Theoretical Studies on Tetragonal, Monoclinic and Orthorhombic Distortions of Germanium Nitride Polymorphs†

doi:10.7503/cjcu20150921

Abstract

Abstract:

Applying the ab initio pseudo-potential technique, we had predicted the lattice structures, density of states, phonon dispersion curves of the recently-discovered tetragonal, monoclinic and orthorhombic phases of Ge₃N₄. The negative formation enthalpy, the satisfactory of Born’s stability criteria and no imaginary frequency can be seen in the phonon dispersion curves proof that the three Ge₃N₄ polymorphs can retain their stabilities in the pressure range of 0―20 GPa. The temperature affects the cell volume, thereby decreasing the bulk modulus. The band gaps show that Ge₃N₄ are semiconductors, while obvious s-p hybridizations can be seen in the density of states. The band gaps decrease with applied pressure, which is due mainly to the generation of non-local electrons. Then, the quasi-harmonic approximation is used to study the thermodynamic properties of Ge₃N₄. The results show that the thermal expansion coefficient, entropy, heat capacity, Debye temperature and Grüneisen parameter are significantly affected by both temperature and pressure. The thermal expansions of m-Ge₃N₄ and t-Ge₃N₄ are three and two times greater than that of o-Ge₃N₄, respectively. The lattice vibration frequency of o-Ge₃N₄ keeps unchanged at different temperatures. Our results are concordant with the experimental data and the previous results. Therefore, the present results indicate that the combination of ab initio calculations and quasi-harmonic approximation is an efficient method to simulate the high-temperature behaviors of different Ge₃N₄ polymorphs. Generally speaking, the results listed in this work are all predictions, which need to be verified by experiments in the near future.

Key words: Ab initio, Germanium nitride, Electronic structure, Stability

CLC Number:

O641

TrendMD:

CANG Yuping, CHEN Dong, YANG Fan, YANG Huiming. Theoretical Studies on Tetragonal, Monoclinic and Orthorhombic Distortions of Germanium Nitride Polymorphs^†[J]. Chem. J. Chinese Universities, 2016, 37(4): 674.

Figures/Tables 9

Fig.1 Crystal structures of tetragonal(A), monoclinic(B) and orthorhombic(C) Ge3N4 phases ^The small and big balls represent the N and Ge atoms, respectively.

Fig.2 Total energy as a function of volume for t-Ge3N4(A), m-Ge3N4(B) and o-Ge3N4(C)

Table 1 Lattice constants a, b, c (nm), formation enthalpy ΔH (eV), bulk modulus B, shear modulus G and elastic constants Cij(GPa) of Ge3N4

Species	t-Ge₃N₄		m-Ge₃N₄		o-Ge₃N₄		c-Ge₃N₄
Species	0 GPa	20 GPa	0 GPa	20 GPa	0 GPa	20 GPa	Calcd.	Expt.
a	0.4410	0.4240	1.0215	0.9735	0.5256	0.5104	a=0.8212	a=0.8173^[34]
b			0.3103	0.2987	1.0074	0.9901	B=221.8	B=242.0^[36]
c	0.8835	0.8524	0.7928	0.7789	0.5319	0.5119	G=170.9	G=176.2^[36]
ΔH	-24.16	-14.06	-24.34	-13.77	-23.09	-14.68	C₁₁=378.8	C₁₁=395.1^[36]
B	146.8	206.8	124.1	189.1	203.4	122.1	C₁₂=147.9	C₁₂=165.4^[36]
G	86.8	85.4	72.8	65.1	296.1	132.5	C₄₄=223.7	C₄₄=234.5^[36]
C₁₁	200.4	249.6	175.2	236.8	300.1	411.6		a=0.8210^[12]
C₁₂	125.5	200.5	31.3	80.3	170.8	268.5		B=296^[22]
C₁₃	109.6	167.7	106.5	169.7	139.7	238.4		B=268.6^[20]
C₂₂			337.9	459.8	418.2	520.7		a=0.8168^[16]
C₂₃			41.1	79.9	99.0	171.9		a=0.8211^[20]
C₂₅			9.8	8.9				a=0.8120^[25]
C₃₃	232.2	286.4	276.7	400.3	311.5	399.1
C₃₅			19.9	35.2		151.8
C₄₄	124.8	140.5	54.6	46.0	140.8
C₄₆			22.4	22.2
C₅₅			90.4	104.2	143.9	164.5
C₆₆	147.6	169.9	62.6	30.8	141.1	161.8

Fig.3 Phonon dispersions and phonon density of states for t-Ge3N4(A), m-Ge3N4(B) and o-Ge3N4(C)^ The blue and red lines are the DOS of N and Ge, respectively.

Fig.4 Total(A) and partial density of states for Ge(B), N(C) atoms of t-Ge3N4

Fig.5 Total(A) and partial density of states for Ge(B), N(C) atoms of m-Ge3N4

Fig.6 Total(A) and partial density of states for Ge(B), N(C) atoms of o-Ge3N4

Fig.7 Temperature dependences of the normalized bulk moduli B/B0(A) and pressure dependences of the bulk moduli B(B) for the new Ge3N4 phases^a. t-Ge3N4; b. m-Ge3N4; c. o-Ge3N4.

Fig.8 Variations of the volume thermal expansion α(V)(A), entropy S(B), heat capacity Cv(C), normalized Debye temperature θD and heat capacity Cv (D) and Grüneisen parameter γ(E) for the three Ge3N4 compounds

References 39

[1]	Lu X., La P., Guo X., Wei Y., Nan X., He L., J. Phys. Chem. Lett., 2013, 4(11), 1878—1881
[2]	Fu R. B., Yang L. Q., Feng L. Y., Guo W., Chem. J. Chinese Universities, 2014, 35(4), 825—830
	(付融冰, 杨兰琴, 冯雷雨, 郭伟. 高等学校化学学报, 2014, 35(4), 825—830)
[3]	Hart J. N., Allan N. L., Claeyssens F., Phys. Rev. B, 2011, 84(24), 245209
[4]	Yang H. M., Xu B., Guo X. F., Wen Z. X., Fan X. H., Tian B., Chem. J. Chinese Universities, 2013, 34(4), 970—974
	(杨红梅, 许斌, 郭晓斐, 温振兴, 范小红, 田彬. 高等学校化学学报, 2013, 34(4), 970—974)
[5]	Salamat A., Hector A. L., Kroll P., McMillan P. F., Coordin. Chem. Rev., 2013, 257(13/14), 2063—2072
[6]	Ding Y. C., Chen M., Wu W. J., J. Theor. Comput. Chem., 2015, 14(4), 1550024
[7]	Boyko T. D., Hunt A., Zerr A., Moewes A., Phys. Rev. Lett., 2013, 111(9), 097402
[8]	Deb S. K., Dong J., Hubert H., McMillan P. F., Sankey O. F., Solid State Commun., 2000, 114(3), 137—142
[9]	Duan Y. H., Zhang K. M., Xie X. D., Acta Phys. Sinica, 1996, 45(3), 512—517
	(段玉华, 张开明, 谢希德. 物理学报, 1996, 45(3), 512—517)
[10]	Serghiou G., Miehe G., Tschauner O., Zerr A., Boehler R., J. Chem. Phys., 1999, 111(10), 4659—4662
[11]	Leinenweber K., O’Keeffe M., Somayazulu M. S., Hubert H., McMillan P. F., Wolf G. H., Chem. Eur. J., 1999, 5(10), 3076—3078
[12]	Yang M., Wang S. J., Feng Y. P., Peng G. W., Sun Y. Y., J. Appl. Phys., 2007, 102(1), 013507
[13]	Chu L. H., Kozhevnikov A., Schulthess T. C., Cheng H. P., J. Chem. Phys., 2014, 141(4), 044709
[14]	He H. L., Sekine T., Kobayashi T., Kimoto K., J. Appl. Phys., 2001, 90(9), 4403—4406
[15]	Wang Z., Zhao Y., Schiferl D., Qian J., Downs R. T., Mao H. K., Sekine T., J. Phys. Chem. B, 2013, 107(51), 14151—14153
[16]	Dong J. J., Sankey O. F., Deb S. K., Wolf G., McMillan P. F., Phys. Rev. B, 2000, 61(18), 11979—11992
[17]	Gao S. P., Cai G. H., Xu Y., Comput. Mater. Sci., 2013, 67, 292—295
[18]	Lü T. Y., Zheng J. C., Chem. Phys. Lett., 2010, 501(1—3), 47—53
[19]	Wang H., Chen Y., Kaneta Y., Iwata S., J. Phys.: Condens. Matter., 2006, 18(47), 10663—10676
[20]	Ching W. Y., Mo S. D., Ouyang L. Z., Phys. Rev. B, 2001, 63(24), 245110
[21]	Horvath-Bordon E., Riedel R., Zerr A., McMillan P. F., Auffermann G., Prots Y., Bronger W., Kniep R., Kroll P., Chem. Soc. Rev., 2006, 35(10), 987—1014
[22]	Soignard E., McMillan P. F., Hejny C., Leinenweber K., J. Solid State Chem., 2004, 177(1), 299—311
[23]	McMillan P. F., Deb S. K., Dong J. J., J. Raman Spectrosc., 2003, 34(7/8), 567—577
[24]	Luo Y., Cang Y., Chen D., Comput. Condens. Matter., 2014, 1, 1—7
[25]	Lowther J. E., Phys. Rev. B, 2000, 62(1), 5—8
[26]	Cui L., Hu M., Wang Q., Xu B., Yu D., Liu Z., He J., J. Solid State Chem., 2015, 228, 20—26
[27]	Kohn W., Sham L. J., Phys. Rev., 1965, 140(4A), A1133—A1138
[28]	Perdew J. P., Burke K., Ernzerhof M., Phys. Rev. Lett., 1996, 77(18), 3865—3868
[29]	Monkhorst H. J., Pack J. D., Phys. Rev. B, 1976, 13(12), 5188—5192
[30]	Ackland G. J., Warren M. C., Clark S. J., J. Phys.: Condens. Matter., 1997, 9(37), 7861—7872
[31]	Shanno D. F., Kettler P. C., Math. Comput., 1970, 24(1—3), 657—664
[32]	Otero-de-la-Roza A., Luańa V., Comput. Phys. Commun., 2011, 182(8), 1708—1720
[33]	Otero-de-la-Roza A., Abbasi-Pérez D., Luańa V., Comput. Phys. Commun., 2011, 182(10), 2232—2248
[34]	Dong J. J., Deslippe J., Sankey O. F., Soignard E., McMillan P. F., Phys. Rev. B, 2003, 67(9), 094104
[35]	Liu Q. J., Ran Z., Liu F. S., Liu Z. T., J. Alloys Compd., 2015, 631, 192—201
[36]	Soignard E., Somayazulu M., Dong J. J., Sankey O. F., McMillan P. F., J. Phys.: Condens. Matter., 2001, 13(4), 557—563
[37]	Yu B. H., Chen D., Chin. Phys. B, 2012, 61(19), 197102
[38]	Zhao Z. F., Li Y. F., Yao N., Chem. J. Chinese Universities, 2015, 36(8), 1648—1654
	(赵昨非, 李元丰, 姚宁. 高等学校化学学报, 2015, 36(8), 1648—1654)
[39]	Petit A. T., Dulong P. L., Ann. Chim. Phys., 1819, 10, 395—413