A description of the formation and growthprocesses of CaTiO3 mesocrystals: a jointexperimental and theoretical approach†
Mario L. Moreira, a José Rafael Bordin, *a Juan Andrés, b
José A. Varelac and Elson Longo d
In this paper, we report on a combined experimental and theoretical study conducted in order to
rationalize the formation and growth mechanism of CaTiO3 mesocrystals through the microwave-assisted
hydrothermal synthesis over short times. The transformation process in which the initial nanoplates are
converted to microcube-like CaTiO3 is investigated in detail. Field emission scanning electron microscopy,
photoluminescence emission analysis and Langevin dynamic simulations were carried out. We determined
how the quenching rate induced by microwave irradiation can be used to finely tune the structural
characteristics of the final CaTiO3 nanoparticles, including size, shape and crystallinity, showing that the
microcube-like particles appear only within a temperature range of 130–200 °C. The theoretical and
experimental results allow us to propose a mechanism involving three steps: i) a nucleation process of
nanoplates below 10 min, ii) a self-assembly process of nanoplates to form microcube-shaped CaTiO3
under specific thermodynamic conditions, and finally, iii) the formation of microcube-like shapes as the
result of a long assembly process. The present results not only provide a deeper insight into the nucleation
and growth processes, but also help to find a relationship between morphology and photoluminescence
behavior throughout the microwave-assisted hydrothermal synthesis of target metal oxides. These findings
shift the focus of the experimental and theoretical research onto the detailed study of the connectivity of
TiO6 octahedra and CaO12 cube-octahedra as the constituent building blocks of the CaTiO3 lattice, paving
the way for quantitative predictions of the events involved in the self-assembly processes of CaTiO3
nanocrystals.
1 Introduction
Crystallization processes, i.e. the formation of crystallinematerials from aqueous solutions, begin with the nucleationof the initial precursors (ions/atoms/molecules), whichinvolves dynamic and stochastic aggregation processes andrepresents a key step in tuning the desired size andmanipulating the properties of crystalline solids.1–3 Theseseparated precursors can join together with a certaincomposition in definite geometric relations to form a definedcrystal structure, and play an important role in the areas of
a Departamento de Física, Instituto de Física e Matemática, Universidade Federal
de Pelotas, PO Box 354, 96010-900, Pelotas, Brazil. E-mail: [email protected] Departament de Química Física i Analítica, Universitat Jaume I, Campus de Riu
Sec, Castelló 12080, Spainc INCTMN - Departamento de Físico-Química, Instituto de Química, Universidade
Estadual Paulista, P.O. Box 355, 14801-907R. Francisco Degni, 55, Bairro
Quitandinha, Araraquara, SP, Brazild INCTMN - Institute of Chemistry, Universidade Federal de São Carlos, Rod.
Washington Luis, Km 235, CEP: 13565-905, São Carlos, São Paulo, Brazil
† Tribute: the authors dedicate this work to our friend and mentor, ProfessorJosé Arana Varela, recently deceased. He was one of the pioneers in this researchfield and showed us the ways to carry it out with excellence.
Design, System, Application
In this work a combined experimental and theoretical study is conducted in order to rationalize the formation and growth mechanism of CaTiO3
mesocrystals through microwave-assisted hydrothermal synthesis over short times. We chose CaTiO3 as our representative system due to the fact that it isthe subject of extensive structural research, with considerable interest from the electronic industry and potential biological applications. However, whileCaTiO3 nanoparticles are found in more and more technological applications, their formation mechanisms are still poorly understood. In addition, as aperovskite-type material, CTO provides an excellent opportunity to illustrate morphogenesis strategies involving self-assembly formation or classical/nonclassical growth with interesting optical properties. Our results provide deep insights into non-classical and classical multistep nucleation at theatomic-scale and confirm the existence of time-dependent critical size and intermediate states during different multistep nucleation pathways, whichshould be helpful in guiding the synthesis and growth of cluster, amorphous and crystalline materials; our findings further enrich the nucleation theory.
science and technology.4,5 However, how these discreteparticles are able to achieve the bonding patterns, and thengrow into large crystals, is a poorly understood phenomenonand has remained a demanding challenge for researchers.6
As an important event in the crystallization process, the self-assembly process describes the spontaneous association ofnumerous individual entities into a coherent organizationthat is structurally well defined and quite stable,7,8 leading tothe formation of one (1D), two (2D), and three (3D)dimensional mesostructures.9
Mesocrystals are nanocrystals that are aligned intoordered superstructures, with the assembled nanoparticleshaving the same orientation, thereby leading to diffractionpatterns similar to those of single crystals.6 Exploring thereasons for the initiation of self-assembly processes innanocrystals is a key topic in the materials sciencecommunity. The self-assembly process of nanoscopiccomponents into ordered suprastructures is a promisingroute to create novel advanced materials and bridge the gapbetween nanoscale objects and the macroscale world. Theformation of 1D and 2D assembled superstructures, whichinevitably brings them into contact with the surfaces of thesurrounding materials, is a fundamental strategy for buildinghierarchical structures in novel advanced materials.10–12 Withthe advent of new experimental methods to disclose thefundamental interactions between nanocrystals, significantprogress has been made in understanding thesephenomena.13,14 On the other hand, theoretical frameworkshave succeeded in explaining, describing, and predicting thenucleation and crystallization processes and they are neededat both the qualitative and the quantitative levels.15–17
However, the different durations and time scales of theseevents make it difficult to fully encompass the origin of theanisotropy of the interactions between nanocrystals.
Advances in complex oxide crystallization methodspromise to enable the creation of crystalline nanostructuresand 3D architectures with desired properties, such asthermal, electronic, and optical properties that are modifiedby nanoscale effects. To this end, considerable effort hasbeen made to understand and utilize ways to control theintermolecular interactions between supramolecular buildingblocks, and directing the self-assembly process so as toconstruct complex architectures with tailored functions hasnow become an important concept in nanotechnology. 3Dorganized superstructures based on building blocks, whichare larger than ions/atoms/molecules but still have nanoscaledimensions, have been reported. These nanoscale buildingblocks can be of very different natures, including metals,18–26
semiconductors,26 inorganic complexes,27,28 inorganicmaterials29–31 and biological substances,32 to name just afew. These self-assembled structures, with highly specificshapes and novel properties, are of great interest formaterials synthesis and device fabrication, and are also asubject of intense practical interest.
One of the most important insights from recent workpublished in the literature has been the discovery of
nonclassical pathways for crystallization involving theformation of crystalline materials where species larger thanmonomeric chemical constituents, i.e. ions or singlemolecules, play crucial roles; these pathways are not coveredby the classical theories, which date back to the 1870s and1920s.2,3,33–38 As an example of nonclassical crystallization,the self-assembly process exhibits not only an abundance ofgrain boundaries like polycrystals, but also nearly the samecrystallographic orientations among the nanoparticlebuilding units, and can therefore present some relativelydifferent physical characteristics, including optical features.39
Undoubtedly, these novel physical characteristics are closelylinked to the structure of the crystals as well as the synthesisprocedure. The driving force of the structural transformation,the formation mechanisms, and the relationships betweenthe microstructures and shapes need to be investigated indetail. It is very important to note that even though theprocess does not follow typical classical growth, a stronginfluence from the classical process is still preserved.However, examples of both plates exhibiting a regularexternal polyhedral morphology as well as computationalstudies on the self-assembly architectures of nanoplates andtheir properties are rare.40–46 Detailed knowledge of thenature of the mechanism underlying the self-assemblyprocess and the interaction between active building blocks isthus of considerable importance, but it still poses asignificant challenge. Understanding their formationmechanisms and controlling both the mechanism underlyingthe self-assembly process and the interactions among theactive building blocks, enabled by surface modifications, iscrucially important to be able to adjust their properties andfacilitate their use in diverse applications.
Rapid improvements in theory and simulation47,48 andremarkable progress in observation and characterizationtechniques38,49,50 of inorganic compounds have led totremendous advances in our understanding of structure–property relationships. Nevertheless, it is well establishedthat the process of obtaining a crystalline material involves acomplex scenario.51,52 In this context, quantitative andpredictive theories for understanding the relationshipsbetween synthesis–structure–morphology and opticalproperties remain largely undeveloped. Computationalmodeling is a useful tool to study systems with self-assemblyproperties.16,17,31,53–55 We embrace this task here, and tocomplement and validate our experimental framework and tounderstand the formation of nanocrystals, we conductLangevin dynamic simulations under varying conditions toobtain snapshots of the crystal at different reaction times inorder to elucidate the evolution of the morphologies. Ourtheoretical results are then linked to experimental data.
The microwave-assisted hydrothermal (MAH) method is agreener approach to synthesize materials in a shorter time(on the scale of several minutes to hours, or less) and withlower power consumption (hundreds of watts) as aconsequence of direct and uniform heating. Accordingly,microwave-assisted synthesis routes have also been applied
to obtain high quality nanomaterials via direct microwaveheating of the molecular precursors,56–60 which is aninnovative technique for the production of several materialswith unique physical and chemical properties with or withoutthe addition of surfactants, control over the overall particlesize and aggregation process, in addition to being anenvironmentally friendly method.61–76 However, MAHsynthesis is challenging due to its extreme complexity andquickness, and it is often sensitive to subtle variations in thesynthesis parameters. This sensitivity is rooted in the non-equilibrium nature of low-temperature crystallization, wherecompetition between different metastable phases can lead tocomplex multistage crystallization pathways.
We chose CaTiO3 (CTO) in the Pbnm space group as ourrepresentative system due to the fact that it is the subject ofextensive structural research,77 with considerable interestfrom the electronic industry78,79 and potential biologicalapplications.80–87 While CaTO3 nanoparticles are found inmore and more technological applications, their formationmechanisms are still poorly understood. In addition, as aperovskite-type material, CTO provides an excellentopportunity to illustrate morphogenesis strategies involvingself-assembly formation or classical/nonclassical growth withinteresting optical properties.
It is difficult to determine the details of the mechanismsand processes of nanocrystal formation that take place inmulticomponent systems, in which a plethora of interactions,chemical reactions, equilibrium, nucleation and crystalgrowth processes occur throughout the reaction mixture.Understanding the analogies between the experimental andsimulated scenarios enables new strategies for rationalcomprehension of the self-assembly process. To this end, inthis work a joint experimental and theoretical study isperformed to rationalize the growth mechanism in which theinitial nanoplates, as the building blocks, are assembled torender microcube-like CaTiO3 through microwave-assistedhydrothermal synthesis at low temperatures and over shorttimes. X-ray diffraction (XRD) patterns were used for thestructural characterization, while morphology images wereobtained by field emission scanning electron microscopy (FE-SEM). Photoluminescence (PL) emissions were used to probethe structural and electronic order/disorder effects, andhence the progress of the CTO self-assembly processthroughout the synthesis can be estimated. To gain a fullcomprehension of the experimental results, as well as tofollow the evolution of the structural, morphological andoptical properties throughout the self-assembly process, wecarried out Langevin dynamic simulations of a CTOnanoplate model under varying conditions. Based on thisknowledge and the results of the present work, the followingthree questions will be answered: i) How does the formationof nanocubes from nanoplates of CTO take place? ii) Whatphysical parameters determine the rate of this process? iii)How are the PL emissions correlated with the morphology asthe synthesis progresses? Finally, a possible formationmechanism is proposed.
2 Experimental details
CTO was synthesized using TiCl4 (99.99%, Aldrich), addedslowly to 125 mL of de-ionized water at 0 °C under vigorousstirring, forming TiIJOH)4. In a similar way, 0.05 mol of CaCl2·2H2O (99.9%, Merck) was dissolved in 125 mL of de-ionizedwater under stirring until the solution turned transparent.Then, the two precursor solutions were mixed under Ca/Ti =1 quotient and divided into five 50 mL portions, to which 50mL portions of KOH (99%, Merck) solution (6 M) were addedunder constant stirring to act as a mineralizing agent,88
taking the pH to 14. Thus, the KOH solution was employedas a co-precipitation agent for titanium and calciumhydroxides.
The co-precipitate hydroxides in aqueous solution wereloaded into a reaction cell, which was sealed and placed in amicrowave hydrothermal system using 2.45 GHz microwaveradiation with a maximum output power of 800 W. Thereaction mixture was heated to 140 °C in one min (at 800 W)by direct interaction of water molecules with microwaveradiation and kept at this temperature for 10 (CTO10), 20(CTO20), 40 (CTO40), 80 (CTO80) and 160 (CTO160) minutesunder a stable pressure of 2.5 bar. The time evolution wasbased on the kinetic model 10 × 2n, where n = 0, 1, 2, 3 and4. After the reaction, the autoclave was taken out of thesystem and allowed to cool naturally to room temperature.The solid product was then washed several times with de-ionized water until it reached neutral pH, and then dried at80 °C for 12 h.
3 Model and simulation details
Langevin Dynamics simulations were performed using theESPRESSO package.89,90 Since the computational system is inequilibrium, we do not expect the hydrodynamics effects tobe relevant in the self-assembly process. However, viscosityeffects were included in the Langevin dynamic forces.91 Thefriction coefficient was defined as γ = 1.0σ2/(τε), where ε =kBT0 is the energy parameter, with kB the Boltzmann constantand T0 = 27 °C, room temperature; σ is the size of onemonomer of our plate and τ is the time unit in standard LJreduced units.91 The system temperature, T, was varied from27 °C to 477 °C. The nanoplate number density is defined asϕ = (nnpnmon)/V, where V is the volume of the simulation box.Here, ϕ was varied from 0.10σ−3 to 0.70σ−3. The time stepemployed in our simulations was 0.002τ. For each point werun four distinct simulations: two with the plates randomlydistributed in the space and two with the plates orderedalong the xy-plane. The system was equilibrated during 5 ×106 time steps and the results were obtained over 1 × 107
time steps, with measurements at every 104 steps. Regardlessof the initial configuration, the same morphologies andphysical properties were observed after the equilibrationphase. To ensure that the system was well equilibrated wechecked the system’s total energy, kinetic energy andpressure. To analyze the transitions between distinct
morphologies and phases we evaluated the specific heatalong an isochore using16,17,91,92
Cv ¼ U2h i − Uh i2kBT2 ; (1)
where U is the potential energy of the system.One thousand system snapshots were taken to visualize
and characterize the morphologies. Moreover, to confirm thatthere are no internal holes in the cubic phase we use theprocedure proposed in our previous paper to find holes inthe mesoporous assembled structures.17 The mean squaredisplacement of each plate’s center of mass was evaluated tosee if the system is fluid (has diffusion) or solid (does nothave diffusion).
To adequately simulate the geometry of the nanoplates,we used a model system composed of nnp = 1000 squarenanoplates, each one composed of nmon = 9 monomers ofdiameter σ in a square lattice. Two first neighbor monomers iand j in the same nanoplate are bonded by a harmonicpotential,
Ubond rij� � ¼ 1
2kbond rij − σ
� �2 (2)
where rij is the distance between the monomers i and j, σ isthe equilibrium position and kbond = 30ε/σ2. To keep the plateflat and avoid it bending we use a cosine square bond anglepotential between the three monomers i, j and k in the sameline or row:
Ubondangle ¼ k2
cos ϕð Þ − cos ϕ0ð Þ½ �2 (3)
Here, kangle = 50ε/σ2 and θ0 = 180°. Also, in our proposal ofa minimal model we assume that the interaction betweenplates is ruled by van der Waals forces, in such a way thatelectrostatic forces play a small role and can be neglected. Inthis way, two monomers i and j in distinct plates interactonly by a standard 12-6 Lennard Jones (LJ) potential:91
ULJ rij� � ¼ 4ε
σ
rij
� �12− σ
rij
� �6� �: (4)
The depth of the attractive well in the LJ potential was setto ε = kBT0. This value is compatible with the strength of thevan der Waals interaction between two plates obtained usingthe procedure proposed by Ye and co-authors in ref. 40. Thecutoff for the LJ potential is rcut = 3.0σ.
4 Results and discussion
Ten years ago we synthesized orthorhombic CTO samples inthe Pbmn space group via the MAH method and theircorresponding photoluminescence characteristics werediscussed.93 The same methodology and subsequently thesame samples were employed in this study, and theircrystallographic features will be discussed later in this work.Fig. 1 shows a schematic representation of the PL emissions
and the shape evolution throughout the transformationprocess, from individual nanoplates to assembled nanoplatesas microcube-like CTO at different synthesis times. Ananalysis of the results displayed in this figure reveals that awide band profile can be sensed in the ultraviolet–green (UV–green) range, followed by well-defined emissions centered atthe orange region, thus indicating a multiphotonic processinvolving numerous states within the band gap of thematerial, as already discussed in previous studies.94–97 In thefirst stages, wherever the nanocrystals (nanoplates) areassembled to form mesocrystals as in ref. 98, it is necessaryto surmount an energy barrier to form CTO nanoplates. Theprocess is a random and spontaneous aggregation of CTOnanocrystals to form larger nanoplate CTO crystals and it isthermodynamically driven because larger crystals areenergetically favored more than smaller crystals. A rise inenergy occurs throughout the self-assembly process ofnanoplates due to structural lattice disorder remaining in theindividual nanoplates and as a result of interface eliminationduring the final mesoscopic makeover.93,99,100
Following the sequence shown in Fig. 1, first CTO10 andCTO20 have a low-defined microcube shape and there is anintense broad band from the UV to the green region in thevisible range (350–580 nm), with a low intense peak in theorange region (around 615 nm). As the processing timeincreases, for CTO40, CTO80 and CTO160, a microcube-likeshape is achieved with a concomitant decrease in emissionintensity in the UV–green region, while an opposite effect isobserved in the orange region. This effect may be related tothe elimination of surface defects by the process of mergingthe nanoplates, although they are not completely eliminatedbecause there are still self-assembled microcube-likenanoplates after 160 min synthesis. It is well known that PL
Fig. 1 A schematic representation of the photoluminescence behavior(color emissions) and the evolution of morphologies in thetransformation process from individual nanoplates to the microcube-like shape of CTO, at different synthesis times.
properties are sensitive to synthetic conditions, shape, size,surface defect states, and so forth. In the present case, PLemission is employed as a signature of the morphology ofthe as-synthesized samples throughout the progress of theself-assembly process. Therefore, in the next sections, we willanalyze in detail the phase formation and self-assemblyprocess, as well as the mesoscopic transitions.
It is important to emphasize that in the present case themicrowave activation, through the MAH method, achievesfast and effective thermal activation in which thetemperature of 140 °C is attained in one minute, therebyplaying a key role in the nucleation and subsequent crystalgrowth processes due to modification of the activation-energybarriers. In particular, this result agrees with Lencka’s101
statement that under conventional hydrothermal conditions(without microwave radiation) the temperature has a limitedeffect on CTO nucleation at low pressures (<5 bar). On theother hand, our experiments revealed that at a temperatureof 140 °C outside a hydrothermal system, co-precipitatedCTO does not have any kind of crystalline order orluminescence emission, or even a defined shape. Wehypothesize that a set of parameters such as temperature,pressure, reaction medium and electromagnetic radiation areable to promote the specific structural, self-assembled shapeand optical characteristics obtained for CTO.
In general, the formation of an oxide in aqueous solutionis expected via hydrolysis–condensation (nucleation–growth)processes by microwave action. One of the advantages ofusing KOH as a strong base over other mineralizing agents93
is that it allows us to reach a high degree of supersaturationduring the precipitation process due to the fact that thepotassium cation, K+, prevents absorption on the surface ofthe particles because of its greater solubility in water.Moreover, large amounts of mineralizing agent are needed ifnon-alkaline precursors are used to obtain a final yield ofCTO that is greater than 99%. The mineralizing agent isalways necessary if the synthesis is performed in very dilutesolution.101 The OH− groups that are abundant in alkalinemedia are able to form hydrogen bonds with titanium andcalcium hydroxides, thereby facilitating the dehydrationprocess. In the present case, the nucleation process in analkaline aqueous medium can be simplified in terms of thefollowing chemical reactions:
In principle, an aqueous solution with an excess of OH−
and a higher Ca2+ concentration can render CaIJOH)2 in thesecond stage. Subsequently, the corresponding TiOIJOH)2 wasalso formed through a hydrolysis–condensation reaction asfollows.
During the hydrothermal synthesis, the water viscosityquickly decreases with increasing temperature,102 and it istherefore plausible to assume that the mobility of the ionsand molecules dispersed in the reaction solution are higherunder hydrothermal conditions than at ambient pressureand temperature. This fact justifies the use of Langevindynamics to study the time evolution of the assemblyprocess, since the viscosity plays a key role in the net forceevaluation.91 Moreover, the microwave energy acts directly onthe rotational barriers of the water uniform heating103 and iscapable of enhancing the crystallization kinetic behavior byseveral orders of magnitude64,65,104,105 due to the directinteraction of radiation with matter. In the present case, thequality and rapid formation of the uniform nanoplates areminimized, possibly due to thermal gradients.
At this point it is worth discussing the importance of theMAH process to grow structures faster than by theconventional method, i.e., how do the electromagneticmicrowaves act on the water solution to promote dielectricheating? Nevertheless, it is important to recognize that theanswer to this question is still controversial.106 Generally,microwave irradiation induces molecular rotation arisingfrom dipole alignment with the external, oscillating electricfield.107–112 This phenomenon is dependent on the capabilityof a specific compound (solvent or reagent) to absorbmicrowave energy and convert it into heat.107 It is clear thatthe electromagnetic field applies a force on charged particles,and as a result the particles start to migrate or rotate in thewater solution. In our system, TiOIJOH)2 and CaIJOH)2 areneutral clusters. Subsequently, their mobility in solution andupon heating is affected by polar and charged molecules,namely H2O and Cl− and K+ ions. This effect is related todielectric loss (ε′), which measures the ability of the mediumto convert electromagnetic energy into heat.113 Furthermore,the electric field is able to polarize the water molecules andthe dielectric constant (ε″) describes the ability of the watermolecules to be polarized.107,108 The ratio between ε′ and ε″results in a dimensionless factor (tan δ), which for thesolvents used in microwave synthesis can generally beclassified as high (tan δ > 0.5), medium (tan δ = 0.1–0.5), andlow microwave absorbing (tan δ < 0.1). In our case, thesolvent is water, for which a favorable condition of tan δ =0.123 is reported.107,108 On the other hand, if the temperatureis increased up to 100 °C, the decrease in value isaccompanied by a further decrease in dielectric loss, ε′, andthus the absorbance is quickly reduced and it becomes moredifficult to heat the solution.108 For instance, potassium (K+)
and chloride (Cl−) ions are appropriate candidates to improvethe dielectric constants above 100 °C. These ions wereprovided by our reactants, as previously expressed inreactions (5) and (6).114
A nucleation mechanism for the formation of micro-cube-shaped CTO, in terms of chemical reactions and crystalgrowth, is described as follows and shown in Fig. 2. Insolution, Ti4+ and Ca2+ cations are chelated by a randomdistribution of H2O and OH groups to form an almostregular TiOIJOH)2·xH2O complex and CaIJOH)2.
Structural organization takes place throughout thesynthesis process and, in particular, the clusters form theconstituent building blocks of the perovskite based materials,i.e. TiO6 (octahedral cluster) and CaO12 (cuboctahedralcluster). Subsequently, complete nucleation is achieved bylong range organization. The next step is the formation ofnanoplates, and the sequence is finished by the self-assemblyof nanoplates to yield microcube-shaped CTO. Themicrocube-like crystallographic shape is unexpected for theorthorhombic Pbmn space group. Indeed, our grains are notreal cubes, but just resemble them as the result of nanoplateassembly. A schematic representation of these stages isdisplayed in Fig. 2. In the second step the agglomeration
process takes place, which can happen under appropriateintermediate interaction forces.
The colloidal stabilization of the nanoparticles has to beso weak that two nanoparticles can approach each otherwithin the primary minimum. This minimum is achieved butthe flexibility and dynamics must still be high enough torearrange the low energy configuration represented by acoherent particle–particle interface.115 These aspects wereused to construct the minimal model used in the Langevindynamic simulations. Geometric effects due to the shape ofthe nanoplates and the particle–particle interactions wereconsidered the main factors to understand the dynamics ofthe self-assembly process. Our main candidates to lead thecoherent interactions between CTO nanoplates are thehydrogen bonds between OH groups, thereby avoiding thecoalescence process at short times and giving rise to a self-assembled organization, as suggested in Fig. 2. To confirmthis hypothesis, infrared spectra are performed throughoutthe synthesis process. Fig. 3 shows these spectra for 10 and160 min. Three signals can be monitored: (i) the weakshoulder at 1642 cm−1 is related to the presence of OH bondsand/or pure hydration as a result of the strong hydrationcommonly expected for systems synthesized via hydrothermalconditions; (ii) the band around 2350 cm−1, associated withthe O–H stretching mode;116,117 and (iii) the asymmetryresulting from the increase in intensity of a band on the lowfrequency side (3550–3350 cm−1) corresponds to thehydration processes of OH groups.118 Hydrogen bonding isusually characterized by (a) broadening of the OH bandaccompanied by an increase in the absorbency, and (b)frequency shifts of the absorption bands to a lower frequencydue to ν(OH) stretching vibrations.
The low frequency absorption bands between 450 and 600cm−1 indicated in Fig. 3 correspond to the symmetric andasymmetric stretching modes of partially or totallydehydrated metal–oxygen octahedra within TiO6 clusters,respectively. The formation of TiO6 clusters is directly relatedto CaO12 clusters, which are necessary for the formation of aperiodic crystalline system. This process is a result offavorable thermodynamic conditions for the formation of a
Fig. 2 Schematic representation of the three fundamental steps in thesynthesis of microcube-like shaped CTO using MAH methods: 1) 3Dlattice formation, 2) formation of nanoplates, and 3) self-assembly ofnanoplates.
Fig. 3 Infra-red absorption spectra of CTO nanocubes synthesizedunder hydrothermal conditions for 10 and 160 min.
new solid phase on the particle surface,80 like an assembly ofnanoplates with intermediate HO groups instead of newisolated particles. The particles can then be stuck to eachother or grow on each other, depending on the instantaneousthermodynamic conditions. Bonding between the particlesreduces the overall energy by removing the surface energyassociated with unsatisfied bonds through completeelimination of the mineral–air or mineral–fluid interface. Inaddition, the fact that the solubility of calcium titanateremains quite low prevents resolubilization of theparticles.119 This mechanism is relevant in cases where theparticles are free to move (such as in solution or where theparticles have abundant surface-bound water)77,78,120 andprobably occurs in nature.121
To complement and rationalize these experimental results,Langevin dynamic simulations were carried out. Thefollowing parameters were controlled for: the temperaturefrom 27 °C to 477 °C, and the density of nanoplates ϕσ−3
from 0.10 to 0.80, i.e., as the system is dehydrated there isless water and the density of the nanoplates increases inrelation to the water density. This increase in the density alsocorresponds to an increase in the pressure.122
Fig. 4(a) shows the ϕ × T phase diagram. We haveidentified three distinct kinds of clusters. First, at lowtemperatures and low densities, the CTO nanoplates arearranged in small clusters without a cubic shape, similar tomesocrystals. The region of this phase is indicated by thegreen circles in Fig. 4(a) and an example of the shapeobserved in the simulation is shown in Fig. 4(b). At mediumto high densities and low temperatures, the clustermorphology displays an architecture similar to that of aporous cube – magenta diamonds in Fig. 4(a) – representedin Fig. 4(c). To fill the holes in the porous cube it is necessaryto increase the temperature to specific values. At these values,the entropic contribution to the free energy allows the platesto break the bonds in the porous phase and accommodatemore easily, thus filling the holes and achieving the cubicphase. This entropic patchiness is well known in theliterature, and helps colloids with unusual shapes, such asnanoplates, dumbbells30,31,55,123,124 and nanorods16 toachieve the energy minima and assemble in the mostfavorable shape.125 This phase is represented by the redtriangles in Fig. 4(a) and can be seen in Fig. 4(d).Interestingly, the simulation indicates that the cubic shapeoccurs in the range of T ≈ 130 °C to T ≈ 200 °C, whichcorresponds exactly to the range observed at the experimentaltemperature, T ≈ 140 °C. Also, when T > 200 °C, all theclusters melt to a fluid phase, where the CTO nanoplateshave large mobility and no well defined structure is obtained.This indicates that “hotspots” at temperatures above 200 °Ccan in fact melt the cluster and do not help to form themicrocube shape.
Another interesting finding from the computationalanalysis is that the cubic clusters are in the energy minimaalong the isotherms. In Fig. 5 we show the mean potentialenergy per particle (in units of the thermal ambient
temperature kBT0) as a function of ϕ. For an isotherm whereno cubic clustering was observed, such as T = 252 °C, theenergy increases linearly with ϕ as the system goes from theporous clusters to the fluid phase. On the other hand, for T =132 °C, we can measure a minimum in the energy profile.This minimum corresponds to the region in the phasediagram were we observe the cubic clustering, from ϕ = 0.20to ϕ = 0.60. Therefore the microcube-like CTO is stable andcorresponds to the minimum energy in the thermodynamicphase diagram.
Regardless of the synthesis time, in Fig. 6 the crystals areidentified as orthorhombic phase with a Pbnm space groupwith ICSD cif number 74212. Secondary phases are notpresent, indicating that extended times are not required toobtain the desired CTO compound. This result corroborates
Fig. 4 (a) ϕ × T phase diagram for the CTO nanoplate model. Eachphase is identified by distinct symbols and colors. The separationbetween the phases was defined using the Cv system. Examples of theobserved morphologies are: (b) small clusters at T = 102 °C and ϕ =0.10, (c) porous clusters at T = 102 °C and ϕ = 0.30, and (d) cubicclusters at T = 162 °C and ϕ = 0.60.
the previous observations from the IR spectra and is inagreement with our crystallization model. In addition, theobservation of cubic-like clusters in the Langevin dynamicsimulations indicates that the time necessary to obtain theCTO compound through the synthesis is short. Based onthese facts, we are able to consider the MAH method anadequate bottom-up process for the synthesis of perovskiteceramics under mild conditions.
The favorable reaction conditions are attributed to the fastinteractions between the microwave radiation and thepermanent dipole moment of water, as discussed earlier.67,103
Based on the facts described above, we can consider theMAH method as a typical bottom-up process for perovskiteceramics. From a morphological point of view, the evolutionof CTO nanoplates via a self-assembly process involves theformation of mesocrystal-like structures, as shown in Fig. 7,which are kinetically stable, and these superstructures canonly be formed and stabilized under certain conditions. Ifthe specific conditions are changed, the mesocrystal-like
structures can be destroyed or fused to single crystals orreach a cube-like lens shape, as shown in Fig. 7 for CTO160.Based on the aforementioned arguments, the high-temperature water reaction environment (100–300 °C) is idealfor processing mesocrystal-like structures utilizing microwaveheating under sealed-vessel conditions.108,114 On the otherhand, if the temperature is increased, the stability will be lostand the microcube-like shapes will be converted into typicalsingle crystals, even within short times. These findings arecorroborated by the computational study, in which we haveobserved that the CTO self-assembled morphology is affectedby the temperature.
Fig. 7 displays the assembly of a large number ofmicrocube-shaped CTO to yield 3D architectures that aretypical of mesocrystals. A detailed analysis shows that themicrocube shapes present large diameter values, rangingfrom 1.8 to 2.1 μm, and the three-dimensional assembliesare formed from pseudo-two-dimensional nanoplates.126 Theattachment events among the nanoplates do not follow apreferential growth direction, especially when the attachmenttakes place at several points on the same nanoplate at thesame time. From these results, a possible formationmechanism underlying the three well-defined stages can beproposed: i) first, fast nanoplate nucleation takes place under10 min; ii) the self-assembly of nanoplates to form microcubeshapes under specific thermodynamic conditions.
Fig. 5 Mean potential energy per particle as function of ϕ for theisotherms T = 252 °C (red squares) and T = 132 °C (black circles). Errorbars are smaller than the points.
Fig. 6 X-ray diffraction of micro-cube-shaped CTO self-assembledcrystals obtained by different times from 10 to 160 min at atemperature of 140 °C.
Fig. 7 FE-SEM images of the CTO samples at different synthesis times.The nano-plates, assembled nano-plates, and nano-cubes arehighlighted.
Throughout this process mesocrystals appear, which arecomposed of individual crystallographically alignednanocrystalline building blocks;9,127 and finally, iii) theformation of well-defined microcube-like structures.Throughout the synthesis process, the changes inmorphology occur with concomitant variations in theluminescence emissions, as presented in Fig. 8.
5 Conclusion
Crystallization plays an important role in many areas, and toderive a fundamental understanding of crystallizationprocesses it is essential to understand the sequence of solidphases produced as a function of time. Hence, knowledge ofthe crystal formation mechanism starting from the initialbuilding units can be considered the workhorse of themodern science of materials chemistry. The advances inseeded growth are the ultimate approach to producingnanocrystals with precisely controlled sizes, shapes, andcompositions. Nanocrystals can be used as building blocksthroughout the self-assembly process to obtain new solid-state materials. Understanding and manipulating self-assembled materials are prerequisites for exploring theirpotential for applications. Therefore, the capability tounderstand, drive the mechanisms, and control the assemblyprocess of nanocrystals in laboratory synthesis is a fully openquestion and will be one of the exciting challenges fornanoscientists in the near future. In this article, wedemonstrate a meticulous and in-depth analysis of thenucleation and crystal growth mechanism to obtainmicrocube-shaped CTO from nanoplates through a self-assembly process, and the final mesoscopic transformations.PL emission is used as an appropriate tool to follow theseprocesses, allowing the optical properties to be adjusted bytuning the 3D architectures related to their structuraldistortions caused by vacancies, strains, surface states or tiltsamong adjacent TiO6 octahedra and CaO12 cube-octahedra asbuilding blocks of the CTO lattice. Consequently, snapshotsof the crystals at different reaction times can be obtained by
Langevin dynamic simulations to explain the appearance ofcube-shaped mesoscopic CTO in the range of temperaturesfrom 130 °C to 200 °C, as is observed experimentally. Theresults reported herein and the implied growth mechanismshould be representative, and therefore the findings shouldbe highly valuable for the future engineering of functionalnanomaterials. We are currently pursuing furtherapplications of the present procedure to understand the self-assembly process through the MAH synthesis of otherperovskite- and/or scheelite-based materials.
Conflicts of interest
There are no conflicts to declare.
Acknowledgements
The authors acknowledge the support of CNPq and partialfunding by the Coordenação de Aperfeiçoamento de Pessoalde Nível Superior-Brasil (CAPES)-Finance Code 001. M. L. M.and J. R. B. acknowledge FAPERGS (grants no. 16/2551-0000525-7 and no. 17/2551-0001). J. A. acknowledgesUniversitat Jaume I for project UJI-B2019-30, and Ministeriode Ciencia, Innovación y Universidades (Spain) projectPGC2018-094417-B-I00 for supporting this research financially.The authors also thank LIEC-São Carlos, Rorivaldo Camargoand Madalena Tursi for technical contributions.
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