Question

The difference between \(X_{\text{An}}\) and \(X_{\text{Ab}}\) in a feldspar represented by \(X\) in the given triangular diagram is _________ (answer in one decimal place). 

Hint:

In ternary diagrams, the position of the point determines the proportion of each component. The difference between compositions can be measured by comparing the relative distances to the vertices.

Answer 1

Correct Answer: 0.2

Step 1: Understand the Composition in the Ternary Diagram.
In the given ternary diagram, \(X\) represents a specific composition of feldspar that lies between the axes NaAlSi\(_3\)O\(_8\) (albite), CaAl\(_2\)Si\(_2\)O\(_8\) (anorthite), and KAlSi\(_3\)O\(_8\) (K-feldspar). The composition of \(X\) is determined by its distance from each of these vertices. Step 2: Determine the Values of \(X_{\text{An}}\) and \(X_{\text{Ab}}\).
The values of \(X_{\text{An}}\) (anorthite composition) and \(X_{\text{Ab}}\) (albite composition) are given by the percentage of each component in the composition \(X\). From the diagram, the composition of \(X\) lies closer to albite (NaAlSi\(_3\)O\(_8\)) than anorthite (CaAl\(_2\)Si\(_2\)O\(_8\)), which suggests a higher proportion of NaAlSi\(_3\)O\(_8\) than CaAl\(_2\)Si\(_2\)O\(_8\). By measuring the distance between the composition \(X\) and the NaAlSi\(_3\)O\(_8\) and CaAl\(_2\)Si\(_2\)O\(_8\) vertices on the ternary diagram, we determine that the difference between \(X_{\text{An}}\) and \(X_{\text{Ab}}\) is approximately 0.5.
Step 3: Conclusion.
The difference between \(X_{\text{An}}\) and \(X_{\text{Ab}}\) is 0.5.