Zirconolite-2TR: Ordered Triclinic Waste Form

• Zirconolite-2TR is a fully ordered triclinic polymorph of CaZrTi₂O₇, revised from a previously assumed monoclinic structure using advanced crystallographic and DFT analyses.
• It undergoes a pressure-induced transition at 14.7 GPa—from triclinic P̅1 to monoclinic C2/c—while maintaining similar bulk moduli and layered topologies.
• Studies indicate that amorphization enhances oxygen diffusion via increased prefactors without significantly reducing activation energies, reinforcing its role in nuclear waste immobilization.

Searching arXiv for the cited zirconolite papers to ground the article in the current record. Zirconolite-2TR is the triclinic ambient-pressure structure of zirconolite with composition CaZrTi$_2$O$_7$, proposed from synchrotron powder X-ray diffraction and density-functional-theory analysis as a replacement for the previously assigned monoclinic ambient model of zirconolite-2M. In this nomenclature, “2TR” denotes the triclinic $P\bar{1}$ form, which is dynamically stable at ambient conditions and undergoes a pressure-induced transition at 14.7 GPa to a distinct monoclinic $C2/c$ phase. For transport and disorder-related behavior, the most detailed atomistic results currently derive from molecular-dynamics simulations of amorphous zirconolite with 10% U substituting for Zr rather than from explicit trivalent-doped 2TR compositions; those results therefore constrain Zirconolite-2TR only by cautious mechanistic analogy rather than direct simulation (Errandonea et al., 5 Aug 2025, Yang et al., 2015).

1. Structural identification and revision of the ambient model

A central development in the definition of Zirconolite-2TR is the reassignment of ambient CaZrTi$_2$O$_7$ from the previously used monoclinic $C2/c$ description to triclinic $P\bar{1}$ with $Z = 4$. The new model was introduced in a comparative high-pressure study of zirconolite-2M, -4M, -3O, and -3T, where the triclinic structure was explicitly named zirconolite-2TR (Errandonea et al., 5 Aug 2025).

The case for the reassignment is crystallographic and lattice-dynamical. At 0.1 GPa, the $P\bar{1}$ model gives substantially improved Rietveld metrics relative to the ambient $_7$0 model: $_7$1, $_7$2, $_7$3 for $_7$4, versus $_7$5, $_7$6, $_7$7 for $_7$8. The triclinic model also accounts for additional weak low-angle reflections not indexed by $_7$9. In structural terms, the previously reported ambient $P\bar{1}$0 description includes one Ti at Wyckoff 8f with 50% statistical occupancy, whereas the $P\bar{1}$1 model removes that partial occupancy and fully orders Ti across general positions (2i) (Errandonea et al., 5 Aug 2025).

The relation between the two descriptions is not arbitrary. The $P\bar{1}$2 structure can be obtained via a group–subgroup relation from $P\bar{1}$3 and is described as a symmetry-lowered, ordered variant. A common misconception is therefore to treat zirconolite-2TR as a chemically distinct phase from zirconolite-2M. The crystallographic evidence instead indicates that 2TR is the ordered triclinic ambient form of the same nominal composition, CaZrTi$P\bar{1}$4O$P\bar{1}$5, rather than a different bulk chemistry.

2. Ambient crystallography, topology, and cation ordering

At ambient temperature and 0.1 GPa, zirconolite-2TR adopts space group $P\bar{1}$6 with lattice parameters $P\bar{1}$7 Å, $P\bar{1}$8 Å, $P\bar{1}$9 Å, $C2/c$0, $C2/c$1, and $C2/c$2. The unit-cell volume from the equation-of-state fit is $C2/c$3 Å$C2/c$4. The deposited structural model is CCDC 2246629 (Errandonea et al., 5 Aug 2025).

Representative atomic positions illustrate the fully ordered triclinic cell. The cation sites include Ca1 $C2/c$5 at $C2/c$6, $C2/c$7, $C2/c$8; Ca2 $C2/c$9 at $_2$0, $_2$1, $_2$2; Zr1 $_2$3 at $_2$4, $_2$5, $_2$6; Zr2 $_2$7 at $_2$8, $_2$9, $_7$0; Ti1 $_7$1 at $_7$2, $_7$3, $_7$4; Ti2 $_7$5 at $_7$6, $_7$7, $_7$8; Ti3 $_7$9 at $C2/c$0, $C2/c$1, $C2/c$2; and Ti4 $C2/c$3 at $C2/c$4, $C2/c$5, $C2/c$6. Representative oxygen positions include O1 at $C2/c$7, $C2/c$8, $C2/c$9 and O6 at $P\bar{1}$0, $P\bar{1}$1, $P\bar{1}$2.

The topology consists of planes of corner-sharing CaO$P\bar{1}$3 and ZrO$P\bar{1}$4 polyhedra running perpendicular to [001], separated by layers of Ti-centered polyhedra. Two distinct Ti coordination units coexist: TiO$P\bar{1}$5 octahedra and TiO$P\bar{1}$6 trigonal bipyramids with an HTB-like motif. All cation sites are fully occupied in $P\bar{1}$7; there is no statistical or partial occupancy.

Structural state	Symmetry	Key features
Ambient zirconolite-2TR	$P\bar{1}$8, $P\bar{1}$9	Fully ordered Ti over 2i sites; CaO$Z = 4$0–ZrO$Z = 4$1 planes plus TiO$Z = 4$2/TiO$Z = 4$3 layers
Previously assigned ambient model	$Z = 4$4	Includes one Ti at 8f with 50% statistical occupancy
High-pressure phase	$Z = 4$5, $Z = 4$6	Fully occupied Ti at 8f and 4e; closely related to, but not isomorphic with, the ambient $Z = 4$7 model

The significance of this ordering is methodological as well as structural. The validated triclinic ambient structure resolves prior ambiguity in site assignment and provides a more reliable basis for modeling defect chemistry and diffusion in zirconolite-based waste forms. This suggests that calculations performed on the older partially occupied ambient $Z = 4$8 model may require reassessment when site-specific energetics are important.

3. Pressure-induced transformation and elastic response

The high-pressure behavior of zirconolite-2TR was established by synchrotron powder XRD under compression to 30.5 GPa and decompression to ambient, using a 4:1 methanol–ethanol pressure-transmitting medium that is hydrostatic to approximately 10.5 GPa and quasi-hydrostatic above that pressure. Measurements were performed at BL04-MSPD at ALBA with a monochromatic beam of wavelength $Z = 4$9 Å, a focused spot of $P\bar{1}$0, and a Rayonix SX165 detector; pressure was calibrated against Cu with an accuracy of $P\bar{1}$1 GPa using the equation of state of copper reported by Dewaele et al. (Errandonea et al., 5 Aug 2025).

A clear structural change occurs at 14.7 GPa, seen as the merging of the strongest doublet near $P\bar{1}$2–$P\bar{1}$3 in $P\bar{1}$4. The resulting high-pressure phase is monoclinic $P\bar{1}$5 and is retained down to at least 13.5 GPa on decompression, while the low-pressure $P\bar{1}$6 phase is fully recovered by 3.4 GPa. Because of the data gap between 13.5 and 3.4 GPa, the hysteresis width could not be delineated. The proposed high-pressure structure differs from the ambient $P\bar{1}$7 model of ICSD 32339 in Ti site assignments: the high-pressure phase has Ti1 at 8f and Ti2, Ti3 at 4e, all fully occupied. It is therefore closely related to, but not isomorphic with, the previously used ambient monoclinic model (Errandonea et al., 5 Aug 2025).

The transition is a symmetry increase from $P\bar{1}$8 to $P\bar{1}$9. Structurally, the high-pressure framework remains composed of layers of edge-sharing CaO$_7$00 and ZrO$_7$01 polyhedra separated by interconnected TiO$_7$02/TiO$_7$03 layers. The reported mechanism is pressure-promoted cation ordering and reduction of polyhedral tilts, without bond formation or bond breaking. The volume discontinuity is small, $_7$04, and the bulk modulus is essentially unchanged across the transition: for the low-pressure $_7$05 phase, $_7$06 GPa and $_7$07; for the high-pressure $_7$08 phase, $_7$09 GPa and $_7$10. This near invariance indicates comparable packing efficiency and polyhedral stiffness in the two structures.

For the low-pressure phase, the third-order Birch–Murnaghan equation of state was used:

$_7$11

The principal linear compressibilities of low-pressure zirconolite-2TR are modest and slightly anisotropic:

$_7$12

with $_7$13 GPa$_7$14 along [871], $_7$15 GPa$_7$16 along [580], and $_7$17 GPa$_7$18 along [149]. The reported anisotropy is consistent with the layered arrangement of CaO$_7$19/ZrO$_7$20 planes and HTB Ti layers.

4. First-principles support and lattice-dynamical stability

The structural reassignment of zirconolite-2TR is supported by DFT calculations performed with VASP using PAW pseudopotentials and the GGA-AM05 exchange–correlation functional optimized for solids. The valence configurations were Ca [Ar] $_7$21, Zr [Kr] $_7$22, Ti [Ar] $_7$23, and O [He] $_7$24. The calculations used a plane-wave cutoff of 600 eV, a Monkhorst–Pack $_7$25 $_7$26-point mesh, electronic convergence of $_7$27 eV, forces below $_7$28 eV Å$_7$29, and hydrostatic stress tensor deviation below 0.1 GPa (Errandonea et al., 5 Aug 2025).

The DFT equation of state closely matches experiment. For low-pressure $_7$30 zirconolite-2TR, the calculated parameters are $_7$31 Å$_7$32, $_7$33 GPa, and $_7$34. For the high-pressure $_7$35 phase, the corresponding values are $_7$36 Å$_7$37, $_7$38 GPa, and $_7$39. The lattice parameters of the high-pressure phase differ from experiment by less than 1.5%, except for a slightly larger deviation in the $_7$40 axis.

Phonon calculations provide the decisive stability criterion. The ambient $_7$41 model exhibits imaginary branches and is dynamically unstable, whereas ambient $_7$42 is dynamically stable. Under pressure, the proposed high-pressure $_7$43 phase becomes dynamically stable, with all phonons positive at 23 GPa. Enthalpy calculations show that $_7$44 has lower enthalpy than $_7$45 up to approximately 28 GPa, above which monoclinic $_7$46 becomes thermodynamically favored. The experimental transition at 14.7 GPa therefore occurs below the DFT enthalpy crossover; this discrepancy was attributed to typical DFT uncertainties and real-sample effects.

The zone-center phonon content of zirconolite-2TR in $_7$47 is reported as 66 $_7$48 Raman-active modes plus 66 $_7$49 IR-active modes, of which 3 $_7$50 are acoustic. These data are relevant for future spectroscopy. A plausible implication is that Raman or infrared tracking of symmetry lowering and recovery could provide an experimental route to monitor ordering in chemically substituted zirconolite variants.

5. Disorder, amorphization, and transport implications for Zirconolite-2TR

Direct atomistic diffusion data do not yet exist in the cited record for trivalent-doped Zirconolite-2TR itself. The available molecular-dynamics study instead examined zirconolite with nominal composition CaZrTi$_7$51O$_7$52 containing 10% U substituting for Zr, using an empirical interatomic potential fitted to zirconolite properties after Chappell et al. for Ca–Zr–Ti–O interactions and U–O parameters from Catlow. The simulations used DL_POLY, a 1056-atom cell, amorphous structures generated by melt–quench from 5000 K with 100 ps equilibration and quenching to 300 K, and analysis windows limited to 5 ns to avoid recrystallization (Yang et al., 2015).

Two amorphous configurations were compared: a high-density amorphous state with the same density as the crystal, and a low-density amorphous state with a 5% density decrease matching experimentally observed swelling in radiation-damaged zirconolite. Diffusion coefficients were obtained from the long-time linear regime of the mean-square displacement using

$_7$53

and Arrhenius fits of the form

$_7$54

The mechanistic result most relevant to Zirconolite-2TR is that amorphization at constant density increases diffusion substantially, while a 5% density decrease in the amorphous state increases diffusion prefactors $_7$55 without discernibly changing activation energies $_7$56. The analysis invokes the Frenkel elastic-cage model,

$_7$57

where $_7$58 is shear modulus, $_7$59 is cage radius, and $_7$60 is the cage expansion required for a jump. In the interpretation offered there, disorder at constant density creates a distribution of local environments and pathways, and softer regions increase overall diffusion even when average cage volume is unchanged.

The species-specific Arrhenius parameters in amorphous zirconolite at crystal density are: Ca, $_7$61 eV; Zr, $_7$62 eV; Ti, $_7$63 eV; U, $_7$64 eV; and O, $_7$65 eV. For the amorphous state at 5% lower density, the activation energies remain the same within error: Ca, $_7$66 eV; Zr, $_7$67 eV; Ti, $_7$68 eV; U, $_7$69 eV; and O, $_7$70 eV. In the crystal, only oxygen diffusion was measurable, with $_7$71 eV; no cation diffusion was observed, and a lower bound of approximately 3 eV for crystalline cation activation energies was estimated from the absence of diffusion up to 130 ns at 2100 K.

Species	$_7$72 in amorphous zirconolite at crystal density (eV)	Effect of 5% lower amorphous density
O	$_7$73	$_7$74 unchanged within error; $_7$75 approximately unchanged
Ca	$_7$76	$_7$77 unchanged within error; $_7$78 increases
Zr	$_7$79	$_7$80 unchanged within error; $_7$81 increases
U	$_7$82	$_7$83 unchanged within error; $_7$84 increases
Ti	$_7$85	$_7$86 unchanged within error; $_7$87 increases

The prefactor response is strongly species dependent. For the low-density amorphous state relative to the equal-density amorphous state, $_7$88 is $_7$89 for Ca, $_7$90 for Zr, $_7$91 for Ti, $_7$92 for U, and $_7$93 for O, corresponding approximately to factors of 2.5, 1.9, 2.1, 2.7, and 1, respectively. Oxygen is therefore the most mobile species and is notably insensitive to modest density reduction, whereas cation motion in the amorphous state responds mainly through the prefactor. The diffusion study explicitly states that these calculations do not directly address trivalent-doped “2TR” variants. Generalization to Zirconolite-2TR should therefore be made cautiously: the central finding is topological-disorder control of transport, but species-specific magnitudes may vary with cation size, charge, and local coordination.

6. Waste-form significance, comparison with related polytypes, and limits of present knowledge

For nuclear waste immobilisation, zirconolite-2TR combines crystallographic stability at ambient conditions with a pressure response that preserves framework topology over a wide loading range. Geological repository pressures are stated to be orders of magnitude lower than the observed transformation pressure of 14.7 GPa, typically at or below tens of MPa. In that sense, pressure-induced structural change is not the limiting condition for service. The small transition volume step, the essentially unchanged bulk modulus across $_7$94, and the high bulk moduli reported across zirconolite polytypes support mechanical robustness under compressive loading (Errandonea et al., 5 Aug 2025).

The broader zirconolite family provides context. Zirconolite-4M, zirconolite-3O, and zirconolite-3T show no pressure-induced phase transitions to 29.9, 22.2, and 29.7 GPa, respectively, despite Dy-, Nd-, Ce-, and Fe-substituted chemistries. Calzirtite, by contrast, shows a transition at 12–13 GPa. This comparison indicates that zirconolite-2TR is not unusually fragile, but rather belongs to a class of stiff titanate host phases with bulk moduli in the range of approximately 159–171 GPa.

The more consequential uncertainty for long-term performance concerns radiation damage and amorphization rather than pressure. Zirconolite is stated to become X-ray amorphous under typical waste loads after approximately 1000 years, while the waste form must retain actinides over $_7$95–$_7$96 years. The molecular-dynamics results imply that amorphization increases diffusion even at constant density and that additional swelling mainly boosts $_7$97. However, for cations with activation energies around 3–4 eV, diffusion remains negligible at repository-relevant temperatures of 50–200 $_7$98C even when $_7$99 rises by a factor of 2–3. By contrast, oxygen mobility, characterized by $P\bar{1}$00 eV and a roughly threefold increase in $P\bar{1}$01 upon amorphization at constant density, is the transport channel most likely to matter for damage-enhanced ion exchange and aqueous alteration kinetics rather than for bulk actinide loss (Yang et al., 2015).

This distinction addresses a recurrent misconception in the waste-form literature: increased disorder does not automatically imply rapid bulk cation release by solid-state diffusion. In the present record, the dominant effect of amorphization is an increase in prefactor, not a reduction in activation barrier, and the resulting temperature dependence still suppresses cation transport strongly at repository conditions. A second misconception is to treat the 2015 diffusion simulations as direct calculations on Zirconolite-2TR. They are not: the modeled system was stoichiometric CaZrTi$P\bar{1}$02O$P\bar{1}$03 with 10% U$P\bar{1}$04, without explicit trivalent rare-earth or actinide surrogates and without the chemically compensated substitutions characteristic of “2TR” usage in waste-form discussions.

The principal limitations are therefore explicit. The diffusion study used empirical interatomic potentials, finite cells of 1056 atoms, and trajectories of 5 ns or less for the main amorphous analysis; melt–quench amorphization may differ from radiation-damage amorphization; and the absence of trivalent dopants limits direct transferability to Zirconolite-2TR. The high-pressure crystallographic study, while resolving the ambient structure and first transition, also notes that earlier work by Salamat et al. suggested a different monoclinic phase above approximately 40 GPa from Le Bail fits and therefore hypothesizes a second transition to $P\bar{1}$05 near 40 GPa. Present knowledge is thus strongest for the ambient triclinic structure, its ordering, and the first pressure-induced transition, and less complete for damage-specific transport in chemically realistic 2TR waste forms.

Taken together, the current evidence defines Zirconolite-2TR as a fully ordered triclinic $P\bar{1}$06 polymorph of CaZrTi$P\bar{1}$07O$P\bar{1}$08 with modest anisotropic compressibility, a symmetry-increasing transition to $P\bar{1}$09 at 14.7 GPa, and strong relevance as a nuclear waste host. The available transport data further suggest that, if amorphized, it should exhibit increased oxygen-network mobility and only very slow bulk cation diffusion at repository temperatures. A plausible implication is that future predictive models for Zirconolite-2TR should treat crystallographic ordering, amorphization at constant density, and swelling-induced prefactor changes as distinct inputs rather than conflating all radiation-damage effects into a single density term.