Utilizing a unified structure model in (3 + 1)-dimensional superspace to identify a homologous phase (Ga_1−αAl_α)₂O₃(ZnO)_m in ZnO-based thermoelectric composites

A unified structure model in (3 + 1)-dimensional superspace proved suitable for identification of a homologous phase (Ga_1−αAl_α)₂O₃(ZnO)_m by the profile fitting of powder X-ray diffraction intensities for thermoelectric composite materials in the pseudoternary system ZnO–Al₂O₃–Ga₂O₃. A homologous compound of the phase parameter m ≃ 37 was found to coexist with (Al,Ga)-doped ZnO in samples sintered at 1723 K in air. The thermoelectric properties of the composite materials were closely related to the phase fractions. The higher the phase fraction of (Al,Ga)-doped ZnO with the wurtzite structure, the higher the electrical conductivity. On the other hand, the homologous compound with the long-period structure was effective in lowering the thermal conductivity of the materials.

Computing details

(sample_I_m=37_3d)

Crystal data

Zn39O40	V = 7479.9 (17) Å^3
Mr = 3189.8	Z = 8
Orthorhombic, Cmcm	F(000) = 76
Hall symbol: -C -2x;-2yc;-2zc	Dx = 5.665 Mg m^−3
a = 3.2573 (5) Å	Cu Kα radiation
b = 19.796 (3) Å	T = 293 K
c = 115.99889 (17) Å	colourless

Data collection

Rigaku Smart Lab 3 diffractometer

2θmin = 20.02°, 2θmax = 90°, 2θstep = 0.02°

Refinement

Rp = 0.120	38 parameters
Rwp = 0.160	0 restraints
Rexp = 0.085	2 constraints
R(F) = 0.055	Weighting scheme based on measured s.u.'s
4001 data points	(Δ/σ)max = 0.048
Excluded region(s): from 9.99 to 20.000, from 100 to 90.090	Background function: 15 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: March & Dollase

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

	x	y	z	Uiso*/Ueq
Zn1	0	0.194404	0.007418	0.01*
Zn2	0	0.816347	0.020059	0.01*
Zn3	0	0.438481	0.032687	0.01*
Zn4	0	0.06052	0.045377	0.01*
Zn5	0	0.68221	0.058187	0.01*
Zn6	0	0.303429	0.071127	0.01*
Zn7	0	0.924233	0.084154	0.01*
Zn8	0	0.544838	0.097188	0.01*
Zn9	0	0.165532	0.110139	0.01*
Zn10	0	0.786571	0.122945	0.01*
Zn11	0	0.408081	0.135592	0.01*
Zn12	0	0.030024	0.148112	0.01*
Zn13	0	0.652222	0.160573	0.01*
Zn14	0	0.274453	0.173053	0.01*
Zn15	0	0.896564	0.185615	0.01*
Zn16	0	0.51856	0.198296	0.01*
Zn17	0	0.140635	0.2111	0.01*
Zn18	0	0.763129	0.224007	0.01*
Zn19	0	0.386424	0.236985	0.01*
Zn20	0	0.572846	0.505298	0.01*
Zn21	0	0.951752	0.518108	0.01*
Zn22	0	0.330981	0.53098	0.01*
Zn23	0	0.710288	0.543848	0.01*
Zn24	0	0.089401	0.556642	0.01*
Zn25	0	0.468134	0.569326	0.01*
Zn26	0	0.846449	0.581911	0.01*
Zn27	0	0.224472	0.594457	0.01*
Zn28	0	0.60242	0.607039	0.01*
Zn29	0	0.980519	0.61972	0.01*
Zn30	0	0.358884	0.632526	0.01*
Zn31	0	0.737478	0.645437	0.01*
Zn32	0	0.116098	0.658408	0.01*
Zn33	0	0.494458	0.671396	0.01*
Zn34	0	0.872275	0.684381	0.01*
Zn35	0	0.249379	0.697377	0.01*
Zn36	0	0.625746	0.71042	0.01*
Zn37	0	0.001503	0.72354	0.01*
Zn38	0	0.376839	0.736743	0.01*
Zn39	0	0.77555	0.75	0.01*
Zn40	0	0.983639	0.25	0.01*
O1	0	0.508925	0.013508	0.02*
O2	0	0.133015	0.025369	0.02*
O3	0	0.756225	0.037282	0.02*
O4	0	0.378415	0.049367	0.02*
O5	0	0	0.061656	0.02*
O6	0	0.621901	0.074102	0.02*
O7	0	0.244244	0.086628	0.02*
O8	0	0.866815	0.099195	0.02*
O9	0	0.488951	0.111825	0.02*
O10	0	0.110212	0.124569	0.02*
O11	0	0.730837	0.137443	0.02*
O12	0	0.351653	0.150375	0.02*
O13	0	0.973471	0.163218	0.02*
O14	0	0.596415	0.175826	0.02*
O15	0	0.219736	0.188146	0.02*
O16	0	0.842326	0.200264	0.02*
O17	0	0.463597	0.212375	0.02*
O18	0	0.084085	0.224672	0.02*
O19	0	0.705289	0.23724	0.02*
O20	0	0.328799	0.25	0.02*
O21	0	0.88464	0.498448	0.02*
O22	0	0.260972	0.510603	0.02*
O23	0	0.638258	0.522966	0.02*
O24	0	0.016243	0.535459	0.02*
O25	0	0.39433	0.547977	0.02*
O26	0	0.772078	0.560449	0.02*
O27	0	0.149505	0.572873	0.02*
O28	0	0.527021	0.585292	0.02*
O29	0	0.90506	0.597746	0.02*
O30	0	0.283714	0.610232	0.02*
O31	0	0.662664	0.622708	0.02*
O32	0	0.041408	0.635134	0.02*
O33	0	0.419612	0.647515	0.02*
O34	0	0.797324	0.659923	0.02*
O35	0	0.174884	0.672456	0.02*
O36	0	0.552666	0.685185	0.02*
O37	0	0.930793	0.698103	0.02*
O38	0	0.309041	0.711128	0.02*
O39	0	0.686931	0.724153	0.02*
O40	0	0.06393	0.737108	0.02*
O41	0	0.439644	0.75	0.02*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

Geometric parameters (Å, º)

Zn1—O2	2.4110 (2)	Zn21—O1^xii	1.8823 (5)
Zn1—O21^i	1.8791 (4)	Zn21—O1^xiii	1.8823 (5)
Zn1—O22^ii	1.8893 (5)	Zn21—O2^ix	1.8776 (5)
Zn1—O22^iii	1.8893 (5)	Zn21—O24^xiv	2.3834 (2)
Zn1—O22^iv	2.4711 (2)	Zn22—O2^xv	1.8932 (5)
Zn2—O3	2.3255 (2)	Zn22—O2^xvi	1.8932 (5)
Zn2—O22^i	1.8831 (4)	Zn22—O3^ix	1.8747 (5)
Zn2—O23^v	1.8905 (5)	Zn22—O25	2.3367 (2)
Zn2—O23^vi	1.8905 (5)	Zn23—O3^xii	1.9163 (5)
Zn3—O4	2.2710 (2)	Zn23—O3^xiii	1.9163 (5)
Zn3—O23^i	1.8919 (4)	Zn23—O4^ix	1.8690 (5)
Zn3—O24^ii	1.8866 (5)	Zn23—O26	2.2813 (2)
Zn3—O24^iii	1.8866 (5)	Zn24—O4^xv	1.9418 (5)
Zn4—O5	2.2363 (2)	Zn24—O4^xvi	1.9418 (5)
Zn4—O24^vii	1.9060 (4)	Zn24—O5^xvii	1.8629 (5)
Zn4—O25^ii	1.8821 (5)	Zn24—O27	2.2272 (2)
Zn4—O25^iii	1.8821 (5)	Zn25—O5^xv	1.9601 (5)
Zn5—O6	2.1985 (2)	Zn25—O5^xvi	1.9601 (5)
Zn5—O25^i	1.9231 (4)	Zn25—O6^ix	1.8665 (5)
Zn5—O26^v	1.8816 (5)	Zn25—O28	2.1884 (2)
Zn5—O26^vi	1.8816 (5)	Zn26—O6^xii	1.9661 (5)
Zn6—O7	2.1461 (2)	Zn26—O6^xiii	1.9661 (5)
Zn6—O26^i	1.9413 (4)	Zn26—O7^ix	1.8769 (5)
Zn6—O27^ii	1.8872 (5)	Zn26—O29	2.1726 (2)
Zn6—O27^iii	1.8872 (5)	Zn27—O7^xv	1.9649 (5)
Zn7—O8	2.0823 (2)	Zn27—O7^xvi	1.9649 (5)
Zn7—O27^i	1.9604 (3)	Zn27—O8^ix	1.8889 (5)
Zn7—O28^v	1.8977 (5)	Zn27—O30	2.1734 (2)
Zn7—O28^vi	1.8977 (5)	Zn28—O8^xii	1.9625 (5)
Zn8—O9	2.0265 (2)	Zn28—O8^xiii	1.9625 (5)
Zn8—O28^i	1.9819 (3)	Zn28—O9^ix	1.8921 (5)
Zn8—O29^v	1.9080 (5)	Zn28—O31	2.1739 (2)
Zn8—O29^vi	1.9080 (5)	Zn29—O9^xii	1.9638 (5)
Zn9—O10	2.0003 (2)	Zn29—O9^xiii	1.9638 (5)
Zn9—O29^i	2.0049 (3)	Zn29—O10^ix	1.8821 (5)
Zn9—O30^ii	1.9137 (5)	Zn29—O32^xiv	2.1564 (2)
Zn9—O30^iii	1.9137 (5)	Zn30—O10^xv	1.9695 (5)
Zn10—O11	2.0114 (2)	Zn30—O10^xvi	1.9695 (5)
Zn10—O30^i	2.0275 (3)	Zn30—O11^ix	1.8655 (5)
Zn10—O31^v	1.9140 (5)	Zn30—O33	2.1138 (2)
Zn10—O31^vi	1.9140 (5)	Zn31—O11^xii	1.9763 (5)
Zn11—O12	2.0466 (2)	Zn31—O11^xiii	1.9763 (5)
Zn11—O31^i	2.0481 (3)	Zn31—O12^ix	1.8551 (5)
Zn11—O32^ii	1.9119 (5)	Zn31—O34	2.0560 (2)
Zn11—O32^iii	1.9119 (5)	Zn32—O12^xv	1.9820 (5)
Zn12—O13^viii	2.0794 (2)	Zn32—O12^xvi	1.9820 (5)
Zn12—O32^vii	2.0654 (3)	Zn32—O13^ix	1.8588 (5)
Zn12—O33^ii	1.9109 (5)	Zn32—O35	2.0024 (2)
Zn12—O33^iii	1.9109 (5)	Zn33—O13^xii	1.9889 (4)
Zn13—O14	2.0859 (2)	Zn33—O13^xiii	1.9889 (4)
Zn13—O33^i	2.0776 (3)	Zn33—O14^ix	1.8709 (5)
Zn13—O34^v	1.9120 (5)	Zn33—O36	1.9713 (2)
Zn13—O34^vi	1.9120 (5)	Zn34—O14^xii	2.0054 (4)
Zn14—O15	2.0588 (2)	Zn34—O14^xiii	2.0054 (4)
Zn14—O34^i	2.0829 (3)	Zn34—O15^ix	1.8731 (6)
Zn14—O35^ii	1.9140 (5)	Zn34—O37	1.9686 (2)
Zn14—O35^iii	1.9140 (5)	Zn35—O15^xv	2.0428 (4)
Zn15—O16	2.0101 (2)	Zn35—O15^xvi	2.0428 (4)
Zn15—O35^i	2.0810 (3)	Zn35—O16^ix	1.8460 (6)
Zn15—O36^v	1.9145 (5)	Zn35—O38	1.9848 (2)
Zn15—O36^vi	1.9145 (5)	Zn36—O16^xii	2.1071 (4)
Zn16—O17	1.9624 (2)	Zn36—O16^xiii	2.1071 (4)
Zn16—O36^i	2.0739 (3)	Zn36—O17^ix	1.7831 (6)
Zn16—O37^v	1.9127 (5)	Zn36—O39	2.0012 (2)
Zn16—O37^vi	1.9127 (5)	Zn37—O17^xv	2.1925 (4)
Zn17—O18	1.9318 (2)	Zn37—O17^xvi	2.1925 (4)
Zn17—O37^i	2.0670 (3)	Zn37—O18^xvii	1.6994 (5)
Zn17—O38^ii	1.9092 (5)	Zn37—O40	2.0011 (2)
Zn17—O38^iii	1.9092 (5)	Zn38—O18^xv	2.2829 (4)
Zn18—O19	1.9150 (2)	Zn38—O18^xvi	2.2829 (4)
Zn18—O38^i	2.0671 (3)	Zn38—O19^ix	1.6268 (5)
Zn18—O39^v	1.9053 (5)	Zn38—O41	1.9775 (2)
Zn18—O39^vi	1.9053 (5)	Zn39—O19^xii	2.2332 (4)
Zn19—O20	1.8922 (2)	Zn39—O19^xiii	2.2332 (4)
Zn19—O39^i	2.0795 (3)	Zn39—O19^x	2.2332 (4)
Zn19—O40^ii	1.9023 (5)	Zn39—O19^xi	2.2332 (4)
Zn19—O40^iii	1.9023 (5)	Zn39—O20^ix	2.0657 (6)
Zn20—O1^ix	1.8781 (4)	Zn40—O40^i	1.7673 (2)
Zn20—O21^x	1.8841 (5)	Zn40—O40^xviii	1.7673 (2)
Zn20—O21^xi	1.8841 (5)	Zn40—O41^v	2.2269 (5)
Zn20—O23	2.4243 (2)	Zn40—O41^vi	2.2269 (5)
O2—Zn1—O21^i	93.354 (8)	O1^xii—Zn21—O1^xiii	119.818 (10)
O2—Zn1—O22^ii	93.830 (4)	O1^xii—Zn21—O2^ix	119.786 (5)
O2—Zn1—O22^iii	93.830 (4)	O1^xii—Zn21—O24^xiv	91.024 (4)
O2—Zn1—O22^iv	178.0415 (1)	O1^xiii—Zn21—O2^ix	119.786 (5)
O21^i—Zn1—O22^ii	119.843 (5)	O1^xiii—Zn21—O24^xiv	91.024 (4)
O21^i—Zn1—O22^iii	119.843 (5)	O2^ix—Zn21—O24^xiv	95.734 (8)
O21^i—Zn1—O22^iv	88.605 (8)	O2^xv—Zn22—O2^xvi	118.695 (9)
O22^ii—Zn1—O22^iii	119.096 (11)	O2^xv—Zn22—O3^ix	118.733 (4)
O22^ii—Zn1—O22^iv	85.186 (4)	O2^xv—Zn22—O25	95.051 (4)
O22^iii—Zn1—O22^iv	85.186 (4)	O2^xvi—Zn22—O3^ix	118.733 (4)
O3—Zn2—O22^i	94.843 (8)	O2^xvi—Zn22—O25	95.051 (4)
O3—Zn2—O23^v	95.166 (4)	O3^ix—Zn22—O25	99.508 (7)
O3—Zn2—O23^vi	95.166 (4)	O3^xii—Zn23—O3^xiii	116.404 (9)
O22^i—Zn2—O23^v	119.360 (5)	O3^xii—Zn23—O4^ix	117.462 (4)
O22^i—Zn2—O23^vi	119.360 (5)	O3^xii—Zn23—O26	98.628 (4)
O23^v—Zn2—O23^vi	118.975 (11)	O3^xiii—Zn23—O4^ix	117.462 (4)
O4—Zn3—O23^i	95.013 (8)	O3^xiii—Zn23—O26	98.628 (4)
O4—Zn3—O24^ii	95.943 (4)	O4^ix—Zn23—O26	102.392 (7)
O4—Zn3—O24^iii	95.943 (4)	O4^xv—Zn24—O4^xvi	114.014 (9)
O23^i—Zn3—O24^ii	118.885 (5)	O4^xv—Zn24—O5^xvii	116.576 (4)
O23^i—Zn3—O24^iii	118.885 (5)	O4^xv—Zn24—O27	101.075 (4)
O24^ii—Zn3—O24^iii	119.373 (11)	O4^xvi—Zn24—O5^xvii	116.576 (4)
O5—Zn4—O24^vii	94.736 (8)	O4^xvi—Zn24—O27	101.075 (4)
O5—Zn4—O25^ii	96.840 (4)	O5^xvii—Zn24—O27	104.098 (7)
O5—Zn4—O25^iii	96.840 (4)	O5^xv—Zn25—O5^xvi	112.383 (9)
O24^vii—Zn4—O25^ii	118.382 (5)	O5^xv—Zn25—O6^ix	116.235 (4)
O24^vii—Zn4—O25^iii	118.382 (5)	O5^xv—Zn25—O28	102.281 (4)
O25^ii—Zn4—O25^iii	119.842 (11)	O5^xvi—Zn25—O6^ix	116.235 (4)
O6—Zn5—O25^i	95.122 (8)	O5^xvi—Zn25—O28	102.281 (4)
O6—Zn5—O26^v	98.283 (4)	O6^ix—Zn25—O28	104.921 (7)
O6—Zn5—O26^vi	98.283 (4)	O6^xii—Zn26—O6^xiii	111.862 (9)
O25^i—Zn5—O26^v	117.697 (5)	O6^xii—Zn26—O7^ix	116.049 (4)
O25^i—Zn5—O26^vi	117.697 (5)	O6^xii—Zn26—O29	102.670 (4)
O26^v—Zn5—O26^vi	119.901 (11)	O6^xiii—Zn26—O7^ix	116.049 (4)
O7—Zn6—O26^i	96.559 (9)	O6^xiii—Zn26—O29	102.670 (4)
O7—Zn6—O27^ii	100.347 (4)	O7^ix—Zn26—O29	105.330 (7)
O7—Zn6—O27^iii	100.347 (4)	O7^xv—Zn27—O7^xvi	111.968 (9)
O26^i—Zn6—O27^ii	116.655 (5)	O7^xv—Zn27—O8^ix	115.851 (4)
O26^i—Zn6—O27^iii	116.655 (5)	O7^xv—Zn27—O30	102.654 (4)
O27^ii—Zn6—O27^iii	119.307 (11)	O7^xvi—Zn27—O8^ix	115.851 (4)
O8—Zn7—O27^i	98.792 (9)	O7^xvi—Zn27—O30	102.654 (4)
O8—Zn7—O28^v	102.667 (4)	O8^ix—Zn27—O30	105.739 (7)
O8—Zn7—O28^vi	102.667 (4)	O8^xii—Zn28—O8^xiii	112.176 (9)
O27^i—Zn7—O28^v	115.155 (5)	O8^xii—Zn28—O9^ix	115.640 (4)
O27^i—Zn7—O28^vi	115.155 (5)	O8^xii—Zn28—O31	102.556 (4)
O28^v—Zn7—O28^vi	118.240 (11)	O8^xiii—Zn28—O9^ix	115.640 (4)
O9—Zn8—O28^i	101.041 (9)	O8^xiii—Zn28—O31	102.556 (4)
O9—Zn8—O29^v	104.795 (4)	O9^ix—Zn28—O31	106.208 (7)
O9—Zn8—O29^vi	104.795 (4)	O9^xii—Zn29—O9^xiii	112.062 (9)
O28^i—Zn8—O29^v	113.374 (5)	O9^xii—Zn29—O10^ix	115.662 (3)
O28^i—Zn8—O29^vi	113.374 (5)	O9^xii—Zn29—O32^xiv	102.395 (4)
O29^v—Zn8—O29^vi	117.211 (12)	O9^xiii—Zn29—O10^ix	115.662 (3)
O10—Zn9—O29^i	102.616 (9)	O9^xiii—Zn29—O32^xiv	102.395 (4)
O10—Zn9—O30^ii	106.423 (4)	O10^ix—Zn29—O32^xiv	106.597 (7)
O10—Zn9—O30^iii	106.423 (4)	O10^xv—Zn30—O10^xvi	111.576 (9)
O29^i—Zn9—O30^ii	111.716 (5)	O10^xv—Zn30—O11^ix	116.043 (4)
O29^i—Zn9—O30^iii	111.716 (5)	O10^xv—Zn30—O33	102.054 (4)
O30^ii—Zn9—O30^iii	116.656 (12)	O10^xvi—Zn30—O11^ix	116.043 (4)
O11—Zn10—O30^i	103.398 (9)	O10^xvi—Zn30—O33	102.054 (4)
O11—Zn10—O31^v	107.459 (4)	O11^ix—Zn30—O33	106.857 (7)
O11—Zn10—O31^vi	107.459 (4)	O11^xii—Zn31—O11^xiii	110.992 (9)
O30^i—Zn10—O31^v	110.480 (5)	O11^xii—Zn31—O12^ix	116.535 (4)
O30^i—Zn10—O31^vi	110.480 (5)	O11^xii—Zn31—O34	101.572 (4)
O31^v—Zn10—O31^vi	116.629 (12)	O11^xiii—Zn31—O12^ix	116.535 (4)
O12—Zn11—O31^i	103.780 (9)	O11^xiii—Zn31—O34	101.572 (4)
O12—Zn11—O32^ii	107.984 (4)	O12^ix—Zn31—O34	107.200 (7)
O12—Zn11—O32^iii	107.984 (4)	O12^xv—Zn32—O12^xvi	110.515 (9)
O31^i—Zn11—O32^ii	109.715 (5)	O12^xv—Zn32—O13^ix	116.639 (4)
O31^i—Zn11—O32^iii	109.715 (5)	O12^xv—Zn32—O35	101.268 (4)
O32^ii—Zn11—O32^iii	116.832 (12)	O12^xvi—Zn32—O13^ix	116.639 (4)
O13^viii—Zn12—O32^vii	104.218 (9)	O12^xvi—Zn32—O35	101.268 (4)
O13^viii—Zn12—O33^ii	108.147 (4)	O13^ix—Zn32—O35	108.065 (7)
O13^viii—Zn12—O33^iii	108.147 (4)	O13^xii—Zn33—O13^xiii	109.949 (9)
O32^vii—Zn12—O33^ii	109.318 (5)	O13^xii—Zn33—O14^ix	115.973 (4)
O32^vii—Zn12—O33^iii	109.318 (5)	O13^xii—Zn33—O36	101.561 (4)
O33^ii—Zn12—O33^iii	116.930 (12)	O13^xiii—Zn33—O14^ix	115.973 (4)
O14—Zn13—O33^i	104.827 (9)	O13^xiii—Zn33—O36	101.561 (4)
O14—Zn13—O34^v	108.066 (4)	O14^ix—Zn33—O36	109.827 (7)
O14—Zn13—O34^vi	108.066 (4)	O14^xii—Zn34—O14^xiii	108.613 (9)
O33^i—Zn13—O34^v	109.196 (5)	O14^xii—Zn34—O15^ix	114.579 (3)
O33^i—Zn13—O34^vi	109.196 (5)	O14^xii—Zn34—O37	102.606 (4)
O34^v—Zn13—O34^vi	116.817 (12)	O14^xiii—Zn34—O15^ix	114.579 (3)
O15—Zn14—O34^i	105.243 (9)	O14^xiii—Zn34—O37	102.606 (4)
O15—Zn14—O35^ii	107.846 (4)	O15^ix—Zn34—O37	112.563 (6)
O15—Zn14—O35^iii	107.846 (4)	O15^xv—Zn35—O15^xvi	105.742 (9)
O34^i—Zn14—O35^ii	109.330 (5)	O15^xv—Zn35—O16^ix	112.919 (3)
O34^i—Zn14—O35^iii	109.330 (5)	O15^xv—Zn35—O38	104.074 (5)
O35^ii—Zn14—O35^iii	116.629 (12)	O15^xvi—Zn35—O16^ix	112.919 (3)
O16—Zn15—O35^i	104.895 (9)	O15^xvi—Zn35—O38	104.074 (5)
O16—Zn15—O36^v	107.605 (4)	O16^ix—Zn35—O38	116.066 (6)
O16—Zn15—O36^vi	107.605 (4)	O16^xii—Zn36—O16^xiii	101.237 (10)
O35^i—Zn15—O36^v	109.737 (5)	O16^xii—Zn36—O17^ix	111.631 (3)
O35^i—Zn15—O36^vi	109.737 (5)	O16^xii—Zn36—O39	105.278 (5)
O36^v—Zn15—O36^vi	116.580 (12)	O16^xiii—Zn36—O17^ix	111.631 (3)
O17—Zn16—O36^i	103.494 (9)	O16^xiii—Zn36—O39	105.278 (5)
O17—Zn16—O37^v	107.481 (4)	O17^ix—Zn36—O39	119.940 (5)
O17—Zn16—O37^vi	107.481 (4)	O17^xv—Zn37—O17^xvi	95.945 (10)
O36^i—Zn16—O37^v	110.353 (5)	O17^xv—Zn37—O18^xvii	111.088 (3)
O36^i—Zn16—O37^vi	110.353 (5)	O17^xv—Zn37—O40	105.664 (5)
O37^v—Zn16—O37^vi	116.754 (12)	O17^xvi—Zn37—O18^xvii	111.088 (3)
O18—Zn17—O37^i	101.420 (9)	O17^xvi—Zn37—O40	105.664 (5)
O18—Zn17—O38^ii	107.518 (5)	O18^xvii—Zn37—O40	123.707 (5)
O18—Zn17—O38^iii	107.518 (5)	O18^xv—Zn38—O18^xvi	91.029 (10)
O37^i—Zn17—O38^ii	110.990 (5)	O18^xv—Zn38—O19^ix	111.123 (3)
O37^i—Zn17—O38^iii	110.990 (5)	O18^xv—Zn38—O41	105.303 (5)
O38^ii—Zn17—O38^iii	117.093 (12)	O18^xvi—Zn38—O19^ix	111.123 (3)
O19—Zn18—O38^i	99.559 (9)	O18^xvi—Zn38—O41	105.303 (5)
O19—Zn18—O39^v	107.645 (5)	O19^ix—Zn38—O41	126.924 (5)
O19—Zn18—O39^vi	107.645 (5)	O19^xii—Zn39—O19^xiii	93.654 (10)
O38^i—Zn18—O39^v	111.410 (5)	O19^xii—Zn39—O19^x	83.025 (9)
O38^i—Zn18—O39^vi	111.410 (5)	O19^xii—Zn39—O19^xi	160.442 (3)
O39^v—Zn18—O39^vi	117.476 (12)	O19^xii—Zn39—O20^ix	99.7791 (17)
O20—Zn19—O39^i	98.634 (9)	O19^xiii—Zn39—O19^x	160.442 (3)
O20—Zn19—O40^ii	107.787 (5)	O19^xiii—Zn39—O19^xi	83.025 (9)
O20—Zn19—O40^iii	107.787 (5)	O19^xiii—Zn39—O20^ix	99.7791 (17)
O39^i—Zn19—O40^ii	111.478 (5)	O19^x—Zn39—O19^xi	93.654 (10)
O39^i—Zn19—O40^iii	111.478 (5)	O19^x—Zn39—O20^ix	99.7791 (17)
O40^ii—Zn19—O40^iii	117.778 (12)	O19^xi—Zn39—O20^ix	99.7791 (17)
O1^ix—Zn20—O21^x	120.130 (5)	O40^i—Zn40—O40^xviii	115.603 (8)
O1^ix—Zn20—O21^xi	120.130 (5)	O40^i—Zn40—O41^v	111.309 (5)
O1^ix—Zn20—O23	91.816 (8)	O40^i—Zn40—O41^vi	111.309 (5)
O21^x—Zn20—O21^xi	119.639 (10)	O40^xviii—Zn40—O41^v	111.309 (5)
O21^x—Zn20—O23	87.500 (4)	O40^xviii—Zn40—O41^vi	111.309 (5)
O21^xi—Zn20—O23	87.500 (4)	O41^v—Zn40—O41^vi	94.002 (13)

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

(sample_I_m=37_4d)

Crystal data

Ga0.397Zn1.785O2.182	V = 95.90 (2) Å^3
Mr = 179.3	Z = 1
Orthorhombic, Cmmm(00γ)0s0†	F(000) = 76
q = 0.012821c*‡	Dx = 3.105 Mg m^−3
a = 3.2573 (5) Å	Cu Kα radiation
b = 19.796 (3) Å	T = 293 K
c = 1.48716 (17) Å	colourless

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, −x₂, x₃, x₄+1/2; (3) −x₁, x₂, −x₃, −x₄+1/2; (4) x₁, −x₂, −x₃, −x₄; (5) −x₁, −x₂, −x₃, −x₄; (6) x₁, x₂, −x₃, −x₄+1/2; (7) x₁, −x₂, x₃, x₄+1/2; (8) −x₁, x₂, x₃, x₄; (9) x₁+1/2, x₂+1/2, x₃, x₄; (10) −x₁+1/2, −x₂+1/2, x₃, x₄+1/2; (11) −x₁+1/2, x₂+1/2, −x₃, −x₄+1/2; (12) x₁+1/2, −x₂+1/2, −x₃, −x₄; (13) −x₁+1/2, −x₂+1/2, −x₃, −x₄; (14) x₁+1/2, x₂+1/2, −x₃, −x₄+1/2; (15) x₁+1/2, −x₂+1/2, x₃, x₄+1/2; (16) −x₁+1/2, x₂+1/2, x₃, x₄.

‡ ;

Data collection

Rigalu Smart Lab 3 diffractometer

2θmin = 20.02°, 2θmax = 90°, 2θstep = 0.02°

Refinement

Rp = 0.120	38 parameters
Rwp = 0.160	0 restraints
Rexp = 0.085	2 constraints
R(F) = 0.055	Weighting scheme based on measured s.u.'s
4001 data points	(Δ/σ)max = 0.048
Excluded region(s): from 9.99 to 20.000, from 100 to 90.090	Background function: 15 Legendre polynoms
Profile function: Pseudo-Voigt	Preferred orientation correction: March & Dollase

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
M1	0	0.3841 (5)	0	0.01*	0.5
M1a	0	0.776 (6)	0	0.01*	0.0128
M1c	0	−0.016 (6)	0	0.01*	0.0128
O1	0	0.886 (3)	0.5	0.02*	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
?	?	?	?	?	?	?

Geometric parameters (Å, º)

	Average	Minimum	Maximum
M1a—M1a^i		3.26 (4)	3.26 (4)
M1a—M1a^ii		3.26 (4)	3.26 (4)
M1a^i—M1a—M1a^ii	180	180	180

Symmetry codes: (i) x₁−1, x₂, x₃, x₄; (ii) x₁+1, x₂, x₃, x₄.