Specimen preparation and characterisation

Zircon was synthesised from an equimolar mixture of reagent-grade ZrO₂ (>99%, Wako Co.) and SiO₂ (>99%, Kanto Kagaku Co.) by heating at 1773 K for 314 hr with nine times intermittent mixing. Reidite was synthesised from synthesised zircon using a Kawai-type double-staged multianvil apparatus at Gakushuin University. The starting material was put into a cylindrical Pt capsule heater in a 5 wt.% Cr₂O₃-doped MgO octahedron, and was kept at 15 GPa and 1773 K for 3 h. After quenching under pressure, the sample was recovered to ambient conditions. The synthesised sample was confirmed as single-phase reidite by microfocus X-ray diffraction and powder X-ray diffraction.

Natural zircon crystals were obtained from granite in Okueyama, Miyazaki Prefecture, Japan, and are light yellow under sunlight and fluorescent yellow under ultraviolet light. The Okueyama granite is part of the Miocene pluton of the Outer Zone of Southwest Japan, and has been aged radiometrically at 14 Ma (Shibata, Reference Shibata1978). The compositions of the samples were determined with a JEOL scanning electron microscope (SEM JSM-7001F) and an Oxford energy dispersive X-ray analyser (EDS INCA SYSTEM). The composition of the Okueyama zircons is shown in Table 1. Wollastonite CaSiO₃, and pure metals of Zr, Hf and U were used as standard materials. The average content (ten spot analyses) totals ~102 wt.%. The Okueyama zircon contains 1.75(23) wt.% Hf and 1.34(18) wt.% U at the A site and no impurities at the B site. According to this result, the averaged chemical formula of the Okueyama zircon is (Zr_0.97Hf_0.02U_0.01)_Σ1.00Si_0.98O₄, with a somewhat low B-site total of 0.98(1) Si per formula unit. Lower B-site and excess A-site cations in the Okueyama zircon are also observed in Sri Lankan zircons (Murakami et al., Reference Murakami, Chakoumakos, Ewing, Lumpkin and Weber1991).

Table 1. Averaged chemical composition of Okueyama and Sri Lankan zircons (Ríos et al., Reference Ríos, Malcherek, Salje and Domeneghetti2000)*.

* Apfu – atoms per formula unit on the basis of O = 4.00 apfu.

Single-crystal X-ray diffraction

Single-crystal X-ray diffraction for the synthetic reidite and natural Okueyama zircon was performed using a SuperNova, Single source at offset/far, HyPix3000 diffractometer. Monochromated MoKα radiation obtained by an X-ray generator (50 kV and 0.8 mA) was focused by a mirror. Details of the data collection are listed in Table 2.

Table 2. Crystal structure and single-crystal X-ray diffraction data for reidite and Okueyama zircon.

*w = 1/[σ²(F_O²) + (aP)² + bP]; P = (Max(F_O², 0) + 2F_C²)/3

Refinement

The structure was obtained with the ShelXT solution program using intrinsic phasing and refined with the ShelXL refinement package using least-squares minimisation (Sheldrick, Reference Sheldrick2015). During the least-square refinements a correction for isotropic extinction was applied. After several refinement cycles the displacement parameters were converted from an isotropic to an anisotropic model. The refined coordination and atomic displacement parameters are listed in Table 3. The final R1 factors of reidite and zircon were 0.0156 and 0.0235, respectively.

Table 3. Atom coordinates and refined anisotropic displacement parameters (Ų) for reidite, Okueyama zircon and previous reports.*

* RD = radiation damaged, NRD = non-radiation damaged.

Pressure-induced phase transition from zircon to reidite

Generally, pressure-induced phase transitions occur with increasing cation coordination number. However, an increase of cation coordination number is not sufficient to explain high-pressure transformation in ABO₄ compounds. Monazite-type arsenates and vanadates, for example, are known to transform to a scheelite-type structure under high pressure with no change of cation coordination number (Stubican and Roy, Reference Stubican and Roy1959). As for the zircon–reidite phase transition, the cation coordination number does not change. The density of reidite increases ~10% from that of low-pressure-phase zircon. This compression was explained by Kusaba et al. (Reference Kusaba, Yagi, Kikuchi and Syono1986). The [110] direction in the zircon structure is converted by simple shearing to the [001] direction in the scheelite structure, during which the intersecting angle between [100] and [010] increases from 90° to ~115°, which causes the increase in ZrSiO₄ density. This mechanism accounts for structural transformation without long-range atomic diffusion. Hence, the c axis of the scheelite structure in reidite corresponds to the [110] direction of the zircon structure, as shown in Fig 1. The respective vectors a_z, b_z and c_z can be represented by a linear combination with the vectors a_r, b_r and c_r in zircon:

(1)$$\eqalign{& {\bi a}_z = \cos 53.4^\circ {\bi a}_r + \cos 67.6^\circ {\bi b}_r + \cos 45^\circ {\bi c}_r \cr & {\bi b}_z = \cos 126.7^\circ {\bi a}_r + \cos 112.4^\circ {\bi b}_r + \cos 45^\circ {\bi c}_r \cr & {\bi c}_z = \cos 57.4^\circ {\bi a}_r + \cos 147.4^\circ {\bi b}_r + \cos 90^\circ {\bi c}_r} $$

where a _z, b _z and c _z correspond to reidite axes and a _r, b _r and c _r to zircon axes. In the discussion of the zircon and reidite structures, attention should be given to the above correspondence of axes.

The configuration of SiO₄ tetrahedra is important in understanding the phase transition from zircon to reidite. A comparison of SiO₄ configurations between zircon and reidite is shown in Fig. 2. The zircon–reidite phase transition can be understood by twisting and translations of SiO₄ tetrahedra. From the view of the a _r axis in reidite (Fig. 2a), there is no tetrahedral displacement along the b _r axis. The SiO₄ translations are along the a _r and c _r axes. The large expansion (~12%) along the c _r axis is caused, however, by the large contraction (~17%) along the a _r axis observed from the view of the b _r axis.

Fig. 2. Comparison of SiO₄ configurations between zircon (Kolesov, et al., Reference Kolesov, Geiger and Armbruster2001) and reidite projected on (100)_reidite (a) and (010)_reidite (b). The grey and black tetrahedra correspond to the SiO₄ of zircon and reidite, respectively.

The twisting and translations of SiO₄ tetrahedra in the zircon structure cause the shared edge between SiO₄ tetrahedra and ZrO₈ dodecahedra to disappear, as shown in Fig. 3. The disappearance of the SiO₄–ZrO₈ shared edge yields structural stability according to Pauling's third rule (Pauling, Reference Pauling1929, Reference Pauling1960). Although the density of reidite is higher than that of zircon, the volume of the SiO₄ tetrahedron of reidite is larger than that of zircon. The O–O atomic distances of SiO₄ also change in the phase transition. In the zircon structure, there are four larger O–O distances and two shorter O–O distances corresponding to the SiO₄–ZrO₈ shared edge. However, there are four shorter O–O distances and two longer ones in the reidite structure (Table 4). Such changes in O–O distance are caused by twisting of the SiO₄ tetrahedra. The SiO₄ twisting is represented by the rotation of O1–O2 and O3–O4 bonds perpendicular to the a _r axis, as shown in Fig. 3. The O1–O3 and O2–O4 distances in reidite expand as the SiO₄–ZrO₈ shared edge disappears. Although the mean-square displacement (MSD) of the Si atom in pure zircon is nearly isotropic despite the SiO₄–ZrO₈ shared edge, the MSD of the Si atom in reidite is anisotropic (U ¹¹ < U ³³). The thermal vibration ellipsoid of reidite Si is elongated only towards the longer O1–O2 and O3–O4 bonds in the tetrahedron. Because of the SiO₄ twisting, the 4₁ axis in zircon, which is the c _z axis, disappears, and the new 4₁ axis is generated as a primary axis along [110]_z, which corresponds to the c _r axis.

Fig. 3. Twisting of SiO₄ in (a) zircon (Kolesov, et al., Reference Kolesov, Geiger and Armbruster2001) and (b) reidite. Dot-dash lines are the compressed directions of SiO₄ tetrahedra parallel to the a _r axis. Twisting of SiO₄ is represented by angles formed by dot-dash lines and O1–O2 and O3–O4 bonds. The O1–O3 and O2–O4 bonds correspond to the SiO₄–ZrO₈ shared edge in the zircon structure.

Table 4. Comparison of bond distances (Å) and angles (°) for reidite and zircon.

Although the SiO₄–ZrO₈ shared edges disappear, the ZrO₈–ZrO₈ shared edges remain through the phase transition. The ZrO₈–ZrO₈ shared-edge length in reidite is longer than that in zircon despite the closer Zr–Zr distance. As far as Zr⁴⁺–Zr⁴⁺ repulsion between ZrO₈–ZrO₈, this cation–cation repulsion contributes a structural destabilisation energetically. We can deduce that the structural stability brought by the disappearance of SiO₄–ZrO₈ shared edges overcomes the instability from enhanced Zr⁴⁺–Zr⁴⁺ repulsions. If this hypothesis is correct, we can conclude that the Si⁴⁺–Zr⁴⁺ repulsion is stronger than the Zr⁴⁺–Zr⁴⁺ repulsion.

Radiation-damaged natural zircon

To compare with previous studies of natural zircon (Robinson et al., Reference Robinson, Gibbs and Ribbe1971 and Ríos et al., Reference Ríos, Malcherek, Salje and Domeneghetti2000) and synthetic zircon (Kolesov et al., Reference Kolesov, Geiger and Armbruster2001), their structural information is listed in Table 5. Robinson et al. (Reference Robinson, Gibbs and Ribbe1971) investigated natural non-radiation-damaged zircon from a syenite in Kragerø, Norway, that contained only ~1 wt.% Hf. Ríos et al. (Reference Ríos, Malcherek, Salje and Domeneghetti2000) used radiation-damaged zircon from Sri Lanka (age 570 ± 20 Ma), whose composition was Zr_0.99Hf_0.01Si_0.95O₄ (1.3 wt.% Hf and <0.01 wt.% U). The lattice parameters of natural zircon are greater than those of synthetic zircon. On the basis of the lattice parameters of synthetic zircon, the ratios Δa/a and Δc/c of the non-radiation-damaged zircon are 0.047(15)% and 0.062(17)%, respectively, while those of the Okueyama zircon are 0.591(3)% and 0.595(3)%, respectively. The lattice expansion of the radiation-damaged zircon is obviously greater than that of the non-radiation damaged one.

Table 5. Comparison of structural parameters for radiation-damaged and non-radiation-damaged zircons.

When a zircon is subjected to a stress, the unit cell of the zircon structure elongates along the a _z axis rather than along the c _z axis (Hazen and Finger, Reference Hazen and Finger1979). However, the expansion in the Sri Lankan radiation-damaged zircon is greater along the c axis (Δc/c = 0.681(50)%) than the a axis (Δa/a = 0.214(45)%), where Δa/a and Δc/c represent the difference in lattice parameter between analysed sample and standard (Kolesov et al., Reference Kolesov, Geiger and Armbruster2001) divided with the lattice parameter of the standard. In studies of ²³⁹Pu-doped zircon and neutron-irradiated zircon, the net lattice expansion by radiation damage is almost equal, within 5.0 ×10¹⁸ α-decays/mg (Weber et al., Reference Weber, Ewing, Catlow, Díaz de la Rubia, Hobbs, Kinoshita, Matzke, Motta, Nastasi, Salje, Vance and Zinkle1998). Murakami et al. (Reference Murakami, Chakoumakos, Ewing, Lumpkin and Weber1991) suggested that point defects in the early stages of damage accumulation (<3.0 ×10¹⁵ α-decays/mg) undergo self-annealing in natural zircon under ambient conditions. We expect that the relaxation of the expansion along the a _z axis is energetically more favourable than that along the c _z axis. The Sri Lankan zircon underwent defect annealing over a long geological time period. The Okueyama zircon is younger and, moreover, the Okueyama granite consists of a single magma chamber, which solidified as a zoned pluton (Takahashi, Reference Takahashi1986). Accordingly, we conclude that Okueyama zircons did not undergo thermal recovery of the lattice expansion.

The differences between the Sri Lankan and Okueyama zircons appear in the SiO₄ tetrahedron. The Si–O bond distances in radiation-damaged zircons are significantly longer than in non-radiation-damaged zircons. The increase in Si–O bond distances of radiation-damaged zircon comes from a disordered static displacement of atoms due to the α-decay event. Note that the Si vacancy also contributes to the expansion of the Si–O bond length in radiation-damaged zircon. The O–O shared-edge lengths of radiation-damaged zircon are longer than that of non-radiation-damaged zircon. In non-radiation-damaged zircon, effects of Si⁺⁴–Zr⁺⁴ repulsions are shielded by the shorter O–O shared-edge length. There are two kinds of O–Si–O bond angle in the zircon structure, as shown in Fig. 4: (1) the O–Si–O angle is with the shared edge between SiO₄ and ZrO₈; and (2) the O–Si–O angle is with the unshared edge. The O–Si–O (1) angle of the Sri Lankan zircon is smaller than that of the Okueyama zircon, which yields a shorter O–O shared-edge length (Table 5). As for the ZrO₈ dodecahedron, the Zr–O bond distance, which links to Si–O bonds in the Sri Lankan zircon, is also shorter than that of the Okueyama zircon. The O–Zr–O (1) angle is with the shared edge between SiO₄ and ZrO₈. The O–Zr–O angle of the Sri Lankan zircon is smaller than that of the Okueyama zircon. The shorter Zr–O bond distances and O–O shared-edge lengths mean that the cation–cation repulsion between SiO₄ and ZrO₈ is suppressed more in zircon studied by Ríos et al. (Reference Ríos, Malcherek, Salje and Domeneghetti2000) than in the Okueyama zircon. Old Sri Lankan zircons are more structurally relaxed than the young Okueyama zircons. The relaxation of the expansion along the a axis may result from the suppression of the cation–cation repulsion between SiO₄ and ZrO₈.

Fig. 4. SiO₄ tetrahedron in the Okueyama zircon. Dotted and dot-dash lines correspond to the O–O shared edge and unshared edge, respectively. Thermal motions of atoms are drawn as ellipsoids of 99% probability. Note: RD = radiation damaged, NRD = non-radiation damaged.

This can be evaluated by comparing the amplitude of the anisotropic temperature factor as an index of repulsion between cations, as observed in garnet-type (pyrope) and rutile-type (stishovite) structures, where the amplitude decreases in parallel to the direction of repulsion between cations. However, in contrast, it is observed in this work that the amplitude increases in the vertical direction. We observed larger MSD parameters in the Okueyama zircon than in the non-radiation-damaged zircons. In radiation-damaged zircon, the larger MSD of the atoms contains the contribution of disordered static displacements of atoms due to the α-decay event. Although Zr and Si thermal ellipsoids in non-radiation-damaged zircon are almost spherical (U ¹¹ ≈ U ³³), the thermal ellipsoids in radiation-damaged zircon are obviously flattened (U ¹¹ > U ³³). The parameters U ¹¹ and U ³³ of Zr and Si are the MSD along the a _z and c _z axes, respectively. In particular, U ¹¹ > U ³³ implies Si⁴⁺–Zr⁴⁺ repulsion between SiO₄ and ZrO₈. Although the MSD parameters of all atoms in the Sri Lankan zircon show the same tendency as in the Okueyama zircon, those values are smaller than those for the Okueyama zircon. From this result, we expect the Si⁴⁺–Zr⁴⁺ repulsion in SiO₄–ZrO₈ to be weakened by thermal recovery over geological time. The static displacement of Si and Zr from the 8d site due to radiation damage contributes to the flattening of vibration ellipsoids perpendicular to the SiO₄–ZrO₄ shared edge.