Structure change of monoclinic ZrO₂ baddeleyite involving softenings of bulk modulus and atom vibrations

Monoclinic ZrO₂ baddeleyite exhibits anomalous softenings of the bulk modulus and atom vibrations with compression. The pressure evolution of the structure is investigated using neutron powder diffraction combined with ab initio calculations. The results show that the anomalous pressure response of the bulk modulus is related not to the change in the bonding characters but to the deformation of an oxygen sublattice, especially one of the layers made of oxygen atoms in the crystallographic a* plane. The layer consists of two parallelograms; one is rotated with little distortion and the other is distorted with increasing pressure. The deformation of this layer lengthens one of the Zr—O distances, resulting in the softening of some atom vibrational modes.

Computing details

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

(34744)

Crystal data

O2Zr	c = 5.3166 (2) Å
Mr = 123.22	β = 99.206 (3)°
Monoclinic, P21/c	V = 140.71 (1) Å^3
a = 5.1473 (2) Å	Z = 4
b = 5.2088 (2) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 443.0 #6 (sig-2) = 101.7 #7 (gam-0) = 0.00 #8 (gam-1) = 20.17 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.018	29 parameters
Rwp = 0.020	0 restraints
Rexp = 0.018	(Δ/σ)max = 0.01
R(F^2) = 0.03690	Background function: GSAS Background function number 1 with 12 terms. Shifted Chebyshev function of 1st kind 1: 0.209201 2: 6.290160E-02 3: 2.598780E-02 4: 5.436260E-03 5: 2.672990E-03 6: 1.514170E-03 7: -1.827530E-03 8: 1.994330E-03 9: -1.515970E-0310: 1.382260E-0311: 7.833570E-0412: -9.672290E-04
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2751 (4)	0.0402 (4)	0.2097 (4)	0.00204*
O1	0.0693 (6)	0.3320 (5)	0.3441 (5)	0.00363*
O2	0.4501 (4)	0.7557 (5)	0.4780 (4)	0.00101*

Geometric parameters (Å, º)

Zr—Zr^i	3.466 (3)	Zr—O2^i	2.170 (3)
Zr—Zr^ii	3.466 (3)	Zr—O2^x	2.267 (4)
Zr—Zr^iii	3.338 (4)	Zr—O2^vi	2.249 (4)
Zr—Zr^iv	3.487 (4)	O1—Zr	2.046 (4)
Zr—Zr^v	3.575 (4)	O1—Zr^xi	2.059 (3)
Zr—Zr^vi	3.441 (3)	O1—Zr^vii	2.164 (4)
Zr—Zr^vii	3.441 (3)	O2—Zr^xii	2.152 (3)
Zr—O1	2.046 (4)	O2—Zr^ii	2.170 (3)
Zr—O1^viii	2.059 (3)	O2—Zr^x	2.267 (4)
Zr—O1^vi	2.164 (4)	O2—Zr^vii	2.249 (4)
Zr—O2^ix	2.152 (3)
O1—Zr—O1^viii	87.56 (10)	O2^ix—Zr—O2^i	115.24 (11)
O1—Zr—O1^xiii	83.04 (11)	O2^ix—Zr—O2^x	72.01 (14)
O1—Zr—O2^ix	117.72 (14)	O2^ix—Zr—O2^xiii	74.29 (9)
O1—Zr—O2^i	100.86 (14)	O2^i—Zr—O2^x	73.61 (9)
O1—Zr—O2^x	72.12 (14)	O2^i—Zr—O2^xiii	75.83 (11)
O1—Zr—O2^xiii	167.30 (16)	O2^x—Zr—O2^xiii	117.71 (12)
O1^viii—Zr—O1^xiii	75.56 (12)	Zr—O1—Zr^xi	145.63 (14)
O1^viii—Zr—O2^ix	89.37 (12)	Zr—O1—Zr^vii	109.63 (16)
O1^viii—Zr—O2^i	144.99 (13)	Zr^xi—O1—Zr^vii	104.44 (12)
O1^viii—Zr—O2^x	140.47 (12)	Zr^xii—O2—Zr^ii	106.62 (12)
O1^viii—Zr—O2^xiii	88.53 (13)	Zr^xii—O2—Zr^x	107.99 (14)
O1^xiii—Zr—O2^ix	154.15 (11)	Zr^xii—O2—Zr^vii	132.30 (16)
O1^xiii—Zr—O2^i	71.90 (12)	Zr^ii—O2—Zr^x	101.72 (12)
O1^xiii—Zr—O2^x	132.24 (11)	Zr^ii—O2—Zr^vii	104.17 (11)
O1^xiii—Zr—O2^xiii	84.28 (11)	Zr^x—O2—Zr^vii	100.24 (10)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34758)

Crystal data

O2Zr	c = 5.3099 (2) Å
Mr = 123.22	β = 99.173 (3)°
Monoclinic, P21/c	V = 140.40 (1) Å^3
a = 5.14204 (19) Å	Z = 4
b = 5.2087 (2) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 400.9 #6 (sig-2) = 99.5 #7 (gam-0) = 0.00 #8 (gam-1) = 24.45 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.017	27 parameters
Rwp = 0.019	0 restraints
Rexp = 0.015	(Δ/σ)max = 0.03
R(F^2) = 0.11471	Background function: GSAS Background function number 1 with 10 terms. Shifted Chebyshev function of 1st kind 1: 0.224270 2: 8.176580E-02 3: 2.663380E-02 4: 1.104520E-02 5: -2.699160E-03 6: 3.827990E-03 7: -5.643760E-03 8: 1.322710E-03 9: -3.198850E-0310: -3.310250E-04
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2751 (4)	0.0386 (4)	0.2090 (4)	0.00204*
O1	0.0734 (5)	0.3354 (4)	0.3421 (4)	0.00363*
O	0.4506 (4)	0.7581 (5)	0.4795 (4)	0.00101*

Geometric parameters (Å, º)

Zr—Zr^i	3.464 (3)	Zr—O2^i	2.179 (3)
Zr—Zr^ii	3.464 (3)	Zr—O2^x	2.259 (3)
Zr—Zr^iii	3.330 (4)	Zr—O2^vi	2.245 (4)
Zr—Zr^iv	3.475 (4)	O1—Zr	2.049 (4)
Zr—Zr^v	3.575 (4)	O1—Zr^xi	2.062 (3)
Zr—Zr^vi	3.449 (3)	O1—Zr^vii	2.158 (4)
Zr—Zr^vii	3.449 (3)	O2—Zr^xii	2.145 (3)
Zr—O1	2.049 (4)	O2—Zr^ii	2.179 (3)
Zr—O1^viii	2.062 (3)	O2—Zr^x	2.259 (3)
Zr—O1^vi	2.158 (4)	O2—Zr^vii	2.245 (4)
Zr—O2^ix	2.145 (3)
O1—Zr—O1^viii	87.45 (9)	O2^ix—Zr—O2^i	115.54 (11)
O1—Zr—O1^xiii	83.40 (10)	O2^ix—Zr—O2^x	71.45 (12)
O1—Zr—O2^ix	117.71 (13)	O2^ix—Zr—O2^xiii	74.44 (8)
O1—Zr—O2^i	99.39 (13)	O2^i—Zr—O2^x	73.51 (8)
O1—Zr—O2^x	71.66 (13)	O2^i—Zr—O2^xiii	76.48 (10)
O1—Zr—O2^xiii	167.45 (15)	O2^x—Zr—O2^xiii	117.52 (11)
O1^viii—Zr—O1^xiii	75.80 (11)	Zr—O1—Zr^xi	145.01 (14)
O1^viii—Zr—O2^ix	90.13 (11)	Zr—O1—Zr^vii	110.10 (15)
O1^viii—Zr—O2^i	145.25 (12)	Zr^xi—O1—Zr^vii	104.20 (11)
O1^viii—Zr—O2^x	139.92 (11)	Zr^xii—O2—Zr^ii	106.48 (12)
O1^viii—Zr—O2^xiii	89.49 (12)	Zr^xii—O2—Zr^x	108.55 (12)
O1^xiii—Zr—O2^ix	154.43 (11)	Zr^xii—O2—Zr^vii	132.08 (16)
O1^xiii—Zr—O2^i	71.28 (11)	Zr^ii—O2—Zr^x	101.99 (11)
O1^xiii—Zr—O2^x	132.28 (10)	Zr^ii—O2—Zr^vii	103.52 (10)
O1^xiii—Zr—O2^xiii	84.04 (11)	Zr^x—O2—Zr^vii	100.57 (9)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34800)

Crystal data

O2Zr	c = 5.2829 (2) Å
Mr = 123.22	β = 99.048 (4)°
Monoclinic, P21/c	V = 139.23 (1) Å^3
a = 5.1242 (2) Å	Z = 4
b = 5.2080 (2) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 473.0 #6 (sig-2) = 104.8 #7 (gam-0) = 0.00 #8 (gam-1) = 22.65 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.018	33 parameters
Rwp = 0.020	0 restraints
Rexp = 0.016	(Δ/σ)max = 0.02
R(F^2) = 0.06266	Background function: GSAS Background function number 1 with 16 terms. Shifted Chebyshev function of 1st kind 1: 0.231529 2: 7.972690E-02 3: 1.985010E-02 4: -8.271670E-05 5: -1.164490E-02 6: -3.707700E-03 7: -1.142620E-02 8: -1.386380E-03 9: -1.172040E-0310: 1.338090E-0311: 1.196800E-0312: -6.080360E-04 13: 7.124650E-0414: -3.884560E-0415: -1.108020E-0316: -1.019030E-04
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2759 (4)	0.0378 (4)	0.2102 (4)	0.00204*
O1	0.0727 (6)	0.3400 (5)	0.3382 (5)	0.00363*
O2	0.4486 (5)	0.7587 (5)	0.4823 (5)	0.00101*

Geometric parameters (Å, º)

Zr—Zr^i	3.454 (3)	Zr—O2^i	2.191 (3)
Zr—Zr^ii	3.454 (3)	Zr—O2^x	2.243 (4)
Zr—Zr^iii	3.333 (5)	Zr—O2^vi	2.225 (4)
Zr—Zr^iv	3.459 (4)	O1—Zr	2.059 (4)
Zr—Zr^v	3.549 (5)	O1—Zr^xi	2.043 (3)
Zr—Zr^vi	3.444 (3)	O1—Zr^vii	2.170 (4)
Zr—Zr^vii	3.444 (3)	O2—Zr^xii	2.136 (3)
Zr—O1	2.059 (4)	O2—Zr^ii	2.191 (3)
Zr—O1^viii	2.043 (3)	O2—Zr^x	2.243 (4)
Zr—O1^vi	2.170 (4)	O2—Zr^vii	2.225 (4)
Zr—O2^ix	2.136 (3)
O1—Zr—O1^viii	87.07 (10)	O2^ix—Zr—O2^i	116.16 (12)
O1—Zr—O1^xiii	82.98 (12)	O2^ix—Zr—O2^x	71.76 (13)
O1—Zr—O2^ix	118.45 (15)	O2^ix—Zr—O2^xiii	74.57 (9)
O1—Zr—O2^i	98.45 (15)	O2^i—Zr—O2^x	73.16 (9)
O1—Zr—O2^x	72.19 (14)	O2^i—Zr—O2^xiii	76.91 (11)
O1—Zr—O2^xiii	166.59 (17)	O2^x—Zr—O2^xiii	117.46 (12)
O1^viii—Zr—O1^xiii	75.46 (12)	Zr—O1—Zr^xi	145.26 (16)
O1^viii—Zr—O2^ix	90.15 (13)	Zr—O1—Zr^vii	109.03 (16)
O1^viii—Zr—O2^i	145.19 (13)	Zr^xi—O1—Zr^vii	104.54 (12)
O1^viii—Zr—O2^x	140.07 (13)	Zr^xii—O2—Zr^ii	105.89 (13)
O1^viii—Zr—O2^xiii	89.82 (15)	Zr^xii—O2—Zr^x	108.24 (13)
O1^xiii—Zr—O2^ix	153.93 (12)	Zr^xii—O2—Zr^vii	132.72 (17)
O1^xiii—Zr—O2^i	71.22 (12)	Zr^ii—O2—Zr^x	101.91 (12)
O1^xiii—Zr—O2^x	132.46 (11)	Zr^ii—O2—Zr^vii	103.09 (11)
O1^xiii—Zr—O2^xiii	83.61 (12)	Zr^x—O2—Zr^vii	101.22 (11)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34841)

Crystal data

O2Zr	c = 5.2539 (3) Å
Mr = 123.22	β = 98.868 (5)°
Monoclinic, P21/c	V = 138.03 (1) Å^3
a = 5.1054 (3) Å	Z = 4
b = 5.2083 (3) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 487.0 #6 (sig-2) = 117.6 #7 (gam-0) = 0.00 #8 (gam-1) = 26.47 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.022	31 parameters
Rwp = 0.023	0 restraints
Rexp = 0.017	(Δ/σ)max = 0.01
R(F^2) = 0.07094	Background function: GSAS Background function number 1 with 14 terms. Shifted Chebyshev function of 1st kind 1: 0.223123 2: 6.286750E-02 3: 6.764820E-03 4: -1.065590E-02 5: -1.624130E-02 6: -4.966240E-03 7: -1.091090E-02 8: 1.705260E-03 9: 3.301190E-0310: 3.855320E-0311: 2.284390E-0312: 6.999260E-04 13: 2.139500E-0314: -7.210700E-04
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2774 (5)	0.0386 (5)	0.2106 (5)	0.00204*
O1	0.0764 (7)	0.3453 (6)	0.3318 (6)	0.00363*
O2	0.4469 (6)	0.7587 (6)	0.4852 (6)	0.00101*

Geometric parameters (Å, º)

Zr—Zr^i	3.439 (3)	Zr—O2^i	2.191 (4)
Zr—Zr^ii	3.439 (3)	Zr—O2^x	2.226 (4)
Zr—Zr^iii	3.339 (5)	Zr—O2^vi	2.206 (5)
Zr—Zr^iv	3.432 (5)	O1—Zr	2.052 (5)
Zr—Zr^v	3.528 (5)	O1—Zr^xi	2.050 (4)
Zr—Zr^vi	3.428 (3)	O1—Zr^vii	2.179 (5)
Zr—Zr^vii	3.428 (3)	O2—Zr^xii	2.138 (4)
Zr—O1	2.052 (5)	O2—Zr^ii	2.191 (4)
Zr—O1^viii	2.050 (4)	O2—Zr^x	2.226 (4)
Zr—O1^vi	2.179 (5)	O2—Zr^vii	2.206 (5)
Zr—O2^ix	2.138 (4)
O1—Zr—O1^viii	86.66 (12)	O2^ix—Zr—O2^i	116.82 (14)
O1—Zr—O1^xiii	83.10 (14)	O2^ix—Zr—O2^x	72.15 (15)
O1—Zr—O2^ix	119.41 (18)	O2^ix—Zr—O2^xiii	74.46 (11)
O1—Zr—O2^i	97.27 (19)	O2^i—Zr—O2^x	73.03 (10)
O1—Zr—O2^x	72.49 (17)	O2^i—Zr—O2^xiii	77.39 (13)
O1—Zr—O2^xiii	165.8 (2)	O2^x—Zr—O2^xiii	117.47 (14)
O1^viii—Zr—O1^xiii	75.77 (14)	Zr—O1—Zr^xi	145.38 (19)
O1^viii—Zr—O2^ix	89.81 (16)	Zr—O1—Zr^vii	108.17 (18)
O1^viii—Zr—O2^i	145.60 (16)	Zr^xi—O1—Zr^vii	104.23 (14)
O1^viii—Zr—O2^x	139.46 (16)	Zr^xii—O2—Zr^ii	105.21 (17)
O1^viii—Zr—O2^xiii	90.52 (18)	Zr^xii—O2—Zr^x	107.85 (15)
O1^xiii—Zr—O2^ix	152.88 (14)	Zr^xii—O2—Zr^vii	133.6 (2)
O1^xiii—Zr—O2^i	70.85 (14)	Zr^ii—O2—Zr^x	101.79 (14)
O1^xiii—Zr—O2^x	132.89 (13)	Zr^ii—O2—Zr^vii	102.61 (13)
O1^xiii—Zr—O2^xiii	82.70 (15)	Zr^x—O2—Zr^vii	101.81 (13)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34855)

Crystal data

O2Zr	c = 5.2320 (3) Å
Mr = 123.22	β = 98.706 (5)°
Monoclinic, P21/c	V = 137.16 (1) Å^3
a = 5.0910 (3) Å	Z = 4
b = 5.2093 (3) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 354.1 #6 (sig-2) = 113.3 #7 (gam-0) = 0.00 #8 (gam-1) = 38.92 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.021	35 parameters
Rwp = 0.023	0 restraints
Rexp = 0.017	(Δ/σ)max = 0.02
R(F^2) = 0.06231	Background function: GSAS Background function number 1 with 18 terms. Shifted Chebyshev function of 1st kind 1: 0.220392 2: 5.475970E-02 3: -6.935650E-04 4: -1.550670E-02 5: -1.599520E-02 6: -3.332530E-03 7: -9.268370E-03 8: 3.203870E-03 9: 4.725210E-0310: 3.599950E-0311: 1.187920E-0312: 8.565980E-04 13: 1.639110E-0314: -1.174560E-0315: 7.275620E-0416: 2.303690E-03 17: 1.989760E-0318: -6.173770E-04
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2761 (5)	0.0388 (5)	0.2080 (5)	0.0015*
O1	0.0775 (7)	0.3501 (6)	0.3278 (6)	0.00375*
O2	0.4449 (6)	0.7591 (6)	0.4870 (7)	0.00066*

Geometric parameters (Å, º)

Zr—Zr^i	3.446 (4)	Zr—O2^i	2.194 (4)
Zr—Zr^ii	3.446 (4)	Zr—O2^x	2.233 (4)
Zr—Zr^iii	3.309 (6)	Zr—O2^vi	2.188 (5)
Zr—Zr^iv	3.406 (5)	O1—Zr	2.058 (5)
Zr—Zr^v	3.548 (6)	O1—Zr^xi	2.035 (4)
Zr—Zr^vi	3.418 (3)	O1—Zr^vii	2.169 (5)
Zr—Zr^vii	3.418 (3)	O2—Zr^xii	2.148 (4)
Zr—O1	2.058 (5)	O2—Zr^ii	2.194 (4)
Zr—O1^viii	2.035 (4)	O2—Zr^x	2.233 (4)
Zr—O1^vi	2.169 (5)	O2—Zr^vii	2.188 (5)
Zr—O2^ix	2.148 (4)
O1—Zr—O1^viii	86.57 (12)	O2^ix—Zr—O2^i	116.75 (15)
O1—Zr—O1^xiii	83.51 (16)	O2^ix—Zr—O2^x	71.84 (16)
O1—Zr—O2^ix	119.5 (2)	O2^ix—Zr—O2^xiii	74.28 (11)
O1—Zr—O2^i	96.42 (19)	O2^i—Zr—O2^x	72.50 (10)
O1—Zr—O2^x	72.51 (17)	O2^i—Zr—O2^xiii	77.96 (13)
O1—Zr—O2^xiii	166.0 (2)	O2^x—Zr—O2^xiii	117.00 (15)
O1^viii—Zr—O1^xiii	76.20 (15)	Zr—O1—Zr^xi	145.2 (2)
O1^viii—Zr—O2^ix	89.55 (16)	Zr—O1—Zr^vii	107.89 (19)
O1^viii—Zr—O2^i	146.72 (16)	Zr^xi—O1—Zr^vii	103.80 (15)
O1^viii—Zr—O2^x	138.73 (17)	Zr^xii—O2—Zr^ii	105.05 (18)
O1^viii—Zr—O2^xiii	91.24 (18)	Zr^xii—O2—Zr^x	108.16 (16)
O1^xiii—Zr—O2^ix	152.52 (15)	Zr^xii—O2—Zr^vii	133.8 (2)
O1^xiii—Zr—O2^i	71.27 (14)	Zr^ii—O2—Zr^x	101.09 (14)
O1^xiii—Zr—O2^x	133.43 (14)	Zr^ii—O2—Zr^vii	102.04 (13)
O1^xiii—Zr—O2^xiii	82.55 (16)	Zr^x—O2—Zr^vii	102.41 (14)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34883)

Crystal data

O2Zr	c = 5.1975 (4) Å
Mr = 123.22	β = 98.441 (6)°
Monoclinic, P21/c	V = 135.79 (1) Å^3
a = 5.0701 (3) Å	Z = 4
b = 5.2095 (4) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 437.2 #6 (sig-2) = 125.7 #7 (gam-0) = 0.00 #8 (gam-1) = 38.58 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.021	33 parameters
Rwp = 0.023	0 restraints
Rexp = 0.016	(Δ/σ)max = 0.02
R(F^2) = 0.07915	Background function: GSAS Background function number 1 with 16 terms. Shifted Chebyshev function of 1st kind 1: 0.231857 2: 4.529640E-02 3: -1.051210E-02 4: -2.065130E-02 5: -1.576760E-02 6: -3.858070E-04 7: -7.106330E-03 8: 6.184440E-03 9: 5.817850E-0310: 1.984060E-0311: -1.385880E-0412: 5.862530E-04 13: 8.259240E-0414: -1.749620E-0315: -4.510430E-0416: 2.472780E-03
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2752 (6)	0.0372 (5)	0.2091 (5)	0.00204*
O1	0.0819 (7)	0.3562 (6)	0.3208 (7)	0.00363*
O2	0.4441 (7)	0.7584 (6)	0.4893 (7)	0.00101*

Geometric parameters (Å, º)

Zr—Zr^i	3.446 (4)	Zr—O2^i	2.201 (4)
Zr—Zr^ii	3.446 (4)	Zr—O2^x	2.228 (4)
Zr—Zr^iii	3.299 (6)	Zr—O2^vi	2.167 (5)
Zr—Zr^iv	3.394 (5)	O1—Zr	2.056 (5)
Zr—Zr^v	3.531 (6)	O1—Zr^xi	2.027 (4)
Zr—Zr^vi	3.416 (3)	O1—Zr^vii	2.182 (5)
Zr—Zr^vii	3.416 (3)	O2—Zr^xii	2.144 (4)
Zr—O1	2.056 (5)	O2—Zr^ii	2.201 (4)
Zr—O1^viii	2.027 (4)	O2—Zr^x	2.228 (4)
Zr—O1^vi	2.182 (5)	O2—Zr^vii	2.167 (5)
Zr—O2^ix	2.144 (4)
O1—Zr—O1^viii	86.56 (13)	O2^ix—Zr—O2^i	116.84 (17)
O1—Zr—O1^xiii	83.54 (16)	O2^ix—Zr—O2^x	72.28 (17)
O1—Zr—O2^ix	121.0 (2)	O2^ix—Zr—O2^xiii	74.18 (12)
O1—Zr—O2^i	94.4 (2)	O2^i—Zr—O2^x	71.90 (10)
O1—Zr—O2^x	72.33 (17)	O2^i—Zr—O2^xiii	78.03 (13)
O1—Zr—O2^xiii	164.8 (2)	O2^x—Zr—O2^xiii	116.73 (15)
O1^viii—Zr—O1^xiii	76.85 (17)	Zr—O1—Zr^xi	144.3 (2)
O1^viii—Zr—O2^ix	90.00 (16)	Zr—O1—Zr^vii	107.39 (19)
O1^viii—Zr—O2^i	147.05 (17)	Zr^xi—O1—Zr^vii	103.15 (17)
O1^viii—Zr—O2^x	138.36 (18)	Zr^xii—O2—Zr^ii	104.9 (2)
O1^viii—Zr—O2^xiii	92.68 (18)	Zr^xii—O2—Zr^x	107.72 (17)
O1^xiii—Zr—O2^ix	151.75 (16)	Zr^xii—O2—Zr^vii	133.6 (2)
O1^xiii—Zr—O2^i	70.56 (15)	Zr^ii—O2—Zr^x	100.94 (15)
O1^xiii—Zr—O2^x	133.10 (15)	Zr^ii—O2—Zr^vii	101.97 (13)
O1^xiii—Zr—O2^xiii	81.47 (15)	Zr^x—O2—Zr^vii	103.27 (15)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.

(34897)

Crystal data

O2Zr	c = 5.1763 (4) Å
Mr = 123.22	β = 98.276 (6)°
Monoclinic, P21/c	V = 135.01 (1) Å^3
a = 5.0590 (3) Å	Z = 4
b = 5.2097 (4) Å

Refinement

Least-squares matrix: full	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = ******** #2 (bet-0) = 0.015258 #3 (bet-1) = 0.731691 #4 (sig-0) = 2.8 #5 (sig-1) = 447.5 #6 (sig-2) = 132.0 #7 (gam-0) = 0.00 #8 (gam-1) = 42.19 #9 (gam-2) = 0.93 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0
Rp = 0.020	33 parameters
Rwp = 0.022	0 restraints
Rexp = 0.015	(Δ/σ)max = 0.07
R(F^2) = 0.09108	Background function: GSAS Background function number 1 with 16 terms. Shifted Chebyshev function of 1st kind 1: 0.225697 2: 4.059960E-02 3: -1.636550E-02 4: -2.162990E-02 5: -1.428920E-02 6: 1.774470E-03 7: -5.329060E-03 8: 7.147440E-03 9: 5.132650E-0310: -6.506340E-0411: -1.463580E-0312: -2.705860E-04 13: 1.180440E-0414: -1.575590E-0315: 2.213210E-0416: 3.227220E-03
3712 data points

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

	x	y	z	Uiso*/Ueq
Zr	0.2753 (6)	0.0365 (4)	0.2101 (5)	0.002*
O1	0.0827 (7)	0.3585 (5)	0.3176 (7)	0.002*
O2	0.4436 (7)	0.7595 (6)	0.4903 (7)	0.002*

Geometric parameters (Å, º)

Zr—Zr^i	3.443 (4)	Zr—O2^i	2.207 (4)
Zr—Zr^ii	3.443 (4)	Zr—O2^x	2.218 (4)
Zr—Zr^iii	3.300 (6)	Zr—O2^vi	2.163 (5)
Zr—Zr^iv	3.387 (5)	O1—Zr	2.056 (5)
Zr—Zr^v	3.515 (6)	O1—Zr^xi	2.022 (4)
Zr—Zr^vi	3.413 (3)	O1—Zr^vii	2.193 (5)
Zr—Zr^vii	3.413 (3)	O2—Zr^xii	2.134 (4)
Zr—O1	2.056 (5)	O2—Zr^ii	2.207 (4)
Zr—O1^viii	2.022 (4)	O2—Zr^x	2.218 (4)
Zr—O1^vi	2.193 (5)	O2—Zr^vii	2.163 (5)
Zr—O2^ix	2.134 (4)
O1—Zr—O1^viii	86.50 (13)	O2^ix—Zr—O2^i	117.01 (16)
O1—Zr—O1^xiii	83.26 (15)	O2^ix—Zr—O2^x	72.30 (17)
O1—Zr—O2^ix	121.75 (19)	O2^ix—Zr—O2^xiii	74.13 (12)
O1—Zr—O2^i	93.45 (18)	O2^i—Zr—O2^x	71.64 (10)
O1—Zr—O2^x	72.61 (16)	O2^i—Zr—O2^xiii	78.40 (13)
O1—Zr—O2^xiii	164.1 (2)	O2^x—Zr—O2^xiii	116.62 (15)
O1^viii—Zr—O1^xiii	76.98 (17)	Zr—O1—Zr^xi	144.06 (19)
O1^viii—Zr—O2^ix	90.21 (15)	Zr—O1—Zr^vii	106.83 (18)
O1^viii—Zr—O2^i	147.07 (17)	Zr^xi—O1—Zr^vii	103.02 (17)
O1^viii—Zr—O2^x	138.33 (18)	Zr^xii—O2—Zr^ii	104.93 (19)
O1^viii—Zr—O2^xiii	92.99 (17)	Zr^xii—O2—Zr^x	107.70 (17)
O1^xiii—Zr—O2^ix	151.51 (15)	Zr^xii—O2—Zr^vii	133.7 (2)
O1^xiii—Zr—O2^i	70.34 (14)	Zr^ii—O2—Zr^x	100.90 (15)
O1^xiii—Zr—O2^x	133.08 (14)	Zr^ii—O2—Zr^vii	101.60 (13)
O1^xiii—Zr—O2^xiii	81.15 (14)	Zr^x—O2—Zr^vii	103.59 (15)

Symmetry codes: (i) −x+1, y−1/2, −z+1/2; (ii) −x+1, y+1/2, −z+1/2; (iii) −x, −y, −z; (iv) −x+1, −y, −z; (v) −x+1, −y, −z+1; (vi) x, −y+1/2, z−1/2; (vii) x, −y+1/2, z+1/2; (viii) −x, y−1/2, −z+1/2; (ix) x, y−1, z; (x) −x+1, −y+1, −z+1; (xi) −x, y+1/2, −z+1/2; (xii) x, y+1, z; (xiii) x, −y+3/2, z+1/2.