Modal Mineralogy Data

The table below presents the modal volume percentages of essential minerals for rocks X and Y, which are used for their classification:

IUGS Classification Principles

The International Union of Geological Sciences (IUGS) classifies coarse-grained granitoid rocks using the QAPF diagram. This classification hinges on the relative proportions of Quartz (Q), Alkali feldspar (A), and Plagioclase (P).

The classification criteria involve:

• The ratio of Alkali feldspar to the total feldspar (Alkali feldspar + Plagioclase).
• The percentage of Quartz relative to the sum of Quartz, Alkali feldspar, and Plagioclase (QAPF).

Specific boundaries relevant here are:

• If Alkali Feldspar $ > \frac{2}{3} $ of total feldspar: The rock falls into fields dominated by Alkali feldspar. Further division depends on Quartz content.
  • $ 5\% \le \text{Quartz} < 20\% $: Classified as Quartz syenite.
  • $ 20\% \le \text{Quartz} \le 60\% $: Classified as Alkali Feldspar Granite.
• If Alkali Feldspar $ < \frac{1}{3} $ of total feldspar: The rock falls into fields dominated by Plagioclase. Further division depends on Quartz content.
  • $ 20\% \le \text{Quartz} \le 60\% $: Classified as Granodiorite.
  • $ 5\% \le \text{Quartz} < 20\% $: Classified as Quartz Diorite/Gabbro.

Rock X Analysis

Evaluate the mineral composition of Rock X against the IUGS criteria:

• Calculate the proportion of Alkali feldspar relative to total feldspar:
  • Total Feldspar = Plagioclase + Alkali feldspar = $ 20\% + 65\% = 85\% $.
  • Ratio = $ \frac{\text{Alkali feldspar}}{\text{Total Feldspar}} = \frac{65\%}{85\%} \approx 0.76 $.
• This ratio $ \approx 0.76 $ is greater than $ \frac{2}{3} $, indicating Alkali feldspar dominance.
• The Quartz content is $ 15\% $.
• According to the IUGS classification, rocks with Alkali feldspar dominance and $ 5\% \le \text{Quartz} < 20\% $ are named Quartz syenite.

Rock Y Analysis

Evaluate the mineral composition of Rock Y against the IUGS criteria:

• Calculate the proportion of Alkali feldspar relative to total feldspar:
  • Total Feldspar = Plagioclase + Alkali feldspar = $ 60\% + 15\% = 75\% $.
  • Ratio = $ \frac{\text{Alkali feldspar}}{\text{Total Feldspar}} = \frac{15\%}{75\%} = 0.2 $.
• This ratio $ = 0.2 $ is less than $ \frac{1}{3} $, indicating Plagioclase dominance.
• The Quartz content is $ 25\% $.
• According to the IUGS classification, rocks with Plagioclase dominance and $ 20\% \le \text{Quartz} \le 60\% $ are named Granodiorite.

Conclusion on Rock Names

Based on the analysis using IUGS criteria:

• Rock X is classified as Quartz syenite.
• Rock Y is classified as Granodiorite.