# Feasibility Study on Color Grading of Blue Iolite Based on GemDialogue Color Comparison Charts
## 1 Introduction  
Cordierite mineral is a common diagenetic mineral in amphibolite, granullite, and high-grade aluminite [1], with the ideal chemical formula (Mg, Fe)\({}_{2}\)[Al\({}_{4}\)Si\({}_{5}\)O\({}_{18}\)] (H\({}_{2}\)O, CO\({}_{2}\)). In regional metamorphic rocks, granulites, and greisess, coderiite coexists with other magnesium facies, such as garnet, biotite, orthopyroxene, spinel, or hornblende. It also coexists with aluminum-containing minerals, such as sillimantie and corundum [2]. Cordierite is used as a gemstone, which is known as \"iolite\" in the gem and jewelry industry [3]. Gem-grade iolite is mainly produced in Sri Lanka, Madagascar, the United States, Tanzania, Namibia, etc. [4]. Iolite is rich in color, which can be colorless, yellowish white, green, brown, and gray, etc., while iolite with gem-grade quality is generally blue or bluish-purple [5]. According to previous studies, the interlance charge transfer between Fe\({}^{2+}\) on the octahedron and Fe\({}^{3+}\) on the co-sided T\({}_{1}\)1 tetrahedron leads to the color and pleochroism of iolite [6; 7; 8]. Color grading plays an important role in the quality evaluation of colored gemstones. In 1994, [PERSON] et al. [9] proposed a color classification method for colored diamonds: a 6504 K fluorescent lamp was used as the evaluation light source and colored diamonds were placed in a standard lighting box for grading. This method has been widely used around the world since it was announced. Then, the color classification methods of pink diamond [10], blue diamond [11], yellow diamond [12], and colorless diamond [13] were introduced. Although the color classification of diamond is well established, the grading of other colored gems and jade remains a problem to be solved. In order to better ensure the accuracy of color grading of colored gemstones, the CIE1976 _L_*_*_b_* uniform color space system was introduced and played an important role in the color quantization research of gemology. It mainly involves jadeite [14], peridot [15; 16], iolite [3], amethyst [17], citrine [18], chromic garnet [19; 20; 21], tourmaline [23; 24], sapphire [25], chrysoberyl [26], cubic zirconia [27], blue amber [28], and diamond [29]. The GemDialogue color chart is widely used in the world for expressing and classifying the color of gemstones. As a color comparison tool for precious stones, GemDialogue colorcharts cover a wide range of colors and are easy to perform. [PERSON] et al. [30] used the GemDialogue color chart to classify jade green into seven grades, which confirmed that it is effective and feasible to use the GemDialogue color chart to evaluate the quality grade of jade color. [PERSON] et al. [25] set the hue angle range of the GemDialogue color chart between 186-300\({}^{\circ}\), including four hues of sapphire, aquamarine blue, cyan, blue, and blue purple, and established a sapphire color evaluation system. Blue jolite is close in color to sapphire, but has a narrower range of hue. Considering the physical characteristics of jolite, this paper removed the aquamarine blue and cyan tones, and added purple tones to simulate the color of jolite. The principle of clustering is to group data within a set in such a way that the differences between groups are maximized and the differences within groups are minimized. Therefore, a clustering algorithm is often used to objectively and accurately describe the classification of gems 'colors [31,32]. [PERSON] et al. [33] compared the Affinity Propagation (AP) and K-Means clustering methods applied to the grading of gemstone colors; it is believed that K-Means is more conducive to the selection of centers that are more representative of the entire population when the sample size is large and concentrated. This algorithm is simple and fast, and is more suitable for samples with a large initial number. Therefore, this paper uses K-Means clustering analysis to classify the color data of the color charts.