Morphological study of Czochralski-grown lanthanide orthovanadate single crystals and implications on the mechanism of bulk spiral formation

Single crystals of monoclinic Nd:LaVO₄ with dimensions up to Ø28 × 21 mm have been grown from the near-stoichiometric melt by the Czochralski method, making use of various seed orientations that are perpendicular to the (010), (10), (001) and (00) crystal planes. A sample was also prepared with the seed orientation in an arbitrary direction relative to the crystal. The anisotropic properties of the crystal are manifested in the growth morphology of the as-grown crystals, where different degrees of bulk spiral growth were observed. It was also found that employing the (001) or (00) seed faces severely suppressed the bulk spiral growth, and thus high quality and large-scale Nd:LaVO₄ crystals were obtained. The constituent segregation coefficients and high-temperature stability, including the melting point, were determined and evaluated. Based on the attachment energy model of Hartman-Perdok theory, morphology predictions were made for monoclinic LaVO₄ and tetragonal YVO₄ ortho­vanadate single crystals. Correlating with the as-grown morphology of both crystals developed along different seed orientations, a theoretical explanation is provided for the influences of seed crystals on bulk spiral formation, crystal quality and utilization ratio. It suggests that breaking the axial symmetry of the ideal atomic level interface between crystal and melt plays a crucial triggering role in bulk spiral formation in the Czochralski growth of lanthanide orthovanadate single crystals. Selecting a proper seed orientation that yields such a highly axially symmetric surface structure consisting of a series of large-area facets with similar growth velocities can greatly reduce bulk spiral formation and thus is preferable in the Czochralski growth of large-sized low-symmetry oxide crystals.

Computing details

Data collection: APEX2 Software Suite (Bruker,2005); cell refinement: APEX2 Software Suite (Bruker,2005); data reduction: APEX2 Software Suite (Bruker,2005); program(s) used to solve structure: SIR97 (Altomare,1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Bruker, 1997); software used to prepare material for publication: WinGX (Farrugia,1999).

Figures

(LaVO4)

Crystal data

LaO4V	F(000) = 448
Mr = 253.85	Dx = 5.054 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
a = 7.0492 (3) Å	Cell parameters from 2959 reflections
b = 7.2827 (3) Å	θ = 3.7–33.2°
c = 6.7250 (3) Å	µ = 15.26 mm^−1
β = 104.901 (2)°	T = 293 K
V = 333.63 (2) Å^3	Prism, colourless
Z = 4	0.09 × 0.08 × 0.06 mm

Data collection

Bruker APEX2 CCD area-detector diffractometer	1265 independent reflections
Radiation source: fine-focus sealed tube	1170 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.027
φ and ω scans	θmax = 33.2°, θmin = 3.7°
Absorption correction: numerical APEX2 Software Suite (Bruker,2005)	h = −10→10
Tmin = 0.344, Tmax = 0.466	k = −11→11
6077 measured reflections	l = −10→9

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.016	w = 1/[σ^2(Fo^2) + (0.015P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.034	(Δ/σ)max < 0.001
S = 1.06	Δρmax = 1.16 e Å^−3
1265 reflections	Δρmin = −0.73 e Å^−3
56 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0420 (9)

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
La1	0.276224 (17)	0.157198 (16)	0.103623 (17)	0.00767 (6)
O1	0.2554 (2)	0.4979 (2)	0.0725 (2)	0.0124 (3)
O2	0.6179 (2)	0.2795 (2)	0.2277 (2)	0.0117 (3)
O3	0.5171 (2)	−0.1050 (2)	0.1758 (2)	0.0134 (3)
O4	0.1143 (3)	−0.1564 (2)	0.0041 (3)	0.0121 (3)
V1	0.30083 (5)	0.16481 (5)	−0.38488 (5)	0.00678 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
La1	0.00755 (7)	0.00725 (8)	0.00790 (7)	0.00017 (4)	0.00144 (4)	0.00099 (3)
O1	0.0169 (8)	0.0095 (8)	0.0100 (7)	0.0018 (6)	0.0021 (6)	−0.0004 (5)
O2	0.0090 (7)	0.0159 (8)	0.0108 (7)	−0.0021 (6)	0.0040 (5)	−0.0017 (6)
O3	0.0130 (8)	0.0137 (8)	0.0109 (7)	0.0044 (6)	−0.0019 (6)	−0.0012 (5)
O4	0.0114 (8)	0.0104 (8)	0.0154 (7)	0.0005 (6)	0.0052 (6)	−0.0021 (5)
V1	0.00672 (15)	0.00713 (18)	0.00646 (15)	−0.00018 (11)	0.00163 (12)	−0.00020 (10)

Geometric parameters (Å, º)

La1—O1	2.4912 (17)	O2—V1^ix	1.7039 (16)
La1—O2	2.5015 (16)	O2—La1^ix	2.5292 (16)
La1—O3	2.5182 (17)	O3—V1^iv	1.6990 (16)
La1—O1^i	2.5275 (16)	O3—La1^iv	2.6845 (17)
La1—O2^ii	2.5292 (16)	O4—V1^x	1.7154 (16)
La1—O4	2.5640 (16)	O4—La1^iii	2.6604 (17)
La1—O4^iii	2.6604 (17)	O4—La1^i	2.8898 (17)
La1—O3^iv	2.6845 (17)	V1—O3^iv	1.6990 (16)
La1—O4^v	2.8898 (17)	V1—O2^ii	1.7039 (16)
La1—V1	3.3345 (4)	V1—O4^viii	1.7154 (16)
La1—V1^vi	3.3998 (4)	V1—O1^x	1.7233 (17)
La1—V1^vii	3.6124 (4)	V1—La1^xi	3.3998 (4)
O1—V1^viii	1.7233 (17)	V1—La1^xii	3.6124 (4)
O1—La1^v	2.5275 (16)
O1—La1—O2	72.80 (6)	O4^iii—La1—V1^vi	93.18 (4)
O1—La1—O3	142.54 (6)	O3^iv—La1—V1^vi	144.57 (4)
O2—La1—O3	70.25 (6)	O4^v—La1—V1^vi	30.29 (3)
O1—La1—O1^i	120.87 (4)	V1—La1—V1^vi	173.988 (13)
O2—La1—O1^i	99.59 (5)	O1—La1—V1^vii	67.01 (4)
O3—La1—O1^i	71.96 (5)	O2—La1—V1^vii	133.16 (4)
O1—La1—O2^ii	74.53 (6)	O3—La1—V1^vii	148.34 (4)
O2—La1—O2^ii	114.09 (5)	O1^i—La1—V1^vii	81.86 (4)
O3—La1—O2^ii	115.67 (5)	O2^ii—La1—V1^vii	77.45 (4)
O1^i—La1—O2^ii	146.18 (5)	O4—La1—V1^vii	88.40 (4)
O1—La1—O4	148.50 (6)	O4^iii—La1—V1^vii	26.61 (3)
O2—La1—O4	136.89 (6)	O3^iv—La1—V1^vii	137.67 (4)
O3—La1—O4	66.89 (5)	O4^v—La1—V1^vii	80.99 (3)
O1^i—La1—O4	71.59 (5)	V1—La1—V1^vii	107.379 (10)
O2^ii—La1—O4	81.32 (6)	V1^vi—La1—V1^vii	77.218 (7)
O1—La1—O4^iii	86.84 (5)	V1^viii—O1—La1	139.59 (9)
O2—La1—O4^iii	158.71 (5)	V1^viii—O1—La1^v	104.63 (8)
O3—La1—O4^iii	130.54 (5)	La1—O1—La1^v	113.65 (6)
O1^i—La1—O4^iii	85.37 (5)	V1^ix—O2—La1	135.25 (8)
O2^ii—La1—O4^iii	64.44 (5)	V1^ix—O2—La1^ix	102.18 (7)
O4—La1—O4^iii	64.34 (6)	La1—O2—La1^ix	122.54 (6)
O1—La1—O3^iv	96.49 (5)	V1^iv—O3—La1	133.02 (9)
O2—La1—O3^iv	68.57 (5)	V1^iv—O3—La1^iv	96.46 (7)
O3—La1—O3^iv	64.35 (6)	La1—O3—La1^iv	115.65 (6)
O1^i—La1—O3^iv	136.24 (5)	V1^x—O4—La1	127.79 (9)
O2^ii—La1—O3^iv	60.37 (5)	V1^x—O4—La1^iii	109.38 (8)
O4—La1—O3^iv	88.66 (5)	La1—O4—La1^iii	115.66 (6)
O4^iii—La1—O3^iv	121.27 (5)	V1^x—O4—La1^i	91.53 (7)
O1—La1—O4^v	66.73 (5)	La1—O4—La1^i	100.58 (6)
O2—La1—O4^v	61.31 (5)	La1^iii—O4—La1^i	105.20 (5)
O3—La1—O4^v	99.89 (5)	O3^iv—V1—O2^ii	100.96 (8)
O1^i—La1—O4^v	59.40 (5)	O3^iv—V1—O4^viii	107.53 (9)
O2^ii—La1—O4^v	140.57 (5)	O2^ii—V1—O4^viii	114.95 (8)
O4—La1—O4^v	130.78 (4)	O3^iv—V1—O1^x	114.08 (8)
O4^iii—La1—O4^v	105.32 (5)	O2^ii—V1—O1^x	115.82 (8)
O3^iv—La1—O4^v	129.78 (5)	O4^viii—V1—O1^x	103.61 (8)
O1—La1—V1	85.27 (4)	O3^iv—V1—La1	53.13 (6)
O2—La1—V1	91.91 (4)	O2^ii—V1—La1	47.85 (5)
O3—La1—V1	89.95 (4)	O4^viii—V1—La1	125.86 (6)
O1^i—La1—V1	153.51 (4)	O1^x—V1—La1	130.49 (6)
O2^ii—La1—V1	29.96 (4)	O3^iv—V1—La1^xi	131.64 (6)
O4—La1—V1	83.69 (4)	O2^ii—V1—La1^xi	127.31 (6)
O4^iii—La1—V1	92.53 (4)	O4^viii—V1—La1^xi	58.18 (6)
O3^iv—La1—V1	30.42 (3)	O1^x—V1—La1^xi	46.00 (5)
O4^v—La1—V1	145.31 (3)	La1—V1—La1^xi	173.988 (13)
O1—La1—V1^vi	93.17 (4)	O3^iv—V1—La1^xii	66.55 (6)
O2—La1—V1^vi	82.09 (4)	O2^ii—V1—La1^xii	137.42 (6)
O3—La1—V1^vi	87.76 (4)	O4^viii—V1—La1^xii	44.00 (6)
O1^i—La1—V1^vi	29.37 (4)	O1^x—V1—La1^xii	106.11 (5)
O2^ii—La1—V1^vi	154.53 (4)	La1—V1—La1^xii	108.096 (10)
O4—La1—V1^vi	100.49 (4)	La1^xi—V1—La1^xii	77.904 (7)

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