**Perple_X**** Defining and Extracting Phase Compositions with WERAMI**

**Contents**

Example 1: Mole fraction of albite and the Na/Ca ratio in Feldspar, in terms of species

Example 2: Mole/Mass fraction of albite in Feldspar, in terms of components

Example 3: Using species of an order-disorder solution model (omphacite) to define a composition

Example 4: Number of cations on the A-site of an amphibole model

WERAMI permits the user to extract information from a phase diagram section at a point (operational mode 1), throughout a region (mode 2), or along a line or curve (modes 3 and 4). This page documents the various ways the composition of a solution phase can be defined in WERAMI computational modes 2-4. Once the user has selected property choice 8 (composition of a solution), and specified a solution, e.g. Feldspar, the user is confronted with the prompt:

**Prompt 1****:** Define the composition in terms of the species/endmembers of
Feldspar (y/n)?

The best answer to this question is dependent on the user’s
knowledge of the solution model. If the user is confident about his/her
knowledge of the chemical identities of the endmembers, then it is usually
easiest to define compositions in terms of endmembers or species, a notable
exception to this are order-disorder models, this exception and other variants
are illustrated by annotated examples below. An additional advantage to
defining compositions in terms of components is that mass rather than molar
units can be used by setting the composition_phase option to **wt**, this option is not illustrated here because it is
otherwise identical to the procedure in Example 2.

Once a compositional variable has been defined, WERAMI computes its value and outputs the data to a “tab” file. The tab file data can be manipulated in a spreadsheet or plotted as illustrated for seismic wave speeds in the seismic velocity tutorial.

**Example
1****: Mole fraction of albite and the
Na/Ca ratio in Feldspar, in terms of species:**

After Prompt 1 is answered **y**, WERAMI outputs the blurb:

Compositions are defined as a ratio of the form:

Sum {w(i)*y(i), i = 1, c1} / Sum {w(i)*y(i), i = c2, c3}

y(j) = mole fraction of species j

w(j) = weighting factor of species j (usually 1)

This blurb about how compositions are defined may look complicated, but it merely states that a composition can be defined as the ratio of a numerator and denominator, each of which is an arbitrary linear combination of the species fractions. The mysterious weighting factor is simply a stoichiometric coefficient that may be adjusted for some purposes, but most often is set to 1. The blurb is followed by the prompts which are answered as indicated to define the compositional variable that corresponds to the mole fraction of albite in plagioclase.

How many species in the numerator of the composition (<13)?

**1**

Enter species indices and weighting factors for the numerator:

1 - an

2 - abh

3 - san

**2 1**

How many species in the denominator of the composition (<12)?

Enter zero to use the numerator as a composition.

**0**

The compositional variable is: 1.0 y(abh)

Change it (y/n)?

**n**

This composition will be
designated: **C[Feldspar1]**

In subsequent output WERAMI identifies the composition as **C[Feldspar1]**, so if multiple
compositions are to be defined in a single session it is helpful to note which
name corresponds to which variable.

Usually, there is no need to use and define a denominator for compositions expressed in terms of species, but if instead of the albite mole fraction, the molar Na/Ca ratio was of interest, this variable would be defined by the prompt/response sequence:

How many species in the numerator of the composition (<13)?

**1**

Enter species indices and weighting factors for the numerator:

1 - an

2 - abh

3 - san

**2 1**

How many species in the denominator of the composition (<13)?

Enter zero to use the numerator as a composition.

**1**

Enter species indices and weighting factors for the denominator:

1 - an

2 - abh

3 - san

**2 1 **

The compositional variable is: 1.0 y(abh)/ [1.0 y(an)]

...

**Example
2****: Mole/Mass fraction of albite
in Feldspar, in terms of components:**

Although it is probable that every petrologist will recognize the endmembers of the Feldspar model, in less common phases the stoichiometry of the endmembers may be unfamiliar in which case it is preferable to define phase compositions in terms of the components specified in the header of the thermodynamic data file. This example illustrates that procedure:

After Prompt 1 is answered **n**, WERAMI outputs the blurb:

Compositions are defined as a ratio of the form:

Sum {w(i)*n(i), i = 1, c1} / Sum {w(i)*n(i), i = c2, c3}

n(j) = molar amount of component j

w(j) = weighting factor of component j (usually 1)

This blurb differs from the previous example only in that n(j), the molar amount of component j, now appears in place of y(j), the mole fraction of species j. Here the goal is to define mole fraction of Na on the octahedral site (n(Na)/[n(Na) + n(Ca) + n(K)]), i.e., the mole fraction of the albite endmember. The WERAMI dialog below accomplishes this:

How many components in the numerator of the composition (<13)?

**1**

Enter component indices and weighting factors for the numerator:

1 - CaO

2 - Na2O

3 - K2O

4 - Al2O3

5 - SiO2

**2 2**

How many components in the denominator of the composition (<12)?

Enter zero to use the numerator as a composition.

**3**

Enter component indices and weighting factors for the dominator:

1 - CaO

2 - Na2O

3 - K2O

4 - Al2O3

5 - SiO2

**1 1**

**2 2**

**3 2**

The compositional variable is: 0.5 n(Na2O)/[ 1.0 n(CaO) + 2.0 n(Na2O) + 2.0 n(K2O)]

Change it (y/n)?

**n**

This composition will be
designated: **C[Feldspar2]**

The weighting factors on K2O and Na2O are 2 to convert the molar amount of the oxide to the molar amount of the element. For the standard 8-oxygen per formula unit of feldspar there is one octahedral cation and the numerator C = 2 n(Na2O) would be sufficient to specify the composition variable. The utility of specifying the denominator, is that the formulation of the compositional variable does not require knowledge of the formula unit assumed in the Feldspar solution model.

As noted earlier, compositions in terms of components can be
defined in mass units by setting the composition_phase option to **wt.** Usually this option is only used for WERAMI mode 1 calculations
when the mass (weight) fractions of the oxides are desired for comparison with
analytical results.

**Example 3: Using
species of an order-disorder solution model (omphacitic
clinopyroxene) to define a composition.**

Order-disorder models can be confusing because they include
compositionally degenerate species, the simplest way to avoid this confusion in
WERAMI is to define compositions in terms of components rather than species.
However, users who are confident about their knowledge of the model may prefer
using species for this purpose. Species are particularly convenient if the
composition of interest represents the site fraction of a cation on a
particular crystallographic site (see Example 4, below). This example
illustrates computation of the bulk jadeite content of a clinopyroxene
order-disorder solution model between jadeite (jd), diopside (di), and omphacite (om
= [jd+di]/2) species. In such a model, the bulk
jadeite content is y(jd) + 1/2 y(om), ergo after
answering **y** to Prompt
1, the bulk jadeite content of the clinopyroxene
model would be defined in terms of species by the dialog:

How many species in the numerator of the composition (<13)?

**2**

Enter species indices and weighting factors for the numerator:

1 - jd

2 - di

3 - om

**1 1**

**3 0.5**

How many species in the denominator of the composition (<12)?

Enter zero to use the numerator as a composition.

**0**

...

**Example
4****:** **Number of cations on the A-site of an amphibole model.**

refer to perplex/faq/extracting_site_fractions_with_WERAMI.txt