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CIPW NORMS CALCULATIONS

CIPW NORMS CALCULATIONS

The CIPW norm is named after the four petrologists, Cross, Iddings, Pirsson and Washington, who devised it in 1931.

What is a Norm and why it is needed?

A norm is a means of converting the chemical composition of an igneous rock to an ideal mineral 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 is simply treated as a separate phase) and at low pressure. Other more complex norms have been devised for high-pressure or very hydrous situations. In an ideal world, a norm would match the observed mineral phases perfectly. To create such a norm, we would have to understand magma crystallization perfectly (and we don't), and the norm would be extremely complex to calculate.

Basis for the CIPW calculation

The original intent of the CIPW calculation was to produce a consistent way to compare glassy volcanic rocks to phaneritic intrusive rocks to, for example, determine if the intrusive rock was genetically related to the volcanic rock. The result of the calculation is a calculated mineral content and abundance- i.e. the normative mineralogy. Major element oxides are used as input into the calculation. The calculation is based on the following assumptions:

The magma from which the rock is derived is assumed to be “dry” so hydrous phases such as amphibole and mica are ignored by the calculation.

The ferromagnesian minerals are assumed to be free of Al2O3 so that the amount of that component can be used to fix the abundance of feldspar and feldspathoid in the norm.

The magnesium/iron ratio of all of the ferromagnesian minerals is assumed to be the same.

Several mineral pairs are considered to be incompatible, such as feldspathoids and quartz, and therefore never appear together in the norm although in real rocks that may be present.

The result of the calculation often shows a close correspondence to the actual mineralogy of the rock, especially if the rock formed from a slowly cooling anhydrous magma. If an igneous rock contains significant proportions of amphibole and/or mica the calculated norm will deviate significantly from the actual modes.

Calculating of a CIPW norm from a bulk chemical analysis

This is a set of instructions for calculating a basic norm. For the more production-minded, here are two spreadsheet programs that will calculate norms for you: a simple one for individual analyses, and a macro-enabled one for automatically calculating norms for a large number of analyses at once.

A norm is essentially a set of idealized mineral-like components that are calculated from a bulk chemical analysis of a rock. Norms are usually used for classification or comparison purposes. Norms are commonly calculated for glassy or fine-grained volcanic rocks that are otherwise difficult to classify, and for metamorphosed igneous rocks that no longer have their original igneous mineralogy. The normative ‘minerals’ are calculated to represent, in some ways, the actual minerals that might crystallize if the rock were cooled under perfect dry equilibrium conditions at low pressure. For example, in natural rocks the following mineral pairs are mutually exclusive:

Real mutually exclusive minerals normative equivalents

Quartz and Mg-rich olivine.                                   Quartz and any olivine

Quartz and nepheline.                                             Quartz and nepheline

Al-silicates and augite.                                           Corundum and diopside

Orthopyroxene and nepheline.                               Orthopyroxene and nepheline

Normative ‘minerals’ are shown here in italics. These mutually exclusive mineral pairs result in four common normative assemblages:

(@) Normative assemblages                              (#)  What they mean

(@) Quartz–corundum–orthopyroxene              (#)Silica-saturated, peraluminous, subalkaline

(@) Quartz–diopside–orthopyroxene                  (#)  Silica-saturated, subaluminous, subalkaline

(@) Olivine–diopside–orthopyroxene                (#)Silica-undersaturated, subaluminous, subalkaline

(@) Olivine–diopside–nepheline                         (#) Silica-undersaturated, subaluminous, peralkaline

Norm calculation procedure

The following is similar to the original CIPW norm procedure and works for most common igneous rocks. It does not include the methods to calculate, for example, normative leucite in strongly silica-undersaturated rocks, aegirine in alumina-poor alkalic rocks, or hematite in highly oxidized rocks. The

procedure below also departs from the original CIPW norm in that normative pyroxenes, plagioclase, and olivine are calculated as their solid solutions rather than their end member components. If you are unfortunate enough to be doing a norm calculation by hand, you should do the calculations to at least five decimal places to avoid rounding error problems. To begin, make a table with the 11 major oxides, and below that a list of the normative ‘minerals’ (quartz, orthoclase, albite, anorthite, plagioclase, corundum, nepheline, diopside, orthopyroxene, olivine, magnetite, ilmenite, apatite). Space will also be needed for FMO and other calculated intermediate values.

1.Use only the eleven major element oxides, for which the gram formula weights are:

SiO2       60.0843

TiO2       79.8988

Al2O3     101.9613

Fe2O3     159.6922

FeO         71.8464

MnO        70.9374

MgO        40.3044

CaO         56.0794

Na2O       61.9789

K2O         94.1960

P2O5      141.9445

2. Take the oxide weight percents in the chemical analysis and divide them by their respective formula weights to give molar oxide proportions. Use these molar oxide proportions in all subsequent calculations.

3. Add MnO to FeO. MnO is now zero. The combined FeO and MnO will still be called FeO.

4. Apatite: Subtract 3.333 times P2O5 from CaO. Multiply P2O5 by 0.6667, and put this number in apatite. P2O5 is now zero.

5. Ilmenite: Subtract TiO2 from FeO. Put the TiO2 value in Ilmenite. TiO2 is now zero.

6. Magnetite: Subtract Fe2O3 from FeO. Put the Fe2O3 value in magnetite. Fe2O3 is now zero.

7. Orthoclase: Subtract K2O from Al2O3. Put the K2O value in orthoclase. K2O is now zero.

8. Albite (provisional): Subtract Na2O from Al2O3. Put the Na2O value in albite. Retain the Na2O value for possible normative nepheline.

9. Anorthite:

A. If CaO is more than the remaining Al2O3, subtract the Al2O3 value from CaO. Put all Al2O3 into Anorthite. Al2O3 is now zero.

B. If Al2O3 is more than the remaining CaO, subtract CaO from Al2O3. Put all CaO into anorthite. CaO is now zero.

10. Corundum: If Al2O3 is not zero, put the remaining Al2O3 into corundum. Diopside and Al2O3 are now zero.

11. Calculate the current ratio of Mg/(Mg+Fe2+ ). This ratio is called Mg' and will be the Mg/(Mg+Fe2+) ratio for all normative silicates.

12. Calculate the mean formula weight of the remaining FeO and MgO. This combined Fe–Mg oxide, called FMO, will be used in subsequent calculations.

Formula weight of FMO = (Mg'*40.3044)+((1-Mg')*71.8464)

13. Add FeO and MgO to make FMO.

14. Diopside: If CaO is not zero, subtract CaO from FMO. Put all CaO into diopside. CaO is now zero.

15. Orthopyroxene (provisional): Put all remaining FMO into orthopyroxene. Retain the FMO value for the possible normative olivine.

16. Calculate the amount of SiO2 needed for each of the normative silicates so far:

Orthoclase * 6

Albite * 6

Anorthite * 2

Diopside * 2

Orthopyroxene * 1

17. Sum the five SiO2 values just calculated, and call this number 1pSi for the first provisional SiO2.

18. Quartz:

A. If 1pSi in #17 is less than SiO2, then there is excess silica. Subtract pSi1 from SiO2, and put the remaining SiO2 in quartz. SiO2, nepheline, and olivine are now zero. Skip to #23.

B. If 1pSi in #17 is more than SiO2, then the rock is silica-undersaturated. Proceed to #19.

19. Olivine, orthopyroxene (final): If 1pSi calculated in #17 is more than SiO2, then quartz is now zero. Calculate a 2pSi value, like 1pSi in #17, but omitting orthopyroxene.

Orthoclase * 6

Albite * 6

Anorthite * 2

Diopside * 2

20. Sum the four SiO2 values just calculated to get 2pSi. Subtract 2pSi from SiO2 to get the amount of SiO2 available for olivine and orthopyroxene, called 3pSi.

A. If FMO is greater than or equal to 2 times 3pSi, then put all FMO in Olivine. FMO and Orthopyroxene are now zero. Proceed to #21.

B. If FMO is less than 2 times pSi3, then nepheline is zero. Calculate the amount of orthopyroxene and olivine as follows:

Orthopyroxene = ((2 * 3pSi) - FMO)

Olivine = (FMO - orthopyroxene)

Skip to #23.

21. Nepheline, albite (final): If you reached this step, then turning orthopyroxene into olivine in #20A did not yield enough silica to make orthoclase, albite, anorthite, diopside, and olivine. Calculate 4pSi:

Orthoclase * 6

Anorthite * 2

Diopside * 2

Olivine * 0.5

22. Sum the four SiO2 values just calculated to get 4pSi. Subtract 4pSi from SiO2 to get 5pSi, which is the amount of SiO2 available for albite and nepheline.

Albite = (5pSi-(2*Na2O))/4

Nepheline = Na2O-Albite

23. Multiply orthoclase, albite, and nepheline by two. Divide olivine by two.

24. Calculate An', which is the Ca/(Ca+Na) ratio in normative plagioclase:

An' = Anorthite/(Anorthite+Albite)

25. Plagioclase: Add albite to anorthite to make plagioclase. Retain the albite value, but anorthite is now zero.

26. Calculate the formula weight of plagioclase, using the An' value from #24.

Formula weight of plagioclase = (An'*278.2093)+((1-An')*262.2230)

27. Multiply all of the normative ‘mineral’ values by their respective formula weights. The formula weight of FMO is from #12.

‘Mineral’                        Formula/                                                         weight Formula

Quartz                             60.0843/                                                               SiO2

Orthoclase                       278.3315/                                                            KAlSi3O8

Plagioclase                  Calculated in #26/                                                (Ca,Na)(Al,Si)4O8

Corundum                       101.9613/                                                            Al2O3

Nepheline                        142.0544/                                                               NaAlSiO4

Diopside           176.2480 + formula weight of                                                     FMO/                                                           Ca(Fe,Mg)Si2O6

Orthopyroxene                60.0843 + formula                                           weight of FMO/                                                            (Fe,Mg)SiO3

Olivine                            60.0843 + (2 *                                              formula weight of FMO)/                                               (Fe,Mg)2SiO4

Magnetite                          231.5386/                                                                 Fe3O4

Ilmenite                             151.7452/                                                                 FeTiO3

Apatite                             504.3125/                                                             Ca5(PO4)3F

28. This is your weight norm, which you may want to normalize to a sum of 100%. This might be published along with four other useful parameters:

Total: The sum of all normative component weights, calculated in #27. Within rounding error the Total should be the same as the original total of the weight % of the oxides from the chemical analysis.

Mg'%: 100*Mg' From #11. An'%: 100*An' from #24.

DI: The Differentiation Index of Thornton and Tuttle (1960). This is the weight ratio: (quartz + orthoclase + albite + nepheline)/total. Albite is from #23 multiplied by 262.2230.

29. The weight norm is the way norms are usually expressed. If you want to compare norms to modes, which are volume fractions, you should divide each normative mineral by its density and normalize the total back to 100%. The density of plagioclase and the Fe-Mg silicates can be approximated by linearly interpolating from the end member densities.

Note: The above material is reprinted from the reference given below.

References:

(1.) http://academic.sun.ac.za/natural/geology/undergraduate/G314/G314-06-Prac2-

Calculating%20CIPW%20norms.pdf

(2.) https://minerva.union.edu/hollochk/c_petrology/other_files/norm_calculation.pdf

(3.) https://www.southalabama.edu/geography/allison/gy303/CIPWNORM.pdf

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