question: solve for the dimension of unit

3. Place 7 marbles again on top of the 2nd layer in a position like the first layer and fasten with glue again. 4. Measure the length of sides (A and C) of the HCP structure using the caliper. (Note: Six spheres surround a central sphere in the first and third. Three spheres triangulate in the second layer between the first and third. See Figure 2A.1) B. Face Centered Cubic 1. Place 7 marbles in a hexagonal position and fasten the marbles in place using the molten glue stick. Place 5 marbles in a square position with 1 marble at the center. Glue all the marbles to secure its shape. Place 4 marbles on top of the Ist, then fasten it with molten glue 3 . Place 5 marbles like the Ist layer on top of the 2nd layer and fasten with molten glue 4. Measure the length of the side (ao) using a caliper (Note: FCC structure should look like Figure 2A.2) C. Body Centered Cubic 1. Place 4 marbles in a square position. 2. Place 1 marble on top of the center the Ist layer then fasten with glue altogether. 3. Place the 3rd layer like the Ist layer with 4 marbles at each corner, secure all marbles in place with molten glue 4. Measure the length of the side (ao) using a caliper. (Note: BCC structure should look like Figure 2A.3) Figure 2A. Model for crystalline structures (1) IICP (2) FCC (3) BCC PB. 3\fy, a crystal will be grown from an actual saturated solution. The unit cells of the most common crystalline structures will also be constructed using readily available materials. For each crystalline structure, the APF will be calculated and will be compared against scientifically accepted values. METHODOLOGY Materials: Alum powder Vernier caliper . . . Thread Grease or oil 40 marbles . Rubber band Glue stick Filter paper Glue Gun Procedure: Crystal growth 1. Weigh out 10 g of alum and place it in a clean 250-ml beaker. For each gram of alum used, add 7 mL of water. Heat the mixture and stir it with a stirring rod until a clear solution is obtained. (Note: If the mixture remains cloudy, allow the mixture to stand for a few minutes until the sediment has settled out, then carefully decant the clear solution into another clean 250-mL beaker.) Allow the solution to cool to room temperature. 2. Tie a piece of thread to a glass rod so that when suspended in the solution the thread will extend no more than 1 cm below the surface of the solution. Smear grease on the part of the thread that will be above the solution to keep the solution from creeping up the thread. Cover the top of the beaker with a piece of filter paper, and use a rubber band to hold the paper in place. Punch a hole in the center of the paper. Lower the thread through it until the thread is submerged and the stirring rod rests on top of the beaker. Keep the beaker in a safe storage place. Crystals should have formed on the string and/or at the bottom of the solution by the time you return for your next lab period. 3. If crystals have formed on the string, crush off all the best one. If not, decant the liquid from the crystal(s) at the bottom of the container into another clean container. If more than one crystal grew, inspect them and pick one that shows good faces. Tie a fine thread to this "seed" crystal and tie the other end to the glass rod. 4. Suspend the crystal in a freshly prepared solution of 10 g of alum in 70 mL of water. This solution must be allowed to cool to room temperature before the crystal is introduced. II. Model Building A. Hexagonal Close Packed 1. Place 7 marbles in a hexagonal position and fasten the marbles in place using the molten glue stick. 2. Place 3 marbles on top of the Ist layer of marbles and fasten again with molten glue stick. pg. 2CRYSTALLINE SOLID-STATE STRUCTURE INTRODUCTION The regular geometric shapes of well-formed crystals reflect orderly three dimensional network of the atoms, ions, or molecules that constitute the crystal lattice. Although the arrangements of atoms and ions which lead to regular crystal lattice structures are quite simple, it is difficult to visualize the arrangements in 3-dimensions. One of the purposes of modelling some of the common crystal structures is to clearly see how the atoms and ions are arranged on the molecular level. Growing a crystal on a microscopic level lead to orderly structures on the macroscopic level. Macroscopic crystals are perfectly stacked unit cells in the molecular level. A unit cell can be represented in the hard sphere model, which utilizes the fewest number of atoms while maintaining the structural makeup of a material. It is an effective representation of the physical arrangement of atoms in a solid. The unit cell is also defined by its ability to be "stacked" to form larger blocks of material. This model assumes that the atom is akin to a sphere, and therefore the unit cell is often tightly packed. Several properties have been defined to describe the unit cell and consequently tell something about the structural makeup of the material they represent. The atomic packing factor (APF), for example, is the ratio of the volume of atoms in the unit cell over the volume of the unit cell, as described by the following equation: Natoms Vatom Natoms 4 APF = cell cell * 3 Tr3 Vunit cell unit cell cell *Natoms = no. of atoms in a unit cell; Vatom = volume of the atom; Vunit cell = volume of the unit cell The three common arrangements that describe most materials are the Body Centric Cubic (BCC), Face Centered Cubic (FCC), and the Hexagonal Close Packed (HCP), wherein the relationship between the arrangements and their respective dimensions for packing are described below: HCP: Vunit cell = 2 42C; A = 27; C = WI co FCC: Vunit cell = (do)3; do = - 4r V3 BCC: Vunit cell = (ao)3; do = 2rv2 * do = length of a side of a unit cell : r = radius of the atom pg. 1