Three–dimensional visualization of ternary prisms (T–prism): Development of a spreadsheet–based tool for Earth and material sciences

Abstract

T-prism is a Microsoft-Excel-based tool that visualizes ternary space diagrams (i.e., ternary prisms) in threedimensional (3D) space. This tool allows us to examine the overall features of a dataset in both three-and twodimensional spaces by altering the viewing angles. T-prism involves two algorithms that coordinate the transformation and rotation of diagrams in a virtual 3D space. This paper describes a new and simple coordinate transformation from a ternary space diagram (i.e., ternary prisms) to an XYZ orthogonal system. Coordinates of a point of interest in the ternary space diagram, expressed using the proportions of three components of a basal triangle (r, l, and t, where r + l + t = 100) and an additional variable (h), are converted into coordinates in the orthogonal system as follows: x = (r + 100 − l)/2, y = ffiffi ffi 3 p /2t, and z = fh. Here, f represents the correction factor used to appropriately express the length of an axis perpendicular to the basal ternary diagram. T-prism is particularly suitable for visualizing phase relations in multicomponent systems, the physical properties of materials, and compositional variations in solid solutions. Hence, the tool is applicable to a broad variety of research and teaching fields, including Earth science, material science, and physical chemistry.

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