*3.4. Orientation Bias of Boundary Planes*

In the polycrystalline structure, the boundary can be defined either as a high-angle boundary when the misorientation angle across the boundary is higher than 15◦, or a low-angle grain boundary when the misorientation angle across the boundary is between 2◦ and 15◦. The image quality maps of the samples are displayed in Figure 5, where the high-angle and low-angle grain boundaries are highlighted in different colors.

It is evident that the sample HBM (Figure 5a) has prevalent low-angle boundaries with a fraction about 67%. As a contrast, the fraction of the low-angle boundaries is merely 30% for the sample TBM with an inhomogeneous lamellar structure (Figure 5c). Furthermore, the microstructure of the sample TBM shows several severely coarse "deformation bands" separated by thin lamellae. The lamellae grains contain high fractions of low-angle boundaries (up to 61%), while little low-angle boundaries and high-angle boundaries within the coarse "deformation bands" can be observed. Thus, a pronounce difference in the grain boundary misorientation of the base metal between the horizontal surface and the transversal section of the welded joint could be found.

For the weld metal, specific difference in the boundary misorientation distributions can be observed between sample HWM (Figure 5b) and sample TWM (Figure 5d). Here, the fraction of the high-angle boundaries for samples HWM and TWM are 67.6% and 53.8%, respectively, that is to say, the weld metal in the horizontal surface has much higher fraction of the high-angle boundaries. A comparison of these results with those of the base metal demonstrates the clear shift in the boundary misorientation distributions from low to high angles. Another difference is, the clustering of the low-angle boundaries is often found within grains, whereas the high-angle boundaries are more prone to occur along grain contours, or, between grain pairs. Hence, there might have a distinct difference in the grain boundary misorientation of the weld metal along different directions.

**Figure 5.** Grain boundary traces imposed on image quality map of base metal and weld metal in 5A90 Al–Li alloys along different sample directions: (**a**) Sample HBM, (**b**) sample HWM, (**c**) sample TBM, and (**d**) sample TWM, with high angle (>15◦) grain boundaries shown as blue and low angle (2~15◦) boundaries as red.

A frequency distribution of misorientation angles for sample HWM and sample TWM with a superimposed random McKenzie distribution [28] is shown in Figure 6. The average misorientation angles deduced from the histograms are 30.4◦, and 24.9◦ form sample HWM and sample TWM, respectively. Figure 6 overall illustrates that the misorientation distribution of sample HWM and sample TWM is much different from random distribution. In addition, the relative frequency of intermediate (30◦ to 50◦) for the sample HWM is higher than that of the sample TWM. Meanwhile, the relative frequency of low-angle boundaries for sample HWM is lower than that of the sample TWM. The above results on the whole illustrate the heterogeneity of misorientation of the weld metal on different directions.

**Figure 6.** Misorientation angles distributions of the laser weld metal of 5A90 Al–Li alloys along different directions.

The GBP-ODF requires large amount of boundary quantity for a complete analysis [22] and in the current work, only sample HBM and sample TBM can meet this standard. The GBP-ODFs of Σ3 boundaries in the sample HBM and sample TBM were calculated and the outcomes are presented in Figure 7. In the sample HBM, the Σ3 boundary shows a tilt boundary feature [29], with distribution intensity in units of 63.5 multiples of a random distribution (MRD); while in the sample TBM, the Σ3 boundary shows a twist boundary character [29], with distribution intensity of 97.3 MRD. Since the Σ3 boundary can be regarded as a 60◦ rotation along the <111> axis [20], the above results show that the Σ3 boundary exhibit simple geometries. Nevertheless, Σ3 tilt (in sample HBM) and Σ3 twist (in sample TBM) may correspond to specific structures and, consequently, to special physical properties of boundaries. The indexed twist and tilt Σ3 boundaries in the cubic case clearly illustrated that the misorientation distribution in the base metal is not homogeneous along different directions, which could cause the diversity of mechanical properties along different directions in the weld metal. The microhardness across the welded joint from left to right including the base metal, HAZ and weld metal for sample HWM and sample TWM were measured, and the results are shown in Figure 8a,b, respectively. For the base metal, the average hardness value of the base metal is 128 HV in sample HWM, while the average hardness value of the base metal in sample TWM is 117 HV. It indicates that the indexed twist and tilt Σ3 boundaries in the base metal along different directions have resulted in the diversity of the microhardness due to the homogeneous microstructure along different directions. For the weld metal, the microhardness along different directions is affected strongly by its own base metal. As observed in Figure 8, the hardness value measured in the weld metal is ~102 HV for sample HWM, whereas the hardness value measured in the weld metal is ~92 HV for sample TWM. Thus, it can be seen that the hardness value of weld metal is evidently lower than that of the base metal, meaning the softening of the weld metal. Although both sample HWM and sample TWM reveal the softening of the weld metal, the degree of the drop in the hardness of the weld metal is highly correlated to the microtexture developed in the base metal.

**Figure 7.** Grain boundary plane orientation distribution function along different sample directions in the base metal of 5A90 Al–Li alloys, showing orientation texture of boundary planes plotted along the [001] direction: (**a**) sample HBM, and (**b**) sample TBM. Texture intensities are given in unit of MRD.

 **Figure 8.** Hardness profiles along different sample directions in the welded 5A90 Al–Li alloys: (**a**) sample HBM, and (**b**) sample TBM.

### **4. Conclusions**

Based on the above results and discussion, the following conclusions can be made from this work:


**Author Contributions:** L.C. and D.H. conceived and designed the experiment. X.Y. and Z.P. performed the experiments; Z.P. and X.Y. analyzed the data; D.H. and L.C. contributed materials and analysis tools; and L.C. wrote the paper.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant no. 51475006, no. 51471007) and the Key Program of Science and Technology Projects of Beijing Municipal Commission of Education (grant no. KZ201610005004).

**Conflicts of Interest:** The authors declare no conflict of interest.
