Computational prediction of high ZT of n-type Mg 3 Sb 2 - based compounds with isotropic thermoelectric conduction performance
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1 Elcronic Supplnary Marial (ES for Physical Chisry Chical Physics. This journal is h Ownr Sociis 08 Supporing nforaion Copuaional prdicion of high ZT of n-yp Mg 3 Sb - basd copounds wih isoropic hrolcric conducion prforanc Juan i, Shuqi Zhng, Tng Fang, uo Yu, Shuai Zhang and Guiwu u Sa Ky aboraory of Havy Oil Procssing, Dparn of Marials Scinc and Enginring, China Univrsiy of Prolu, ijing 049, Popl s Rpublic of China Fig. S Calculad band srucurs (a wihou and (b wih spin orbi coupling (SOC in Mg 3 Sb. Fig. S Calculad oal DOS of Mg 3 Sb. Th back and rd solid lins rprsn h calculad DOS wihou and wih spin orbi coupling (SOC, rspcivly. Corrsponding auhor. Tl: ; Fax: E-ail: zhngsq09@63.co (Shuqi Zhng.
2 Fig. S3 Calculad band-dcoposd charg dnsiy of (a conducion band iniu (CM, isosurfac valu and (b valnc band axiu (M, isosurfac valu Purpl, pink and grn balls rprsn Mg, Mg, and Sb aos, rspcivly. Fig. S4 Effciv band srucur of (a suprcll of h priiiv uni cll Mg 3 Sb (40 aos and (b Mg 3 Sb.5 i 0.5 by PE funcional wihou SOC. Esiaion of carrir s obiliy and scaring i asd on h dforaion ponial (DF hory, h carrir s obiliy scar i can b xprssd as: and h c 3/ 3( k T 4 ii 5/ ( h c 3( k T 4 ii 3/ (
3 whr cii is h laic lasic consan ( i =,, 3, is h dforaion ponial consan calculad as E dg ( a a, whr E is h conducion band axiu (CM, a is h laic consan and a, givn by a a a, is h dg 0 corrsponding laic disorion, and is h conduciviy ffciv ass. asd on h band srucur, w us h ffciv ass calculaor (EMC o calcula h ffciv ass nsor ij of a singl vally, dfind as: h ( E( k k k, i, j x, y, z (3 ij i j Th conduciviy ffciv ass can b xprss as: 3 ( xx yy zz (4 Th ffciv asss of h K conducion band ar siad o b = =0.3580, 0. 03, which yild h conduciviy ffciv ass a K poin, K zz 0.899, and h ffciv asss of h C conducion band ar siad o b 0.54, , 0.650, lading o h conduciviy xx yy zz xx yy ffciv ass a C poin, C Du o h nrgy diffrnc bwn h K and h C iniu is 0., sallr han ~ 3k T a roo praur, so h conducion band iniu a K poin and C poin can b considrd as narly convrgd a lvad praur for n-yp ranspor in Mg 3 Sb. h conduciviy ffciv ass is calculad using h avrag conduciviy ffciv ass of wo band ( and dscribd as:,k,c (, K, C (5 Thus, h calculad conduciviy ffciv ass of n-yp Mg 3 Sb is 0.. Using quaion (, h calculad ar 0.8 c - s - along Γ - M dircion and 08. c - s - along Γ - A dircion a 300 K, and 7 c - s - along Γ - M dircion and 8.69 c - s - along Γ - A dircion a 75 K. Using quaion (, h
4 calculad ar.6 fs along Γ - M dircion and 3.39 fs along Γ - A dircion a 300 K, and fs along Γ - M dircion and fs along Γ - A dircion a 75 K. Calculaion of h iniu laic hral conduciviy Th iniu laic hral conduciviy in is calculad using h Cahill s forula as: 3,4 in [( ] k ( (v v l (6 whr is h avrag volu pr ao, v is ravrs lasic wav vlociy and is longiudinal lasic wav vlociy. v and v can b obaind using h following quaions: 5,6 l vl v G (7 v l 4 ( G 3 (8 whr is h bulk odulus, G is h shar odulus and is h dnsiy. and G ar drind adoping h oig-russ-hill avraging sch in hxagonal sys givn by: 5,6 ( R G ( G GR (9 (0 (( c c 4c3 c 9 G c R M 33 ( M c 44 c ( ( (3
5 G R (3 c 44 5c c44c66 c c ( c c 66 (4 M c c c33 4 c 3 (5 c ( c c c c 33 3 (6 c c33 c44 c 3 whr,,, and c ar fiv indpndn lasic consans for hxagonal sys. Th calculad in Mg 3 Sb is 0.58 W - K - in. Esiaion of h laic hral conduciviy According h Slack s forula, h laic hral conduciviy xprssd as: 7 3 MD A 3 n T 3 pr can b (5 whr M,,, n and rprsn h avrag aoic ass, h Dby D pr praur, h volu pr ao, h nubr of aos in h priiiv cll and h Grünisn parar, and A is a physical consan whn is in W - K - 3, M is in au, and is in Å. is proporional o h avragd sound vlociy pr D v s and can b valuad by: 3,7 D h k ( 6 n a 3 v s (6 whr n is h nubr dnsiy of aos. v can b calculad via: 5,6 a s v s ( 3 v 3 3 vl 3 (7, drining h low, is calculad using h cobind dnsiy funcional prurbaion hory (DFPT and h quasi-haronic approxiaion (QHA, givn by: 8
6 3 C (8 whr,, and C rprsn h linar hral xpansion cofficin, h bulk odulus, h olar volu and h isoric ha capaciy. phonon disprsion, xprssd as: 8 C is obaind fro h C h n ( q kt h ( n q k n, q kt h ( q k T n (9 whr (q n is h phonon frquncy of h n-h branch wih wav vcor q. Th volu changs in 3%, %, %, 0%, -%, -%, -3% ar applid in QHA procss. in Mg 3 Sb is siad o b.55 W - K - a 300 K and 0.8 W - K - a 75 K, which ar sall valus drivd fro h larg Grünisn parar of.86 a 300 K and.48 a 75 K. Rfrnc: J. ardn and W. Shockly, Phys. Rv., 950, 80, 7. A. Fonari and C. Suon, Effciv Mass Calculaor, 0. 3 D. G. Cahill, S. K. Wason and P. Ro, Phys. Rv., 99, 46, T. Fang, S. Zhng, H. Chn, H. Chng,. Wang and P. Zhang, RSC Adv., 06. 6, J.. Tani, M. Takahashi and H. Kido, Physica, 00, 405, Z. J. Wu, E. J. Zhao, H. P. Xiang, X. F. Hao, X. J. iu and J. Mng, Phys. Rv., 007, 76, G. A. Slack, J. Phys. Ch. Solids, 973, 34, 3. 8 T. Fang, S. Zhng, T. Zhou,. Yan and P. Zhang, Phys. Ch. Ch. Phys., 07, 9, 44.
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