History and specifics
The transphasic torpedoes work by delivering a subspace compression pulse existing in an asymmetric superposition of phase states. If one subcomponent of the pulse is blocked by shielding, others will still succeed in penetrating to the target to ensure that the majority of the pulse is still delivered. Each torpedo's transphasic configuration is different, randomly generated by a dissonant feedback effect, so there is no way for the Borg to predict the configuration of its phase states in order to shield against them. (TNG novel: Greater Than the Sum)
In the year 2381, the USS Enterprise-E was the only vessel that had been fitted with transphasic torpedoes. During the Borg sieges in February of this year, Captain Jean-Luc Picard recommended that the whole fleet be outfitted with the devices, to give the fleet a better chance of survival. He was over-ruled by Admiral Alynna Nechayev, who feared that the more the weapons were used, the more opportunity it gave the Borg to adapt. (ST - Destiny novel: Gods of Night)
Once the Borg invasion began, the Enterprise and Starfleet Command distributed the torpedo's specifications to every vessel they could. Starfleet also provided the technology to the Klingon Defense Force. By the conclusion of the Borg conflict, the Borg ships had adapted to transphasic torpedoes before the invasion could be stopped. (ST - Destiny novel: Lost Souls)
It was noted by engineers that the transphasic technology used in the torpedoes could be adapted to other parts of vessels' tactical systems. Using the principles in shielding caused a power drain, cutting warp speed (down to 9.1 on Sovereign-class ships), had the potential to quickly burn out shield emitters, and the Borg would be able to utilize wide-dispersal firing patterns to counter. The same principles could not be applied to phaser systems without an iron-60 crystal matrix to handle the strain, but it wouldn't output at sufficiently high energy levels to be effective. (ST - Destiny novel: Gods of Night)
In the 25th century, transphasic torpedoes are regularly used in combat by the various powers of the Alpha, Beta, and even Delta quadrants, even against non-Borg vessels. The Breen and the Voth use them regularly. They are not nearly as deadly as they were when used in the 24th century, but are still useful as they are capable of inflicting damage on targets which still have their shields up.
The Breen developed specialized variants of transphasic torpedoes, including a "cluster torpedo" that deploys a large transphasic mine net on impact and a "rapid reload" transphasic torpedo which can fire at a faster rate than standard launchers. The Voth employ hybrid transphasic-chroniton torpedoes, which have the additional effect of saturating a target with chroniton particles, affecting their ability to maneuver effectively. (STO video game: Star Trek Online)
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