Close packing radii

To calculate the fraction of occupied space in a close-packed structure, we considei a ccp structure, e can use the radius of the atoms to find the volume of the cube and ow muc o t at volume is taken up by atoms. First, we look at how the cube is built rom t e atoms. In Fig. 5.29, we see that the corners of the cubes are at the centers of etg t atoms, n y 1/8 of each corner atom projects into the cube, so the corner atoms collectively contribute 8xi/S=1 atom to the cube. There is half an atom on each of t e six aces, so the atoms on each face contribute 6 X 1/2 = 3 atoms, giving four... 

The density of copper is 8.93 g-cm 3 and its atomic radius is 128 pm. Is the metal (a) close-packed or (b) body-centered cubic ... 

Self-Test 5.5A The atomic radius of silver is 144 pm and its density is 10.5 g-cm 3. Is the structure close-packed or body-centered cubic ... 

Self-Test 5.5B The atomic radius of iron is 124 pm and its density is 7.87 g-cm-3. Is this density consistent with a close-packed or a body-centered cubic structure ... 

When the radius ratio of an ionic compound is less than about 0.4, corresponding to cations that are significantly smaller than the anion, the small tetrahedral holes may be occupied. An example is the zinc-blende structure (which is also called the sphalerite structure), named after a form of the mineral ZnS (Fig. 5.43). This structure is based on an expanded cubic close-packed lattice of the big S2 anions, with the small Zn2+ cations occupying half the tetrahedral holes. Each Zn2+ ion is surrounded by four S2 ions, and each S2" ion is surrounded by four Zn2+ ions so the zinc-blende structure has (4,4)-coordination. 

What percentage of space is occupied by close-packed cylinders of length / and radius r ... 

Buckminsterfullerene is an allotrope of carbon in which the carbon atoms form spheres of 60 atoms each (see Section 14.16). In the pure compound the spheres pack in a cubic close-packed array, (a) The length of a side of the face-centered cubic cell formed by buckminsterfullerene is 142 pm. Use this information to calculate the radius of the buckminsterfullerene molecule treated as a hard sphere, (b) The compound K3C60 is a superconductor at low temperatures. In this compound the K+ ions lie in holes in the C60 face-centered cubic lattice. Considering the radius of the K+ ion and assuming that the radius of Q,0 is the same as for the Cft0 molecule, predict in what type of holes the K ions lie (tetrahedral, octahedral, or both) and indicate what percentage of those holes are filled. 

Many ionic compounds are considered to pack in such as way that the anions form a close-packed lattice in which the metal cations fill holes or interstitial sites left between the anions. These lattices, however, may not necessarily he as tightly packed as the label close-packed implies. The radius of an F ion is approximately 133 pm. The edge distances of the cubic unit cells of LiF, NaF, KF, RbF, and CsF, all of which... 

An important phenomenon when considering the differences between ice I and liquid water is that water achieves its maximum density not in the solid state, but at 4 °C, i.e. in the liquid state. The reasons for this were first discussed by Bernal Fowler (1933). They noted that the separation of molecules in ice I is about 0-28 nm, corresponding to an effective molecular radius of 014 nm. Close packing of molecules of such radius would yield a substance of density 1-84 g cm" . To account for the observed density of 10 g cm" , it was necessary to postulate that the arrangement of molecules was very open compared with the disordered, close-packed structures of simple liquids such as argon and neon. 

An important reason for the exceptions to the radius ratio predictions is that ions are not hard spheres but somewhat compressible, hence do not have a truly constant radius. Another reason for the inadequacy of the radius ratio rules, particularly when the anions are much larger than the cations, is that some structures are determined by the close packing of the anions, leaving the cations in holes between the anions. In such a case more anions may be packed around a cation of a given fixed radius than are predicted by the radius ratio, so that although the anions are touching each other, they are not touching the cation. However, if... 

Pejova et al. [72] (2008) have obtained three-dimensional arrays of close-packed semiconducting AgBiS2 quantum dots with an average QD radius of 4.2 nm using sonochemical method which was twice as small as compared to the QD solid obtained without ultrasonic irradiation. 

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