## 3 Results and Discussion
### Elastic Properties
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Compd.** & \multicolumn{3}{c}{**Space Group**} & **Structure Type** & **a (A)** & **V (Å)** & **B\({}_{0}\) (GPa)** & **B\({}_{0}\)\({}^{\prime}\)** & **B\({}_{0}\)\({}^{\prime\prime}\)** \\ \hline \multirow{3}{*}{Co\({}_{2}\)Zr} & Present & Fd\(\overline{3}\)m & Cu\({}_{2}\)Mg & 6.918 & 331 & 192 \({}^{\rm a}\) & 4.370 \({}^{\rm a}\) & \(-\)0.031 \({}^{\rm a}\) \\  & work & — & — & — & — & 192 \({}^{\rm b}\) & 4.426 \({}^{\rm b}\) & \(-\)0.034 \({}^{\rm b}\) \\ \cline{2-10}  & Ref. [18] & Fd\(\overline{3}\)m & Cu\({}_{2}\)Mg & 6.951 & 336 & — & — & — \\ \hline \multirow{3}{*}{Co\({}_{2}\)Ti} & Present & Fd\(\overline{3}\)m & Cu\({}_{2}\)Mg & 6.675 & 297 & 213 \({}^{\rm a}\) & 4.533 \({}^{\rm a}\) & \(-\)0.033 \({}^{\rm a}\) \\  & work & — & — & — & — & 199.29 \({}^{\rm b}\) & 5.247 \({}^{\rm b}\) & \(-\)0.045 \({}^{\rm b}\) \\ \cline{2-10}  & Ref. [18] & Fd\(\overline{3}\)m & Cu\({}_{2}\)Mg & 6.692 & 299.69 & — & — & — \\ \hline \end{tabular}  
\({}^{\rm a}\) quasi-harmonic Debye model. \({}^{\rm b}\) natural strain equation of state (EOS).  
\begin{tabular}{c c c c c c c c c} \hline \hline
**Compd.** & \multicolumn{3}{c}{**C\({}_{\rm II}\)**} & **C\({}_{\rm II}\)** & **C\({}_{\rm II}\)** & **C\({}_{\rm 44}\)** & **B\({}_{\rm 5}\)** & **G** & **\(\Theta\)** \\ \hline \multirow{3}{*}{Co\({}_{2}\)Ti} & Present work & 331 & 154 & 132 & 231 & 112 & 834 \\ \cline{2-10}  & Ref. [23] & 300 & 134 & 127 & — & 107 & — \\ \cline{2-10}  & Ref. [26] & CoTi & 287 & 114 & 75 & — & 79 & 314 \\ \cline{2-10}  & Ref. [24] & Co\({}_{3}\)Ti & 269 & 168 & 119 & — & 84 & — \\ \hline \multirow{3}{*}{Co\({}_{2}\)Zr} & Present work & 283 & 137 & 107 & 192 & 92 & 721 \\ \cline{2-10}  & Ref. [26] & CoZr & 201 & 113 & 45 & — & 45 & 207 \\ \hline \hline \end{tabular}  
\end{table} 
Table 1: The structure parameters of Co\({}_{2}\)Zr and Co\({}_{2}\)Ti at 0 GPa and 0 K.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**P (GPa)** & **C\({}_{\rm II}\)** & **C\({}_{\rm II}\)** & **C\({}_{\rm 44}\)** & **B** & **G\({}_{\rm V}\)** & **G\({}_{\rm R}\)** & **G** & **E** & \(\Theta\) & **\(\sigma\)** & **A** & **G/B** \\ \hline
0 & 283 & 137 & 107 & 186 & 93 & 90 & 92 & 193 & 721 & 0.326 & 0.238 & 0.493 \\ \hline
10 & 262 & 92 & 125 & 149 & 109 & 105 & 107 & 214 & 790 & 0.260 & 0.302 & 0.718 \\ \hline
20 & 421 & 231 & 141 & 295 & 122 & 118 & 120 & 256 & 850 & 0.355 & 0.219 & 0.407 \\ \hline
30 & 349 & 141 & 158 & 211 & 137 & 131 & 134 & 268 & 906 & 0.288 & 0.310 & 0.635 \\ \hline
40 & 501 & 275 & 171 & 351 & 148 & 142 & 145 & 30 The shear modulus G represents the plastic deformation resistance, while the bulk modulus B represents the fracture resistance. In 1954, the ratio between shear modulus G and bulk modulus B G/B was given by [PERSON] [41] to evaluate the ductility of given materials. A smaller G/B value indicates toughness while a larger G/B value shows brittleness, and G/B = 0.57 is the critical value between toughness and brittleness. The G/B values of Co\({}_{2}\)Zr and Co\({}_{2}\)Ti that change by pressure (0-100 GPa) at 0 K are given in Tables 3 and 4. For Co\({}_{2}\)Zr crystal, the G/B values are abnormal at 10 and 30 GPa, which were 0.718 and 0.635, respectively, both over 0.57, which illustrates the Co\({}_{2}\)Zr crystals are brittle at 10 and 30 GPa. Under other pressures, we can find that the G/B decreases continuously and is far less than 0.57 with the increase in pressure, indicating the toughness of Co\({}_{2}\)Zr increases with the increment of pressure except at 10 and 30 GPa. For Co\({}_{2}\)Ti, G/B = 0.528, Co\({}_{2}\)Ti is apt to ductile at 0 K and 0 GPa. The G/B is in proportion to the pressure between 10 and 60 GPa, and the G/B is equal to 0.559 at the pressure of 60 and 70 GPa.