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1 Supplemental document Thermodynamic analysis on energy densities of batteries Chen-Xi Zu 1, 2, Hong Li 1, * 1 Institute of Physics, Chinese Academy of Sciences, Beijing , China 2 School of Materials Science and Engineering, Beihang University, Beijing , China Corresponding author: hli@aphy.iphy.ac.cn Supplementary data caption: Table S1. All chemical reactions calculated. Table S2. Thermodynamic data of typical battery systems. The volumetric energy densities of the batteries containing gas components are not calculated. Table S3. Thermodynamic data of selected typical lithium battery systems. Table S4. Thermodynamic data of all lithium battery systems calculated. Table S5. Thermodynamic data of lithium-ion battery systems with high gravimetric energy densities. Table S6. Capacity values of typical lithium-free cathodes. Table S7. Capacity values of lithium-contained cathodes. Table S8. Capacity values of typical anodes. Table S9. Capacity values calculated in all. Table S10. Calculated EMF values (V) of conversion reactions between binary transition mental compounds and lithium. Table S11. Calculated EMF (V) of conversion reactions between fluorides and

2 Li, Na, Mg or Al. Table S12. Key elements in the battery assembling and the toxicity. Figure S1. Capacity values of typical lithium-free cathodes. Figure S2. Capacity values of lithium-contained cathodes. Figure S3. Capacity values of typical anodes. Figure S4. Calculated EMF values (V) of conversion reactions between transition mental salts and lithium. Figure S5. Calculated EMF values (V) of conversion reactions between binary transition mental compounds and sodium. Figure S6. Calculated EMF values (V) of conversion reactions between binary transition mental compounds and magnesium. Figure S7. Calculated EMF values (V) of conversion reactions between binary transition mental compounds and aluminum. Figure S8. Calculated EMF (V) of conversion reactions between oxides and Li, Na, Mg or Al. Figure S9. Calculated EMF (V) of conversion reactions between sulphides and Li, Na, Mg or Al. Figure S10. Calculated EMF (V) of conversion reactions between nitrides and Li, Na, Mg or Al. Figure S11. Calculated EMF (V) of conversion reactions between fluorides and Li, Na, Mg or Al. Figure S12. Elements abundance in the earth.

3 Table S1. All chemical reactions calculated. M a X b n r G (kj mol -1 ) Li EMF (V) Capacity (m A h g -1 ) Cal. Energy density (W h kg -1 ) Cal. Energy density (W h L -1 ) F BeF NaF MgF AlF KF CaF ScF TiF TiF VF CrF MnF MnF FeF FeF CoF CoF NiF CuF CuF ZnF GaF RbF YF ZrF ZrF ZrF

4 NbF RuF RuF AgF SnF LaF CeF O BeO-α B 2 O Na 2 O MgO microcrystal Al 2 O SiO 2 quartz SiO 2 high cristobalite P 4 O K 2 O CaO Sc 2 O TiO Ti 2 O Ti 3 O TiO 2 -R TiO TiO 2 -A VO V 2 O VO V 3 O V 2 O CrO Cr 2 O Cr 3 O 4 (Δ H=-1513 kj mol -1 )

5 CrO MnO Mn 2 O MnO Mn 3 O FeO Fe 2 O 3 hematite Fe 3 O 4 magnetite CoO Co 3 O NiO Ni 2 O CuO Cu 2 O ZnO Ga 2 O GeO GeO As 4 O 6 octahedral As 2 O SeO Y 2 O ZrO NbO NbO Nb 2 O MoO MoO RuO RuO AgO Ag 2 O Ag 2 O La 2 O

6 CeO Ce 2 O WO WO Na 2 O K 2 O Ag 2 O NaO KO CaO S BeS B 2 S Na 2 S MgS Al 2 S SiS P 4 S P 4 S P 2 S K 2 S CaS Sc 2 S TiS TiS Ti 2 S VS V 2 S VS V 2 S CrS Cr 2 S MnS MnS FeS FeS 2(marcasite

7 ) FeS 2(pyrite) CoS Co 2 S CoS Co 3 S NiS Ni 3 S Ni 3 S NiS CuS Cu 2 S ZnS Ga 2 S GaS GeS GeS As 2 S Se 2 S Se 4 S RuS Y 2 S ZrS NbS MoS Mo 2 S Ag 2 S(argent ite) LaS La 2 S CeS WS Na 2 S N Be 3 N BN (CN)

8 Na 3 N Mg 3 N AlN Si 3 N K 3 N Ca 3 N ScN TiN VN CrN Cr 2 N Mn 4 N Mn 5 N Fe 2 N Fe 4 N Co 3 N NiN Cu 3 N Zn 3 N GaN Ge 3 N As 3 N SeN YN ZrN NbN MoN RuN Ag 3 N LaN CeN WN NaN KN AgN P - Be 3 P

9 BP Na 3 P Mg 3 P AlP Si 3 P K 3 P Ca 3 P ScP TiP (VP) CrP MnP Mn 2 P FeP Fe 2 P Fe 3 P Co 2 P Ni 2 P Ni 3 P Ni 5 P CuP Cu 3 P Zn 3 P GaP GeP Ge 3 P As 3 P Se(P) YP ZrP NbP MoP RuP AgP AgP LaP Ce 3 P

10 WP Cl BeCl PCl NaCl MgCl AlCl KCl CaCl ScCl TiCl TiCl VCl VCl CrCl CrCl MnCl FeCl FeCl CoCl NiCl CuCl CuCl ZnCl GaCl AsCl SeCl YCl ZrCl ZrCl ZrCl NbCl NbCl MoCl MoCl

11 MoCl RuCl AgCl SnCl LaCl CeCl WCl WCl WCl WCl BO 2 - NaBO Mg(BO 2 ) Al (BO 2 ) KBO Sc(BO 2 ) Ti (BO 2 ) V(BO 2 ) Cr(BO 2 ) Mn (BO 2 ) Fe (BO 2 ) Co (BO 2 ) Ni(BO 2 ) Cu(BO 2 ) Zn(BO 2 ) Ga(BO 2 ) Ge(BO 2 ) Y (BO 2 ) Zr (BO 2 ) Nb BO MoBO Ru(BO 2 ) Ag BO La (BO 2 ) Ce(BO 2 )

12 W (BO 2 ) Be 3 (BO 3 ) Ca 3 (BO 3 ) CO 3 2- Be CO B 2 (CO 3 ) Na 2 CO Mg CO Al 2 ( CO 3 ) K 2 CO CaCO Sc 2 (CO 3) Ti (CO 3 ) V 2 (CO 3 ) Cr (CO 3 ) MnCO Fe 2 (CO 3 ) FeCO Co CO Ni CO CuCO Zn CO Ga 2 (CO 3 ) Ge(CO 3 ) Y 2 (CO 3 ) ZrCO Nb 2 CO Mo 2 CO Ru 2 CO Ag 2 CO La 2 (CO 3 ) Ce 2 (CO 3 ) W (CO 3 ) PO 4

13 Be 3( PO 4) Na 3 PO Mg 3 (PO 4 ) Al PO K 3 PO Ca 3 (PO 4 ) Sc PO Ti 3 (PO 4 ) V 3 (PO 4 ) CrPO Mn PO Mn3( PO 4 ) Fe PO Co3(PO 4) Ni 3 (PO 4 ) Cu 3 (PO 4 ) Zn 3 (PO 4 ) Ga PO Ge 3 (PO 4 ) Y PO Zr 3 (PO 4 ) Nb 3 PO Mo 3 PO Ru 3 PO Ag 3 PO La PO CePO W (PO 4 ) SO 4 2- Be SO Na 2 SO Mg SO Al 2 ( SO 4 ) AlK(SO 4 )

14 K 2 SO CaSO Sc 2 (SO 4) Ti (SO 4 ) V 2 (SO 4 ) Cr 2(SO 4 ) MnSO FeSO Fe 2 (SO 4 ) Co SO Ni SO CuSO Zn SO Y 2 (SO 4 ) Zr(SO 4) Nb 2 SO Mo 2 SO Ru 2 SO Ag 2 SO La 2 (SO 4 ) Ce 2 (SO 4 ) W (SO 4 ) M a X b n r G (kj mol -1 ) Na EMF (V) Capacity (m A h g -1 ) Cal. Energy density (W h kg -1 ) Cal. Energy density (W h L -1 ) F BeF LiF MgF AlF KF CaF

15 ScF TiF TiF VF CrF MnF MnF FeF FeF CoF CoF NiF CuF CuF ZnF GaF RbF YF ZrF ZrF ZrF NbF RuF RuF AgF SnF LaF CeF O BeO-α B 2 O Li 2 O MgO microcrystal Al 2 O SiO 2 quartz

16 SiO 2 high cristobalite P 4 O K 2 O CaO Sc 2 O TiO Ti 2 O Ti 3 O TiO 2 -R TiO TiO 2 -A VO V 2 O VO V 3 O V 2 O CrO Cr 2 O Cr 3 O 4 ( Δ H=-1513 kj mol -1 ) CrO MnO Mn 2 O MnO Mn 3 O FeO Fe 2 O 3 hematite Fe 3 O 4 magnetite CoO Co 3 O NiO Ni 2 O CuO Cu 2 O

17 ZnO Ga 2 O GeO GeO As 4 O 6 octahedral As 2 O SeO Y 2 O ZrO NbO NbO Nb 2 O MoO MoO RuO RuO AgO Ag 2 O Ag 2 O La 2 O CeO Ce 2 O WO WO Li 2 O K 2 O Ag 2 O LiO KO CaO S BeS B 2 S Li 2 S MgS

18 Al 2 S SiS P 4 S P 4 S P 2 S K 2 S CaS Sc 2 S TiS TiS Ti 2 S VS V 2 S VS V 2 S CrS Cr 2 S MnS MnS FeS FeS 2(marcasite ) FeS 2(pyrite) CoS Co 2 S CoS Co 3 S NiS Ni 3 S Ni 3 S NiS CuS Cu 2 S ZnS Ga 2 S GaS GeS

19 GeS As 2 S Se 2 S Se 4 S RuS Y 2 S ZrS NbS MoS Mo 2 S Ag 2 S (argentite) LaS La 2 S CeS WS Li 2 S N Be 3 N BN (CN) Li 3 N Mg 3 N AlN Si 3 N K 3 N Ca 3 N ScN TiN VN CrN Cr 2 N Mn 4 N Mn 5 N Fe 2 N Fe 4 N Co 3 N

20 NiN Cu 3 N Zn 3 N GaN Ge 3 N As 3 N SeN YN ZrN NbN MoN RuN Ag 3 N LaN CeN WN LiN KN AgN P Supplementary Material (ESI) for Energy & Environmental Science Be 3 P BP Li 3 P Mg 3 P AlP Si 3 P K 3 P Ca 3 P ScP TiP (VP) CrP MnP Mn 2 P FeP Fe 2 P Fe 3 P Co 2 P

21 Ni 2 P Ni 3 P Ni 5 P CuP Cu 3 P Zn 3 P GaP GeP Ge 3 P As 3 P Se(P) YP ZrP NbP MoP RuP AgP AgP LaP Ce 3 P WP Cl BeCl PCl LiCl MgCl AlCl KCl CaCl ScCl TiCl TiCl VCl VCl CrCl CrCl

22 MnCl FeCl FeCl CoCl NiCl CuCl CuCl ZnCl GaCl AsCl SeCl YCl ZrCl ZrCl ZrCl NbCl NbCl MoCl MoCl MoCl RuCl AgCl SnCl LaCl CeCl WCl WCl WCl WCl BO 2 - LiBO Mg(BO 2 ) Al (BO 2 ) KBO Sc(BO 2 )

23 Ti (BO 2 ) V(BO 2 ) Cr(BO 2 ) Mn (BO 2 ) Fe (BO 2 ) Co (BO 2 ) Ni(BO 2 ) Cu(BO 2 ) Zn(BO 2 ) Ga(BO 2 ) Ge(BO 2 ) Y (BO 2 ) Zr (BO 2 ) Nb BO MoBO Ru(BO 2 ) Ag BO La (BO 2 ) Ce(BO 2 ) W (BO 2 ) Be 3 (BO 3 ) Ca 3 (BO 3 ) CO 3 2- Be CO B 2 (CO 3 ) Li 2 CO Mg CO Al 2 ( CO 3 ) K 2 CO CaCO Sc 2 (CO 3) Ti (CO 3 ) V 2 (CO 3 ) Cr (CO 3 )

24 MnCO Fe 2 (CO 3 ) FeCO Co CO Ni CO CuCO Zn CO Ga 2 (CO 3 ) Ge(CO 3 ) Y 2 (CO 3 ) ZrCO Nb 2 CO Mo 2 CO Ru 2 CO Ag 2 CO La 2 (CO 3 ) Ce 2 (CO 3 ) W (CO 3 ) PO 4 3- Be 3 (PO 4 ) Li 3 PO 4( Δ H= kj mol -1 ) Mg 3 (PO 4 ) Al PO K 3 PO Ca 3 (PO 4 ) Sc PO Ti 3 (PO 4 ) V 3 (PO 4 ) CrPO Mn PO Mn 3 ( PO 4 ) Fe PO Co3(PO 4)

25 Ni 3 (PO 4 ) Cu 3 (PO 4 ) Zn 3 (PO 4 ) Ga PO Ge 3 (PO 4 ) Y PO Zr 3 (PO 4 ) Nb 3 PO Mo 3 PO Ru 3 PO Ag 3 PO La PO CePO W (PO 4 ) SO 4 2- Be SO Li 2 SO Mg SO Al 2 ( SO 4 ) AlK(SO 4 ) K 2 SO CaSO Sc 2 (SO 4) Ti (SO 4 ) V 2 (SO 4 ) Cr 2(SO 4 ) MnSO FeSO Fe 2 (SO 4 ) Co SO Ni SO CuSO Zn SO Y 2 (SO 4 )

26 Zr(SO 4) Nb 2 SO Mo 2 SO Ru 2 SO Ag 2 SO La 2 (SO 4 ) Ce 2 (SO 4 ) W (SO 4 ) M a X b n r G (kj mol -1 ) Mg EMF (V) Capacity (m A h g -1 ) Cal. Energy density (W h kg -1 ) Cal. Energy density (W h L -1 ) F BeF NaF LiF AlF KF CaF ScF TiF TiF VF CrF MnF MnF FeF FeF CoF CoF NiF CuF CuF

27 ZnF GaF RbF YF ZrF ZrF ZrF NbF RuF RuF AgF SnF LaF CeF O BeO-α B 2 O Na 2 O Li 2 O Al 2 O SiO 2 quartz SiO 2 high cristobalite P 4 O K 2 O CaO Sc 2 O TiO Ti 2 O Ti 3 O TiO 2 -R TiO TiO 2 -A VO V 2 O VO

28 V 3 O V 2 O CrO Cr 2 O Cr 3 O 4 ( Δ H=-1513 kj mol -1 ) CrO MnO Mn 2 O MnO Mn 3 O FeO Fe 2 O 3 hematite Fe 3 O 4 magnetite CoO Co 3 O NiO Ni 2 O CuO Cu 2 O ZnO Ga 2 O GeO GeO As 4 O 6 octahedral As 2 O SeO Y 2 O ZrO NbO NbO Nb 2 O MoO MoO

29 RuO RuO AgO Ag 2 O Ag 2 O La 2 O CeO Ce 2 O WO WO Na 2 O K 2 O Ag 2 O S BeS B 2 S Na 2 S Li 2 S Al 2 S SiS P 4 S P 4 S P 2 S K 2 S CaS Sc 2 S TiS TiS Ti 2 S VS V 2 S VS V 2 S CrS Cr 2 S MnS

30 MnS FeS FeS 2(marcasite ) FeS 2(pyrite) CoS Co 2 S CoS Co 3 S NiS Ni 3 S Ni 3 S NiS CuS Cu 2 S ZnS Ga 2 S GaS GeS GeS As 2 S Se 2 S Se 4 S RuS Y 2 S ZrS NbS MoS Mo 2 S Ag 2 S(argent ite) LaS La 2 S CeS WS Na 2 S N

31 Be 3 N BN (CN) Na 3 N Li 3 N AlN Si 3 N K 3 N Ca 3 N ScN TiN VN CrN Cr 2 N Mn 4 N Mn 5 N Fe 2 N Fe 4 N Co 3 N NiN Cu 3 N Zn 3 N GaN Ge 3 N As 3 N SeN YN ZrN NbN MoN RuN Ag 3 N LaN CeN WN P Be 3 P BP

32 Na 3 P Li 3 P AlP Si 3 P K 3 P Ca 3 P ScP TiP (VP) CrP MnP Mn 2 P FeP Fe 2 P Fe 3 P Co 2 P Ni 2 P Ni 3 P Ni 5 P CuP Cu 3 P Zn 3 P GaP GeP Ge 3 P As 3 P Se(P) YP ZrP NbP MoP RuP AgP AgP LaP Ce 3 P WP

33 Cl BeCl PCl NaCl LiCl AlCl KCl CaCl ScCl TiCl TiCl VCl VCl CrCl CrCl MnCl FeCl FeCl CoCl NiCl CuCl CuCl ZnCl GaCl AsCl SeCl YCl ZrCl ZrCl ZrCl NbCl NbCl MoCl MoCl MoCl

34 RuCl AgCl SnCl LaCl CeCl WCl WCl WCl WCl BO 2 - NaBO LiBO Al (BO 2 ) KBO Sc(BO 2 ) Ti (BO 2 ) V(BO 2 ) Cr(BO 2 ) Mn (BO 2 ) Fe (BO 2 ) Co (BO 2 ) Ni(BO 2 ) Cu(BO 2 ) Zn(BO 2 ) Ga(BO 2 ) Ge(BO 2 ) Y (BO 2 ) Zr (BO 2 ) Nb BO MoBO Ru(BO 2 ) Ag BO La (BO 2 ) Ce(BO 2 ) W (BO 2 )

35 Be 3 (BO 3 ) Ca 3 (BO 3 ) CO 3 2- Be CO B 2 (CO 3 ) Na 2 CO Li 2 CO Al 2 ( CO 3 ) K 2 CO CaCO Sc 2 (CO 3) Ti (CO 3 ) V 2 (CO 3 ) Cr (CO 3 ) MnCO Fe 2 (CO 3 ) FeCO CoCO Ni CO CuCO Zn CO Ga 2 (CO 3 ) Ge(CO 3 ) Y 2 (CO 3 ) ZrCO Nb 2 CO Mo 2 CO Ru 2 CO Ag 2 CO La 2 (CO 3 ) Ce 2 (CO 3 ) W (CO 3 ) PO 4 3- Be 3( PO 4)

36 Na 3 PO Li 3 PO 4( Δ H= kj mol -1 ) Al PO K 3 PO Ca 3 (PO 4 ) Sc PO Ti 3 (PO 4 ) V 3 (PO 4 ) CrPO Mn PO Mn 3 ( PO 4 ) Fe PO Co 3 (PO 4) Ni 3 (PO 4 ) Cu 3 (PO 4 ) Zn 3 (PO 4 ) Ga PO Ge 3 (PO 4 ) Y PO Zr 3 (PO 4 ) Nb 3 PO Mo 3 PO Ru 3 PO Ag 3 PO La PO CePO W (PO 4 ) SO 4 2- Be SO Na 2 SO Li 2 SO Al 2 ( SO 4 ) AlK(SO 4 )

37 K 2 SO CaSO Sc 2 (SO 4) Ti (SO 4 ) V 2 (SO 4 ) Cr 2 (SO 4 ) MnSO FeSO Fe 2 (SO 4 ) Co SO Ni SO CuSO Zn SO Y 2 (SO 4 ) Zr(SO 4) Nb 2 SO Mo 2 SO Ru 2 SO Ag 2 SO La 2 (SO 4 ) Ce 2 (SO 4 ) W (SO 4 ) M a X b F n r G (kj mol -1 ) Al EMF (V) Capacity (m A h g -1 ) Cal. Energy density (W h kg -1 ) Cal. Energy density (W h L -1 ) BeF NaF MgF LiF KF CaF

38 ScF TiF TiF VF CrF MnF MnF FeF FeF CoF CoF NiF CuF CuF ZnF GaF RbF YF ZrF ZrF ZrF NbF RuF RuF AgF SnF LaF CeF O BeO-α B 2 O Na 2 O MgO microcrystal Li 2 O SiO 2 quartz

39 SiO 2 high cristobalite P 4 O K 2 O CaO Sc 2 O TiO Ti 2 O Ti 3 O TiO 2 -R TiO TiO 2 -A VO V 2 O VO V 3 O V 2 O CrO Cr 2 O Cr 3 O 4 ( Δ H=-1513 kj mol -1 ) CrO MnO Mn 2 O MnO Mn 3 O FeO Fe 2 O 3 hematite Fe 3 O 4 magnetite CoO Co 3 O NiO Ni 2 O CuO Cu 2 O

40 ZnO Ga 2 O GeO GeO As 4 O 6 octahedral As 2 O SeO Y 2 O ZrO NbO NbO Nb 2 O MoO MoO RuO RuO AgO Ag 2 O Ag 2 O La 2 O CeO Ce 2 O WO WO S BeS B 2 S Na 2 S MgS Li 2 S SiS P 4 S P 4 S P 2 S K 2 S

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