Supporting Information

Transcription

1 Supporting Information Designing an excellent deep-ultraviolet birefringent material for light polarization Xinglong Chen 1, Bingbing Zhang 1, Fangfang Zhang 1, Ying Wang 1, Min Zhang 1, Zhihua Yang 1 *, Kenneth R. Poeppelmeier 2 *, Shilie Pan 1 * 1 CAS Key Laboratory of Functional Materials and Devices for Special Environments, Xinjiang Technical Institute of Physics & Chemistry, CAS, Xinjiang Key Laboratory of Electronic Information Materials and Devices,40-1 South Beijing Road, Urumqi , China. 2 Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois , USA. These authors contributed equally to this work. *To whom correspondence should be addressed. zhyang@ms.xjb.ac.cn; krp@northwestern.edu; slpan@ms.xjb.ac.cn Phone: (+86) , Fax: (+86) S1

2 Figure S1. (a) Polarizability and (b) the average polarizability per oxygen atom of multi-chain (B 4 O 9 )n (n = 1, 2, 3, 4). From the result of the single-chain model, we can find that the interaction range of polarization among oxygen atoms which could reach a distance about 13 Å (a half-length of B 12 O 25 ). Therefore, the interactions among chains cannot be neglected in crystal. Here, we use B 4 O 9 as single chain to build multi-chain models extending along the x direction. It is of interest to find that, the polarizability along the x direction (P x ) increases faster than that of P y (Figure S1(a)), and the average polarizabilities increase along the x direction, decrease along the y direction, and finally reverse when the numbers of chains reach 4 (Figure S1(b)). Furthermore, the average anisotropy of polarizabilities between x and z direction also show a rising trend when the number of the chains increases. Figure S2. Calculated response electron distribution anisotropy (REDA) of the selected crystals by using the REDA approximation method. It is clear that [BO 2 ] -type crystals, including LiBO 2, Ca(BO 2 ) 2, Sr(BO 2 ) 2, facilitates the largest optical anisotropy (corresponding to the largest REDA values and birefringences from DFT code) among the selected crystals. S2

3 Figure S3. Crystal structure of Ca(BO 2 ) 2 : (a) Asymmetric unit; (b) Coordination of Ca and B atoms; (c) Unit cell; (d) [CaO 4 ] single layer viewed along the a-axis; (e) [CaO 4 ] layers viewed along the c-axis; (f) Three-dimensional crystal structure viewed along the c-axis. The Ca cations lie in (100) and (200) planes and are eight-coordinated forming the CaO 8 polyhedra. The CaO 8 polyhedra link with each other by edge-sharing to form the [CaO 4 ] layers parallel to the bc plane. The neighbouring [CaO 4 ] layers are further connected by [BO 2 ] infinite chains to form the three dimensional crystal structure. Figure S4. (a) Thermal TGA and DSC curves of Ca(BO 2 ) 2 ; (b) Experimental (original and after melting) and simulated XRD patterns of Ca(BO 2 ) 2. TGA curve shows that there is scarcely any weight loss up to 1200 C. Meanwhile, one endothermic (1152 C) and one exothermic (867 C) peaks are observed from DSC curve. The endothermic peak corresponds to the melting point and the exothermic peak represents the crystallization point. In addition, the powder XRD pattern of the solidified product after melting agrees with that of the initial Ca(BO 2 ) 2 powder, the results confirm that Ca(BO 2 ) 2 is a congruently melting compound without first-order S3

4 phase transition between room temperature and the melting point at atmospheric pressure. Figure S5. Thermal expansion vs. temperature curves. The thermal expansion curves along three crystallographic axes are almost linear in the measured temperature range, indicating that Ca(BO 2 ) 2 is stable between 100 and 600 C. The calculated average thermal expansion coefficients are α a = K 1, α b = K 1 and α c = K 1 from 100 to 600 C, respectively. Figure S6. Schematic representations of the Ca(BO 2 ) 2 right-angle prisms. For the two prisms, the (001) and (100) faces are the incident faces, respectively. S4

5 Figure S7. Fabricated Ca(BO 2 ) 2 prisms for refractive indices determination. Figure S8. Apparatus set up for laser extinction experiment of Ca(BO 2 ) 2 Glan polarizer. S5

6 Table S1. Crystal data and structure refinement for Ca(BO 2 ) 2. Empirical formula CaB 2 O 4 Formula weight (g mol 1 ) Temperature Crystal system 296(2) K Orthorhombic Space group, Z Pbcn, 4 Unit cell dimensions a = (4) Å b = (14) Å c = 6.209(2) Å Volume (Å 3 ) (18) Density (calculated) g cm 3 F(000) 248 Crystal size mm mm mm Theta range for data collection 3.51 to Limiting indices 15 h 14, 5 k 5, 8 l 5 Reflections collected / unique 1611 / 354 [R(int) = ] Completeness to theta = 27.51º % Refinement method Full-matrix least-squares on F 2 Goodness-of-fit on F Final R indices [F 2 o >2σ( F 2 o )] [a] R 1 = , wr 2 = R indices (all data) [a] R 1 = , wr 2 = Largest diff. peak and hole and e Å 3 [a] R 1 = Σ F o F c / Σ F o and wr 2 = [Σw(F o 2 F c 2 ) 2 / ΣwF o 4 ] 1/2 for F o 2 > 2σ(F o 2 ) S6

7 Table S2. Atomic coordinates ( 10 4 ) and equivalent isotropic displacement parameters (Å ) for Ca(BO 2 ) 2. U(eq) is defined as one third of the trace of the orthogonalized Uij tensor. Atoms x y z U(eq) Ca(1) (1) (1) B(1) 1921(2) 1702(5) 1257(4) 11(1) O(1) 2919(1) 3482(3) 1485(2) 15(1) O(2) 865(1) 2707(3) 908(2) 12(1) S7

8 Table S3. Selected bond distances (Å) and angles (deg) for Ca(BO 2 ) 2. Ca(1)-O(2)# (16) O(2)#1-Ca(1)-O(1) (5) Ca(1)-O(2)# (16) O(2)#2-Ca(1)-O(1) 79.44(5) Ca(1)-O(2)# (14) O(2)#3-Ca(1)-O(1) 70.58(5) Ca(1)-O(2)# (14) O(2)#4-Ca(1)-O(1) (5) Ca(1)-O(1)# (15) O(1)#5-Ca(1)-O(1) (7) Ca(1)-O(1) (15) O(2)#1-Ca(1)-O(2)# (4) Ca(1)-O(2)# (15) O(2)#2-Ca(1)-O(2)# (5) Ca(1)-O(2)# (15) O(2)#3-Ca(1)-O(2)# (3) B(1)-O(2) 1.316(3) O(2)#4-Ca(1)-O(2)# (6) B(1)-O(1) 1.392(2) O(1)#5-Ca(1)-O(2)# (4) B(1)-O(1)# (3) O(1)-Ca(1)-O(2)# (5) O(2)#1-Ca(1)-O(2)# (6) O(2)#1-Ca(1)-O(2)# (5) O(2)#1-Ca(1)-O(2)# (5) O(2)#2-Ca(1)-O(2)# (4) O(2)#2-Ca(1)-O(2)# (5) O(2)#3-Ca(1)-O(2)# (6) O(2)#1-Ca(1)-O(2)# (5) O(2)#4-Ca(1)-O(2)# (3) O(2)#2-Ca(1)-O(2)# (5) O(1)#5-Ca(1)-O(2)# (5) O(2)#3-Ca(1)-O(2)# (7) O(1)-Ca(1)-O(2)# (4) O(2)#1-Ca(1)-O(1)# (5) O(2)#6-Ca(1)-O(2)# (6) O(2)#2-Ca(1)-O(1)# (5) O(2)-B(1)-O(1) (19) O(2)#3-Ca(1)-O(1)# (5) O(2)-B(1)-O(1)# (18) O(2)#4-Ca(1)-O(1)# (5) O(1)-B(1)-O(1)# (16) Symmetry transformations used to generate equivalent atoms: #1 x + 1/2, y + 1/2, z #2 x + 1/2, y + 1/2, z + 1/2 #3 x + 1/2, y 1/2, z #4 x + 1/2, y 1/2, z + 1/2 #5 x + 1, y, z + 1/2 #6 x + 1/2, y + 1/2, z + 1/2 #7 x + 1/2, y + 1/2, z #8 x 1/2, y 1/2, z + 1/2 #9 x + 1/2, y + 1/2, z 1/2 #10 x 1/2, y + 1/2, z + 1/2 S8

9 Table S4. Space groups, fundamental building blocks (FBB), calculated and experimental bandgap (E g ), and calculated birefringence for selected crystals. One can easily find that the bandgaps calculated by HSE06 are very close to experimental ones and much better than those of GGA. The birefringences of selected crystals were calculated with correction of bandgap by using scissor operator. Crystals Space FBB E g E g E g n group (GGA a ) (HSE06 b ) nm Ca 3 (BO 3 ) 2 R3 c BO Sr 3 (BO 3 ) 2 R3 c BO no report NaBO 2 R3 c B 3 O no report KBO 2 R3 c B 3 O no report RbBO 2 R3 c B 3 O no report CsBO 2 R3 c B 3 O no report α-bab 2 O 4 R3 c B 3 O β-bab 2 O 4 R3c B 3 O Li 6 B 4 O 9 P2 1 /c B 4 O no report LiBO 2 P2 1 /c [BO 2 ] c Ca(BO 2 ) 2 Pbcn [BO 2 ] d Sr(BO 2 ) 2 Pbcn [BO 2 ] c a GGA represent Generalized Gradient Approximation b HSE06 represent Heyd, Scuseria, and Ernzerh of 06 c Data from our lab d This work S9

10 Table S5. Vickers hardness (HV) and Mohs hardness (HM) of (100), (010) and (001) face of the Ca(BO 2 ) 2 crystal. As we can see from the results, the Ca(BO 2 ) 2 crystal also exhibits anisotropy of mechanical property. Hardness (100) face (010) face (001) face HV HM S10

11 Table S6. Experimental and fitted refractive indices and birefringence of Ca(BO 2 ) 2. Wavelength (nm) n x (n c ) n y (n b ) n z (n a ) n (n z -n x ) Exp. Calc. Exp. Calc. Exp. Calc. Exp. Calc S11

12 Table S7. n x and n y of Ca(BO 2 ) 2 and the corresponding critical angle of total internal reflection (i c ) in the wavelength range from 170 to 200 nm. Wavelength (nm) n x i c-x ( ) n y i c-y ( ) S12