sp

sp

Polytypism: 1D polymorphism (see related references[A. R. Verma and P. Krishna])

3C-BN (

Possible symmetries of

Symmetry of Stacked Closest-packed Layers (Table 7.1.5B in Ref. [A. L. Patterson and J. S. Kasper])

[

[Examples of

[Examples of

Total energies of BN and AlN polytypes have relation with hexagonality (

We have investigated sp

10H-BN and 10H-AlN[6] have been investigated in order to compare them with the previous results[2][3]. The 10H polytype has 18 structures[6]. All possible symmetries and stacking sequences of the 10H polytype are tabulated in Table I of ref. [6]. We choose four structures as ABCABCBACB(

As for the electronic band structures of 2H - 6H and 10H-BN(AlN) polytypes, most band gaps of them are indirect with the exception of 2H-AlN. The difference of delta_1 and delta_2[6] for 10H-AlN(ABCBCACBCB,

Electronic and structural properties of 6H-AlN(ABCBCB) under various pressure conditions were calculated in order to realize the direct band gap. The indirect band gap of 6H-AlN(ABCBCB) transforms to direct under expansion. The indirect band gap is enhanced under compression. This was presented in the international conference of "Joint AIRAPT-22 & HPCJ-50" (7/26 - 7/31, 2009, Odaiba, Tokyo)[7].

Electronic and lattice properties of 2H - 12H-SiC by LDA[BH] and GGA[PBE] were calculated[3][10]. We have found that 10H-SiC(ABCACBCACB,

Crystal structures of 2H - 6H, 10H and 12H polytypes are as follows.

- 2H and 3H potytypes(png, 30kb)
- 4H and 5H potytypes(png, 130kb)
- 6H potytypes(png, 138kb)
- 10H potytypes(png, 182kb, see ref. [6])
- 12H potytype(ABCABCACBACB,
*H*= 17 %, png, 171kb) and its electronic band structure(Indirect band gap: Gamma - M) - 2H - 12H polytypes(png, 48kb)[medium](png, 88kb)[small](png, 45kb)
- [Total energies of BN,SiC,AlN - Hexiagonality](png, 43.1 kb)
- [Total energies of SiC - Hexagonality](png, 28.1 kb)
- [Band gaps of SiC - Hexagonality](png[color], 33.4 kb)

- Ramsdell notation: 2H, 3C, 4H, 5H, 6H,..... (H: Hexagonal), 3C (C: Cubic), 9R, 15R,..... (R: Rhombohedral)
- ABC notation: ABC (3C [3H]), ABCACB (6H), ABCBCB (6H), ABCABCBCBC (10H),.....
- Zhdanov notation: 33 (6H, ABCACB), 2112 (6H, ABCBCB), 41 (5H, ABCBC),.....
- Jagodzinski notation (
*h*-*c*notation):*hcchcc*(6H, ABCACB),*hhhchc*(6H, ABCBCB),*hhccc*(5H, ABCBC),..... - Hägg notation: +++--- (6H, ABCACB), ++-+-- (6H, ABCBCB), ++++- (5H, ABCBC),.....
- A -> B -> C -> A : Cyclic -> Hägg notation "+"
- A -> C -> B -> A : Anticyclic -> Hägg notation "-"

"++" ->

"--" ->

"+-" ->

"-+" ->

The BN polytype consists of cubic and hexagonal BN bilayers. This is the same for other sp

For example: 2H (

Zhdanov notation (2H - 9H)

2H : 11

3H(=3C) : Infinite

4H : 22

5H : 41

6H : 33

6H : 2211

7H : 52

7H : 4111

7H : 3121

8H : 71

8H : 44

8H : 3212

8H : 3311

8H : 221111

8H : 211211

9H : 63

9H : 5211

9H : 5112

9H : 4221

9H : 4122

9H : 3231

9H : 312111

9H : 311121

9H : 411111

Table of possible stacking sequences for [5H polytype](png, 9kb)

It is possible to consider 30 stacking sequences in the 5H polytype. All of them are the same structure.

Table of possible stacking sequences for [6H polytype](png, 9kb)

It is possible to consider 54 stacking sequences in the 6H polytype. They are classified into three groups as ABCACB(

In detail, please see references [2][3].

- [References]
- [1] S. Komatsu, K. Okada, Y. Shimizu, and Y. Moriyoshi: J. Phys. Chem. B
**103**(1999) 3289 [5H-BN]. - [2] K. Kobayashi and S. Komatsu: J. Phys. Soc. Jpn.
**76**(2007) 113707 [5H-BN]. - [3] K. Kobayashi and S. Komatsu: J. Phys. Soc. Jpn.
**77**(2008) 084703 [2H - 6H-BN(AlN, SiC)][6H-AlN][6H-SiC]), and related references therein. - [4] K. Kobayashi, K. Watanabe, and T. Taniguchi: J. Phys. Soc. Jpn.
**76**(2007) 104707 [*h*-BN]. - [5] K. Watanabe, T. Taniguchi, and H. Kanda: Nat. Mater.
**3**(2004) 404 [Experiment for*h*-BN]. - [6] K. Kobayashi and S. Komatsu: J Phys. Soc. Jpn.
**78**(2009) 044706 [10H-BN, 10H-AlN]. - [7] K. Kobayashi and S. Komatsu, "First-Principles Study of 6H-AlN under various pressure conditions", J. Phys.: Conf. Ser. 215, 012111(2010)[AIRAPT22].
- [8] S. Komatsu, K. Kobayashi, Y. Sato, D. Hirano, T. Nakamura, T. Nagata, T. Chikyo, T. Watanabe, T. Takizawa, K. Nakamura, and T. Hashimoto: Journal of Physical Chemistry C 114, 13176 - 13186(2010).
- [9] K. Kobayashi and S. Komatsu: "First-Principles Study of 30H-BN polytypes", Materials Transactions, Vol. 51, No. 9 (2010) 1497[6H-BN, 30H-BN].
- [10] K. Kobayashi and S. Komatsu: "First-Principles Study of 8H-, 10H-, 12H-, and 18H-SiC Polytypes", Journal of the Physical Society of Japan, Vol. 81, No. 2 (2012) 024714[8H-SiC, 10H-SiC, 12H-SiC, 18H-SiC][BH][PBE].
- [11] K. Kobayashi and S. Komatsu, "First-Principles Study of Various BN, SiC, and AlN polytypes", Trans. MRS-J, Vol. 37, 583-588 (2012)[go to JST][IUMRS-ICEM2012][48H-BN][20H-SiC][30H-AlN].
- [12] K. Kobayashi and S. Komatsu, "First-Principles Study of AlBN and Related Polytypes", Trans. MRS-J, Vol. 38[3], 485-492 (2013)[4H-AlBN][4H-AlAsN][4H-AlPN][2H-, 3H-, 5H-, 6H-, and 12H-AlBN][3x2H-AlBN].
- [13] No data.
- (Other related papers)
- [Z] K. Kobayashi: Materials Transactions, Vol. 46, No. 6 (2005) 1094 [Anisotropic compression].
- [Electronic band structures of BN compounds]
- [10H-BN](ABCABCBACB [
*H*= 20%],*P*6_{3}*mc*, png[46 kb]) - [5H-BN](
*P*3*m*1, png[40 kb]) - [4H-BN](
*P*6_{3}*mc*, wide, png[63.5 kb]) - [
*c*-BN](3C-BN, png[7 kb]) - [3H-BN](= 3C-BN,
*P*3*m*1, png[33.3 kb]) - [
*w*-BN](2H-BN, png[7.6 kb]) - [2H-BN](
*w*-BN,*P*6_{3}*mc*, wide, png[27.8 kb]) - [
*h*-BN](A-B stacking,*P*6_{3}/*mmc*, png[26 kb]) - [
*h*-BN](A-A stacking,*P*6_*m*2, png[23.4 kb]) - [
*h*-BN](type B,*P*6_{3}/*mmc*, png[26 kb]) - [
*r*-BN](rhombohedral BN, ABC stacking, png[28 kb]) - [Elctronic band structures of AlN polytypes]
- [10H-AlN](ABCBCBCBCB [
*H*= 80%],*P*3*m*1, png[43.7 kb]) - [6H-AlN] as ABCACB [
*P*6_{3}*mc*] and ABCBCB [*P*3*m*1] (png[173 kb]) - [3H-AlN](= 3C-AlN,
*P*3*m*1, png[27 kb]) - [2H-AlN](
*P*6_{3}*mc*, png[24.3 kb]) - [Elctronic band structures of SiC polytypes]
- [4H-SiC](
*P*6_{3}*mc*, wide, png[36 kb]) - [10H-SiC](ABCACBCACB [
*H*= 40%],*P*3*m*1, png[56 kb]) - [Related web pages]
- [BN compounds]
- [BC-compounds]
- [LiBC]
- Close-packed structures by P. Krishna and D. Pandey: International Union of CRYSTALLOGRAPHY(IUCr)[Useful]
- POLYTYPISM IN SILICON CARBIDE by Dr. J. F. Kelly(Industrial Materials Group of Birkbeck College, University of London)
- [Related references for BN]
- [R1] O. Mishima and K. Era: in
*Electric Refractory Materials*, ed. Y. Kumashiro (Marcel Dekker, New York, 2000) pp. 495-556, and references therein. - [R2] S. Komatsu: J. Phys. D: Appl. Phys.
**40**(2007) 2320 [Review]. - [R3] S. Komatsu, Y. Sato, D. Hirano, T. Nakamura, K. Koga, A. Yamamoto, T. Nagata, T. Chikyo, T. Watanabe, and T. Takizawa: Journal of Physics D: Applied Physics
**42**(2009) 225107[P-type sp^{3}-bonded BN/n-type Si][Heterodiode][Solar cell][Laser-plasma synchronous CVD method]. - [Ra] F. Oba, A. Togo, I. Tanaka, K. Watanabe, and T. Taniguchi, Phys. Rev. B
**81**, 075125(2010)[VASP-PAW][Doping of*h*-BN][Intercalation][Prediction]. **[**L. Liu, Y. P. Feng, and Z. X. Shen: Phys. Rev. B*h*-BN]**68**(2003) 104102.- [ADDF]H. Tokoyama, H. Yamakado and K. Ohno, Chemistry Letters (doi:10.1246/cl.151114)(2015)[Automated exploration][ADDF][GRRM]
- [Recent papers for
*h*-BN] - [
*h*-BN][Layered BN] B. Huang, X. K. Cao, H. X. Jiang, J. Y. Lin and S.-H. Wei, Phys. Rev. B**86**, 155202(2012)[Significantly enhanced optical transition]. - [
*h*-BN] S.-P. Gao, Solid State Communications 152 (2012) 1817[Band gap characters][Dispersion corrected][GW]. - [
*h*-BN] G. Cassabois, P. Valvin, B. Gil, "Hexagonal boron nitride is an indirect bandgap semiconductor", arXiv:1512.02962. - [
*h*-BN] S. M. Gilbert, T. Pham, M. Dogan, S. Oh, B. Shevitski, G. Schumm, S. Liu, P. Ercius, S. Aloni, M. L. Cohen, A. Zettl, "Alternative Stacking Sequences in Hexagonal Boron Nitride", arXiv:1810.04814. - [Related references for Polytype (Polytypism)]
*International Table for Crystallography*, ed. A. J. C. Wilson and E. Prince (Kluwer, Dordrecht, 2004) Vol. C, Chap. 9.2 by S. Durovic, P. Krishna ans D. Pandey, pp. 744 - 765.- A. R. Verma and P. Krishna:
*Polymorphism and Polytypism in Crystals*(Wiley, New York, 1966). - J. E. Iglesias:
*Acta. Cryst*. A**62**(2006) 178. - A. L. Patterson and J. S. Kasper: ``International Tables for X-ray Crystallography'', ed. J. S. Kasper and K. Lonsdale (The Kynoch Press, Birmingham, 1967) Vol. 2, pp. 342 - 354.
- T. J. McLarnan: Z. Kristallogr.
**155**(1981) 269. - Z. Inoue: J. Mater. Sci.
**17**(1982) 3189. - A. L. Ortiz, F. Sanchez-Bajo, F. L. Cumbrera and F. Guiberteau, J. Appl. Cryst.
**46**(2013) 242 -247[Prolific polytypism][SiC]. - [Related papers for BN, SiC, AlN and related materials]
- Z. Pan, H. Sun, Yi Zhang and C. Chen: Phys. Rev. Lett., Vol. 102, No. 5, 055503(2009)[Harder than diamond][Hexagonal diamond,
*w*-BN][PARATEC]. - L. Zhou, X. Ni, Ü. Özgür, H. Morkoç, R. P. Devaty, W. J. Choyke and D. J. Smith: Journal of Crystal Growth, Vol. 311, Issue 6 (2009) 1456-1459 [6H-AlN, m-plane AlN/SiC interface, Experiment]. <-- Consistent with our resutls for 6H-AlN polytypes [3].
- [C][Si][SiC][BN][AlN][GaN][InN]K. Moriguchi, K. Kamei, K. Kusunoki, N. Yashiro and N. Okada, J. Mater. Res., Vol. 28 (2013) 7-16[Comparative studies][Nonequivalent hexagonal polytypes].
- [Related paper](IUCr)
- [Code by author of above related paper](text format, IUCr electronic archives[Reference: ZM5042])
- [Floating Electron States]Y. Matsushita, S. Furuya and A. Oshiyama, Phys. Rev. Lett., Vol. 108, No. 24, 246404(2012)[Covalent semiconductor][SiC][GaN][AlN][BN][Si][C].
- [Interstitial Channels]Y. Matsushita and A. Oshiyama, Phys. Rev. Lett., Vol. 112, No. 13, 136403(2014)[Control band gaps][Effective mass][Tetrahedrally bonded][SiC].
- [Electron Confinement Due to Stacking Control of Atomic Layers]Y. Matsushita, S. Furuya and A. Oshiyama, J. Phys. Soc. Jpn.
**83**(2014) 094713[RSDFT][SiC][Roles of floating states][Spontaneous polarization]. - [Electronic states floating]Y. Matsushita A. Oshiyama, J. Phys. Soc. Jpn.
**86**(2017) 054702[Comprehensive study][Band-gap variation][sp^{3}-bonded semiconductor][Electronic states floating][Internal space]. - [Design and formation of SiC(0001)/SiO
_{2}interfaces]T. Kobayashi, T. Okuda, K. Tachiki, K. Ito, Y. Matsushita and T. Kimoto, Appl. Phys. Express**13**091003 (2020)[Si deposition][Low-temperature oxidation][High-temperature nitridation]. - [Electron and Hole Confinement in Hetero-Crystalline SiC Superlattice]Y. Sugihara, K. Uchida and A. Oshiyama, J. Phys. Soc. Jpn.
**84**(2015) 084709. - [SiC][A simple approach to the polytypism in SiC]T. Ito, T. Akiyama and K. Nakamura, Journal of Crystal Growth
**362**, 207-210(2013). - [SiC][Systematic theoretical investigations][Vacancy][N substitution]T. Ito, T. Akiyama and K. Nakamura, Phys. Status Solidi C (2013) in press.
- [10H-SiC]S. Nakashima, T. Tomita, N. Kuwahara, T. Mitani, M. Tomobe, S. Nishizawa and H. Okumura, J. Appl. Phys.
**114**, 193510(2013)[Raman intensity profiles][Zone-folded modes][3322] - [SiC]S. Kawanishi, T. Mizoguchi, arXiv:1512.04626[Effect of van der Waals interactions][Stability]
- [SiC]M. Uemoto, N. Komatsu, Y. Egami and T. Ono, J. Phys. Soc. Jpn.
**90**, 124713 (2021)[First-principles study][Structure][Anisotropy][High N-atom density layer][4H-SiC] - [STAM][Superconductor][SiC]Science and Technology of Advanced Materials(STAM)[Focus on Superconductivity in Semiconductors], Vol.9, Issue 4(2008).
- [AlN]Y. C. Cheng, H. T. Chen, X. X. Li, X. L. Wu, J. Zhu, S. H. Li, and Paul K. Chu: Journal of Applied Physics
**105**(2009) 083511[CASTEP][PWSCF][2H-,4H- and 6H-AlN][Optical and vibrational properties]. - [AlN]Y. C. Cheng, X. L. Wu, S. H. Li, and Paul K. Chu: Applied Physics Letters
**95**(2009) 121902[QUANTUM-ESPRESSO][4H-AlN][Stress influence][Band-edge luminescence]. - [BH] U. von Barth and L. Hedin, J. Phys. C
**5**, 1629(1972). - [PBE] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett.
**77**, 3865(1996).

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