On the use of Hirsh­feld surfaces for estimating atomic charges in ionic species: crystal structure of the natural ilmenite (Mg0.4168Fe0.5832)TiO3

Almeida, L.F. de; Rodrigues, B.L.

doi:10.1107/S2053229622009366

On the use of Hirshfeld surfaces for estimating atomic charges in ionic species: crystal structure of the natural ilmenite (Mg_0.4168Fe_0.5832)TiO₃

We performed an analysis by single-crystal X-ray diffraction and scanning electron microscopy (SEM), aiming to solve and refine the structure of an ilmenite single crystal [(Fe_0.5832Mg₀₄₁₆₈)TiO₃] from the city of Ouvidor (Goiás, Brazil). Hirshfeld partition was used to explore the values of w(r), d_norm and curvedness that achieve complementary surfaces for neighbouring atoms in this ionic system, and the subsequent impact on the charge distribution, allowing the ionic radius and the charges of the ilmenite sample to be modelled.

Keywords: ilmenite; geikielite; Hirshfeld surface; crystal structure; ionic charge; structure refinement.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229622009366/ov3161sup1.cif Contains datablocks I, global
	Structure factor file (CIF format) https://doi.org/10.1107/S2053229622009366/ov3161Isup2.hkl Contains datablock I
	Text file https://doi.org/10.1107/S2053229622009366/ov3161sup3.txt shelxl.res file refinement results considering all data

CCDC reference: 2209182

Computing details top

Data collection: CrysAlis PRO (Rigaku OD, 2018); cell refinement: CrysAlis PRO (Rigaku OD, 2018); data reduction: CrysAlis PRO (Rigaku OD, 2018); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015b); molecular graphics: ORTEP-3 for Windows (Farrugia, 2012).

(I) top

Crystal data top

Mg_2.50Fe_3.50Ti₆O₁₈	D_x = 4.404 Mg m⁻³
M_r = 831.65	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3	Cell parameters from 1298 reflections
a = 5.08348 (5) Å	θ = 4.4–67.7°
c = 14.01305 (12) Å	µ = 7.77 mm⁻¹
V = 313.61 (1) Å³	T = 293 K
Z = 1	Natural mineral single-crystal, black
F(000) = 397	0.30 × 0.15 × 0.10 mm

Data collection top

Rigaku Xcalibur Gemini ultra with an Atlas detector diffractometer	584 independent reflections
Radiation source: fine-focus sealed tube	545 reflections with I > 2σ(I)
Detector resolution: 10.4186 pixels mm^-1	R_int = 0.048
ω scans	θ_max = 45.3°, θ_min = 4.4°
Absorption correction: multi-scan (CrysAlis PRO; Rigaku OD, 2018)	h = −10→10
T_min = 0.239, T_max = 0.430	k = −10→10
15715 measured reflections	l = −27→27

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.023	Secondary atom site location: difference Fourier map
wR(F²) = 0.060	w = 1/[σ²(F_o²) + (0.0222P)² + 0.9027P] where P = (F_o² + 2F_c²)/3
S = 1.29	(Δ/σ)_max < 0.001
582 reflections	Δρ_max = 0.54 e Å⁻³
18 parameters	Δρ_min = −1.25 e Å⁻³

Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Fe1	0.0000	0.0000	0.35436 (17)	0.00171 (8)	0.583 (4)
Mg1	0.0000	0.0000	0.3533 (7)	0.00171 (8)	0.417 (4)
Ti1	0.0000	0.0000	0.14423 (2)	0.00926 (8)
O1	0.29407 (16)	−0.02234 (16)	0.25430 (5)	0.00675 (11)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Fe1	0.00171 (8)	0.00171 (8)	0.00171 (12)	0.00085 (4)	0.000	0.000
Mg1	0.00171 (8)	0.00171 (8)	0.00171 (12)	0.00085 (4)	0.000	0.000
Ti1	0.00920 (9)	0.00920 (9)	0.00940 (12)	0.00460 (4)	0.000	0.000
O1	0.0073 (2)	0.0068 (2)	0.0071 (2)	0.00420 (18)	0.00105 (16)	0.00126 (16)

Geometric parameters (Å, º) top

Fe1—O1ⁱ	1.8750 (12)	Mg1—Mg1^vii	2.988 (4)
Fe1—O1ⁱⁱ	1.8750 (12)	Mg1—Mg1ⁱⁱⁱ	2.988 (4)
Fe1—O1ⁱⁱⁱ	1.8750 (12)	Mg1—Fe1^vi	2.9907 (14)
Fe1—O1	2.0937 (17)	Mg1—Fe1^vii	2.9907 (14)
Fe1—O1^iv	2.0937 (17)	Ti1—O1^viii	2.0655 (7)
Fe1—O1^v	2.0937 (17)	Ti1—O1^ix	2.0655 (7)
Fe1—Ti1	2.945 (2)	Ti1—O1^x	2.0656 (7)
Fe1—Mg1^vi	2.9907 (14)	Ti1—O1^v	2.1900 (7)
Fe1—Mg1^vii	2.9907 (14)	Ti1—O1^iv	2.1900 (7)
Fe1—Mg1ⁱⁱⁱ	2.9907 (14)	Ti1—O1	2.1901 (7)
Mg1—O1ⁱ	1.881 (4)	Ti1—Ti1^ix	3.0016 (1)
Mg1—O1ⁱⁱ	1.881 (4)	Ti1—Ti1^xi	3.0016 (1)
Mg1—O1ⁱⁱⁱ	1.881 (4)	Ti1—Ti1^xii	3.0016 (1)
Mg1—O1	2.084 (6)	Ti1—Mg1^xiii	3.413 (5)
Mg1—O1^iv	2.084 (6)	O1—Fe1ⁱⁱⁱ	1.8750 (12)
Mg1—O1^v	2.084 (6)	O1—Mg1ⁱⁱⁱ	1.881 (4)
Mg1—Ti1	2.930 (9)	O1—Ti1^ix	2.0655 (7)
Mg1—Mg1^vi	2.988 (4)

O1ⁱ—Fe1—O1ⁱⁱ	102.59 (8)	Ti1—Mg1—Fe1^vi	78.92 (13)
O1ⁱ—Fe1—O1ⁱⁱⁱ	102.59 (8)	Mg1^vi—Mg1—Fe1^vi	0.3 (2)
O1ⁱⁱ—Fe1—O1ⁱⁱⁱ	102.59 (8)	Mg1^vii—Mg1—Fe1^vi	116.49 (15)
O1ⁱ—Fe1—O1	93.21 (5)	Mg1ⁱⁱⁱ—Mg1—Fe1^vi	116.48 (15)
O1ⁱⁱ—Fe1—O1	161.87 (11)	O1ⁱ—Mg1—Fe1^vii	43.96 (10)
O1ⁱⁱⁱ—Fe1—O1	82.23 (3)	O1ⁱⁱ—Mg1—Fe1^vii	100.06 (3)
O1ⁱ—Fe1—O1^iv	161.87 (11)	O1ⁱⁱⁱ—Mg1—Fe1^vii	143.01 (14)
O1ⁱⁱ—Fe1—O1^iv	82.23 (3)	O1—Mg1—Fe1^vii	85.32 (13)
O1ⁱⁱⁱ—Fe1—O1^iv	93.21 (5)	O1^iv—Mg1—Fe1^vii	118.8 (3)
O1—Fe1—O1^iv	80.05 (8)	O1^v—Mg1—Fe1^vii	38.38 (3)
O1ⁱ—Fe1—O1^v	82.23 (3)	Ti1—Mg1—Fe1^vii	78.92 (13)
O1ⁱⁱ—Fe1—O1^v	93.21 (5)	Mg1^vi—Mg1—Fe1^vii	116.49 (15)
O1ⁱⁱⁱ—Fe1—O1^v	161.87 (11)	Mg1^vii—Mg1—Fe1^vii	0.3 (2)
O1—Fe1—O1^v	80.05 (8)	Mg1ⁱⁱⁱ—Mg1—Fe1^vii	116.48 (15)
O1^iv—Fe1—O1^v	80.05 (8)	Fe1^vi—Mg1—Fe1^vii	116.40 (8)
O1ⁱ—Fe1—Ti1	115.69 (7)	O1^viii—Ti1—O1^ix	101.93 (2)
O1ⁱⁱ—Fe1—Ti1	115.69 (7)	O1^viii—Ti1—O1^x	101.92 (2)
O1ⁱⁱⁱ—Fe1—Ti1	115.69 (7)	O1^ix—Ti1—O1^x	101.92 (2)
O1—Fe1—Ti1	47.95 (5)	O1^viii—Ti1—O1^v	161.45 (2)
O1^iv—Fe1—Ti1	47.95 (5)	O1^ix—Ti1—O1^v	88.88 (4)
O1^v—Fe1—Ti1	47.95 (5)	O1^x—Ti1—O1^v	90.34 (3)
O1ⁱ—Fe1—Mg1^vi	143.12 (5)	O1^viii—Ti1—O1^iv	90.34 (3)
O1ⁱⁱ—Fe1—Mg1^vi	43.63 (17)	O1^ix—Ti1—O1^iv	161.45 (2)
O1ⁱⁱⁱ—Fe1—Mg1^vi	100.01 (7)	O1^x—Ti1—O1^iv	88.88 (4)
O1—Fe1—Mg1^vi	118.56 (8)	O1^v—Ti1—O1^iv	75.88 (3)
O1^iv—Fe1—Mg1^vi	38.59 (15)	O1^viii—Ti1—O1	88.88 (4)
O1^v—Fe1—Mg1^vi	85.26 (8)	O1^ix—Ti1—O1	90.34 (3)
Ti1—Fe1—Mg1^vi	78.92 (13)	O1^x—Ti1—O1	161.45 (2)
O1ⁱ—Fe1—Mg1^vii	43.63 (17)	O1^v—Ti1—O1	75.88 (3)
O1ⁱⁱ—Fe1—Mg1^vii	100.01 (7)	O1^iv—Ti1—O1	75.88 (3)
O1ⁱⁱⁱ—Fe1—Mg1^vii	143.12 (5)	O1^viii—Ti1—Mg1	116.25 (2)
O1—Fe1—Mg1^vii	85.26 (8)	O1^ix—Ti1—Mg1	116.25 (2)
O1^iv—Fe1—Mg1^vii	118.56 (8)	O1^x—Ti1—Mg1	116.25 (2)
O1^v—Fe1—Mg1^vii	38.59 (15)	O1^v—Ti1—Mg1	45.230 (18)
Ti1—Fe1—Mg1^vii	78.92 (13)	O1^iv—Ti1—Mg1	45.230 (18)
Mg1^vi—Fe1—Mg1^vii	116.40 (8)	O1—Ti1—Mg1	45.229 (18)
O1ⁱ—Fe1—Mg1ⁱⁱⁱ	100.01 (7)	O1^viii—Ti1—Fe1	116.25 (2)
O1ⁱⁱ—Fe1—Mg1ⁱⁱⁱ	143.12 (5)	O1^ix—Ti1—Fe1	116.25 (2)
O1ⁱⁱⁱ—Fe1—Mg1ⁱⁱⁱ	43.63 (17)	O1^x—Ti1—Fe1	116.25 (2)
O1—Fe1—Mg1ⁱⁱⁱ	38.59 (15)	O1^v—Ti1—Fe1	45.230 (18)
O1^iv—Fe1—Mg1ⁱⁱⁱ	85.26 (8)	O1^iv—Ti1—Fe1	45.230 (18)
O1^v—Fe1—Mg1ⁱⁱⁱ	118.56 (8)	O1—Ti1—Fe1	45.229 (18)
Ti1—Fe1—Mg1ⁱⁱⁱ	78.92 (13)	Mg1—Ti1—Fe1	0.000 (1)
Mg1^vi—Fe1—Mg1ⁱⁱⁱ	116.40 (9)	O1^viii—Ti1—Ti1^ix	97.351 (19)
Mg1^vii—Fe1—Mg1ⁱⁱⁱ	116.40 (9)	O1^ix—Ti1—Ti1^ix	46.856 (19)
O1ⁱ—Mg1—O1ⁱⁱ	102.1 (3)	O1^x—Ti1—Ti1^ix	146.50 (2)
O1ⁱ—Mg1—O1ⁱⁱⁱ	102.1 (3)	O1^v—Ti1—Ti1^ix	78.96 (2)
O1ⁱⁱ—Mg1—O1ⁱⁱⁱ	102.1 (3)	O1^iv—Ti1—Ti1^ix	118.32 (2)
O1ⁱ—Mg1—O1	93.34 (9)	O1—Ti1—Ti1^ix	43.483 (19)
O1ⁱⁱ—Mg1—O1	162.5 (4)	Mg1—Ti1—Ti1^ix	77.905 (11)
O1ⁱⁱⁱ—Mg1—O1	82.34 (8)	Fe1—Ti1—Ti1^ix	77.905 (11)
O1ⁱ—Mg1—O1^iv	162.5 (4)	O1^viii—Ti1—Ti1^xi	46.855 (19)
O1ⁱⁱ—Mg1—O1^iv	82.34 (8)	O1^ix—Ti1—Ti1^xi	146.50 (2)
O1ⁱⁱⁱ—Mg1—O1^iv	93.34 (9)	O1^x—Ti1—Ti1^xi	97.350 (19)
O1—Mg1—O1^iv	80.5 (3)	O1^v—Ti1—Ti1^xi	118.32 (2)
O1ⁱ—Mg1—O1^v	82.34 (8)	O1^iv—Ti1—Ti1^xi	43.483 (19)
O1ⁱⁱ—Mg1—O1^v	93.34 (9)	O1—Ti1—Ti1^xi	78.96 (2)
O1ⁱⁱⁱ—Mg1—O1^v	162.5 (4)	Mg1—Ti1—Ti1^xi	77.905 (11)
O1—Mg1—O1^v	80.5 (3)	Fe1—Ti1—Ti1^xi	77.905 (11)
O1^iv—Mg1—O1^v	80.5 (3)	Ti1^ix—Ti1—Ti1^xi	115.732 (8)
O1ⁱ—Mg1—Ti1	116.1 (3)	O1^viii—Ti1—Ti1^xii	146.50 (2)
O1ⁱⁱ—Mg1—Ti1	116.1 (3)	O1^ix—Ti1—Ti1^xii	97.349 (19)
O1ⁱⁱⁱ—Mg1—Ti1	116.1 (3)	O1^x—Ti1—Ti1^xii	46.854 (19)
O1—Mg1—Ti1	48.25 (19)	O1^v—Ti1—Ti1^xii	43.483 (19)
O1^iv—Mg1—Ti1	48.25 (19)	O1^iv—Ti1—Ti1^xii	78.96 (2)
O1^v—Mg1—Ti1	48.25 (19)	O1—Ti1—Ti1^xii	118.32 (2)
O1ⁱ—Mg1—Mg1^vi	142.9 (3)	Mg1—Ti1—Ti1^xii	77.905 (11)
O1ⁱⁱ—Mg1—Mg1^vi	43.73 (9)	Fe1—Ti1—Ti1^xii	77.905 (11)
O1ⁱⁱⁱ—Mg1—Mg1^vi	99.94 (12)	Ti1^ix—Ti1—Ti1^xii	115.731 (8)
O1—Mg1—Mg1^vi	119.0 (5)	Ti1^xi—Ti1—Ti1^xii	115.731 (8)
O1^iv—Mg1—Mg1^vi	38.61 (16)	O1^viii—Ti1—Mg1^xiii	75.13 (6)
O1^v—Mg1—Mg1^vi	85.5 (3)	O1^ix—Ti1—Mg1^xiii	117.22 (12)
Ti1—Mg1—Mg1^vi	79.2 (4)	O1^x—Ti1—Mg1^xiii	28.645 (19)
O1ⁱ—Mg1—Mg1^vii	43.73 (9)	O1^v—Ti1—Mg1^xiii	113.45 (9)
O1ⁱⁱ—Mg1—Mg1^vii	99.94 (12)	O1^iv—Ti1—Mg1^xiii	79.18 (13)
O1ⁱⁱⁱ—Mg1—Mg1^vii	142.9 (3)	O1—Ti1—Mg1^xiii	150.20 (9)
O1—Mg1—Mg1^vii	85.5 (3)	Mg1—Ti1—Mg1^xiii	120.68 (14)
O1^iv—Mg1—Mg1^vii	119.0 (5)	Fe1—Ti1—Mg1^xiii	120.68 (14)
O1^v—Mg1—Mg1^vii	38.61 (16)	Ti1^ix—Ti1—Mg1^xiii	161.42 (14)
Ti1—Mg1—Mg1^vii	79.2 (4)	Ti1^xi—Ti1—Mg1^xiii	71.72 (6)
Mg1^vi—Mg1—Mg1^vii	116.6 (2)	Ti1^xii—Ti1—Mg1^xiii	71.73 (6)
O1ⁱ—Mg1—Mg1ⁱⁱⁱ	99.94 (12)	Fe1ⁱⁱⁱ—O1—Mg1ⁱⁱⁱ	0.4 (3)
O1ⁱⁱ—Mg1—Mg1ⁱⁱⁱ	142.9 (3)	Fe1ⁱⁱⁱ—O1—Ti1^ix	119.48 (4)
O1ⁱⁱⁱ—Mg1—Mg1ⁱⁱⁱ	43.73 (9)	Mg1ⁱⁱⁱ—O1—Ti1^ix	119.60 (8)
O1—Mg1—Mg1ⁱⁱⁱ	38.61 (16)	Fe1ⁱⁱⁱ—O1—Mg1	97.99 (19)
O1^iv—Mg1—Mg1ⁱⁱⁱ	85.5 (3)	Mg1ⁱⁱⁱ—O1—Mg1	97.66 (8)
O1^v—Mg1—Mg1ⁱⁱⁱ	119.0 (5)	Ti1^ix—O1—Mg1	128.00 (4)
Ti1—Mg1—Mg1ⁱⁱⁱ	79.2 (4)	Fe1ⁱⁱⁱ—O1—Fe1	97.78 (3)
Mg1^vi—Mg1—Mg1ⁱⁱⁱ	116.6 (2)	Mg1ⁱⁱⁱ—O1—Fe1	97.4 (2)
Mg1^vii—Mg1—Mg1ⁱⁱⁱ	116.6 (2)	Ti1^ix—O1—Fe1	128.01 (3)
O1ⁱ—Mg1—Fe1^vi	143.01 (14)	Mg1—O1—Fe1	0.3 (2)
O1ⁱⁱ—Mg1—Fe1^vi	43.96 (10)	Fe1ⁱⁱⁱ—O1—Ti1	135.42 (6)
O1ⁱⁱⁱ—Mg1—Fe1^vi	100.06 (3)	Mg1ⁱⁱⁱ—O1—Ti1	135.67 (17)
O1—Mg1—Fe1^vi	118.8 (3)	Ti1^ix—O1—Ti1	89.66 (3)
O1^iv—Mg1—Fe1^vi	38.38 (3)	Mg1—O1—Ti1	86.5 (2)
O1^v—Mg1—Fe1^vi	85.32 (13)	Fe1—O1—Ti1	86.82 (5)

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

Chemical composition by SEM of the ilmenite single crystal top

Oxide	Wt (%)	s^a	Points
TiO₂	55.76	1.25	30
FeO	33.53	1.03	30
Nb₂O₅	1.43	0.19	30
MgO	8.63	0.97	30
SiO₂	0.09	0.06	30
MnO	3.03	0.17	30

Note: (a) the standard deviation value refers to the dispersion estimative of chemical composition over the analyzed crystal surface.

Atomic parameters for the ilmenite single crystal top

Site	X	Y	Z	Site occupancy	U_eq
Fe	0.00000	0.00000	0.35436 (17)	0.19439	0.00171 (8)
Mg	0.00000	0.00000	0.3533 (7)	0.13894	0.00171 (8)
Ti	0.00000	0.00000	0.14423 (2)	0.33333	0.00926 (8)
O	0.29407 (16)	-0.02234 (16)	0.25430 (5)	1.00000	0.00675 (11)

Metal–oxygen distances (Å) for the refined structure of ilmenite top

Bond	Fe—O	Mg—O	Ti—O
M—O_min	1.875 (2)	1.881 (4)	2.0655 (7)
M—O_max	2.094 (2)	2.084 (6)	2.1900 (7)
M—O_average	1.984 (2)	1.983 (5)	2.1278 (7)

Hirshfeld surface [w(r) = 0.5] parameters for FeTiO₃ model (pure ilmenite) top

Atom	Volume (Å³)	Area (Å²)	Globularity	Sphericity
Fe	7.92	21.43	0.897	0.004
Ti	9.74	24.16	0.913	0.002
O	5.74	15.74	0.985	0.005

Hirshfeld surface [w(r) = 0.5] parameters for MgTiO₃ model (pure geikielite) top

Atom	Volume (Å³)	Area (Å²)	Globularity	Sphericity
Mg	2.45	9.00	0.978	0.001
Ti	10.92	27.15	0.877	0.005
O	7.39	18.53	0.990	0.003

Directional Hirshfeld surface properties in different bond directions: FeTiO₃ model top

Bond axis^a	d_i (Å)	d_e (Å)	d_norm	d_norm*^b	Shape	Curvedness
Fe—O_Min	0.9608	0.9214	-0.9134	0.3668	-0.5005	-2.2996
O_Min—Fe	0.9038	0.9580	-0.9173	-0.3768	0.9197	-1.4045

Fe—O_Max	1.0662	1.0331	-0.7872	0.3993	-0.7778	-2.4788
O_Max—Fe	0.9914	1.1048	-0.7954	-0.4719	0.9465	-1.0169

Ti—O_Min	1.0628	1.0102	-0.8040	0.6838	-0.6324	-2.3120
O_Min—Ti	0.9847	1.0853	-0.8095	-0.7327	0.9241	-1.2800

Ti—O_Max	1.1188	1.0765	-0.7324	0.7102	-0.3779	-2.9132
O_Max—Ti	0.9854	1.0874	-0.8080	-0.7350	0.9228	-1.2907

Notes: (a) Hirshfeld surface plotted centred in the first atom and parameters obtained in the direction of the second atom. For the bond axis with `O_Min', the oxygen anion has the lower bond distance and for `O_Max' the oxygen anion has the higher bond distance. (b) Recalculated d_norm using the ionic radius.

Directional Hirshfeld surface properties in different bond directions: MgTiO₃ model top

Bond axis^a	d_i (Å)	d_e (Å)	d_norm	d_norm*^b	Shape	Curvedness
Mg—O_Max	0.8083	1.2851	-0.6873	-0.0050	0.8811	-0.7978
O_Max—Mg	1.2031	0.8916	-0.6931	-0.1521	0.7645	-0.9541

Mg—O_Min	0.7400	1.1461	-0.8183	0.0177	0.8917	-0.8278
O_Min—Mg	1.0371	1.1559	-0.7397	-0.5815	0.8946	-1.0915

Ti—O_Min	1.0664	1.0067	-0.8045	0.6912	-0.7669	-2.0222
O_Min—Ti	1.1175	0.7705	-0.8213	-0.2125	-0.5671	-1.6507

Ti—O_Max	1.1264	1.0710	-0.7325	0.7244	-0.6349	-1.9917
O_Max—Ti	0.9883	1.0821	-0.8088	-0.7258	0.9402	-1.3490

Comparison between van der Waals and ionic radii for the target system atoms top

Atom	Ion	Ionic radius (Å)^a	Crystal radius (Å)^b	van der Waals radius (Å)^c
Fe	Fe²⁺	0.78	0.92	1.96
Mg	Mg²⁺	0.72	0.86	1.41
Ti	Ti⁴⁺	0.605	0.745	2.14
O	O^2-	1.22	1.36	1.47

Notes: (a) Pauling ionic radius. (b) Ionic radius in crystalline solids as determined by Shannon & Prewitt (1969). (c) van der Waals radius for the neutral atom.

Derived parameters from Hirshfeld surface analysis from natural ilmenite sample – pure ilmenite fragment top

Ion	Bond axis^a	Base w(r)^b	Base d_norm*^b^,^c	Base curvedness^b	w(r)^d	Curvedness^d	d_norm* modulus^c^,^d
Fe^2,0+	Fe—O_Min	0.5417	0.3318	-2.3512	0.5474	-2.2749	0.3303
O^2,0-	O_Min—Fe	0.4000	-0.3204	-2.5226	0.4135

Fe^2,0+	Fe—O_Max	0.5417	0.3628	-2.3423	0.5739	-1.6074	0.3340
O^2,0-	O_Max—Fe	0.4000	-0.3800	-1.3523	0.3434

Ti^4,0+	Ti—O_Max	0.6111	0.6002	-1.4313	0.5233	-1.8016	0.6547
O^2,0-	O_Max—Ti	0.4000	-0.7016	-1.3620	0.4171

Ti^4,0+	Ti—O_Min	0.6111	0.5841	-1.6829	0.5685	-1.9858	0.6269
O^2,0-	O_Min—Ti	0.4000	-0.6408	-1.9198	0.3710

Notes: (a) Hirshfeld surface plotted centred in the first atom and parameters obtained in the direction of the second atom. For the bond axis with `O_Min', the oxygen–metal bond distance is the smaller and for `O_Max', the oxygen–metal bond distance is the greater. (b) Values of w(r), d_norm* and curvedness obtained using the standard ionic charges for the Hirshfeld surface build. (c) Recalculated d_norm using the ionic radius. (d) Values of w(r), d_norm* and curvedness obtained for complementary surfaces between neighbouring cations and anions.

Derived parameters from Hirshfeld surface analysis from natural ilmenite sample – geikielite fragment top

Ion	Bond axis^a	Base w(r)^b	Base d_norm*^b^,^c	Base curvedness^b	w(r)^d	Curvedness^d	d_norm* modulus^c^,^d
Mg^2,0+	Fe—O_Max	0.6000	-0.0436	-0.5827	0.3558	-1.0658	0.2033
O^2,0-	O_Max—Fe	0.4000	0.0002	-1.0815	0.4135

Mg^2,0+	Fe—O_Min	0.6000	-0.0842	-0.5560	0.3558	-0.3240	0.0628
O^2,0-	O_Min—Fe	0.4000	-0.0587	-1.5264	0.4555

Ti^4,0+	Ti—O_Max	0.6111	0.6167	-1.6574	0.5874	-1.7974	0.8825
O^2,0-	O_Max—Ti	0.4000	-0.6909	-1.5163	0.3463

Ti^4,0+	Ti—O_Min	0.6111	0.5927	-1.7522	0.5699	-2.2565	0.8646
O^2,0-	O_Min—Ti	0.4000	-0.6370	-2.1884	0.3916

Derived parameters from Hirshfeld surface analysis from a natural ilmenite sample – pure ilmenite/geikielite models top

Ion	Pure ilmenite model			Geikielite model
	R_DMax^a	R_DMin^b	Charge	R_DMax^a	R_DMin^b	Charge
Fe²⁺	0.6048	0.6677	2.27	–	–	–
Mg²⁺	–	–	–	0.8362	0.8362	1.77
Ti⁴⁺	0.7830	0.6145	2.69	0.5218	-	3.31
O^2- (M²⁺ octahedra)	1.2796	1.2702	-1.70	1.3278	1.4756	-1.65
O^2- (M⁴⁺ octahedra)	1.2735	1.4525		1.5653

Notes: (a) ion–surface distance in the direction of the longer bond distance; (b) ion-surface distance in the direction of the shorter bond distance.

Comparison data for rutile TiO₂ top

Ion	Charge – Hartree–Fock computational method^a	Charge – Hartree–Fock computational method^b	Charge – Hirshfeld surface analysis
Ti⁴⁺	2.75	2.6	3.41
O^2-	-1.38^c	-1.3	-1.75

Notes: (a) from Reinhardt et al. (1996); (b) from Silvi et al. (1991); (c) obtained by charge balance from Silvi et al. (1991).

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On the use of Hirsh­feld surfaces for estimating atomic charges in ionic species: crystal structure of the natural ilmenite (Mg0.4168Fe0.5832)TiO3

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On the use of Hirshfeld surfaces for estimating atomic charges in ionic species: crystal structure of the natural ilmenite (Mg_0.4168Fe_0.5832)TiO₃