What dictates soft clay-like lithium superionic conductor formation from rigid salts mixture

Soft clay-like Li-superionic conductors, integral to realizing all-solid-state batteries, have been recently synthesized by mixing rigid-salts. Here, through computational and experimental analysis, we clarify how a soft clay-like material can be created from a mixture of rigid-salts. Using molecular dynamics simulations with a deep learning-based interatomic potential energy model, we uncover the microscopic features responsible for soft clay-formation from ionic solid mixtures. We find that salt mixtures capable of forming molecular solid units on anion exchange, along with the slow kinetics of such reactions, are key to soft-clay formation. Molecular solid units serve as sites for shear transformation zones, and their inherent softness enables plasticity at low stress. Extended X-ray absorption fine structure spectroscopy confirms the formation of molecular solid units. A general strategy for creating soft clay-like materials from ionic solid mixtures is formulated.


Introduction
Mechanically soft materials that can be easily deformed by hand are ubiquitous in nature, such as natural soft-clay 1 , dough 2 , gel 3 , etc.Such materials usually consist of hard and soft components 1,3,4 , where the former gives rigidity, while the latter gives soft rheological behavior.For example, in natural soft-clays, hard components are layered-minerals such as pyrophyllite 1 , while the soft component is water.Soft materials are highly sought after in various applications such as in flexible electronics 5 , pharmaceuticals for drug delivery 4 , and all-solid state batteries to improve fabrication, and interfacial kinetics [6][7][8] .
Recently, such soft clay-like materials were introduced into the energy storage field as potential fast Li-ion conductors.Somewhat surprisingly, a soft clay-like material was synthesized by ball milling two rigid salts, LiCl and GaF3, at room temperature (RT) without water. 9,10The resulting amorphous solid had high RT Li-ion conductivity of ~4 mS/cm, which is comparable to that of liquid organic electrolytes.Pliable solid-state ionic conductors are of particular interest as they have the potential to facilitate the fabrication of solid-state batteries and accommodate the swelling of active cathode materials 11 .The fact that a soft material can be created by merely mixing two rigid ionic solids contradicts conventional thinking.Understanding the physical mechanism behind mechanical softness in such materials and identifying the general criteria for soft-clay formation from mixtures of ionic solids could help to establish design principles for creating innovative soft materials.Combining the exotic properties that can be achieved in ionic materials, such as magnetism 12,13 , polaronic optical absorption 14 , color centers host 15 , magnetooptical response 16 , etc., and the novel concept of creating mechanically soft systems from mixtures of ionic solids has far reaching implications.
This study presents a combined computational and experimental analysis of the microscopic mechanism governing soft-clay formation upon mixing two rigid salts, GaF3 and LiCl.By training a deep learning-based interatomic potential energy (PE) model we were able to explore the mechanical behavior of an amorphous structure with ~10k atoms using molecular dynamics (MD) simulations.The results reveal that the formation of molecular solid-like (MS) units from the chemical reaction between the hard solids, is responsible for the material's mechanical softness.These units serve as sites for shear transformation zones and are inherently soft, enabling plasticity at low stress.Extended X-ray absorption fine structure (EXAFS) of the synthesized soft clay-like material confirmed the formation of these molecular units.This study provides a detailed understanding of the microscopic mechanism of soft-clay formation from rigid ionic solid mixtures and proposes criteria and design strategies for realizing other mechanically soft materials.

Results
LiCl and GaF3, two rigid salts with melting points 878 K and 1070 K, respectively, were recently found 9 to form a soft clay-like amorphous solid with a glass transition at Tg ~ -60 o C, when ball milled in a molar ratio xLiCl:GaF3 (2 ≤ x ≤ 4) for 18 hours at RT (a powder state remained for x < 2).To explore the reaction mechanism and mechanical behavior, a deep learning-based interatomic PE model was trained for the Ga-F-Li-Cl chemical system using DeepMD 17,18 (details in Supplemental material SM-1,2).Training was performed using the atomic forces and energies of ab initio molecular dynamics (AIMD) trajectories of 13 stable crystalline phases in the Ga-F-Li-Cl quaternary chemical space, and 3 slab-like structures of LiCl|GaF3 (where multilayer slabs of [001] LiCl and [001] GaF3 having 3 different thicknesses are interfaced "|") (see Fig. S1 and Table SM-1 for the full list of structures).The atomic configurations were obtained by melting and quenching each structure using AIMD simulations.In total, >700k AIMD frames were generated, from which 250k atomic configurations were randomly chosen for training.Our trained model was validated on a subset of training structures, and the RMSE error in energy and forces were <1 meV/atom and <70 meV/Å 2 after training (Fig. S2).The trained model was also tested on atomic forces and energies of several additional structural configurations (not included in the training and validation set), and benchmarked against their bulk modulus calculated with density functional theory (DFT), and tensile stress-strain response and Li-ion conductivity calculated with DFT-AIMD, and showed good agreement with actual DFT values (see Table SM-2, Fig. S3, S4).
In recent experiments 9,10 , the amorphous clay-like solid obtained from ball-milled LiCl and GaF3 was found to contain domains of unreacted parent constituents distributed randomly within the amorphous matrix.To emulate conditions observed in experiments, where LiCl and GaF3 particles come into contact and react during ball-milling, a specific procedure was designated to create large supercells with domains of each constituent (LiCl and GaF3).The procedure involved firstly creating a slab-like geometry of LiCl|GaF3, where a multilayer slab of [001] LiCl and [001] GaF3 was interfaced in a LiCl:GaF3 molar ratio of 2. This slab-like structure was subjected to an AIMD simulation under the NVT ensemble for t = 5 ps at T = 800 K to equilibrate the interface, and then relaxed at T = 0 K to a local energy minimum.The resulting structure, as shown in Fig. S5a, was then periodically repeated along the two directions perpendicular to the interface, and a ~2.5 nm cubic "particle" was cut out from it.Eight of these identical ~2.5 nm aperiodic particles, adding up to ~10k atoms, were arranged in a larger cell of size ~5.4 nm (Fig. S5b).To achieve many distinct interfacial environments, each of the ~2.5 nm particles was rotated 90 o with respect to their neighbors, such that the axis normal to the interface between LiCl and GaF3 in each particle did not align in the same direction as that of the neighboring particles (additional details in SM-3 and Fig. S5).Relaxing the cell in LAMMPS 19 using the trained deep-learning based PE model at T = 0 K, densified the system by removing the vacuum between each ~2.5 nm cube of material.This relaxed structure with ~10k atoms was subjected to a high-temperature classical MD simulation (hereafter, unless specified, all MD simulations were done with LAMMPS 19 using the trained deep learning-based PE model) under the NVT ensemble for t = 50 ps at T = 900 K to allow mixing of the atoms.To obtain a representative structure in which domains of reactant materials are visible, an atomic configuration at t = 50 ps was selected and this configuration was relaxed in LAMMPS at T = 0 K to a local energy minimum (this procedure is analogous to the commonly used melt and quench techniques 20,21 to create amorphous structures).The relaxed structure was further equilibrated in an MD simulation under the NPT ensemble for a duration of 2 ns at T = 300 K and zero external stress, until there was no further change in density, lattice constant, angles, or total potential energy.The resulting amorphous structure is shown in Fig. 1a and exhibits chemical heterogeneity with domains of unreacted LiCl and GaF3, as well as the formation of GaCl3-like units.The specific volume of the structure was computed at different temperatures, and a glass-like transition was observed at Tg ~ -58 o C (Fig. S7), in good agreement with experiments 9 .Fig. 1b shows the element-wise radial pair distribution function g(r) before and after the high temperature (T = 900 K) MD simulation of t = 50 ps.The Ga-F and Li-Cl peak decrease, while the Ga-Cl and Li-F peak increase, indicating that anion exchange occurs when the two salts are mixed.This anion exchange is consistent with thermodynamic driving force.Considering all possible phases that can form when LiCl and GaF3 react, using entries from the Materials Project database 22 , the thermodynamic driving force is found to be maximum (reaction energy is most negative) for the anion exchange reaction 3LiCl + 2GaF3 → 1Li3GaF6 + 1GaCl3, Erxn.= -87 meV/atom (Fig. S6).To determine whether our amorphous structure (Fig. 1a) exhibits soft mechanical behavior similar to that observed in experiments, we simulated the response of the system in a stresscontrolled MD simulation under an NPT ensemble at 300 K.The simulation involved subjecting the system to an external shear stress, specifically setting the yz-component σyz to either 10 MPa or 50 MPa, while keeping all the other external stress components at zero.The shear stress was applied for 400 ps and then released for 400 ps, and this stress pulse was repeated three times.Fig. 1c shows the resulting shear strain yz, and total potential energy ΔE.The external stresses' yz-component was arbitrarily chosen and was found not to influence the results (see Fig. S10 for results when xz-component of external stress was applied and other components were kept at zero).The accumulated shear strain after three loading cycles is non-negligible, and the structure exhibits permanent deformation and plastic behavior, even at low σyz = 10 MPa.This shows that the amorphous structure is mechanically soft, similar to what is observed in experiments.The change in potential energy after deformation is small <3 meV/atom.The small change in potential energy upon application of stress cycles is expected in glasses, which typically have a fractal-like PE surface 23,24 , and indicates that the amorphous structure (Fig. 1a) is in a meta-basin.A glassy material can hop between near-degenerate sub-basins within a meta-basin and achieve plasticity even at low stresses 24 .Analysis at even lower shear stresses σyz < 10 MPa, could not be performed due to stress fluctuations of that order in the simulations.
To further investigate the microscopic features responsible for the material's soft plastic response, we performed another MD simulation at a constant strain rate and T = 300 K (additional details in SM-1).Such strain-controlled MD simulations are commonly employed 24,25 to identify the microscopic plastic events, as they enable the separation of the elastic and plastic regions based on strain magnitudes.Fig. 2a shows the shear stress-strain response of the structure (Fig. 1a) at an applied shear strain rate of 10 9 s -1 on the yz plane.While the obtained yield stress under this very high strain rate is ~0.5 GPa (Fig. 2a), the stress is expected to be much lower under a lower strain rate 24,25 .Lower strain rates, as used in experiments are not directly accessible in molecular dynamics, and methods such as metadynamics 24 would have to be used.However, our results using a constant stress (Fig. 1c) demonstrate that the material is indeed soft.A non-elastic plastic response is evident at yz > 0.05 in Fig. 2a.Deviation from the elastic response in amorphous materials can be quantified by the non-affine displacements (D 2 min) 24,26 .A method previously 26 reported to calculate D 2 min was used here (see details in SM-6).Fig. 2b-d shows snapshots of the structures at three different (i -iii) yz values with the local value of D 2 min represented by the color legend.In structure i (Fig. 2b), at a low shear strain, the areas with nonzero D 2 min indicate local plastic deformation, commonly known as Shear Transformation Zones (STZs) 24,26,27 in amorphous materials.In structure ii (Fig. 2c), where yz has increased, these STZs form shear bands [24][25][26][27] .Moreover, in structure iii (Fig. 2d), with further increased yz, localized STZs similar to those observed in structure i (Fig. 2b) reappear.The MD simulation at a constant strain rate (Fig. 2a-d) reveals that our structure exhibits plastic deformation by forming STZs and shear bands, which are characteristic of plastic deformation in amorphous materials [24][25][26][27] .To understand the local chemical environment of STZs responsible for plastic deformation, we plotted in Fig. 2f the radial distribution function g(r) around Ga atoms with the highest and lowest D 2 min values.The g(r) was averaged over the strain interval yz = 0.09 -0.14.We found that Ga atoms in the areas involved in plastic deformation have a Cl-rich environment, as evidenced by the lower Ga-F peak for Ga atoms with D 2 min >90% of maximum compared to those with D 2 min values <10% of maximum (Fig. 2f).Additionally, we visually examined the local structure in STZs and found that it mostly consists of GaCl3-like and Cl-rich GaClxFy complexes (Fig. 2e).As illustrated in Fig. 3b bulk GaCl3 is a molecular solid consisting of Ga2Cl6 complexes that are Van der Waals bonded to each other.The weak intermolecular interactions in molecular solids render them intrinsically very soft 28 .The nature of this weak bonding rationalizes why strain localizes in areas where Ga is mostly coordinated by Cl in our simulations.These findings indicate that the soft plastic behavior in the 2LiCl-GaF3 structure arises due to the formation of molecular solid-like GaCl3-units and Cl-rich GaClxFy complexes during anion exchange.These complexes are activated at low stresses to form STZs, ultimately leading to soft-plastic deformation.Thus, the formation of molecular solid units is the key to the soft clay-like plastic response.
Table 1: Showing different salt combinations (precursors) considered in this study for possible soft-clay formation.The predicted products are based on the maximum thermodynamic driving force with the maximum (most negative) reaction energy (Erxn).Possible molecular solid component that can form is also listed.Additionally, the crystalline phases in the product, formed after ball milling (BM) the precursors in experiments are identified with X-ray diffraction (XRD) and listed under the column -XRD peak after BM.The rheological behavior of ballmilled products is also tabulated.To validate anion exchange and the formation of molecular units in the 2LiCl-1GaF3 and 3LiCl-1GaF3 soft clay-like materials, we prepared samples by mechanochemically mixing (ball milling) LiCl and GaF3 precursors in the ratio of 2:1 and 3:1, as previously reported 9 (further experimental details in SM-5).The inset in Fig. 3a shows an image of the resulting soft clay-like material bent into a specific shape.The RT Li-ion conductivity measured using electrochemical impedance spectroscopy was found to be ~2.9mS/cm (details in SM-5), similar to that reported in ref. [ 9 ].To understand the local atomic chemical environment of Ga atoms in the soft clay-like materials we performed EXAFS 29 .Fig. 3a compares the Ga-K edge EXAFS of the ball-milled 2LiCl-1GaF3 and 3LiCl-1GaF3 with that of bulk GaF3 and GaCl3.The Ga EXAFS curves of 2LiCl-1GaF3 and 3LiCl-1GaF3 lie between the curves of bulk-GaF3 and bulk-GaCl3 indicating contributions from both GaF3-like as well GaCl3-like units.This confirms that anion exchange takes place during the ball milling of a LiCl-GaF3 mixture forming GaCl3-like molecular units, consistent with the observations in the MD simulations (Fig. 1b).XRD of the soft clay-like materials (Fig. S8e) did not reveal any peaks corresponding to bulk GaCl3, indicating that no distinct crystalline GaCl3 phase formed.

Precursors
To achieve soft clay-like mechanical behavior, it is necessary to have both soft and hard components 1 .In our particular case, hard components are provided by unreacted LiCl and GaF3, while the GaCl3-like molecular component provides softness.Soft-clay will not form if the soft component is deficient or in excess, analogous to the appropriate ratio 30 of water and pyrophyllitelike minerals to form natural soft-clay.This can happen for GaF3-rich compositions, x < 2 in xLiCl:GaF3, which have been observed not to form soft-clay 9,31 .Moreover, if the soft and hard components phase segregates into macroscopic separate phases, then soft clay-like deformation will also not be achieved.Indeed, ball milling the compounds that would constitute the terminal products of anion-exchange, LiF and GaCl3, does not lead to a soft-clay.This points at the importance of the kinetics of anion exchange, in addition to the mixture having the right ratio of components.Anion exchange must occur but should not be completed, and the products should not separate into macroscopic phases.Hence, to form soft-clay from ionic solids, three criteria must be met -(i) the combination of salts must have a thermodynamic driving force for anion exchange leading to units that form molecular solids, (ii) the kinetics of the reaction must be slow enough to avoid complete anion exchange and phase separation, and (iii) the ratio of salts must be in an appropriate range, ensuring that neither of the salt components is in much excess.
In an attempt to find other soft-clay-forming mixtures, we searched the Materials Project database 22 and identified three other molecular solids, SbCl3, InI3, and GaI3, which can form through anion exchange from rigid solid mixtures 1SbF3-3LiCl, 1InBr3-3LiI, and 1GaF3-3LiI, respectively (SM-4).The crystal structures of SbCl3 and InI3, depicted in Fig. 3c,d, consist of molecular units that are held together through Van der Waals interactions, while GaI3 has a similar crystal structure as GaCl3 (Fig. 3b).Table 1 displays the different salt combinations evaluated in this study for possible soft-clay formation.The mixtures were ball milled and characterized by XRD to identify any crystalline phases formed.We find that in the case of 3LiCl-1SbF3, 3LiI-1InBr3, and 3LiI-1GaF3, a powder state remains after ball milling and a soft-clay does not form (hereafter called non-clay).Additionally, in all three non-clay cases, peaks corresponding to crystalline molecular solid phases (SbCl3, InI3, and GaI3) were visible in XRD (see Table 1, Fig. S8).In contrast, for 2LiCl-1GaF3 and 3LiCl-1GaF3, a mechanically soft solid was obtained after ball milling (hereafter called clay).XRD spectra of the 3LiCl-1GaF3 (clay) only showed peaks corresponding to LiCl (unreacted precursor), while no peaks corresponding to any crystalline GaCl3 were visible (see Table 1, Fig. S8).The appearance of peaks corresponding to crystalline molecular solid phases in the XRD of the non-clay systems, signifies that the molecular solid units have separated into macroscopic phases.Moreover, in the non-clay systems 3LiCl-1SbF3, and 3LiI-1InBr3, XRD peaks corresponding to the anion exchanged products (apart from MS), LiF and LiBr, were also observed, signifying that the anion exchange products have separated into macroscopic phases.These findings reveal that non-clay formation is linked with the separation of anion exchanged products into macroscopic phases, thereby validating the role of kinetics in soft-clay formation.To form a soft-clay, anion exchange must occur, but the products should not phase segregate into macroscopic separate phases.Furthermore, we tracked the XRD peaks of phases formed at different instances of time during ball milling (see Fig. S8d).For a representative non-clay material 3LiI-1InBr3, XRD peaks corresponding to LiBr and InI3 were seen after just 20 minutes of ball milling, indicating a rapid anion exchange and phase separation, while for the soft clay-like 3LiCl-1GaF3, no signatures of anion exchange completion or phase separation were seen even after 24 hours of ball milling.This indicates that the inherent chemistry of GaF3 impedes kinetics of complete anion exchange and phase separation.Additionally, in non-clay systems, strategies to suppress kinetics, such as regulating temperature during ball milling, can be used for soft-clay formation.

Discussion
Our combined computational and experimental study shows that when a rigid salt mixture of 2LiCl-1GaF3 mechanochemically reacts, the resulting system mechanically behaves like a softclay, as evidenced in both MD simulations (Fig. 1c) and experiments (Fig. 3a inset), consistent with prior studies 9,31 .We find that during the ball milling reaction, partial anion exchange takes place and GaCl3-like molecular solid (MS) units are formed, which is consistent with the thermodynamic driving force (Fig. S6).This process was confirmed both with MD simulations (Fig. 1a,b and Fig. 2b) and EXAFS (Fig. 3a).MD simulations of the shear stress-strain response of the material (Fig. 2) show that MS-like units serve as sites for shear transformation zones which get activated at low stress and lead to soft-plastic deformation.These findings point to the formation of molecular solid units as a result of the partial anion exchange, as the key to the soft clay-like mechanical response.Our experiments on other ion-exchange solids indicate that careful tuning of the composition and processing is required to obtain the proper soft mechanical response.Some salt mixtures have a thermodynamic driving force (TDF) for anion exchange reaction, but if the anion exchange reaction does not lead to MS formation, soft-clay with not be obtained.This phenomenon was observed in prior studies 9,31 for salt mixtures such as 1NaCl-1GaF3, 3LiCl-1InF3, 6LiCl-1Ga2O3, 3LiOH-1GaF3, 1Li2O-1GaF3, 3LiCl-1LaF3, where soft-clay formation was unsuccessful.Except for the case of 3LiCl-1InF3, where there is no TDF for anion exchange reaction, in all other cases, the salt mixtures have a TDF for anion exchange reaction, but the anion exchange reaction does not lead to MS formation (see SM-4).In contrast, the 3LiBr-1GaF3 mixture was found 9 to exhibit soft clay-like mechanical behavior driven by the favorable reaction energy of an anion exchange between LiBr and GaF3 to form GaBr3 (see SM-4), which is a molecular solid and has a similar crystal structure as GaCl3 (Fig. 3b).
The kinetics of anion exchange is also important for soft-clay formation.If the anion exchanged molecular species phase segregate into distinct macroscopic phases, then the MSlike soft units will not be interfaced between the hard solids, and soft clay-like mechanical response will not occur.This phenomenon is observed in salts mixture 3LiCl-1SbF3, 3LiI-1InBr3, and 3LiI-1GaF3 (Table 1), where the XRD spectra (Fig. S8) of the ball milled products showed peaks corresponding to crystalline molecular solid phases, indicating that the MS units have separated into macroscopic phases.To suppress kinetics of anion exchange, temperature during ball milling can be regulated.It is intuitive that the appropriate ratio of salts in the mixture is also crucial for soft-clay formation; neither of the salt components should be in much excess.Although important, the exact ratio of salts in the mixture to form soft-clay is challenging to predict, apriori.
The mechanism behind mechanical softness in clay-like Li superionic conductors synthesized from a mixture of rigid salts, in this and prior studies 9,10,31 , bears resemblance to both natural soft-clays, 1,30,32 and synthetic soft-clays [33][34][35] formed from a blend of hard minerals and soft polymers.The unifying feature responsible for the pliability of all these soft-clays is the presence of soft components within a rigid matrix.In natural soft-clays, a mixture of hard minerals and water, plasticity arises when platelet-like hard minerals slide over each other upon the addition of water, 30,32 which acts as the soft component.Moreover, synthetic soft-clays composed of hard minerals dispersed in a soft polymer matrix exhibit plasticity through shear banding of the soft polymers, accompanied by momentum transfer to the rigid minerals. 33,34Analogously, in soft claylike Li superionic conductors created from a mixture of rigid salts, we find that plasticity occurs through the formation of shear transformation zones (STZs) and shear bands at the sites of soft MS-like units between the hard solids (Fig. 2).The inherent softness of MS-like units leads to the activation of STZs at low stresses, resulting in a soft clay-like mechanical response.Additionally, in natural and synthetic soft-clays, factors such as the ratio of rigid to soft units, particle size distribution, specific surface area of particles, and temperature also contribute to the plasticity. 32,33lthough, determining the precise role of these factors can be challenging, we anticipate that they will significantly influence the pliability of clay-like materials synthesized from a mixture of rigid salts.
In summary, we have uncovered the microscopic mechanism of soft-clay formation from the ionic solid mixtures by studying the mechanical behavior of amorphous 2LiCl-1GaF3 using MD simulations and with a deep learning-based interatomic PE model.We find that the formation of molecular solid-like units as a result of anion exchange is the key to soft clay-like mechanical behavior.MS-like units serve as the sites for STZs which get activated at low stress and lead to soft-plastic deformation.Additionally, to form soft clay-like systems from generic ionic solid mixtures, three criteria must be met -(i) the combination of salts must have a thermodynamic driving force for anion exchange leading to units that form molecular solids, (ii) the kinetics of the reaction must be slow enough to avoid complete anion exchange and phase separation, and (iii) the ratio of salts must be in an appropriate range, ensuring that neither of the salt components is in much excess.These strategies can be applied to discover other soft clay-like systems from ionic solid mixtures.Additionally, exploiting the inherent properties of ionic solids, these approaches can be used to create flexible magnets, electronic conductors, and other pliable superionic (Mg, Ca, etc.) conductors with wide-ranging implications.
The authors acknowledge the ACCESS (formerly XSEDE) supercomputing resources for providing computing facilities.

Fig. 1 .
Fig. 1.(a) An amorphous Ga-F-Li-Cl structure constructed for computational modeling, containing domains of LiCl, GaF3, and GaCl3-like molecules formed during the high temperature MD simulations.(b) The element-wise radial pair distribution function g(r) plotted at t = 1 ps and t = 50 ps of the MD simulation at T = 900 K. (c) The applied external shear stress σyz, accumulated shear strain yz, and total potential energy change ΔE of the amorphous structure as a function of time in the MD simulation at T = 300 K.The external shear stress ranged from 10 to 50 MPa.The accumulated shear strain after three cycles is non-negligible (yz ≠ 0), signifying permanent deformation.

Fig. 2 .
Fig. 2. (a) Shear stress (σyz) strain (yz) response of the amorphous structure at T = 300 K at a constant applied shear strain rate of 10 9 s -1 .(b -d) Shows snapshots of the material at different strain values iiii in (a).The color (red-low and blue-high) represents the value of non-affine displacement D 2 min, at an interval of Δyz = 0.01.In (b, i) the shear transformation zone (STZ) formed is indicated by an arrow and marked by a pink square.In (c, ii) the arrow points to shear bands (SB).(e) Shows the atoms that are part of the STZ in the pink square in (b, i) and have large D 2 min values.These are mostly GaCl3like and Cl-rich GaClxFy complexes.(f) The Ga-Cl and Ga-F pair distribution function g(r) of Ga-atoms with largest (D 2 min > 90% of maximum) and smallest (D 2 min < 10% of maximum) non-affine displacement values.The g(r) values were averaged over the strain interval yz = 0.09 -0.14.