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Crystallography

  1. PRE-LABORATORY QUESTIONS

    1. Faces
    2. Corners
    3. Edges

  2. What is the volume of a sphere in terms of the radius (r)? Volume =

  3. What is the area of a parallelogram in terms of the lengths of the base (C) and altitude (A)? Area =

  4. What is the volume of a cube in terms of the edge length (E)? Volume =

  5. How many of each of the following are there on a cube?

    1. What is the length of the edge (E) of a cube in terms of the face diagonal (FD)? (See Figure 1.) E/FD =

    2. What is the length of the face diagonal (FD) of a cube in terms of the body diagonal (BD)? (See Figure 2.) FD/BD =

    3. What is the length of the edge(E) of a cube in terms of the body diagonal(BD)? E/BD =

PROCEDURE

  1. Fasten eight 1-inch spheres together in the form of two squares, such as shown at the right. This is done by inserting the cutoff end of the pin into a sphere with a pair of pliers. The second sphere is easily attached to the sharpened end of the pin. Note that the spheres must be touching each other. Attach the two squares together, one over the other, so that the centers of the spheres are directly above each other. This model represents a portion of a simple cubic (SC) lattice.

  2. As above, assemble two groups of 1-inch spheres into squares, but this time the distances between spheres should be about 1/4 inch. Nest the single sphere in the center of one group of four. Then place the second group of four on top so that the spheres in the second group are directly over the spheres in the first group. Note that the single sphere should be in contact with each sphere of the two groups of four. This model represents a portion of a body-centered cubic (BCC) lattice.

  3. Here you can recycle one of the tetrads from the BCC model, and then assemble two groups of five 1-inch spheres. Place the group of four over one of the groups of five so that each of the sphere of the group of four fits between the outer spheres of the group of five. The second group of five should then be placed on top so that the spheres in the second group of five are directly over the spheres of the first group of five. The spheres in each face should be in contact through the face diagonal but not along the edges. This model represents a portion of a face-centered cubic (FCC) lattice.

  4. The chloride ion has a diameter roughly twice that of the sodium ion. Thus, in constructing a model of sodium chloride, we will use 1-inch spheres for the chloride ions and 1/2-inch spheres for the sodium ions. Assemble two groups of spheres as shown in Figure 4-8 (textbook). Also assemble one group of sphere as shown in Figure 4-9 (textbook). Then place the group that has the 1/2-inch spheres at the corners between the two groups that have the 1/2-inch spheres on the edges so that 1-inch and 1/2-inch spheres are alternately placed.

  5. Construct a body-centered cubic model in which the center is a 1/2-inch sphere and the corners are 1-inch spheres.

  6. Construct a face-centered cubic model in which the center of each face is a 1/2-inch sphere and the corners are 1-inch spheres.

    Print out these four data pages:
    DATA PAGE FOR PARTS A THROUGH C
    Volumes - Interstitial and Atomic
    DATA PAGE FOR PARTS D THROUGH F
    The Empirical Formula

    PROBLEMS

    1. Which of the three basic types of unit cells (simple cubic, body-centered cubic, face-centered cubic) contains the most empty space?

      Which has the least empty space?

    2. Solid argon (Ar) is face-centered cubic.The edge length of the unit cell is 4.79 angstroms (1.00 Å = 1.00 x10-8 cm). The atomic weight of Ar is 39.95. Calculate

      1. the atomic radius of Ar in cm,

      2. the volume of the unit cell in cubic centimeters,

      3. the mass of the unit cell in grams,

      4. the density of solid Ar.

    3. The atomic radius of the neon (Ne) atom is 1.39 Å. What is the density of solid neon if it is face-centered cubic? The atomic weight of Ne is 20.18.

    4. The atomic weights of Na and Cl are 22.99 and 35.45, respectively. If the ionic radii of the Na+ and Cl- ions are 0.98 Å and 1.81 Å, respectively, calculate the density of solid NaCl. Work out problem on extra sheet of paper but put answer here.