Transmission electron microscopy (TEM) is a powerful technique that allows us to form images and diffraction patterns from diverse nanomaterials. These images can be used to determine the morphological and structural features of the samples under study. However, what in practice is needed is a full structural characterization of the samples. For this task, techniques such as X-ray diffraction (XRD), high resolution TEM (HRTEM), optical spectroscopy, Raman spectroscopy, infrared spectroscopy (IR) and fluorescence analysis must be used. All these in addition to the physical and chemical information are already available.

In this work, we describe a structural characterization of nanoparticles based on high resolution TEM images using our own software as well as commercial programs. To achieve this goal we study the synthesis of bismuth oxide particles through a biosynthesis method, using tannic acid as reducing agent, since these samples are very rich in structural details. Nowadays several research groups work on the synthesis of nanoparticles with technological applications using novel preparation methods, preferably those that are cheap end environmentally friendly. One of the interesting materials is bismuth oxide Bi₂O₃, which has many applications including medical ones since the α-Bi₂O₃ phase due shows fungicidal activity against Candida Albicans [1] and also selectivity detection of NO as gas sensor [2] , etc. In its most stable phase, α-Bi₂O₃ is a p-type semiconductor [3] that has been synthetized by several methods such as: hydrothermal [4] , sol-gel [5] , laser ablation [6] [7] , Bismuth oxidation [8] , microwaves [9] , micro emulsion [10] , PEG Precipitation [11] .

In order to prepare our samples, we use a small variation of the method of synthesis previously published [12] . In this method where used tannic acid (C₇₆H₅₂O₄₆) and bismuth nitrate pentahydrate Bi(NO₃)₃*5H₂O, the pH value was changed with NaOH and stabilized in pH = 11 in order to obtain a more alkaline environment in the synthesis to continue the process of lyophilization [13] . Yellow-brown powder was obtained from which the samples for both HRTEM and XRD were prepared.

The microscopy characterization was done with a JEOL JEM-2010F FasTem microscope operating at 200 kV with a spherical aberration coefficient Cs = 0.5 mm and fitted with analytical facilities. The X-ray measurements were carried out with a D8 Advance Bruker AXS diffractometer with CuK_α radiation. The X-ray Diffraction Pattern was measured in the 2θ range from 4˚ to 130˚ with a step 0.019˚.

For image processing and indexing of the nanoparticles, the computer programs Digital Micrograph and Diffraction Pattern Indexing Program (DPIP) [14] were used. Simulation of the nanoparticle morphology, TEM images and electron diffraction patterns was done with SimulaTEM [15] , Materials Studio Version 2.1.5 and CaRiNe version 4.0 software.

The procedure followed is shown in a schematic way in Figure 1. The starting point is a high resolution image obtained from the Transmission Electron Microscope, and then the digital Fast Fourier transform (FFT) of the image (or of a desired part thereof) was obtained with the help of the commercial Digital Micrograph software. From this diffractogram we select at least two different spots and the (x,y) coordinates (with respect to a given rectangular coordinate system) are obtained. The center of the pattern is taken as the origin (0,0) of the reference frame.

In the next stage we use our own tool DPIP to which we feed the relevant diffraction data from the powder diffraction files (such as h,k,l reflections and intensities, lattice parameters of the candidate structures, etc). We also input the (x,y) coordinates of the spots from the diffractogram and we select tolerance limits ∆angle and ∆distance (the difference between measured and calculated values).

DPIP provides the zone axis and the Miller indexes of the lattice planes considered that best match the measured spots. The program considers as many structures as needed (each represented by its x-ray table) but takes into account only solutions within the established error limits (∆angle and ∆distance).

The next step is to calculate the coordinates of all the atoms in a cluster of the same size as the actual cluster in the original image. For this, we use data from the literature and sometimes we are assisted by Materials Studio. The structure calculated is based on the identification provided by DPIP software.

After this, we feed the structure to SimulaTEM with which we can simulate images and diffraction patterns using the multislice method [16] . The input in this case consists of the coordinates (x,y,z) and atomic number of each atom together with the operating conditions of the microscope (accelerating voltage, spherical aberration etc.).

Once the data are introduced, the particle is oriented along the desired zone axes. Then focal series are calculated in a neighborhood of the Scherzer defocus condition. The procedure is repeated as many times as desired depending on how many zone axes and structure solutions are given by DPIP software. Finally the calculated and observed images are compared. Once the best matches are obtained we calculate the corresponding diffraction patterns for comparison with the diffractograms. The CaRiNe 4.0 software can be used to verify that the indexing is consistent and in agreement with the geometry (space group) of the sample.

Here a full example of the procedure is shown outlined above where we want to identify a phase present in a particle starting with a HREM image (obtained with a JEOL JEM-2010F microscope).

Figure 2(A) shows the experimental image; Figure 2(B) presents an enlarged view of the selected particle, and finally Figure 2(C) displays the corresponding FFT (diffractogram). As described before, the images Figure 2(B) and Figure 2(C) were obtained with the help of the Digital Micrograph software.

For this example we selected the spots encircled in the figure. With Digital Micrograph the positions (x,y) of the spots are measured. ((0,0) is assigned to the center of the diffractogram).

Given the preparation procedure, the nanoparticle is expected to be one of the possible bismuth oxides such as BiO [17] , Bi₂O₃ [18] , Bi₂O₄ [19] , among others, but the most interesting is Bi₂O₃ due the polymorphs that this oxide presents, and their possible applications.

We considered the Bi₂O₃ polymorphs α-Bi₂O₃ (Monoclinic,) [20] , β-Bi₂O₃ (Tetragonal) [21] , γ-Bi₂O₃ (BCC) [22] , δ-Bi₂O₃ (FCC) [23] and H-Bi₂O₃ (hexagonal) [24] respectively. The crystallographic information for each of these is taken from the Powder Diffraction Files. PCPDFWIN x-ray card (version 2.2, 2003). Table 1 shows these data.

With the positions of the spots and the known crystallographic data of the candidate structures we index the diffractograms using an error bound of ∆angle and ∆distance less than 1.1 degrees and 0.5 Å. After running DPIP for each of the polymorphs described above and for pure Bi (Monoclinic) [25] . We find that the smallest error of ∆angle corresponds to the δ-Bi₂O₃ phase (77-0374). However, this phase present a ∆distance out of the error limits that we set; so that this solution was not taken. In the same way, the error limit in ∆angle was higher than the permitted error for phases such as Bi monoclinic (65-6203), Bi rombohedral (05-0519) and H-Bi₂O₃ (51-1161). At this stage, the remained possibilities are α-Bi₂O₃ and β-Bi₂O₃, so the analysis is now limited to

only two phases. X-Ray diffraction results pointed out that the predominant bismuth oxide in the sample correspond to the β-Bi₂O₃. Therefore, the use of complementary information allowed to discern between those proposed solutions. Several studies on bismuth oxide polymorphs have been reported and it is known that in bulk, β-Bi₂O₃ is metastable; however, this phase has been observed at the nanoscale level [26] -[28] .

Once the phase has been determined we see, Table 1, that there are two possible zone axes: [121] and [211].

To compare this result HRTEM images were simulated by using Simula TEM software. In figure 3(A) starting with the unit cell for β-Bi₂O₃ [29] , we construct a super cell (Figure 3(B) and finally larger nanoparticle with the help of Materials Studio till we get a cuboctahedral shape with 24425 atoms and 10.86 nm width, as shown in Figure 3(C).

Once the structure is obtained, the cluster is rotated to any desired zone axis; given that the positions (x,y,z) and atomic numbers of all the atoms are known SimulaTEM can be used with the parameters describing the actual microscope operation. The experimental image is shown in Figure 2 and the microscope parameters are enlisted in Table 2. The starting point for the focal series was taken to be the Scherzer defocus condition.

The focal series can be seen in figures 4(A)-(C) for [121]. Figures 4(D)-(F) focal series for [211] in comparison with Figure 2 shows that the best visual fit is to a [121] zone axis orientation.

In Figure 5(A), the experimental HREM is shown together with the simulated images figure 5(B) and its simulated diffraction pattern, figure 5(C).

So far the phase and the zone axis have been determined and it only remains to complete the indexing of the points in the diffractogram. CaRiNe software was employed for comparison.

The final result is shown in Figure 6, where we display the indexed diffraction pattern for a β-Bi₂O₃ (Tetragonal) structure. The points d₁ and d₂ from the diffractogram correspond to the planes (−2 1 0) and (0 −1 2) respectively. In Figure 7, the X-ray diffraction pattern confirms the presence of β-Bi₂O₃ which corresponds to ICDD:PDF-2 card 00-0027-0050. In addition to this phase NaNO₃ (Nitratine) is detected (PDF-2 card 00-036- 1474). The characterization of the particle has been completed.

A protocol for structural characterization of nanoparticles based in high resolution TEM images was described. High resolution images must be Fourier-transformed to obtain reciprocal space information, in general a direct electron diffraction pattern is difficult (but not impossible) to obtain for particles in this size range. These diffractograms together with x-ray spectra (necessarily from large samples) represent an excellent option for the identification of the phase. The images provide information on the shape (habit) of the nanoparticles, indicates whether they are single crystals or twins or if there are structural defects such as stacking faults or dislocations. Working with many particles provides size distributions. Greater certainty is provided from the comparison between actual and simulated images and diffraction patterns.

Although the X-ray spectrum indicates the presence of β-Bi₂O₃ only the detailed analysis we have presented confirms that a given particle is (or is not) β-Bi₂O₃. Figure 1 summarizes the analysis procedure that we propose, the message being that both actual measurements and simulations complement each other.

Our gratitude to Roberto Hernández Reyes for his aid with the Electron Microscope, Antonio Morales for X-Ray measurements at IFUNAM and to Dr. José Guadalupe Pérez for allowing us to use his licensed copy of CaRIne. The financial support from DGAPA (grant PAPIIT IN108915) is also acknowledged. Francisco M. Ascencio Aguirre thanks to CONACyT for the Ph.D. scholar fellowship.

Francisco Miguel AscencioAguirre,LourdesBazán-Díaz,RubénMendoza-Cruz,AlfredoGómez-Rodríguez,CristinaZorrilla-Cangas,RaúlHerrera-Becerra, (2015) Nano Phase Characterization by Transmission Electron Microscopy: Experimental and Simulation. Materials Sciences and Applications,06,935-942. doi: 10.4236/msa.2015.611094