By: Abu Bakar bin Aramjat Department of Ceramic Processing Technology

1. INTRODUCTION TO CERAMIC MINERALS ( DCP 1113 ) 1.6 ATOMIC STRUCTURE AND PACKING By: Abu Bakar bin Aramjat Department of Ceramic Processing Technology KolejKemahiranTinggi MARA Masjidtanah Melaka

2. Learning Outcomes • Write the definition of unit cell • Explain how atoms pack together • Explain the stack layer represent the CCP and HCP • Explain why BCC usually harder and less malleable than FCC • Explain Interstitial sites in closed packed structure

4. CRYSTAL:- A solid composed of atoms, ions, or molecules arranged in a pattern that is repeated in three dimension CRYSTAL STRUCTURE:- a regular 3D pattern of atoms or ions in space SPACE LATTICE:- 3D array of points have identical surroundings

5. LATTICE POINT: One point in array in which all the points have identical surroundings UNIT CELL: The smallest unit of a mineral that possesses the symmetry and properties of the mineral . A convenient repeating unit of a space lattice. The axial lengths and axial angles are the lattice constant of the unit cell

6. Figure 17: Unit cell in 2D array

7. When substances form solids, they tend to pack together to form ordered arrays of atoms, ions, or molecules that we call crystals. • Why does this order arise, and what kinds of arrangements are possible?

8. Crystals are of course three-dimensional objects, but we will begin by exploring the properties of arrays in two-dimensional space. This will make it easier to develop some of the basic ideas without the added complication of getting you to visualize in 3-D — something that often requires a bit of practice.

9. The underlying order of a crystalline solid can be represented by an array of regularly spaced points that indicate the locations of the crystal's basic structural units. • This array is called a crystal lattice. • Crystal lattices can be thought of as being built up from repeating units containing just a few atoms. • These repeating units act much as a rubber stamp: press it on the paper, move ("translate") it by an amount equal to the lattice spacing, and stamp the paper again.

11. Although real crystals do not actually grow in this manner, this process is conceptually important because it allows us to classify a lattice type in terms of the simple repeating unit that is used to "build" it. • We call this shape the unit cell

12. Any number of primitive shapes can be used to define the unit cell of a given crystal lattice. • The one that is actually used is largely a matter of convenience, and it may contain a lattice point in its center, as you see in two of the unit cells shown here. • In general, the best unit cell is the simplest one that is capable of building out the lattice.

13. Figure 18: Atomic close pack HOW DO ATOM PACKING TOGETHER • This was actually how structures were first visualised before computers. • The balls will pack together to fill up all the space. • This is called close packing • Each orange labelledA will be surrounded by six other oranges within one layer (Figure 18) • The holes labelledB and C. • We can place a second layer of close-packed oranges on either the B-sites or the C-sites (but not both). • In this way we can build up a 3D structure. CLOSE PACKING

14. The three types of cubic lattices The three Bravais lattices which form the cubic crystal system are shown here.

15. Close-packed lattices allow the maximum amount of interaction between atoms. • If these interactions are mainly attractive, then close-packing usually leads to more energetically stable structures. • These lattice geometries are widely seen in metallic, atomic, and simple ionic crystals. • As we pointed out above, hexagonal packing of a single layer is more efficient than square-packing • Imagine that we start with the single layer of green atoms shown below.

16. We will call this the A layer. • If we place a second layer of atoms (orange) on top of the A-layer, we would expect the atoms of the new layer to nestle in the hollows in the first layer. • But if all the atoms are identical, only some of these void spaces will be accessible.

17. In the diagram, notice that there are two classes of void spaces between the A atoms; one set (colored blue) has a vertex pointing up, while the other set (not colored) has down-pointing vertices. • Each void space constitutes a depression in which atoms of a second layer (the B-layer) can nest. • The two sets of void spaces are completely equivalent, but only one of these sets can be occupied by a second layer of atoms whose size is similar to those in the bottom layer. • In the illustration on the right above we have arbitrarily placed the B-layer atoms in the blue voids, but could just as well have selected the white ones

18. Two choices for the third layer lead to two different close-packed lattice types • Now consider what happens when we lay down a third layer of atoms. • These will fit into the void spaces within the B-layer. • As before, there are two sets of these positions, but unlike the case described above, they are not equivalent

21. The atoms in the third layer are represented by open blue circles in order to avoid obscuring the layers underneath. • In the illustration on the left, this third layer is placed on the B-layer at locations that are directly above the atoms of the A-layer, so our third layer is just a another A layer. • If we add still more layers, the vertical sequence A-B-A-B-A-B-A... repeats indefinitely.

22. In the diagram on the right above, the blue atoms have been placed above the white (unoccupied) void spaces in layer A. • Because this third layer is displaced horizontally (in our view) from layer A, we will call it layer C. • As we add more layers of atoms, the sequence of layers is A-B-C-A-B-C-A-B-C..., so we call it ABC packing.

23. These two diagrams that show exploded views of the vertical stacking further illustrate the rather small fundamental difference between these two arrangements— but, as you will see, they have widely divergent structural consequences. Note the opposite orientations of the A and C layers

24. Hexagonal closed-packed structure The HCP stacking shown on the left just above takes us out of the cubic crystal system into the hexagonal system, so we will not say much more about it here except to point out each atom has 12 nearest neighbors: six in its own layer, and three in each layer above and below it.

25. Figure 20: Hexagonal closed-pack A • Another common form of close-packing, corresponding to layers with stacking AB.AB... or AC.AC... (these are equivalent). • This is called hexagonal close-packing HCP, and the competition between CCP and HCP is determined by longer range forces between the atoms. • This is the structure of sodium at low temperatures. B A C

26. HEXAGONAL CLOSED PACKED, HCP • Stacking sequence: ABABAB…. • Stacking direction: c-axis of the hexagonal unit cell • Closed packed planes= basal planes of the unit cell • 2 atom per unit cell ( 0,0,0 & 2/3,1/3,1/2 ) • Interstices (per cell) : 4 tetrahedral, 2 octahedral • Examples material: Mg, Ti, Zn, Be, Co, Zr, Cd

27. The cubic close-packed structure • FCC structure • You will notice that the B-layer atoms form a hexagon, but this is a cubic structure. • How can this be? • The answer is that the FCC stack is inclined with respect to the faces of the cube, and is in fact concident with one of the three-fold axes that passes through opposite corners. • The one on the left shows the cube in the normal isometric projection; the one on the right looks down upon the top of the cube at a slightly inclined angle

28. A stack of layers of types ABC.ABC... represents the cubic close-packed CCP atomic structure of gold as determined by X-rays. • Atoms lie on the corners of a cube, with additional atoms at the centers of each cube face: for that reason it is often called face centered cubic or FCC (Figure 19). • Many simple metals have this FCC structure, whose symmetry is described as Fm-3m where F means Face-centered, m signifies a mirror-plane (there are two) and -3 tells us that there is a 3-fold symmetry axis (along the body diagonal) as well as inversion symmetry. Figure 19: Cubic closed pack

29. CUBIC CLOSED-PACKED, CCP • Stacking sequence: ABCABC…. • Stacking direction: [111] in FCC lattice • Closed packed planes: {111} • 4 atom per unit cell • Interstices (per cell) : 8 tetrahedral, 4 octahedral • Examples material: ɣ-Fe , Al, Ni, Cu ,Ag, Pt, Au, Pb

30. Figure 21: Body centred-cubic BODY CENTERED CUBIC, BCC • The third common metallic structure is called body-centered cubic BCC and consists of a unit cube with atoms at its corners and center. • The BCC structure is slightly less closely packed than FCC or HCP and is often the high temperature form of metals that are close-packed at lower temperatures. • For example sodium changes from HCP to BCC above -237 oC • The structure of iron (Fe) can be either CCP or BCC depending on its heat treatment, while metals such as chromium are always BCC

31. BODY CENTERED CUBIC, BCC • Metals which are BCC are, like chromium, usually harder and less malleable than close-packed metals such as gold. • When the metal is deformed, the planes of atoms must slip over each other, and this is more difficult in the BCC structure. • Note that there are other important mechanisms for hardening metals, and these involve introducing impurities or defects which also block slipping.

32. Interstitial sites or vacancies • The packing fraction in both FCC and HCP cells is 74%, leaving 26% of the volume unfilled • The unfilled lattices sites between the atoms in a cell are called interstitial sites • In both FCC and HCP cells most of the space within these atoms lies within two different sites known as octahedral sites and tetrahedral sites • Tetrahedral - surrounded by 4 atoms • Octahedral - surrounded by 6 atom • FCC – 4 octahedral & 8 tetrahedral in per unit cell • HCP – 2 octahedral & 4 tetrahedral in per unit cell

33. Interstitial sites or vacancies

34. Interstitial void spaces The atoms in each layer in these close-packing stacks sit in a depression in the layer below it. As we explained above, these void spaces are not completely filled. (It is geometrically impossible for more than two identical spheres to be in contact at a single point.) We will see later that these interstitial void spaces can sometimes accommodate additional (but generally smaller) atoms or ions If we look down on top of two layers of close-packed spheres, we can pick out two classes of void spaces which we call tetrahedral and octahedralholes

35. Tetrahedral holes • If we direct our attention to a region in the above diagram where a single atom is in contact with the three atoms in the layers directly below it, the void space is known as a tetrahedral hole. • A similar space will be be found between this single atom and the three atoms (not shown) that would lie on top of it in an extended lattice. • Any interstitial atom that might occupy this site will interact with the four atoms surrounding it, so this is also called a four-coordinate interstitial space

36. Octahedral holes • Similarly, when two sets of three trigonally-oriented spheres are in close-packed contact, they will be oriented 60° apart and the centers of the spheres will define the six corners of an imaginary octahedron centered in the void space between the two layers, so we call these octahedral holes or six-coordinate interstitial sites. • Octahedral sites are larger than tetrahedral sites

37. An octahedron has six corners and eight sides. We usually draw octahedral as a double square pyramid standing on one corner (left), but in order to visualize the octahedral shape in a close-packed lattice, it is better to think of the octahedron as lying on one of its faces (right). Each sphere in a close-packed lattice is associated with one octahedral site, whereas there are only half as many tetrahedral sites. This can be seen in this diagram that shows the central atom in the B layer in alignment with the hollows in the C and A layers above and below.

38. The face-centered cubic unit cell contains a single octahedral hole within itself, but octahedral holes shared with adjacent cells exist at the centers of each edge. • Each of these twelve edge-located sites is shared with four adjacent cells, and thus contributes (12 × ¼) = 3 atoms to the cell. • Added to the single hole contained in the middle of the cell, this makes a total of 4 octahedral sites per unit cell.

39. Octahedral and tetrahedral site in a CCP unit cell 1/2 0,1 0,1 1/2 0,1 1/2 ¼, 3/4 0,1 1/4., 3/4 1/2 0,1 1/2 0,1 0,1 ¼, 3/4 ¼,3/4 1/2 1/2 0,1 0,1 1/2 0,1 Atom 4 Octahedral >Share with 4 others unit cell ( 12 x ¼ = 3 ) >1 at the center 8 Tetrahedral Octahedral Tetrahedral

40. Octahedral and tetrahedral site in a CCP unit cell • 8 Tetrahedral • 1/4,1/4,1/4 3/4,1/4,1/4 1/4,3/4,1/4 3/4,3/4,1/4 • 1/4,1/4,3/4 3/4,1/4,3/4 3/4,3/4,3/4 3/4,3/4,3/4 • 4 Octahedral: • One at cell center: 1/2,1/2,1/2 • Three at middle of cell edges: • 1/2, 0,0 0,1/2,0 0,0,1/2

41. Octahedral and tetrahedral site in a HCP unit cell • 4 Tetrahedral • 0,0,3/8 0,0,5/8 2/3,1/3,1/8 2/3,1/3,7/8 • 2 Octahedral: • 1/3,2/3,1/4 1/3,2/3,3/4

43. NaCl

44. End of lecture Thank you…