Anharmonic Displacements Research Articles

Breakdown of the perfect crystal dynamics in dynamically disordered over-stoichiometric Nd2NiO4.25

The lattice dynamics of oxygen-doped ${\mathrm{Nd}}_{2}\mathrm{Ni}{\mathrm{O}}_{4+\ensuremath{\delta}}$ is explored by a combination of single-crystal neutron spectroscopy, ab initio molecular dynamics (AIMD), and harmonic phonon calculations using density functional theory. The inelastic response computed from AIMD finds better correspondence with the experimental inelastic neutron spectra than the harmonic phonon calculations. The comparison of experimental and simulated data indicates that the presence of extra oxygen in interstitial sites leads to marked differences in the dynamics of the system compared to the stoichiometric parent compound. In particular, a nondispersive scattering signal was detected below 15 meV in all the experimental spectra in the $(ab)$ plane. Its origin has been rationalized as an important incoherent scattering from Nd atoms, which emerges from in-plane atomic self-motions in the ${\mathrm{Nd}}_{2}{\mathrm{O}}_{2+\ensuremath{\delta}}$ rock-salt layers. The presence of additional interstitial oxygen atoms both dampens the long-range lattice dynamics as well as enhances oxygen and neodymium anharmonic displacements. The experimental observation of coherent and incoherent responses allows assessing the effect of interstitials on the vibrations of the whole crystal as well as on the dynamics of each atom independently.

Oxonium diimidotriphosphate from the hydrolysis of trimetaphosphimic acid

Trimetaphosphimates decompose not only upon heating but also in water. Hydrolysis of trimetaphosphimic acid leads to the formation of diimidotriphosphoric acid by ring opening. Single-crystal structure determination using synchrotron radiation revealed the oxonium salt of the latter acid with double stacks of rod-shaped anions along [001]. Anharmonic displacement parameters were used to model slight disorder of part of the anions. These are interconnected by hydrogen bonds within and between the stacks. Powder X-ray diffraction confirmed phase purity. At temperatures above 120 °C, diimidotriphosphoric acid decomposes into unknown crystalline compounds. It thus seems a promising precursor for the synthesis of oxonitridophosphates at moderate temperatures.Graphical abstract

X-ray diffraction study of the atomic interactions, anharmonic displacements and inner-crystal field in orthorhombic KNbO3

An X-ray diffraction study aimed at establishing the subtle details of the electron density and anharmonicity of the atomic vibrations in a stoichiometric monodomain single crystal of potassium niobate, KNbO3, has been conducted at room temperature (orthorhombic ferroelectric phase Amm2). The cation and anion displacements obtained from the experiment are weakly anharmonic without any manifestation of structural disorder. The chemical bond and interatomic interactions inside and between crystal substructures at the balance of intracrystalline forces are characterized in detail. The role of each of the ions in the formation of the ferroelectric phase was studied and the features of the electron-density deformation in the niobium and oxygen substructures, and the role of each of them in the occurrence of spontaneous polarization are established. The position-space distribution of electrostatic and quantum forces in KNbO3 is restored. It is emphasized that for the completeness of the analysis of the nature of the ferroelectric properties it is necessary to consider both static and kinetic electronic factors, which are of a quantum origin. The experimental results and theoretical estimations by the Kohn–Sham calculation with periodic boundary conditions are in reasonable agreement, thus indicating the physical significance of the findings of this study.

Infrared furnace for in situ neutron single-crystal diffraction studies in controlled gas atmospheres at high temperatures

To understand oxygen diffusion mechanisms in non-stoichiometric oxides, the possibility to explore structural changes as a function of the oxygen partial pressure with temperature and related oxygen bulk stoichiometry is mandatory. This article reports on the realization of a high-temperature furnace, suitable for single-crystal neutron diffraction, working continuously at temperatures of up to 1000°C at different and adjustable partial gas pressures of up to 2 bar (1 bar = 100 kPa). This allows exploration of the phase diagrams of non-stoichiometric oxides under in situ conditions and controlled oxygen partial pressure. As a pilot study, the structural changes of Pr2NiO4+δ were explored at room temperature (δ ≃ 0.24) and at 900°C under 1 bar P(O2) (δ ≃ 0.13) as well as under secondary vacuum (approximately 10−5 mbar) conditions yielding a δ close to zero. The strong anharmonic displacements of the apical oxygen atoms along the [110] shallow diffusion pathway, which were previously observed at room temperature and 400°C, become more isotropic at 900°C. The study shows that the anisotropic oxygen displacements, here related to lattice instabilities, play a major role in understanding oxygen diffusion pathways and related activation energies at moderate temperatures. This also shows the importance of the availability of reaction cells for single-crystal neutron diffraction to explore the phase diagram and associated structural changes of non-stoichiometric oxygen ion conductors and respective diffusion mechanisms.

Lithium atom mobility in lithium germanium antimony tellurides elucidated by neutron diffraction and quasielastic neutron scattering

Lithium germanium antimony tellurides are known as promising thermoelectric materials. Earlier 7Li solid state NMR studies had revealed pronounced lithium atom mobility. Further insights into the diffusion mechanism are investigated by means of neutron powder diffraction in combination with quasielastic neutron scattering (QENS). In vacancy-containing LiGe3.5Sb2Te7, the isotropic displacement parameters of the cations are larger than in vacancy-free Li2Ge3Sb2Te7 and thus indicate more pronounced atom mobility in the investigated temperature range from room temperature to 600 °C. In contrast, temperature-dependent isotropic displacement parameters of the anions are similar for both solid solutions. Comparable to the situation in the important thermoelectric material PbTe, anharmonic displacement parameters for LiGe3.5Sb2Te7 – a lithium germanium antimony telluride with optimized thermoelectric properties – are significant already at room temperature. The extrapolation of displacement parameters toward low temperatures indicates that the displacements are predominantly dynamic. The temperature-dependent evaluation of lattice parameters and isotropic displacement parameters reveals three different regimes. From room temperature to 250 °C, a NaCl-type model with anharmonic displacement parameters for cation sites fits well. Between 250 °C and 400 °C, the unit cell volume increases less than in the other regimes and small lattice distortions may occur. At temperatures higher than 400 °C (investigated up to 600 °C), lithium atoms also occupy tetrahedral voids of the fcc Te substructure. Whereas QENS data probing the picosecond time scale show no significant lithium atom mobility in the Q range of 0.08–1.68 Å−1, a temperature-dependent change in the elastic scattering term hints at a different time window or a combination of motions with different time scales.

Centrosymmetric LaRh2Ga2

Abstract Polycrystalline samples of LaRh2Ga2 with the centrosymmetric CaBe2Ge2 type structure were obtained by arc-melting. Small single crystals were grown through a special annealing sequence in an induction furnace. The structures of two different crystals were refined from diffractometer data, confirming the centrosymmetric structure. The 2c Rh sites were refined with anharmonic atomic displacement parameters.

(Nd/Pr)2NiO4+δ: Reaction Intermediates and Redox Behavior Explored by in Situ Neutron Powder Diffraction during Electrochemical Oxygen Intercalation.

Oxygen intercalation/deintercalation in Pr2NiO4+δ and Nd2NiO4+δ was followed by in situ neutron powder diffraction during electrochemical oxidation/reduction, in a dedicated reaction cell at room temperature. For both systems three phases, all showing the same line width, were identified. The starting phases Pr2NiO4.23 and Nd2NiO4.24, considered with an average orthorhombic Fmmm symmetry, although both show a slight monoclinic distortion, get reduced in a two-phase reaction step to tetragonal intermediate phases with 0.07 ≤ δ ≤ 0.10 and P42/ ncm space group, which on further reduction transform, again in a two-phase reaction step, toward the respective stoichiometric (Pr/Nd)2NiO4.0 phases, with Bmab space group. Electrochemical oxidation does, however, not proceed fully reversibly for both cases: while the reoxidation of Nd2NiO4+δ is limited to the tetragonal intermediate phase with δ = 0.10, the homologous Pr2NiO4+δ can be reoxidized up to δ = 0.17, showing orthorhombic symmetry. For the intermediate tetragonal phase, we were able to establish for Pr2NiO4.09 a complex anharmonic displacement behavior of the apical oxygen atoms, as analyzed by single-crystal neutron diffraction and maximum entropy analysis, in agreement with a low- T diffusion pathway for oxygen ions, activated by lattice dynamics.

Cubic Sr2ScGaO5 Perovskite: Structural Stability, Oxygen Defect Structure, and Ion Conductivity Explored on Single Crystals.

Oxygen-deficient Sr2ScGaO5 single crystals with a cubic perovskite structure were grown by the floating-zone technique. The transparent crystals of this pure 3D oxygen electrolyte are metastable at ambient temperature, showing one-sixth of all oxygen positions vacant. While neutron single-crystal diffraction, followed by maximum entropy analysis, revealed a strong anharmonic displacements for the oxygen atoms, a predominant formation of ScO6 octahedra and GaO4 tetrahedra is indicated by Raman spectroscopic studies, resulting in a complex oxygen defect structure with short-range order. Temperature-dependent X-ray powder diffraction (XPD) and neutron powder diffraction (NPD) studies reveal the cubic Sr2ScGaO5 to be thermodynamically stable only above 1400 °C, while the stable modification below this temperature shows the brownmillerite framework with orthorhombic symmetry. Cubic Sr2ScGaO5 remains surprisingly kinetically stable upon heating from ambient temperature to 1300 °C, indicating a huge inertia for the retransformation toward the thermodynamically stable brownmillerite phase. Ionic conductivity investigated by impedance spectroscopy was found to be 10-4 S/cm at 600 °C, while oxygen 18O/16O isotope exchange indicates a free oxygen mobility to set in at around 500 °C.

The Modified Debye–Grüneisen Model for Highly Compressed Diamond

A new modification of the Debye–Gruneisen model is proposed. It takes explicitly into account the anharmonicity of phonon modes, which leads to the nonlinear dependence of energy levels on quantum numbers. The low-temperature version of this model considering anharmonic displacement of only the lowest energy levels of both longitudinal and transverse phonons is developed. This model, calibrated on results of DFT ab initio calculations, reproduces all predicted low-temperature thermodynamic properties of diamond at pressures up to 1 TPa, including the region of its negative thermal expansion.

An exceptionally-high diffraction quality dodecaboride LUB12: Growth and single-crystal structure

Single crystals of LuB12 of exceptionally high diffraction quality confirmed by an accurate X-ray structure analysis are grown by the modified crucibleless inductive floating zone melting. A thoroughly treated single crystal is used to collect a high-resolution data set up to sinθ/λ = 1.36 Å−1 at 293 K, which has been reduced to 271 symmetry-independent reflections. Residual factors of the structure refinement in the Fm3¯m symmetry group are R1(|F|)/wR2(|F|) = 0.20/0.14% in a 13-parametric structure model. Revealed asymmetry of electron density distribution near average position of the Lu atom described using anharmonic displacement parameters.

Localised Ag(+) vibrations at the origin of ultralow thermal conductivity in layered thermoelectric AgCrSe2.

In materials science, the substructure approach consists in imagining complex materials in which a particular property is associated with a distinct structural feature, so as to combine different chosen physical characteristics, which otherwise have little chance to coexist. Applied to thermoelectric materials, it has been used to achieve simultaneously phonon-glass and electron-crystal properties. Mostly studied for its superionic conductivity, AgCrSe2 is a naturally layered compound, which achieves very low thermal conductivity, ~0.4 W.K−1.m−1 at RT (room temperature), and is considered a promising thermoelectric. The Cr atoms of the [CrSe2]∞ layer bear a spin S = 3/2, which orders below TN = 55 K. Here we report low temperature inelastic neutron scattering experiments on AgCrSe2, alongside the magnetic field evolution of its thermal and electrical transport. We observe a very low frequency mode at 3 meV, ascribed to large anharmonic displacements of the Ag+ ions in the [Ag]∞ layer, and 2D magnetic fluctuations up to 3 TN in the chromium layer. The low thermal conductivity of AgCrSe2 is attributed to acoustic phonon scattering by a regular lattice of Ag+ oscillating in quasi-2D potential wells. These findings highlight a new way to achieve localised phonon modes in a perfectly crystalline solid.

Low-temperature powder X-ray diffraction measurements in vacuum: analysis of the thermal displacement of copper

A serious limitation of the all-in-vacuum diffractometer reported by Straasø, Dippel, Becker & Als-Nielsen [J. Synchrotron Rad.(2014),21, 119–126] has so far been the inability to cool samples to near-cryogenic temperatures during measurement. The problem is solved by placing the sample in a jet of helium gas cooled by liquid nitrogen. The resulting temperature change is quantified by determining the change in unit-cell parameter and atomic displacement parameter of copper. The cooling proved successful, with a resulting temperature of ∼95 (3) K. The measured powder X-ray diffraction data are of superb quality and high resolution [up to sinθ/λ = 2.2 Å−1], permitting an extensive modelling of the thermal displacement. The anharmonic displacement of copper was modelled by a Gram–Charlier expansion of the temperature factor. As expected, the corresponding probability distribution function shows an increased probability away from neighbouring atoms and a decreased probability towards them.

On the structural basis of the presence of two optical axes in α-HIO3 crystal

An X-ray diffraction study of α-HIO3 crystal has been performed with the following results: sp. gr. P212121, Z = 4, a = 5.5360(3) A, b = 5.8723(6) A, c = 7.7291(5) A, and R factors R(F)/wR(F) = 0.86/0.69%. Disordering of iodine site is revealed, which is described in terms of anharmonic atomic displacements. Packing (likely unique) of all structure atoms over two systems of planes rotated by an angle close to the rotation of optical axes (47°) is revealed. The rotation of the plane of polarization of light based on the structural data is calculated for the first time for the α-HIO3 crystal.

Linear Compressibility and Thermal Expansion of KMn[Ag(CN)2]3 Studied by Raman Spectroscopy and First-Principles Calculations

We have investigated the linear compressibility and thermal expansion properties of KMn[Ag(CN)2]3 using Raman spectroscopy and DFT calculations. Phonon frequencies and mode assignments from polarized Raman measurements and DFT calculations agree with each other satisfactorily. Computed linear compressibilities and thermal expansion coefficients corroborate the reported measured values. Pressure variation of mean partial phonon frequencies of KMn[Ag(CN)2]3 shows that large amplitude anharmonic displacements of Ag atoms can occur with minimum enthalpy cost even with increasing pressure. This means that Ag layer can be squeezed relatively easily, which manifests as PLC in the basal plane and coupled NLC along trigonal axis due to the rigid Mn-NC-Ag-CN-Mn chain along ⟨101⟩ crystal direction. Elastic constants of KMn[Ag(CN)2]3 indicate that the crystal is highly anisotropic and becomes unstable with increasing pressure. Directional Gruneisen parameters of KMn[Ag(CN)2]3 are found to be highly anisotropic. These properties show that NLC/NTE and PLC/PTE in KMn[Ag(CN)2]3 are driven by elastic and Gruneisen anisotropies combined with anharmonic lattice vibrations of Ag atoms. Partial phonon frequencies of KMn[Ag(CN)2]3 are found to be higher than those of Ag3[Co(CN)6]. The partial frequency of K atom increases rapidly with pressure and becomes comparable to that of Ag around 2 GPa. This shows that K inclusion stiffens the lattice and changes the dynamics, causing the pressure-induced phase transformation of KMn[Ag(CN)2]3 to occur at a higher pressure rather than at 0.2 GPa as in Ag3[Co(CN)6]. The phase transformation can be attributed to the softening of two low-energy optic modes (A2 and E) and the softening of C44 shear elastic constant and hence the transverse acoustic mode.

Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate

The need for both high electrical conductivity and low thermal conductivity creates a design conflict for thermoelectric systems, leading to the consideration of materials with complicated crystal structures. Rattling of ions in cages results in low thermal conductivity, but understanding the mechanism through studies of the phonon dispersion using momentum-resolved spectroscopy is made difficult by the complexity of the unit cells. We have performed inelastic X-ray and neutron scattering experiments that are in remarkable agreement with our first-principles density-functional calculations of the phonon dispersion for thermoelectric Na(0.8)CoO2, which has a large-period superstructure. We have directly observed an Einstein-like rattling mode at low energy, involving large anharmonic displacements of the sodium ions inside multi-vacancy clusters. These rattling modes suppress the thermal conductivity by a factor of six compared with vacancy-free NaCoO2. Our results will guide the design of the next generation of materials for applications in solid-state refrigerators and power recovery.

Crystal Structure and Oxide-Ion Conductivity along c-Axis of Si-Deficient Apatite-Type Lanthanum Silicate

We have prepared the highly c-axis-oriented polycrystalline material of Si-deficient apatite-type lanthanum silicate by isothermal heating of the sandwich-type La2SiO5/La2Si2O7/La2SiO5 diffusion couple at 1873 K for 100 h. The resulting polycrystal of La9.50(Si5.87□0.13)O26, where □ denotes a vacancy in Si site, was characterized using optical microscopy, X-ray diffractometry, and impedance spectroscopy. The annealed couple was mechanically processed, and the textured thin-plate electrolyte was obtained. The ionic conductivity (σ) along the c-axis steadily increased from 1.6 × 10–2 S/cm to 1.26 × 10–1 S/cm with increasing temperature from 623 to 1073 K. The Arrhenius plot of σ showed the marked slope change at ca. 800 K; the activation energies of conduction were, above and below 800 K, 0.53 and 0.17 eV, respectively. The crystal structure of La9.50(Si5.87□0.13)O26 at ambient temperature (space group P63/m) showed the appreciable positional disordering of O atoms (12i site) that are bonded to Si atoms, together with the anharmonic displacements of La atoms (4f and 6h sites). The Si-deficient apatite was formed by the extraction of the SiO2 component from the La2O3-excess apatite according to La9.33+2xSi6O26+3x – 1.5xSiO2 → La9.33+2x(Si6–1.5x□1.5x)O26 (x ∼ 0.087).

Disorder in BaThF6– refinement of anharmonic displacement parameters from high-pressure single-crystal X-ray diffraction data

The structure of BaThF(6) has been investigated as a function of temperature and pressure with single-crystal X-ray diffraction using synchrotron radiation. The compound crystallizes in the tysonite structure, space group P6(3)/mmc (a = 4.296(1) Å and c = 7.571(1) Å at ambient conditions). It is stable at least down to 150 K and up to 4 GPa. In the entire range of pressures and temperatures studied here, the compound is characterized by a high degree of disorder, both on the cationic and anionic positions. Despite the different valence states and sizes, both cations occupy the same crystallographic site in the ideal tysonite structure. The cationic disorder is described by two alternative approaches. The first model corresponds to a split-atom position model in which Ba(2+) is maintained on a special position with site symmetry 6m2, while Th(4+) is slightly displaced from the respective position. In the second model, both cations are maintained on the ideal position and anharmonic displacement parameters using a tensor of third order are introduced. Anharmonic displacement parameters have been refined from high-pressure single-crystal X-ray data measured in situ in a diamond anvil cell for the first time. The feasibility and general problems of anharmonic refinements of high-pressure X-ray data are further commented.

Strategies for the structure determination of endohedral fullerenes applied to the example of Ba@C(74)xCo(octaethylporphyrin)x2C(6)H(6).

The structure determination of endohedral fullerenes is complicated because of the high degree of disorder which may affect the different structural components, e.g. the endohedral atom/molecule, the fullerene cage and solvent molecules. Even worse, the data-to-parameter ratio and, in particular, the scattering power is low. Different strategies are employed to deal with these problems. The observed fraction of the reciprocal lattice may be increased by means of synchrotron diffraction studies. The number of parameters may be reduced by applying rigid-body refinement strategies and by restricting the displacement parameters in the framework of the TLS approach. In the first section, we will give a short overview of the structure determinations of endohedral fullerenes from single-crystal data and discuss the severe problems one may encounter. Then we will give an example of a successful structure analysis of a metal-containing endohedral fullerene, i.e. Ba@C(74)xCo(OEP)x2C(6)H(6) (OEP = octaethylporphyrin). Several strategies of refinement, beyond the black box level, have been checked and compared, e.g. TLS, split-atom models, twin and single crystal models, anharmonic displacement parameters, and rigid-body models.

Features of the electron density in magnesium diboride: reconstruction from X-ray diffraction data and comparison with TB-LMTO and FPLO calculations.

Features of the electron density in MgB(2) reconstructed from room-temperature single-crystal X-ray diffraction intensities using a multipole model are considered. Topological analysis of the total electron density has been applied to characterize the atomic interactions in magnesium diboride. The shared-type B-B interaction in the B-atom layer reveals that both sigma and pi components of the bonding are strong. A closed-shell-type weak B-B pi interaction along the c axis of the unit cell has also been found. The Mg-B closed-shell interaction exhibits a bond path that is significantly curved towards the vertical Mg-atom chain ([110] direction). The latter two facts reflect two sorts of bonding interactions along the [001] direction. Integration of the electron density over the zero-flux atomic basins reveals a charge transfer of approximately 1.4 (1) electrons from the Mg atoms to the B-atom network. The calculated electric-field gradients at nuclear positions are in good agreement with experimental NMR values. The anharmonic displacement of the B atoms is also discussed. Calculations of the electron density by tight-binding linear muffin-tin orbital (TB-LMTO) and full-potential non-orthogonal local orbital (FPLO) methods confirm the results of the reconstruction from X-ray diffraction; for example, a charge transfer of 1.5 and 1.6 electrons, respectively, was found.

A novel perovskite-like Ta-bronze KTa1+zO3: preparation, stoichiometry, conductivity and crystal structure studies.

A new cubic Ta-bronze (1) KTa(1+z)(+(5-delta))O(3) [z approximately 0.107 (3)] was obtained on a cathode by molten salt electrolysis of the system K(2)TaOF(5)-K(3)TaO(2)F(4)-(KF + NaF + LiF)(eutectic). Black, metallic cubic crystals of (1) are formed together with tetragonal beta-Ta. The perovskite-like crystal structure of (1) [a = 4.005 (1) A, space group Pm3m] was refined with anharmonic displacement parameters for Ta and K atoms and anisotropic displacement parameters for a split O-atom position [KM4CCD diffractometer; lambda(Mo Kalpha); 3320 measured reflections with I > 3sigma(I); R = 0.0095, wR = 0.0065, Deltarho(min) = -0.91 e A(-3), Deltarho(max) = 0.65 e A(-3)]. Defects in the O and K atomic positions were found. (1) is a semiconductor in the temperature range 4-300 K, whereas the well studied and closely related colourless transparent crystals KTa(+5)O(3) (2) are dielectric. Differences in the properties of (1) and (2) are assumed to be connected with the existence of Ta dumb-bells statistically distributed into the KTaO(3) matrix.