Abstract
Numerically, the formation of rock forming minerals from magma, depends on the numerical values of each mineral under thermodynamic conditions. This research was focused on geochemical classification of Miango basalt using numerical analysis. Findings have shown that, under mathematical context with Bowenโs and Goldschmidt rules, the Miango basaltic sample of MIANGO VOLCANIC FIELD falls within gabbro clan and the estimated minerals using an empirical approach, are Ferro-augite (Basic Clino-pyroxene), Hortonolite (Basic olivine), Labradorite (Basic Plagioclase) and Ulvospinel (Iron ore). The gabbro clan includes basalt, dolerite, norite, scoria and gabbro and therefore empirically, Miango basaltic sample of MIANGO VOLCANIC FIELD was found to be characteristics of rock of Gabbro clan and the rock type for Miango basaltic sample in MIANGO VOLCANIC FIELD is Alkaline Olivine basalt magma type. Finally, the โmathematical connectionโ between Bowenโs and Goldschmidt concepts was used in this research for a concise explanation of rock forming minerals from the beginning to the end of crystallization and would help the โbeginnersโ especially students of Earth sciences such as Geology, Mineralogy, Petrology and other chemical sciences such as Chemistry, Geochemistry and Petroleum Geology to have clear understanding of rock forming minerals from the Resident magma.
Keywords:Numerical, Geology, Bowen, Goldschmidt, Basalt
1. Introduction
The occurrences of volcanic hills (cones) on the Jos Plateau in particular and Nigeria in general are indication of previous eruptive sites. The surface area of Nigeria is approximately 923,768 Km2 and is underlain in nearly equal proportions by crystalline and sedimentary rocks with volcanic rocks dotting the central and northeastern portions. Volcanic rocks (acid/basic) are generally formed from solidifying magma or lava whether ejected or poured on the surface of the earth. There are three principal magma series recognized on the Earth with each composed of group of related magma types that are emplaced on the Earthโs crust. They are: Basaltic (tholeiitic), Andesitic (calc-alkaline) and Rhyolitic (alkaline magma) series.
2. Results
The Miango basaltic rocks are classified using their major oxide compositions and this shown in Table 1 below. The SiOโ contents range between 45.8โ52.4 wt %, while total alkalis (NaโO + KโO) vary from 3.1โ5.7 wt %, indicating a mildly alkaline character. The FeโOโ/MgO ratios (1.6โ2.3) and TiOโ > 1 wt % further suggest a transitional to alkaline affinity, typical of intraplate continental basalts. The classification aligns with the tholeiiticโ alkaline basalt spectrum of Yoder and Tilley (1962) and corresponds to basaltic magmas derived from a heterogeneous upper-mantle source that experienced limited fractional crystallization prior to eruption.
3. Conclusion
Using Bowenโs and Goldschmidt concepts according Achuenu and others (2025), the formula ๐๐ (๐0 ) = [๐ฝ + โ]๐+๐๐0 for mafic minerals and (ฯ + ฮง )๐+๐(๐ฝ + ๐ผ)๐+๐ (๐ฌ + ๐ฉ)๐ฆ+๐ ๐ฒ๐ = (ฯ๐โ๐ฮง๐) (๐ฝ๐โ๐๐ผ๐)(๐ฌ๐ฆโ๐๐ฉ๐)๐ฒ๐) for felsic and complex minerals were successfully used in this research to calculate the numerical values of minerals in Kassa basalt, particularly, For MIA. From the Mathematical modeling, it is also concluded, that the examinations of sampled rocks collected from Miango Volcanic Basalts, under thin section, chemical analysis using ICPMS, and mathematical computation indicate, that minerals observed and chemical composition analyzed, fall within gabbro clan. The gabbro clan includes basalt, dolerite, norite, scoria and gabbro. The minerals observed in these rocks under thin section are restricted to Gabbro clan and they are mainly basic, because of its instability in the presence of free silica. It is on this note, conclusion was made that, mathematically Miango volcanic Basalts particularly for average samples of Miango basalt as shown in Table 1 above, are characteristics of rocks of Gabbro clan and the rock type for Miango basalt is olivine, alkali basalt magma type as shown in Table 1 above.
References
[1] Achuenu I., Lekmang.C.I.,Hyeladi.D,. And Geoffry M.K., (2025). Application of Matrix and Set Notation to Rock forming minerals using combined Goldschmidt and Bowenโs concept with respect to thermodynamic principles. Smart Materials and Engineering Applications: Vol. 1(1) May, Pp. 29-61, 2025
[2] Achuenu I., Lekmang.C.I.,Hyeladi.D,. And Geoffry M.K., (2025). Mathematical Modeling of Goldschmidt and Bowenโs Crystallization of Mafic Magma: Implication for the Crystallization of Basaltic Rocks. Global educational Research: 2360-7963 Vol. 13(4), Pp. 141-158, 2025
[3] Achuenu I., Lekmang.C.I.,Hyeladi.D,.(2025). Mathematical Analysis and its Application to Kassa Basaltic Rocks of Jos Plateau State, Nigeria: Smart Materials and Engineering Applications: Vol. 1(1), Pp. 1-28, 2025
[4] Achuenu I., Lekmang.C.I.,Hyeladi.D,. And Geoffry M.K., (2025). Modification Bowenโs Reaction Series of Rock Forming Minerals Using Mathematical Mapping Method with Respect to thermodynamic Principles. Convergent Materials Horizons: Vol. 1(1), Pp. 14-47, 2025
[5] Bowen N. L., (1928). The later stages of the Evolution of the Igneous Rocks, Journal of Geology xxiii. Supplement, 91 pp.
Full reference list available in the PDF version.