Phases Diagrams Of Ceramics Third Stage 2-4-2 Alkemade Lines: A straight line connecting the points representing the compositions of the crystals in the ternary system is called a binary join. A join connecting the compositions of the primary crystals of two areas having a common boundary line is called an Alkemade line. The use of Alkemade lines simplifies the analysis and interpretation of ternary phase relations. The following example should help to clarify the distinction between joins and Alkemade lines. In the system shown in fig.(35), there is an intermediate binary compound BC which has a primary phase field labeled bc. The line A-BC is a join connecting the compositions of the primary crystals of two areas having a common boundary line, ED, and therefore, the line A-BC is an Alkemade line. Lines AC, AB, B-BC, and BC-C are also Alkemade lines. Line BC, although a join, does not fulfil1 the condition of the common boundary line because areas c and b are not adjacent; consequently, BC is not an Alkemade line. Fig (35) Join BC is not an Alkemade line. 1 Phases Diagrams Of Ceramics Third Stage The Alkemade theorem states that the intersection of a boundary line (or boundary line extended) with its corresponding Alkemade line (or Alkemade line extended) represents a temperature maximum on that boundary line and a temperature minimum on the Alkemade line. The Alkemade theorem permits one to analyze with respect to temperature the direction of slope of boundary lines. In fig.(36) the slopes of the boundary lines for the system A-B-C have been determined by applying the Alkemade theorem. Three boundary lines slope to a common junction at E and at D. These points are eutectic points. Fig. (36) Application of the Alkemade theorem to determine slopes of boundary lines. 2-4-2 Composition Triangles: Alkemade lines divide a ternary diagram into composition triangles. In the diagram of fig.(35), triangles A-BC-B and A-BC-C are composition triangles. A composition triangle is always made up of three Alkemade lines. 2 Phases Diagrams Of Ceramics Third Stage It should be noted that Alkemade lines never cross one another. Example: For fig. (37), label primary phase fields and construct Alkemade lines. Fig. (37) Ternary systems for example. 3