Order vs. disorder — a huge increase in ionic conductivity of nanocrystalline LiAlO 2 embedded in an amorphous-like matrix of lithium aluminate , 20295 – 20306 |

a Coarse grained, well crystalline g -LiAlO 2 ( P 4 3 2 1 2) is known as an electronic insulator and a very poor ion conductor with the lithium ions occupying tetrahedral voids in the oxide structure. The introduction of structural disorder such as point defects or higher-dimensional defects, however, may greatly a ﬀ ect ionic conduction on both short-range as well as long-range length scales. In the present study, we used high-energy ball milling to prepare defect-rich, nanocrystalline LiAlO 2 that was characterized from a structural point of view by powder X-ray di ﬀ raction, TEM as well as small angle X-ray scattering (SAXS). Temperature-dependent conductivity spectroscopy revealed an increase of the room-temperature ionic conduction by several orders of magnitude when going from microcrystalline g -LiAlO 2 to its nanocrystalline form. The enhanced ion transport found is ascribed to the increase of Li ions near defective sites both in the bulk as well as in the large volume fraction of interfacial regions in nano-LiAlO 2 . The nanocrystalline ceramic prepared at long milling times is a mixture of g -LiAlO 2 and the high-pressure phase d -LiAlO 2 ; it adapts an amorphous like structure after it has been treated in a planetary mill under extremely harsh conditions.


Introduction
Diffusive motion of small particles is an omnipresent phenomenon in nature. In particular, it is of great interest when (ionic) solids are considered. [1][2][3] In solid-state materials science the temperature-dependent diffusion behavior of cations and anions, such as H, Li, Na, F, and O, is of enormous importance for manifold technological processes. At present, solid electrolytes with high lithium-ion conductivity 4 are feverishly searched to realize next generation rechargeable solid-state batteries that benet from long lifetime, safety and reliability. 5,6 In the course of recent years, Li-bearing oxides and suldes have been prepared and characterized that show extremely high bulk Li + conductivities. Prominent ultrafast electrolytes are, for example, Li 7 La 3 Zr 2 O 12 , 7,8 Li 10 GeP 2 S 12 (ref. 9) (and related compounds 10 ), b-Li 3 PS 4 , 11 argyrodite-type suldes such as Li 6 PS 5 Br, 12,13 and glass ceramic Li 7 P 3 S 11 . 14,15 Considering their electrochemical stability, economical viability, and versatility with respect to preparation techniques usually applied to manufacture, for example, all-solid-state (thin-lm) batteries, further studies are urgently needed to throw light on these aspects. Even though other materials show lower bulk conductivities, if used as amorphous and/or very thin electrolyte lms with low cell resistance, they may seriously compete with the ultrafast ion conductors discovered recently. This might be due to their easy and cheap preparation, chemical robustness, and electrochemical stability that result in an extremely good durability and cyclability of the batteries.
Lithium aluminium oxide, LiAlO 2 , if prepared in a defectrich form, might serve as such an alternative against other oxides, see for e.g., the well-known lithium phosphorous oxynitride 16 (LIPON) that is commonly applied in secondary lithium-ion batteries. Tetragonal g-LiAlO 2 (space group P4 3 2 1 2) is known as an electronic insulator and, in its coarse grained and well crystalline form, a very poor ion conductor 17 with the lithium ions fully occupying the tetrahedral voids in the oxide structure, 18 thus being trapped on these sites. Besides a report to use LiAlO 2 as coating for Li x (Ni,Co,Mn)O 2 -based cathodes, 19,20 Goodenough and co-workers 21 as well as Cheng et al. 22 have recently shown that during the preparation of the highly conducting electrolyte Al-doped Li 7 La 3 Zr 2 O 12 (Al-doped LLZ) the crystallites are oen covered by an amorphous layer of LiAlO 2 . Such a grain-boundary phase can have a crucial effect on longrange ion transport of Al-doped LLZ-type electrolytes.
Considering these aspects, the present study is two-fold and combines the following fundamental and application-oriented questions: (i) how and to what extent does the introduction of structural disorder affect lithium-ion transport in g-LiAlO 2 ? The results shall be compared with those from a sample with mmsized crystallites. Such information is also a key element of many applications where crystalline LiAlO 2 is intentionally used to strictly prevent diffusion. As an example, besides Li 2 MeO 3 (with Me ¼ Ti or Zr) g-LiAlO 2 is considered as an advanced tritium breeding blanket material in fusion reactors. 23 (ii) If the structure resulting aer ball milling can be regarded as amorphous-like, how does ionic conductivity of such a sample with the composition LiAlO 2 compare with that of structurally disordered electrolytes prepared by deposition techniques that can be used in thin-lm micro-batteries? Moreover, with respect to its role forming amorphous grain-boundary phases in (Al-doped) LLZ-based electrolytes (see above), ionic conductivities of nanostructured or amorphous LiAlO 2 have not been reported so far.
In the present case, we prepared nanocrystalline LiAlO 2 following a top-down approach by employing high-energy ball milling. Starting from coarse-grained commercially available g-LiAlO 2 several nanocrystalline samples were prepared by dry milling in a planetary mill. Structural sample characterization was carried out via X-ray powder diffraction, small angle X-ray scattering (SAXS), 27 Al magic angle spinning (MAS) nuclear magnetic resonance (NMR) as well as by scanning and highresolution transmission electron microscopy (SEM, HR-TEM). SAXS patterns have been recorded to correlate the inner surface parameter with the results from ion transport measurements. Ion dynamics has been mainly evaluated by conductivity spectroscopy; rst 7 Li NMR line shape measurements complement the present study.
Indeed, it turned out that the introduction of structural disorder via mechanical treatment has a giant effect on Li ion dynamics in LiAlO 2 . The resulting defect-rich nanocrystalline material, which is equipped with a large volume fraction of amorphous material, reveals room temperature dc conductivity that is by several orders of magnitude larger than that of (single) crystalline LiAlO 2 . The results resemble those of previously studied nanocrystalline LiTaO 3 and LiNbO 3 (ref. [24][25][26] as well as single-and two-phase composites that are based on lithium oxide. 27-29

Experimental
Pure lithium aluminum oxide (99.5%) was obtained from Alfa Aesar. The transparent crystallites, with diameters in the mm range, revealed the typical X-ray powder diffraction pattern of the well-known g-phase of LiAlO 2 ( Fig. 1(a)). Nanocrystalline g-LiAlO 2 was prepared from the microcrystalline source material by ball milling using a high-energy planetary mill (Fritsch, Pulverisette 7). We used a grinding beaker made of zirconium dioxide (Fritsch) equipped with 180 milling balls (zirconium dioxide, 5 mm in diameter). The air-tight beaker was loaded and opened in an Ar-lled glove box with less than 0.1 ppm water vapor inside to avoid any contact with air or moisture. To obtain different nanocrystalline samples the milling time was varied from 5 min to 8 h; the rotational speed of the mill was set to 400 rpm in order to reduce the formation of side products as effectively as possible.
Prior to our impedance measurements and for structural characterization X-ray powder diffraction patterns were recorded on a Bruker D8 Advance diffractometer with Bragg Brentano geometry using Cu Ka radiation (10 to 100 2q, step size 0.02 2q, and step time 1 s). Rietveld renement was carried out with an X-PertHighScorePlus (PANalytical). In addition to XRD, TEM images were acquired with a TECNAI F20, Schottky cathode, operated at 200 kV. Samples were prepared using standard TEM preparation routines for powder samples. The particles were mounted on Cu grids covered with a carbon coated holey polymer lm.
Small-angle X-ray scattering (SAXS) measurements complement the techniques applied to characterize our nanocrystalline samples. For this purpose, a high-ux SAXSess camera (Anton Paar, Graz, Austria) connected to a Debyeex 3003 X-ray generator (GE-Electric, Germany), operating at 40 kV and 50 mA with a sealed-tube Cu anode was used. The Goebel-mirror focused and Kratky-slit collimated X-ray beam was line shaped (17 mm horizontal dimension at the sample) and scattered radiation from the sample measured in the transmission mode was recorded by highly X-ray sensitive image plates (Fuji, Japan) within a q-range (with q being the scattering vector) of 0.25 to 5 nm À1 . Aer each SAXS measurement with an exposure time of 8 min, the image plates were transferred to a Cyclone Plus image plate reader (Perkin Elmer, USA), laser-scanned and converted digitally into intensity values (I). The 2D recorded intensity data were then integrated with a 10 mm width, normal to the direction of the scattering angle, to result in a 1D-scattering curve I(q) within the angular range mentioned above. 27 Al MAS NMR spectra have been recorded at 130 MHz using a Bruker Avance III solid-state NMR spectrometer; a single pulse sequence has been used for data acquisition. We employed a 4 mm probe and rotors made of ZrO 2 allowing rotation frequencies of 15 kHz. Spectra were referenced to aqueous Al(NO 3 ) 3 . 7 Li NMR spectra were recorded at 194 MHz with the same setup but using a probe designed for static temperaturevariable NMR experiments. Non-selective excitation with a single pulse was carried out. For the broadband impedance measurements dense tablets were prepared by cold-pressing the milled LiAlO 2 samples with a uniaxial pressure of 10 kN in a 10 mm press set. It is important to note that the samples have not been densied and that the overall conductivity measured might slightly differ from that of pellets that are sintered additionally. Due to the amorphous character of the nanocrystalline samples, which has been revealed by XRD and TEM, we anticipate that this inuence is of minor importance and that the conductivity values measured (see below) are close to the intrinsic ones.
To ensure electrical contact of the pellets pressed, Au electrodes of about 100 nm thickness were applied with a sputter coater (Leica EM SCD050). The impedance measurements were carried out with a Novocontrol Concept 80 broadband analyzer (Alpha-AN, Novocontrol). The analyzer was connected to a BDS 1200 cell in combination with an active ZGS cell interface from Novocontrol, which allows temperature-variable 2-electrode measurements. The temperature is automatically controlled by using a QUATRO cyrosystem (Novocontrol). In order to create a highly constant nitrogen gas ow the cryosystem is working with a heating element that builds up a specied pressure in a liquid nitrogen dewar. Aer heating by using a gas jet, the freshly evaporated nitrogen ows directly through the sample cell that is mounted in the cryostat. Such a setup allows very stable system operation with an accuracy of AE0.01 K. In summary, the whole device is able to record impedance and the permittivities at frequencies ranging from few mHz up to 20 MHz at temperatures ranging from 150 K to 570 K.

Results and discussion
3.1 Analysis via X-ray diffraction and TEM Nanostructured g-LiAlO 2 was prepared from the microcrystalline source material, which was obtained from Alfa Aesar (99.5%). The coarse grained microcrystalline g-LiAlO 2 consists of irregularly shaped crystallites with an average crystallite size in the order of 100 nm. Although g-LiAlO 2 is known to be stable in air the whole procedure was performed under an Ar atmosphere to avoid a reaction of the hygroscopic nanocrystalline powder with moisture and to keep the inuence of water on the subsequent conductivity measurements as small as possible.
By varying the milling times, powders with different mean particle sizes were obtained. The effect of ball milling on the XRD patterns is shown in Fig. 1(a) to (c). The value of the mean crystallite size was roughly estimated from the broadening of the XRD patterns using the well-known Scherrer equation 30 In this equation K is a dimensionless shape factor with a value close to unity. The shape factor has a typical value of 0.89 for spherical particles. l is the X-ray wavelength, q is the Bragg angle and b represents the line broadening at half magnitude (FWHM); it is already corrected for any instrumental line broadening. For the estimation of L 0 we used the XRD peaks at 2q ¼ 22.3 , 28.3 , 34.8 and 61.3 (hkl ¼ 011, 111, 012 and 032). b is calculated according to b ¼ B m À B ref where B m is the measured line width and B ref is the width of the reference which was obtained by using microcrystalline LaB 6 . In Fig. 1(c) the broadening of the reection at 2q ¼ 34.8 (012) is shown as an example. In Fig. 1(b) a quantitative analysis of the broadening of the reection at 22.3 is shown together with the corresponding L 0 values.
Anyway, it should be noted that a possible inuence of stress caused by high-energy ball milling is not taken into the account by the Scherrer equation. Hence, the calculated crystallite sizes should be seen as a rough estimation indeed. For example, milling times of 4 and 8 h lead to mean crystallite sizes of about 16 and 20 nm, respectively. The mean crystallite size is only slightly reduced at milling times of about 5 min. The largest change in crystallite size was between the starting sample (ca. 70 nm) and those milled for 30 and 60 minutes (approximately 40 nm). The corresponding decrease in L 0 is associated with a huge increase in Li ion dynamics as probed via conductivity measurements (see the next section).
For milling times longer than 60 minutes further XRD reections than those assigned to LiAlO 2 arise pointing to the formation of a small amount of other nanocrystalline and structurally disordered phases (see Fig. 1(a) and the magnication in Fig. 2); these reections may stem from the highpressure phases a-LiAlO 2 , d-LiAlO 2 or even LiAl 5 O 8 . a-LiAlO 2 can be synthesized at 3.5 GPa and 850 C; it crystallizes with a NaHF 2 structure. [31][32][33] Besides this high-pressure phase a monoclinic one 34 is known that can be obtained at an intermediate pressure and temperature.
Here, the additional XRD peaks, marked by black triangles in Fig. 1(a) and by arrows in Fig. 2, most likely reect the formation of the d-modication of LiAlO 2 . Although there is some overlap with those peaks being attributed to a-LiAlO 2 , with regard to our XRD patterns measured down to very low 2q values, one of the characteristic XRD reections of the a-form, which shows up slightly below 20 , is missing (see Fig. 2). This conrms our anticipation that mainly the d-modication is formed during mechanical treatment at long milling times. The positions of the reections marked by lled triangles resemble those reported by Li et al. 31 for a sample with a certain amount of d-LiAlO 2 (I4 1 /amd). The latter has been prepared by impact technology using pressures of up to 48 GPa with hot spots of 1570 K. d-LiAlO 2 prepared in such a way, that is, shock compressing of g-LiAlO 2 , crystallizes with a distorted NaCl structure being similar to that of the tetragonal phase of LiFeO 2 (see Fig. 3). This d-form (3.51 g cm À3 ) is denser than the a-phase (3.40 g cm À3 ) and much denser than the g-modication (2.62 g cm À3 ). 31 Obviously, during high-energy ball milling the oxide was exposed to similar reaction conditions as it is the case during the high-energy impact experiments reported previously. 31 In order to underpin the assignment of the new peaks to the d-form of LiAlO 2 , we have recorded 27 Al MAS NMR spectra (see Fig. 4). While in the low-pressure g-modication (as well as in the orthorhombic b-form of LiAlO 2 ) Li and Al are solely tetrahedrally coordinated by oxygen anions, in d-LiAlO 2 both Li and Al ions are six-fold coordinated (see Fig. 3). The same is found for a-LiAlO 2 ; 32 in the monoclinic form of LiAlO 2 the lithium cations are six-fold coordinated and aluminum cations display both four-and sixfold coordination (Fig. 3). Thus, if we assume that high-pressure phases of LiAlO 2 have been formed during ball-milling, characteristic NMR lines representing octahedrally coordinated Al should show upand indeed, this is found here. The spectrum of microcrystalline g-LiAlO 2 as well as those of the samples milled for 5 min and 30 min are mainly composed of a single signal at 80 ppm representing Al ions being tetrahedrally coordinated. This value is in agreement with the result by Müller et al. 35 who found a 27 Al NMR isotropic chemical shi of 82 ppm for the g-form. Additional intensities, however, show up if the milling time is increased to 4 h and 8 h, respectively.
In the unit cell of g-LiAlO 2 there are four chemically equivalent but magnetically inequivalent Al sites; the same holds for the Li sites. In particular, the line at 15 ppm (see Fig. 3) is indicative of six-fold coordinated Al as expected for d-LiAlO 2 (for b-LiAlO 2 a chemical shi of ca. 17 ppm is reported 35 ). While the line with low intensity located at approximately 43 ppm points to ve-fold coordinated Al, which is presumably located in the surface regions of nanocrystalline LiAlO 2 , see also ref. 36, the asymmetric broadening of the main intensities is (i) either due to second order quadrupole effects affecting the central transition of the spin-5/2 nucleus (a coupling constant of 3.2 MHz is reported for g-LiAlO 2 with an asymmetry parameter h s 0 (ref. 35)) or (ii) stems from local structural disorder introduced during milling. The latter would easily lead to both a distribution of chemical shi values and electric eld gradients at the Al sites. This is shown in detail in Fig. 4(b) presenting   Most importantly for our conductivity measurements presented below, mechanically induced phase transformations are almost absent for those samples treated only for 5 or 30 min in the planetary mill under the relatively harsh conditions chosen here. This can be seen by both XRD and 27 Al MAS NMR. Thus, the samples prepared aer 30 min of milling represent almost phase pure nanocrystalline LiAlO 2 equipped with a large fraction of mechanically introduced defects.
As illustrated in Fig. 1(a)(i) and (ii), annealing of the 8 h milled sample for about 16 hours at 1173 K leads to signicant narrowing of the XRD patterns due to grain boundary relaxation as well as grain growth. Aer annealing, almost phase pure g-LiAlO 2 is re-obtained. The same observation has been documented by Li and co-workers 31 aer annealing the d-form of LiAlO 2 at the same temperature; d-LiAlO 2 transforms into the g-form, being stable at lower pressures, via a-modication. The mean crystallite size of our annealed sample is comparable to the initial microcrystalline sample purchased from Alpha Aesar. Some of the minor impurity phases of the original sample disappeared (see unlled triangles in Fig. 1(a) Turning now back to the investigation of the morphology of the samples prepared, as shown in Fig. 5, scanning electron microscopy (SEM) pictures of the materials ball milled for 5 minutes and 8 hours are presented. The so-called microcrystalline sample shows particles with a size of around 100 nm which is in good agreement with the results estimated by the Scherrer equation. The sample mechanically treated for 8 hours exhibits a rather large distribution of particle sizes. Besides larger ones, rather small particles in the tens of nanometer range are visible. Large agglomerates result from compaction during high energy ball milling.
As veried by HR-TEM (see Fig. 6) these agglomerates are clearly composed of differently orientated smaller crystallites. Most importantly, extended amorphous regions are visible in between these crystallites when LiAlO 2 is treated for 8 h in a planetary mill at 400 rpm. For comparison, a similar observation is documented for mechanically treated LiNbO 3 ; as has been shown in ref. 24, a layer of amorphous material with a thickness of about 2 nm covers the crystallites revealing a socalled core-shell structure of (nano-)crystalline and amorphous fractions. In our case, aer 8 hours of milling the crystallites are completely embedded in an amorphous matrix of LiAlO 2 ; the structure resembles that of a glass ceramic that can be prepared by thermal annealing of glassy materials, for example. Considering the XRD powder patterns and the broad reexes of the d-modication of LiAlO 2 formed, the nal product obtained seems to consist of three "phases": (i) structurally disordered nanocrystalline g-LiAlO 2 , (ii) amorphous material and (iii) extremely small nanocrystals of the d-form that may cover the larger nm-sized g-LiAlO 2 particles. The structural disorder found for nano g-LiAlO 2 is supported by 27 Al MAS NMR spectra revealing a broadening of the NMR line located at around 80 ppm.

Small-angle X-ray scattering
For our SAXS measurements the polycrystalline powders were lled into a vacuum-tight foil-sealed at sample-cell. The beam path through the powdered sample was about 1 mm including the foils of 20 mm in thickness. All measurements, even that of the empty cell, were done in vacuum and at ambient temperature (ca. 293 K). The scattering of the foils was subtracted from the scattering of the samples aer normalizing the two patterns to the same transmission intensity. In Fig. 7(a) the SAXS curves obtained are shown. Using CuK a radiation, having a wavelength of 0.154 nm, and a sample-to-detector distance of 265 mm this corresponds to a total 2q region of 0.3 to 5 when the following conversion is applied: Here, 2q is the scattering angle with respect to the incident beam and l denotes the wavelength of the X-rays.
The data were then analyzed in terms of the inner surface parameter (S i ) according to the procedure of Porod. 38,39 The inner surface area S i represents the total surface area of the porous or powdered compound with respect to its volume (or to its mass if the macroscopic density of the powder is known). From SAXS measurements this information on the nm-scale can be obtained by evaluating two parameters of the SAXS curve I(q). In our setup the vertical SAXS pattern I(q) were considered to be convoluted by an innitely long horizontal beam prole (line focus). In that case Porod's law and the invariant can be applied to extract S i from the scattering curve I(q) convoluted by a innitely long horizontal beam prole: k is the so-called Porod constant and Q is the invariant which represents the integral over the normalized rst moment of the entire scattering curve, (extrapolated to q / 0 and q / N). The ratio of k/Q, when multiplied with 4, results in the specic inner surface S i area (or interfacial area) per volume (nm 2 nm À3 ). This value, normalized to the density r (g cm À3 ) of the powder, is then proportional to the surface area per mass (m 2 g À1 ): In Fig. 7(b) this surface area per mass is plotted versus the milling time. The mean surface areas per masses are in good agreement with the decreasing crystallite size as estimated by means of the Scherrer equation. Furthermore, the measurements indicate that the amount of amorphous material produced via milling increases with milling time. This corroborates the amorphous regions seen by HR TEM.

Long-range ion transport as probed by impedance spectroscopy
Impedance spectroscopy was used to characterize ion transport in ball-milled g-LiAlO 2 as a function of mechanical impact. The corresponding conductivity isotherms are shown in Fig. 8; they reveal the typical characteristics for structurally disordered materials. The sample milled for 30 min shall serve as an example here. Similar spectra were obtained for the other samples, however, with ion conductivities shied towards higher or lower values.
The same holds for the corresponding permittivity spectra 3 0 (n) (see Fig. 9). Disregarding any electrode polarization at the lowest frequencies, permittivities 3 0 (0) of ca. 30 are obtained  being typical for bulk ion conduction. 3 0 (N) is approximately 4; values in the order of 10 or below are commonly expected for high-frequency permittivities of glasses. This gives D3 ¼ 3 0 (0) À 3 0 (N) z 26, being the dielectric relaxation strength that is a measure for the dipole uctuations.
The frequency dependent conductivity spectra, which are composed of a dc plateau and a Jonscher type dispersive region, 40 can be approximated by a power law.
where s dc corresponds to the conductivity plateau and n is the Jonscher exponent; here n takes values ranging from 0.5 to 0.8 (313 K to 573 K). This range is in good agreement with the results found in many previous studies on disordered materials and glasses; in particular, see the studies focusing on nanocrystalline LiTaO 3 (ref. 25) and amorphous LiNbO 3 . 24,41-43 The decrease of s 0 at low frequencies and sufficiently high temperatures, that is, above 450 K and at frequencies u/2p < 100 Hz, is due to polarization effects because of the ion blocking electrodes used. As has been conrmed by preliminary potentiostatic polarization experiments carried out in our lab, the electronic fraction, s eon , of the overall conductivity s dc seems to be many orders of magnitude lower than the total value measured under a N 2 atmosphere. To estimate s eon and s ion , we placed the goldsputtered pellets of the samples treated for 4 h and 8 h in airtight Swagelok cells, see also the procedure described in ref. 44. The polarization experiments were carried out at 293 K with a Parstat MC instrument from Princeton Applied Research; a constant voltage of 0.5 V was applied. Here, s dc is mainly determined by ion transport if measured in an oxygen-free, inert gas atmosphere. In a qualitative way the same holds for nanocrystalline LiTaO 3 studied previously by some of us. 25 To quantify thermal activation of the long-range ion transport, to which s dc is sensitive, the dc conductivity values (s dc T) have been plotted versus 1000/T, see Fig. 10. Solid lines represent ts according to an Arrhenius law: where k B is Boltzmann's constant. Starting from E a ¼ 1.14 eV for the non-treated sample, the activation energy decreases to 0.78 eV aer mechanical treatment for 8 h. A value of 1.14 eV is in good agreement with that reported by Indris et al. 17 for a LiAlO 2 single crystal (1.26 eV along the [110] direction and 1.14 eV along the [001] direction). Here, the largest increase in s dc is found when the initially coarse-grained material is compared with that treated for only 30 min. Doing so, at 450 K the dc conductivity increases by more than ve orders of magnitude clearly illustrating to what extent the defective structure introduced by milling changes through-going Li ion transport in g-LiAlO 2 (Fig. 10). Milling for 5 minutes, however, does only slightly alter Li ion dynamics of g-LiAlO 2 . Interestingly, for the 30 min-sample the X-ray powder pattern recorded reveals almost no side phases or high-pressure forms of LiAlO 2 . This corroborates our expectation that, while both the overall chemical composition as well as the long-range crystal structure of the sample is unchanged, mainly the defects generated during milling are responsible for the enhancement observed. For comparison, when internally referenced to microcrystalline  LiAlO 2 , between milling times of 5 and 30 minutes the largest changes in X-ray peak broadening occur. Comparing the samples milled for different durations, aer approximately 4 hours of milling an upper limit of s dc is reached (see Fig. 10(a)). Further increase to 8 hours does not change ion dynamics much although X-ray peak broadening, and thus also the formation of the amorphous material, continues. This leads us to the conclusion that in the case of LiAlO 2 additional nano-size effects, especially those of nontrivial nature, 45,46 do not signicantly contribute to the enhancement found aer 30 min of milling. The defect level reached aer 4 hours is fully sufficient to completely control long-range Li ion dynamics in nanocrystalline/amorphous LiAlO 2 prepared by mechanical treatment.
As can be seen from the Arrhenius plot shown in Fig. 10(a), at elevated temperatures the s dc T values deviate from linear temperature behavior. This 'sub-Arrhenian' feature means that the conductivity properties of the sample steadily changes at sufficiently high T. If we, however, record s dc T during cooling the (linear) Arrhenius behavior, being characterized by relatively large activation energies, is re-observed. As an example, in the case of the sample milled for 8 h, aer heat treatment the activation energy increases again. Note that the measuring time between each data point during heating was approximately 30 min. In Fig. 11 the heating and cooling runs measured for two samples, milled for 30 min and 8 h, respectively, are shown. While the initial conductivities are even larger than those shown in Fig. 10, heat treatment at elevated T leads to a continuous decrease of s dc and a slight increase of E a . The bold lines show ts of those data points which are also presented in Fig. 10 (2nd heating run). All data points have been recorded aer the samples were dried at 373 K inside the impedance cell.
The temperature effects observed here were also detected for LiTaO 3 previously. 25 Considering the samples milled only shortly these features might be ascribed to healing of defects and grain growth setting in. Interestingly, the larger the milling time, i.e., the larger the extent of structural disorder introduced, the less pronounced the effect observed. Obviously, the more the microstructure of the sample mechanically treated resembles that of the original structure, the easier the system transforms back. This view is supported by the above-mentioned fact that g-LiAlO 2 continuously transforms into high-pressure modications, particularly the d-form, crystallizing with different space groups. Here, the 2nd heating runs are shown (see Fig. 11 for explanation). The solid lines represent fits with an Arrhenius law. For comparison, the non-milled sample is also shown. (b) Results from (a) compared with those previously obtained for nanocrystalline LiTaO 3 , 25 which has also been prepared by high-energy ball milling but in a shaker mill from SPEX. The dashed lines in indicate the change of s dc T during cooling from high temperatures towards ambient (see also Fig. 11). For the sample milled for 8 h the activation energy slightly increases again. For a brief overview, in Fig. 10(b) the s dc T values of microand nanocrystalline LiAlO 2 of the 2nd heating run are compared with results from polycrystalline LiTaO 3 treated in a shaker mill and studied previously. 25 In contrast to LiAlO 2 , for LiTaO 3 no phase transformations are known. Even though the increase of Li ion conductivity in LiAlO 2 is less pronounced than that found for LiTaO 3 the same characteristics show up: (i) a poor ion conductor can be transformed into a conducting one by mechanical treatment with a sufficiently high impact; (ii) the largest increase in s dc is already observed in the early stages of milling, that is, if high-energy ball mills are used, aer milling periods of less than 1 hour. The ion conductors prepared in such a way reveal activation energies with values of ca. 0.8 eV or less.
The fact that lower ion conductivities are found for LiAlO 2 aer treatment for many hours (cf. the comparison with LiTaO 3 in Fig. 10(b)) is presumably linked with the formation of the highly dense, high pressure phases of LiAlO 2 limiting the increase in s dc compared to that found for LiXO 3 with X ¼ Nb, Ta. 24,25 On the other hand, Li in aand d-LiAlO 2 is coordinated octahedrally and the octahedra are connected by edge sharing. With regard to the LiO 4 -tetrahedra connected by sharing common edges in the g-form, the arrangement in d-LiAlO 2 might be more benecial for Li ion transporteven if longrange length scales are considered.
3.4 Ion self-diffusion as seen by 7 Li NMR 7 Li NMR line shape measurements (Fig. 12) can provide additional information on short-as well as long-range ion diffusivity. 25 At sufficiently low temperatures, that is in the NMR rigid-lattice regime, the line width of the central line is dipolarly broadened due to the absence of rapid Li exchange; such exchange would lead to motional averaging of homonuclear Li-Li interactions. As soon as the Li jump rate reaches values in the order of 1 kHz (or larger) the NMR line starts to narrow.
As is illustrated by the 7 Li NMR spectra shown in Fig. 12(a), line narrowing sets in at approximately 375 K (see Fig. 12(b)) for the sample that has been treated for 8 hours in the planetary mill. The corresponding NMR line of the microcrystalline source material, however, does not change up to temperatures as high as 430 K; compared to the nanocrystalline/amorphous sample motional narrowing is expected to occur at much higher temperatures. A slight motional narrowing effect is also detected for the sample milled for 30 min. It is, however, signicantly less distinct than that observed for the samples treated for many hours. Even though the mean jump rates are still in the order of 1 kHz in this T range, which is as expected from the conductivity values probed, when referenced to the microcrystalline sample, s dc has drastically been increased aer 30 min of milling (see Fig. 10). Altogether, in a qualitative way, the preliminary 7 Li NMR line shape measurements corroborate enhanced ion diffusivity in ball-milled LiAlO 2 .
If we assume that at 375 K, this is the temperature at which MN starts, the mean jump rate is in the order of 10 3 s À1 ; we can estimate a Li diffusion coefficient according to the Einstein-Smoluchowski equation. Using a mean jump distance of 2.5Å this yields, anticipating 3D uncorrelated motion, a self-diffusion coefficient D in the order of 6 Â 10 À18 m 2 s À1 . This result corresponds to a conductivity value of 8 Â 10 À9 S cm À1 if we use the Nernst-Einstein equation to correlate D with s. Experimentally we found that s dc is ca. 2 Â 10 À9 S cm À1 at 375 K. Thus, the D value estimated from NMR agrees reasonably well with the result from conductivity spectroscopy. It gives further evidence that s dc , which has been determined from the plateau of the Fig. 12 (a) Temperature-variable 7 Li NMR spectra of LiAlO 2 milled for 8 h and 30 min, respectively. Spectra have been recorded under static conditions. The sample milled for 8 h shows significant motional narrowing at temperatures above 350 K. Starting from about 9.6 kHz the line width decreases to 7.4 kHz at 433 K. At this temperature, LiAlO 2 treated for only 30 min does not reveal any significant line narrowing (see also the spectrum shown by a dashed line). Thus, jump rates are still below 1 kHz in this T range. However, compared to the microcrystalline sample Li ion conductivity has increased drastically as shown in Fig. 9. (b) 7 Li NMR line widths of microcrystalline (-) g-LiAlO 2 in comparison with the line narrowing of the sample milled for 8 h (,). s 0 (u) isotherms, is mainly governed by ionic contributions as has been indicated by the preliminary polarization experiments mentioned above.
Noteworthy, the rigid-lattice line widths of the two samples shown in Fig. 12(b) differ from each other. The line widths of the ball milled samples exceeds that of the microcrystalline one. According to van Vleck's formula, 47 see also ref. 48, the NMR line width in the rigid lattice regime is inversely proportional to the mean Li-Li distance r. Thus, one might conclude that the mean value of r in LiAlO 2 that has been mechanically treated is slightly smaller than in the non-treated form or that heteronuclear 7   Al dipolar couplings are somewhat larger than that in the crystalline starting material. A smaller distance r is consistent with the change of the crystal structure from g-LiAlO 2 towards d-LiAlO 2 having a much higher density. Independent of any phase transformations, a similar effect on the rigid-lattice line widths has also been observed for amorphous LiNbO 3 (ref. 24) and ball-milled LiTaO 3 . 25

Summary and conclusions
LiAlO 2 is a new example that shows a drastic increase of the Li ion conductivity aer it has been mechanically treated in a highenergy ball mill. We used the commercially available g-modication of lithium aluminate to study the inuence of highenergy ball milling on Li ion transport, specically the Li ion conductivity by evaluating s 0 isotherms recorded over a broad frequency range.
Already aer 30 min of milling, the ion conductivity increased by four orders of magnitude when temperatures around 400 K are considered. This is related to the large number of defects introduced during milling. Another increase of s dc by approximately two orders of magnitude is detected aer milling the source material for 8 h. Owing to the signicant reduction in activation energy (0.79 eV (8 h, nanocrystalline/amorphous) vs. 1.13 eV (microcrystalline source material)), this corresponds to an increase of s dc at room temperature by a factor of 10 7 . HR-TEM and XRD (as well as SAXS) measurements show that a large amount of amorphous LiAlO 2 is responsible for the overall huge increase observed. Aer the starting material has been treated for many hours in a high-energy planetary mill, nanocrystallites of LiAlO 2 are formed that seem to be embedded in an amorphous matrix of the same chemical composition. The latter is corroborated by the fact that aer annealing the nanocrystalline/amorphous sample at 1173 K, phase-pure, microcrystalline g-LiAlO 2 is re-obtained. Recent work pointed out that in certain cases, and especially aer annealing, thin layers of LiAlO 2 cover the surfaces of polycrystalline LLZ. The conductivity of such thin layers formed aer surface impurity segregation is key to the functionality of solid electrolytes and thus long-range ion transport in all-solid-state energy storage systems.
Besides studying ionic conductivity, we investigated the structural changes which occur during the milling process; they seem to be rather complex. For milling times longer than one hour further XRD reections to those assigned to g-LiAlO 2 arise that point to the formation of another nanocrystalline and structurally disordered phase. Both XRD and 27 Al MAS NMR measurements lead to the assumption that this new nanocrystalline phase can be identied with the high pressure phase d-LiAlO 2 ; it has been reported that d-LiAlO 2 is formed at extremely high pressures of up to 48 GPa combined with hot spots of 1570 K.
Summing up, microcrystalline lithium aluminate, which is a very poor ion conductor in its crystalline form, can be turned into an Li ion conductor by a mechanical action using highenergy ball milling. Mechanical treatment leads to the formation of amorphous LiAlO 2 with drastically enhanced transport properties. By variation of the milling time it is possible to adjust the degree of structural disorder and, thus, also to control the ion conductivity of the oxide ceramic giving the freedom to design solid electrolytes with desired properties.