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 three–dimensional (3D) space. This tool allows us to examine the overall features of a dataset in both three– and two–dimensional 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 = √3/2t, 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.