{"paper_id":"381f9383-b5a1-4cd5-a279-1995b0dcce75","body_text":"License and Terms: This document is copyright 2021 the Author(s); licensee Beilstein-Institut.\nThis is an open access work under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0). Please note that the reuse,\nredistribution and reproduction in particular requires that the author(s) and source are credited and that individual graphics may be subject to special legal provisions.\nThe license is subject to the Beilstein Archives terms and conditions: https://www.beilstein-archives.org/xiv/terms.\nThe definitive version of this work can be found at https://doi.org/10.3762/bxiv.2021.46.v1\nThis open access document is posted as a preprint in the Beilstein Archives at https://doi.org/10.3762/bxiv.2021.46.v1 and is\nconsidered to be an early communication for feedback before peer review. Before citing this document, please check if a final,\npeer-reviewed version has been published.\nThis document is not formatted, has not undergone copyediting or typesetting, and may contain errors, unsubstantiated scientific\nclaims or preliminary data.\nPreprint Title Revealing the formation mechanism and band gap tuning of Sb2S3\nnanoparticles\nAuthors Maximilian Joschko, Franck Yvan Fotue Wafo, Christina Malsi,\nDanilo Kisić, Ivana Validžić and Christina Graf\nPublication Date 15 Juni 2021\nArticle Type Full Research Paper\nSupporting Information File 1 Supporting_Information_Formation mechanism band gap tuning\nSb2S3 NP Joschko_2021.pdf; 389.8 KB\nORCID® iDs Maximilian Joschko - https://orcid.org/0000-0002-8462-8019; Franck\nYvan Fotue Wafo - https://orcid.org/0000-0002-3150-6560; Danilo\nKisić - https://orcid.org/0000-0001-5541-7020; Ivana Validžić -\nhttps://orcid.org/0000-0001-9874-8583; Christina Graf -\nhttps://orcid.org/0000-0002-3308-5640\n\n \n1 \nRevealing the formation mechanism and band gap \ntuning of Sb2S3 nanoparticles \nMaximilian Joschko1, Franck Yvan Fotue Wafo1, Christina Malsi1, Danilo Kisić2, Ivana \nValidžić 2*, and Christina Graf1* \n \nAddress: 1Hochschule Darmstadt - University of Applied Sciences, Fachbereich \nChemie- und Biotechnologie, Stephanstr. 7, D-64295 Darmstadt, Germany \n2Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, \nUniversity of Belgrade, Mike Petrovi ća Alasa 12 -14, 11351 P.O. Box 522, Belgrade, \nSerbia \n \nEmail: Prof. Dr. Ivana Validžić - validzic@vin.bg.ac.rs, Prof. Dr. Christina Graf - \nchristina.graf@h-da.de \n* Corresponding authors \n \nAbstract \nSb2S3 is a promising nanomaterial for application in solar cells and other fields of \nelectronics and optoelectronics. Sb2S3 nanoparticles were prepared via the hot -\ninjection approach. In contrast to earlier work, the reaction temperature was decreased \nto 150°C, so  that the reaction was slowed down and could be stopped at defined \nreaction stages . Thereby,  the formation mechanism of the nanomaterial and the \nassociated kinetics could be revealed. Based on morphological and structural analysis, \nit is suggested that seed particles (type 0) form immediately after injecting the antimony \nprecursor into the sulfur precursor. These seeds fuse to form amorphous nanoparticles \n\n \n2 \n(type I) that contain a lower percentage of sulfur than that corresponding to the \nexpected stoichiometric ratio of Sb2S3. The reason for this possibly lies in the formation \nof an oxygen - or carbon -containing intermediate during the seeding process. \nAfterward, the type I  nanoparticles aggregate into larger amorphous nanoparticles \n(type II) in a second hierarchical assembly process and form superordinated structures \n(type III). This process is followed by the crystallization of these particles and a layer -\nlike growth of the crystalline particles  by an Ostwald ripening process at the expense \nof the amorphous particles. It was demonstrated that the kinetic control of the reaction \nallows tuning of the optical bandgap of the amorphous nanoparticles in the range of \n2.2 – 2.0 eV. On the contrary, the optical bandgap of the crystalline particles decreases \nto a value of 1.7 eV and remains constant when the reaction progresses. Based on the \nproposed formation mechanism, future syntheses for Sb 2S3 particles can be \ndeveloped, allowing tuning the particles' properties in a broad range. In this way, the \nselective use of this material in a wide range of applications will become possible. \n \nKeywords \nSb2S3; nanoparticles; band gap; solar cells; kinetics \n \nIntroduction \nThe search for efficient, renewable energies with broad availability has become one of \nthe most important challenges of our century. With an usable radiation energy per year \nseveral times larger than the world's energy consumption [1], solar energy is a suitable \nsource for future energy supply. However, there are several requirements for materials \nto be eligible for application in the field of photovoltaics , such as  high absorption \nperformance, non-toxicity, abundance, efficiency and low cost. \n\n \n3 \nAs a semiconductor with a low bandgap and a high absorption coefficient, antimony(III) \nsulfide ( Sb2S3) has become a promising absorption material for photovoltaic \napplications [2–4]. Furthermore, the material is also suitable for various electronic and \noptoelectronic applications , such as energy storage  [5] or optical data storage  [6]. \nSb2S3 appears in two modifications: an orange, amorphous one and a grayish-black, \ncrystalline one, known as the mineral stibnite [7, 8]. \nSb2S3 nanomaterials with different morphologies and a broad distribution of band gap \nvalues were synthesized by the solvothermal [9], hydrothermal [10], and sonochemical \n[11] approach, as well as by chemical bath [12], and chemical vapor deposition  [13] \nmethod. Up to now, the syntheses of Sb2S3 nanomaterials lack sufficient control of the \ngrowth conditions. The result is nanoparticles whose size, shape and crystallinity can \nonly be tuned to a limited extent . However, for several applications, like electronic \ncircuits [14], or for transferring th e synthesis into a microreactor for continuous \nproduction [15], it is crucial to adjust these parameters. Mainly two synthesis strategies \nto gain nanoparticles with uniform size and shape have been described in the literature \nin the past two decades : the heat-up and the hot -injection method  [16]. While the \nformer is rarely applied to synthesize Sb2S3 nanoparticles [9], the hot -injection \napproach has been used in several studies [17–19]. \nSyntheses reported so far, using the hot-injection method at temperatures between \n180 and 240°C  [20, 18, 17] , yield nanoparticles not smaller than 100  nm or almost \ninstantaneously rods, tubes, or wires in micron size. \nAbulikemu et al. investigated the influence of different sulfur and antimony precursors, \ninjection (140 – 220°C) and reaction (100 – 220°C) temperatures, and the overall \nreaction times (90 s – 2.5 h) on the structural, optical, and morphological properties of \nSb2S3 nanoparticles via the hot-injection route [19]. They showed that higher injection \ntemperatures lead to smaller nuclei and higher reaction temperatures lead to larger \n\n \n4 \nparticles. Furthermore, they concluded that a chlorine -containing antimony precursor \naffects the morphology and crystallinity of the particles . Nevertheless, th e study o f \nAbulikemu et al. focuses on using bis(trimethylsilyl) sulfide (TMS) as sulfur precursor \nsince with this compound, the highest reactivity was reached. However, TMS is toxic \nand also costly compared to the widely used elemental sulfur, limiting its broad use in \nthe preparation of Sb2S3 materials [19]. \nLi et al . performed mechanistic studies on the temperature dependency of Sb2S3 \nnanoparticles in the range of 180 – 210°C to facilitate the synthesis process following \nthe hot-injection method with a sulfur-oleylamine (S-OlAm) precursor. They found that \nthe temperature influences the crystallinity, shape, and size of the particles [21]. \nThese studies revealed growth processes comprising  a primary formation of \namorphous Sb2S3 nanoparticles, which started to crystallize in an orthorhombic \nstructure and continued to grow. However, in the studies performed so far, both the \nformation of the nanoparticles and their subsequent growth occurred rapidly. Detailed \nknowledge of the exact formation and growth mechanisms and, in particular, the \nassociated kinetics of Sb 2S3 nanoparticles is therefore still lacking. Nevertheless, it is \nnecessary to understand the nanomaterial formation mechanism  to achieve control \nover the morphological and optical properties of the particles, which is crucial for their \nfurther application. \nIn the present work, a hot -injection approach at a moderate temperature (150°C) is \npresented. The reaction was analyzed in the time sections from 30 s to 30 h. A sulfur-\noleylamine precursor was selected to achieve a high reactivity while avoiding toxic \nsubstances such as TMS. A relatively low injection temperature was chosen to slow \ndown the reaction rate and, hence, increase the duration of different reaction steps and \ndecrease th e primary particle size. S ystematically, the Sb2S3 nanoparticles in the \ndifferent formation steps were analyzed regarding their morphology, crystallinity, and \n\n \n5 \noptical properties, and a detailed formation mechanism was proposed. The mechanism \ninvolves a see ding process, growth of amorphous particles, crystallization of the \nparticles, and a following growth of the crystals. The synthesis demonstrates that it is \npossible to tune the band gap of the Sb2S3 nanoparticles until the particles reach a fully \ncrystalline state. \n \nResults and Discussion \nThe Sb 2S3 nanoparticles were synthesized via a hot -injection synthesis at 150°C , \nwhere a complex consisting of Sb and 2-ethylhexanoic acid (Sb-EHA) was injected into \na sulfur-oleylamine ( S-OlAm) precursor solution.  Subsequently, the reaction took \nplace, whose course is characterized by several color changes. Immediately after \ninjecting the precursor, the clear, yellowish reaction mixture turned orange and then \nred but still stayed clear. After 2  min reaction time, the solution became turbid and \nchanged back to an orange color. Next, the mixture turned red (~20  min) and brown \n(~8 h) until it finally became greyish -black (~18 h). To follow the formation kinetics of \nthe nanoparticles, the reaction was stopped at different characteristic times by abrupt \ncooling. Afterward, the received products were washed by repeated centrifugation and \nredispersion and washing with a 2:3 volumetric mixture of chlorobenzene and 1,2 -\ndichlorobenzene (HAS) to remove excess sulfur [22]. The experiments were repeated \nat least three times to ensure reproducibility. \n \nMorphology and Structure \nAt first, t he as -synthesized products  obtained after different reaction times  were \ncharacterized by transmission electron microscopy (TEM) (Fig. 1 a -c) and scanning \nelectron microscopy (SEM) (Fig. 1 d-f). The images show that small nanoparticles (type \n\n \n6 \nI) are formed about 2 min (a) after injecting the antimony precursor Sb-EHA. The bright \norange product c ontains nanoparticles of a diameter of 33±5  nm. The nanoparticles \nare irregularly formed but, in general, spherically shaped. \nFigure 1: EM images of Sb 2S3 nanoparticles after different reaction times : (a) TEM, \n2 min; (b) TEM, 5 min; (c) TEM, 30 min; (d) SEM, 12 h; (e) SEM, 16 h; (f) SEM, 30 h. \n \nWith increasing reaction time, the dispersion turns darker and becomes more reddish. \nAfter 5 min (b), larger clusters (type II) were found, consisting of approximately 20-30 \nsmaller individual nanoparticles. The smaller nanoparticles have the same diameter as \nthe type I nanoparticles  leading to the assumption  that the former ones  were \naggregating. These aggregates tend to have a spherical shape but are somewhat \nirregularly formed. Their mean diameter is 210±30 nm. Neither the appearance nor the \nsize (220±30 nm) of the obtained nanostructures significantly changed when stopping \nthe reaction after 10 min (s. Fig. S1 (a) in the Supporting Information). \n\n\n \n7 \nAs the reaction continues, a dark red dispersion is received. While the average particle \nsize remains unchanged (210±30 nm) 30 min after the reaction was started (c), the \naggregated type I nanoparticles now  appear to have merged  as the  type II  \nnanoparticles preserved their shape, but no  individual type I nanoparticles could be \nidentified in TEM at this stage anymore. Also, the type II nanoparticles appear to have \nformed superordinated structures  (type III) . Such multistep hierarchical growth \nmechanisms were already observed for different materials such as TiO2 [23], ZnO [24], \nand Co [25]. For ZnO, Bamiduro et al. also found a merging process after stacks of \nseveral nanoplatelets had formed [24]. \nAfter 12 h, the dispersion got a brownish color and the first rod-, branch-, and urchin-\nlike particles are found (d). These particles are 2.6±0.9 µm in length with an aspect \nratio between 4 and 5  and resemble the type III structures . Still, t here are mainly \nparticles of the prior stage remaining. \nThe crystalline rods grow apparently at the expense  of the spherical , amorphous  \nnanoparticles (see XRD below) in an Ostwald ripening process . This assumption is \nsupported by the decreasing diameter of these nanoparticles from 22 0±30 nm to \n150±40 nm, which one can see in Fig. 2, as the reaction progresses from 12 h to 16 h \n(e) and their decreasing amount (s. Fig. S2 in the Supporting Information) . At this \nstage, the rods have a length of 5.7±1.8 µm. Rod-like crystal growth by the dissolution \nof spherical, amorphous nanoparticles was already suggested by Validžić et al.  for \nsimilar processes at a higher temperature [20], supporting this assumption. \n \n\n \n8 \nFigure 2: Histograms showing the size distribution of the spherical, amorphous  \nparticles in the samples obtained after 12 and 16  h, respectively. A decreasing \ndiameter with progressing reaction time is  visible and likely due to Ostwald ripening.  \nThe size distribution curves were calculated assuming a Gaussian distribution. \n \nThe rods grow anisotropically, i.e., preferentially in the longitudinal direction, as shown \nby the changing aspect ratio from ~4 -5 to ~6  after 12 h and 16  h, respectively. This \nobservation agrees with the findings of authors who describe a growth along the c-axis \nof Sb2S3 nanomaterial [26, 27] . This anisotropic growth corresponds to the \northorhombic structure of stibnite, the crystalline modification of Sb2S3 [28]. \nAfter 18 h (s. Fig. S1 (b) in the Supporting Information), the solution got grayish-black \nand no more spherical particles were found. The size of the rods obtained after 18 h is \nidentical compared to that in the sample after 30  h within the measurement \nuncertainties (5.5±1.9 µm and 5.4±1.6 µm). Histograms of the length and width \ndistribution of the crystalline particles obtained after 16, 18, and 30  h can be found in \nFig. S3 in the Supporting Information. \nTEM images of growing rods show layered structures (s. Fig. S 4 in the Supporting \nInformation) with bristle-shaped tips, which get more distinct with increasing reaction \ntime (s. Fig. S5 Supporting Information). The bristles become thicker but do not appear \n\n\n \n9 \nto change in length at reaction times between 16 to 30  h. These findings suggest a \nfiber-like growth at the tips and a layered growth around the individual bristles and the \nwhole rod. However, the particles do not seem to be bundles of nanowires, leading to \nthe assumption that the different, fiber -like growing parts of one particle are fusing. \nSince the tips remain their bristle-like shape, even after the growth stops after 18  h \nreaction time , a merging process is excluded. The growth of individual particle \nfragments, such as the bristles, was described in the literature as a dendrite -like \nsplitting or branching of primary particles in an autoclave synthesis with ethylene glycol \nor polyethylene glycol as solvent [29, 30]. The authors reasoned the cleavage at the \nparticle tips by weak van -der-Waals forces between (Sb 4S6)n chains, of which the \nparticles consist, or by strongly bound ligands interfering with the crystal growth, \nrespectively. However, as crystal growth is a kinetically controlled  process, mild \nreaction conditions lead to delayed growth in the preferred direction , and the other \ncrystal planes also grow. Hence, it is likely that integration of the dissolving amorphous \nparticles will fuse the fibers of the crystalline ones.  This behavior was also found by \nValidžić et al. in a different approach of synthesizing Sb 2S3 nanoparticles at a higher \ntemperature (240°C) [31]. \nTable 1 gives an overview of the characteristics of the particles received after different \nreaction times. One can see the size of the amorphous nanoparticles/aggregates, the \nsize and aspect ratios  of the crystalline particles, as well as the corresponding molar \nratios of Sb and S obtained by EDX, and the associated band gaps obtained by \nreflectance measurements (s. discussion of the optical data below). \n \n \n \n\n \n10 \nTable 1: Time-dependent characteristics of Sb2S3. \nReaction \ntime \nSize amorphous \nparticle/aggregate \n(nm) \nCrystalline \nparticles' length \n(µm) \nCrystalline \nparticles' width \n(µm) \nMolar ratio \nSb:S \n(EDX) \nBandgap \n±0.03 \n(eV) \n2 min 33±5 - - 48:52 2.18 \n5 min 210±30 - - 41:59 2.12 \n10 min 220±30 - - 41:59 2.07 \n30 min 210±30 - - 38:62 2.07 \n12 h 220±30 2.6±0.9 0.6±0.2 41:59 2.01/1.68a \n16 h 150±40 5.7±1.8 1.0±0.3 40:60 -/1.72b \n18 h - 5.5±1.9 1.0±0.4 40:60 1.72 \n30 h - 5.4±1.6 1.0±0.3 39:61 1.71 \naThe two band gaps correspond to an amorphous and a crystalline species present in the sample  (s. \nmain text for details). \nbThe amorphous fraction in this stage is too small to cause a visible slope in the reflectance spectrum. \n \nX-ray powder diffraction (XRPD) measurements  of an orange -red (30  min) and a \ngrayish-black (18  h) sample were exemplarily  performed to examine the samples ' \nstructures. The diffractograms shown in Fig. 3 reveal a low crystallinity for the sample \nobtained after 30 min (Fig. 3 (a)) as no specific diffraction peaks are found, and a high \ncrystallinity in accordance with the stibnite structure  (COD 9003460) for the sample \nobtained after 18h (Fig. 3 (b)). These results show that the rather spherically shaped \norange nanoparticles are mainly amorphous and crystallize into rod-like, grayish-black \nparticles. \n\n \n11 \nFigure 3: X-ray diffractograms of a sample after a reaction time of (a) 30 min and (b) \n18 h (red lines are corresponding to stibnite, COD 9003460). \n \nThus, the kinetics of the reaction progress can be followed by the dispersion color. As \nlong as there are only amorphous structures present, the dispersion has an orange -\nred appearance. We assume that some of the a morphous, orange -red type III \nstructures act as crystallization nuclei after 7-9 h. The particles start to crystallize in the \nshape of the  superordinated type III structures described previously , leading to a \nbrownish color. Owing to the preferred growth direction, rods, branch-like, or urchin -\nlike stibnite particles are finally received, which have a grayish-black appearance. \n \nA major advantage of slowing down the reaction kinetics is the possibility of looking at \nthe early stage of the reaction. Therefore, i n addition to the experiments described \nabove, the reaction was also stopped after 30 s when the solution was still transparent. \nIn this case, next to nanoparticles of a similar size and shape as the type I nanoparticles \nobtained after 2  min, an even smaller species of seed particles  (type 0)  could be \nobserved (Fig. 4 (a)). These type 0 seed particles are 5-10 nm in size and seem to \nassemble into the larger type I nanoparticles as the latter ones have a raspberry-like \nappearance (Fig. 4 (a) and (b)). The larger nanoparticles have sizes between 15 and \n\n\n \n12 \n35 nm (Fig. 4 (b)), with the particle fraction of a size around 35  nm found more \nfrequently (Fig. 4 (c)). Together with the finding that the type I nanoparticles are also \naround 35  nm in diameter  (s. Fig. 1) , this leads to the assumption that there is an \naggregation and merging step from the type 0 to the type I nanoparticles additional to \nthe one occurring from the type I to the type II nanoparticles . Thus, there is a double \nhierarchical assembly and subsequent merging process of the amorphous \nnanoparticles. \nIt was not possible to isolate visible nanoparticles immediately after injection. \nFigure 4: Nanoparticles obtained after 30 s reaction time: (a) small, individual \nnanoparticles, (b) raspberry-like, larger nanoparticles , intermediate state, and (c) \nraspberry-like, larger nanoparticles, final state. \n \nAtomic force microscopy (AFM) as an additional method of size determination was \napplied to confirm the TEM results of the sample obtained after 30  s reaction time. \nAFM enables imaging of the nanoparticles under milder conditions than TEM and \nambient conditions so that thermal damage of the nanostructures due to the electron \nbeam can be excluded [32]. The data of the AFM measurements are displayed in Fig. \n4. \n\n\n \n13 \nOn the one hand, one can see single deflection peaks in Fig. 5 (a), which are  \n1.5 and 2.3 nm in width (green and red marks) . On the other hand,  Fig. 5 (b) shows \nfour deflection peaks directly next to each other. The peaks' width is about 3.5 nm (red \nmark), and they appear rather individually. It is suggested that these single deflection \npeaks correspond to the type 0 nanoparticles already found in TEM (Fig. 4 (a)). The \nsize difference to the TEM data  is likely due to damage by the electron beam, which \ncauses the particles to appear larger. Consequently, the stacked deflection peaks (Fig. \n5 (b), 14.7 nm, red + green mark) correspond to a nanoparticle cluster similar to those \nfound in Fig. 4 (b).  \nFigure 5: AFM measurements of n anoparticles obtained after 30 s reaction time: (a) \nindividual single nanoparticles and (b) cluster of small nanoparticles of about the same \nsize as the individual ones in (a) . Both images are taken from the same sample.  The \nresults contain the measured area with height differences displayed in different \nbrightness, a height evaluation along a drawn line (lever deflection in ° vs. distance in \nnm), and a sum-up of marked distances along the drawn line. The particle/cluster size \nis given as the horizontal distance (Horiz distances(L)).  \n \n\n\n \n14 \nChemical composition \nTo confirm the XRD results for stibnite and to examine the amorphous particles ' \ncomposition, an energy dispersive x-ray (EDX) analysis was performed in conjunction \nwith SEM for selected samples obtained after reaction times from 2 min to 30h. It was \nnot possible to examine the samples obtained after  30 s since the yield is too low at \nthis reaction stage . The sample, which reacted for 2  min (Fig. 6 (a)), contained less \nsulfur than expected by the stoichiometric ratio of Sb 2S3. However, the results of the \nsamples obtained after  reaction times between  5 min and 30 h are all in good \nagreement with the stoichiometric ratio of antimony and sulfur in Sb2S3 (Tab. 1, Fig. 6 \n(b), and Fig. S6 in the Supplementary Information). \n \nFigure 6: EDX spectr a of the nanoparticles obtained after  (a) 2 min and (b) 5 min \nreaction duration. The samples were measured on a carbon-coated copper grid on an \naluminum holder, explaining the detection of these elements. Oxygen may have been \ndetected due to contamination of the sample, the grid or the holder. \n \nThe non-stoichiometric Sb:S ratio  in the early reaction stage is probably due to  the \noleylamine used in the synthesis. Several authors have already described  that \nhydrolysis of antimony in fatty amine s can lead to the formation of  Sb2O3 [33–35]. \nBaum et al. obtained cubic α-Sb2O3 (senarmontite) when they performed a synthesis \n\n\n \n15 \nto obtain copper thioantimonate,  by injecting a heated (60°C) and degassed S -OlAm \nprecursor into a heated (200-250°C) and degassed mixture of Cu(I)Cl, Sb(III)Cl 3, and \nOlAm, but omitted both sulfur and Cu(I)Cl [33]. In contrast, they could synthesize the \ndesired copper thioantimonate when they used Sb 2O3 instead of Sb(III)Cl 3 in a \nfollowing synthesis. They concluded that Sb 2S3 works as an intermediate product \nrather than as a byproduct. \nTo show that antimony oxide can also be formed under the reaction conditions used in \nthis work, the Sb precursor was injected directly into the oleylamine at 150°C without \nadding sulfur, and the solution turned white immediately.  Fig. 7 shows the SEM and \nXRD results of the white product obtained by this reaction. The yielded nanoparticles \nare 6 0±15 nm in diameter and can be assigned to the cubic α-phase of Sb2O3, \nsenarmontite (COD 1011201). \nFigure 7: Measurement results of the white product obtained by the direct injection of \nthe Sb precursor into oleylamine at 150°C without the addition of sulfur: (a) SEM image \nand (b) XRD pattern (Red line s are corresponding to the diffraction peaks of \nsenarmontite, COD 1011201). \n \nThese results indicate that the first species formed consist of a compound of antimony, \nsulfur, and oxygen, with the oxygen being replaced by sulfur with increasing reaction \n\n\n \n16 \ntime while the nanoparticles transform  into pure Sb 2S3. This species could act as an \nintermediate for the particles formed at later stages or as an intermediate species \nformed parallel to the main reaction. It is also possible that initially , a species forms, \nwhich contains antimony, sulfur and carbon -residues from the precursors , as it has \nbeen found in high -temperature seeding process es from other  metallo-organic \nsyntheses [36]. A changing chemical composition could also be a reason for the \nnanoparticles to undergo a second hierarchical assembly.  A similar behavior was \nfound by Liu et al., who synthesized cobalt particles with a cobalt alkoxide intermediate \n[25]. \n \nFig. 8 summarizes the results discussed above and suggests a growth mechanism for \nSb2S3: Instantly after injecting the colorless Sb-EHA precursor into the clear yellowish \nS-OlAm precursor solution at 150°C, the reaction mixture turns orange before it turns \nred about 30 s later but stayed clear. At this stage, type 0 seed particles of a size of 2-\n4 nm (diameter determined by AFM) are formed, which assemble into 20-40 nm large \nclusters. These particle s are amorphous and do not have a stoichiometric ratio \ncorresponding to Sb 2S3. When 2 min have passed, the mixture bec omes turbid and \nchanges back to an orange color. The clustered type 0 seeds merged into type I  \nnanoparticles of about 3 5 nm in diameter , which begin to aggregate  again into \nspherical structures of about 200  nm in size.  At this point, the particles ' chemical \ncomposition complies with Sb 2S3. The color becomes darker and start s turning red \n(~20 min) since the aggregates merge into type II particles which seem to assemble \ninto the superordinated type III structures. After 7-9 h, the solution becomes brownish. \nMost likely, this is the point at which significant crystallization begins  as some of the \namorphous type III structures act as crystallization nuclei. The orthorhombic crystals \n\n \n17 \ngrow, probably at the expense of the amorphous particles, until a grayish-black mixture \nof crystalline material without spherical, amorphous particles (~18 h) is finally obtained. \n \nFigure 8: Growth scheme of Sb2S3. After injection, type 0 seeds (yellow) are formed, \nwhich turn into small type I amorphous nanoparticles (orange). These small particles \naggregate and merge into type II nanoparticles (red), which assemble into \nsuperordinated type III structures before crystallizing. The crystals (black) grow at the \nexpense of the amorphous nanoparticles in an Ostwald ripening process. \n \nOptical characterization  \nThe materials ' optical properties were measured by reflectance spectroscopy and \nanalyzed by applying the Tauc plot to receive the band gap values of the material [37, \n38]. As shown in Eq. 1, the absorption coefficient α is expressed by the Planck constant \nh, the photon 's frequency ν, a constant B, which Davis and Mott described as the \nmagnitude of the optical absorption constant [38], and a transition factor γ: \n(𝛼ℎ𝜈)\n1 𝛾⁄ = 𝐵(ℎ𝜈 − 𝐸𝑔) (1) \n \nThe transition factor γ depends on the type of the band gap transition. It equals 1/2 for \na direct allowed transition and 2 for an indirect allowed transition. \n\n\n \n18 \nFor reflectance data, α is expressed by the Kubelka-Munk function F(R∞) (Eq. 2), which \nis the quotient of the absorption coefficient k and the scattering coefficient s, which, in \nturn, is correlated to the reflectance of an infinitely thick specimen R∞ [39]: \n𝐹(𝑅∞) = 𝑘\n𝑠 = (1 − 𝑅∞)2\n2𝑅∞\n (2) \n \nIn the literature, there are different opinions regarding the type of electron transition of \nSb2S3. Some authors assume a direct transition for the amorphous and the crystalline \nmaterial [30, 40, 41], while others propose an indirect transition [42–45]. \n \nHowever, amorphous materials exhibit neither an indirect nor a direct transition as \nthese materials are highly disordered and do not have a band structure based on the \nBloch theorem. Nevertheless, the electronic states in amorphous materials can be \ndivided into loca lized and delocalized states, forming a so -called mobility gap  [46]. \nInitially, the Tauc  plot (Eq. 1) was used to calculate band gap values for  amorphous \nmaterials, i.e. , mobility gaps , with a transition factor γ equal to 2  [37]. Hence, an \namorphous materi al can mathematically be treated as a material with an indirect \nallowed transition. \n \nFor crystalline Sb 2S3, Filip et al.  [47] and Vadapoo et al.  [48] did first -principle \ncalculations of the band structures. Both found indirect transitions as energetically \nmost favorable but with only a little difference to a direct transition. They concluded \nthat the direct transition w ould most likely be dominant, especially at ambient \ntemperature. Filip et al. defined the band gap as \"effectively direct gap\". Therefore, and \nbecause most references assume a direct transition, the transition will be considered  \n\n \n19 \na direct one  in the present work. In contrast, Validžić et al. performed calculations \nbased on the density functional theory and found a direct band gap [31]. \n \nThe measured reflectance data can be seen in Fig. 9 (a). They show that the onsets \nof the spectra of the different samples shift towards higher wavelengths with increasing \nreaction time. The spectrum obtained after 12 h reaction time exhibits two slopes at \nλ < 670 nm and λ  > 670 nm, likely due to amorphous and crystalline particles' \nsimultaneous presence. Although SEM images indicate (see Fig. 1 (e)) that the sample \nobtained after 16  h still contains some amorphous particles, their influence on the \noptical behavior seems negligible since the second slope is no more visible. \nFig. 9 (b) and (c) show the Tauc plots of the amorphous and crystalline samples. The \ntwo slopes of the sample obtained after 12 h reaction time were fitted individually as \nindirect and direct transition, assuming that the first slope (λ < 670 nm) corresponds to \nthe amorphous and the second slope (λ > 670 nm) to the crystalline particles. As one \ncan see, the band g ap value s change throughout the different samples (values in \nTab. 1) and depend on the reaction time and crystallinity of the sample. While the \nparticles after 2 min reaction time have a band gap value of 2.18  eV, this value \ndecreases to 2.01 eV after 12 h.  \n\n \n20 \nFigure 9: Optical characterization of Sb 2S3 samples obtained after different reaction \ntimes: (a) reflectance spectra, (b) Tauc plots of the spectra of the amorphous particles, \nand (c) Tauc plots of the spectra of the crystalline particles. All spectra were normalized \nto the maximum intensity. The band transitions of the amorphous particles are treated \nas allowed, indirect transitions, while the transitions of the crystalline material  are \nconsidered to be allowed, direct transitions. Tangents were drawn at the slope of each \ngraph to estimate the band gap value.  The sample obtained after 12  h reaction time \nexhibits two slopes which correspond to the absorption of amorphous (λ < 670 nm) \nand crystalline (λ > 670 nm) particles present. \n\n\n \n21 \n \nThere are already different band gap values reported for amorphous Sb 2S3 \nnanomaterials. For example, Abulikemu et al. reported a value of 2.15 eV while Wang \net al. reported 2.02 eV for nanoparticles received from a hot-injection synthesis using \ndifferent solvents [19, 17]. Variation in band gap values is also known to occur in other \namorphous semiconductors, e.g., amorphous, hydrogenated silicon. This is explained \nby different preparation conditions [49]. Different formation mechanisms can lead to \ndifferent bonding lengths and angles in an amorphous material and , therefore, to a \ndifferent mobility gap [46]. Hence, a decreasing mobility gap  suggests that an \nelectronic relaxation process occurs after longer reaction times. The band fluctuations \nand the bonding lengths and angles get closer to the band  and material structure of \nthe corresponding crystalline modification until crystallization itself starts.  \nThe material shows a different band gap energy after the crystallization has started. \nAll samples containing crystalline particles have a band gap energy of around 1.70 eV, \nindependent of the reaction time. This value agrees well  with previously reported \nvalues for crystalline Sb2S3 particles of a similar size [50]. \n \nConclusion \nThe formation mechanism of Sb2S3 nanoparticles via a hot-injection synthesis at 150°C \nis revealed. In this way, we could gain a more in -depth insight into the kinetics of \nparticle formation, while earlier studies of Abulikemu et al. and Li et al.  were focusing \non the temperature-dependent evolution of Sb2S3 particles. The suggested mechanism \nassumes that seeds (type 0 particles) are formed directly after injecti ng the antimony \nprecursor into the sulfur precursor. These seeds merge into type I  amorphous \nnanoparticles containing a smaller percentage of sulfur than the  expected \n\n \n22 \nstoichiometric ratio of Sb and S, possibly due to oxygen being involved in the seeding \nprocess. Subsequently, the type I nanoparticles aggregate into type II nanoparticles \nand form superordinated type III structures that finally crystallize in an orthorhombic \ncrystal structure. \nFurthermore, the kinetic control of the reaction enables tuning of the optical band gap \nof the amorphous material in the range of 2.18±0.03 to 2.01±0.03  eV. In contrast, the \noptical band gap of the crystalline particles decreased to a value of 1.71±0.03 eV and \ndid not change any further. The reduction of the mobility gap of the amorphous states \nof the particles is likely due to a n electronic relaxation effect with increasing reaction \ntime. \nWith the  knowledge provided by this study , different strategies can be developed  \ncapable of controlling the size of the amorphous and cry stalline particles on a n even \nbroader range than it has been  done up to now. In this way,  the customizable \napplication of Sb 2S3 nanomaterial in solar cells and other fields of electronics and \noptoelectronics will be enhanced. \n \nExperimental  \nAll experiments were carried out using standard glass equipment. The reaction vessels \nwere cleaned before use with nitric acid (65 vol. %, VWR Chemicals) and were \nsubsequently repeatedly rinsed with deionized ( DI) water. The nanoparticles were \nredispersed using an ultrasonic bath (Sonorex RK512H (860 W, 35 kHz) from \nBandelin). A controlled heating rate and temperature in the reaction vessel was \nachieved by a temperature controller (LTR 3500, Juchheim Solingen). Injections into \nthe reaction vessel were performed with a 14 gauge cannula (L = 200 mm, neoLab). \n \n\n \n23 \nMaterials \nAntimony(III) chloride (Sb(III)Cl3, >99.95 %), sulfur (S, 99.98 %), 2-ethylhexanoic acid \n(EHA, >99 %), paraffin oil (visc. liq., d = 0.827 -0.890 g/mL), oleylamine (OlAm, 70 %) \nand isopropyl alcohol (IPA, 99.5 %) were obtained by Sigma-Aldrich. Hexane (>98 %) \nwas purchased by Alfa Aesar, chlorobenzene (>99  %) by Merck KGaA, and 1,2 -\ndichlorobenzene (>98 %) by Fisher Scientific. All chemicals were used without further \npurification.  \n \nSynthesis \nUndoped Sb2S3 nanoparticles \nAll reaction steps were performed under an argon atmosphere. \nPrior to the reaction, two precursor solutions were freshly prepared. First, the sulfur \nprecursor, an S-OlAm solution, was produced by dissolving 1.5 mmol elemental sulfur \nin 6 mL OlAm via sonification in an ultrasonic bath for 10 min. Afterward, 25 mL paraffin \noil was added. The solution was heated to 150°C with a heating rate of 3.3 K/min under \nmagnetic stirring (800  rpm). Second, an Sb(III) complex solution was prepared by \nadding 1 mmol Sb(III)Cl3 to 5 mL EHA. The mixture was magnetically stirred (750 rpm) \nand heated up to 90°C in an oil bath. \nWhen both precursor solutions reached the desired temperatures, the Sb precur sor \nwas swiftly injected into the S precursor solution, and the reaction mixture was kept \nunder magnetic stirring (800 rpm) at 150°C for 60 s to 30 h.  \nTo stop the reaction, the heating mantle under the reaction vessel was replaced by an \nice bath, and 15 mL hexane was injected into the reaction. The received product was \n\n \n24 \nprecipitated by adding 30 mL IPA and separated by centrifugation at 50 -2500 g for 5-\n20 min (depending on the reaction time ; for details, s . Tab. S1 in the Supporting \nInformation). The precipitate was redispersed in 20 mL of a 2:3 mixture (volumetric) of \nchlorobenzene and 1,2 -dichlorobenzene (HAS) [22]. Precipitation and centrifugation \nwere repeated twice. For the second redispersion step, 20 mL hexane instead of HAS \nwas used. Finally, the nanoparticles were redispersed in 20 mL IPA. \n \nCharacterization \nScanning electron microscopy (SEM) \nSEM images were recorded with a Hitachi SU 5000 scanning electron microscope in \nSE mode with an electron acceleration voltage of 15 kV and a spot intensity of 40. The \nworking distance was 3 mm. A droplet of a dispersion (c = 1.5-2 g/L) of the particles in \nIPA was dried on a carbon -coated copper grid ( carbon-coating type A, 6 -10 nm \nthickness, Cu 200 mesh, Plano GmbH).  The software FIJI was used to evaluate the \nparticle size for 200-300 particles per synthesis on several images [51]. \n \nTransmission electron microscopy (TEM) \nA Zeiss EM 109 was used at 80  kV acceleration voltage to record the TEM images. \nThe grid preparation and image processing were performed as stated above for SEM. \n \nAtomic force microscopy (AFM) \nAtomic force microscopy (AFM) was performed with a Multimode quadrex SPM with \nNanoscope IIIe controller (Veeco Instrument Inc) operated under ambient conditions \nto determine the particle size using the sample in the form of a highly diluted solution. \n\n \n25 \nThe drive frequency was kept constant during the imaging, while the drive amplitude \nwas set to 7171 mV. \n \nEnergy-dispersive X-ray analysis (EDX) \nElemental analysis was performed with an EDAX X -ray detector (Octane Elect Plus) \nattached to the SEM.  The SEM was run with an acceleration voltage of 15  kV and a \nspot intensity of 50. The working distance was 10  mm. The resolution of the detector \nwas 126.2 eV. \n \nReflectance measurements \nReflectance measurements were performed with a Cary 5000 UV -Vis-NIR \nspectrometer (Agilent Technologies) equipped with an integrating sphere  (internal \nDRA 2500). Particles were measured as a dispersion in IPA (c = 2-2.5 g/L) in standard \ncuvettes made of special optical glass (OS, Hellma) in the range of 400 to 850 nm. \nAt 800 nm, the instrument's detector changes, which causes a small artifact at this \nwavelength. While this artifact is visible in Fig. 7 (a), it gets negligible in Fig. 7 (b) and \n(c) because it corresponds to an energy of 1.55 eV, which is not in a relevant range for \nthe band gap analysis of the measured samples, and the intensity decreases to a non-\nvisible level. The estimation of the accuracy of the Tauc method was based on a study \nby Viezbicke et al. , who evaluated the accuracy of the Tauc plot for 120 individual \nanalyses of polycrystalline ZnO and found a deviation of about 0.03 eV [52]. \n \nX-ray diffraction spectrometry (XRD) \nFor XRD measurements, a minimum amount of 10 mg of dried particles was used. The \nsamples were measured in a capillary in transmission geometry. \n\n \n26 \nTwo different diffractometers were used to perform the measurements. The first XRD \ndevice was a Bruker D8 Advanced equipped with a LYNXEYE XE-T detector and a Cu \nKα1 radiation source (40 kV, 40 mA) with a radiation wavelength of 0.15405  nm. The \nangle range of the measurements was 6-80° 2θ with a step size of 0.025°. The second \ndevice was a STOE STADI P equipped with a Dectris MYTHEN2 R detector and a Cu \nKα1 radiation source (40 kV, 40 mA) with a radiation wavelength of 0.15405  nm. The \nangle range of the measurements was 6-96° 2θ with a step size of 0.015°. \n \nSupporting Information \nSupporting Information: \nFile Name: Sb2S3_NP_Supporting Information.pdf \nFile Format: PDF \nTitle: Additional SEM and TEM images, EDX data, and synthesis details \n \nAcknowledgments \nWe thank Dr. Michael Evans from Bruker Corporation and Michael Teck from STOE & \nCie GmbH for recording the X-ray diffractograms. \n \nFinancial Support \nThe research was funded by the Bilateral project between the Federal Republic of \nGermany and the Republic of Serbia, funded by the Serbian Ministry of Education, \nScience and Technological Development  (grant 451-03-01971/2018-09/19) and the \nGerman Academic Exchange Service (DAAD) within the PPP Serbia program (grant \n57447826). This work was supported by a fellowship of the Platform for Ph. D. students \n\n \n27 \nof the Technical University of Darmstadt and the Darmstadt University of Applied \nSciences. \n \nReferences \n1. Smil, V.; OECD Observer 2006,19, 22–24. \n2. Versavel, M. Y.; Haber, J. A. Thin Solid Films 2007, 515, 7171–7176. \ndoi:10.1016/j.tsf.2007.03.043 \n3. Tang, R.; Wang, X.; Jiang, C.; Li, S.; Jiang, G.; Yang, S.; Zhu, C.; Chen, T. J. \nMater. Chem. A 2018, 6, 16322–16327. doi:10.1039/C8TA05614E \n4. Validžić, I. L.; Janošević, V.; Mitrić, M. Environ. Prog. Sustainable Energy 2016, \n35, 512–516. doi:10.1002/ep.12221 \n5. Cao, F.; Liu, W.; Zhou, L.; Deng, R.; Song, S.; Wang, S.; Su, S.; Zhang, H. Solid \nState Sciences 2011, 13, 1226–1231. \ndoi:10.1016/j.solidstatesciences.2011.02.007 \n6. Shaji, S.; Arato, A.; O'Brien, J. J.; Liu, J.; Castillo, G. A.; Palma, M. I. M.; Roy, T. \nK. D.; Krishnan, B. J. Phys. D: Appl. Phys. 2010, 43, 75404. doi:10.1088/0022-\n3727/43/7/075404 \n7. Itzhaik, Y.; Niitsoo, O.; Page, M.; Hodes, G. J. Phys. Chem. C 2009, 113, 4254–\n4256. doi:10.1021/jp900302b \n8. Zakaznova-Herzog, V. P.; Harmer, S. L.; Nesbitt, H. W.; Bancroft, G. M.; \nFlemming, R.; Pratt, A. R. Surf. Sci. 2006, 600, 348–356. \ndoi:10.1016/j.susc.2005.10.034 \n9. Lou, W.; Chen, M.; Wang, X.; Liu, W. Chem. Mater. 2007, 19, 872–878. \ndoi:10.1021/cm062549o \n\n \n28 \n10. Ota, J.; Roy, P.; Srivastava, S. K.; Nayak, B. B.; Saxena, A. K. Cryst. Growth \nDes. 2008, 8, 2019–2023. doi:10.1021/cg701133b \n11. Salinas-Estevané, P.; Sánchez, E. M. Cryst. Growth Des. 2010, 10, 3917–3924. \ndoi:10.1021/cg100365z \n12. Salem, A. M.; Selim, M. S. J. Phys. D: Appl. Phys. 2001, 34, 12–17. \ndoi:10.1088/0022-3727/34/1/303 \n13. Murtaza, G.; Akhtar, M.; Azad Malik, M.; O'Brien, P.; Revaprasadu, N. Mater. Sci. \nSemicond. Process. 2015, 40, 643–649. doi:10.1016/j.mssp.2015.07.038 \n14. Talapin, D. V.; Lee, J.-S.; Kovalenko, M. V.; Shevchenko, E. V. Chem. Rev. \n2010, 110, 389–458. doi:10.1021/cr900137k \n15. Yao, X.; Zhang, Y.; Du, L.; Liu, J.; Yao, J. Renewable Sustainable Energy Rev. \n2015, 47, 519–539. doi:10.1016/j.rser.2015.03.078 \n16. Kwon, S. G.; Hyeon, T. Small 2011, 7, 2685–2702. doi:10.1002/smll.201002022 \n17. Wang, W.; Strössner, F.; Zimmermann, E.; Schmidt-Mende, L. Sol. Energy \nMater. Sol. Cells 2017, 172, 335–340. doi:10.1016/j.solmat.2017.07.046 \n18. Deng, Z.; Mansuripur, M.; Muscat, A. J. Nano Lett. 2009, 9, 2015–2020. \ndoi:10.1021/nl9002816 \n19. Abulikemu, M.; Del Gobbo, S.; Anjum, D. H.; Malik, M. A.; Bakr, O. M. J. Mater. \nChem. A 2016, 4, 6809–6814. doi:10.1039/c5ta09546h \n20. Validžić, I. L.; Abazović, N. D.; Mitrić, M. Met. Mater. Int. 2012, 18, 989–995. \ndoi:10.1007/s12540-012-6010-7 \n21. Li, L.; Yang, L.; Fu, B.; Li, Z. Bull Mater Sci 2020, 43. doi:10.1007/s12034-020-\n02121-7 \n22. Wang, R.; Shen, B.; Sun, H.; Zhao, J. J. Chem. Eng. Data 2018, 63, 553–558. \ndoi:10.1021/acs.jced.7b00699 \n\n \n29 \n23. Roca, R. A.; Leite, E. R. J. Am. Ceram. Soc. 2013, 96, 96–102. \ndoi:10.1111/jace.12078 \n24. Bamiduro, F.; Ward, M. B.; Brydson, R.; Milne, S. J. J. Am. Ceram. Soc. 2014, \n97, 1619–1624. doi:10.1111/jace.12809 \n25. Liu, Q.; Guo, X.; Li, Y.; Shen, W. J. Phys. Chem. C 2009, 113, 3436–3441. \ndoi:10.1021/jp8081744 \n26. Geng, Z. R.; Wang, M. X.; Yue, G. H.; Yan, P. X. J. Cryst. Growth 2008, 310, \n341–344. doi:10.1016/j.jcrysgro.2007.10.052 \n27. Zhang, L.; Chen, L.; Wan, H.; Zhoul, H.; Chen, J. Cryst. Res. Technol. 2010, 45, \n178–182. doi:10.1002/crat.200900535 \n28. Wang, H.; Lu, Y.-N.; Zhu, J.-J.; Chen, H.-Y. Inorg. Chem. 2003, 42, 6404–6411. \ndoi:10.1021/ic0342604 \n29. Tao, W.; Wang, J.; Wu, D.; Chang, J.; Wang, F.; Gao, Z.; Xu, F.; Jiang, K. Dalton \nTrans. 2013, 42, 11411–11417. doi:10.1039/c3dt51439k \n30. Wang, G.; Cheung, C. L. Mater. Lett. 2012, 67, 222–225. \ndoi:10.1016/j.matlet.2011.09.074 \n31. Validžić, I. L.; Mitrić, M.; Abazović, N. D.; Jokić, B. M.; Milošević, A. S.; Popović, \nZ. S.; Vukajlović, F. R. Semicond. Sci. Technol. 2014, 29, 35007. \ndoi:10.1088/0268-1242/29/3/035007 \n32. Grobelny, J.; DelRio, F. W.; Pradeep, N.; Kim, D.-I.; Hackley, V. A.; Cook, R. F. \nMethods Mol. Biol. 2011, 697, 71–82. doi:10.1007/978-1-60327-198-1_7 \n33. Baum, F.; Pretto, T.; Brolo, A. G.; Santos, M. J. L. Cryst. Growth Des. 2018, 18, \n6521–6527. doi:10.1021/acs.cgd.8b00667 \n34. Christian, P.; O'Brien, P. J. Mater. Chem. 2005, 15), 4949. doi:10.1039/b511952a \n35. Zou, Y.; Jiang, J. Mater. Lett. 2014, 123, 66–69. doi:10.1016/j.matlet.2014.02.069 \n\n \n30 \n36. Bronstein, L. M.; Huang, X.; Retrum, J.; Schmucker, A.; Pink, M.; Stein, B. D.; \nDragnea, B. Chem. Mater. 2007, 19, 3624–3632. doi:10.1021/cm062948j \n37. Tauc, J.; Grigorovici, R.; Vancu, A. Phys. Stat. Sol. (b) 1966, 15, 627–637. \ndoi:10.1002/pssb.19660150224 \n38. Davis, E. A.; Mott, N. F. Philos. Mag. 1970, 22, 903–922. \ndoi:10.1080/14786437008221061 \n39. Kubelka, P.; Munk, F. Z. Tech. Phys. 1931, 593–601. \n40. Han, Q.; Sun, S.; Sun, D.; Zhu, J.; Wang, X. RSC Adv. 2011,, 1364. \ndoi:10.1039/c1ra00379h \n41. Lei, H.; Lin, T.; Wang, X.; Zhang, S.; Cheng, Q.; Chen, X.; Tan, Z.; Chen, J. \nMater. Lett. 2018, 233, 90–93. doi:10.1016/j.matlet.2018.08.058 \n42. Gao, C.; Huang, J.; Li, H.; Sun, K.; Lai, Y.; Jia, M.; Jiang, L.; Liu, F. Ceram. Int. \n2019, 45, 3044–3051. doi:10.1016/j.ceramint.2018.10.155 \n43. Yesugade, N. S.; Lokhande, C. D.; Bhosale, C. H. Thin Solid Films 1995, 263, \n145–149. doi:10.1016/0040-6090(95)06577-6 \n44. Ţigaˇu, N.; Gheorghieş, C.; Rusu, G. I.; Condurache-Bota, S. J. Non-Cryst. Solids  \n2005, 351, 987–992. doi:10.1016/j.jnoncrysol.2004.12.014 \n45. Perales, F.; Lifante, G.; Agulló-Rueda, F.; Heras, C. d. l. J. Phys. D: Appl. Phys. \n2007, 40, 2440–2444. doi:10.1088/0022-3727/40/8/005 \n46. Kasap, S.; Capper, P. Springer Handbook of Electronic and Photonic Materials; \nSpringer International Publishing: Cham, 2017. \n47. Filip, M. R.; Patrick, C. E.; Giustino, F. Phys. Rev. B 2013, 87. \ndoi:10.1103/PhysRevB.87.205125 \n48. Vadapoo, R.; Krishnan, S.; Yilmaz, H.; Marin, C. Nanotechnology 2011, 22, \n175705. doi:10.1088/0957-4484/22/17/175705 \n\n \n31 \n49. Pyshkin, S. L.; Ballato, J. Long-Term Convergence of Bulk- and Nano-Crystal \nProperties; INTECH Open Access Publisher, 2011. doi: 10.5772/21418 \n50. Chao, J.; Liang, B.; Hou, X.; Liu, Z.; Xie, Z.; Liu, B.; Song, W.; Chen, G.; Di Chen; \nShen, G.  Opt. Express 2013, 21, 13639–13647. \ndoi:10.1364/OE.21.013639 \n51. Schindelin, J.; Arganda-Carreras, I.; Frise, E.; Kaynig, V.; Longair, M.; Pietzsch, \nT.; Preibisch, S.; Rueden, C.; Saalfeld, S.; Schmid, B.; Tinevez, J.-Y.; White, D. \nJ.; Hartenstein, V.; Eliceiri, K.; Tomancak, P.; Cardona, A. Nat. Methods 2012, 9, \n676–682. doi:10.1038/nmeth.2019 \n52. B. D. Viezbicke, S. Patel, B. E. Davis, D. P. Birnie, Phys. Status Solidi B 2015, \n252, 1700-1710. doi: 10.1002/pssb.201552007","source_license":"CC-BY-4.0","license_restricted":false}