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1
Crystal Chemistry of Borates: the Classification and Algebraic
Description by Topological Types of Fundamental Building Blocks
Guanghui Yuan and Dongfeng Xue* State Key Laboratory of Fine Chemicals, Department of Materials Science and Chemical Engineering, School of Chemical Engineering, Dalian University of
Technology, 158 Zhongshan Road, Dalian 116012, China
* Corresponding author. E-mail: dfxue@chem.dlut.edu.cn
Supplementary
545 anhydrous borates and 296 hydrated borates are statisticed and classified into 6
kinds (single ∆ or T borates; branched borates; normal-ring borates; bridge-ring
borates; ‘8’-shaped-ring borates and combined-ring borates) based on the different
topological structures of their FBBs. Subsequent division related on the linkages
(isolate, chains, layers and networks) between these FBBs in borate structures. On the
basis of the two restrictive factors, all borates (including boron minerals and synthetic
borates) can be classified into 22 kinds, as shown in Figure 5 in article.
It should be noted that the FBBs of single ∆ or T borates are impossible to
polymerize layers or network. Because besides including the information of the
fundamental building block, the FBB should reflect the structure hypostasis of the
polyanions. When polymerizing layers or network, the anions must be connected
together in many ways and induce the FBB to become more complex structure block
not single ∆ or T. For example, although single BO4 (T) can repeat the polyanions in
LaAl2.03(B4O10)O0.54 (ICSD 59318), it couldn’t indicate the ring structure (Figure S1).
Therefore, the FBB of this compound is <6T> not T, and this compound is classified
as normal-ring layer borate with descriptor: 6: ∞2[<6T>].
2
a
(a)
(b)
Figure S1
(a) Two-dimensional anion-layer in the structure of LaAl2.03 (B4O10) O0.54. All the La
atoms and Al atoms are omitted for clarity. (b) FBB structure and FBB topology in
LaAl2.03 (B4O10) O0.54.
3
Tables S1 to S6 are for anhydrous borates and Tables S1’ to S6’ are for hydrated
borates. Some hypothesizes and treatments should be pointed out:
(1) Some multi-borates such as borate-silicates or borate-arsenates are ignored,
because in these compounds the bond valences of a bond Si-O in SiO4 or
As-O in AsO4 are higher than that of B-O in BO3 or BO4 structural unit. The
structural characteristics are dominated by the SiO4 or AsO4 structural units
and less by the borate units.
(2) In borate-phosphates, PO4 (T’) is treated as BO4 (T) because many
borate-phosphates (ICSD 409327, 409459, 409515, etc.) are synthesized and
their properties especially the nonlinear optical property are similar to borates,
furthermore, P atom can only form PO4 with O atom, which are stable
relatively.
(3) As for other multi-anion borates only poly-borate anions are considered.
(4) Some new borates, which are found or synthetic after ICSD (2004), are also
listed in these tables.
Table S1 Anhydrous borates with the Single BO3 or BO4 FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
LiGeBO4 T 0 Orthorhombic No
KGe2BO6 T 0 Orthorhombic No
α-Ag3BO3 ∆ 0 Trigonal No
K2LiBO3 ∆ 0 Monoclinic No
CaM(BO3)O ∆ 0 Orthorhombic No M=Al, Ga
BaRECu (BO3)O2 ∆ 0 Tetragonal No RE=La, Nd
MBe2BO3F2 ∆ 0 Monoclinic No M=Cs, Rb
KBe2BO3F2 ∆ 0 Trigonal No
M5BO9 ∆ 0 Orthorhombic No M5=Al5, Al4.5Cr0.5, Al4.8Cr0.2
(Ln)3WBO9 ∆ 0 Hexagonal No Ln=La, Eu
BaZr (BO3)2 ∆ 0 Trigonal No
BaZn2(BO3)2 ∆ 0 Orthorhombic No
4
MCu2 (BO3)2 ∆ 0 Tetragonal No M=Sr, Sr0.74Ba0.27, Sr0.66Ca0.34
MgBa2 (BO3)2 ∆ 0 Trigonal No
K3M3(BO3)2O6 ∆ 0 Hexagonal No M=Ta, Nb
Sr2Be2B2O7 ∆ 0 Hexagonal No
K2Al2B2O7 ∆ 0 Trigonal No
SrAl2B2O7 ∆ 0 Trigonal No
Ba3Ln(BO3)3 ∆ 0 Hexagonal No Ln=Lu, Ho, Tm, Yb, Sc
RECa4(BO3)3O ∆ 0 Monoclinic No RE=Gd, Sm, Tb, Lu, La, Nd,
Er, Y
Ca3(BO3)3F ∆ 0 Monoclinic No
MM’3(BO3)4 ∆ 0 Trigonal No MM’=YbAl, NdGa, NdAl,
CeSc, YAl, (Y0.5Eu0.5)Al,
CeSc, (Y0.9Eu0.1)Al,
(Y0.5Be0.5)Fe, LaFe, NdFe,
TbFe, (Nb0.5Ti0.5)Fe,
Y(Al0.5Ga0.5), β-LaSc
REAl3(BO3)4 ∆ 0 Monoclinic No RE=Gd, Yb, Gd0.97Eu0.03
Sr3(RE)2(BO3)4 ∆ 0 Orthorhombic No RE=Er, Nd, Pr, La
Pb3B4O9 ∆ 0 Trigonal No
Ca3La3(BO3)5 ∆ 0 Hexagonal No
Na3La9(BO3)8O3 ∆ 0 Hexagonal No
MBO3 ∆ 0 Trigonal Yes M=Al, Nd, Eu, Fe, In, Dy, Er,
Ti, Sm, Sc, (Sc0.75Tb0.25)
LnBO3 ∆ 0 Hexagonal Yes Ln=Gd, Ho, Er, Tm
M3BO3 ∆ 0 Monoclinic Yes M=Li, Na
LaBO3 ∆ 0 Monoclinic Yes
MZn4BO3 ∆ 0 Monoclinic Yes M=K, Rb
β-Ag3BO3 ∆ 0 Trigonal Yes
M3PBO3 ∆ 0 Hexagonal Yes M=Sr, Ba
CrBO3 ∆ 0 Orthorhombic Yes
REBO3 ∆ 0 Trigonal Yes RE=Yb, Lu, V
MM’BO3 ∆ 0 Monoclinic Yes MM’=LiCo, NaBa, LiFe,
LiMg, LiBa, LiSr, LiMn,
LiZn, Li1.13Zn0.93
LiCdBO3 ∆ 0 Cubic Yes
MM’2BO3 ∆ 0 Orthorhombic Yes MM’2=KNa2, CsNa2, RbNa2,
KLi2
M2(BO3)O ∆ 0 Orthorhombic Yes M2= Mn2, Co1.5Zr0.5, α-PbAl,
β-PbAl, Co1.5Ti0.5,
Mg1.33Al0.21Fe0.12Ti0.34,
Mg1.1Fe0.64Ti0.16Al0.1
MM’(BO3)O ∆ 0 Orthorhombic Yes MM’=CaY, SrAl, MgSc,
MgGa, NiSc, FeMn, FeCo,
FeZn, PbGa,
5
Mg(Mg0.12Fe0.64Al0.1Ti0.16)
MM’(BO3)O ∆ 0 Monoclinic Yes MM’= Mn(Al0.5Y0.5),
(Mg0.76Mn0.24)Mn, FeFe, Li2Al
Be2BO3F ∆ 0 Monoclinic Yes
Ca2BO3Cl ∆ 0 Monoclinic Yes
Gd3(BO3)F3 ∆ 0 Monoclinic Yes
M2M’(BO3)O2 ∆ 0 Orthorhombic Yes M2M’=Ni2Cr, Cu2Al, Mn2Mn,
Ni2Al, Ni2Fe, Ni2Ga, Ni2V,
(Mg1.81Mn0.08Fe0.01)Mn,
Mg1.9(Mn0.91Sb0.19),
(Fe1.25Mg0.75)Fe,
(Mg1.85Fe0.15)(Fe0.60Al0.40),
(Mg1.92Fe0.0825)(Fe0.566Al0.41Ti0.02)
Mg1.93Fe0.967Al0.093,
Mg1.941Fe0.967Al0.083,
Mg1.966Fe0.911Al0.118,
Mg2.11Al0.31Fe0.53Ti0.05,
Mg2.33Al0.17Fe0.37Ti0.02Sb0.12,
Mg1.707Fe1.213Al0.08,
(Mg1.84Fe0.16)(Fe0.54Ti0.21Mg0.15Al0.10)
LiU(BO3)O2 ∆ 0 Monoclinic Yes
M3(BO3)O2 ∆ 0 Orthorhombic Yes M3=Co3, Co2.1Al0.9,
Mg1.71Mn1.29,
Mg1.33Mn1.49Sb0.17,
Mg1.93Mn1.07,
Mg1.98Fe0.02Mn0.78Fe0.2Al0.02,
Mg1.25Mn1.57Sb0.18,
Mg1.42Mn1.43Fe0.22Mn0.88
NaU(BO3)O2 ∆ 0 Orthorhombic Yes
Li0.31V0.69(BO3)O2 ∆ 0 Orthorhombic Yes
M2M'(BO3)O2 ∆ 0 Monoclinic Yes M2M’=Cu2Fe, Cu2Ga, Mn2Sr
M3(BO3)2 ∆ 0 Orthorhombic Yes M=Mg, Co, Ni, Mn, Sr, Cd
M3(BO3)2 ∆ 0 Trigonal Yes M=Ca, Hg, Eu
MM’(BO3)2 ∆ 0 Trigonal Yes MM’=SrSn, BaZr, MgSn,
CaSn, K2Zr,
(Mn0.83Fe0.15Ca0.02)Sn,
(Mn0.83Fe0.15Ca0.02)Sn
M2M’(BO3)2 ∆ 0 Monoclinic Yes M2M’=Sr2Cu, Ba2Ca, Be2Sr,
Zn2Zn
CsLi5(BO3)2 ∆ 0 Monoclinic Yes
MM’2(BO3)2 ∆ 0 Orthorhombic Yes MM’2=BaBe2, BaZn2, CuBa2
Li3RE(BO3)2 ∆ 0 Monoclinic Yes RE=In, Gd, Al
Li4Ca(BO3)2 ∆ 0 Orthorhombic Yes
M2M’2(BO3)2O ∆ 0 Trigonal Yes M2M’2=Na2Al2, K2Ga2,
6
Zn2Zn2
Na2Gd2(BO3)2O ∆ 0 Monoclinic Yes
Ca(RE)2 (BO3)2O ∆ 0 Trigonal Yes RE=Al, Eu
Mg3Ti (BO3)2O2 ∆ 0 Orthorhombic Yes
Sr2Al2 (BO3)2O2 ∆ 0 Orthorhombic Yes
Bi4(BO3)2O3 ∆ 0 Monoclinic Yes
M5M’(BO3)2O4 ∆ 0 Orthorhombic Yes M5M’=Co5Sn, Co5Mn, Cu5Sn,
Ni5Ti, Ni5Mn, Ni5Ge, Ni5Zr,
Ni5Sn, Ni5(Ni0.33Sb0.67),
Ni5(Ni0.33Ta0.67), Ni5Hf, Ni5V,
Zn5Mn
M3M’3(BO3)2O4 ∆ 0 Monoclinic Yes M3M’3=Nb3(Nb2.33Nb0.67),
Mg3Sn3
Nd2Sr3Cu3(BO3)2O6 ∆ 0 Tetragonal Yes
Ba3Ti3(BO3)2O6 ∆ 0 Hexagonal Yes
Ba2RE(BO3)2Cl ∆ 0 Monoclinic Yes RE=Yb, Ho
Li2Yb5(BO3)3O4 ∆ 0 Monoclinic Yes
LiLn6(BO3)3O5 ∆ 0 Monoclinic Yes Ln=Pr→Tm, Y
Li6RE(BO3)3 ∆ 0 Monoclinic Yes RE=Yb, Ho
Ba3Dy(BO3)3 ∆ 0 Trigonal Yes
MM’4 (BO3)3 ∆ 0 Cubic Yes MM’4=LiSr4, NaSr4, NaBa4
Sr3Sc(BO3)3 ∆ 0 Trigonal Yes
Sr5(BO3)3F ∆ 0 Orthorhombic Yes
Cu2Al6(BO3)4O5 ∆ 0 Tetragonal Yes
Ba3(RE)2(BO3)4 ∆ 0 Orthorhombic Yes RE=La, Pr, Nd
MM’3 (BO3)4 ∆ 0 Monoclinic Yes MM’3=LaSc3, NdAl3, PrSc3
Ba2Sc2B4O11 ∆ 0 Monoclinic Yes
Al6(BO3)5F3 ∆ 0 Hexagonal Yes
Sr6RESc(BO3)6 ∆ 0 Trigonal Yes RE=Ho, Y
La26B8O21 ∆ 0 Monoclinic Yes
Sb3Mn8.72Al0.28Mn21.4
Mg13.6(BO3)16O32 ∆ 0 Orthorhombic Yes
MBO4 T 0 Tetragonal Yes M=Nb, Nb0.53Ta0.47, Ta
AlMgBO4 T 0 Orthorhombic Yes
BaBOF3 T 0 Orthorhombic Yes F is treated as O
Al4Co(BO4)2O2 T 0 Monoclinic Yes
Ni2NbBO6 T 0 Orthorhombic Yes
(RE)3BO6 T 0 Orthorhombic Yes RE=Cr, Fe
Ni7U(BO4)4 T 0 Orthorhombic Yes
Na2AlAs4BO14 T 0 Monoclinic Yes
PbAsBO5 T 1 Trigonal No
BaAsBO5 T 1 Hexagonal Yes
MB2O4 ∆ 1 Orthorhombic Yes M=β-Ca, Sr, Eu
7
Table S2 Anhydrous borates with the Branched FBB
Chemical
Formula
FBB R Crystal System Centro
symmetric
Note
BaCuB2O5 2∆ 0 Monoclinic No
MM’B2O6 2∆ 0 Monoclinic No MM’=RbNb, CsTa,
CsNb, TlNb
Cu(Cu1.63Zn0.37)
Se2B2O7 2T 0 Orthorhombic No
CaU2B2O10 2∆ 0 Monoclinic No
*Li3Eu2B3O9 2∆ & ∆ 0 Monoclinic No
Cr2BP3O12 ∆3 |T’| 0 Trigonal No
Pb6BP5O20 T 4 |T’| 0 Tetragonal No
*Y16.86B8O38 2∆ & ∆ 0 Monoclinic No
χ-LnBO3 ∆2T 0 Triclinic Yes Ln=Dy, Er
LnB2O4Cl 2∆ 0 Triclinic Yes Ln=La, Pr
MM’B2O5 2∆ 0 Triclinic Yes MM’=MgMn, MnCo,
Ni1.5Zn0.5, Co2, Cd2,
(β-Mg)2, (Co1.5Zn0.5)2
MB2O5 2∆ 0 Monoclinic Yes M=Th, U, Na4, Mg2,
Sr2, Ca2
MM’B2O5 2∆ 0 Monoclinic Yes MM’=CaMn, MgCa,
NaSc, LiAl
Er2B2O5Cl2 2∆ 0 Orthorhombic Yes
MCu2B2O6 2∆ 0 Monoclinic Yes M=Co, Cd
*Cu3B2O6 2∆ & ∆ 0 Triclinic Yes
Co5BP3O14 ∆T’ 0 Monoclinic Yes
MgUB2O7 2∆ 0 Orthorhombic Yes
MGa2B2O7 2∆ 0 Orthorhombic Yes M=Sr, Ba
M2M’M’’B4O10 2∆ 0 Monoclinic Yes M2M’M’’=Sr2LiSc,
Sr2LiIn,
Ca2(Mg0.86Fe0.14)(Mg0.92Fe0.08)
Ba5B4O10F2 2∆ 0 Monoclinic Yes
*Sr2Sc2B4O11 2∆ & ∆ 0 Triclinic Yes
*Ho8.66B4O19 2∆ & ∆ 0 Monoclinic Yes
Cu9Ti2B6O16 2∆ 0 Triclinic Yes
TlBO2 ∆T 1 Tetragonal No
CuLnB5O10 T 4 |∆| 1 Orthorhombic No Ln=Tb, Lu, Tm
CaBeB2O5 ∆2T∆ 1 Monoclinic Yes
Ba3BP3O12 T 3 |T’| 1 Orthorhombic Yes
BiB3O6 ∆T∆ 2 Monoclinic No
Li14BeB10O27 T 4 |∆| 2 Hexagonal Yes
Li4B7O12Cl ∆T∆ 3 Cubic No
NiGdB5O10 O 4 |T| 3 Cubic No
8
M3B7O13X O 4 |T| 3 Cubic No M...X=Cr..Br,
Cr..Cl, Cr..I,
Mn..Br, Ni..I,Co..I
Cu..Br, Cu..I,
Fe..I, β-Mg..Cl
Table S3 Anhydrous borates with the Normal-ring FBB
Chemical
Formula
FBB R Crystal
System
Centro
symmetric
Note
GdBO3 <3T> 0 Trigonal No
β-BaB2O4 <3∆> 0 Trigonal No
YBO3 <3T> 0 Orthorhombic Yes
α-BaB2O4 <3∆> 0 Trigonal Yes
Sr3B3O3N3 <3∆> 0 Monoclinic Yes N is treated as O
MM’B6O12 <3∆> 0 Trigonal Yes MM’=Ba2Ca,
Ba2Co,
Sr1.16Ba1.84,
Ba2Mn
Ba2ZnB6O12 <3∆> 0 Triclinic Yes
AgBO2 <∆2T> + ∆ 1 Orthorhombic Yes
LiBa2B5O10 ∆ + <∆2T> + ∆ 1 Monoclinic Yes
Cu(RE)2B8O16 |∆|∆| +<2∆2T> +|∆|∆| 1 Monoclinic Yes RE=Tb, Dy, Ho
Bi2B8O15 ∆T + <3∆> + ∆T∆ 2 Monoclinic No
La0.785Th0.215
Al2B4O10O0.67
<6T> 2 Hexagonal No
REAl2.03B4O10O0.54 <6T> 2 Hexagonal No RE=La, Nd
*Ba2Al3Nd2B12O27.5 <6T> & <6∆> 2 Hexagonal No
CaAlB3O7 <3T> 2 Orthorhombic Yes
MZnBP2O8 T’ + <2T2T’> + T’ 2 Monoclinic Yes M=K, NH4
Pb3BP3O12 T + <∆2T> + T 2 Orthorhombic Yes
NiHo2B4O10 <4T> 2 Monoclinic Yes
Cu(Ln)2B4O10 <4T> 2 Monoclinic Yes Ln=Tm, Ho, Lu, Er
(RE)4B6O15 2T + TT + 2T 2 Monoclinic Yes RE=Dy, Ho
*Ba2KZn3B9O19 <3∆> & 2<2∆T> 2 Triclinic Yes
M3B3O6 <3∆> 2 Trigonal Yes M=Na, K, Rb, Cs
γ-LiBO2 <6T> 3 Tetragonal No
MB3O5 <2∆T> 3 Orthorhombic No M=Li, Cs, Rb, Tl
CsLiB6O10 <2∆T> 3 Tetragonal No
MM’B9O15 <2∆T> 3 Trigonal No MM’=BaLi,
BaNa, SrLi
α-CsB9O14 <3∆> + <2∆T> +
<3∆>
3 Tetragonal No
9
CsAl4Be4B12O18 <4T> 3 Cubic No
MB2O4 <3T> 3 Tetragonal No M=Pb, Cu
M4B6O13 <4T> 3 Cubic No M=Zn, Co
Li4NaKAl4Be3
B10O27
<3T> 3 Cubic No
Zn6Ga2P6B12O24 <4T> 3 Cubic No
Zn8Se2B12O24 <4T> 3 Cubic No
SrB2O4 <3T> 3 Cubic Yes
CaB2O4(IV) <3T> 3 Cubic Yes
LnBa3B9O18 <3∆> 3 Hexagonal Yes Ln=Pr→Yb
M3B7O12 <2∆T> + <∆2T> + ∆ 3 Triclinic Yes M=Na, Li
β-REB5O9 <∆2T> + |∆|∆| 3 Monoclinic Yes RE=Ce, La
Table S4 Anhydrous borates with the Bridge-ring FBB
Chemical
Formula
FBB R Crystal
System
Centro-
symmetric
Note
Na3GaB4O9 <2∆2T>b 0 Monoclinic Yes
Pb6B10O21 <2∆2T>b + 2∆ +
<2∆2T>b
0 Triclinic Yes
Na5B2P3O13 <2T2T’> + T’ 1 Monoclinic No
β-Dy2B4O9 ∆ + <6T>2b + ∆ 1 Triclinic Yes
Na3B6O9VO4 <3∆3T>B 2 Orthorhombic No
α-(Ln)2B4O9 |T|T| +<14T+TT>B, 2b
+ |T|T|
2 Monoclinic Yes Ln=Eu, Gd, Tb, Dy
Ca2Al2B6O14 <8T>b 2 Orthorhombic Yes
Li2B4O7 <2∆2T>b 3 Tetragonal No
MB4O7 <8T>2b 3 Orthorhombic No M=β-Sr, Pb, Eu, β-Ca
M3B7O13X <6T>B + ∆ 3 Orthorhombic No M=Mn, Fe, Mg, Co,
Ni, X=Cl, Br, I
M3B7O13Cl <6T>B + ∆ 3 Trigonal No M=Mg, Fe,
Li5B7O12.5Cl <6T>B + ∆ 3 Cubic No
LnB3O6 <6T>B 3 Orthorhombic Yes Ln=Dy, Ho, Er, Tm,
Yb, Lu
MB4O7 <2∆2T>b 3 Orthorhombic Yes M=Co, Cd, Mn, Zn
Hg, Mg
β-ZnB4O7 <8T>2b 3 Orthorhombic Yes
α-LnB5O9 <2∆2T>b + ∆ 3 Orthorhombic Yes Ln=Pr, Nd, Sm, Pm, Eu
M3B7O13Cl <6T>B + ∆ 3 Trigonal Yes M=Fe2.4Mg0.6,
Mg1.55Fe1.43Mn0.02
10
Table S5 Anhydrous borates with the ‘8’-shaped-ring FBB
Chemical
Formula
FBB R Crystal
System
Centro
symmetric
Note
CaNa3B5O10 <4∆T>8 0 Triclinic Yes
Li2AlB5O10 <4∆T>8 0 Monoclinic Yes
Bi2B5O12 <3∆2T>8 0 Orthorhombic Yes
BaBPO5 <∆4T’>8 1 Trigonal No
MBPO5 T’ + <2T3T’>n-8 +T’ 1 Trigonal No M= Ca, Pb, Sr
TlBO2 <2∆3T>n-8 + ∆ 1 Tetragonal No
AgBO2 <2∆3T>n-8 + ∆ 1 Orthorhombic Yes
CaB2O4(II) <2∆3T>n-8 + ∆ 1 Orthorhombic Yes
MM’BP2O8 T + <7T>n-8 + T 1 Triclinic Yes MM’=CsZn, RbZn,
(NH4)(Zn0.88Co0.12),
(NH4)Zn
REB3O6 <4∆3T>n-8 1 Orthorhombic Yes RE=La, Pr, Tb, Nd
Li5.5Fe0.5FePb
B12O24
<2∆3T>n-8 + ∆ 1 Trigonal Yes
La2CaB10O19 <2∆3T>8 2 Monoclinic No
MM’B5O10 <2∆3T>8 2 Monoclinic Yes MM’=YCo, LaCo,
YbCo, HoCo,
SmCo,NdCo,
CdLa,CdSm,
CdEu, NiNd,
NiGd, CeZn,
NdZn, TbZn,
LaMg
α-CsB5O8 <4∆T>8 2 Monoclinic Yes
MM’B5O9 <3∆2T>8 2 Monoclinic Yes MM’=NaCa, SrK
Cs3B7O12 <4∆3T>2-8 +
10<3∆2T>8 +
<2∆3T>8 + T
2 Monoclinic Yes
(MM’)2B10O17 <3∆2T>8 2 Monoclinic Yes MM’=CsNa, CsK,
TlNa
CaB2O4(III) <∆4T>8 + ∆ 3 Orthorhombic No
M2B5O9X <2∆3T>8 3 Orthorhombic No M=Ca, Ba, Pb, Eu
X=Cl, Br
Ag2CsB15O24 <4∆T>8 3 Orthorhombic No
β-Tl2B4O7 <2∆3T>8 +
<4∆3T>2-8
3 Triclinic Yes
MB5O8 <4∆T>8 3 Orthorhombic Yes M=α-K, β-K,
α-Rb, β-Rb, Tl,
β-Cs, γ-Cs
Ca2B6O11 <2∆3T>8 + T 3 Monoclinic Yes
11
Table S6 Anhydrous borates with the Combined-rings FBB
Chemical
Formula
FBB R Crystal
System
Centro
symmetric
Note
Rb3B7O12 <3∆2T>8 + T + <2∆T> +
<3∆2T>8
2 Triclinic Yes
AgSrB7O12 <2∆T> + T∆ + <2∆2T>b +
∆T + <2∆T>
2 Monoclinic Yes
β-Na3B9O15 <4∆T>8 + <2∆T> + T 2 Monoclinic Yes
BaB8O13 <4∆T>8 + <∆2T> 3 Tetragonal No
M2M’2B8O14 <4∆T>8 + <∆2T> 3 Orthorhombic No MM’=KLi,
RbLi
BaB4O7 <3∆2T>8 + <∆2T> 3 Monoclinic Yes
Na4B8O14 <3∆2T>8 + <2∆T> 3 Triclinic Yes
Na3B9O15 <4∆T>8 + <2∆T> + T 3 Monoclinic Yes
M2B8O13 <4∆T>8 + <2∆T> 3 Monoclinic Yes M=α-Na,
β-Na, α-Ag,
β-Ag
K3AlB8O15 <4∆T>8 + <2∆T> 3 Monoclinic Yes
Cs3B13O21 2<4∆T>8 + 4(<2∆T> + ∆) 3 Monoclinic Yes
M5B19O31 2(<4∆T>8 + ∆ + <2∆T>)
+T
3 Monoclinic Yes M=K, Rb
M2B4O7 <2∆2T>b + <∆2T> + ∆ 3 Triclinic Yes M=K, Rb
CaB4O7 <2∆2T>b + T + <2∆T> 3 Monoclinic Yes
α-NaB3O5 <4∆T>8 + <2∆2T>b 3 Monoclinic Yes
Na6B13O22.5 <3∆2T>8 + <2∆2T>b +
<2∆2T>b
3 Orthorhombic Yes
Table S1’ Hydrated borates with the Single BO3 or BO4 FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
Be2BO3(OH)(H2O) ∆ 0 Trigonal No
β-Be2BO3(OH)(H2O) ∆ 0 Hexagonal No
Zn2BO3(OH)0.75F0.25 ∆ 0 Monoclinic No
Ca3Mg(BO3)(CO3)(H2O)x ∆ 0 Cubic No x=0.125, 0.36
Mg6.05Al0.3Fe0.15(BO3)3(OH)4Cl0.4 ∆ 0 Orthorhombic No
Pb5B3O8(OH)3(H2O) ∆ 0 Hexagonal No
NaBF3(OH) ∆ 0 Hexagonal No F is treated as O
Na2BO2(OH) ∆ 0 Orthorhombic Yes
SrBO2(OH) ∆ 0 Orthorhombic Yes
Be2BO3(OH) ∆ 0 Orthorhombic Yes OH=
(OH)0.94F0.06,
12
(OH)0.93F0.07,
(OH)0.7F0.3,
(OH)0.59F0.41,
(OH)0.52F0.48
Cu2BO(OH)5 ∆ 0 Orthorhombic Yes
CdBO3(OH) ∆ 0 Cubic Yes
Mg3BO3(OH)3 ∆ 0 Hexagonal Yes
Mg5O(BO3)(OH)5(H2O)1.4 ∆ 0 Monoclinic Yes
Sr3Ga3O(BO3)4(OH) ∆ 0 Monoclinic Yes
LiNdBO3(OH) T 0 Monoclinic No
LiB(OH)4(H2O)6 T 0 Trigonal No
CsB(OH)4(H2O)2 T 0 Tetragonal No
Ca2Cu(OH)4B2(OH)8 T 0 Triclinic No
SrB2(OH)8 T 0 Triclinic No
Ca2AsO4B(OH)4 T 0 Tetragonal No
MB(OH)4 T 0 Orthorhombic Yes M=Li, Na
Na2B(OH)4Cl T 0 Tetragonal Yes
CuB(OH)4Cl T 0 Tetragonal Yes
NaB(OH)4(H2O)2 T 0 Triclinic Yes
NaHoBO2(OH)3 T 0 Monoclinic Yes
YB(OH)4(CO3) T 0 Orthorhombic Yes
Mn3B(OH)4(PO4)(OH)2 T 0 Orthorhombic Yes
AgBF4(H2O) T 0 Orthorhombic Yes F is treated as O
LiBF4(H2O) T 0 Orthorhombic Yes F is treated as O
Hg2BF4(OH) T 0 Orthorhombic Yes F is treated as O
CaB2(OH)8 T 0 Triclinic Yes
β-CaB2(OH)8 T 0 Orthorhombic Yes
MB2(OH)8(H2O)2 T 0 Monoclinic Yes M=Ca, x=2;
M=Ba, x=1
CaB2O4(H2O)6 T 0 Monoclinic Yes
MB2(OH)8 T 0 Monoclinic Yes M=β-Sr, Ba
BaB2O4(H2O)5 T 0 Monoclinic Yes
Mg3B2(OH)8(SO4)(OH)2 T 0 Orthorhombic Yes (OH)2=(OH)F
MgCa2B2(OH)8(CO3)(H2O)4 T 0 Monoclinic Yes
MgB2(PO4)2(OH)6(H2O)6 T 0 Triclinic Yes
Mg2Al3O(BO4)2(OH) T 0 Monoclinic Yes
CaB2O2(OH)4 T 1 Monoclinic Yes
Table S2’ Hydrated borates with the Branched FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
K3B3O4(OH)4(H2O)2 2∆T 0 Orthorhombic No
Mg2B2O(OH)6 2T 0 Tetragonal No
13
MgBP2O7(OH)3 T’TT’ 0 Triclinic No
M2B2O4(OH)2 2∆ 0 Monoclinic Yes M2=Mg2,
Mn1.812Mg0.188
Mg2B2O4(H2O)3 2T 0 Tetragonal Yes
CaB2O(OH)6(H2O)2 2T 0 Triclinic Yes
NH4AlBP2O8(OH) T’TT’ 0 Monoclinic Yes
(NH4)5V3BP3O19(H2O) T 3|T’| 0 Triclinic Yes
CsV3B2P4(OH)4O16(H2O)2 T’TT’ 0 Monoclinic Yes
Mn14Mg0.5(B2O5)4(Si0.5O2.2)
(OH)9.8Cl0.8
2∆ 0 Tetragonal Yes
(NH4)6V12B6P12O60(OH)12(H2O)12 T’TT’ 0 Trigonal Yes
MM’BP2O7(OH)3 T’TT’ 1 Monoclinic Yes MM’=NaFe,
NaAl, NaV,
NaGa, NaIn,
KGa, KAl
FeBP2O7(OH)5 T’T 1 Monoclinic Yes
RbMM’BP2O8(OH) T’TT’ 1 Monoclinic Yes MM’=RbV, RbAl,
RbGa, RbFe,
CsFe, CsAl, Pb2,
CsGa, NH4Fe,
NH4Ga, NH4V,
NH4Fe0.47V0.50
Na2BP2O7(OH) T’TT’ 2 Monoclinic No
Table S3’ Hydrated borates with the Normal-ring FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
KBO2(H2O) <∆2T> 0 Orthorhombic No
M3B3O4(OH)4(H2O)2 <∆2T> 0 Orthorhombic No M=K, x=2;
M=Rb, x=1
Na1.89Ag0.11BP2O7(OH) <3T3T’> 0 Orthorhombic No
Li2B2O4(OH)4 <2T> 0 Monoclinic Yes [3]
Na2B2O4(OH)4(H2O)6 <2T> 0 Triclinic Yes [3]
CaB2O2(OH)4 <3T> + T 0 Monoclinic Yes
MgBPO4(OH)2(H2O)2 <3T’3T> 0 Trigonal Yes
KB3O5(H2O)3 <2∆T> 0 Monoclinic Yes
MB3O3(OH)5(H2O)5 <∆2T> 0 Monoclinic Yes M=Mg, x=5;
M=Ca, x=4
Ca2B3O4(OH)4Cl <∆2T> 0 Monoclinic Yes
MB3O3(OH)5(H2O)5 <∆2T> 0 Triclinic Yes M=β-Mg, x=5
M=Ca, x=1, 2
Ca2B3O3(OH)7(H2O)3 <3T> 0 Triclinic Yes
ZnB3O5(OH)5(H2O) <∆2T> 0 Orthorhombic Yes
14
NaInBP2O8(OH) T’ + <2T2T’> + T’ 0 Monoclinic Yes
MM’BP2O8(OH) T’ + <2T2T’> + T’ 0 Triclinic Yes MM’=RbIn, KIn,
NH4In, KFe
MgB4O4(OH)6(H2O)6 <∆2T> + T 0 Monoclinic Yes
Ca4MgB4O6(OH)6(CO3)2 <4T> 0 Monoclinic Yes
Ca2B4O4(OH)7Cl(H2O)7 <3T> + T 0 Monoclinic Yes
Na6B6O12(H2O)2 <2∆T> 0 Orthorhombic Yes
Na2B6O6(OH)8 <2∆T> 0 Monoclinic Yes
M2B6O11(H2O)15 <∆2T> 0 Triclinic Yes M=Mg, x=15;
M=Ca, x=7, 9
β-Mg2B6O11(H2O)15 <∆2T> 0 Monoclinic Yes
CaMgB6O6(OH)10(H2O)6 <∆2T> 0 Monoclinic Yes
Ca3B6O6(OH)12(H2O)2 <3T> 0 Monoclinic Yes
Ni1.5Mg1.5B3P3O12(OH)6
(H2O)6
<3T’3T> 0 Trigonal Yes
K3PtB7O11(OH)6(H2O)3 |∆|∆| +<∆2T> +|∆|∆| 0 Orthorhombic Yes
BiB4O6(OH)3 <2∆T> + T 1 Triclinic No
CaB3O4(OH)3(H2O) <∆2T> 1 Monoclinic Yes
TlB3O4(OH)2(H2O)0.5 <2∆T> 1 Orthorhombic Yes
Na2B4O7(H2O)10 <4∆> 1 Monoclinic Yes
LiB3PO6(OH)3 <2∆T> + T’ 1 Orthorhombic Yes
(NH4)2B3PO7(OH)2 <2∆T> + T’ 1 Monoclinic Yes
*Ca2SiB5O9(OH)5 <∆2T> & 2T 1 Monoclinic Yes SiO4 is ignored
KB6PO10(OH)4 <∆2T>+T’+<∆2T> 1 Tetragonal Yes
CaMgB6O8(OH)6(H2O)3 <∆2T> 1 Monoclinic Yes
CaB3O5(OH) <∆2T> 2 Orthorhombic No
REB4O6(OH)2Cl <∆2T> + ∆ 2 Monoclinic No RE=Pr, Nd
Ca3B5O6(OH)7Cl(H2O)8 <6∆6T> 2 Monoclinic No
CaB3O4(OH)3 <∆2T> 2 Monoclinic Yes
Co(C2H10N2)B2P3O12(OH) T’ + <T’2T> + T’ 2 Orthorhombic Yes
K3CuB2P4O14(OH)3 T’ + <2TT’> + |T’|T’| 2 Monoclinic Yes
Rb2Co3B4P6O24(OH)2
(H2O)2
T’ + <2TT’> + T’ 2 Orthorhombic Yes
(Cs0.52K0.42)BeAlB11O27(H2O) <4T> 3 Cubic No
Ca16MgB13O17(OH)12)4
Cl6(H2O)28
|T|T| ∆ +<∆2T> +
∆T |∆|∆| + ∆ |T|T| 3 Orthorhombic No
MB2P2O8(OH) T’ + <2TT’> 3 Monoclinic Yes M=Rb, Cs
LnB6O9(OH)3 <3∆3T> 3 Trigonal Yes Ln=Sm→Lu
Ca2B8O13(OH)2 ∆+<2∆T>+T+<∆2T> 3 Triclinic Yes
MgB12O19(H2O)5 <2∆T> + <∆2T> 3 Monoclinic Yes
15
Table S4’ Hydrated borates with the Bridge-ring FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
(NH4)2B4O5(OH)4(H2O)2 <2∆2T>b 0 Monoclinic No
K2B4O5(OH)4(H2O)2 <2∆2T>b 0 Orthorhombic No
Na2B4O5(OH)4(H2O)x <2∆2T>b 0 Trigonal No x=3, 2.668
K1.67Na0.33B4O5(OH)4(H2O)3 <2∆2T>b 0 Hexagonal No
Ca(RE)2(B4O5(OH)4)2(H2O)8 <2∆2T>b 0 Orthorhombic No MM2’=CaK2,
Ca(NH4)2,
SrRb2, x=8;
MM2’=SrK2,
x=10
β-NiB6O7(OH)6(H2O)5 <3∆3T>B 0 Triclinic No
*K7MnB13O21(OH)6(H2O) <6∆6T>6b & ∆ 0 Orthorhombic No
M2B4O5(OH)4(H2O)x <2∆2T>b 0 Monoclinic Yes M2=NaRb, x=4;
M2=Na2, x=8;
M2=Cs2, x=3
Ca2MnB4O7(OH)6 <2∆2T>b 0 Orthorhombic Yes
Rb2B4O5(OH)4(H2O)3.6 <2∆2T>b 0 Orthorhombic Yes
MB4O5(OH)4(H2O)7 <2∆2T>b 0 Triclinic Yes M=Mn, Mg
MgB6O7(OH)6(H2O)2 <3∆3T>B 0 Orthorhombic Yes
MB6O7(OH)6(H2O)x <3∆3T>B 0 Monoclinic Yes M=Mg, x=3;
M=Mg, x=4;
M=Ni, x=5;
M=Ni(C2H5OH)
x=3.42
Ca4MgAs2(B6O7(OH)6)2
(H2O)14
<3∆3T>B 0 Monoclinic Yes
Na6Mg(B6O7(OH)6)4(H2O)10 <3∆3T>B 0 Monoclinic Yes
M2M’(B6O7(OH)6)2(H2O)4 <3∆3T>B 0 Triclinic Yes M2M’=K2Co,
K2NH4, K2Mg
x=4;
M2M’=Na2Co,
x=8.67
Mg2(B6O7(OH)6)2(H2O)9 <3∆3T>B 0 Trigonal Yes
Na8B12O20(OH)4 <6∆6T>6b 0 Monoclinic Yes
Ag6B12O18(OH)6(H2O)3 <6∆6T>6b 0 Monoclinic Yes
ZnB2O4(H2O)1.12 <6∆6T>6b 0 Trigonal Yes
*Na4Cu3B2P4O15(OH)2
(HPO4)2
T’ + <2T2T’>b
+ T’ & T’
0 Monoclinic Yes
K6UO2B16O24(OH)8(H2O)12 <8∆8T>8b 0 Monoclinic Yes
16
Rb4V6O6B20O32(OH)12
(H2O)0.5
<3∆7T>3B 0 Monoclinic Yes
Na2MgB12O16(OH)8(H2O)4 <3∆3T>B 1 Monoclinic Yes
MB8O13(H2O)2 <3∆3T>B + 2∆ 2 Monoclinic No M=Ca, Sr, Pb
CaB3O5(OH) <2∆4T>2b 2 Monoclinic Yes
Na2B4O6(OH)2 <2∆2T>b 2 Monoclinic Yes
LnB8O11(OH)5 ∆T + <3∆3T>B 2 Monoclinic Yes Ln=La→Nd
SrCaB14O24(OH)6(H2O)5 <3∆3T>B +
<3∆3T>B + 2∆
2 Monoclinic Yes
Co3B7O13F(OH) <3∆3T>B + ∆ 3 Trigonal No
Cd3B7O13(OH) <3∆3T>B + ∆ 3 Trigonal No
*Pb3B10O16(OH)4 <3∆6T>B,3b & ∆ 3 Trigonal No
Table S5’ Hydrated borates with the ‘8’-shaped-ring FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
KB5O8(H2O)4 <4∆T>8 0 Orthorhombic No
MB5O6(OH)4(H2O)x <4∆T>8 0 Orthorhombic No M=K, Rb, NH4,
x=2;
M=K, x=4
NH4B5O6(OH)4(H2O)2 <4∆T>8 0 Monoclinic No
MB5O6(OH)4(H2O)x <4∆T>8 0 Monoclinic Yes M=Na, Li, x=3;
M=Na, x=0;
M=Cs, β-Cs, Tl,
x=2
NH4B5O8(H2O)4 <4∆T>8 0 Monoclinic Yes
NaCaB5O6(OH)4(H2O)5 <2∆3T>8 0 Triclinic Yes
(NH4)3B15O20(OH)8(H2O)4 3<4∆T>8 0 Monoclinic Yes
(C(NH2)3)3B9O12(OH)6 <6∆3T>2-8 0 Monoclinic Yes
NaBa3Si2B7O16(OH)4 T + <2∆3T>8 + T 0 Monoclinic Yes SiO4 is ignored
TlB2O3(OH)(H2O) ∆ + <2∆3T>n-8 1 Orthorhombic No
MM’BP2O8(H2O)x T’ + <3T4T’>8
+ T’
1 Hexagonal No MM’=NaMn, Fe,
NaMg, NaLi,
NaFe, NaZn, LiCu,
LiCd, x=3;
MM’=NaCd,
x=2.8;
MM’=NaZn, x=1
MM’=KFe, x=2.5
MM’=H0.5Mn1.25,
H0.5Co1.25,
(NH4)0.5Co1.25,
17
x=2.5;
MM’=(NH4)0.4
Fe1.25, x=2.5;
MM’=In, x=0.8
Bi3B6O13(OH) <∆5T>n-8 1 Triclinic No
*Pb6B11O18(OH)9 ∆ + <∆6T>n-8 &
∆2T
1 Trigonal No
*Sr(Ca0.8Sr0.2)(B10O16(O
H)2(B(OH)3)(H2O)
∆ + <4∆T>8 &
<4∆T>8
1 Monoclinic No
LiB2O3(OH)(H2O) ∆ + <3∆4T>n-8 1 Orthorhombic Yes
TlB2O3(OH)(H2O)0.5 ∆ + <2∆3T>n-8 1 Triclinic Yes
Na2B4O6(OH)2(H2O)3 ∆ + <3∆4T>n-8 1 Monoclinic Yes
LiB5O7(OH)2 <4∆T>8 1 Monoclinic Yes
Na2B5O7(OH)3(H2O)2 <3∆2T>8 1 Triclinic Yes
CaNaB5O7(OH)4(H2O)3 <2∆3T>8 1 Monoclinic Yes
Ca2B5O7(OH)5(H2O) <4∆T>8 1 Monoclinic Yes
NaCaB5O9(H2O)5 <2∆3T>8 1 Monoclinic Yes
K3PB5O8(OH)3 T’ + <2∆5T’>n-8 1 Monoclinic Yes
Ba3B6O9(OH)6 T + <5T>n-8 1 Monoclinic Yes
Mg6B11O15(OH)9 T+<4∆5T>3-8 +T 1 Orthorhombic Yes
M2B5O8(OH)(H2O)2 <3∆2T>8 2 Orthorhombic No M2=K2, Na2
*M2B11O16(OH)5(H2O) 2 <3∆2T>8 & ∆ 2 Monoclinic No M2=β-Sr2, Sr2
Sr(Ca0.8Sr0.2)
*KCa4B22O32(OH)10Cl
(H2O)4
<3∆2T>8 & ∆ 2 Triclinic No
NH4B5O7(OH)2(H2O) <4∆T>8 2 Monoclinic Yes
BaB5O8(OH)(H2O) <3∆2T>8 2 Triclinic Yes
MB5O8(OH)(H2O) <3∆2T>8 2 Monoclinic Yes M=Ca, Na2
CeB5O8(OH)NO3(H2O)3 <3∆2T>8 2 Monoclinic Yes
NaCaB5O8(OH)2(H2O)3 <2∆3T>8 2 Monoclinic Yes
Na3B5O8(OH)2(H2O) <2∆3T>8 2 Monoclinic Yes
Ba2B5O8(OH)3 <2∆3T>8 2 Monoclinic Yes
Na2Ca3B5O8(OH)2(SO4)2Cl <2∆3T>8 2 Orthorhombic Yes
LiBa2B10O16(OH)3 <3∆2T>8 + <2∆3T>8 2 Triclinic Yes
Ba5B20O33(OH)4(H2O) <2∆3T>8 2 Monoclinic Yes
Li3B5O8(OH)2 <2∆3T>8 3 Tetragonal No
Na3B5O9(H2O) <2∆3T>8 3 Orthorhombic No
MM’B5O9Cl <2∆3T>8 3 Triclinic No MM’=Ca2, CaSr
β-Ca2B5O9Cl(H2O) <2∆3T>8 3 Monoclinic No
Sr2B5O9(OH)(H2O) <2∆3T>8 3 Monoclinic No
Ba2B5O9Cl(H2O)0.5 <2∆3T>8 3 Orthorhombic No
Na2Ba2B10O17(OH)2 <2∆3T>8 3 Monoclinic No
Ca2MB9O13(OH)6Cl
(H2O)4
<2∆3T>8 +
|∆T|∆T| 3 Monoclinic No M=Fe,
Fe0.67Mg0.33
18
Ca9B26O34(OH)24Cl4
(H2O)13
∆ + <7∆8T>8 3 Triclinic No
β-Ca9B26O34(OH)24Cl4
(H2O)13
∆ + <7∆8T>8 3 Monoclinic No
Na0.5Pb2B5O9(OH)0.5Cl <4∆T>8 3 Orthorhombic Yes
Pb2B5O9(OH)(H2O)x <2∆3T>8 3 Monoclinic Yes x=0.5, 1
HKMg2B12O16(OH)10(H2O)4 ∆ + <2∆3T>8 3 Monoclinic Yes
Table S6’. Hydrated borates with the ‘8’-shaped-ring FBB
Chemical Formula FBB R Crystal
System
Centro
symmetric
Note
Tl4Cu3B18O28(OH)8
(H2O)10
<2(<2∆2T>b + ∆ +
<2∆2T>b)>
0 Orthorhombic No
K5HCu4B20O32(OH)8
(H2O)33
<4(<2∆2T>b + ∆)> 0 Triclinic Yes
Na6Cu2B16O24(OH)10
(H2O)12
<2(<3∆4T>2-8 +∆)> 0 Triclinic Yes
LnB9O13(OH)4(H2O) <3∆3T>B + <∆2T> 2 Monoclinic Yes Ln=Pr→Eu
NaCa2B9O14(OH)4
(H2O)2
<2∆2T>b +
<2∆3T>8
2 Monoclinic Yes
Na10HB9O14(OH)4
(H2O)2
<2∆2T>b +
<2∆3T>8
2 Triclinic Yes
Footnote:
[1] R may take the value 0, 1, 2 or 3 if the FBB forms isolated, chain, sheet or three-dimensional
network.
[2] Note gives the following information: the compounds having the same structure and the other
treatments about the compound.
[3] In the structures of Na2B2O4(OH)4(H2O)6 (ICSD 27488) and Li2B2O4(OH)4 (ICSD 100854),
two BO4 tetrahedra are connected into a ring by two O-O bonds (O22−), not by sharing an edge.
Therefore, the FBBs of them are treated as normal-rings in the current topological classification.
The corresponding configuration of this FBB is given in Figure S4f.
19
Figures S2 to S7 give some configurations of FBBs and their corresponding topology figures. The principles of topology figure follow the reference by Burns et al. (1995).
Figure S2 Structure and topology of BO3 and BO4 (all the H atoms are omitted for clarity).
Figure S3 Structure and topology of branched FBB (all the H atoms are omitted for clarity).
20
(a)
(b)
(c)
(d)
(e)
(f)
Figure S4
Structure and topology of normal-ring FBBs (all the H atoms are omitted for clarity):
(a) 3-normal-ring FBBs; (b) 4-normal-ring FBBs; (c) 6-normal-ring FBB; (d) tailed
normal-ring FBBs; (e) the linear combination of normal-ring FBB; (f) the
configuration and topology of FBB of Na2B2O4(OH)4(H2O)6 (ICSD 27488) and
Li2B2O4(OH)4 (ICSD 100854).
21
(a)
(b)
(c)
(d)
(e) Figure S5 Structure and topology of bridge-ring FBBs (all the H atoms are omitted for clarity): (a) typical bridge-ring FBB; (b) the linear combination of bridge-ring FBB; (c) double-bridge-ring FBB; (d) 6-bridge-ring FBB; (e) big-bridge-ring FBBs.
22
(a)
(b)
(c)
Figure S6
Structure and topology of ‘8’-shaped-ring FBB (all the H atoms are omitted for
clarity): (a) typical ‘8’-shaped-ring FBBs; (b) double-’8’-shaped-ring FBB; (c) the
linear combination of ‘8’-shaped-ring FBBs.
23
(a)
(b)
Figure S7 Structure and topology of combined-ring FBBs (all the H atoms are omitted for clarity): (a) the linear combination of combined-ring FBBs; (b) the mosaic combination of combined-ring FBBs.
24
Table S7 The number of anhydrous borates and the number of non-centrosymmetric anhydrous (behind the /) borates in each kind
Single ∆ or
T Branched Normal
-ring Bridge-ring
‘8’-shaped-ring
Combined-ring
Total
Isolate 264/68 49/12 10/2 2/0 3/0 0 328/82
Chain 5/1 6/4 5/0 2/1 16/5 0 34/11
Layer Non-existed 2/1 20/5 6/1 23/1 3/0 54/8
Network Non-existed 13/13 37/19 43/23 17/8 19/3 129/66
Total 269/69 70/30 72/26 53/25 59/14 22/3 545/167
Table S8 The number of hydrated borates and the number of non-centrosymmetric hydrated (behind the /) borates in each kind
Single ∆ or
T Branched Normal
-ring Bridge-ring
‘8’-shaped-ring
Combined-ring
Total
Isolate 51/14 12/3 35/4 36/11 17/6 3/1 154/39
Chain 1/0 21/1 9/1 1/0 32/21 0 64/23
Layer Non-existed 1/1 9/4 10/3 16/6 7/0 43/14
Network Non-existed 0 16/2 3/3 16/12 0 35/17
Total 52/14 34/5 69/11 50/17 81/45 10/1 296/93
FBB
Linkage
Linkage
FBB
25
Figure S7 Classes of the 6 topological structures of FBBs (by our classification) involved in 841 borates; the percentages are calculated for the occurrence of each kind of borate. Figure S8 Classes of the 4 degrees of polymerization of FBBs (by other classifications) involved in 841 borates; the percentages are calculated for the occurrence of each kind of borate.
Single ∆ or T borates
(36.7%)
Combined-ring
(3.3%)
‘8’-shaped-rin
g
Branched borates
(12.4%)
Normal-ring
(16.3%)
Bridge-ring
(13.3%)
Layered borates
(10.7%)
Isolate borates
(54.8%)
Chained borates
(11.9%)
Network borates
(22.6%)
Recommended