Thermoelastic properties of magnesiowüstite, (Mg1−xFex)O: determination of the Anderson–Grüneisen parameter by time-of-flight neutron powder diffraction at simultaneous high pressures and temperatures

Wood, I.G.; Vočadlo, L.; Dobson, D.P.; Price, G.D.; Fortes, A.D.; Cooper, F.J.; Neale, J.W.; Walker, A.M.; Marshall, W.G.; Tucker, M.G.; Francis, D.J.; Stone, H.J.; McCammon, C.A.

doi:10.1107/S0021889808025417

Thermoelastic properties of magnesiowüstite, (Mg_1−xFe_x)O: determination of the Anderson–Grüneisen parameter by time-of-flight neutron powder diffraction at simultaneous high pressures and temperatures

I. G. Wood, L. Vočadlo, D. P. Dobson, G. D. Price, A. D. Fortes, F. J. Cooper, J. W. Neale, A. M. Walker, W. G. Marshall, M. G. Tucker, D. J. Francis, H. J. Stone and C. A. McCammon

The ability to perform neutron diffraction studies at simultaneous high pressures and high temperatures is a relatively recent development. The suitability of this technique for determining P–V–T equations of state has been investigated by measuring the lattice parameters of Mg_1−xFe_xO (x = 0.2, 0.3, 0.4), in the range P < 10.3 GPa and 300 < T < 986 K, by time-of-flight neutron powder diffraction. Pressures were determined using metallic Fe as a marker and temperatures were measured by neutron absorption resonance radiography. Within the resolution of the experiment, no evidence was found for any change in the temperature derivative of the isothermal incompressibility, ∂K_T/∂T, with composition. By assuming that the equation-of-state parameters either varied linearly or were invariant with composition, the 60 measured state points were fitted simultaneously to a P–V–T–x equation of state, leading to values of ∂K_T/∂T = −0.024 (9) GPa K⁻¹ and of the isothermal Anderson–Grüneisen parameter δ_T = 4.0 (16) at 300 K. Two designs of simultaneous high-P/T cell were employed during this study. It appears that, by virtue of its extended pressure range, a design using toroidal gaskets is more suitable for equation-of-state studies than is the system described by Le Godec, Dove, Francis, Kohn, Marshall, Pawley, Price, Redfern, Rhodes, Ross, Schofield, Schooneveld, Syfosse, Tucker & Welch [Mineral. Mag. (2001), 65, 737–748].

Keywords: time-of-flight neutron powder diffraction; high pressure; high temperature; Anderson–Grüneisen parameter; thermoelasticity; magnesiowüstite.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0021889808025417/ks5172sup1.cif Contains datablocks PRL42703_publ, PRL47388_ZRO2_publ, PRL42703_phase_1, PRL42703_phase_2, PRL47388_ZRO2_phase_1, PRL47388_ZRO2_phase_2, PRL47388_ZRO2_phase_3, PRL42703_p_01, PRL47388_ZRO2_p_01, PRL42703_overall, PRL47388_ZRO2_overall
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0021889808025417/ks5172PRL42703_p_01sup2.rtv Contains datablock PRL42703_p_01
	Structure factor file (CIF format) https://doi.org/10.1107/S0021889808025417/ks5172PRL42703_p_01sup3.hkl Contains datablock PRL42703_p_01
	Rietveld powder data file (CIF format) https://doi.org/10.1107/S0021889808025417/ks5172PRL47388_ZRO2_p_01sup4.rtv Contains datablock PRL47388_ZRO2_p_01
	Structure factor file (CIF format) https://doi.org/10.1107/S0021889808025417/ks5172PRL47388_ZRO2_p_01sup5.hkl Contains datablock PRL47388_ZRO2_p_01
	Zip compressed file https://doi.org/10.1107/S0021889808025417/ks5172sup6.zip Supplementary data for Mg0.8Fe0.2O, Mg0.7Fe0.3O and Mg0.6Fe0.4O

Computing details top

Figures top

(PRL42703_phase_1) top

Crystal data top

Fe_0.20Mg_0.80O	V = 74.07 Å³
M_r = 46.62	Z = 4
Cubic, Fm3m	? radiation, λ = ? Å
a = 4.19971 (13) Å	?, ? × ? × ? mm

Data collection top

Refinement top

Least-squares matrix: full	2524 data points
R_p = 0.283	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 47.4 #6 (sig-2) = 9.9 #7 (gam-0) = 0.00 #8 (gam-1) = 9.53 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 14 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 73.3 #6 (sig-2) = 8.9 #7 (gam-0) = 0.00 #8 (gam-1) = 5.71 #9 (gam-2) = 0.00 #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
R_wp = 0.136	12 parameters
R_exp = 0.092	0 restraints
R(F²) = 0.15908	(Δ/σ)_max = 0.29
χ² = 2.190	Background function: GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.238471 2: -2.329730E-02 3: 8.919900E-02 4: -5.781030E-02

Crystal data top

Fe_0.20Mg_0.80O	V = 74.07 Å³
M_r = 46.62	Z = 4
Cubic, Fm3m	? radiation, λ = ? Å
a = 4.19971 (13) Å	?, ? × ? × ? mm

Data collection top

Refinement top

R_p = 0.283	2524 data points
R_wp = 0.136	12 parameters
R_exp = 0.092	0 restraints
R(F²) = 0.15908	(Δ/σ)_max = 0.29
χ² = 2.190

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mg	0.0	0.0	0.0	0.0101 (11)*	0.8
Fe	0.0	0.0	0.0	−0.0060 (3)*	0.2
O	0.5	0.5	0.5	0.0072 (5)*

(PRL42703_phase_2) top

Crystal data top

Fe	V = 22.92 Å³
M_r = 55.85	Z = 2
Cubic, Im3m	? radiation, λ = ? Å
a = 2.8403 (3) Å	?, ? × ? × ? mm

Data collection top

Refinement top

Least-squares matrix: full	2524 data points
R_p = 0.283	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 47.4 #6 (sig-2) = 9.9 #7 (gam-0) = 0.00 #8 (gam-1) = 9.53 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 14 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 73.3 #6 (sig-2) = 8.9 #7 (gam-0) = 0.00 #8 (gam-1) = 5.71 #9 (gam-2) = 0.00 #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
R_wp = 0.136	12 parameters
R_exp = 0.092	0 restraints
R(F²) = 0.15908	(Δ/σ)_max = 0.29
χ² = 2.190	Background function: GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.238471 2: -2.329730E-02 3: 8.919900E-02 4: -5.781030E-02

Crystal data top

Fe	V = 22.92 Å³
M_r = 55.85	Z = 2
Cubic, Im3m	? radiation, λ = ? Å
a = 2.8403 (3) Å	?, ? × ? × ? mm

Data collection top

Refinement top

R_p = 0.283	2524 data points
R_wp = 0.136	12 parameters
R_exp = 0.092	0 restraints
R(F²) = 0.15908	(Δ/σ)_max = 0.29
χ² = 2.190

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
FE1	0.0	0.0	0.0	0.0081 (13)*

(PRL47388_ZRO2_phase_1) top

Crystal data top

Fe_0.30Mg_0.70O	V = 73.54 Å³
M_r = 49.77	Z = 4
Cubic, Fm3m	? radiation, λ = ? Å
a = 4.1896 (2) Å	?, ? × ? × ? mm

Data collection top

Refinement top

Least-squares matrix: full	2524 data points
R_p = 0.083	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 203.9 #6 (sig-2) = -16.0 #7 (gam-0) = 0.00 #8 (gam-1) = 31.42 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 104.6 #6 (sig-2) = -34.9 #7 (gam-0) = 0.00 #8 (gam-1) = 25.65 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 14 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2248 #2 (bet-0) = 0.026918 #3 (bet-1) = 0.029309 #4 (sig-0) = 0.0 #5 (sig-1) = 71.8 #6 (sig-2) = 8.3 #7 (gam-0) = 0.00 #8 (gam-1) = 6.00 #9 (gam-2) = 0.00 #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
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993	Background function: GSAS Background function number 2 with 8 terms. Cosine Fourier series 1: -13.9330 2: 27.0721 3: -21.7005 4: 15.3369 5: -8.91545 6: 4.30403 7: -1.50325 8: 0.342467

Crystal data top

Fe_0.30Mg_0.70O	V = 73.54 Å³
M_r = 49.77	Z = 4
Cubic, Fm3m	? radiation, λ = ? Å
a = 4.1896 (2) Å	?, ? × ? × ? mm

Data collection top

Refinement top

R_p = 0.083	2524 data points
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mg	0.0	0.0	0.0	0.0072 (13)*	0.7
Fe	0.0	0.0	0.0	0.0072 (13)*	0.3
O	0.5	0.5	0.5	0.0086 (16)*

(PRL47388_ZRO2_phase_2) top

Crystal data top

Fe	V = 22.60 Å³
M_r = 55.85	Z = 2
Cubic, Im3m	? radiation, λ = ? Å
a = 2.8274 (4) Å	?, ? × ? × ? mm

Data collection top

Refinement top

Least-squares matrix: full	2524 data points
R_p = 0.083	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 203.9 #6 (sig-2) = -16.0 #7 (gam-0) = 0.00 #8 (gam-1) = 31.42 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 104.6 #6 (sig-2) = -34.9 #7 (gam-0) = 0.00 #8 (gam-1) = 25.65 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 14 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2248 #2 (bet-0) = 0.026918 #3 (bet-1) = 0.029309 #4 (sig-0) = 0.0 #5 (sig-1) = 71.8 #6 (sig-2) = 8.3 #7 (gam-0) = 0.00 #8 (gam-1) = 6.00 #9 (gam-2) = 0.00 #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
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993	Background function: GSAS Background function number 2 with 8 terms. Cosine Fourier series 1: -13.9330 2: 27.0721 3: -21.7005 4: 15.3369 5: -8.91545 6: 4.30403 7: -1.50325 8: 0.342467

Crystal data top

Fe	V = 22.60 Å³
M_r = 55.85	Z = 2
Cubic, Im3m	? radiation, λ = ? Å
a = 2.8274 (4) Å	?, ? × ? × ? mm

Data collection top

Refinement top

R_p = 0.083	2524 data points
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
FE1	0.0	0.0	0.0	0.005*

(PRL47388_ZRO2_phase_3) top

Crystal data top

O₂Zr	β = 100.16 (9)°
M_r = 123.22	V = 135.53 Å³
Monoclinic, P2₁/c	Z = 4
a = 5.213 (5) Å	? radiation, λ = ? Å
b = 4.967 (6) Å	?, ? × ? × ? mm
c = 5.318 (5) Å

Data collection top

Refinement top

Least-squares matrix: full	2524 data points
R_p = 0.083	Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 203.9 #6 (sig-2) = -16.0 #7 (gam-0) = 0.00 #8 (gam-1) = 31.42 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2342 #2 (bet-0) = 0.025207 #3 (bet-1) = 0.028487 #4 (sig-0) = 0.0 #5 (sig-1) = 104.6 #6 (sig-2) = -34.9 #7 (gam-0) = 0.00 #8 (gam-1) = 25.65 #9 (gam-2) = 0.00 #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, TOF Profile function number 3 with 14 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2248 #2 (bet-0) = 0.026918 #3 (bet-1) = 0.029309 #4 (sig-0) = 0.0 #5 (sig-1) = 71.8 #6 (sig-2) = 8.3 #7 (gam-0) = 0.00 #8 (gam-1) = 6.00 #9 (gam-2) = 0.00 #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
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993	Background function: GSAS Background function number 2 with 8 terms. Cosine Fourier series 1: -13.9330 2: 27.0721 3: -21.7005 4: 15.3369 5: -8.91545 6: 4.30403 7: -1.50325 8: 0.342467

Crystal data top

O₂Zr	β = 100.16 (9)°
M_r = 123.22	V = 135.53 Å³
Monoclinic, P2₁/c	Z = 4
a = 5.213 (5) Å	? radiation, λ = ? Å
b = 4.967 (6) Å	?, ? × ? × ? mm
c = 5.318 (5) Å

Data collection top

Refinement top

R_p = 0.083	2524 data points
R_wp = 0.083	19 parameters
R_exp = 0.048	0 restraints
R(F²) = 0.38423	(Δ/σ)_max = 0.46
χ² = 2.993

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
ZR1	0.2758	0.0411	0.2082	0.01*
O2	0.0703	0.3359	0.3406	0.01*
O3	0.4423	0.7549	0.4789	0.01*

Experimental details

	(PRL42703_phase_1)	(PRL42703_phase_2)	(PRL47388_ZRO2_phase_1)	(PRL47388_ZRO2_phase_2)
Crystal data
Chemical formula	Fe_0.20Mg_0.80O	Fe	Fe_0.30Mg_0.70O	Fe
M_r	46.62	55.85	49.77	55.85
Crystal system, space group	Cubic, Fm3m	Cubic, Im3m	Cubic, Fm3m	Cubic, Im3m
Temperature (K)	?	?	?	?
a, b, c (Å)	4.19971 (13), 4.19971, 4.19971	2.8403 (3), 2.84034, 2.84034	4.1896 (2), 4.18955, 4.18955	2.8274 (4), 2.8274, 2.8274
α, β, γ (°)	90, 90, 90	90, 90, 90	90, 90, 90	90, 90, 90
V (Å³)	74.07	22.92	73.54	22.60
Z	4	2	4	2
Radiation type	?, λ = ? Å	?, λ = ? Å	?, λ = ? Å	?, λ = ? Å
Specimen shape, size (mm)	?, ? × ? × ?	?, ? × ? × ?	?, ? × ? × ?	?, ? × ? × ?

Data collection
Diffractometer	?	?	?	?
Specimen mounting	?	?	?	?
Data collection mode	?	?	?	?
Scan method	?	?	?	?
2θ values (°)	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?	2θ_min = ? 2θ_max = ? 2θ_step = ?

Refinement
R factors and goodness of fit	R_p = 0.283, R_wp = 0.136, R_exp = 0.092, R(F²) = 0.15908, χ² = 2.190	R_p = 0.283, R_wp = 0.136, R_exp = 0.092, R(F²) = 0.15908, χ² = 2.190	R_p = 0.083, R_wp = 0.083, R_exp = 0.048, R(F²) = 0.38423, χ² = 2.993	R_p = 0.083, R_wp = 0.083, R_exp = 0.048, R(F²) = 0.38423, χ² = 2.993
No. of data points	2524	2524	2524	2524
No. of parameters	12	12	19	19
(Δ/σ)_max	0.29	0.29	0.46	0.46

	(PRL47388_ZRO2_phase_3)
Crystal data
Chemical formula	O₂Zr
M_r	123.22
Crystal system, space group	Monoclinic, P2₁/c
Temperature (K)	?
a, b, c (Å)	5.213 (5), 4.967 (6), 5.318 (5)
α, β, γ (°)	90, 100.16 (9), 90
V (Å³)	135.53
Z	4
Radiation type	?, λ = ? Å
Specimen shape, size (mm)	?, ? × ? × ?

Data collection
Diffractometer	?
Specimen mounting	?
Data collection mode	?
Scan method	?
2θ values (°)	2θ_min = ? 2θ_max = ? 2θ_step = ?

Refinement
R factors and goodness of fit	R_p = 0.083, R_wp = 0.083, R_exp = 0.048, R(F²) = 0.38423, χ² = 2.993
No. of data points	2524
No. of parameters	19
(Δ/σ)_max	0.46

Computer programs: GSAS.

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Format		BIBTeX
		EndNote
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		Medline
		CIF
		SGML
		Text
		Plain Text

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