Closest Packing of Spheres
Closest packing describes the geometric arrangement in which equal-sized spheres are stacked to occupy the maximum possible volume while leaving the least void space. [1] The concept applies most directly to metals, whose atoms bond through metallic bonding with low directional constraints, allowing them to pack as tightly as geometry permits. It also underlies the structure of many ionic minerals, where the larger anions adopt a closest-packed framework and the smaller cations occupy the voids between them.
Close-Packed Layers
Hexagonal and cubic arrangements represent the two fundamental strategies for packing identical spheres into the smallest possible total volume. [1] Any closest-packed arrangement begins with a single layer in which each sphere contacts six neighbors in the same plane, and the spheres of the layer above nestle into the hollows between them. [1] In both hexagonal and cubic closest packing, each sphere is in contact with exactly 12 neighboring spheres: six in the same layer, three in the layer immediately above, and three in the layer immediately below. [1] When a second layer (called B) is placed on top of the first (A), two types of void spaces open up between the layers. Tetrahedral sites (T sites) are enclosed by four spheres - three from one layer and one from the other. Octahedral sites (O sites) are enclosed by six spheres - three from each layer. [1] These interstices become the cation sites in ionic mineral structures built on a closest-packed anion framework.
Hexagonal Closest Packing (HCP)
In hexagonal closest packing, each successive layer alternates between only two positions. If the initial layer occupies position A, the next occupies position B, then A again, then B - producing the repeating ABAB stacking sequence. [1] This repeating sequence yields a structure with true hexagonal symmetry, where the close-packed atomic layers correspond directly to the (001) basal plane of the resulting crystal lattice. [1]
Cubic Closest Packing (CCP)
In cubic closest packing, every third layer - not every second - returns to the original position. The first layer is A, the second B, the third C (shifted further in the same direction), and then the fourth is A again, giving the repeating ABCABC stacking sequence. [1] This arrangement generates a face-centered cubic lattice, and the close-packed planes of atoms are parallel to the (111) crystallographic plane. [1] Many native metals adopt this structure, including gold, silver, and copper. [1]
Body-Centered Cubic Packing (BCC)
A less tightly packed alternative, body-centered cubic (BCC) packing, is used by iron. [1] In this arrangement, atoms sit at the nodes of a body-centered cubic lattice - one atom at each corner of the cube and one at the center of each unit cell. Each atom contacts 8 neighbors, rather than the 12 neighbors of HCP or CCP, making BCC the less dense of the two configurations. [1]
Alloys and Solid Solutions in Metal Structures
Because the atoms in closest-packed metal structures are not bonded directionally, metals with similar atomic sizes and chemistry can substitute for one another in the structure, forming alloys. [1] Gold and silver are a familiar example: they have nearly identical atomic radii and belong to the same group in the periodic table, so they can mix in any proportion to form gold-silver alloys ranging continuously from pure gold to pure silver. [1] This is the metallic equivalent of ionic solid solution in silicate minerals - the structural framework is the same regardless of composition, and the physical properties of the alloy vary smoothly with the mixing ratio.
Physical Properties
The tight packing of atoms in metallic structures, combined with the relatively high atomic weights of most metals, makes metallic-bonded minerals dense compared to ionic-bonded minerals of similar composition. Metallic bonding also produces good electrical conductivity and a degree of mechanical malleability - the layers of atoms can slide past each other without breaking the non-directional metallic bonds. [1]
Related Topics
Metallic Bonding
Metallic bonding can be understood as a limiting form of covalent bonding in which the shared electrons are not localised between any specific pair of atoms but are instead free to roam throughout...
Solid Solution
When the same mineral is collected from different localities and its chemistry measured, the analyses rarely come out identical. The compositions vary - sometimes by a little, sometimes...
Crystal
The word crystal is used in two distinct ways in mineralogy, and the difference between them matters more than it might first appear.{/* SRC: Nesse p.5: "grains. It might be better to use the term...
Silicate Minerals: Structure and Classification
Silicate minerals are by far the most abundant group of minerals in the Earth's crust, and their diversity and economic importance make them the dominant focus of systematic mineralogy. The common...
References & Citations
- 1.Introduction to Mineralogy Nesse, W. D.
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