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The recipes available for the crucible are as follows:

Basic Recipes

Thaumium - 4 Praecantio + iron ingot.
The first of the overtly magical products, thaumium is a versatile and useful metal which can be used for tools, swords and armor. The resulting items alike rival diamond for durability, and approach it for effectiveness. The tools and swords can also be Infusion-crafted into various special items with unique abilities. Normally this recipe will be done with phials of Praecantio, 1 phial for each 2 ingots of iron.
Magical Tallow - 2 Praecantio + rotten flesh
Like thaumium, this will normally be produced with phials of Praecantio, 1 phial for 4 pieces of flesh. The tallow can be crafted into magical candles, which help reduce instability in Infusion.
Nitor - 3 Ignis, 3 Potentia, 3 Vis + glowstone dust.
This eternal flame can provide both light and heat, with no risk of being set afire. It is notably useful for heating the crucible itself, as Nitor is unaffected by flowing water. This recipe can be done by tossing in 3 (char)coal and 6 torches for each 2 glowstone dust to be converted.
Alumentum - 3 Ignis, 3 Potentia, 3 Perditio + 1 coal or charcoal
This mystical fuel will make furnaces and Arcane furnaces run much faster. The recipe can be done with 3 phials of Perditio and 20 lumps of coal or charcoal -- 12 of them will go for essentia, the other 8 will be transformed. An alternate recipe would be 3 phials of Potentia and 6 pieces of gunpowder, followed up with 8 pieces of coal. Naturally, 3 phials of each essentia type will also convert 8 pieces of coal.
Ethereal Blooms - 16 Herba, 16 Praecantio, 16 Sano, 8 Vitium
The fabled ethereal bloom, used for combating Taint, is produced in the crucible (or Thaumatorium). Note that this recipe isn't unlocked until you've scanned something with Taint.

Metalwork

Metal transmutation - 2 Metallum, and (except iron) 1 of another aspect, + metal nugget.
Essentia can be used to multiply nuggets of various metals, including several which are not found in basic Thaumcraft, but may be provided by other mods. (You will only see the recipes for the metals present in your game.) All these recipes require 2 points of Metallum, which suffices to turn one nugget of iron into three. All other metals also require one point of the metal's characteristic aspect: Lucrum for gold or silver, Praecantio for copper, Vitreus for tin, and Ordo for lead. In all cases, one nugget of the metal will be turned into three. This can be used to directly scavenge material from iron, gold, or chain armor, swords, or tools, but this will leave extra aspects in the cauldron, especially if the items were enchanted. This extra essentia will eventually become flux as it breaks down. It is safer to use an Arcane Furnace to break the items down to essentia, and then use phials of the essentia for the recipes: 2 phials of Metallum, and 1 phial of the extra aspect, for each 8 nuggets to be multiplied. For iron, the essentia used is the same as found in the nuggets themselves, so simply tossing in three nuggets will get them back -- two used for essentia, the other duplicated. (Tip: Emeralds have Lucrum.)
Ore Purification
1 Metallum, 1 Ordo + Gold or Iron Ore Block.
Metallum and Ordo can be used to convert Gold or Iron ore into "native clusters", which smelt to twice as much metal. This does not currently work for cinnabar ore, and may or may not work for other metal ores provided by other mods. It does work for Silver, Tin, and Copper provided by Metallurgy 4.

Golems

Golem Bodies - 4/8 Humanus, 4/8 Motus, 4/8 Spiritus
The raw golem bodies all use the same aspects, transforming a block of their respective materials. Straw (hay), Wood (greatwood log), Stone (stone brick), and Iron cost 4 essentia of each type, while Tallow, Clay (bricks), Flesh, and Thaumium cost twice that.
Golem cores
Most of the golem cores are produced by using a crucible to transform a Blank Golem Core. (Some of these are also the base for an Infusion to produce another core.) By type:
  • Gather - 5 Lucrum, 5 Terra.
  • Fill - 5 Fames, 5 Vacuuos.
  • Empty - 5 Lucrum, 5 Vacuuos. Base for Use
  • Harvest - 5 Messis, 5 Meto. Base for Chop
  • Guard - 5 Telum, 5 Vinculum.
  • Decanting - 5 Aqua, 5 Vacuuos. Base for Alchemy
  • Butcher 5 Bestia, 5 Corpus (4.1, in 4.2 this is an advanced core)

Recipe notes: A few of these aspects have "perfect" sources with only 1 or 2 points of the single aspect: Vacuuos (wooden bowl), Fames (meat nuggets from the Infernal Furnace), Telum (arrow), Messis (pumpkin, 2 points), Terra (dirt, 2 points). For the tough ones, you can use 5 phials each (for 8 cores), or 2 phials each (3 cores, with 1 point per aspect left over.)

Alchemical Duplication

A number of materials can be duplicated with crucible recipes. In all cases, one piece of the material is used to produce two.

Gunpowder - 4 Ignis, 4 Perditio
Slimeball - 2 Aqua, 2 Victus
Clay (balls) - 1 Aqua, 2 Terra
Glowstone Dust - 3 Lux, 1 Sensus
Ink Sac - 2 Aqua, 2 Sensus

Entropic Processing

The recipes for gravel and sand were removed in 4.2 for balance reasons.

Cracked Stone Bricks - 2 Perditio + Stone Bricks
Allows producing Cracked Stone Bricks.
4 Bone Meal - 1 Perditio + Bone
Produces more bone meal than simply crafting the bones.
Gravel - 2 Perditio + Cobblestone (removed in 4.2)
Gravel is needed to produce flint. Besides being used for arrows, flint is a "perfect" source of the useful aspect Instrumentum.
Sand - 2 Perditio + Gravel (removed in 4.2)
Sand is needed to produce glass. Making it from cobblestone via gravel is pretty useful!

Alchemical Manufacture

Several materials can be produced which are otherwise hard to obtain:

Cobweb - 2 Pannus, 2 Vinculum + String
Very useful for traps and barriers.
Moss Stone - 2 Herba, 1 Praecantio + Cobblestone
Decorative and otherwise scarce
Ice - 1 Gelum, 1 Ordo + Snow (block)
Stackable water blocks. Otherwise requires Silk Touch and a snow biome.
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