Multiple high-temperature transitions driven by dynamical structures in NaI

Multiple, consecutive high-temperature transitions in NaI involving dynamical order and/or localization in the energy-momentum spectrum but not in the average crystal structure are revealed by lattice dynamics, x-ray lattice spacing, and heat-capacity measurements. Distinctive energy-momentum patterns and lattice distortions indicate dynamical structures forming within randomly stacked planes, rather than the isolated point-defect-like intrinsic localized modes predicted. Transition entropies are accounted for by vibrational entropy changes, and the transition enthalpies are explained by the strain energy of forming stacking-fault-like planar distortions deduced from x-ray-diffraction peak shifts. The vibrational entropy of the dynamical structures stabilizes surrounding elastic distortions.

Figure 1

A summary of the measurements performed on crystals of pure NaI [results were not noticeably different with NaI(0.002Tl)]. (a) Heat capacity measured using both a laser flash (symbols) and the DSC (solid dark red line). The solid black line is a guide to the eye for the laser flash calorimetry data points. The inset shows how convoluting the laser flash data with Gaussian temperature smearing functions—with widths σ = 4, 8, and 12 K—produces improved agreement with the DSC measurement; σ ∼ 12 K is in very good agreement with the DSC data. (b) Percent change in the lattice $d$ spacing determined from the positions of several single-crystal diffraction peaks indicated as well as from the dilatometry measurements (the dilatometry is labeled “(000)” because the macroscopic measurement scale corresponds to effectively infinite $d$ spacing or zero in reciprocal units). The inset shows a two-dimensional x-ray-diffraction pattern from single-crystal NaI at ambient temperature; the orientation of the crystal is close to the [100] direction. The dashed light-orange rings represent the Bragg reflections for the NaI crystal structure. The three innermost rings, corresponding to the (111), (200), and (220) reflections, are excluded to show faint powder rings that arise from the sample surface. (c) Schematic summary of the lattice-dynamical structures reported in different temperature ranges; Region “I. Normal” is based on the measurements of Woods et al. [15] and Manley et al. [5]; Region “II. [111] ILMs” is based on the measurements of Manley et al. [5]; and Region “III. Dynamical order” is based on the measurements of Manley et al. [6].

Figure 2

Inelastic-neutron-scattering measurements on NaI(0.002Tl) crystals collected around three high symmetry $X$ points: (a) (233), (b) (011), and (c) (033). The “cuts” from the time-of-flight neutron-scattering data are integrated over the dashed green boxes shown in the illustration and are indicated numerically in the header of each panel. The out-of-plane direction, labeled kmk for [0,$K$,−$K$], is integrated over ±0.25 reciprocal lattice units.

Figure 3

Comparison of the total transition entropies estimated from the features in the laser flash calorimetry data [Fig. 1] with the vibrational entropy changes estimated from the vibrational spectral features associated with the formation and breakup of the dynamical superlattice structures from Fig. 2. The values are consistent. See text for calculation details.

Figure 4

These illustrations show an arrangement of ILM superlattices [6] that might explain the observed dynamical and stacking-fault-like structures inferred from the measurements near 636 K. (a) The shaded areas indicate planes where the ILMs form a superlattice with the ILMs repeating every third site to explain the $q$ = 1/3 scale in the dynamical superlattice, which is described in detail in Ref. [6] and partly summarized in Fig. 1. To explain the stacking-fault-like shifts in the diffraction peaks, it is assumed that these planes of dynamical superlattices (shaded areas) are stacked randomly along [011] while ordered along [100] and that the lattice spacing in the occupied planes d* is different from the value of the unoccupied planes $d$. (b) A scenario similar to (a) except that the dynamical superlattice of the ILMs fills the larger regions between the faults.