Introduction

Single crystal hydroxide, hydrocarbonates and oxides containing rare earths (RE) present diverse morphology, chemical composition, structural and optical properties of interest to the scientific community ^[1]. The structural properties of inorganic RE nanocrystals are systematically examined by various research groups and theoretical-experimental studies have been carried out, since they show a significant optical-structural correlation ^[2]. It is of primary interest to investigate the structural properties of nanocrystals; these are significantly correlated with the optical response. Consequently, RE inorganic nanocrystals are strong candidates for their application as base material in the construction of optoelectronic devices, as well as in a variety of applications ^[3,^4]. On the other hand, crystal growth is one interesting and vitally important feature science, which has contributed to significant improvements in producing nanocrystals with specific properties ^[5]. However, the synthesis conditions of crystal growth require systematic and optimal control of the physicochemical and thermodynamic parameters depending on the applied technique ^[6,⁷,^8]. Some interesting reports of crystal growth are available investigating RE cations by systematic study and their experimental theoretical correlation with physicochemical parameters ^[9]. Furthermore, the inorganic nanocrystals of RE are systematically prepared, which allows monitoring the different parameters associated with crystal growth, with the aim of controlling the decrease in grain size (GS). Therefore, to reduce the relative cost between other parameters associated with the synthesis and the experimental equipment used, crystal growth parameters can be systematically controlled. A recently proposed mechanism of grain boundary migration known as the “mixed control mechanism” and the associated principles of microstructural evolution represent the basis of the solid-state single crystal growth technique ^[10]. Various ER synthesis techniques, both chemical and physical; have been reported in the last decades: hydrothermal synthesis ^[11], spray pyrolysis technique ^[12], thermal decomposition ^[13], Chemical Bath Deposition (CBD) technique ^[7,^8,]. CBD technique has been applied in the preparation of various nanocrystals; Semiconductors ^[16], ER oxides ^[7,⁸,¹⁴,^15]. In this paper we systematically apply the CBD technique for the synthesis in aqueous solution of four RE, and the crystal growth parameters constant throughout the chemical synthesis process. The inorganic nanocrystals examined here are: samarium hydroxide Sm(OH)₃, neodymium hydro carbonates (NdOHCO₃), cerium oxide (CeO₂), and holmium oxide (Ho₂O₃) were previously reported ^[7,⁸,¹⁴,^17], now focuses on the study related to physicochemical parameters in chemical synthesis. Therefore, our study focuses specifically on the systematic structural analysis associated at crystalline parameters that govern the chemical kinetics performed. In particular, our study focuses specifically on the systematic structural analysis associated with the crystalline parameters that govern the chemical kinetics performed in aqueous solution. In this report, we consider the creation of the coordination complex cation in the critical step of chemical synthesis. The creation of the corresponding coordination complex ion of chemical formula [M(NH₃)₆]³⁺, (where M = Sm³⁺, Nd³⁺, Ce³⁺, and Ho³⁺), which is a key chemical parameter in the intermediate stage of chemical kinetics. The experimental characterization of the structural part is investigated by X-Ray Diffraction (XRD) technique. Taking XRD diffractograms, then using the Debye-Scherer equation GS is quantified numerically. The morphology and optical properties have been previously published by some of us ^[7,⁸,¹⁴,^17]. A systematic analysis of the products obtained is carried out and the comparative study in the key stages of crystal growth. The influence of the following physicochemical parameters: electronic affinity, ionic radii, are associated in the chemical kinetics of the crystalline growth.

Experimental

Results and discussion

Figure 1 shows the X-ray Diffraction (XRD) diffractogram of samarium hydroxide Sm(OH)₃. The inorganic nanomaterial is identified in the hexagonal crystalline phase (JCPDS 01-083-2036), which belongs to space group P63/m. Three crystalline angular reflections of small relative intensity are located at angular positions: 2θ ~28.04°, ~30.80° and 47.0°, associated with (101), (210) and (210) crystal plane. Different crystalline planes of another material are not identified, which shows in principle that does not contain other than Sm(OH)₃ nanocrystal. Experimental structural results are very close to those obtained by us; they were reported by Kang et. al.^[28]. The broadening of crystalline reflections, weak relative intensity, is generally associated with crystals with nanometric dimensions, as well as the presence of distributed amorphous regions that are found in a disorderly manner in different regions of the nanocrystals. Understanding, atomic, molecular and/or ionic disorder interactions is key to achieving control of materials at the molecular level, which is essential for various areas of physics and for nanotechnology ^[29]. This structural phenomenon molecular and/or ionic disorder created intrinsically in crystal growth. Self-organization of atoms and molecules into crystals plays a key role in diverse areas of science and the environment. On the other hand, the three -OH groups (-Sm-OH^…OH-Sm-), generates weak short-range electrostatic interactions associated with van der Waals forces. However, weak in comparison to chemical bonds, their long-range nature and their collective effect play a strong role in the structure of molecules and their electrical interaction with surfaces ^[30]. A dislocation or Taylor’s dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the crystalline arrangement of ions or atoms ^[31]. Table 3 shows the full width at half-maximum (FWHM), GS and Dislocation density (δ) of Sm(OH)₃ powders, the GS located at range ~1.4-2.03 nm.

Figure 1 XRD diffractogram of samarium hydroxide Sm(OH)₃ nanocrystals.  

Figure 2 show XRD of neodymium hydroxycarbonate NdOHCO₃ nanocrystals. The strong and sharp diffraction reflections indicate that the nanomaterial is well crystallized. The angular positions are located at 2θ ~18.00°, ~25.00°, ~31.28°, ~36.00°, ~44.88°, ~49.40°, ~52.42°, ~53.93°, ~58.00°, ~62.50°, ~65.00°, ~70,00°, and ~73.00°, corresponding to (002), (300) (300), (302), (004), (304), (134), (600). (602), (334), (306), (604), (630) and (362) crystal planes, respectively. Can be indexed to hexagonal structure NdOHCO₃ which are consistent with the data in the standard card (PDF 04-014-7918). Compared with the standard reflection, and those of (300), (302), (304), and (602) crystalline planes become strong. Thus, the changes in the relative intensity of the diffraction planes imply the orientation growth of NdOHCO₃^[32]. Also, reflections located at 2θ ~43.27°, and ~67.20° can be seen (they are shown by an asterisk at the top of the crystal plane), which are identified as belonging to Nd(NO₃)₃ inorganic nanocrystal, a precursor reagent used in this work, not completely dissociated. A plausible explanation regarding the structural behavior of NdOHCO₃, a first approximation is proposed: The chemical -OH and CO32- species in the nanocrystal, are located symmetrically surrounding Nd³⁺ cation, the electrostatic interaction in the crystal boundary creates van der Waals forces associated with hydrogen bonds. In addition, the electrostatic interaction created by -OH and CO32- ions located around the Nd³⁺ cation, generated by the electron cloud in the crystalline environment associated with the distribution of the electronic cloud of concentrated charge favors the creation of well-defined nanocrystals ^[33]. In the crystal growth carried out in our experimental conditions, strong and compact crystal-crystal ordering is generated. The -Nd-O-H^…H-O-Nd- chemical bonds, must be less favored with respect to the -Sm-OH^…HO-Sm- bonds, therefore; crystal growth shows higher relative order. Table 4 shows FWHM, GS and Dislocation density (δ) of NdOHCO₃ nanocrystals, the GS located at range ~14.33 - 22. 25 nm.

Figure 2 XRD of neodymium hydroxycarbonate NdOHCO₃ nanocrystals.  

Figure 3 shows the XRD patterns of CeO₂ nanocrystal. Four broad crystalline reflections are observed, located at the following angular positions: 2θ ~28.13°, 32.75°, 47.25° and 56.35°. XRD patterns from 2θ ~20-80 range exhibit main crystalline plane, which are assigned to the (111), (200), (220) and (311) crystalline planes of CeO₂. XRD pattern of CeO₂ shows broad reflections, which confirmed the formation of small-sized nanoparticles. The XRD results indicate that the CeO₂ nanocrystal, the patterns are in good agreement with a cubic structure (space group, Fm3hm (No. 225 from bulk CeO₂) (JCPDS Card No. 75-0076). In principle, it is possible to intuit the structural behavior associated with the phenomenon of electronic charge transfer from Ce⁴⁺ cation to the nearest neighbor according to Ce⁴⁺→Ce³⁺ + e^-. The O^2--Ce⁴⁺ charge transfer, we propose to attribute electronic intra-transitions on isolated Ce³⁺ ions in CeO₂. The transfer of charge from one cation to another indexes the growth of nanocrystals favorably ^[34]. However, having been studied almost exclusively by chemists, molecular crystals still lack the appropriate investigations that reliably evaluate their reproducibility and some important drawbacks have diverted the interest of engineers from these crystals in science applications ^[35]. The structural phenomenon associated with load transfer correlates with the decrease in GS according to our preliminary report ^[34]. The crystalline structure is favored by creating nanocrystals and additionally amorphous regions are generated as a first approximation by disordered electrostatic interactions that have a short-range Ce=O^…Ce=O, weaker than those presented by -Nd-OH^...OH-Nd- and Sm.-OH^…HO-Sm- interactions. Their conformation strongly depends on both the charge density and distribution along the sequence (i.e., charge decoration) as highlighted by recent experimental and theoretical studies that have introduced novel descriptors ^[36]. Table 5 shows FWHM, GS and Dislocation density (δ) of CeO₂ powders, the GS is located at range ~1.65-3.03 nm.

Figure 3 XRD of cerium oxide (CeO₂) nanocrystal  

Figure 4 shows the diffractograms of X-Ray Diffraction (XRD) of Ho₂O₃ nanocrystals. The materials show crystalline reflections correspond to Ho₂O₃ in the cubic phase (00-067-0222 JCPDS). No reflections other than are observed. The diffraction planes located at 2θ ~29.10°, ~44.00° and ~53.20° correspond to (222), (134) and (440) planes of Ho₂O₃ cubic phase, respectively ^[37]. Problems like polymorphic transitions, ions migration, slow crystallization and formation of crystalline aggregates stand out. Therefore, studies have focused on controlling the crystallization in order to determine the functionality of crystals.. A plausible explanation of the crystalline and structural behavior is associated with the nucleation time, this generates that the small nanocoloids induce the formation of crystal small and prevent rapid growth to larger dimensions. The affecting chemical and physical parameters factors (including nucleation temperature, freezing rate, and temperature fluctuation, etc.) on the size, number, distribution, and shape of crystals are also examined in detail ^[38]. The physicochemical phenomenon associated with crystal growth carried out systematically in aqueous solution, shows the importance of the parameters compiled in Tables 1 and 2, in which they are tentatively compared with each other semi-empirically. The approximate theoretical-experimental correlation with the chemical kinetic model examined here is observed. The kinetics of crystal growth is postulated semi-empirically with the change associated with the thermodynamic stability of the nanocrystal and the relative increase in GS, which presents the following order: Sm(OH)₃<Ho(OH)₃<CeO₂<NdOHCO₃ in the experimental conditions applied in the crystalline growth carried out in aqueous solution. Table 5 show FWHM, GS and Dislocation density (δ) of Ho₂O₃, the GS is located at range ~3.72-6.08 nm.

Figure 4 XRD of Holmium oxide Ho₂O₃ nanocrystals. 

Using the Williamson-Hall (W-H) plot, defined by βcosθ = kλ/GS + 4εsinθ equation, where ε is the strain, k a constant, β is the FWHM measured in radians and θ is the Bragg angle of the reflection, λ is the wavelength of X-ray used ^[21]. It can be determined from the slope (4ε) and from the intercept (kλ/GS), respectively. The βcos vs 4sinθ plots for Sm(OH)₃, NdOHCO₃, CeO₂ and Ho₂O₃ nanocrystals powders are showed in Figure 5. The nearly flat W-H straight lines show that the nanomaterials possess less ε. The experimental results presented here do not exactly fit the linear behavior, which may be due to anisotropic variation in the residual ε. This disordered behavior is associated with the gradual incorporation ions and cation into the crystalline structure with a drastic change in the anisotropy, as was expected into the crystalline lattice. The ε is very much reduced in the smaller particles; a trend that is difficult to achieve in the processing of nanocrystals, and one can notice the smaller stress obtained in NdOHCO₃ and Ho₂O₃ samples. The anisotropy could be modified although the behavior will be for a deeper analysis to be done in due course.

Figure 5 βcos vs 4sinθ plots for NdOHCO₃, Sm(OH)₃, CeO₂, and Ho₂O₃ nanocrystals. 

Conclusions

The CBD technique is versatile, it presents physicochemical parameters of easy experimental control, and this allows us to semi-empirically compare the structural properties of the obtained nanocrystal. The chemical kinetics of crystal growth proposed in this report shows a certain approximate correlation with the physicochemical properties of the ions and/or cation examined here. However, the semi-empirical experimental results are not very far from each other when compared with the theoretical and the experimental part. According to the experimental results successfully obtained in this report, it is possible to obtain a semi-empirical correlation of the parameters associated with crystal growth: ionic radii, hydration enthalpy and electronic affinity of M³⁺ cation (M³⁺ = Sm³⁺, Nd³⁺, Ce³⁺ and Ho³⁺), in principle they adjust to each other experimentally theoretical in an approximate way. The nanocrystals of these inorganic compounds grow with GS located at range ~1.04-22.25 nm, which is of interest to investigate the quantum confinement phenomenon, as well as for the application in the construction of optoelectronic devices. The Dislocation density (δ) shows that the nanocrystals present intrinsic crystalline defects (vacancies, interstices, stacking faults and grain boundaries), in semi-empirical correlation with the M³⁺ cation, these can be controlled experimentally.