**2. Alloys design**

The two series of alloys were designed across the single β-phase boundary, β/β+ω+(α"), with the aid of the *<sup>B</sup>*¯ *o*- *M*¯ *d* diagram. At this boundary, the elastic anisotropy factor, *A=C44/C'*, is rather high since the value of the elastic shear modulus, *C' = (C11-C12)/2*, is di‐ minishing as the alloy approaches this boundary [23,24], as shown in figure 1. Also, it has been reported that the *(C11-C12)/2* is related to the electronic parameter *e/a* (electron-peratom ratio) and its value approaches zero when the e/a value is about 4.24 [23]. This is the reason why, in this work, the *e/a* value was kept at 4.24 in almost all the designed alloys. Here, *<sup>B</sup>*¯ *<sup>o</sup>*is the average bond order between atoms, and *<sup>M</sup>*¯ *d*is the average d-orbital energy level (eV) of the elements in the alloy.

In A-alloys, A00 alloy is designed to be located in the β+α"(+ω) phase zone in the *<sup>B</sup>*¯ *o*-*M*¯ *d*dia‐ gram [20], as shown in figure 3. The composition of A-alloys is listed in table 1. The Fe and O were added to stabilize the β-phase of the alloys. Fe was chosen to stabilize β-phase due to its very strong β-stabilizing effect as obvious from its alloying vector in the *<sup>B</sup>*¯ *o*-*M*¯ *d*dia‐ gram [22]. The oxygen was added to the alloys to suppress the ω and martensite phases, as discussed in ref.[20].

As for Z-alloys, four alloys were designed with the aid of the *<sup>B</sup>*¯ *o*-*M*¯ *d* diagram across the β/β +ω+(α") phase boundary in two steps; in the 1st step, four alloys were designed, consist mainly of β-stabilizers, Ta, Nb, Mo, Cr and V. These four alloys are shown across the β/β+ω+ (α") phase boundary with the dashed arrow in figure 3.

As discussed above, Zr works as β-stabilizer in the β-type Ti alloys and also raises the *<sup>B</sup>*¯ *o* value of the alloy. The 2nd step was to add Zr to the alloys with different amounts varies with the required β-phase stability of each alloy. So, the stability difference between the al‐ loys will be much bigger and the properties difference would be clearer. Considering that the e/a value of the alloys did not change after Zr addition.

**Figure 3.** Extended *B*¯*o*-*M*¯*<sup>d</sup>* diagram showing the β/β+ω+(α") phase boundary and the location of the designed alloys, A00 and Z1-4. Also, the alloys A, B, C, and D are 35mass%Nb-4mass%Sn, Ti-24Nb-3Al, Ti-35mass%Nb-7.9mass% Sn, and Ti-22Nb-6Ta, respectively.

At last, the four designed Z-alloys, namely Z1 - 4, are located across the β/β+ω+(α") phase boundary in the high *<sup>B</sup>*¯ *<sup>o</sup>* region (i.e., high Zr-Containing alloys zone) in the extended *<sup>B</sup>*¯ *o*-*M*¯ *d* diagram shown in figure 3, and the chemical compositions are listed in Table 1.
