From Diablo Wiki
Demonic Essence (DE) is a rare-quality crafting material first added to Diablo 3 patch v1.07. This material is still found in D3v2 and Reaper of Souls, but it is used only for level 1-60 crafting, enchanting, gem upgrading, and Artisan training. Above level 60, Death's Breaths take the place of DEs.
Demonic Essences are Account Bound (BoA) and can not be traded or given to other players. The developers' intent with DEs was to force players to play some and farm their own DEs for the new v1.07 crafting recipes, rather than simply being able to buy DEs along with all the other crafting materials required. They remain BoA in Reaper of Souls, though since all legendary crafting materials and gold are also BoA, there's no longer anything specially "you must farm them" about DEs. (Or their higher level replacement, Death's Breaths.)
 Demonic Essence Drop Rates
The drop rate for Demonic Essences were increased considerably in D3v2 and Reaper of Souls. The odds to drop (from valid sources) are identical for Death's Breaths and all legendary materials that drop from enemies, and can only be increased by increasing the difficulty level. Magic Find and the number of players in the game have no impact on the DE drop rate.
- Normal – 15%
- Hard – 18%
- Expert – 21%
- Master – 25%
- Torment 1 – 31%
- Torment 2 – 37%
- Torment 3 – 44%
- Torment 4 – 53%
- Torment 5 – 64%
- Torment 6 – 77%
 Diablo 3 classic
Demonic Essences were added to Diablo 3 in the v1.07 patch along with five new crafting recipes, all of which required 1 DE per item, and all of which could produce top quality rare items. All these recipes have since been superseded by much higher quality crafting options, but they were a big thing at the time. (The following recipes are altered in D3v2 since Tomes of Secret are no longer found in Diablo 3.
- Archon Chest Armor of Vit/Dex/Str/Int:
- 150k gold + 1 Demonic Essence + 2 Tomes of Secret
- Archon Amulet of Vit/Str/Int/Dex:
- 100k gold + 1 Fiery Brimstone + 1 Demonic Essence + 1 Perfect Square gem
- Archon Gauntlets of Vit/Str/Int/Dex:
- 50k gold + 20 Iridescent Tears (yellow) + 5 Tomes of Secret + 1 Demonic Essence
- Archon Shoulders of Vit/Str/Int/Dex:
- 75k gold + 10 Tomes of Secret + 1 Demonic Essence
- Archon Razorspikes of Vit/Str/Int/Dex:
- 50k gold + 30 Exquisite Essence (blue) + 5 Tomes of Secret + 1 Demonic Essence
 Demonic Essence Drop Rates
Demonic Essence drop rates were lower in Diablo 3 classic than they are today. In D3v they were only found on the Inferno difficulty level, and only the Monster Power difficulty setting affected their drop rate. Factors such as Magic Find or the number of players in the game do not impact DEs in any way.
The odds were as follows:, with the % chance increasing 10% on each higher difficulty level.
- MP 0: 15.0000%
- MP 1: 16.5000%
- MP 2: 18.1500%
- MP 3: 19.9650%
- MP 4: 21.9615%
- MP 5: 24.1577%
- MP 6: 26.5734%
- MP 7: 29.2308%
- MP 8: 32.1538%
- MP 9: 35.3692%
- MP 10: 38.9061%
 Marquise Gems
Demonic Essences were also required to create Marquise Gems.
The costs to create Marquise gems are much different/lower in D3v2, though DBs are still involved.
Images of Demonic Essences.