğüt, S., Ziegler, A., Browning, N.D., Ritchie, R.O.: Ab initio structural energetics of \(\beta-\hbox{Si}_3\hbox{N}_4\) surfaces. Phys. Rev. B (Rapid Communications) 72, 241301 (2005)Google Scholar
  102. 102.
    Skorodumova, N.V., Ahuja, R., Simak, S.I., Abrikosov, I.A., Johansson, B., Lundqvist, B.I.: Electronic, bonding, and optical properties of \(\hbox{CeO}_2\) and \(\hbox{Ce}_2\hbox{O}_3\) from first principles. Phys. Rev. B 64, 115108 (2001)CrossRefGoogle Scholar
  103. 103.
    Andersson, D.A., Simak, S.I., Johansson, B., Abrikosov, I.A., Skorodumova, N.V.: Modeling of \(\hbox{CeO}_2\), \(\hbox{Ce}_2\hbox{O}_3\), and \(\hbox{CeO}_{2-x}\) in the LDA+\(U\) formalism. Phys. Rev. B 75, 035109 (2007)Google Scholar

Copyright information

© Springer Science+Business Media, LLC  2011

Authors and Affiliations

  1. 1.Argonne National LaboratoryArgonneUSA

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