Beyond Rattling: Tetrahedrites as Incipient Ionic Conductors

Materials with ultralow thermal conductivity are crucial to many technological applications, including thermoelectric energy harvesting, thermal barrier coatings, and optoelectronics. Liquid-like mobile ions are effective at disrupting phonon propagation, hence suppressing thermal conduction. However, high ionic mobility leads to the degradation of liquid-like thermoelectric materials under operating conditions due to ion migration and metal deposition at the cathode, hindering their practical application. Here, a new type of behavior, incipient ionic conduction, which leads to ultralow thermal conductivity, while overcoming the issues of degradation inherent in liquid-like materials, is identified. Using neutron spectroscopy and molecular dynamics (MD) simulations, it is demonstrated that in tetrahedrite, an established thermoelectric material with a remarkably low thermal conductivity, copper ions, although mobile above 200 K, are predominantly confined to cages within the crystal structure. Hence the undesirable migration of cations to the cathode can be avoided. These findings unveil a new approach for the design of materials with ultralow thermal conductivity, by exploring systems in which incipient ionic conduction may be present.

Lone Pair Rotation and Bond Heterogeneity Leading to Ultralow Thermal Conductivity in Aikinite

Understanding the relationship between the crystal structure, chemical bonding, and lattice dynamics is crucial for the design of materials with low thermal conductivities, which are essential in fields as diverse as thermoelectrics, thermal barrier coatings, and optoelectronics. The bismuthinite-aikinite series, Cu_1-x□_xPb_1-xBi_1+xS₃ (0 ≤ x ≤ 1, where □ represents a vacancy), has recently emerged as a family of n-type semiconductors with exceptionally low lattice thermal conductivities. We present a detailed investigation of the structure, electronic properties, and the vibrational spectrum of aikinite, CuPbBiS₃ (x = 0), in order to elucidate the origin of its ultralow thermal conductivity (0.48 W m^-1 K^-1 at 573 K), which is close to the calculated minimum for amorphous and disordered materials, despite its polycrystalline nature. Inelastic neutron scattering data reveal an anharmonic optical phonon mode at ca. 30 cm^-1, attributed mainly to the motion of Pb²⁺ cations. Analysis of neutron diffraction data, together with ab-initio molecular dynamics simulations, shows that the Pb²⁺ lone pairs are rotating and that, with increasing temperature, Cu⁺ and Pb²⁺ cations, which are separated at distances of ca. 3.3 Å, exhibit significantly larger displacements from their equilibrium positions than Bi³⁺ cations. In addition to bond heterogeneity, a temperature-dependent interaction between Cu⁺ and the rotating Pb²⁺ lone pair is a key contributor to the scattering effects that lower the thermal conductivity in aikinite. This work demonstrates that coupling of rotating lone pairs and the vibrational motion is an effective mechanism to achieve ultralow thermal conductivity in crystalline materials.

z+: Neutron cross section separation from wide-angle uniaxial polarization analysis

We introduce a simple method to extract the nuclear coherent and isotope incoherent, spin incoherent, and magnetic neutron scattering cross section components from powder scattering data measured using a single neutron beam polarization direction and a position-sensitive detector with large out-of-plane coverage. The method draws inspiration from polarized small-angle neutron scattering and contrasts with conventional so-called "xyz" polarization analysis on wide-angle instruments, which requires measurements with three orthogonal polarization directions. The viability of the method is demonstrated on both simulated and experimental data for the classical "spin ice" system Ho₂Ti₂O₇, the latter from the LET direct geometry spectrometer at the ISIS facility. The cross section components can be reproduced with good fidelity by either fitting the out-of-plane angle dependence around a Debye-Scherrer cone or grouping the data by angle and performing a matrix inversion. The limitations of the method and its practical uses are discussed.

Multiple Magnetic Bilayers and Unconventional Criticality without Frustration in BaCuSi_{2}O_{6}

The dimerized quantum magnet BaCuSi_{2}O_{6} was proposed as an example of "dimensional reduction" arising near the magnetic-field-induced quantum critical point (QCP) due to perfect geometrical frustration of its interbilayer interactions. We demonstrate by high-resolution neutron spectroscopy experiments that the effective intrabilayer interactions are ferromagnetic, thereby excluding frustration. We explain the apparent dimensional reduction by establishing the presence of three magnetically inequivalent bilayers, with ratios 3∶2∶1, whose differing interaction parameters create an extra field-temperature scaling regime near the QCP with a nontrivial but nonuniversal exponent. We demonstrate by detailed quantum Monte Carlo simulations that the magnetic interaction parameters we deduce can account for all the measured properties of BaCuSi_{2}O_{6}, opening the way to a quantitative understanding of nonuniversal scaling in any modulated layered system.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Polarization analysis on the LET cold neutron spectrometer using a 3He spin-filter: first results

We report on the design and construction of a neutron polarization analyzer based on a 3He spin filter for the LET spectrometer at the ISIS facility. Its commissioning completes the uniaxial polarized mode of the instrument. Besides the 3He spin filter cell, the analyzer consists of a set of electromagnetic coils to provide a uniform magnetic field, and a collimator to eliminate background from the sample environment and analyzer infrastructure. The 3He cell is separated from the LET main tank vacuum by means of a gas tank, which permits rapid cell changeovers and guarantees safe operation. In addition to the analyzer hardware, software has been written to reduce and correct polarized data. The successful operation of the polarized mode was realized for the separation of coherent and incoherent dynamics in an organic solar cell polymer blend.

z=2 Quantum Critical Dynamics in a Spin Ladder

By means of inelastic neutron scattering we investigate finite temperature dynamics in the quantum spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB) near the magnetic field induced quantum critical point with dynamical exponent z=2. We observe universal finite-temperature scaling of the transverse local dynamic structure factor in spectacular quantitative agreement with long-standing theoretical predictions. At the same time, already at rather low temperatures, we observe strong nonuniversal longitudinal fluctuations. To separate the two, we make use of an intrinsic leg-exchange symmetry of the spin ladder. Complementary measurements of specific heat also reveal striking scaling behavior near the quantum critical point.

Diffusion mechanism in the sodium-ion battery material sodium cobaltate

High performance batteries based on the movement of Li ions in Li_xCoO₂ have made possible a revolution in mobile electronic technology, from laptops to mobile phones. However, the scarcity of Li and the demand for energy storage for renewables has led to intense interest in Na-ion batteries, including structurally-related Na_xCoO₂. Here we have determined the diffusion mechanism for Na_0.8CoO₂ using diffuse x-ray scattering, quasi-elastic neutron scattering and ab-initio molecular dynamics simulations, and we find that the sodium ordering provides diffusion pathways and governs the diffusion rate. Above T ~ 290 K the so-called partially disordered stripe superstructure provides channels for quasi-1D diffusion, and melting of the sodium ordering leads to 2D superionic diffusion above T ~ 370 K. We obtain quantitative agreement between our microscopic study of the hopping mechanism and bulk self-diffusion measurements. Our approach can be applied widely to other Na- or Li-ion battery materials.

Hopping Time Scales and the Phonon-Liquid Electron-Crystal Picture in Thermoelectric Copper Selenide

The suppression of transverse phonons by liquidlike diffusion in superionic conductors has been proposed as a means to dramatically reduce thermal conductivity in thermoelectric materials [H. Lui et al. Nat. Mater. 11, 422 (2012)NMAACR1476-112210.1038/nmat3273]. We have measured the ion transport and lattice dynamics in the original phonon-liquid electron-crystal Cu_{2}Se using neutron spectroscopy. We show that hopping time scales are too slow to significantly affect lattice vibrations and that the transverse phonons persist at all temperatures. Substantial changes to the phonon spectrum occur well below the transition to the superionic phase, and the ultralow thermal conductivity is instead attributed to anharmonicity.

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.