High-temperature structural evolution of hexagonal multiferroic YMnO₃ and YbMnO₃

Neutron powder diffraction studies on the structural evolution of hexagonal multiferroic YMnO₃ and YbMnO₃ from 1000 K to 1400 K, and from 1000 K to 1350 K, respectively, are presented. The temperature evolution of diffraction patterns suggests that YMnO₃ undergoes a phase transition to a non-polar structure above 1200 K, while YbMnO₃ remains ferroelectric up to 1350 K. Detailed structural parameters were obtained as a function of temperature from Rietveld refinements. Based on this result, the distinct differences in temperature behaviour between YMnO₃ and YbMnO₃, and the origin of the ferroelectricity in these hexagonal multiferroics are discussed.

Computing details

For all compounds, program(s) used to refine structure: GSAS.

Figures

(YMO-1000K)

Crystal data

MnO3Y	V = 381.24 (1) Å^3
Mr = 191.84	Z = 6
Hexagonal, P63cm	? radiation, λ = ? Å
a = 6.22215 (8) Å	?, ? × ? × ? mm
c = 11.37072 (16) Å

Data collection

Refinement

Least-squares matrix: full	4888 data points
Rp = 0.020	Profile function: TOF Profile function number 1 with 12 terms Profile coefficients for Von Dreele, Jorgensen & Windsor convolution function J. Appl. Cryst., 15,581-589(1982) Modified by Von Dreele - unpublished (1983). #1(alp-0) = 0.0000 #3(bet-0) = 3.6008E-02 #5(sig-0) = 0.000 #2(alp-1) = 0.1002 #4(bet-1) = 1.5210E-02 #6(sig-1) = 172.609 #8(rstr ) = 0.000 #9(rsta ) = 0.000 #7(sig-2) = 0.000 #10(rsca) = 0.000 #11(s1ec) = 0.00 #12(s2ec) = 0.00 Peak tails are ignored where the intensity is below 0.0100 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.028	37 parameters
Rexp = 0.012	0 restraints
R(F^2) = 0.13213	(Δ/σ)max = 0.04
χ^2 = 5.476	Background function: GSAS Background function number 7 with 15 terms. Linear interpolation 1: 0.269324 2: 0.258212 3: 0.242578 4: 0.242548 5: 0.236113 6: 0.241551 7: 0.246771 8: 0.254022 9: 0.271245 10: 0.258747 11: 0.318729 12: 0.300540 13: 0.348946 14: 0.329324 15: 0.313133

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Y1	0.0	0.0	0.2726 (6)	0.0170 (7)*
Y2	0.33333	0.66667	0.2388 (5)	0.0223 (6)*
Mn3	0.3516 (10)	0.0	0.0	0.0147 (6)*
O4	0.3127 (7)	0.0	0.1647 (6)	0.0227 (8)*
O5	0.6549 (6)	0.0	0.3367 (6)	0.0207 (6)*
O6	0.0	0.0	0.4974 (8)	0.038 (3)*
O7	0.33333	0.66667	0.0197 (5)	0.0186 (7)*

Geometric parameters (Å, º)

Y1—Y2^i	3.6128 (4)	Y2—O5^xiv	2.323 (3)
Y1—Y2^ii	3.6128 (4)	Y2—O5^ix	2.323 (3)
Y1—Y2	3.6128 (4)	Y2—O5^xiii	2.323 (3)
Y1—Y2^iii	3.6128 (4)	Y2—O7	2.491 (5)
Y1—Y2^iv	3.6128 (4)	Mn3—Y1^xvii	3.387 (7)
Y1—Y2^v	3.6128 (4)	Mn3—Y2^ii	3.384 (5)
Y1—Mn3^vi	3.387 (7)	Mn3—Y2^v	3.384 (5)
Y1—Mn3^vii	3.387 (7)	Mn3—O4	1.888 (7)
Y1—Mn3^viii	3.387 (7)	Mn3—O5^xviii	1.857 (6)
Y1—O4	2.300 (5)	Mn3—O6^xvii	2.188 (6)
Y1—O4^ix	2.300 (5)	Mn3—O7^ii	2.032 (3)
Y1—O4^x	2.300 (5)	Mn3—O7^v	2.032 (3)
Y1—O5^xi	2.267 (4)	O4—Y1	2.300 (5)
Y1—O5^xii	2.267 (4)	O4—Y2^ii	2.301 (3)
Y1—O5^xiii	2.267 (4)	O4—Y2^v	2.301 (3)
Y1—O6	2.556 (8)	O4—Mn3	1.888 (7)
Y2—Y1	3.6128 (4)	O5—Y1^xix	2.267 (4)
Y2—Y1^xiv	3.6128 (4)	O5—Y2^ii	2.323 (3)
Y2—Y1^xv	3.6128 (4)	O5—Y2^v	2.323 (3)
Y2—Y2^iv	3.5924 (1)	O5—Mn3^xx	1.857 (6)
Y2—Y2^v	3.5924 (1)	O6—Y1	2.556 (8)
Y2—Y2^xvi	3.5924 (1)	O6—Mn3^vi	2.188 (6)
Y2—Mn3^xiv	3.384 (5)	O6—Mn3^vii	2.188 (6)
Y2—Mn3^ix	3.384 (5)	O6—Mn3^viii	2.188 (6)
Y2—Mn3^xiii	3.384 (5)	O7—Y2	2.491 (5)
Y2—O4^xiv	2.301 (3)	O7—Mn3^xiv	2.032 (3)
Y2—O4^ix	2.301 (3)	O7—Mn3^ix	2.032 (3)
Y2—O4^xiii	2.301 (3)	O7—Mn3^xiii	2.032 (3)
O4—Y1—O4^ix	94.2 (2)	O4^xiv—Y2—O7	68.50 (13)
O4—Y1—O4^x	94.2 (2)	O4^ix—Y2—O4^xiii	107.37 (14)
O4—Y1—O5^xi	166.5 (3)	O4^ix—Y2—O5^xiv	172.8 (2)
O4—Y1—O5^xii	76.77 (7)	O4^ix—Y2—O5^ix	77.42 (11)
O4—Y1—O5^xiii	76.77 (7)	O4^ix—Y2—O5^xiii	75.68 (15)
O4—Y1—O6	122.25 (16)	O4^ix—Y2—O7	68.50 (13)
O4^ix—Y1—O4^x	94.2 (2)	O4^xiii—Y2—O5^xiv	75.68 (15)
O4^ix—Y1—O5^xi	76.77 (7)	O4^xiii—Y2—O5^ix	172.8 (2)
O4^ix—Y1—O5^xii	166.5 (3)	O4^xiii—Y2—O5^xiii	77.42 (11)
O4^ix—Y1—O5^xiii	76.77 (7)	O4^xiii—Y2—O7	68.50 (13)
O4^ix—Y1—O6	122.25 (16)	O5^xiv—Y2—O5^ix	98.95 (15)
O4^x—Y1—O5^xi	76.77 (7)	O5^xiv—Y2—O5^xiii	98.95 (15)
O4^x—Y1—O5^xii	76.77 (7)	O5^xiv—Y2—O7	118.64 (11)
O4^x—Y1—O5^xiii	166.5 (3)	O5^ix—Y2—O5^xiii	98.95 (15)
O4^x—Y1—O6	122.25 (16)	O5^ix—Y2—O7	118.64 (11)
O5^xi—Y1—O5^xii	110.18 (18)	O5^xiii—Y2—O7	118.64 (11)
O5^xi—Y1—O5^xiii	110.18 (18)	O4—Mn3—O5^xviii	171.4 (4)
O5^xi—Y1—O6	71.25 (19)	O4—Mn3—O6^xvii	83.4 (3)
O5^xii—Y1—O5^xiii	110.18 (18)	O4—Mn3—O7^ii	87.06 (19)
O5^xii—Y1—O6	71.25 (19)	O4—Mn3—O7^v	87.06 (19)
O5^xiii—Y1—O6	71.25 (19)	O5^xviii—Mn3—O6^xvii	88.0 (3)
Y2^iv—Y2—Y2^v	120.0	O5^xviii—Mn3—O7^ii	96.9 (2)
Y2^iv—Y2—Y2^xvi	120.0	O5^xviii—Mn3—O7^v	96.9 (2)
Y2^iv—Y2—O4^xiv	87.23 (9)	O6^xvii—Mn3—O7^ii	117.12 (16)
Y2^iv—Y2—O4^ix	38.69 (9)	O6^xvii—Mn3—O7^v	117.12 (16)
Y2^iv—Y2—O4^xiii	145.98 (11)	O7^ii—Mn3—O7^v	124.2 (3)
Y2^iv—Y2—O5^xiv	138.26 (10)	Y1—O4—Y2^ii	103.46 (18)
Y2^iv—Y2—O5^ix	39.34 (10)	Y1—O4—Y2^v	103.46 (18)
Y2^iv—Y2—O5^xiii	91.56 (9)	Y1—O4—Mn3	129.6 (2)
Y2^iv—Y2—O7	90.0	Y2^ii—O4—Y2^v	102.62 (18)
Y2^v—Y2—Y2^xvi	119.9999	Y2^ii—O4—Mn3	107.37 (18)
Y2^v—Y2—O4^xiv	145.98 (11)	Y2^v—O4—Mn3	107.37 (18)
Y2^v—Y2—O4^ix	87.23 (9)	Y1^xix—O5—Y2^ii	103.83 (17)
Y2^v—Y2—O4^xiii	38.69 (9)	Y1^xix—O5—Y2^v	103.83 (17)
Y2^v—Y2—O5^xiv	91.56 (9)	Y1^xix—O5—Mn3^xx	110.0 (4)
Y2^v—Y2—O5^ix	138.26 (10)	Y2^ii—O5—Y2^v	101.31 (19)
Y2^v—Y2—O5^xiii	39.34 (10)	Y2^ii—O5—Mn3^xx	118.04 (15)
Y2^v—Y2—O7	90.0	Y2^v—O5—Mn3^xx	118.04 (15)
Y2^xvi—Y2—O4^xiv	38.69 (9)	Y1—O6—Mn3^vi	90.8 (3)
Y2^xvi—Y2—O4^ix	145.98 (11)	Y1—O6—Mn3^vii	90.8 (3)
Y2^xvi—Y2—O4^xiii	87.23 (9)	Y1—O6—Mn3^viii	90.8 (3)
Y2^xvi—Y2—O5^xiv	39.34 (10)	Mn3^vi—O6—Mn3^vii	119.982 (12)
Y2^xvi—Y2—O5^ix	91.56 (9)	Mn3^vi—O6—Mn3^viii	119.982 (12)
Y2^xvi—Y2—O5^xiii	138.26 (10)	Mn3^vii—O6—Mn3^viii	119.982 (12)
Y2^xvi—Y2—O7	90.0	Y2—O7—Mn3^xiv	96.34 (17)
O4^xiv—Y2—O4^ix	107.37 (14)	Y2—O7—Mn3^ix	96.34 (17)
O4^xiv—Y2—O4^xiii	107.37 (14)	Y2—O7—Mn3^xiii	96.34 (17)
O4^xiv—Y2—O5^xiv	77.42 (11)	Mn3^xiv—O7—Mn3^ix	118.80 (6)
O4^xiv—Y2—O5^ix	75.68 (15)	Mn3^xiv—O7—Mn3^xiii	118.80 (6)
O4^xiv—Y2—O5^xiii	172.8 (2)	Mn3^ix—O7—Mn3^xiii	118.80 (6)

Symmetry codes: (i) x−1, y−1, z; (ii) x, y−1, z; (iii) −x, y−x−1, z; (iv) −x, y−x, z; (v) −x+1, y−x, z; (vi) x−y, x, z+1/2; (vii) −x, −y, z+1/2; (viii) y, y−x, z+1/2; (ix) −y, x−y, z; (x) y−x, −x, z; (xi) x−1, y, z; (xii) −y, x−y−1, z; (xiii) y−x+1, −x+1, z; (xiv) x, y+1, z; (xv) x+1, y+1, z; (xvi) −x+1, y−x+1, z; (xvii) x−y, x, z−1/2; (xviii) −x+1, −y, z−1/2; (xix) x+1, y, z; (xx) −x+1, −y, z+1/2.

(YMO-1400K)

Crystal data

MnO3Y	V = 129.57 (1) Å^3
Mr = 191.84	Z = 2
Hexagonal, P63/mmc	? radiation, λ = ? Å
a = 3.63011 (4) Å	?, ? × ? × ? mm
c = 11.35350 (17) Å

Data collection

Refinement

Least-squares matrix: full	4888 data points
Rp = 0.024	Profile function: TOF Profile function number 1 with 12 terms Profile coefficients for Von Dreele, Jorgensen & Windsor convolution function J. Appl. Cryst., 15,581-589(1982) Modified by Von Dreele - unpublished (1983). #1(alp-0) = 0.0000 #3(bet-0) = 4.1067E-02 #5(sig-0) = 0.000 #2(alp-1) = 0.0798 #4(bet-1) = 4.3966E-03 #6(sig-1) = 143.515 #8(rstr ) = 0.000 #9(rsta ) = 0.000 #7(sig-2) = 0.000 #10(rsca) = 0.000 #11(s1ec) = 0.00 #12(s2ec) = 0.00 Peak tails are ignored where the intensity is below 0.0100 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.038	24 parameters
Rexp = 0.013	0 restraints
R(F^2) = 0.25865	(Δ/σ)max = 0.02
χ^2 = 9.000	Background function: GSAS Background function number 7 with 15 terms. Linear interpolation 1: 0.297310 2: 0.299857 3: 0.285274 4: 0.297646 5: 0.290407 6: 0.295158 7: 0.301538 8: 0.319386 9: 0.331278 10: 0.331911 11: 0.387527 12: 0.381450 13: 0.418404 14: 0.430463 15: 0.376814

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Y1	0.0	0.0	0.0	0.0311 (3)*
Mn2	0.33333	0.66667	0.25	0.0268 (6)*
O3	0.0	0.0	0.25	0.0400 (5)*
O4	0.33333	0.66667	0.08707 (16)	0.0284 (3)*

Geometric parameters (Å, º)

Y1—Y1^i	3.6301 (1)	Mn2—O3	2.0958 (1)
Y1—Y1^ii	3.6301 (1)	Mn2—O3^iv	2.0958 (1)
Y1—Y1^iii	3.6301 (1)	Mn2—O3^vi	2.0958 (1)
Y1—Y1^iv	3.6301 (1)	Mn2—O4	1.8498 (19)
Y1—Y1^v	3.6301 (1)	Mn2—O4^xi	1.8498 (19)
Y1—Y1^vi	3.6301 (1)	O3—Y1	2.8384 (1)
Y1—O3	2.8384 (1)	O3—Y1^xii	2.8384 (1)
Y1—O3^vii	2.8384 (1)	O3—Mn2^i	2.0958 (1)
Y1—O4^i	2.3173 (8)	O3—Mn2^iii	2.0958 (1)
Y1—O4^iii	2.3173 (8)	O3—Mn2	2.0958 (1)
Y1—O4	2.3173 (8)	O4—Y1	2.3173 (8)
Y1—O4^viii	2.3173 (8)	O4—Y1^iv	2.3173 (8)
Y1—O4^ix	2.3173 (8)	O4—Y1^vi	2.3173 (8)
Y1—O4^x	2.3173 (8)	O4—Mn2	1.8498 (19)
O4^i—Y1—O4^iii	103.12 (5)	O3—Mn2—O4	90.0
O4^i—Y1—O4	103.12 (5)	O3—Mn2—O4^xi	90.0
O4^i—Y1—O4^viii	76.88 (5)	O3^iv—Mn2—O3^vi	120.0
O4^i—Y1—O4^ix	76.88 (5)	O3^iv—Mn2—O4	90.0
O4^i—Y1—O4^x	179.9515	O3^iv—Mn2—O4^xi	90.0001
O4^iii—Y1—O4	103.12 (5)	O3^vi—Mn2—O4	90.0
O4^iii—Y1—O4^viii	76.88 (5)	O3^vi—Mn2—O4^xi	89.9999
O4^iii—Y1—O4^ix	179.9802	O4—Mn2—O4^xi	180.0
O4^iii—Y1—O4^x	76.88 (5)	Mn2^i—O3—Mn2^iii	120.0
O4—Y1—O4^viii	180.0	Mn2^i—O3—Mn2	119.9999
O4—Y1—O4^ix	76.88 (5)	Mn2^iii—O3—Mn2	120.0001
O4—Y1—O4^x	76.88 (5)	Y1—O4—Y1^iv	103.12 (5)
O4^viii—Y1—O4^ix	103.12 (5)	Y1—O4—Y1^vi	103.12 (5)
O4^viii—Y1—O4^x	103.12 (5)	Y1—O4—Mn2	115.25 (4)
O4^ix—Y1—O4^x	103.12 (5)	Y1^iv—O4—Y1^vi	103.12 (5)
O3—Mn2—O3^iv	120.0001	Y1^iv—O4—Mn2	115.25 (4)
O3—Mn2—O3^vi	119.9999	Y1^vi—O4—Mn2	115.25 (4)

Symmetry codes: (i) x−1, y−1, z; (ii) x−1, y, z; (iii) x, y−1, z; (iv) x, y+1, z; (v) x+1, y, z; (vi) x+1, y+1, z; (vii) x−y, x, z−1/2; (viii) −x, −y, −z; (ix) −x, −y+1, −z; (x) −x+1, −y+1, −z; (xi) y−x, −x+1, −z+1/2; (xii) x−y, x, z+1/2.

(YBMO-1000K)

Crystal data

MnO3Yb	V = 370.76 (1) Å^3
Mr = 275.97	Z = 6
Hexagonal, P63cm	? radiation, λ = ? Å
a = 6.13202 (3) Å	?, ? × ? × ? mm
c = 11.38556 (12) Å

Data collection

Refinement

Least-squares matrix: full	4888 data points
Rp = 0.020	Profile function: TOF Profile function number 1 with 12 terms Profile coefficients for Von Dreele, Jorgensen & Windsor convolution function J. Appl. Cryst., 15,581-589(1982) Modified by Von Dreele - unpublished (1983). #1(alp-0) = 0.0034 #3(bet-0) = 4.1269E-02 #5(sig-0) = 22.616 #2(alp-1) = 0.0713 #4(bet-1) = 1.7478E-03 #6(sig-1) = 90.631 #8(rstr ) = 0.000 #9(rsta ) = 0.000 #7(sig-2) = 20.498 #10(rsca) = 0.000 #11(s1ec) = 0.00 #12(s2ec) = 0.00 Peak tails are ignored where the intensity is below 0.0100 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rwp = 0.027	20 parameters
Rexp = 0.008	0 restraints
R(F^2) = 0.11142	(Δ/σ)max = 0.03
χ^2 = 10.304	Background function: GSAS Background function number 7 with 15 terms. Linear interpolation 1: 0.526725 2: 0.486738 3: 0.440959 4: 0.434004 5: 0.410003 6: 0.394718 7: 0.403923 8: 0.404579 9: 0.419840 10: 0.387649 11: 0.464335 12: 0.432354 13: 0.484822 14: 0.465887 15: 0.434145

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
YB1	0.0	0.0	0.2729 (6)	0.0132 (4)*
YB2	0.33333	0.66667	0.2350 (5)	0.0154 (3)*
Mn3	0.3465 (16)	0.0	0.0	0.0106 (7)*
O4	0.3061 (6)	0.0	0.1631 (6)	0.0198 (6)*
O5	0.6497 (6)	0.0	0.3339 (6)	0.0123 (5)*
O6	0.0	0.0	0.4961 (7)	0.022 (2)*
O7	0.33333	0.66667	0.0230 (5)	0.0143 (7)*

Geometric parameters (Å, º)

YB1—YB2^i	3.5665 (3)	YB2—O5^xv	2.290 (3)
YB1—YB2^ii	3.5664 (3)	YB2—O5^ix	2.290 (3)
YB1—YB2	3.5665 (3)	YB2—O5^xiii	2.290 (3)
YB1—YB2^iii	3.5664 (3)	YB2—O7	2.414 (4)
YB1—YB2^iv	3.5665 (3)	Mn3—YB1^xiv	3.347 (9)
YB1—YB2^v	3.5665 (3)	Mn3—YB2^ii	3.344 (6)
YB1—Mn3^vi	3.347 (9)	Mn3—YB2^v	3.344 (6)
YB1—Mn3^vii	3.347 (9)	Mn3—O4	1.874 (7)
YB1—Mn3^viii	3.347 (9)	Mn3—O5^xviii	1.892 (7)
YB1—O4	2.255 (4)	Mn3—O6^xiv	2.125 (10)
YB1—O4^ix	2.255 (4)	Mn3—O7^ii	2.022 (5)
YB1—O4^x	2.255 (4)	Mn3—O7^v	2.022 (5)
YB1—O5^xi	2.258 (4)	O4—YB1	2.255 (4)
YB1—O5^xii	2.258 (4)	O4—YB2^ii	2.284 (2)
YB1—O5^xiii	2.258 (4)	O4—YB2^v	2.284 (2)
YB1—O6	2.541 (5)	O4—Mn3	1.874 (7)
YB1—O6^xiv	3.152 (5)	O5—YB1^xix	2.258 (4)
YB2—YB1	3.5665 (3)	O5—YB2^ii	2.290 (3)
YB2—YB1^xv	3.5664 (3)	O5—YB2^v	2.290 (3)
YB2—YB1^xvi	3.5665 (3)	O5—Mn3^xx	1.892 (7)
YB2—YB2^iv	3.5403 (1)	O6—YB1	2.541 (5)
YB2—YB2^v	3.5403 (1)	O6—YB1^vi	3.152 (5)
YB2—YB2^xvii	3.5403 (1)	O6—Mn3^vi	2.125 (10)
YB2—Mn3^xv	3.344 (6)	O6—Mn3^vii	2.125 (10)
YB2—Mn3^ix	3.344 (6)	O6—Mn3^viii	2.125 (10)
YB2—Mn3^xiii	3.344 (6)	O7—YB2	2.414 (4)
YB2—O4^xv	2.284 (2)	O7—Mn3^xv	2.022 (5)
YB2—O4^ix	2.284 (2)	O7—Mn3^ix	2.022 (5)
YB2—O4^xiii	2.284 (2)	O7—Mn3^xiii	2.022 (5)
YB2^i—YB1—YB2^ii	118.563 (14)	YB1^xv—YB2—O4^ix	96.10 (7)
YB2^i—YB1—YB2	118.562 (14)	YB1^xv—YB2—O4^xiii	144.35 (7)
YB2^i—YB1—YB2^iii	59.517 (5)	YB1^xv—YB2—O5^xv	84.35 (8)
YB2^i—YB1—YB2^iv	59.516 (5)	YB1^xv—YB2—O5^ix	38.02 (9)
YB2^i—YB1—YB2^v	166.13 (7)	YB1^xv—YB2—O5^xiii	135.09 (8)
YB2^i—YB1—O4	130.44 (11)	YB1^xv—YB2—O7	96.94 (3)
YB2^i—YB1—O4^ix	86.16 (3)	YB1^xvi—YB2—YB2^iv	173.06 (3)
YB2^i—YB1—O4^x	38.51 (6)	YB1^xvi—YB2—YB2^v	60.241 (2)
YB2^i—YB1—O5^xi	38.66 (7)	YB1^xvi—YB2—YB2^xvii	60.242 (2)
YB2^i—YB1—O5^xii	92.129 (12)	YB1^xvi—YB2—O4^xv	96.09 (7)
YB2^i—YB1—O5^xiii	148.78 (5)	YB1^xvi—YB2—O4^ix	144.35 (7)
YB2^i—YB1—O6	96.94 (3)	YB1^xvi—YB2—O4^xiii	37.92 (11)
YB2^ii—YB1—YB2	118.563 (14)	YB1^xvi—YB2—O5^xv	38.02 (9)
YB2^ii—YB1—YB2^iii	59.516 (5)	YB1^xvi—YB2—O5^ix	135.09 (8)
YB2^ii—YB1—YB2^iv	166.13 (7)	YB1^xvi—YB2—O5^xiii	84.35 (8)
YB2^ii—YB1—YB2^v	59.517 (5)	YB1^xvi—YB2—O7	96.94 (3)
YB2^ii—YB1—O4	38.51 (6)	YB2^iv—YB2—YB2^v	120.0005
YB2^ii—YB1—O4^ix	130.44 (11)	YB2^iv—YB2—YB2^xvii	120.0005
YB2^ii—YB1—O4^x	86.16 (3)	YB2^iv—YB2—O4^xv	86.37 (8)
YB2^ii—YB1—O5^xi	148.78 (5)	YB2^iv—YB2—O4^ix	39.20 (7)
YB2^ii—YB1—O5^xii	38.66 (7)	YB2^iv—YB2—O4^xiii	146.96 (10)
YB2^ii—YB1—O5^xiii	92.129 (12)	YB2^iv—YB2—O5^xv	137.20 (9)
YB2^ii—YB1—O6	96.94 (3)	YB2^iv—YB2—O5^ix	39.36 (8)
YB2—YB1—YB2^iii	166.13 (7)	YB2^iv—YB2—O5^xiii	92.26 (8)
YB2—YB1—YB2^iv	59.515 (5)	YB2^iv—YB2—O7	90.0004
YB2—YB1—YB2^v	59.516 (5)	YB2^v—YB2—YB2^xvii	119.999
YB2—YB1—O4	86.16 (3)	YB2^v—YB2—O4^xv	146.96 (10)
YB2—YB1—O4^ix	38.51 (6)	YB2^v—YB2—O4^ix	86.37 (8)
YB2—YB1—O4^x	130.44 (11)	YB2^v—YB2—O4^xiii	39.20 (7)
YB2—YB1—O5^xi	92.128 (12)	YB2^v—YB2—O5^xv	92.26 (8)
YB2—YB1—O5^xii	148.78 (5)	YB2^v—YB2—O5^ix	137.20 (9)
YB2—YB1—O5^xiii	38.66 (7)	YB2^v—YB2—O5^xiii	39.36 (8)
YB2—YB1—O6	96.94 (3)	YB2^v—YB2—O7	89.9992
YB2^iii—YB1—YB2^iv	118.563 (14)	YB2^xvii—YB2—O4^xv	39.20 (7)
YB2^iii—YB1—YB2^v	118.563 (14)	YB2^xvii—YB2—O4^ix	146.96 (10)
YB2^iii—YB1—O4	86.16 (3)	YB2^xvii—YB2—O4^xiii	86.37 (8)
YB2^iii—YB1—O4^ix	130.44 (11)	YB2^xvii—YB2—O5^xv	39.36 (8)
YB2^iii—YB1—O4^x	38.51 (6)	YB2^xvii—YB2—O5^ix	92.26 (8)
YB2^iii—YB1—O5^xi	92.129 (12)	YB2^xvii—YB2—O5^xiii	137.20 (9)
YB2^iii—YB1—O5^xii	38.66 (7)	YB2^xvii—YB2—O7	90.0004
YB2^iii—YB1—O5^xiii	148.78 (5)	O4^xv—YB2—O4^ix	107.89 (11)
YB2^iii—YB1—O6	96.94 (3)	O4^xv—YB2—O4^xiii	107.89 (11)
YB2^iv—YB1—YB2^v	118.562 (14)	O4^xv—YB2—O5^xv	77.63 (9)
YB2^iv—YB1—O4	130.44 (11)	O4^xv—YB2—O5^ix	75.75 (14)
YB2^iv—YB1—O4^ix	38.51 (6)	O4^xv—YB2—O5^xiii	171.49 (18)
YB2^iv—YB1—O4^x	86.16 (3)	O4^xv—YB2—O7	68.99 (11)
YB2^iv—YB1—O5^xi	38.66 (7)	O4^ix—YB2—O4^xiii	107.89 (11)
YB2^iv—YB1—O5^xii	148.78 (5)	O4^ix—YB2—O5^xv	171.49 (18)
YB2^iv—YB1—O5^xiii	92.128 (12)	O4^ix—YB2—O5^ix	77.63 (9)
YB2^iv—YB1—O6	96.94 (3)	O4^ix—YB2—O5^xiii	75.75 (14)
YB2^v—YB1—O4	38.51 (6)	O4^ix—YB2—O7	68.99 (11)
YB2^v—YB1—O4^ix	86.16 (3)	O4^xiii—YB2—O5^xv	75.75 (14)
YB2^v—YB1—O4^x	130.44 (11)	O4^xiii—YB2—O5^ix	171.49 (18)
YB2^v—YB1—O5^xi	148.78 (5)	O4^xiii—YB2—O5^xiii	77.62 (9)
YB2^v—YB1—O5^xii	92.129 (12)	O4^xiii—YB2—O7	68.99 (11)
YB2^v—YB1—O5^xiii	38.66 (7)	O5^xv—YB2—O5^ix	97.92 (12)
YB2^v—YB1—O6	96.94 (3)	O5^xv—YB2—O5^xiii	97.92 (12)
O4—YB1—O4^ix	92.25 (16)	O5^xv—YB2—O7	119.43 (9)
O4—YB1—O4^x	92.25 (16)	O5^ix—YB2—O5^xiii	97.92 (12)
O4—YB1—O5^xi	164.3 (2)	O5^ix—YB2—O7	119.43 (9)
O4—YB1—O5^xii	76.96 (6)	O5^xiii—YB2—O7	119.43 (9)
O4—YB1—O5^xiii	76.96 (6)	O4—Mn3—O5^xviii	173.1 (6)
O4—YB1—O6	123.65 (12)	O4—Mn3—O6^xiv	83.6 (3)
O4^ix—YB1—O4^x	92.25 (16)	O4—Mn3—O7^ii	86.2 (2)
O4^ix—YB1—O5^xi	76.96 (6)	O4—Mn3—O7^v	86.2 (2)
O4^ix—YB1—O5^xii	164.3 (2)	O5^xviii—Mn3—O6^xiv	89.5 (4)
O4^ix—YB1—O5^xiii	76.96 (6)	O5^xviii—Mn3—O7^ii	97.1 (2)
O4^ix—YB1—O6	123.65 (12)	O5^xviii—Mn3—O7^v	97.1 (2)
O4^x—YB1—O5^xi	76.96 (6)	O6^xiv—Mn3—O7^ii	117.9 (2)
O4^x—YB1—O5^xii	76.96 (6)	O6^xiv—Mn3—O7^v	117.9 (2)
O4^x—YB1—O5^xiii	164.3 (2)	O7^ii—Mn3—O7^v	122.2 (5)
O4^x—YB1—O6	123.65 (12)	YB1—O4—YB2^ii	103.57 (14)
O5^xi—YB1—O5^xii	110.98 (12)	YB1—O4—YB2^v	103.57 (14)
O5^xi—YB1—O5^xiii	110.98 (12)	YB1—O4—Mn3	131.3 (3)
O5^xi—YB1—O6	72.09 (13)	YB2^ii—O4—YB2^v	101.60 (14)
O5^xii—YB1—O5^xiii	110.98 (12)	YB2^ii—O4—Mn3	106.7 (2)
O5^xii—YB1—O6	72.09 (13)	YB2^v—O4—Mn3	106.7 (2)
O5^xiii—YB1—O6	72.09 (13)	YB1^xix—O5—YB2^ii	103.32 (13)
YB1—YB2—YB1^xv	118.563 (14)	YB1^xix—O5—YB2^v	103.32 (13)
YB1—YB2—YB1^xvi	118.562 (14)	YB1^xix—O5—Mn3^xx	107.2 (4)
YB1—YB2—YB2^iv	60.242 (2)	YB2^ii—O5—YB2^v	101.28 (16)
YB1—YB2—YB2^v	60.242 (2)	YB2^ii—O5—Mn3^xx	119.76 (18)
YB1—YB2—YB2^xvii	173.06 (3)	YB2^v—O5—Mn3^xx	119.76 (18)
YB1—YB2—O4^xv	144.35 (7)	YB1—O6—Mn3^vi	91.2 (2)
YB1—YB2—O4^ix	37.92 (11)	YB1—O6—Mn3^vii	91.2 (2)
YB1—YB2—O4^xiii	96.09 (7)	YB1—O6—Mn3^viii	91.2 (2)
YB1—YB2—O5^xv	135.08 (8)	Mn3^vi—O6—Mn3^vii	119.956 (15)
YB1—YB2—O5^ix	84.35 (8)	Mn3^vi—O6—Mn3^viii	119.956 (15)
YB1—YB2—O5^xiii	38.02 (9)	Mn3^vii—O6—Mn3^viii	119.956 (15)
YB1—YB2—O7	96.94 (3)	YB2—O7—Mn3^xv	97.45 (17)
YB1^xv—YB2—YB1^xvi	118.563 (14)	YB2—O7—Mn3^ix	97.45 (17)
YB1^xv—YB2—YB2^iv	60.242 (2)	YB2—O7—Mn3^xiii	97.45 (17)
YB1^xv—YB2—YB2^v	173.06 (3)	Mn3^xv—O7—Mn3^ix	118.34 (7)
YB1^xv—YB2—YB2^xvii	60.242 (2)	Mn3^xv—O7—Mn3^xiii	118.34 (7)
YB1^xv—YB2—O4^xv	37.92 (11)	Mn3^ix—O7—Mn3^xiii	118.34 (7)

Symmetry codes: (i) x−1, y−1, z; (ii) x, y−1, z; (iii) −x, y−x−1, z; (iv) −x, y−x, z; (v) −x+1, y−x, z; (vi) x−y, x, z+1/2; (vii) −x, −y, z+1/2; (viii) y, y−x, z+1/2; (ix) −y, x−y, z; (x) y−x, −x, z; (xi) x−1, y, z; (xii) −y, x−y−1, z; (xiii) y−x+1, −x+1, z; (xiv) x−y, x, z−1/2; (xv) x, y+1, z; (xvi) x+1, y+1, z; (xvii) −x+1, y−x+1, z; (xviii) −x+1, −y, z−1/2; (xix) x+1, y, z; (xx) −x+1, −y, z+1/2.