Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

Abstract

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

Keywords: computational materials modeling; ice; neutron spectroscopy; nuclear quantum effects; plastic crystals; polymers; soft matter; supramolecular frameworks; sustainable materials; water.

Figure 11

(a) Phase diagram of H${}_2$O in the range T = 4–300 K and p = 0.01–10 GPa, highlighting the thermodynamically stable forms of ice of relevance to our discussion (crystal phases VI and XV). Ice XV is the hydrogen-ordered counterpart of ice VI and is thermodynamically stable below 130 K over the pressure interval 0.8–1.5 GPa [321]. The phase diagram also includes the ranges of observation of metastable amorphous ices (Low-, High-, and very-High-Density Amorphous forms are denoted as LDA, HDA, and vHDA, respectively). The LDA phase is mostly found in the low-pressure region of the phase diagram (0–0.2 GPa), whereas HDA and VHDA occur at intermediate pressures (0.2–2 GPa). At high pressures (>2 GPa), only crystalline phases are stable [350]. (b) INS spectra of ice VI, deep-glassy ice VI, and ice XV, collected at T = 15 K on TOSCA+. The gray-shaded areas highlight the spectral range where major differences between ice VI and XV are observed. The spectra are shifted vertically for clarity. Difference spectra are shown in the lower part of the panel [328]. (c) ND patterns of (1) ice VI, (2) deep-glassy ice VI, and (3) ice XV collected simultaneously on TOSCA+ at T = 15 K. The experimental diffraction data are shown as light data points and the associated Rietveld fits as darker solid lines. Tick-marks indicate the expected positions of Bragg reflections. [328]. (d) Contour plot of the librational region upon heating deep-glassy ice VI from 80 to 138 K, followed by cooling back to 80 K [328]. Adapted with permission from Refs. [328,350]. Copyright (2021) American Chemical Society.

Figure 12

(a) Hydrogen-projected VDOSs as a function of temperature at a pressure of 0.025 GPa. These data have been normalized to unity and vertically offset to facilitate visual comparison. (b) Simulated VDOSs of H₂O at subcritical (bottom) and supercritical (top) conditions. In each case, the full spectrum (solid line) is compared with the projected VDOS (dashed line), after removing translational contributions. The shaded spectra correspond to intramolecular vibrational spectra, with librational and rotational motions projected out. Adapted with permission from Ref. [332]. Copyright (2021) American Chemical Society.

Figure 13

Pictorial representation of the local H-bond geometry for H₂O at supercritical (left) and ambient conditions (right). The figure depicts the coordinate frames used in the interpretation of NCS data, and the corresponding (partially isotropic and anisotropic) proton momentum distributions. Reprinted with permission from Ref. [332]. Copyright (2021) American Chemical Society.

Figure 15

(a) Pictorial representation of the anharmonic potential of the OH-stretch mode of H₂O. The vibrational ZPE measured with NCS (DINS), as well as the fundamental 0 → 1 transition probed with INS, are highlighted. (b) Experimental INS spectra of different forms of amorphous ice (LDA, red; unannealed HDA, green; and vHDA, blue) measured at T = 80 K on MARI. The spectra were obtained after averaging over the indicated Q-range. (c) Mean kinetic energies (<E_K>) from NCS (orange) and corresponding values obtained from INS using the harmonic model discussed in Ref. [399] (blue). (d) Energies of the OH-stretch, bend, and librational modes of H₂O, obtained from INS (blue), as well as the corresponding values derived from NCS (orange). Adapted with permission from Ref. [391]. Copyright (2021) American Chemical Society.

Figure 16

Experimental (a) and computational (b,c) phase diagrams of H₂O in the range T = 50–300 K and p = 0.02–1 GPa. The computational phase diagrams have been obtained with classical (b) and PIMD simulations (c) using a vdW-corrected hybrid-DFT (revPBE0-D3). See Ref. [407] for more details. Adapted with permission from Ref. [407]

Figure 1

Regions of Q and E simultaneously accessible to neutrons, and qualitative comparison with other experimental probes. For ease of comparison, associated length and time scales are given by the bottom and right axes, respectively. Neutron spectroscopic techniques include the use of epithermal (hot neutrons), thermal (time-of-flight and crystal spectroscopy), and cold/ultracold wavelengths (backscattering and NSE). Blue text entries around the main figure illustrate areas of scientific and technological application. Reprinted with permission from Ref. [63].

Figure 2

Color map of the elastic properties of several classes of materials around ambient conditions, including those discussed in the present and subsequent sections of this work. Please note the logarithmic scales of both vertical and horizontal axes. Adapted from Ref. [74] with permission from The Royal Society of Chemistry.

Figure 3

Phase diagram of ${\mathrm{MA}}_{1-\mathrm{x}}{\mathrm{FA}}_{\mathrm{x}}{\mathrm{PbI}}_3$ solid solutions over the temperature range 10–365 K at ambient pressure. Pure MAPbI${}_3$(FAPbI${}_3$) corrresponds to the left (right) edges of the diagram. For further details, see the main text. Adapted with permission from Refs. [75,81]. Copyright (2021) American Chemical Society.

Figure 4

Phonon dispersion relations in the cubic phase of MAPbI₃, measured on both perdeuterated and hydrogenous single-crystals using IXS (cyan circles [123]) and INS-TAS (orange squares [109] and green circles [113], respectively). Wave vectors on the abscissa are given in reduced lattice units. Longitudinal and Transverse Acoustic (LA and TA, respectively) branches are presented along with the lowest-energy Transverse Optical (TO) mode. Adapted with permission from Ref. [109].

Figure 5

INS spectra of hydrogenous MAPbI₃ in the orthorhombic phase at low temperatures (T = 5–20 K). These spectra were recorded on five different instruments: 1T (TAS; single-crystal [116]); AMATERAS (TOF; E_i = 54 meV; single-crystal [121]; TOSCA [144], VISION [109], TOSCA+ [75] (indirect-geometry; powders). Adapted with permission from Refs. [75,109,116,121,144]. Copyright (2021) American Chemical Society.

Figure 6

(a) The lower two panels show experimental INS spectra of the MA_0.4FA_0.6PbI${}_3$ solid-solution recorded on TOSCA+ at T = 10 K, along with the difference spectrum obtained by substracting the signal from FAPbI${}_3$, highlighting contributions from the MA⁺ cations [75]. These data are compared with the results of AIMD simulations in the upper two panels of (a). The theoretical INS spectrum of the MA_0.4FA_0.6 mixed-cation composition was constructed by stoichiometric weighting of the partial hydrogen-projected VDOS. MA⁺ cations were selected based on the analysis of the individual VDOSs for each of the twelve distinct types used in the structural model (see the bold curves in the top panel). The molecular model in (a) illustrates the lowest-energy internal mode of MA⁺. (b) Structural model used to describe the mixture, with FA⁺ omitted to ease visualization. Distinct MA⁺ cations are labeled with Roman numerals. (c) Distribution of closest nitrogen-iodine distances for each of the twelve MA⁺ cations. Two extreme cases are highlighted as bold curves (labeled as II and XII). Their time-evolved structures over a 30-ps interval are presented as cumulative models, as shown in the insets in (c). The same color coding has been used in all panels. [Unpublished data].

Figure 7

INS spectra of bulk (red) and confined (green) PEO. The black trace corresponds to the INS response of the graphite oxide substrate. Adapted from Ref. [202] with permission from The Royal Society of Chemistry.

Figure 8

(a) Structure of Li₄C₆₀ obtained from DFT (VASP) geometry optimization within space group I2/m. Gray sticks are carbon bonds; magenta and brown spheres are carbon atoms involved in covalent intermolecular bonds, including [2 + 2] bridges and single bonds. Red and yellow spheres represent two different types of intercalated ions, Li_T and Li_O, respectively. (b) View along the c-axis of one polymeric plane (the Li ions have been omitted for clarity). (c) (Top) Generalized Density of States (GDOS) derived from INS data collected between 300 K (polymer phase) and 700 K (monomer phase): red, 300 K; yellow, 610 K; brown, 630 K; gray, 640 K; and black, 700 K). (Bottom) GDOS extracted from the MD simulations at 800 K (see text) in the monomer phase (black solid lines, total GDOS; gray solid line, carbon GDOS; red area, lithium GDOS). The INS spectra were collected on Mibemol (LLB, Saclay, FR). Reproduced from Ref. [246] with permission from APS (https://doi.org/10.1103/PhysRevLett.113.215502) (accessed on 28 April 2021).

Figure 9

(a) Nanoporous hybrid framework structures of ZIF-4, ZIF-7, and ZIF-8. The inorganic building blocks are represented by purple ZnN₄ tetrahedra. (b) Experimental (TOSCA T = 10 K) and theoretical (DFT; CRYSTAL14) INS spectra for these compounds. Adapted from Ref. [264] with permission from APS (https://doi.org/10.1103/PhysRevLett.113.215502) (accessed on 28 April 2021).

Figure 10

(a) Experimental (TOSCA+) and simulated (DFT; VASP) INS spectra of closed- (cp) and open-pore (op) ZIF-4(Zn) structures. (b) Schematic diagram of the low-temperature structure of ZIF-4(Zn)-cp and the high-temperature structure ZIF-4(Zn)-op, looking down the b-axis in both phases. A volume contraction of approximately 24% associated with the cp-to-op phase transition is related to a rotation of the imidazolate linkers. Four of such rotations are highlighted by green stars. Reprinted with permission from Ref. [281]. Copyright (2021) American Chemical Society.

Figure 14

Bottom: experimental INS spectrum of liquid H₂O measured on SEQUOIA at ambient conditions. Two different incident energies have been used, as indicated in the figure [388]. Middle: experimental IR spectrum of H₂O at ambient conditions, along with the results of AIMD predictions using vdW-corrected hybrid-DFT (revPBE0-D3 ML-FF) and different computational schemes—classical MD and approximate path-integral simulations (TRPMD and PACMD) [376]. Top: cartoon illustrating competing quantum effects in the H-bonding between two water molecules. There are two qualitatively different contributions to the vibrational ZPE: (i) the one arising from the two bending vibrational modes, in the plane of the water molecule and perpendicular to it (not shown); (ii) a second one associated with the O–H stretch. As the O–O distance R decreases, the contribution of the stretch decreases, and that of the bend increases. Consequently, the two contributions weaken and strengthen the intermolecular H-bond, respectively. [367]. Adapted with permission from Refs. [367,376,388]. Copyright (2021) American Chemical Society.