The recipes available for the Crucible and/or Thaumatorium are as follows:

Basic Recipes Edit

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.  However, beginning thaumaturges can make one or two ingots at a time with greatwood logs.
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. Since the gravel recipe was removed in 4.2, this can also be done on a smaller scale, with 6 cobblestone (or 3 cobblestone stairs) followed by 5 coal. 3 of the coal will be consumed, the other 2 will be transformed.
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 Edit

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.  Notes:
  • Unfortunately, the iron duplication recipe interferes with using iron nuggets for Metallum, because they will duplicate themselves:  Tossing in three nuggets will get them back -- two used for essentia, the other duplicated.
  • However, these recipes can be used to directly scavenge material from iron, gold, or chain armor, swords, or tools, by using iron or gold nuggets to "absorb" the loot's Metallum and/or Lucrum.  Naturally, this will leave extra aspects in the cauldron, especially if the items were enchanted.  It's also tricky -- count the aspects before you toss stuff in!
  • If at all possible, use an Arcane Furnace to break the items down to essentia, and then use phials of essentia for the recipes: 2 phials of Metallum, and 1 phial of the extra aspect, for each 8 nuggets to be multiplied.  (A Thaumatorium makes things even easier.)
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.  Working around the iron duplication recipe, iron nuggets and Silverwood or Smooth Sandstone can be used to convert 1 or 2 ore blocks at a time.

The two recipes needed for creating void metal are only visible once you have received the Eldritch Epiphany.

Void Seeds - 2 Alienis, 8 Tenebrae, 8 Vacuous + seed
Ordinary wheat seeds are imbued with dire magics to create seeds for... something. Probably something horrible.
Void metal - 8 Metallum + Void seed
By enveloping those dark seeds with the essence of metal, a dark and sinister material is created. But oh, how useful!

Golems Edit

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), Clay (bricks), Stone (stone brick), and Iron cost 4 essentia of each type, while Tallow, Flesh, and Thaumium cost twice that. Note that the flesh golem is "forbidden research", so both researching and creating them will inflict warp.
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. Base for Butcher
  • Decanting - 5 Aqua, 5 Vacuuos. Base for Alchemy
  • Butcher - 5 Bestia, 5 Corpus (starting with the Guard core instead of a blank 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, or melon slices), 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.) Like flesh golems, the Butcher core is forbidden research and will inflict warp.

Alchemical Duplication Edit

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 Edit

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.

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

Alchemical Manufacture Edit

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.