SOLID-STATE STRUCTURE.. FUNDAMENTALS
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1 SOLID-STATE STRUCTURE.. FUNDAMENTALS Metallic Elements & Sphere Packing, Unit Celis, Coordination Number, Ionic Structures Stoichiometry PRELAB ASSIGNMENT Properties of Shapes & Patterns following question should be before coming to laboratory. Show this completed assignment to your lab instructor as you come to 1. Based on an examination of figure at the answer the following question. A cube has corners, edges faces. 2. In structures b. c. d. below, draw the outline(s) of their 2-D unit cells (two-dimensional repeating patters). A 2-D unit cell is a parallelogram that encloses a portion of the structure. the unit cell is moved in the Y -plane in directions parallel to its sides and in equal to the length of its it the property of duplicating the original as well as spaces between See Structure a. as an is in bold Structure a. Structure b. Structure c. Can a structure have more than one type of unit 1
2 3. If circle segments enclosed inside each of the bold-faced _",~,~,,.,.~...u shown were cut out and together, how whole could constructed for each one of the patterns? is a 3-D cell a structure of spheres. center of 8 spheres is at a corner of the cube, the part that in the interior of the cube is shown. of the segments enclosed inside the unit be glued together, how many could be constructed? Consult your and examples of metallic elements adopt the following kinds of structures: Hexagonal closest Cubic (ccp): (hcp): Body -centered cubic (bcc): Identify name geometric solids. right, faces. the regular Number comers: Number of faces: of solid: Read the next four pages the Introduction and Experimental Note on pages 7 and 8 of experiment. The next four are from the Solid-State Modeling System instruction manual. 2
3 SOLID-STATE STRUCTURE Fundamentals Metallic Elements & Sphere Packing, Unit Cells, Coordination Number, Ionic and Stoichiometry INTRODUCTION Materials in the solid including semiconductors and ionic compounds, exhibit submicroscopic structures that in principle extend infinitely all dimensions. Closepacking spheres is one example of an arrangement of objects forming such an extended structure. Extended close-packing of results in 74% of space being occupied the spheres, with attributed to the empty the This is highest space-filling efficiency of any sphere-packing, which occurs hexagonal closest packing (hcp) and cubic closest packing (ccp), will activity. Sixty-eight the ninety naturally are of metals have three-dimensional submicroscopic structures that can be described in terms closepacking of spheres. Another sixteen the sixty-eight naturally occurring metallic elements can be described in terms of a different type of extended structure that is not as efficient at spacefilling. structure occupies only 68% of the available space. second largest subgroup exhibits a sphere packing arrangement body-centered cubic (bcc). When spherical objects of equal are packed in some type of arrangement, the of nearest neighbors to any given sphere is dependent upon the efficiency of space filling. number of nearest neighbors is called the coordination number and abbreviated as CN. The sphere packing schemes with the highest space-filling efficiency will have the highest CN. Coordination number will explored in this lab activity. A useful way to extended structures, which, in principle, can be infinitely large, is to conceive of a three-dimensional parallelepiped, which is a six-sided having parallel faces. this a unit cell which can be moved in three directions to duplicate entire structure the crystal; for a cubic cell, cell is shifted in the perpendicular Y Z cell is the repeating three-dimensional pattern for extended structures. unit cell has a pattern for the objects as well as for the void spaces. Unit cells will explored in this lab activity. The remaining unoccupied space any <:nn...t"p' is as void This space occurs between spheres and rise to so-called interstitial sites. A very useful way to describe the extended structure of many particularly ionic compounds, is to assume that ions, which may of different sizes, are spherical. structure then is based on some type of sphere packing exhibited the ion, the ion occupying the unused (interstitial sites). In structures this type, coordination number to the number nearest neighbors of opposite charge. Salts exhibiting packing arrangements will be explored in this lab activity. 3
4 EXPERIMENTAL NOTE: The following directions assume students work groups four, of two partners, Team A Team B. the case of too few students to full a team may have just one student. Each team will have a solid-state modeling kit. In each section of experiment, A and B will construct individual structures that can then be studied and compared by members of both teams working as a group. It is to the so each has a chance to build some structures. For details on to build each of structures, consult indicated page of the instruction manual with Solid- Modeling System kit. Templates are color coded with or yellow dots. Match colored dot a template over same colored dot on the base. (I) Sphere Packing & Metallic Elements. the shaded and dotted line portions of the template- A construct the hexagonal close-packing unit cell (p. 17; -Team B - construct cubic unit cell (p. C6). Team - compare the two structures consult your textbook. Which structure is Which structure is considered to have abca What is about the a and b layers? does C6 use differ for the aba vs abca Team A - Add a 2' on top the existing structure. *Team B - Add a 2' layer on top the existing structure. eteams - compare the two structures. Locate the in the of seven next to the new top layers. sphere, following: Number of touching spheres in N umber of touching Number of touching below- layer above = (hcp) Structure (ccp) Structure packing that this number adjacent and touching nearest neighbors is to as: packing", number of adjacent and touching nearest neighbor spheres is termed: " number",
5 (II) Unit Cells U sing only the shaded portion the construction directions Team A - construct the simple cubic unit cell (p. C4)... Team B construct the body-centered unit cell ( p.ll; C4') Teams AlB compare the two structures. What is the shape of each of unit Simple: Body-Centered: to the drawings at the bottom of this page: Simple Body-centered Where do the centers lie? ---_&_-- How many spheres were used to build each structure? on shown below, determine following for type of unit each comer sphere, what is the fraction of the sphere volume in the boundaries of the unit cell? for a body-centered n/a what is the sum total of spheres lying within the boundaries? (or, if all of the sphere segments could how many would assembled into whole cnl1,prp The only """'"U'''''''' to adopt the simple-cubic structure is polonium. Simple Cubic 5 Body-centered
6 -Team A - Using the shaded and dotted line portion, construct 8 simple cubic unit cells (p. 9; C4; 3 layers high).* -Team B - Using the template, construct 8 body-centered cubic unit cells (p. 11; C4'; 5 layers high). * * This results in two unit cells in the X, Y & Z directions. -Teams AlB - Compare two structures. Locate an interior sphere the 2nd of structure. For structure, determine the following: Number touching spheres 1st layer Number of spheres in layer Number touching spheres in 3rd layer- TOTAL What is the coordination of each type of Are these structures close-packed? Locate the sphere in the middle of the entire structure. To how many unit does it "belong"? What position in the unit cell does it occupy Team A - Construct face-centered cubic unit (p. 20; C6). -Team B - Using only the shaded portion, construct the face-centered cubic Unit (p. 19; C4) Teams AlB - Compare the two structures. Are the two unit the same? Is the face-centered cubic arrangement hexagonal -aba or hexagonal -abca examine the body diagonal structure of 20) How many were used in constructing a face-centered cubic unit cell structure? How many spheres lie with their centers at corners of unit How many unit cells share a corner sphere? many spheres lie with How many unit cells centers on the faces of the unit a face-centered sphere? 6
7 Based on the drawing below, detennine the following for unit each corner sphere, is the fraction of the sphere volume within the boundaries of the unit cell? For a face-centered sphere? What is sum of all spheres lying within the boundaries? all of sphere segments could be assembled into whole spheres, how many would result?) (III) Interstitial and coordination number ofoppositely charged ions. -Team A - Construct CN 8, CN 6 and CN 4 (p. 62). Team B - Construct CN 6, CN 4 (body diagonal) (p. 64). Teams AlB - Compare all structures. What color of lies at of following interstitial sites? CN CN CN If spheres are assumed to an anion? which of the spheres is most acation?. to be CN 8, CN 6 the centers of the outer ~n~\""r~'<': lie, respectively, at the corners of the following gec)me:ti CN.' CN Correlate terms tetrahedral hole, cubic hole and octahedral hole with CN CN CN Beginning with largest, what is the size-order of coordinated spheres? > 7
8 (IV) Ionic Structure and Stoichiometry A - Using only the shaded and dotted line portion, construct 2 NaCl Unit Cells C4). B the NaCl Unit (p. C6). AlB - Compare two structures. Do the two structures have the same unit pattern? Which What is the pattern exhibited by the large spheres? the -? 'Na1+? , ' by small snherelf! What is the CN of the cations in the structure? -anions in the structure? to the below determine following: What is the of spheres lying within the boundaries of unit cell? small spheres? What is the formula representation this unit cell? Na CI or DNaCI DO (V) Extension Team A - Construct calcium fluoride unit cell (Fluorite; p. 1 -Team B - Construct the zinc sulfide unit cell Blende; p. AlB each structure. C4). C6). What is the formula for the Fluorite unit cell? What the formula Zinc unit cell?..team A - Construct the Diamond unit cell (p. C4'). B Construct the Graphite structure (p. 45; C6). Teams - Examine structure. What is the net number atoms lying within the boundaries the diamond unit cell? What is CN of carbon diamond? graphite? 8
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