The first step in identification of a phase is to search for crystallographic information, such as lattice parameters, space groups, interplanar spacings of the (hkl) plane, and the reference SADPs of a known phase from a textbook [1] - [6] , from software, or from the internet. Then, through TEM observations, recording an SADP with a low-order zone axis is necessary to assist the pattern indexing of the known phase. The next priority work is to measure the angle between the diffracted spots and to calculate the d-spacing of the diffracted spots nearest the (000) transmitted spot. The formula for calculating the d-spacing of diffracted spots is as follows [1] - [3] :

The distance, R, is measured from the diffracted spot to the (000) transmitted spot. Because the electron wavelength, l, and the camera length, L, are constant, we can measure the distance R and obtain the d-spacing of the diffracted planes. For example, if the value of l is 0.0251 Å at 200 kV, the value of L is 80 cm, and R is measured to be 0.74 cm, then the d-spacing (d) will be 2.7135 Å. At present, charge coupled device (CCD) cameras are generally used instead of conventional developed film to more readily measure the d-spacings of diffracted planes. If the imaging system of TEM were a conventional developed film, it would be necessary to memorize the camera length (L) while recording the SADPs. If the TEM used a CCD camera to capture the SADPs, the d-spacing of the diffraction patterns should be measured on-site because the measurement software is not available to get for general user. In addition, accurate measurement of the d-spacing of diffracted planes using a CCD camera requires periodical calibration of the imaging system of the TEM instrument.

To begin indexing a known phase, one should measure the angles of diffracted planes and at least two independent, and not co-linear, diffraction spots. Figure 1(a) presents an example of a SADP of Si with a low-order zone axis, recorded using a CCD camera. Two diffraction spots, d1 and d2, nearest the (000) transmitted spot can be measured as having d-spacings of 2.70 and 3.04 Å, respectively. The angles of the diffracted spots in the Figure 1(a) were also measured. The second step of the indexing process involves searching a database for the d-spacings of the diffraction planes and the SADPs of Si [Figure 1(b) and Figure 1(c)]. If possible, all of the reference diffraction patterns should be listed with various zone axes and then matched to the experimental SADPs. After matching the references to the experimental SADP of Si in Figure 1(a), the d-spacings of d1 and d2 and the angles of the diffracted patterns were consistent with those of the reference SADP of Si along with a zone axis of [011]. Figure 1(d) displays the final indexing of the SADP of Si in Figure 1(a).

Using trial-and-error to match the experimental and reference SADPs is a necessary and significant step in phase identification. Thus, having access to a large number of reference SADPs and their related d-spacings and angles of diffracted spots will assist in the indexing the SADP; these references are, however, limited in textbooks [1] [2] [6] , increasing the difficulty of indexing complex crystal structure to known phases. Much crystallographic software has been developed to aid the indexing of SADPs because the reference SADPs and interplanar spacings are easy to identify after inputting the lattice parameters of interest, which are readily obtained

from the internet from crystallographic databases such as the crystallography open database or the inorganic crystal structure database (ICSD).

For identification of an unknown phase, the first step is using EDS to determine its composition, allowing database searching for related references. A series of SADPs from one grain of the unknown phase should then be recorded. Figure 2 displays the procedure for recording a series of SADPs with different zone axes for an unknown phase. To begin with, one grain of unknown phase should be tilted to a pole along with one zone axis, such as zone 1 in Figure 2; the next SADP should be tilted along with the Kikuchi line of g1 in zone 1 or the g1 spot should be kept strongly excited to the SADP with zones 2 and 3. Next, one should return to zone 1 and tilt to zones 4 and 5 along with the Kikuchi line of g2 of zone 1. Finally, a series of SADPs of unknown phase with five zone axes should be captured. In addition, the (X, Y) coordinates of each zone axis should be recorded because the angle between the different zone axes can be calculated from these values. These (X, Y) coordinates should be noted immediately on-site, because these values will not exist either on the developed film or on the digital image of the SADPs out of TEM observations. Moreover, it is necessary to label which SADPs belong to the low-order zone axes, revealing a large number of Kikuchi lines crisscrossed together in the Kikuchi pattern, as in zones 1, 3, and 5 of Figure 2. It is not necessary to draw detailed data of the serial SADPs, as in Figure 2, because it is time-consuming to perform on-site. It is, however, necessary to record the (X, Y) coordinates along which the Kikuchi line is tilted and to at least label the low-order zone axis to help with indexing of the SADP.

Figure 3 presents a transmission electron micrograph (bright-field image, BFI) of the unknown Ti_xO_y phase at the interface between the 96.4Au-3Ni-0.6Ti interlayer and YSZ of a steel/96.4Au-3Ni-0.6Ti interlayer/YSZ joint. Using EDS, the composition of the unknown Ti_xO_y phase is composed of 42.2 at% of Ti, 53.7 at% of O, 1.0 at% of Zr, and 0.1 at% of Y. The next step involved recording a series of SADPs of the unknown Ti_xO_y phase (Figure 4) and determining related information, as mentioned above. After TEM observation, we measured the d-spacing of the diffracted spots, the angle between the diffracted spots, and the tilting angle between the zone axes for the series of SADPs of the unknown Ti_xO_y phase; Figure 4 also displays these calculated values. For instance, in zone axis (1), we measured the two diffracted spots nearest the (000) transmitted spot, labeled as “T”, and the angles between diffracted spots, with values of 4.28 Å, 2.73 Å, 59.0˚, and 33.4˚, respectively. The low-order zone axis was labeled in the SADP with zone axes (2), (4), and (8) of Figure 4, according to the many Kikuchi lines crossing together in the Kikuchi patterns on TEM observations. Figure 4 also displays the calculated tilting angles between the two zone axes; for example, 22.1˚ for zone axes (1) and (2), 16.6˚ for zone axes (2) and (3), and 18.3˚ for zone axes (2) and (7). Figure 5 presents the method for calculating the tilt-

ing angle between two zones. The angle between zones 1 and 2 is the distance between the two zones in the 2D (X, Y) axis, projected by three-dimensional (3D) coordinates. Using the Pythagorean theorem, the distance, or angle, of zones 1 and 2 can be calculated using the equation

.

here, (X1, Y1) and (X2, Y2) are the (X, Y) coordinates of the zone axes 1 and 2, respectively. Again, it is important to record the (X, Y) coordinates of each zone axis on TEM observations, otherwise the information relating

to the tilting angle will be lost. Because the holder is side entry stage, the X and Y tilts are really not equivalent to exactly determine the specimen tilt from goniometer readings. Thus, the actual tilt angle is not obtained by the equation of Figure 5 but it is acceptable to get the tilt angle using the equation because the deviation just about 1 - 2 degrees evidenced by the tilt angle calculation of a known phase, Si.

At this stage, the composition and a series of SADPs of the unknown Ti_xO_y phase have been obtained [Figure 3(b) and Figure 4]. The next step is to establish the crystal structure and lattice parameters of the possible Ti_xO_y phase, using a database such as the crystallography open database or the ICSD, as listed in Table 1. Next, the trial-and-error method is used to match the experimental SADPs in Figure 4 with the simulated or reference SADPs of the possible Ti_xO_y phase. It is, however, difficult to search a series of reference SADPs of all the Ti_xO_y phases in Table 1 from textbooks or reference articles. In contrast, a series of simulated SADPs of unknown phase is easy to produce using crystallographic software once we know some crystallographic information, such as the crystal structure and lattice parameters. Thus, many SADPs with different zone axes can be simulated, but those with low-order zone axes are preferred for initial simulation to quickly match with the experimental SADPs of low-order zone axes. The low-order zone axes probably belong to the <100>, <110>, <111>, <120>, and <112> families. Figure 6 presents a series of simulated SADPs of TiO₂ along with the, , and zone axes. The software should immediately record the d-spacing of two diffracted spots nearest the (000) transmitted spot, the angle between the diffraction spots, and the angle between the two zone axes. Next, the simulated SADPs of TiO₂ along the, , and zone axes in Figure 6 should be compared with the experimental SADPs with zones 2, 4, and 8 (the low-order zone axes) of Figure 4, whether any one set of SADPs is matched or not. The simulated SADP along with the zone axis in Figure 6 appears to match the SADP along with zone 2 of Figure 4, because their d-spacings, angles, and pattern shapes are similar. For instance, in Figure 6 the d-spacings of the two diffracted spots in the simulated SADPs with the zone axis are 2.293 and 2.483 Å; for the experimental SADPs with zone axis (2) of Figure 4, the d-spacings of the two spots were 2.56 and 2.73 Å. In terms of the angles of the diffracted spots, from Figure 6 we measured values of 57.21˚ and 65.57˚ for the simulated SADPs with the zone axis of [100]; in Figure 4, the values are 58.8˚ and 63.1˚ for the experimental SADPs with zone axis 2. Although one set of SADPs might be matched (the SADP with in Figure 6 and that with zone 2 in Figure 4), we must still confirm the matching of the whole set of simulated and experimental SADPs. The angle of the zone axis of to the zone axis along with the plane in Figure 6 is 32.79˚; this value is consistent with that of the experimental SADP with the zone axes (2) and (8) in Figure 4 (18.3˚ + 17.8˚ = 36.1˚). Similarly, the angle between the simulated SADP with the zone axes of and in Figure 6 is 30.74˚, similar to the angle of the experimental SADP with zones (2) and (4) (16.6˚ + 19.6˚ = 36.2˚). Unfortunately, the shape of the simulated SADPs of zone axes of and of Figure 6 does not match that of the experimental SADP of the zone axes (8) and (4) in Figure 4. Thus, the d-spacings of their diffracted spots and the angles between the two spots are different. Consequently, this comparison of the simulated and experimental SADPs suggests that the unknown Ti_xO_y phase is not TiO₂.

Figure 7 displays another simulated SADP of TiO along with, , and zone axes. Following the procedure described above, the simulated SADPs of TiO along with the, , and zone axes in Figure 7 do not match with the experimental SADPs of zones (8), (2), and (4) in Figure 4, including the d- spacings of the diffracted spots, the angles between the two spots, and the tilting angles between the two zone axes. The next step was to use the trial-and-error method to compare the simulated SADPs of all possible Ti-O phases, based on Table 1, with the experimental SADPs of the unknown Ti_xO_y phase.

Figure 8 presents a series of SADPs of Ti₂O₃ along the, , , , , , , and zone axes; they match the experimental SADPs in Figure 4. First, we simulated the SADPs with the low-order index zone axes of and of Ti₂O₃ and compared them with the experimental SADPs with the low-order zone axis, as in the zone axes (2), (4), and (8) in Figure 4. We find that the simulated SADP with the zone axis matches the experimental SADP with zone axis (4) in Figure 4. For instance, in the simulated SADP with the zone axis of in Figure 8, the d-spacings of and are 3.734

and 2.707 Å, respectively; for the experimental SADP of zone (4) in Figure 4, the d-spacings of then corresponding diffracted spots are 3.81 and 2.73 Å, respectively. Moreover, the angle between and of the simulated SADP of the zone axis in Figure 8 is 94.02˚ (56.72˚ + 37.30˚); for the experimental SADP with the zone axis (4) in Figure 4, the angle between the two nearest spots is 94.0˚ (57.2˚ + 37.8˚). Next, we simulated all the SADPs of Ti₂O₃ and compared them with the experimental SADPs of the unknown Ti_xO_y phase in Figure 4. We found that the simulated SADP of the zone axis in Figure 8 was consistent with the experimental SADP with zone axis (4) in Figure 4. The next simulated SADP should be tilted along with the plane of the SADP with zone by approximately 19.95˚ to get the simulated SADP with zone axis of, tilted continuously by approximately 16.03˚ to get the simulated SADP with the zone axis of, and then tilted along the plane of the simulated SADP with the zone axis of to get the simulated SADP of the and zone axes. The tilting direction from a simulated SADP to the next simulated SADP should accord to which Kikuchi line of the SADP is tilted with respect to another SADP when recording a series of experimental SADPs through TEM observations. Thus, it is important to record the position and Kikuchi line of each experimental SADP and which Kikuchi line of the SADP was tilted (or which diffracted spot was excited) with respect to another SADP. In addition, while matching an SADP, the structure factor rules might eliminate certain diffraction spots in the SADP. For example, the diffracted spot, marked as “×”, disappeared in the simulated SADP with zone axes of and. Following the matching procedure, all of the simulated SADPs of Ti₂O₃ will match with the experimental SADPs of the unknown Ti_xO_y phase, including the d-spacings of the nearest diffracted spots, the angles between the two diffracted spots, and the tilting angles between the two zone axes. Figure 9 displays the final indexing of the SADPs of Ti₂O₃. From the EDS spectra in Figure 3(b) and the experimental and simulated SADPs in Figure 4 and Figure 9 for the unknown Ti_xO_y phase, we conclude that the unknown Ti_xO_y phase at the interface between the 96.4Au-3Ni-0.6Ti interlayer and YSZ of a steel/96.4Au-3Ni-0.6Ti interlayer/YSZ joint was Ti₂O₃. The mechanism of formation of Ti₂O₃ has been discussed previously [6] .

Figure 10 outlines the procedure for TEM-based phase identification of known and unknown phases. For the known phase, it is necessary to capture an SADP having a low-order zone axis through TEM observation, if possible. Measurement and calculation of the d-spacing of the nearest diffracted spots and angle between the two zone axes is the next step. The d-spacing of the diffracted spots should be measured on-site in the digital film; alternatively, the camera length and electron voltage for the developed film should be recorded to calculate the d-spacing of the diffracted spots using the equation Rd = lL. Next, the crystallographic information of a known phase should be searched—namely, the lattice parameters, the space group, and the interplanar spacing of the (hkl) plane—and referenced to the SADPs from a textbook or any crystallographic software. The final step is to match the experimental SADP with that of the reference. For an unknown phase, the EDS spectrum and a series of SADPs are required from TEM observations. The Kikuchi line and (X, Y) coordinates of each SADP should be recorded on-site. The d-spacing of the nearest diffracted spots and the tilting angle between two zones should be similar to those of the known phase. Next, crystallographic information (from the crystallography open database, the ICSD, or from the internet) should be listed for all possible unknown phases. Using crystallographic software makes it easy to obtain reference SADPs for matching with possible unknown phases. The trial-and-error method can be used to match the simulated SADPs of all possible unknown phases with the experimental SADPs. The d-spacings of diffracted spots, the angles between two diffracted spots, and the angles between two zone axes for all simulated and experimental SADPs should be consistent.