The CIPW Norm

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay

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The CIPW norm is named for the four petrologists, Cross, Iddings, Pirsson andWashington, who devised it in 1931

What is a Norm and Why is it Needed?

A norm is a means of converting the chemical composition of an igneous rock to an idealmineral composition. It often reveals similarities in rocks that have quite different modes,or observed mineral assemblages. Some of the factors that can cause such variations are:

• Disequilibrium (for example, zoned minerals or reaction rims isolating the interiors of grains)
• Temperature
• Pressure
• Alteration
• Water content (otherwise identical rocks might contain biotite, amphibole, or pyroxene, depending on water content)
• Other minor constituents. For example, excess sulfur or chlorine might cause scapolite to form instead of feldspar. Boron typically causes tourmaline to form.

The CIPW norm calculates mineral composition as if the magma were anhydrous (water issimply treated as a separate phase) and at low pressure. Other more complex norms havebeen devised for high-pressure or very hydrous situations. In an ideal world, a norm wouldmatch the observed mineral phases perfectly. To create such a norm, we would have tounderstand magma crystallization perfectly (and we don't), and the norm would be extremelycomplex to calculate.

Logic of Calculation

The logic of calculating a norm is simple even if the steps are tedious. Deal with thesimplest and most predictable minerals first, then apply corrections if the rock issilica-deficient.

• Allocate the most predictable elements
  • Allot Common Substitution Elements to Major Elements
    Nickel and manganese are combined with ferrous iron, strontium and barium with calcium.
  • Allot Minor Elements to Accessory Minerals. These include P (Apatite), S, (Pyrite), Cr (Chromite), F, (Fluorite), CO₂ (Calcite) and Zr (Zircon)
  • Allot Titanium to ilmenite or sphene. Later on, Ti may need to be alloted to perovskite or rutile.
  • Allot Calcium and Aluminum to anorthite.
• Provisionally form silica-saturated silicates
  • Provisionally Allot Alkalis and Aluminum
  • Begin Alloting Iron and Magnesium
  • Create Provisional Pyroxenes
  • Silica Excess forms Quartz
  • If there is no silica deficit, calculation is complete.
• Convert Provisional Minerals to Remove Silica Deficit
  • Convert Hypersthene to Olivine
  • Convert Sphene to Perovskite
  • Convert Albite to Nepheline
  • Convert Orthoclase to Leucite
  • Convert Wollastonite and Diopside to Calcium Orthosilicate (Rare)
  • Convert Orthoclase to Kaliophilite (Rare)

Calculating the Norm

Preliminary Comments

• Convert all weight percentages to molecular percentages.
• All quantities are running amounts; that is, use the quantity remaining after any previous calculations.
• Formulas follow common computer program syntax. For example, FeO = FeO + MnO + NiO means sum FeO, MnO and NiO, then replace the value of FeO with the calculated value.
• Provisional calculations are denoted by P*; for example, P*Albite means a provisional quantity for albite, which may be converted later on to nepheline. Any provisional amounts remaining at the end become final amounts.

Allot Common Substitution Elements to Major Elements

• FeO = FeO + MnO + NiO
• CaO = CaO + BaO + SrO

Allot Minor Elements to Accessory Minerals

• Apatite = P₂O₅, CaO = CaO - (10/3)P₂O₅, P₂O₅ = 0
• Pyrite = S, FeO = FeO - S/2, S = 0
• Chromite = Cr₂O₃, FeO = FeO - Cr₂O₃, Cr₂O₃ = 0
• Fluorite = F, CaO = CaO - F, F = 0
• Calcite = CO₂, CaO = CaO - CO₂, CO₂ = 0
• Zircon = ZrO₂, SiO₂ = SiO₂ - ZrO₂, ZrO₂ = 0

Allot Titanium

• If FeO exceeds Titanium then Ilmenite = TiO₂, FeO = FeO - TiO₂, TiO₂ = 0
• If TiO₂ exceeds FeO then:
  P*Sphene = TiO₂, CaO = CaO - TiO₂, SiO₂ = SiO₂ - TiO₂, TiO₂ = 0

Provisionally Allot Alkalis and Aluminum

• P*Orthoclase = K₂O, Al₂O₃ = Al₂O₃ - K₂O, SiO₂ = SiO₂ - 6 K₂O
• If Al₂O₃ exceeds Na₂O then:
  P*Albite = Na₂O, Al₂O₃ = Al₂O₃ - Na₂O, SiO₂ = SiO₂ - 6 Na₂O, Na₂O = 0
• If Na₂O exceeds Al₂O₃ then:
  • Albite = Al₂O₃, Na₂O = Na₂O - Al₂O₃, SiO₂ = SiO₂ - 6 Na₂O, Al₂O₃ = 0
  • Aegerine = Na₂O, Fe₂O₃ = Fe₂O₃ - Na₂O, SiO₂ = SiO₂ - 4 Na₂O
  • In the very rare case where Na₂O is left over due to insufficient Fe₂O₃, allot it to sodium metasilicate. SiO₂ = SiO₂ - Na₂O.
• If Al₂O₃ is left after alloting orthoclase and albite, then:
  Anorthite = Al₂O₃, CaO = CaO - Al₂O₃, SiO₂ = SiO₂ - 2 Al₂O₃, Al₂O₃ = 0
• If Al₂O₃ exceeds CaO in the preceding calculation, then:
  • Anorthite = CaO, Al₂O₃ = Al₂O₃ - CaO, SiO₂ = SiO₂ - 2 CaO
  • Corundum = Al₂O₃, CaO =0, Al₂O₃ = 0

Begin Alloting Iron and Magnesium

• If FeO exceeds Fe₂O₃ then:
  Magnetite = Fe₂O₃, FeO = FeO - Fe₂O₃, Fe₂O₃ = 0
• If Fe₂O₃ exceeds FeO then:
  Magnetite = FeO, Fe₂O₃ = Fe₂O₃ - FeO, FeO = 0, Hematite = Fe₂O₃, Fe₂O₃ = 0
• From here on, all FeO and MgO go to pyroxene plus olivine, but their relative proportions are maintained in all minerals. The sum of MgO plus FeO is designated FM in what follows.

Create Provisional Pyroxenes

• If FM exceeds CaO then:
  • P*Diopside = CaO, FM = FM - CaO, SiO₂ = SiO₂ - CaO, CaO = 0
  • P*Hypersthene = FM, SiO₂ = SiO₂ - FM
• If CaO exceeds FM then:
  • P*Diopside = FM, CaO = CaO - FM, SiO₂ = SiO₂ - 2 CaO, FM = 0
  • P*Wollastonite = CaO, SiO₂ = SiO₂ - CaO

Deal With Silica Excess or Deficit

• If SiO₂ is still positive then: Quartz = SiO₂, SiO₂ = 0, Calculation Finished
• If SiO₂ is negative, then we must convert some of the P*minerals. Call the silica deficit D (D = -SiO₂) and proceed as follows. Whenever D = 0, the calculation is done.

Convert Provisional Minerals to Remove Silica Deficit

Form Olivine

• If D is less than 1/2 of P*hypersthene, then:
  Olivine = D, Hypersthene = P*Hypersthene - 2D, D = 0, Calculation Finished
• If D is greater than 1/2 of P*hypersthene, then:
  Olivine = P*Hypersthene, D = D - 1/2(P*Hypersthene), Hypersthene = 0,

Form Perovskite

• If D is less than P*Sphene, then:
  Perovskite = D, Sphene = P*Sphene - D, D = 0, Calculation Finished
• If D is greater than P*Sphene, then:
  Perovskite = P*Sphene, D = D - P*Sphene, Sphene = 0
• Any excess TiO₂ is accounted as Rutile

Form Nepheline

• If D is less than 4(P*Albite) then:
  Nepheline = D/4, Albite = P*Albite - D/4, P*Albite = 0, D = 0, Calculation Finished
• If D is greater than 4(P*Albite) then:
  Nepheline = P*Albite, D = D - 4(P*Albite), Albite = 0

Form Leucite

• If D is less than 2(P*Orthoclase) then:
  Leucite = D/2, Orthoclase = P*Orthoclase - D/2, P*Orthoclase = 0, D = 0, Calculation Finished
• If D is greater than 2(P*Orthoclase) then:
  Leucite = P*Orthoclase, D = D - 2(P*Orthoclase), Orthoclase = 0

Form Calcium Orthosilicate (Rare)

• If D is less than (1/2)(P*Wollasonite) then: Calcium Orthosilicate = D, Wollastonite = P*Wollasonite - 2D, D = 0, Calculation Finished
• If D is greater than (1/2)(P*Wollasonite) then: Calcium Orthosilicate = P*Wollasonite, D = P*Wollastonite/2, Wollastonite = 0
• If there is still a deficit, convert Diopside to Olivine + Calcium Orthosilicate as follows:
  • If D is less than P*Diopside then:
    Additional Calcium Orthosilicate = D/2, Additional Olivine = D/2. Add these amounts to the previously-formed minerals. Diopside = P*Diopside - D, D = 0, Calculation Finished
  • If D is greater than P*Diopside then:
    Additional Calcium Orthosilicate = P*Diopside/2, Additional Olivine = P*Diopside/2. Add these amounts to the previously-formed minerals. D = D-P*Diopside, Diopside = 0

Form Kaliophilite (Rare)

If there is still a deficit, convert Leucite to Kaliophilite: Kaliophilite =D/2, Leucite = Leucite - D/2, D = 0, Calculation Finished

Convert all remaining provisional minerals, if any, to final quantities

Reference

Myron G. Best; Igneous and Metamorphic Petrology, Freeman, 1982, Appendix E, pp.616-619

Acknowledgement

Thanks to Dr. Chris McLaren for catching several errors in the original version of thispage.

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Created 10 Nov 1997, Last Update