Supporting information

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1 Eletroni Supplementary Material (ESI) for Journal of Materials Cemistry A. Tis journal is Te Royal Soiety of Cemistry 017 Supporting information Simultaneous improvement of power fator and termal ondutivity via Ag doping in p-type Mg 3 Sb termoeletri materials Lirong Song, Jiawei Zang, and Bo B. Iversen* Center for Materials Crystallograpy, Department of Cemistry and inano, Aarus University, Langelandsgade 140, Aarus DK-8000, Denmark. * bo@em.au.dk Tese autors ontribute equally. Calulation details of eletroni transport Eletrial transport properties in te main text are simulated using ombined full band struture alulation and semilassial Boltzmann transport teory under te onstant sattering time approximation (CSTA) in BoltzTraP ode. 1 Under te CSTA, it is assumed tat te arrier sattering time τ remains onstant wit varying temperature and doping level. Te simulated Seebek oeffiient is independent of τ, wile eletrial ondutivity and power fator are alulated wit respet to te onstant arrier sattering time τ. Tis approa as been suessfully applied in te predition of Seebek oeffiient values and te trends of eletrial ondutivity and power fator of a wide range of termoeletri materials. -6 In addition to CSTA, te single paraboli band model is also used in te main text. Under a single paraboli band approximation, te Seebek oeffiient and te Lorenz number an be written as 7 S k 5 r F B e 3 r F r3/ r1/ ( ) ( ) 7 5 r Fr 5/( ) r Fr 3/( ) k B L e 3 3 r Fr 1/ ( ) r Fr 1/ ( ) (1) () 1

2 were Fermi integral is n d Fn ( ), (3) 0 1 exp( ) k B is te Boltzmann onstant, is te Plank s onstant, η is te redued Fermi energy. Sattering fator r = -0.5 is assumed for te aousti ponon sattering meanism. Te average zt sown in Figure 8b in te main text was alulated by te following formula: 8 zt T S( T ) dt( T T ) T ( T ) dt ( T ) dt T T avg T T, (4) were T and T are temperatures of te ot side and te old side, respetively. In Figure 8b, T was osen to be 333 K sine te reported termoeletri properties of Mg 3 Sb 1.8 Bi 0. (ref. 9) were measured from 333 K. Table S1. Te nominal and atual ompositions measured by SEM-EDS for Mg 3-x Ag x Sb (0 x 0.05) samples, It sould be noted tat te atual ompositions of Ag by SEM-EDS ave large errors due to te small amount of Ag doping. Intensity Error (%) Mg 3-x Ag x Sb Nominal ompositions Atual ompositions (SEM- EDS) MgK AgL SbL x = 0 Mg 60 Sb 40 Mg 5.89 Sb x = Mg 59.9 Ag 0.1 Sb 40 Mg Ag 0.49 Sb x = 0.01 Mg 59.8 Ag 0. Sb 40 Mg Ag 0.47 Sb x = Mg 59.7 Ag 0.3 Sb 40 Mg Ag 0.76 Sb x = 0.0 Mg 59.6 Ag 0.4 Sb 40 Mg Ag 0.5 Sb x = 0.05 Mg 59.5 Ag 0.5 Sb 40 Mg Ag 0.76 Sb Table S. Te sample densities, teoretial densities and relative densities of Mg 3-x Ag x Sb (0 x 0.05) samples. Te relative densities of all te samples are larger tan 96%. Sample density Teoretial density Relative density Mg 3-x Ag x Sb (g/m 3 ) (g/m 3 ) (%) x = x = x = x = x = x =

3 Fig. S1. Repeated measurements of eletrial resistivity in te last 3 yles for Mg 3-x Ag x Sb (x=0.015), sowing te sample is stable during te measurements. Fig. S. Eletrial resistivity (a) and Seebek oeffiient (b) of Mg 3-x Ag x Sb (0.005 x 0.05) samples wit bot eating and ooling measurements of te final yle. Fig. S3. Temperature dependene of termal diffusivity of Mg 3-x Ag x Sb (0 x 0.05). 3

4 Fig. S4. Sanning Seebek oeffiient map and istogram over te ross setion of Mg 3-x Ag x Sb (x=0.015) pellet. Fig. S5. Lattie parameters as a funtion of te Ag doping ontent in Mg 3-x Ag x Sb (0 x 0.05). Te lattie parameters are estimated by te Rietveld refinement using te Fullprof program. 10 4

5 Fig. S6. Te atomi-sale ig resolution TEM image of te undoped sample, exiibiting te presene of different orientations of te rystallograpi planes: 110 (0.31 nm) and 103 (0.1 nm). Fig. S7. Temperature dependene of te Lorenz numbers of Mg 3-x Ag x Sb (0 x 0.05) estimated by te single paraboli band model. Referenes (1) G. K. H. Madsen, D. J. Sing, Comput. Pys. Commun. 006, 175, () G. K. H. Madsen, J. Am. Cem. So. 006, 18, (3) J. Yang, H. Li, T. Wu, W. Zang, L. Cen, J. Yang, Adv. Funt. Mater. 008, 18, (4) J. Zang, L. Song, G. K. H. Madsen, K. F. F. Fiser, W. Zang, X. Si, B. B. Iversen, Nat. Commun. 016, 7, (5) J. Zang, R. Liu, N. Ceng, Y. Zang, J. Yang, C. Uer, X. Si, L. Cen, W. Zang, Adv. Mater. 014, 6, (6) D. J. Sing, D. Parker, J. Appl. Pys. 013, 114, (7) H. J. Goldsmid, Termoeletri Refrigeration; Plenum Press: New York, (8) H. S. Kim, W. Liu, G. Cen, C.W. Cu, Z. Ren, Pro. Natl. Aad. Si. U.S.A. 015, 11, (9) A. Bardwaj, A. Rajput, A. K. Sukla, J. J. Pulikkotil, A. K. Srivastava, A. Dar, G. Gupta, S. Auluk, D. K. Misra, R. C. Budani, RSC Adv. 013, 3, (10) J. Rodríguez-Carvajal, Pysia B 1993, 19,