Disorder in Ho 2 Ti 2-x Zr x O 7 : pyrochlore to defect fluorite solid solution series
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Ti(OH)2 crystallizes in the orthorhombic Pnnm space group. The structure is three-dimensional. Ti2+ is bonded to six equivalent O2- atoms to form a mixture of distorted edge and corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 49°. There are four shorter (2.20 Å) and two longer (2.25 Å) Ti–O bond lengths. H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. O2- is bonded in a distorted single-bond geometry to three equivalent Ti2+ and one H1+ atom.
The fractionalization of magnetic dipoles into monopoles is revealed through a crossover in the relaxation dynamics of spin ice.
Compositionally complex oxides have garnered attention recently for their potential technological applications in harsh environments such as thermal barrier coatings and nuclear waste forms. Therefore, their response to extreme conditions, including high temperature and intense irradiation fields, must be thoroughly investigated. Here, the structural evolution of two pyrochlore oxides with comparable cation size ratio, r A /r B , (Yb 0.2 Er 0.2 Dy 0.2 Tb 0.2 Gd 0.2 ) 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , was evaluated after irradiation with 946 MeV Au ions up to a fluence of 8 × 10 12 ions/cm2 using synchrotron X-ray diffraction, transmission electron microscopy, and Raman spectroscopy. The overall radiation response is comparable for both titanate oxides and is dominated by a loss of crystallinity. When compared to a series of conventional titanate pyrochlore compositions, the amorphous track diameter of (Yb 0.2 Er 0.2 Dy 0.2 Tb 0.2 Gd 0.2 ) 2 Ti 2 O 7 is slightly larger than that of Ho2Ti2O7 and more in line with the diameter of the endmember with the maximum A-site cation size (Gd 2 Ti 2 O 7 ). Density functional theory calculations suggest that this behavior may be linked to local lattice distortions and the associated energetics of cation antisite formation. TEM and Raman analyses show that a disordered, crystalline shell surrounds the amorphous ion tracks in (Yb 0.2 Er 0.2 Dy 0.2 Tb 0.2 Gd 0.2 ) 2 Ti 2 O 7 , and the corresponding short-range structure resembles a weberite-type atomic arrangement.
Pyrochlore complex oxides (A 2 B 2 O 7 ) are an important class of fluorite-derivative ceramics with exceptional chemical and structural versatility which make them ideal model systems for studying disordering mechanisms over a range of spatial scales. Here, neutron total scattering methods were used to analyze the structural behavior in the non-stoichiometric series Nd x Zr 1-x O 2-0.5x (0.5 ≤ x ≤ 0.23) as a function of Nd content, x. Characterization of the structure functions using Rietveld refinement and the pair distribution functions with small-box refinement reveal complex disordering pathways; the average, long-range phase changes over a very narrow compositional range from pyrochlore ($Fd\bar{3}m$) to defect fluorite ($Fm\bar{3}m$) through full randomization of the cation and anion sublattices at x ~ 0.31, while the local, short-range structure continuously adopts a weberite-type atomic arrangement (C222 1 ). Comparison to a previously studied Ho 2 Ti 2-x Zr x O 7 solid solution series reveals how changes in chemical composition and stoichiometry modify defect formation and determine how disordering progresses across different length scales in pyrochlore oxides.
The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength (J eff ) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho 2 Ti 2 O 7 , and show that the magneto-chemical potential depends on the spin sublattice (α or β), i.e., the Pauling state, involved in the transition. Monte Carlo simulations using the dipolar-spin-ice Hamiltonian support our findings of a sublattice-dependent magneto-chemical potential, but the model underestimates the J eff for the β-sublattice. Additional simulations, including next-nearest neighbor interactions (J 2 ), show that long-range exchange terms in the Hamiltonian are needed to describe the measurements. This demonstrates that torque magnetometry provides a sensitive test for J eff and the spin-spin interactions that contribute to it.
The pyrochlore magnet Ce 2 Zr 2 O 7 has attracted much attention as a quantum spin ice candidate whose novelty derives in part from the dipolar-octupolar nature of the Ce 3+ pseudospin-1/2 degrees of freedom it possesses. We report heat capacity measurements on single crystal samples of Ce 2 Zr 2 O 7 down to T~0.1K in a magnetic field along the [$1,\bar{1},0$] direction. These measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two separate humps by the [$1,\bar{1},0$] magnetic field at ~2T. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: One set of chains (α chains) is polarized by the field while the other (β chains) remains free. This situation is similar to that observed in the classical spin ices Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , but with the twist that here the strong transverse exchange interactions produce substantial quantum effects. Our theoretical modeling suggests that the β chains are close to a critical state, with nearly-gapless excitations. We also report elastic and inelastic neutron scattering measurements on single crystal Ce 2 Zr 2 O 7 in [$1,\bar{1},0$] and [0,0,1] magnetic fields at temperatures down to T=0.03K. The elastic scattering behaves consistently with the formation of independent chains for a [$1,\bar{1},0$] field, while the [0,0,1] field produces a single field-induced elastic magnetic Bragg peak at (0,2,0) and equivalent wavevectors, indicating a polarized spin ice state for fields above ~3T. For both [$1,\bar{1},0$] and [0,0,1] magnetic fields, our inelastic neutron scattering results show an approximately dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modeling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in Ce 2 Zr 2 O 7 and the smallness of the parameter θ, which controls the mixing between dipolar and octupolar degrees of freedom. Finally, these results support previous estimates of the microscopic exchange parameters and place strong constraints on the theoretical description of this prominent spin ice candidate.
Pyrochlore materials are characterized by their hallmark network of corner-sharing rare-earth tetrahedra, which can produce a wide array of complex magnetic ground states. Ferromagnetic Ising pyrochlores often obey the “two-in-two-out” spin ice rules, which can lead to a highly degenerate spin structure. Large moment systems, such as Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , tend to host a classical spin ice state with low-temperature spin freezing and emergent magnetic monopoles. Systems with smaller effective moments, such as Pr 3+ -based pyrochlores, have been proposed as excellent candidates for hosting a “quantum spin ice” characterized by entanglement and a slew of exotic quasiparticle excitations. However, experimental evidence for a quantum spin ice state has remained elusive. Here, in this work, we show that the low-temperature magnetic properties of Pr 2 Sn 2 O 7 satisfy several important criteria for continued consideration as a quantum spin ice. We find that Pr 2 Sn 2 O 7 exhibits two distinct spin-correlation time scales of τ ≥ 10 –4 and ~10 –10 s in the spin ice regime. Our comprehensive bulk characterization and neutron scattering measurements enable us to map out the magnetic field-temperature phase diagram, producing results consistent with expectations for a ferromagnetic Ising pyrochlore. We identify key hallmarks of spin ice physics and show that the application of small magnetic fields (μ 0 H c ~0.5 T) suppresses the spin ice state and induces a field-polarized, ordered spin-ice phase. Together, our work clarifies the current state of Pr 2 Sn 2 O 7 and encourages future studies aimed at exploring the potential for a quantum spin ice ground state in this system.
While the spin-ice state of bulk pyrochlores such as Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 has been extensively studied in the past several decades due to its unique degenerate ground state and emergent monopole excitation, whether it survives in the thin-film form remains a mystery. The limited volume of the thin-film sample makes it challenging to study the intrinsic magnetic properties. Here, we synthesized 18-nm-thick Dy 2 Ti 2 O 7 thin film on yttria-stabilized zirconia with 9.5 mol% Y 2 O 3 substrate and capped it by a thin conductive Bi 2 Ir 2 O 7 layer and performed the proximitized magnetoresistance measurements. Our Letter found that the ice-rule-breaking phase transition survives but with a modified effective nearest-neighbor interaction (𝐽 eff =1.054 K) and distorted Ising spin axes (𝜀 = +0.051) compared to the bulk crystal. Furthermore, the results are supported by the simultaneously measured capacitive torque magnetometry. Our Letter demonstrates that proximitized transport is an effective tool for thin films of insulating frustrated magnets.
Cation off-centering is crystallography frustrated in the pyrochlore but exhibits local ordering.
Ho(TiGa2)2 crystallizes in the tetragonal I4/mmm space group. The structure is three-dimensional. Ho is bonded in a distorted square co-planar geometry to twelve Ga atoms. There are four shorter (2.89 Å) and eight longer (3.32 Å) Ho–Ga bond lengths. Ti is bonded in a 10-coordinate geometry to two equivalent Ti and eight Ga atoms. Both Ti–Ti bond lengths are 2.73 Å. All Ti–Ga bond lengths are 2.80 Å. There are eight inequivalent Ga sites. In the first Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. There are two shorter (2.67 Å) and two longer (2.91 Å) Ga–Ga bond lengths. In the second Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. There are two shorter (2.67 Å) and two longer (2.91 Å) Ga–Ga bond lengths. In the third Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. Both Ga–Ga bond lengths are 2.91 Å. In the fourth Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. Both Ga–Ga bond lengths are 2.91 Å. In the fifth Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. Both Ga–Ga bond lengths are 2.67 Å. In the sixth Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. Both Ga–Ga bond lengths are 2.67 Å. In the seventh Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms. In the eighth Ga site, Ga is bonded in a 11-coordinate geometry to three equivalent Ho, four equivalent Ti, and four Ga atoms.
Here, we report an ion-irradiation study of a compositionally complex (high-entropy) pyrochlore oxide. The damage produced from 4 MeV Au 2+ ion irradiation on single crystal (Yb 0.2 Tm 0.2 Lu 0.2 Ho 0.2 Er 0.2 ) 2 Ti 2 O 7 aligned along the [100] direction is investigated at room temperature by Rutherford backscattering spectrometry in channeling mode (RBS/C). Damage profiles based on RBS/C are presented and compared to single-component pyrochlore titanate oxides to evaluate the relative resistance to irradiation-induced amorphization. The results show that this high-entropy pyrochlore goes amorphous at a dose of 0.13 dpa, which is comparable to that of single-component pyrochlores previously studied. Transmission electron microscopy images unveil the damaged surface layer, which is consistent with the RBS/C results.
Light harvesting, separation of charge carriers, and surface reactions are three fundamental steps that are essential for an efficient photocatalyst. Here we show that these steps in the TiO 2 can be boosted simultaneously by disorder engineering. A solid-state reduction reaction between sodium and TiO 2 forms a core-shell c-TiO 2 @a-TiO 2-x (OH) y heterostructure, comprised of HO-Ti-[O]-Ti surface frustrated Lewis pairs (SFLPs) embedded in an amorphous shell surrounding a crystalline core, which enables a new genre of chemical reactivity. Specifically, these SFLPs heterolytically dissociate dihydrogen at room temperature to form charge-balancing protonated hydroxyl groups and hydrides at unsaturated titanium surface sites, which display high reactivity towards CO 2 reduction. This crystalline-amorphous heterostructure also boosts light absorption, charge carrier separation and transfer to SFLPs, while prolonged carrier lifetimes and photothermal heat generation further enhance reactivity. The collective results of this study motivate a general approach for catalytically generating sustainable chemicals and fuels through engineered disorder in heterogeneous CO 2 photocatalysts.
HoTiFe11N crystallizes in the orthorhombic Imm2 space group. The structure is three-dimensional. Ho is bonded in a linear geometry to one Ti, ten Fe, and two equivalent N atoms. The Ho–Ti bond length is 3.17 Å. There are a spread of Ho–Fe bond distances ranging from 3.08–3.30 Å. Both Ho–N bond lengths are 2.40 Å. Ti is bonded in a 1-coordinate geometry to one Ho and thirteen Fe atoms. There are a spread of Ti–Fe bond distances ranging from 2.37–2.92 Å. There are six inequivalent Fe sites. In the first Fe site, Fe is bonded to two equivalent Ho, one Ti, and nine Fe atoms to form distorted FeHo2TiFe9 cuboctahedra that share corners with ten equivalent FeHo2TiFe9 cuboctahedra, corners with two equivalent NHo2Fe4 octahedra, edges with four equivalent FeHo2TiFe9 cuboctahedra, faces with six equivalent FeHo2TiFe9 cuboctahedra, and faces with two equivalent NHo2Fe4 octahedra. The corner-sharing octahedra tilt angles range from 67–69°. There are a spread of Fe–Fe bond distances ranging from 2.39–2.63 Å. In the second Fe site, Fe is bonded in a single-bond geometry to six Fe and one N atom. Both Fe–Fe bond lengths are 2.63 Å. The Fe–N bond length is 1.92 Å. In the third Fe site, Fe is bonded in a single-bond geometry to two equivalent Ti, six Fe, and one N atom. Both Fe–Fe bond lengths are 2.66 Å. The Fe–N bond length is 1.91 Å. In the fourth Fe site, Fe is bonded in a single-bond geometry to one Ti, six Fe, and one N atom. Both Fe–Fe bond lengths are 2.67 Å. The Fe–N bond length is 1.91 Å. In the fifth Fe site, Fe is bonded in a 1-coordinate geometry to one Ti and eight Fe atoms. All Fe–Fe bond lengths are 2.95 Å. In the sixth Fe site, Fe is bonded in a 12-coordinate geometry to one Ho, two equivalent Ti, and eleven Fe atoms. The Fe–Fe bond length is 2.43 Å. N is bonded to two equivalent Ho and four Fe atoms to form NHo2Fe4 octahedra that share corners with eight equivalent FeHo2TiFe9 cuboctahedra, corners with two equivalent NHo2Fe4 octahedra, and faces with eight equivalent FeHo2TiFe9 cuboctahedra. The corner-sharing octahedral tilt angles are 2°.
Area-selective atomic layer deposition (AS-ALD) is an appealing bottom-up fabrication technique that can produce atomic-scale device features, overcoming challenges in current industrial techniques such as edge alignment errors. TiCI 4 is a common thermal ALD precursor for Ti0 2 thin films, which are appealing candidates for DRAM capacitors due to their excellent dielectric constants. Hydrogen and chlorine termination passivate the Si surface, allowing for selective deposition of TiCI 4 onto HO-terminated areas. However, selectivity loss occurs after several ALD cycles. Ti oxide nucleates onto surface defects on Cl- and H-Si resists. Previously, the use of H-Si as an ALD resist has been studied extensively, but less work has focused on chemical forces driving nucleation, especially for Cl-Si. Here, formation of defect nuclei was investigated with selectivity loss during Ti0 2 ALD with TiCI 4 and water on the (100) and (111) crystal surfaces of hydrogenated, chlorinated, and oxidized Si.
Due to the excellent catalytic properties of Ce-based materials, the development of thermally stable metal-organic frameworks (MOFs) based on Ce-oxo clusters has attracted significant attention but remains challenging. In this work, we report the synthesis of an unreported Ce 4 Ti 2 -TMA (Ce IV 4 Ti IV 2 O 4 (OH) 4 (C(CH 3 ) 3 COO) 12 ·3H 2 O·3MeCN) cluster, which serves as an ideal source for the assembly of robust Ce/Ti-MOFs. Using this cluster, we constructed two isostructural MOFs, denoted as NU-3000 and NU-3001. Single-crystal X-ray diffraction analysis confirms these MOFs as mesoporous structures with 12-coordinated Ce 3 Ti 3 nodes. Furthermore, structural analysis reveals a plane triangular node structure that likely contributes to the excellent thermal stability of these MOFs. Finally, both MOFs show catalytic activity toward high-temperature (250°C) CO oxidation and maintain significant porosity, emphasizing the thermal stability of these materials under practical catalytic conditions. Furthermore, the straightforward synthesis of thermally robust Ce/Ti-MOFs from the Ce 4 Ti 2 -TMA cluster will pave the way for future Ce/Ti-MOF-based catalyst development.
Fourier transform infrared spectrometry (FTIR) and laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) were used to determine water, rare earth (REE), lithophile (LILE), and high field strength (HFSE) element contents in garnet and pyroxene from mantle xenoliths, Kaapvaal craton, southern Africa. Water enters these nominally anhydrous minerals as protons bonded to structural oxygen in lattice defects. Pyroxene water contents (150-400 ppm in clinopyroxene; 40-250 ppm in orthopyroxene) correlate with their Al, Fe, Ca and Na and are homogeneous within a mineral grains and a xenolith. Garnets from Jagersfontein are chemically zoned for Cr, Ca, Ti and water contents. Garnets contain 0 to 20 ppm H2 Despite the fast diffusion rate of H in mantle m inerals, the observations above indicate that the water contents of mantle xenolith minerals were not disturbed during kimberlite entrainment and that the measured water data represent mantle values. Trace elements in all minerals show various degrees of light REE and LILE enrichments indicative of minimal to strong metasomatism. Water contents of peridotite minerals from the Kaapvaal lithosphere are not related to the degree of depletion of the peridotites. Instead, metasomatism exerts a clear control on the amount of water of mantle minerals. Xenoliths from each location record specific types of metasomatism with different outcomes for the water contents of mantle minerals. At pressures . 5.5 GPa, highly alkaline melts metasomatized Liqhobong and Kimberley peridotites, and increased the water contents of their olivine, pyroxenes and garnet. At higher pressures, the circulation of ultramafic melts reacting with peridotite resulted in co-variation of Ca, Ti and water at the edge of garnets at Jagersfontein, overall decreasing their water content, and lowered the water content of olivines at Finsch Mine. The calculated water content of these melts varies depending on whether the water content of the peridotite (2 wt% HO. 2O) or individual m inerals (<0.5-13 wt% H2O) are used, and also depend on the mineral-melt water partition coefficients. These metasomatic events are thought to have occurred during the Archean and Proterozoic, meaning that the water contents measured here have been preserved since that time and can be used to investigate viscocity and longevity of cratonic mantle roots.
Ho2TiO5 crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Ho3+ sites. In the first Ho3+ site, Ho3+ is bonded to six O2- atoms to form distorted HoO6 octahedra that share corners with two equivalent HoO6 octahedra, corners with four equivalent TiO6 octahedra, and edges with six HoO6 octahedra. The corner-sharing octahedra tilt angles range from 58–65°. There are a spread of Ho–O bond distances ranging from 2.28–2.32 Å. In the second Ho3+ site, Ho3+ is bonded to six O2- atoms to form HoO6 octahedra that share corners with four HoO6 octahedra, corners with four equivalent TiO6 octahedra, and edges with four HoO6 octahedra. The corner-sharing octahedra tilt angles range from 51–65°. There are a spread of Ho–O bond distances ranging from 2.20–2.34 Å. Ti4+ is bonded to six O2- atoms to form distorted TiO6 octahedra that share corners with two equivalent TiO6 octahedra, corners with eight HoO6 octahedra, and edges with two equivalent TiO6 octahedra. The corner-sharing octahedra tilt angles range from 34–65°. There are a spread of Ti–O bond distances ranging from 1.85–2.36 Å. There are five inequivalent O2- sites. In the first O2- site, O2- is bonded to four Ho3+ atoms to form OHo4 tetrahedra that share corners with ten OHo4 tetrahedra and edges with three OHo3Ti tetrahedra. In the second O2- site, O2- is bonded in a 2-coordinate geometry to three equivalent Ti4+ atoms. In the third O2- site, O2- is bonded to three Ho3+ and one Ti4+ atom to form a mixture of distorted edge and corner-sharing OHo3Ti tetrahedra. In the fourth O2- site, O2- is bonded to three equivalent Ho3+ and one Ti4+ atom to form a mixture of distorted edge and corner-sharing OHo3Ti tetrahedra. In the fifth O2- site, O2- is bonded in a 3-coordinate geometry to two equivalent Ho3+ and one Ti4+ atom.