Question

Q. 3. Potassium fluoride adopts the rock salt (NaCl type) structure, with a density of 2.48 g/cm3. Using the data for the Part 4 model you constructed, calculate the expected distance between the center of the potassium ion and the center of an adjacent fluoride ion in pm.

Q. 4. The diameter of a Cs+ ion is 334 pm; the diameter of a Br- ion is 392 pm. For CsBr, which crystallizes in the CsCl type structure from Part 5, calculate the volume of one unit cell, calculate the mass of one unit cell, and calculate the density of CsBr using the true radii values (from the diameters). Note: atoms touch along the body diagonal but not along the edge in an actual CsCl type structure.

Part 4 The Sodium Chloride, NaCl, Lattice (rock salt) ICE page 33, Template C, base  Since the sodium ion, Na+, has a diameter of 204 pm and the chloride ion, Cl-, a diameter of 362 pm, you may approximate the relative sizes of these ions by using small blue spheres for Na+ ions and large colorless spheres for Cl- ions. Build the NaCl crystal lattice layers as shown in Figure 5 (shaded area of the pattern in ICE manual). You will need to use 7.4mm(d ) spacers. Your final model is one NaCl unit cell, and should consist of 27 spheres (14 chlorides and 13 sodium ions), but remember the entire sphere may not be within the actual unit cell. •The equivalent of how many sodium ions are within the unit cell (a)? •How many chloride ions (b)? •Compare your answers in (a) and (b) with the simplest empirical formula (c). Note the similarity of the Cl- ions here with the model from Part 2. The thirteen Na+ ions are in the spaces between the Cl- ions, as shown in Figure 5. •Where do the atoms touch here? Note, as shown in Figure 5, the Cl- ions do not touch each other in the real NaCl structure. •What is the geometry of the Cl- ions about each Na+? We say the Na+ ions sit in octahedral holes in the Cl- face-centered cubic lattice. Note that this lattice can also be described as an interpenetrating set of face-centered cubes – one involving Cl- ions and one involving Na+ ions. •Which distance is shorter, from a Cl- to Cl-, from Na+ to Na+ or from Cl- to Na+ ? Thus, what is the nearest neighbor for Cl-? What is the nearest neighbor for Na+? Note the coordination number of each Na+ ion and of each Cl- ion.

Part 5 The Cesium Chloride, CsCl, Lattice ICE page 11, Template A, base  Since the cesium ion, Cs+, has a diameter of 334 pm compared with a diameter of 362 pm for the chloride ion, Cl-, you may approximate the relative sizes of these ions by using medium green spheres for Cs+ ions and large colorless spheres for Cl- ions. Build the area indicated by the dotted lines in the ICE manual, as shown in Figure 6. •Does this represent one or more than one unit cell? •What is the shortest center to center distance here? •Where do atoms touch in this structure type? Note, the Cl- ions do NOT touch each other in the real structure. Note the similarities and differences between this model and both your Part 1 and Part 3 models.

Part 1 Simple (Primitive) Cubic Cell (sc) ICE page 9, Template A, base  Construct a single unit cell of the simple cubic (sc or primitive cubic) lattice using eight large (colorless) spheres (on the shaded region of the pattern). Using four more balls, extend your model in one direction so that you end up with two unit cells in contact. Note that four of the atoms are shared by the two unit cells. In a similar fashion, extend the model in the other direction covering the dotted line area. Add a third layer so you have a large cube of 27 balls containing eight unit cells (three balls wide in all three directions.) Focus your attention on the sphere hidden in the center of your model. •How many cells share this atom? What fraction of this sphere lies in any one cell? Note that any sphere lying at the corner of a cubic unit cell contributes this same fraction of a sphere to the unit cell. •By adding up the fractions of pieces of spheres in one unit cell, what is the equivalent number of atoms in a unit cell (see (a) in the data table)? Now focus your attention on one unit cell. •Where do atoms touch, along the cell edge, the face diagonal or the body diagonal? Note that because the spheres are in contact along the cube edge, the edge length of the unit cell (distance from sphere center to sphere center) is just twice the radius of one sphere (see (c) in the data table). •How many atoms touch the center atom? This is the coordination number (f), the number of nearest neighbors in the lattice, not just in one cell (measured as the shortest center to center distance).

Part 3 Body-Centered Cubic Cell bcc ICE page 18, Template F, base  Construct the layers shown in Figure 4, using the large colorless spheres (on the shaded area of the ICE manual pattern). •Where do the atoms touch here? Note that atoms touch along the body diagonal but NOT along the cube edge. Study the symmetry of this model, note the coordination number (the number of nearest neighbors to an atom) that each atom has, and the relative density of the packing compared to Parts 1 and 2.

Answer 1