Emerald Shard

Emerald Shards (エメラルドのかけら) are fragments of Chaos Emeralds crushed by Doctor Eggman found in Sonic Battle. They are used to operate the E-121 Phi model robots. Once a Phi is destroyed, they drop their Emerald Shard and either break down or retreat. When five Emerald Shards of the same color are united, a Chaos Emerald can be created. Tails is the one who first discovered how Emerald Shards work and characters often visit him to have their Chaos Emerald reassembled which Emerl would soon absorb. Chaos Gamma is also seen with an Emerald Shard which he absorbs to injure Shadow. At the end of Emerl's story, Emerl exploded, smashing the seven Chaos Emeralds within him. They returned to Shards with Emerl's "soul" within them.

Master Emerald Shards
In Sonic Adventure and Sonic Adventure 2, the Master Emerald was broken into shards which Knuckles and Rouge collected. In the gameplay of the Stages, finding the Emerald Shards shattered around the environment are the main objective. To help locate them, the player can use the Emerald Radar.

In Sonic Adventure, Dr. Eggman shattered the Master Emerald to release Chaos. Knuckles then searched every stage for three shards and reassembled it on Angel Island. In Sonic Adventure 2, Rouge and Knuckles were fighting over the Master Emerald. Dr. Eggman attempted to steal it when Knuckles suddenly smashed it. Rouge wondered why and Knuckles revealed that it was his duty to protect it. Both Knuckles and Rouge searched every stage for Master Emerald Shards. Knuckles and Rouge eventually fight again where Knuckles saves her life. Rouge, in turn, returns her Shards to Knuckles, noting that they "stink like echidnas do". Knuckles then reassembles the Master Emerald and runs off. In Sonic Battle, when Sonic tried to use the Master Emerald to neutralize the out-of-control Emerl's Chaos Emeralds, it is said that Emerl smashed the Emerald into tiny pieces and was not seen for the remainder of the game. Some speculate however, that they were recovered along with the other Emerald Shards that were in the Death Egg.

Sonic X
The Emerald Shards make a few appearances in the anime series Sonic X. In this media, the only Emerald Shards shown are the fragments of the Master Emerald. Knuckles himself is shown to have limited control over the Emerald Shards which lets him levitate them through midair.

The Emeralds Shards first appeared in during the Chaos Saga, where Eggman shattered the Master Emerald to free Chaos. As such, Knuckles went of a search across the nearby areas on earth for the Emerald Shards to restore the Master Emerald. He eventually got all the Emerald Shards back and managed to rebuild the Master Emerald. The Emerald Shards appeared again near the end of the Metarex Saga where the Master Emerald shattered into several Emerald Shard after all its power was used to defeat Dark Oak. Knuckles then brought the shards back home to Angel Island where he could watch over them until their powers could return naturally.

Trivia

 * Strangely, Tails claimed that he could reassemble the Emeralds if the Shards were of the same color. However, all the Chaos Emeralds in Sonic Battle were given the same green Chaos Emerald sprite.
 * In the original Sonic Adventure, the Master Emerald shards are a very dark green and hard to see against some backgrounds. In Sonic Adventure DX: Director's Cut, they are much more radiant, and easier to see.