Nanocrystalline LixTiS2 was prepared by intercalating Li+
ions into polycrystalline TiS2 (chemical reaction with butyl-lithium) and
subsequent ball-milling. The estimated particle size obtained by applying the Scherrer
formula to x-ray diffractograms is 11.8nm.|
Fig.1: 7Li NMR spectra of nanocrystalline LixTiS2 at (a) 140K and (b,c) 500K. Note the different frequency scales. The lines in (a,b) indicate best Lorentzian fits. In (c), a double-Lorentzian fit curve is shown along with its two components (dotted).
NMR spectra at low temperature show one broad line indicating a rigid lattice and low mobility of Li+ ions. At higher temperature, the line becomes much narrower since the ions become mobile (mobile probe nuclei facing an averaged environment on the NMR time scale). However, a single-Lorentzian fit does not describe the measured data well. An accurate fit can be obtained if a second, broader, component is added.
The two components are attributed to slow Li+ ions inside the grains (broad
component) and fast ions in the grain boundaries (narrow component).|
Fig.2: (a) Line widths and (b) relative intensities of the narrow and broad components of the NMR central transitions of nanocrystalline LixTiS2 as a function of temperature. Line widths obtained by an (inadequate) single-Lorentzian fit are displayed for comparison in (a). The line in (a) provides a guide to the eye only.
Below about 250K there is only the broad component present, indicating that all spins are rather immobile. In the range from 250K to 350K, the above situation arises, and an increasing fraction of the spins becomes mobile, i.e. the fraction of the narrow component increases, reaching about 50% at 350K. At higher temperatures, no further increase of the narrow component is observed, but the broad component begins to narrow as well (to a lesser extent) above 420K.
The observation that the fraction of mobile spins increases with temperature over a range of 100K indicates that the disordered intergranular phase is not structurally homogeneous since Li+ ions in different regions of the interfaces require a different amount of energy (a different temperature) to become mobile. In the high-temperature limit, 50% of spins are mobile; revealing the total interface fraction.
With the average particle size known from XRD and the interface fraction known from NMR, a model of the particle shape can be developed if reasonable assumptions are made about the interface thickness.
Different techniques see particles with an interface layer in a different way, because
the interface counts as part of the particle for some techniques (e.g. microscopy), while
others are only sensitive to the core (e.g. diffraction).|
Fig.3: (a,b) Spherical and (c,d) cylindrical geometries assumed for the calculations relating particle diameter d, interface thickness g, interface volume fraction f, and --in (c,d)-- particle thickness h. (a,c) reflect the geometries as observed by microscopy techniques, (b,d) those relevant to diffraction methods.
|Fig.4: Interface fraction f as a function of particle diameter d in the case of
(a) spheres and (b) disks with a fixed diameter/thickness ratio d/h = 5, both assuming an
interface thickness of 0.5nm < g < 1nm. The blue area corresponds to the "microscopy" case,
the red area to "diffraction" case. The data range consistent with the observation in
LixTiS2 is indicated by the error bars. For comparison, data on
CaF2 (triangle), LiBO2 (circles), Li2O (cross), and
LiNbO3 (square) from the same laboratory (Paul Heitjans's group at
Universität Hannover) are given.|
While most ball-milled materials are fairly well described by the spherical model, the disk-like geometry of LixTiS2 leads to a much more accurate prediction of the interface fraction. Unlike the other materials, LixTiS2 has a layered structure, which disintegrates into coin-shaped pieces rather than particles with small aspect ratio, which are close to the spherical geometry.
For given particle dimensions, the interface fraction is a function of the interface
Fig.5: Interface fraction f as a function of interface thickness g. Particles have the observed diameter of 11.8nm and a thickness of (left to right) 1, 2, 3, 5, and 10nm.
For a cylindrical particle of the observed diameter (taking the Scherrer radius as an approximation of the disk radius), the observed interface fraction of 50% would require the particle thickness to be only about 1nm if an interface thickness of 0.5nm to 1nm (a typical value for many nanocrystalline materials) is assumed. With a lattice parameter c of 620pm in stacking direction, this is less than two lattice planes and would not constitute a Bragg condition. Thus, even taking the disk-like structure into account, the interfaces must be unusually thick - in accordance with the NMR observation of distinguishable areas of different structure within the interface.
For a given combination of interface fraction and particle diameter, there is a saturation
value of the grain boundary thickness as function of particle thickness.|
Fig.6: Interface thickness g as a function of particle thickness h. The full line corresponds to a particle of the observed diameter and interface fraction. The other lines indicate the range 0.4 < f < 0.6 in the case of a d = 13.0nm particle (dotted) and a d = 10.6nm particle (dashed).
For a particle of the observed dimensions and interface fraction, the limit to the grain boundary thickness is about 3nm.
Ball-milled nanocrystalline LixTiS2 consists of disk-like particles with an unusually high interface fraction. The high interface fraction is in part due to the cylindrical geometry and in part due to thicker interface layers which have a inhomogeneous substructure.