Theoretical prediction and synthesis of (Cr 2/3 Zr 1/3 ) 2 AlC i-max phase

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1 Supporting Information for: Figure Theoretical prediction and synthesis of (Cr 2/3 Zr 1/3 ) 2 AlC i-max phase Liugang Chen 1 *, Martin Dahlqvist 2, Thomas Lapauw 1,3, Bensu Tunca 1,3, Fei Wang 1, Jun Lu 2, Rahele Meshkian 2, Konstantina Lambrinou 3, Bart Blanpain 1, Jozef Vleugels 1, Johanna Rosen 2* 1 KU Leuven, Department of Materials Engineering, Kasteelpark Arenberg 44, B-3001 Leuven, Belgium 2 Department of Physics, Chemistry, and Biology (IFM), Linköping University, SE Linköping, Sweden 3 SCK CEN, Boeretang 200, B2400 Mol, Belgium L.C. and M.D. contributed equally to this work * Corresponding authors. liugang.chen@kuleuven.be (L.C.) and johanna.rosen@liu.se (J.R.) CONTENTS: 1. Prototype structure S2 2. XRD patterns of starting powders S5 3. d-spacings and corresponding 2θ angles S6 4. Magnetic information S9 S1

2 1. Prototype structure Table S1. Prototype structure, with corresponding structural information, and calculated total energy per formula unit for considered competing phases within present paper. Phase Prototype Pearson symbol Space group Energy (ev/fu) Cr W ci2 Im-3m (229) Cr Cu cf4 Fm-3m (225) Cr Mg hp2 P6 3 /mmc (194) Ti Cu cf4 Fm-3m (225) Ti W ci2 Im-3m (229) Ti Mg hp2 P6 3 /mmc (194) Zr Mg hp2 P6 3 /mmc (194) Zr Cu cf4 Fm-3m (225) Zr W ci2 Im-3m (229) Hf Mg hp2 P6 3 /mmc (194) Hf Cu cf4 Fm-3m (225) Hf W ci2 Im-3m (229) Al Cu cf4 Fm-3m (225) Al Mg hp2 P6 3 /mmc (194) Al W ci2 Im-3m (229) C C (graphite) hp4 P6 3 /mmc (194) Al 4 C 3 Al 4 C 3 hr21 R-3m h (166) Cr 2 Al MoSi 2 ti6 I4/mmm (139) Cr 5 Al 8 Cu 5 Zn 8 ci52 I-43m (217) Cr 4 Al 9 PdAl hr26 R3m (160) Cr 5 Al 21 Cr 5 Al 21 hr26 R3m (160) Cr 7 Al 43 V 7 Al 45 mc104 C2/m (12) Ti 3 Al Mg 3 Cd hp8 P6 3 /mmc (194) TiAl AuCu tp4 P4/mmm (123) TiAl 2 HfGa 2 ti24 I41/amd O2 (141) TiAl 3 TiAl3 ti8 I4/mmm (139) Zr 3 Al AuCu 3 cp4 Pm-3m (221) Zr 3 Al Ni 3 Sn hp8 P6 3 /mmc (194) Zr 2 Al Ni 2 In hp6 P6 3 /mmc (194) Zr 2 Al Al 2 Cu op6 Pnnm (58) Zr 5 Al 3 W 5 Si 3 ti32 I4/mcm (140) Zr 5 Al 3 Mn 5 Si 3 hp16 P6 3 /mcm (193) Zr 3 Al 2 Zr 3 Al 2 tp20 P42/mnm (136) Zr 4 Al 3 Zr 4 Al 3 hp7 P6/mmm (191) Zr 5 Al 4 Ti 5 Ga 4 hp18 P6 3 /mcm (193) ZrAl CrB oc8 Cmcm (63) ZrAl CsCl cp2 Pm-3m (221) Zr 2 Al 3 Zr 2 Al 3 of40 Fdd2 (43) ZrAl 2 MgZn 2 hp12 P6 3 /mmc (194) ZrAl 2 Ni 2 In hp6 P6 3 /mmc (194) ZrAl 3 ZrAl 3 ti16 I4/mmm (139) ZrAl 3 AuCu 3 cp4 Pm-3m (221) ZrAl 6 MnAl 6 os28 Cmcm (63) Hf 2 Al Al 2 Cu op6 Pnnm (58) Hf 5 Al 3 Mn 5 Si 3 hp16 P6 3 /mcm (193) Hf 3 Al 2 Zr 3 Al 2 tp20 P4 2 /mnm (136) Hf 4 Al 3 Zr 4 Al 3 hp7 P6/mmm (191) S2

3 HfAl CrB oc8 Cmcm (63) Hf 2 Al 3 Zr 2 Al 3 of40 Fdd2 (43) HfAl 2 MgZn 2 hp12 P6 3 /mmc (194) HfAl 3 ZrAl 3 ti16 I4/mmm (139) HfAl 3 TiAl 3 ti8 I4/mmm (139) HfAl 3 AuCu 3 cp4 Pm-3m (221) Hf 2 Al Al 2 Cu op6 Pnnm (58) Cr 23 C 6 Cr 23 C 6 cf116 Fm-3m (225) Cr 3 C Fe 3 C op16 Pnma (62) Cr 7 C 3 Cr 7 C 3 op40 Pnma (62) Cr 3 C 2 Sb 2 S 3 op20 Pnma (62) Ti2C Ca 33 Ge cf48 Fd-3m (227) TiC 0.75 NaCl cf8 Fm-3m (225) TiC NaCl cf8 Fm-3m (225) TiC NaCl cf8 Fm-3m (225) TiC NiAs hp4 P63/mmc (194) ZrC NaCl cf8 Fm-3m (225) ZrC NaCl cf8 Fm-3m (225) HfC NaCl cf8 Fm-3m (225) HfC NaCl cf8 Fm-3m (225) Ti 0.75 Cr 0.25 W ci2 Im-3m (229) Ti 0.50 Cr 0.50 W ci2 Im-3m (229) Ti 0.25 Cr 0.75 W ci2 Im-3m (229) TiCr 2 MgCu 2 cf24 Fd-3m O2 (227) (Ti 0.25 Cr 0.75 )C NaCl cf8 Fm-3m (225) (Ti 0.50 Cr 0.50 )C NaCl cf8 Fm-3m (225) (Ti 0.75 Cr 0.25 )C NaCl cf8 Fm-3m (225) Ti(Al 0.25 Cr 0.75 ) CsCl cp2 Pm-3m (221) Ti(Al 0.50 Cr 0.50 ) CsCl cp2 Pm-3m (221) Ti(Al 0.75 Cr 0.25 ) CsCl cp2 Pm-3m (221) Ti 3 AlC CaTiO 3 cp5 Pm-3m (221) Ti 2 AlC Cr 2 AlC hp8 P6 3 /mmc (194) Ti 3 AlC 2 Ti 3 SiC 2 hp12 P6 3 /mmc (194) Ti 4 AlC 3 Ti 4 AlN 3 hp16 P6 3 /mmc (194) Ti 12 Al 3 C 8 Ti 4 AlN 3 hp46 P6 3 /mcm (193) Ti 5 AlC 4 Ti 5 AlC 4 hp20 P6 3 /mmc (194) Ti 6 AlC 5 Ti 6 AlC 5 hp24 P6 3 /mmc (194) Ti 5 Al 2 C 3 Ti 5 Al 2 C 3 hp30 P3m1 (156) Ti 7 Al 2 C 5 Ti 7 Al 2 C 5 hp42 P6 3 /mmc (194) Cr 3 AlC CaTiO 3 cp5 Pm-3m (221) Cr 2 AlC Cr 2 AlC hp8 P6 3 /mmc (194) Cr 3 AlC 2 Ti 3 SiC 2 hp12 P6 3 /mmc (194) Cr 4 AlC 3 Ti 4 AlN 3 hp16 P6 3 /mmc (194) Ti 12 Al 3 C 8 Ti 4 AlN 3 hp46 P6 3 /mcm (193) Cr 2 TiAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Ti 2 CrAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Cr 2 Ti 2 AlC 3 Mo 2 Ti 2 AlC 3 hp16 P6 3 /mmc (194) (Cr 2/3 Ti 1/3 ) 2 AlC (Mo 2/3 Sc 1/3 ) 2 AlC ms48 C2/c (15) ZrCr 2 MgCu2 cf24 Fd-3m O2 (227) Zr(Al 0.25 Cr 0.75 ) 2 MgZn 2 hp12 P6 3 /mmc (194) Zr(Al 0.5 Cr 0.5 ) 2 MgZn 2 hp12 P6 3 /mmc (194) Zr 5 Al 3 C 0.5 Mn 5 Si 3 hp16 P6 3 /mcm (193) S3

4 Zr 5 Al 3 C Mn 5 Si 3 hp16 P6 3 /mcm (193) Zr 3 Al 3 C 5 Zr 3 Al 3 C 5 hp22 P6 3 /mmc (194) Zr 2 Al 3 C 4 Zr 2 Al 3 C 4 hp18 P6 3 /mmc (194) ZrAl 4 C 4 ZrAl 4 C 4 hp18 P-3m1 (164) Zr 2 Al 4 C 5 Zr 2 Al 4 C 5 hp33 R-3m (166) Zr 3 Al 4 C 6 Zr 3 Al 4 C 6 hp39 R-3m (166) ZrAlC 2 ZrAlC 2 hp24 P6 3 /mmc (194) Zr 3 AlC Re 3 B op20 Cmcm (63) Zr 3 AlC CaTiO 3 cp5 P6 3 /mmc (194) Zr 2 AlC Cr 2 AlC hp8 P6 3 /mmc (194) Cr 2 ZrAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Ti 2 ZrAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Cr 2 Zr 2 AlC 3 Mo 2 Ti 2 AlC 3 hp16 P6 3 /mmc (194) (Cr 2/3 Zr 1/3 ) 2 AlC (Mo 2/3 Sc 1/3 ) 2 AlC ms48 C2/c (15) HfCr 2 MgNi 2 hp24 P63/mmc (194) Hf(Al 0.25 Cr 0.75 ) 2 MgZn 2 hp12 P63/mmc (194) Hf(Al 0.5 Cr 0.5 ) 2 MgZn 2 hp12 P63/mmc (194) Hf 3 Al 3 C 5 Zr 3 Al 3 C 5 hp22 P63/mmc (194) Hf 2 Al 3 C 4 Zr 2 Al 3 C 4 hp18 P63/mmc (194) HfAl 4 C 4 ZrAl 4 C 4 hp18 P-3m1 (164) Hf 2 Al 4 C 5 Zr 2 Al 4 C 5 hp33 R-3m (166) Hf 3 Al 4 C 6 Zr 3 Al 4 C 6 hp39 R-3m (166) HfAlC 2 ZrAlC 2 hp24 P6 3 /mmc (194) Hf 3 AlC Re 3 B op20 Cmcm (63) Hf 3 AlC CaTiO 3 cp5 Pm-3m (221) Hf 2 AlC Cr 2 AlC hp8 P6 3 /mmc (194) Hf 3 AlC 2 Ti 3 SiC 2 hp12 P6 3 /mmc (194) Hf 4 AlC 3 Ti 4 AlN 3 hp16 P6 3 /mmc (194) Cr 2 HfAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Hf 2 ZHrAlC 2 Cr 2 TiAlC 2 hp12 P6 3 /mmc (194) Cr 2 Hf 2 AlC 3 Mo 2 Ti 2 AlC 3 hp16 P6 3 /mmc (194) (Cr 2/3 Hf 1/3 ) 2 AlC (Mo 2/3 Sc 1/3 ) 2 AlC ms48 C2/c (15) S4

5 Fig. S1. Schematic representation of 10 collinear spin configurations considered for Cr / Zr / AlC in C2/c structure viewed along [010] where the spin direction at each Cr site is represented by a black arrow. Schematics were produced with VESTA XRD patterns of starting powders Fig. S2. XRD patterns of the starting powders of sample Z20 after multidirectional mixing for 24h. S5

6 3. d-spacings and corresponding 2θ angles Table S2. The d-spacings, corresponding 2θ angles, and relative intensities of the (hkl) reflections generated from the software starting with the lattice parameters from the refinement, together with the measured 2θ angles and relative intensities. h k l 2θ ( ) calculated d (Å) I/I max (%) calculated 2θ ( ) measured I/I max (%) measured S6

7 S7

8 S8

9 Magnetic information Table S3. Calculated energy and corresponding structural and magnetic information for (Cr 2/3 Zr 1/3 ) 2 AlC when considering different spin configurations. Relaxation performed using the PBE exchange-correlation functional. Spin configuration Space group a (Å) b (Å) c (Å) β ( ) E NM (mev/atom) magnetic moment (µ B / Cr atom) NM N/A FM AFM1 X2 goes to the NM state goes to the NM state A in-a1 in-a2 in-a3 in-a4 goes to the NM state goes to the NM state goes to the NM state goes to the FM state S9

10 Table S4. Calculated energy and corresponding structural and magnetic information for (Cr 2/3 Zr 1/3 ) 2 AlC when considering different spin configurations. Relaxation performed using the PBE exchange-correlation functional with +U method where U eff = 1 ev. Spin configuration Space group a (Å) b (Å) c (Å) β ( ) E NM (mev/atom) magnetic moment (µ B / Cr atom) NM N/A FM AFM X A in-a in-a in-a in-a S10

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