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What exactly is done to classify minerals in Earth Sciences such as Geology? How can it be known if one mineral is the same as another if they should be visually different?

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Minerals are defined by chemical composition and crystallography. Dana classification scheme or new Dana classification scheme divides known mineral species in eight broad groups based on primary chemical properties and crystal form.

Organic vs inorganic

Silicates vs non-silicates

  Subdivided silicates into smaller groups by crystalline structures

Metals vs non-metals

  Subdivide non-metals into smaller groups
      metal oxides
      metal sulfides
      metal and non-metal acid salts organized by dominant anion (1)(2)

(1) In chemistry, a salt is an ionic compound that can be formed by the neutralization reaction of an acid and a base.1 Salts are composed of related numbers of cations (positively charged ions) and anions (negative ions) so that the product is electrically neutral (without a net charge). These component ions can be inorganic, such as chloride (Cl−), or organic, such as acetate (CH3CO−2); and can be monatomic, such as fluoride (F−), or polyatomic, such as sulfate (SO2−4). (from wikipedia)

(2) Some these subgroups represent hypothetical acid-base reactions not actualy seen in nature but modeled after known acid-base reactions. My opinion here is that this approach was used because it was popular theory in chemistry at the time when James Dwight Dana published his work in 1837.

There are other minerals classfication systems

1) By crystal system -triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, and cubic.

2) By Cleavage, parting, fracture, and tenacity

3) By mineral hardness

4) By specific gravity or density

5) By mineral association (my favorite and often the best way of identifying and unknown mineral especially when the location is known.

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Minerals are classified as follows: Native elements, Sulphides, Sulphosalts, Oxides, Halides, Carbonates, Nitrates, Borates, Phosphates, Sulphates, Tungstates, Silicates I have listed some of the things I know for more details on the classification of minerals follow this [link].1

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