= Solution
<Burgers vector> conservation gives two candidate reactions, depending on the relative signs of the approaching segments:
$$
\mathbf b_1+\mathbf b_2=a[001],\qquad
\mathbf b_1-\mathbf b_2=a[1\bar10].
$$
Initially $b_1^2+b_2^2=3a^2/2$. The sum product has $b^2=a^2$, while the difference product has $b^2=2a^2$. Thus \b[the $a[001]$ product is favoured by <Frank's rule>; the $a[1\bar10]$ product is disfavoured]. The result is not annihilation, because the two supplied vectors are not opposite. The same ordering survives a simple character correction: with $\nu=0.30$, line energy proportional to $Gb^2[\cos^2\chi+\sin^2\chi/(1-\nu)]$ gives the two parent segments a combined coefficient $1.786a^2$, whereas any character of the sum product has coefficient between $a^2$ and $1.429a^2$ and any character of the difference product at least $2a^2$, comparing equal lengths and common logarithmic factors. A favourable <dislocation junction> can obstruct further glide and harden the crystal. Its actual mobility requires the junction line and allowed glide plane: the second screw can occupy several $\{110\}$ planes containing $[\bar111]$, so geometry is not unique. For instance, its $(101)$ plane intersects $(10\bar1)$ along $[010]$; an $a[001]$ junction on that line would glide geometrically on $(100)$, not either original plane. <Dislocation cross-slip>, junction unzipping or bypass can compete under load. An energy inequality alone is not a universal proof of a permanently sessile product.
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