A. Y M."" Flinders University of South Australia Bedford Pork, South Australia 5042
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Models for Simple, Close-Packed crystal Structures
Traditionally, students are introduced to basic crystallographic concepts with lecture demonstration models, a display of crystal models, or perhaps a programmed learning series of experiments. Seldom is the student of a large laboratory class given the opportunity to build crystal structure models from first principles because the cost of conventional models is prohibitive and in many cases the construction of such models is time consuming. This paper describes some simple crystallographic models, which have been found satisfactory in the large laboratory classes for first year students a t this University. The crystal structure models are based on two sets of oartiallvconstructed close packed layers, made from commercially available' and relativelv inex~ensive ~olvstvrene foam . . . spheres. A major problem in teaching (and learning) crystallography is that of crystal structure representation. Invariably, a particular feature of the structure needs to he placed in emphasis, e.g., the close packed layering sequence, the size and symmetry of the unit cell, or the coordination environment of a particular species. Accordingly, one commonly finds crystal structures represented in one or other of the following ways
Figure 1 . Partaly-constructed ciose packed layers (Set A! for cubic close packed structures.
1. Orthoeraohicoroiection
For the first two of these, the unit cell concept of the structure is all important; for the latter two representations, the close packed layering sequence and the mode of site occupancy is of prime concern. In fact, in the overall context, all types of representation (and especially the relationships between them) are important. The models described in this paper, while based on close packed layering sequences, are designed so that the final result can a t the same time be easily interpreted from the unit cell point of view. Experimental Equipment Each student (or pair of students) is supplied with the following set of equipment 14 white spheres, diameter 2%". (for close packed species) 14 black spheres, diameter l-in. (for octahedral sites) 28 red spheres, diameter +in. (for tetrahedral sites)
10 rubber bands 12 toothpicks 1
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Frosty Snow Company, Antiaeh, Illinois. Copies available upon request.
652 /Journal of Chemical Education
Figure 2. Partaliy~constructedclose packed layers (Set B! for hexagonal close packed structures.
and the following two partially constructed close packed layer sets (again white spheres, 2%". diameter). Set A (Cubic close packing set). Four layers, for constructing 1. the cubic close oackine " seouence . ABCA'. as shown in Fieure " Set R (Hexagonal close packing set). Three layers, for constructing the hexagonal close packing sequence ABA', as shown in Figure 2. The sets of close packed spheres can be simply and quickly pre-
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in. each end to allow the rubtact; the wires must protrude ber bands to hold layers together in the final structure (see Fig. 3). In practice, the models are robust and durable; individual spheres can be simply replaced when required if the spheres are not glued. Construction of Models Following the instructions contained within a text2 for the experiment, each student is asked to construct and investigate the following models in turn
Figure 3. Completed model of the sodium chloride ( N a C I ) structure
Close Packed Crystal Structures
1. An octahedral site 2. A tetrahedral site
Fmc-
Using S e t A (cubic elo.sepacking) and appropriate interstitial: 3. The face centered cuhic (f.c.c.) lattice 4. The sodium chloride (NaCI)structure 5. The fluorite (CaF2)and anti-fluorite structures 6. The zinc blends (ZnS) structure Using - Set B (hemzonal close packing) and appropriate interstitiols: 7. The hexagonally close packed (h.c.p.) lattice
tion of
Srruefure Type i.e.c. NaCl CaF?
Clnsp lntpr Typeof s i t p r C.N. C.N. Packine packed rfifial site occu- of of ~ y p o species speeies oceupied pied cation anion
c.c.p
cc.p c.e.p. ccn.
M
1''
CiCa2-
NaF-
octa tetra.
Sg-
202-
tetra.
all aii
?i
6
6
8
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Stoichiornorrv
M MX, MX MX
R. T h e nickel srsenide 1NiAs)structure
rangement of spheres, the coordination numbers and site occupancies are noted before the arrangement is modified to the model for the subsequent structure. No compound is known to c~ystallizewith the structure having all tetrahedral sites of an h.c.p. lattice filled; a model of this arrangement clearly shows why this arrangement is energetically not favored. The structure in which half of these tetrahedral sites are occupied is that for ZnS (wurtzite), ohtained by removing every second layer of red spheres from their tetrahedral sites. A completed model for ZnS (wurtzite) is shown in Figure 4. The type of crystallographic information which an experiment of this nature should generate is shown in the table; a tahle of this type constructed and completed by the student with details obtained during the course of the investieation is a convenient method of summarizing- the experiment. In practice, construction and investigation of the models described here takes the average student approximately three hours to complete; extension of models of this type or other structure types and stoichiometries (e.g., MX3 and MzX3) is of course possihle. Several important advantages are inherent in this particular scheme of investigation of simple structure types. Firstly, relationships between structures differing in stoichiom& and/or-coordination type within each close packed system are made evident. Secondly, the model of any of the simple structure types can he interpreted from both a close packed and a unit cell point of view; in addition. the coordination of both the close packed and interstitial species is made fundamental to the construction of each model. Finallv. .. stoichiometries and structures for simple binary compounds are shown to arise naturally out of the geometric and energetic problems associated with filling, or partially filling, octahedral or tetrahedral sites within a close packed lattice.
Construction of the models for each close packed system follows a specific pattern designed to reinforce the relationships between the common structure types. For the cuhic close packed (c.c.p.) series, the model for a face centered cubic (f.c.c.) metal is first constructed hy forming the layering sequence ABCA' with the layers shown in Figure 1. Layer B is placed onto layer C in the orientation shown (i.e., apex over base) and layers A and A' attached with toothpicks. The B and C layers can he held together by attaching rubber hands to the protruding wires to make the f.c.c. model rigid. The face centered cube, with its [111] direction perpendicular to the close packcd lnycrs, is depicted by the large white spheres in Figure 3. After examining and drawing this f.c.c. arrangement, the student is asked to examine the model for octahedral sites, insert the appropriate sized spheres, and to draw and investigate the model for the NaCl structure so generated. A completed model for the NaCl structure is shown in Figure 3. The black spheres are then removed from the octahedral sites and the model investigated for tetrahedral sites. Smaller red spheres are inserted into the tetrahedral sites and the arrangement of sites noted and recorded; as with the black spheres in octahedral sites, radius ratios here are again approximately correct. The model in this case is that for the fluorite (. C a k-.) and anti-fluorite structures. Partial occupancy of tetrahedral sites, with aualitative cnistal enerev can be introduced -. implications. . to develop the arrangement of spheres representing the ZnS (sphalerite) structure. A similar procedure is followed to develop simple close packed crystal structures based on hexagonal close packing. The model of an h.c.p. metal is first constructed using the layers ABA' shown in Figure 2, and subsequently by filling all octahedral sites, a model for the binary compound NiAs is produced. The layer structure for CdI2, with its van der Waals bonding requirements, is derived by removing every second layer of octahedrally sited spheres from the model for NiAs. In each case the ar-
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Acknowledgment
The author wishes to acknowledge the helpful comment and advice of Dr. M. R. Taylor.
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Volume 50,Number 9 , September 1973 / 653
