Evaluation of the Dispersion Stability of AZO Mesocrystals for Their Processing into Functional Thin Films Using Small Angle X-ray Scattering

Abstract

Within the scope of the comprehensive elucidation of the entire process chain for the production of highly functional thin films made of semiconducting aluminum-doped zinc oxide ($AZO$) nanocrystals, this work deals with the detailed investigation of the stabilization sub-process, considering the requirements for the subsequent coating process. An innovative investigation procedure using non-invasive small angle X-ray scattering ($SAXS$) is developed, enabling an evaluation of qualitative and quantitative dispersion stability criteria of sterically stabilized $AZO$ nanocrystals. On the one hand, qualitative criteria for minimizing layer inhomogeneities due to sedimentation as well as aggregate formation are discussed, enabling a high particle occupancy density. On the other hand, a procedure for determining the $AZO$ concentration using $SAXS$, both in the stable phase and in the non-stabilized phase, is demonstrated to provide a quantitative evaluation of the stabilization success, having a significant impact on the final layer thickness. The obtained insights offer a versatile tool for the precise stabilization process control based on synthesis process using $SAXS$ to meet coating specific requirements and thus a successful integration into the entire process chain for the production of functional $AZO$ thin films.

1. Introduction

The field of printable electronics is gaining increasing economic importance and offers the possibility of producing flexible and (semi-)transparent electronic components for use in complex systems [1,2,3,4,5]. The printing of particulate inks to produce these systems offers an advantage compared to the application of expensive gas phase processes, as the deposition of individual functional layers can be omitted and much simpler equipment can be used. The production of particulate thin films consisting of transparent conductive oxides ($TCOs$), which can be applied in displays, organic light-emitting diodes, or thin-film solar cells [6,7,8,9,10], poses a major challenge, since nanoparticular layers often have very low conductivity due to their high interfacial resistances.

Here, the n-type semiconductor aluminum doped zinc oxide ($AZO$) is intended to replace previously used but poorly available indium-based oxides (e.g., $ITO$), due to similar application properties such as high transparency in the visible spectral range, good electronic conductivity, and high mechanical stability [11,12]. The specific adjustment of the optical, mechanical, and electrical properties of particulate thin films consisting of $AZO$ requires a comprehensive understanding of particle-based properties for the entire process chain within the fabrication process, starting with the synthesis of the $AZO$ nanocrystals followed by their conversion into stable dispersions up to the coating and drying or post-processing of the final layers. For this purpose, small-angle X-ray scattering ($SAXS$) as a non-invasive measuring method basically offers the possibility of recording and correlating structural properties in each individual process step independently of the state of the nanoparticles (e.g., powder, dispersion, or thin film) [13,14,15]. In the course of our own previous work, the synthesis of $AZO$ nanocrystals via the benzylamine route could be comprehensively clarified using X-ray scattering analysis methods, on the one hand, by developing a growth model covering the time-resolved growth to hexagonal-shaped mesocrystalline nanoparticles [16] and, on the other hand, by investigating influences of important process parameters on the growth behavior at low reaction kinetics [17].

Emanating from these prior works, an investigation procedure using the $SAXS$ analysis method is developed in this paper to extensively focus on the dispersion stability of sterically stabilized $AZO$ nanocrystals regarding the requirements of the subsequent coating process.

In detail, the first step is the identification and assignment of several structural levels within the non-stabilized $AZO$ system after synthesis and purification using our $SAXS$ laboratory camera to get deep insights into the initial state before stabilization. All $SAXS$ results are validated by dynamic light scattering ($DLS$) and transmission electron microscopy ($TEM$), concerning both their particulate and fractal properties, and then evaluated in terms of their stabilization potential concerning effects on the coating process.

Subsequently, the sterically stabilized $AZO$ dispersion in the solvent ethanol is first investigated qualitatively using $SAXS$ by time-resolved analysis of the stability behavior towards sedimentation in the Earth’s gravitational field in order to draw conclusions about inhomogeneities due to sedimentation occurring during the coating process. Then, a further $SAXS$ investigation of the structural levels within the stabilized $AZO$ system is carried out, ensuring stabilization at the lowest possible structural level and thus enabling a high particle occupancy density of the final thin film.

Finally, the $AZO$ dispersion is investigated quantitatively using $SAXS$ by demonstrating a new method allowing a non-invasive determination of the $AZO$ concentration, in both the stable phase and the non-stable disperse phase, for significantly higher particle concentrations than can be characterized by common analysis methods (e.g., in the UV-Vis spectral range) after successful calibration of our $SAXS$ laboratory camera. This allows the introduction and determination of a coefficient providing quantitative conclusions regarding the stability success, having a considerable impact on the final layer thickness.

2. Material and Methods

2.1. Synthesis and Sample Purification of AZO Nanocrystals

For the non-aqueous sol-gel synthesis of $AZO$ nanocrystals via the benzylamine route, the crystalline precursors zinc acetylacetonate hydrate ($Zn{\left(acac\right)}_2$ powder, $\ge 99\%$, Aldrich) and aluminum isopropoxide ($Al{\left(OiPr\right)}_3,\ge 98\%, \mathrm{Aldrich}$) with the initial precursor concentration $C_E=25 g{L}^{-1}$ were used, wherein the molar fraction of aluminum precursor was set to $2.5 mol\%$. The aromatic solvent benzylamine ($BnN{H}_2$, benzylamine for synthesis, $\ge 99\%$, Merck) served as reaction medium. An ideally stirred open batch reactor ($500 mL$) was used to carry out the synthesis at the constant process temperature $T_R=110 °C$. Here, the aluminum precursor was pre-dissolved in the reaction medium during the heating phase due to its poor solubility. After reaching the process temperature, the synthesis process was started with addition of the zinc precursor. The endothermic synthesis was ended by quenching the particle growth after $120 min$ by rapid cooling in a water bath. To remove the organic reaction medium from the particle surface necessary for the subsequent stabilization process, the $AZO$ nanocrystals were purified after the synthesis by repetitive centrifugation and dispersion processes and were finally presented in an ethanol-based dispersion, as described in detail in our prior works [16,17].

2.2. Post-Synthetic Stabilization of AZO Nanocrystal Dispersions

Based on preliminary works about steric stabilization and surface modification of nanoscale metal oxide using n-carboxylic acids [18,19,20,21,22,23], $3, 6, 9$-Trioxadecanoic acid ($TODS$, $\ge 99\%$, Merck) was selected as stabilizer for the steric stabilization of the pure $AZO$ nanocrystal dispersion in the solvent ethanol. The carboxyl group of $TODS$, having a negative partial charge in aqueous systems ($pH~7)$ [24], adsorbs on the positively charged particle surface of $AZO$, while the alkyl chain, including three polar oxo groups, provides steric hindrance. Since the amount of used stabilizer $w_{TODS}$ scales with the entire particle surface and thus indirectly with the metrological accessible particle mass, in Equation (1) the added stabilizer concentration $C_{TODS}$ was always based on the particle concentration of the non-stabilized initial dispersion $C_{ 0}$.

$$w_{TODS}=\frac{C_{TODS}}{C_0} [-]$$

(1)

The sequence of the stabilization and centrifugation process is based on the work of Zellmer et al. [25]. In the first step, the ethanol-based initial $AZO$ dispersion was treated with ultrasound for $5 min$ getting a homogeneous particle dispersion. In a second step, the stabilizer was added, followed by reaction between stabilizer and particle surface during stirring at $900 rpm$ for $24 h$ at room temperature (HLC Heating-ThermoMixer, DITABIS). Depending on the procedure, this could result in two particle fractions: a stable phase at the nanoscale level and remaining agglomerates as unstable phase at the micron scale. The subsequent separation of the stable and unstable particle phases was carried out by centrifugation (Centrifuge 5430R, Eppendorf) for a minimum time period of $\Delta t_C\ge t_S$, introducing the separation time $t_S$ of ideal spheres in the centrifugal field according to Stokes, as shown in Equation (2).

$$t_S=\frac{18 {\eta }_S s_{max}}{\mathsf{\Delta }\rho X_S^2 g RCF} \left[ s \right]$$

(2)

On the basis of the known parameters such as the solvent–solid density difference $\mathsf{\Delta }\rho$, the dynamic solvent viscosity ${\eta }_S$, the gravitational force $g$, the maximum sedimentation path of the particles $s_{max}$, and the relative centrifugal force $RCF$, the separation grain limit $X_S$ can be set via the corresponding minimum centrifugation time period $\Delta t_C\ge t_S$. Finally, a stable phase of sterically stabilized $AZO$ nanocrystals in ethanol using $TODS$ with particle sizes $d<X_S$ is obtained by assuming the validity of the Stokes conditions during centrifugation.

2.3. Characterization of AZO Nanocrystal Dispersions

For a comprehensive characterization of the stability properties of $AZO$ nanocrystal dispersions, a non-invasive X-ray analysis was performed using a lab scale $SAXS$ camera (XEUSS 2.0, XENOCS). The point-collimated X-ray beam ($0.5\times 0.5 m{m}^2$), generated from a $30 W$ microfocus X-ray source, was monochromatized on $Cu-K-alpha$ ($\lambda =0.154 nm)$ and parallel focused on detection plane. The samples present in $EtOH$ after purification (see Section 2.1) were injected as a homogeneous suspension into a low-scattering polyimide tube with an inner diameter of $1 mm$ and wall thickness $<25 \mu m$. The X-ray scattering intensity $I\left(q\right)$ on samples was measured as a function of the scattering vector $q$ with $q=4\pi /\lambda ·\sin \left(\theta /2\right)$, wheras $\theta$ is the scattering angle, and recorded by a two-dimensional hybrid photon counting X-ray detector with a pixel size of $0.172 mm$ (PILATUS 300K-S, DECTRIS) for $300 s$. The scattering intensity of a monodisperse particle system, normalized to the squared classical electron radius $r_e^2$, including $N$ monodisperse particles with the single volume $V_P$ and the excess electron density $\Delta {\rho }_e$ in the exposed liquid volume $V$ is generally described in Equation (1).

$$I\left(q\right)=\frac{N}{V}·\Delta {\rho }_e{}^2·V_P{}^2·P\left(q\right)·S\left(q\right) \left[a.u.\right]$$

(3)

Here, the form factor $P\left(q\right)$ describes the intraparticle scatter fraction, whereas the interparticle scatter fraction is specified by the structure factor $S\left(q\right)$. For the description of particulate interactions for $q>0.1 n{m}^{-1}$, the influence of the structure factor with $S\left(q\right) \to 1$ can be neglected [26]. Beaucage et al. introduced a unified approximation with Equation (4) to describe experimental $SAXS$ data from particle systems consisting of $n$ structure levels $i$, such as aggregates or surface fractals [27].

$$I\left(q\right)\cong {\displaystyle \sum }_1^n\left(G_i\exp \left(-q^2{R}_{g,i}^2/3\right)+B_i\exp \left(-q^2{R}_{g,i+1}^2/3\right)\times {\left\{{\left[\mathrm{erf}\left(qk{R}_{g,i}/6^{0.5}\right)\right]}^3/q\right\}}^{v_i}\right)$$

(4)

Equation (4) describes a summation of $n$ local Guinier- and Power-Laws of each structure level within the particle system. The local Guinier-Law

$$I\left(q\right)=G_i \exp \left(-q^2{R}_{g,i}^2/3\right)$$

(5)

is influenced by the radius of gyration $R_{g,i}$ and the pre-factor $G_i$ of the corresponding $i$th structural level, which is given by

$$G_i=K {\left(\frac{\mathrm{N}}{\mathrm{V}}\right)}_i{V}_{p,i}^2,$$

(6)

wherein ${\left(\mathrm{N}/\mathrm{V}\right)}_i$ and $V_{p,i}$ denote the particle number density and the structure volume of the $i$th level. The parameter $K=2\pi \Delta {\rho }_e^2$ can be regarded as constant due to a not changing $\Delta {\rho }_e$. Moreover, from the local Power-Law

$$I\left(q\right)=B_i {\mathrm{q}}^{-v_i}$$

(7)

the respective fractal information can be extracted from the power $v_i$. In case of mass fractals, the mass fractal dimension $D_{fm}$ is described by Equation (8) and for surface fractals Equation (9) is to be used [27,28,29].

$$\nu =D_{fm} \mathrm{with} 1<D_{fm}<3$$

(8)

$$\nu =6-D_{fs} \mathrm{with} 2<D_{fs}<3$$

(9)

In the special case of $\nu =4$ for surface fractals, Equation (7) leads to the Porod-Law describing smooth surfaces with sharp density transition [30], wherein the so-called “Porod constant” $B_i$ is shown in Equation (10) including the average structure surface $S_{p,i}$.

$$B_i=K {\left(\frac{\mathrm{N}}{\mathrm{V}}\right)}_i{S}_{p,i}$$

(10)

In addition to $SAXS$, further particle properties of $AZO$ present in $EtOH$ were analyzed by $DLS$ using a Zetasizer device (Nano ZS, Malvern) and $TEM$ (Osiris ChemiStem, FEI). For $TEM$, the samples had to be diluted with $EtOH$ and air-dried on a $TEM$ grid at $25 °C$. Finally, for recording the $AZO$ concentration by gravimetric analysis, the nanocrystals were completely dried at $80 °C$ for $24 h$ under ambient pressure in a drying oven (UN260, Memmert) and afterwards quantified with an analytical scale (Secura 224-1S, Sartorius).

3. Results and Discussions

3.1. Characterization of Non-stabilized AZO Nanocrystal Dispersions

The aim in this section is to investigate the aggregation behavior, the size range of the stabilizable primary particles, and its mass-fractal structures of non-stabilized $AZO$ nanocrystals being able to make important predictions about the stabilization behavior of $AZO$. In this context, the particle structure and the fractal properties of $AZO$ nanocrystals in an ethanol-based dispersion after synthesis, particle preparation (see Section 2.1), and before stabilization are examined in more detail using $SAXS$, $TEM$, and $DLS$. Figure 1 shows the $SAXS$ curve (black dots) of a non-stabilized initial $AZO$ dispersion with a gravimetrically determined initial particle mass concentration $C_0=15.69 g{L}^{-1}$, wherein $I\left(q\right)$ is plotted twice logarithmically over $q$.

In Figure 1, the qualitative course of $I\left(q\right)$ shows the presence of three structural levels $L_i$ within the particle system examined depending on the $q$-range: $L_1$ (dotted) in $0.038 {\AA }^{-1}<q_{L1}<0.2 {\AA }^{-1}$, $L_2$ (dashed) in $0.017 {\AA }^{-1}<q_{L2}<0.038 {\AA }^{-1}$ and $L_3$ (dotted/dashed) in $q_{L3}<0.017 {\AA }^{-1}$. To each level, one local Guinier area (curved line) can generally be assigned from Equation (5) including the associated local Power-Law (straight line) from Equation (7). The Guinier area of $L_3$, indicated by the Power-Law of $L_3$ and expected in the q-range $q<q_{min}$, was not detectable due to the lower resolution limit $q_{min}=0.00632 {\AA }^{-1}$ of the $SAXS$ camera used. Therefore, the Unified-Fit model according to Beaucage from Equation (4) was approximated with a high degree of certainty ($R^2=98\%$) to the fully resolvable levels $L_1$ and $L_2$ of the $SAXS$ curve in Figure 1, resulting in important structure parameters of the non-stabilized $AZO$ system such as the two local radii of gyration $R_{g,L1}=4.30 nm\left(\pm 2\%\right)$, $R_{g,L2}=14.45 nm\left(\pm 6\%\right)$ as well as the local powers ${\nu }_{L1}=3.9\left(\pm 2\%\right)$, ${\nu }_{L2}=2.7\left(\pm 2\%\right)$. By assuming spherical structures within all levels $L_i$, the respective volume-weighted geometric mean diameters $d_{50,L1}=11 nm\left(\pm 2\%\right)$ and $d_{50,L2}=37 nm\left(\pm 6\%\right)$ were calculated with $d_{50,Li}=2\sqrt{5/3 }{R}_{g,Li}$. The $TEM$ image in Figure 2a is used to assign the structural parameters of the various levels from the Unified-Fit model obtained with $SAXS$ to the actually existing particle structures of the examined non-stabilized $AZO$ nanocrystals.

Figure 2a shows hexagonally shaped mesocrystalline particle structures of $AZO$ (solid line) with remaining internal grain boundaries (dashed line) arising due to non-classical crystal growth with oriented agglomeration processes during the synthesis process, as we reported previously [16,17]. Here, the mesocrystals are arranged in superordinate aggregate structures with clearly visible phase boundaries, resulting in an average mesocrystal size of $d_{50,TEM}=29.5 nm\left(\pm 19\%\right)$ from a statistical imaging evaluation of approximately $200$ mesocrystals using $TEM$ under the assumption of spherical particles. The order of the size of the present aggregate structures of $AZO$ mesocrystals could be estimated on the basis of a log-normal particle size distribution fit ($R^2>99\%)$ using $DLS$ data in Figure 2b to a volume-weighted mean sphere-equivalent diameter $d_{50,3 DLS}=247 nm\left(\pm 4\%\right)$, which is more than $eight$ times larger than the $TEM$-based mesocrystal size. Using the $TEM$ and $DLS$ results in Figure 2, it is possible to clearly assign the structural levels, obtained from $SAXS$ in Figure 1 to the actual particle levels of the investigated $AZO$ nanoparticle system. By comparing the respective orders of magnitude, the local Guinier fit of $L_2$ with $d_{50,L2}=37.31 nm\left(\pm 6\%\right)$ can be assigned to the mesocrystal level with $d_{50,TEM}=29.5nm(\pm 19\%$), while $L_1$ with $d_{50,L1}=11.10 nm\left(\pm 2\%\right)$ corresponds to the visible substructures of the incompletely fused mesocrystals on primary particle level in Figure 2a. The non-resolvable Guinier range of $L_3$ in Figure 1 can be solely associated with the aggregation level of the $AZO$ mesocrystals having the size $d_{50,3 DLS}=247 nm\left(\pm 4\%\right)$. Based on the currently known particle hierarchy of the non-stabilized $AZO$ dispersion, fractal properties can be derived for the structure levels $L_1$ and $L_2$ using the power laws obtained from the Unified-Fit model in Figure 1. While the mass fractals in $L_2$ with $D_{fm}\left({\nu }_{L2}\right)=2.7$ (see Equation (8)) describe a high relative aggregation density in the range $1<D_{fm}<3$ [31], $L_1$ contains surface fractals with $D_{fS}\left({\nu }_{L1}\right)=2.1$ (see Equation (9)), indicating smooth crystal surfaces on primary particle level in accordance to our prior work [16]. Since $L_3$ could not be fully analyzed due to the limited resolution of our $SAXS$-camera, a precise determination of the fractal properties using the Unified-Fit model is not possible. However, based on the $TEM$ and $DLS$ data, mass fractals in the range $1<D_{fm}\left({\nu }_{L3}\right)<3$ could be generally predicted from the aggregation behavior of the $AZO$ mesocrystals in Figure 2.

Hence, the existence of three structural levels within the non-stabilized $AZO$ particle system was verified using predominantly $SAXS$ measurement technology. In addition to the precise assignment of the individual levels to the present $AZO$ system, their magnitude and fractal properties could also be estimated and additionally validated by $TEM$ and $DLS$. The knowledge gained here results in comprehensive objectives for the subsequent stabilization process: the aggregate structure in $L_3$ of approximately $250 nm$ is to be broken up and $AZO$ is to be stabilized on the mesocrystal level $L_2$ to a mean size of approximately maximum $40 nm$, while no post-synthetic stabilization is expected at the irreversibly intergrown primary crystal level $L_1$ of approximately $12 nm$.

3.2. Qualitative Dispersion Stability Criteria of Stabilized AZO Nanocrystals

The stability in the gravitational field is an important qualitative stability criterion of dispersions utilized for the production of particulate thin films, since sedimentation processes can cause inhomogeneities in the layer formation during coating and drying processes. In this context, sterically stabilized $AZO$ dispersions with $TODS$ (see Section 2.2) were examined by time-resolved sedimentation analysis in the Earth’s gravity field using our $SAXS$ laboratory camera. Assuming that all quantities except $N/V$ are constant in Equation (3) during a sedimentation process, the linear relationship $I \left(q \right)~N/V$ allows conclusions to be drawn about the relative temporal change in $N/V$ by normalizing the scatter intensity to the maximum value at constant $q_{min}$. For this purpose, the relative $N/V$ of stabilized $AZO$ dispersions using $w_{TODS}=0.5$ in the initial concentration range of $5.15 g{L}^{-1}<C_0<41.2 g{L}^{-1}$ were recorded and finally plotted in Figure 3a over a sedimentation time period of $24 h$.

Irrespective of $C_0$, the curves show a decrease in $N/V$ with progressive sedimentation time up to a maximum loss of approximately $15\%$ within $24 h$ at $C_0=41.2 g{L}^{-1}$. Thus, an ongoing sedimentation process in the Earth’s gravity field could be observed using $SAXS$ despite previous stabilization. To verify single grain sedimentation according to Stokes for the investigated particle concentration range of $C_0\le 41.2 g{L}^{-1}$, the solid volume concentration $C_V$ can be calculated from the solid mass concentration $C$ using Equation (11) by assuming ideal spheres having the particle density of pure zinc oxide ${\rho }_{AZO}\cong {\rho }_{ZnO}$.

$$C_V=\frac{C}{{\rho }_{ZnO}} [-]$$

(11)

The volume concentrations calculated from Equation (11) for the samples used in Figure 3 are compared in

Table 1. The initial mass concentrations in the range of $5.15 g{L}^{-1}<C_0<41.2 g{L}^{-1}$ from the sedimentation experiment in Figure 3a are compared to their associated solid volume concentrations $C_V$ calculated using Equation (11).

$C_0 \left[g{L}^{-1}\right]$	$5.15$	$20.6$	$41.2$
$C_V [Vol.-\%$]	$0.09$	$0.37$	$0.73$

.

In the literature, the Stokes approach applies i.a. to $C_{V,i}<C_V^{*}=0.5 Vol.-\%$, wherein the sedimentation behavior is considered independent of the solid volume concentration [32,33]. This fact could explain the similar sedimentation behavior observed for the initial concentration range of $C_{AZO,0}\le 20.6 g{L}^{-1}$ in Figure 3a, whereas the sedimentation rate of $C_0=41.2 g{L}^{-1}$ with $C_V=0.73 Vol.-\%>C_V^{*}$ is significantly increased. A slight increase in concentration relative to $C_V^{*}$ leads to the formation of particle clusters, which result in a lower sedimentation resistance leading to the previously observed faster sedimentation compared to the Stokes approach [34]. However, a further increase in concentration would in turn cause a slowdown of the sedimentation due to growing interactions of counter flowing fluid particles, which is considered in the approach of Richardson and Zaki [35]. Consequently, the sedimentation process observed here within a time period of $24 h$ can be attributed to an unstable phase fraction within the stabilized $AZO$ dispersion consisting of aggregate structures that clearly exceed the order of magnitude of the primary crystal and the mesocrystal levels with $d_{50, L1/L2 }<40 nm$, as previously obtained in Section 3.1. After separation of the unstable phase by centrifugation at the defined separation grain limit of $X_S=40 nm$ at the previously observed mesocrystal level using Equation (2), no further sedimentation process could be detected in Figure 3b for all stable $AZO$ phases, consisting solely of $L_1$ and $L_2$. The fluctuations of the values in Figure 3b within the range of approximately $5\%$ are due to the increasing influence of the Brownian molecular motion on the particle movement in the nanoscale range below $100 nm$. Finally, the long-term stability of the stable phase over a period of $24 h$ was successfully demonstrated by $SAXS$ analysis after separating the unstable proportion in the centrifugal field.

As a further qualitative stability criterion regarding optimal application properties of particulate thin films, the highest possible particle occupancy density within the thin film must be ensured by stabilization at the lowest possible structural level of the $AZO$ system. After the previously shown successful separation at the aggregate level, a structural investigation of the stable $AZO$ phase is carried out using $SAXS$ in analogy to Section 3.1. In this context, Figure 4 shows the $SAXS$ curve of the stable $AZO$ phase from the initial $AZO$ dispersion in Figure 1, including the approximated Unified-Fit model ($R^2=96\%$) according to Beaucage from Equation (4) with its respective local Guinier- and Power-Laws of two structural levels $L_1$ (dotted) and $L_2$ (dashed).

Here, the Unified-Fit results in $d_{50,L1}=14 nm\left(\pm 4\%\right)$ with $D_{fS}=2.0$ for $L_1$ and $d_{50,L2}=34 nm\left(\pm 2\%\right)$ with $D_{fm}=2.8$ for $L_2$. By comparing these parameters with the non-stabilized $AZO$ system in Figure 1 from Section 3.1, for $L_1$ and $L_2$ they are all in the same order of magnitude, whereby they can be clearly assigned to the already known primary crystal ($L_1$) and mesocrystal ($L_2$) levels having similar fractal properties. This fact shows that the essential structural properties of the $AZO$ system, such as size and fractal properties, were not significantly influenced by steric stabilization using $TODS$. The presence of the third structural level, which was originally assigned to the aggregate structure in Section 3.1, is no longer detectable for the stable phase in Figure 4, indicating a successful steric stabilization of the $AZO$ system at the mesocrystal level $L_2$. Obviously, the stabilization at the primary crystal level $L_1$ could not be achieved due to irreversible adhesions and intergrowth during synthesis, as expected and reported in our previous works [16,17]. Possibly, the intergrowth of the primary crystals into highly-ordered, regularly shaped hexagonal $AZO$ mesocrystals, having a high aggregation density with $D_{fm}\left({\nu }_{L2}\right)=2.7$, could have a positive effect on the particle occupancy density and thus on the application properties of the final thin films (e.g., lower interfacial resistances), since a comparable density could probably not be generated by self-arrangement of stable particles during the coating and drying processes by stabilization at the primary crystal level alone. To validate the $SAXS$ result in Figure 4 with respect to the successful stabilization at the mesocrystal level, the volume-weighted size density distribution of the stable $AZO$ phase from $DLS$ data in Figure 5 is used, which is additionally compared to the non-stabilized $AZO$ dispersion in Figure 2b.

Due to the stabilization, on the one hand, the log-normal particle size distribution of the stable phase shows a clear shift towards a smaller mean sphere equivalent diameter from originally $d_{50,3}=247 nm\left(\pm 4\%\right)$ to $d_{50,3}=31 nm(\pm 2\%$), being in very good agreement with the mesocrystal level $L_2$ from $SAXS$ data ($d_{50,L2}=34 nm\left(\pm 2\%\right)$) in Figure 4 and $TEM$ data ($d_{50,TEM}=29.5nm\left(\pm 19\%\right)$) in Figure 2a. On the other hand, the significant reduction of the density distribution width is a further qualitative indication for the removal of aggregated structures. To summarize this section, the qualitative stability criteria of the stable $AZO$ dispersion using $SAXS$ offer very good prerequisites for producing homogeneous, particulate $AZO$ thin films, having the highest possible particle occupancy density, both because of the long-term stability towards sedimentation and due to the stability at the minimum possible mesocrystal level $L_2$ of approximately $40 nm$.

3.3. Quantitative Dispersion Stability Criteria of Stabilized AZO Nanocrystals

In addition to the previously investigated qualitative stability criteria, a quantitative evaluation of the stability success by non-invasive determination of the particle concentration of $AZO$, both in the non-stabilized system and in the stable phase using $SAXS$, is reported in this section. Such a quantification is necessary since the particle concentration in the stable phase also significantly influence the layer thickness depending on the selected coating process, which in turn affects their application properties. The stability success $S$ is introduced in Equation (12), which relates the particle concentration in the stable phase $C_S$ to the initial concentration $C_0$, enabling a quantitative evaluation of the particle fraction successfully transferred from the non-stabilized initial $AZO$ system into the stable phase using $TODS$.

$$S=\frac{C_S}{C_0} [-]$$

(12)

For the non-invasive quantitative determination of particle concentrations by means of $SAXS$, the local Guinier-law in Equation (5) from the Unified-Fit model is used, resulting in Equation (6) and the linear relationship $G_i~N/V~C$. Since most of the parameters in Equation (6) are empirically difficult to determine, a theoretical prediction of concentrations based on measured $G_i$ from scattering curves is limited. Consequently, a calibration of our $SAXS$ laboratory camera was necessary for the $AZO$ system, describing the linear relationship between $G_i$ and $C$ from Equation (6) by leaving all particle properties, obtained in Section 3.1 and Section 3.2, constant. For this purpose, stable $AZO$ phases in the range of $0 g{L}^{-1}<C_S\le 22.8 g{L}^{-1}$ were gravimetrically evaluated and their corresponding scattering curves at the mesocrystal level $L_2$ ($q_{L2}<0.038 {\AA }^{-1}$) including corresponding Unified-Fit approximations ($\overline{R^2}>97\%$) are shown in Figure 6a.

Here, the scattering intensity in the Guinier area of $L_2$ increases with rising particle concentration for constant particle properties (arrow). Based on the Unified-Fit models in Figure 6a, the exponential pre-factors $G_{L2}$ of $L_2$ were determined for each concentration from the respective local Guinier-Law in Equation (5) and show a linear correlation concerning the $AZO$ concentration with a very high coefficient of determination ($R^2>99\%$) in Figure 6b. This linear relationship, confirmed by Equation (6), shows the validity of our $SAXS$ laboratory camera used. Using linear regression, a calibration function could be obtained for the non-invasive determination of the $AZO$ concentration $C$ by means of $G_{L2}$ at $L_2$ from $SAXS$ data in Equation (13).

$$C=\left(3.72·{10}^{-3}\left(\pm 2\%\right)\right)·G_{L2} \left[g{L}^{-1}\right]$$

(13)

This calibration function can be generally used for the structural level $L_2$ in the stable as well as in the non-stabilized $AZO$ phases, since the $SAXS$ technique is capable of providing this information from Guinier areas independent of the aggregation state. To verify the validity of Equation (13) also for the non-stabilized $AZO$ phase, after determining the exponential pre-factor of $L_2$ with $G_{L2}\approx 4321 a.u.$ from the Unified-Fit model of the non-stabilized initial $AZO$ dispersion in Figure 1 using $SAXS$, the initial concentration $C_0^{SAXS}\approx 16.07 g{L}^{-1}$ could be calculated, which corresponds very well to the gravimetric result ($C_0^{Gr.}=15.69 g{L}^{-1}$) in Section 3.1. Similarly, extracting $G_{L2}\approx 3038 a.u$ of the stable $AZO$ phase from Figure 4, the corresponding concentration of the stable phase $C_S^{SAXS}\approx 11.30 g{L}^{-1}$ could also be calculated using Equation (13). Finally, with both concentration values obtained here from $SAXS$ data, a stabilization efficiency of $S\approx 70\%$ was derived from Equation (12) for the $AZO$ system investigated in this work.

To summarize this section, a new method for quantitative determination of the $AZO$ concentration, both for the non-stabilized phase and for the stabilized phase using $SAXS$ is successfully demonstrated, leading to an evaluation of the quantitative stability criterion $S$. On the one hand, the non-invasive X-ray scattering offers an advantage to the invasive, non-reversible gravimetric method concerning the further processing of the stable phases into functional thin films. On the other hand, $SAXS$ covers a significantly higher concentration range, being particularly relevant for coating applications, for determining the concentration of particulate systems in contrast to, e.g., UV-Vis methods, in which even $AZO$ concentrations of $C>0.05 g{L}^{-1}$ could no longer be described using the Lambert–Beer law.

4. Conclusions

In this work, we establish a detailed investigation procedure concerning significant dispersion stability criteria of sterically stabilized $AZO$ nanocrystals using a non-invasive $SAXS$ analysis method, evaluating their suitability for subsequent coating processes for the fabrication of functional $AZO$ thin films. Qualitative stability criteria of the $AZO$ system can be generally studied, ensuring a homogeneous particle distribution during post-processing steps and a maximum packing density of particulate thin films. Furthermore, quantitative criteria are examined, influencing the layer thickness of thin films during coating processes.

In detail, we first verified the existence of three structural levels within the initially non-stabilized $AZO$ nanoparticle system using $SAXS$, which could be clearly assigned to the primary crystal, mesocrystal, and aggregation levels with the help of $TEM$ and $DLS$, being consistent with our prior work. Particle-based properties of the individual structural levels, such as shape, sizes, and fractal properties were obtained, allowing significant predictions to be made about the stabilization behavior of $AZO$ at the mesocrystal level. Furthermore, we carried out sedimentation analysis on the sterically stabilized $AZO$ system to detect an unstable phase, being completely removed by centrifugation, on the one hand, and to successfully demonstrate the long-term stability of the stable phase over a period of $24 h$, on the other hand. An additional structural analysis of the stable $AZO$ phase using $SAXS$ showed that the mesocrystal level, representing the smallest possible stabilization level, meets the qualitative stability criteria of the stable $AZO$ dispersion and offers very good prerequisites for the production of homogeneous, particulate thin films with the highest possible particle coverage density. Finally, a new method for non-invasive determination of the $AZO$ concentration for both the non-stabilized and the stabilized phase using $SAXS$ was successfully demonstrated to provide a quantitative evaluation of the stabilization success.

The obtained insights offer a versatile tool for the precise stabilization process control based on synthesis using $SAXS$ to meet coating specific requirements and thus enable a successful integration of the stabilization process into the entire process chain for manufacturing functional $AZO$ thin films.