Localized defects in radiation-damaged zircon

Ríos, S.; Malcherek, T.; Salje, E.K.H.; Domeneghetti, C.

doi:10.1107/S0108768100008582

Localized defects in radiation-damaged zircon

S. Ríos, T. Malcherek, E. K. H. Salje and C. Domeneghetti

The crystal structure of a radiation-damaged natural zircon, ZrSiO $_{4}$ ( $\alpha$ -decay radiation dose is ca 1.8 × 10 $^{18}$ α-decay events g⁻¹), has been determined. The anisotropic unit-cell swelling observed in the early stages of the amorphization process (0.17% along the a axis and 0.62% along the c axis compared with the undamaged material) is a consequence of the anisotropy of the expansion of ZrO $_{8}$ polyhedra. Larger anisotropic displacement parameters were found for Zr and O atoms, indicating that the distortion produced by $\alpha$ particle-induced localized defects mainly affects the ZrO $_{8}$ unit. The overall shape of SiO $_{4}$ tetrahedra remains essentially undistorted, while Si—O bonds are found to lengthen by 0.43%.

Keywords: Radiation-damaged; Zircon; Amorphization.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100008582/bm0029sup1.cif Contains datablock zirconr
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100008582/bm0029sup2.hkl Contains datablock zircon_r

Computing details top

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(zirconr) top

Crystal data top

Hf_.01O₂₄SiZr_.99	D_x = 4.648 Mg m⁻³
M_r = 184.43	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I4₁/amd	Cell parameters from 60 reflections
Hall symbol: -I 4bd 2	θ = 2–50°
a = 6.618 (3) Å	µ = 4.42 mm⁻¹
c = 6.019 (3) Å	T = 293 K
V = 263.58 (19) Å³	, colourless
Z = 4	× × mm
F(000) = 345

Data collection top

Philips PW1100 diffractometer	373 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	R_int = 0.024
Graphite monochromator	θ_max = 50.2°, θ_min = 4.6°
ω–2θ scans	h = −14→14
Absorption correction: empirical (using intensity measurements) ?	k = −14→14
T_min = ?, T_max = ?	l = 0→12
2659 measured reflections	3 standard reflections every 400 reflections
382 independent reflections	intensity decay: none

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.016	w = 1/[σ²(F_o²) + (0.0246P)² + 0.0356P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.040	(Δ/σ)_max < 0.001
S = 1.20	Δρ_max = 1.10 e Å⁻³
382 reflections	Δρ_min = −1.01 e Å⁻³
12 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.023 (3)

Crystal data top

Hf_.01O₂₄SiZr_.99	Z = 4
M_r = 184.43	Mo Kα radiation
Tetragonal, I4₁/amd	µ = 4.42 mm⁻¹
a = 6.618 (3) Å	T = 293 K
c = 6.019 (3) Å	× × mm
V = 263.58 (19) Å³

Data collection top

Philips PW1100 diffractometer	373 reflections with I > 2σ(I)
Absorption correction: empirical (using intensity measurements) ?	R_int = 0.024
T_min = ?, T_max = ?	3 standard reflections every 400 reflections
2659 measured reflections	intensity decay: none
382 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.016	12 parameters
wR(F²) = 0.040	0 restraints
S = 1.20	Δρ_max = 1.10 e Å⁻³
382 reflections	Δρ_min = −1.01 e Å⁻³

Special details top

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 (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Zr	0.0000	0.7500	0.1250	0.00588 (5)	0.99
Hf	0.0000	0.7500	0.1250	0.00588 (5)	0.01
Si	0.0000	0.7500	0.6250	0.00557 (7)
O	0.0000	0.06580 (8)	0.19545 (8)	0.00900 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Zr	0.00600 (6)	0.00600 (6)	0.00566 (7)	0.000	0.000	0.000
Hf	0.00600 (6)	0.00600 (6)	0.00566 (7)	0.000	0.000	0.000
Si	0.00644 (10)	0.00644 (10)	0.00382 (14)	0.000	0.000	0.000
O	0.01292 (18)	0.00716 (15)	0.00690 (14)	0.000	0.000	−0.00100 (12)

Geometric parameters (Å, º) top

Zr—Oⁱ	2.1324 (9)	Hf—O^viii	2.2816 (9)
Zr—Oⁱⁱ	2.1325 (9)	Si—O^x	1.6290 (7)
Zr—Oⁱⁱⁱ	2.1325 (9)	Si—O^vii	1.6290 (7)
Zr—O^iv	2.1325 (9)	Si—O^vi	1.6290 (7)
Zr—O^v	2.2816 (9)	Si—O^ix	1.6291 (7)
Zr—O^vi	2.2816 (9)	Si—Si^ix	3.6349 (12)
Zr—O^vii	2.2816 (9)	O—Si^ix	1.6290 (7)
Zr—O^viii	2.2816 (9)	O—Hf^xi	2.1325 (9)
Zr—Si	3.0093 (14)	O—Zr^xi	2.1325 (9)
Zr—Zr^viii	3.6349 (12)	O—Zr^viii	2.2816 (9)
Zr—Si^ix	3.6349 (12)	O—Hf^viii	2.2816 (9)
Hf—Oⁱ	2.1324 (9)	O—Oⁱ	2.4381 (14)
Hf—Oⁱⁱ	2.1325 (9)	O—O^xii	2.5086 (14)
Hf—Oⁱⁱⁱ	2.1325 (9)	O—O^xiii	2.7646 (12)
Hf—O^iv	2.1325 (9)	O—O^xiv	2.7646 (12)
Hf—O^v	2.2816 (9)	O—O^xv	2.8491 (9)
Hf—O^vi	2.2816 (9)	O—O^xvi	2.8491 (9)
Hf—O^vii	2.2816 (9)	O—O^xvii	2.8491 (9)

Oⁱ—Zr—Oⁱⁱ	92.266 (6)	O^vii—Hf—O^viii	135.60 (3)
Oⁱ—Zr—Oⁱⁱⁱ	92.266 (6)	O^x—Si—O^vii	116.11 (3)
Oⁱⁱ—Zr—Oⁱⁱⁱ	157.06 (3)	O^x—Si—O^vi	116.11 (3)
Oⁱ—Zr—O^iv	157.06 (3)	O^vii—Si—O^vi	96.89 (5)
Oⁱⁱ—Zr—O^iv	92.265 (6)	O^x—Si—O^ix	96.89 (5)
Oⁱⁱⁱ—Zr—O^iv	92.265 (6)	O^vii—Si—O^ix	116.11 (3)
Oⁱ—Zr—O^v	69.17 (3)	O^vi—Si—O^ix	116.11 (3)
Oⁱⁱ—Zr—O^v	80.324 (13)	O^x—Si—Zr	131.56 (2)
Oⁱⁱⁱ—Zr—O^v	80.324 (14)	O^vii—Si—Zr	48.44 (2)
O^iv—Zr—O^v	133.764 (18)	O^vi—Si—Zr	48.44 (2)
Oⁱ—Zr—O^vi	80.325 (13)	O^ix—Si—Zr	131.56 (2)
Oⁱⁱ—Zr—O^vi	133.765 (18)	O^x—Si—Si^ix	66.01 (3)
Oⁱⁱⁱ—Zr—O^vi	69.17 (3)	O^vii—Si—Si^ix	74.064 (14)
O^iv—Zr—O^vi	80.324 (13)	O^vi—Si—Si^ix	74.064 (15)
O^v—Zr—O^vi	135.61 (3)	O^ix—Si—Si^ix	162.897 (18)
Oⁱ—Zr—O^vii	80.325 (13)	Zr—Si—Si^ix	65.548 (13)
Oⁱⁱ—Zr—O^vii	69.17 (3)	Si^ix—O—Hf^xi	149.91 (3)
Oⁱⁱⁱ—Zr—O^vii	133.764 (17)	Si^ix—O—Zr^xi	149.91 (3)
O^iv—Zr—O^vii	80.324 (14)	Hf^xi—O—Zr^xi	0.0
O^v—Zr—O^vii	135.61 (3)	Si^ix—O—Zr^viii	99.26 (4)
O^vi—Zr—O^vii	64.59 (4)	Hf^xi—O—Zr^viii	110.83 (3)
Oⁱ—Zr—O^viii	133.765 (17)	Zr^xi—O—Zr^viii	110.83 (3)
Oⁱⁱ—Zr—O^viii	80.324 (14)	Si^ix—O—Hf^viii	99.26 (4)
Oⁱⁱⁱ—Zr—O^viii	80.324 (14)	Hf^xi—O—Hf^viii	110.83 (3)
O^iv—Zr—O^viii	69.17 (3)	Zr^xi—O—Hf^viii	110.83 (3)
O^v—Zr—O^viii	64.59 (4)	Zr^viii—O—Hf^viii	0.0
O^vi—Zr—O^viii	135.60 (3)	Si^ix—O—Oⁱ	41.56 (2)
O^vii—Zr—O^viii	135.60 (3)	Hf^xi—O—Oⁱ	168.531 (14)
Oⁱ—Zr—Si	78.531 (14)	Zr^xi—O—Oⁱ	168.531 (14)
Oⁱⁱ—Zr—Si	101.469 (15)	Zr^viii—O—Oⁱ	57.70 (2)
Oⁱⁱⁱ—Zr—Si	101.469 (15)	Hf^viii—O—Oⁱ	57.70 (2)
O^iv—Zr—Si	78.531 (15)	Si^ix—O—O^xii	151.87 (4)
O^v—Zr—Si	147.70 (2)	Hf^xi—O—O^xii	58.22 (2)
O^vi—Zr—Si	32.30 (2)	Zr^xi—O—O^xii	58.22 (2)
O^vii—Zr—Si	32.30 (2)	Zr^viii—O—O^xii	52.61 (3)
O^viii—Zr—Si	147.70 (2)	Hf^viii—O—O^xii	52.61 (3)
Oⁱ—Zr—Zr^viii	35.92 (2)	Oⁱ—O—O^xii	110.31 (3)
Oⁱⁱ—Zr—Zr^viii	85.279 (8)	Si^ix—O—O^xiii	31.947 (14)
Oⁱⁱⁱ—Zr—Zr^viii	85.280 (7)	Hf^xi—O—O^xiii	125.986 (19)
O^iv—Zr—Zr^viii	167.016 (14)	Zr^xi—O—O^xiii	125.986 (19)
O^v—Zr—Zr^viii	33.253 (13)	Zr^viii—O—O^xiii	115.17 (4)
O^vi—Zr—Zr^viii	110.482 (14)	Hf^viii—O—O^xiii	115.17 (4)
O^vii—Zr—Zr^viii	110.482 (14)	Oⁱ—O—O^xiii	63.836 (15)
O^viii—Zr—Zr^viii	97.84 (3)	O^xii—O—O^xiii	152.40 (2)
Si—Zr—Zr^viii	114.452 (13)	Si^ix—O—O^xiv	31.947 (13)
Oⁱ—Zr—Si^ix	12.983 (14)	Hf^xi—O—O^xiv	125.986 (19)
Oⁱⁱ—Zr—Si^ix	94.722 (7)	Zr^xi—O—O^xiv	125.986 (19)
Oⁱⁱⁱ—Zr—Si^ix	94.722 (7)	Zr^viii—O—O^xiv	115.17 (4)
O^iv—Zr—Si^ix	144.08 (2)	Hf^viii—O—O^xiv	115.17 (4)
O^v—Zr—Si^ix	82.16 (3)	Oⁱ—O—O^xiv	63.836 (15)
O^vi—Zr—Si^ix	69.519 (14)	O^xii—O—O^xiv	152.40 (2)
O^vii—Zr—Si^ix	69.519 (14)	O^xiii—O—O^xiv	52.33 (3)
O^viii—Zr—Si^ix	146.748 (13)	Si^ix—O—O^xv	101.45 (3)
Si—Zr—Si^ix	65.548 (13)	Hf^xi—O—O^xv	52.13 (2)
Zr^viii—Zr—Si^ix	48.90 (3)	Zr^xi—O—O^xv	52.13 (2)
Oⁱ—Hf—Oⁱⁱ	92.266 (6)	Zr^viii—O—O^xv	146.962 (6)
Oⁱ—Hf—Oⁱⁱⁱ	92.266 (6)	Hf^viii—O—O^xv	146.962 (6)
Oⁱⁱ—Hf—Oⁱⁱⁱ	157.06 (3)	Oⁱ—O—O^xv	137.182 (16)
Oⁱ—Hf—O^iv	157.06 (3)	O^xii—O—O^xv	103.92 (4)
Oⁱⁱ—Hf—O^iv	92.265 (6)	O^xiii—O—O^xv	95.70 (4)
Oⁱⁱⁱ—Hf—O^iv	92.265 (6)	O^xiv—O—O^xv	73.86 (2)
Oⁱ—Hf—O^v	69.17 (3)	Si^ix—O—O^xvi	101.45 (3)
Oⁱⁱ—Hf—O^v	80.324 (13)	Hf^xi—O—O^xvi	52.13 (2)
Oⁱⁱⁱ—Hf—O^v	80.324 (14)	Zr^xi—O—O^xvi	52.13 (2)
O^iv—Hf—O^v	133.764 (18)	Zr^viii—O—O^xvi	146.962 (6)
Oⁱ—Hf—O^vi	80.325 (13)	Hf^viii—O—O^xvi	146.962 (6)
Oⁱⁱ—Hf—O^vi	133.765 (18)	Oⁱ—O—O^xvi	137.182 (16)
Oⁱⁱⁱ—Hf—O^vi	69.17 (3)	O^xii—O—O^xvi	103.92 (4)
O^iv—Hf—O^vi	80.324 (13)	O^xiii—O—O^xvi	73.86 (2)
O^v—Hf—O^vi	135.61 (3)	O^xiv—O—O^xvi	95.70 (4)
Oⁱ—Hf—O^vii	80.325 (13)	O^xv—O—O^xvi	50.66 (3)
Oⁱⁱ—Hf—O^vii	69.17 (3)	Si^ix—O—O^xvii	91.73 (3)
Oⁱⁱⁱ—Hf—O^vii	133.764 (17)	Hf^xi—O—O^xvii	108.319 (17)
O^iv—Hf—O^vii	80.324 (14)	Zr^xi—O—O^xvii	108.319 (17)
O^v—Hf—O^vii	135.61 (3)	Zr^viii—O—O^xvii	47.545 (16)
O^vi—Hf—O^vii	64.59 (4)	Hf^viii—O—O^xvii	47.545 (16)
Oⁱ—Hf—O^viii	133.765 (17)	Oⁱ—O—O^xvii	64.668 (14)
Oⁱⁱ—Hf—O^viii	80.324 (14)	O^xii—O—O^xvii	69.71 (2)
Oⁱⁱⁱ—Hf—O^viii	80.324 (14)	O^xiii—O—O^xvii	123.204 (18)
O^iv—Hf—O^viii	69.17 (3)	O^xiv—O—O^xvii	84.30 (4)
O^v—Hf—O^viii	64.59 (4)	O^xv—O—O^xvii	106.194 (14)
O^vi—Hf—O^viii	135.60 (3)	O^xvi—O—O^xvii	155.04 (3)

Symmetry codes: (i) x, −y+1/2, z; (ii) −y−1/4, −x+3/4, −z+1/4; (iii) y+1/4, −x+3/4, −z+1/4; (iv) x, y+1, z; (v) −x, y+1/2, −z; (vi) −y+1/4, x+3/4, z+1/4; (vii) y−1/4, x+3/4, z+1/4; (viii) −x, −y+1, −z; (ix) −x, −y+1, −z+1; (x) −x, y+1/2, −z+1; (xi) x, y−1, z; (xii) −x, −y, −z; (xiii) −y+1/4, −x+1/4, −z+3/4; (xiv) y−1/4, −x+1/4, −z+3/4; (xv) y−1/4, x−1/4, z+1/4; (xvi) −y+1/4, x−1/4, z+1/4; (xvii) −y−1/4, x+1/4, z−1/4.

Experimental details

Crystal data
Chemical formula	Hf_.01O₂₄SiZr_.99
M_r	184.43
Crystal system, space group	Tetragonal, I4₁/amd
Temperature (K)	293
a, c (Å)	6.618 (3), 6.019 (3)
V (Å³)	263.58 (19)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	4.42
Crystal size (mm)	× ×

Data collection
Diffractometer	Philips PW1100 diffractometer
Absorption correction	Empirical (using intensity measurements)
No. of measured, independent and observed [I > 2σ(I)] reflections	2659, 382, 373
R_int	0.024
(sin θ/λ)_max (Å⁻¹)	1.081

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.016, 0.040, 1.20
No. of reflections	382
No. of parameters	12
Δρ_max, Δρ_min (e Å⁻³)	1.10, −1.01

Computer programs: SHELXS97 (Sheldrick, 1990), SHELXL97 (Sheldrick, 1997).

Room temperature fractional atomic coordinates and anisotropic displacement parameters (Å²) for zircon 269 top

	Zr	Si	O
x	0	0	0
y	0.7500	0.7500	0.06580 (8)
z	0.1250	0.6250	0.19545 (8)
U$_{11}$	0.00600 (6)	0.00644 (10)	0.01292 (18)
U$_{22}$	0.00600 (6)	0.00644 (10)	0.00716 (15)
U$_{33}$	0.00566 (7)	0.00382 (14)	0.00690 (14)
U$_{23}$	0	0	-0.00100 (12)
U$_{13}$	0	0	0
U$_{12}$	0	0	0

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Localized defects in radiation-damaged zircon

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