Thomas Li and Jay H. Wonell Unlversity of South Florida. Tampa. FL 33620 As we annroach the 1990's. X-rav-crvstalloma~hv .. . - . . has become almost as routine a composition tool as elemental analvses and infrared spectra were in the 1970's. Recent articles have discussed poi& group assignments1 and differences between the Schoenflies (spectroscopists) and the Hermann-Mauguin (crystallograpbers)notation systems2. Textbooks typically provide tables that detail the relationshins between crvsialloeranhic unit cell axes and aneles for the' seven shapes of c;ysiallographic unit celW4. ?o get students more intimatelv involved in the three-dimensional nature of the basic units, the following laboratory exercise has students construct models for the seven unit cells. Over a period of time the instructor becomes the owner of some excellent visual aids (save the best) that can be painted and used in lectures. Have two students work together, each pair preparing one of the models. The materials required include balsa wood sheets (6 in. X 36 in. X '/8 in.), wood glue, wood filler (optional), shellac, small paint brush, single edge razor blades, ruler, protractor, carpenter's square, and sandpaper (100 and 300 mesh). he appropriate unit faces are drawn on the balsa wood, cutout, and glued together. Use sandpaper to bevel the inside edge of each face to about 30' to facilitate a better fit. In the cubic, tetraeonal, . orthorhombic or other cells requirine a 90° angle, use a carpenter's square to hold and alignfacesat 90' while they are being glued together. The structural strength of the models is greatly enhanced by glueing small scrap balsa wood strips along the inside edges where faces are ioined. Construction of the rhombohedral and triclinic cells is simplified if one first glues together the three faces that constitute one-half of the cell and then combines the two half units. Wood filler or glue will fill any holes or interstices created by poorly fitting edges. Sand the cell carefully with 100 mesh sandpaper. Apply several coats of shellac, sand using 300 mesh paper, then brush or spray the model with your favorite color of paint. Use of a hair dryer hastens the glue and paint drying processes. By performing this two-hour exercise, students gain a greater functional appreciation for the variations that can exist in the a, b, c crystallographic axes lengths and the a,8, and y angles within eachunit cell, nottomention the considerable pride that is generated by constructing the best model. Traceable templates for each unit are easily drawn using
paper and nencil or generated ahead of time on a Macintosh Eokputer ia compl& set is available from the authors on request). One set of reasonable dimensions and a complete pa& list are given below. Students can vary the cell dimensions as long as they obey the length and angle limitations given for each cell. sixpieces that measure 6rm X 6 cm. Face angles on all sin pieces must be 90". 2. Hexagonal: a = b # c; o = 3 = 90° and 7 = 120'; two pieces that measure 5 cm x 5 cm, each piece having two fiO0 angles and two 120° angles. Four pieces that measure 5 em X 10 rm, with each piece having four 90' angles. 3. Monoclinic: o # b # e; a = y = 90- and 0 # 90" or 120'; two pieces that measure 4 cm X 6 cm, each piece having two 80' and two 100° angles. Two pieces that measure 4 cm X 9 em, each piece havine four 90' aneles. Two oieces that measure 6 ern X 9 ern, each piece having four 90' angles. 4. Ortharhombic: a f b # c; a = @ = y = 90'; two pieces that measure 4 cm X 6 cm; two pieces that measure 9 em X 6 cm; two pieces that measure 9 cm X 4 em. Angles on each face must be 90'. All four angles on each piece must he 90". 5. Rhombohedral: o = b = c; a = 0 = y # 90°; six pieces that measure 7 cm X 7 em. Each niece has two 50' and two 130' angles If instead, the model is made having two fiO' and two 120' angles, it is easy fur students to wsualm elongation or compression along the Ca 6. Tetragonal: a = b # c; a = 0 = y = 90°; two pieces that measure 5 an X 5 cm and four pieces that measure 5 cm X 9 em. All four angles on eaeh face must be 90". I . Triclinic: a # b + e; a + 0 Z y f 90'; two pieces that measure 4.5 cm X 6.5 cm, each piece having two 80' and two 100" angles. Two pieces that measure 9 cm X 6.5 cm, each piece having two 60° and two 120° angles. Two pieces that measure 9 cm X 4.5 cm, eaeh piece having two 80' and two 100' angles. 1. cubic:^^ = h = c; a = B = y = 90';
' Sharma,8. D. J. Chem. Educ. 1982,59,554-557;
1983,60,462-
463.
Breneman. G. L. J. Chem. Educ. 1987.64.216-217. Drago, R. S. Physical Methods in Chemistry; Saunders: Phlladelphia, 1977; p 596. Ladd, M. F. C.; Palmer, R. A. Structure Determination by X-Ray Crystallography, Plenum: New York, 1978; p 34. For a discussion on the relationships between trfgonal, hexagonal, and rhombohedral cells see: Ladd, M. F. C.; Palmer. R. A. Structure Determination by X-Ray Crystallography; Plenum: New York, 1978; Fig. 2.11, p 65.
Volume 66 Number 1 January 1989
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