# 3-D Grain Structure

Grains

##### Equipment:

Only two items are necessary for this show and tell. The first one is a tetrakaidecahedron that I have constructed using poster board, glue, tape, and newspaper to stuff the inside with. The model only costs about \$5 to make. It consists of six squares and eight hexagons, all with sides of 2.5 inches in length. Each square is adjacent to four hexagons, and each hexagon is adjacent to threee squares and three other hexagons in such a way that every other side is adjacent to a square. This can be seen when observing the picture in the back, which is the other item that is necessary for this presentation. The picture can be made into a transparency and be shown to the class on the overhead.

##### Procedure:

This show and tell would work nicely after the bubble blower demonstration, which shows grain growth. It would help the class visualize that grain growth actually occurs in threee instead of two dimensions. All the instructor has to do is show the model of the tetrakaidecahedron to the class and explain the science behind it that I have explained above. Then the transparency of how these figures fit together can be shown to illustrate why a tetrakaidecahedron is an example of an ideal grain that correctly fills space.

##### Science:

A common misconception among MSE 250 students is that grains are two dimensional, since all the pictures in the book are of a two dimensional microstructure. The tetrakaidecahedron model is an ideal grain that would hopefully abandon that false notion. It is considered an ideal grain because the angles of the figure come together in such a way that a group of tetrakaidecahedrons fill space correctly as real grains do. The photo on the back can be used to show the class that indeed these figures actually do fill space. This presentation also illustrates that when one sees a photo of a grain structure, they are actually viewing the sides and cross sections of the grains. Sidenote: Also attached is a pattern that could be used to help aid in constructing another model if necessary. Reference: Smith, Cyril S., "Grain Shapes and Other Metallurgical Applications of Topology", in Metal Interfaces, American Society for Metals, Cleveland, OH, 1952, p.90. [eq].

A common misconception among MSE 250 students is that grains are two dimensional, since all the pictures in the book are of a two dimensional microstructure. The tetrakaidecahedron model is an ideal grain that would hopefully abandon that false notion. It is considered an ideal grain because the angles of the figure come together in such a way that a group of tetrakaidecahedrons fill space correctly as real grains do. The photo on the back can be used to show the class that indeed these figures actually do fill space. This presentation also illustrates that when one sees a photo of a grain structure, they are actually viewing the sides and cross sections of the grains. Sidenote: Also attached is a pattern that could be used to help aid in constructing another model if necessary. Reference: Smith, Cyril S., "Grain Shapes and Other Metallurgical Applications of Topology", in Metal Interfaces, American Society for Metals, Cleveland, OH, 1952, p.90. [eq].

mister X