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1 Crystallography World of Wonders (CWOW). 2 Claudia J. Rawn University of Tennessee New Mexico Museum of Natural History and Science May.

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Presentation on theme: "1 Crystallography World of Wonders (CWOW). 2 Claudia J. Rawn University of Tennessee New Mexico Museum of Natural History and Science May."— Presentation transcript:

1 1 Crystallography World of Wonders (CWOW)

2 2 Claudia J. Rawn University of Tennessee New Mexico Museum of Natural History and Science May 24, 2014 Crystallography World of Wonders

3 3 2014 is the International Year of Crystallography IYCr2014 Some of the major objectives of the IYCr2014 are: to increase public awareness of the science of crystallography and how it underpins most technological developments in our modern society to inspire young people through public exhibitions, conferences and hands-on demonstrations in schools to illustrate the universality of science to promote education and research in crystallography and its links to other sciences

4 4 Acknowledgments Thanks to United States National Committee for Crystallography (USNCCr) American Crystallographic Association Center for Materials Processing, University of Tennessee, Knoxville For providing the funds for travel and CWOW kits and labor

5 5 Crystallography World of Wonders (CWOW) Previous CWOW workshops presented in conjunction with American Crystallographic Association Annual meetings in Chicago, IL (2010) Boston, MA (2012)

6 6

7 7 Al vs Al 2 O 3 Al Melts at 660 o C FCC a = 4.0495 Å Density = 2.71 gm/cm 3 Al 2 O 3 Melts at 2000 o C Based on HCP a = 4.7589 and c = 12.991 Å Density = 3.98 gm/cm 3

8 8 Non dense, random packing Dense, regular packing Dense, regular-packed structures tend to have lower energy

9 9 Face Centered Cubic - FCC Coordination # = 12 Atomic Packing Factor = 0.74

10 10 Coordination # = 12 APF = 0.74 Adapted from Fig. 3.3, Callister 6e. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)

11 11 FCC and HCP close-packed lattices Both lattices are formed by a sequential stacking of planar layers of close packed atoms. Within each layer each atom has six nearest neighbors. A layer

12 12 FCC and HCP close-packed lattices The “ A ” layer all positions that are directly above the centers of the A atoms are referred to as “ A ” positions, whether they are occupied or not Both FCC and HCP lattices are formed by stacking like layers on top of this first layer in a specific order to make a three dimensional lattice. These become close-packed in three dimensions as well as within each planar hexagonal layer. Close packing is achieved by positioning the atoms of the next layer in the troughs between the atoms in the “ A ” layer

13 13 FCC and HCP close-packed lattices Each one of these low positions occurs between a triangle of atoms. Some point towards the top of the page and some point towards the bottom of the page.

14 14 FCC and HCP close-packed lattices Any two of these immediately adjacent triangles are too close to be both occupied by the next layer of atoms. Instead the next close-packed “ B ” layer will fill every other triangle, which will all point in the same direction.

15 15 FCC and HCP close-packed lattices The “ B ” layer is identical to the A-layer except for its slight off translation. Continued stacking of close-packed layers on top of the B-layers generates both the FCC and HCP lattices. “ A ” layer “ B ” layer

16 16 The FCC close-packed lattice The FCC lattice is formed when the third layer is stacked so that its atoms are positioned in downward-pointing triangles of oxygen atoms in the “ B ” layer. These positions do not lie directly over the atoms in either the A or B layers, so it is denoted as the “ C ” layer “ A ” layer “ B ” layer “ C ” layer

17 17 The FCC close-packed lattice The stacking sequence finally repeats itself when a fourth layer is added over the C atoms with its atoms directly over the A layer (the occupied triangles in the C layer again point downward) so it is another A layer. The FCC stacking sequence (ABCA) is repeated indefinitely to form the lattice: …ABCABCABCABC... “ A ” layer “ B ” layer “ C ” layer

18 18 The FCC close-packed lattice Even though this lattice is made by stacking hexagonal planar layers, in three dimensions its unit cell is cubic. A perspective showing the cubic FCC unit cell is shown below, where the body- diagonal planes of the atoms are the original A, B, C, and layers of oxygen atoms

19 19 The HCP close-packed lattice The HCP lattice is formed when the third layer is stacked so that its atoms are positioned directly above the “ A ” layer (in the upward facing triangles of the “ B ” layer). The HCP stacking sequence (ABAB) is repeated indefinitely to form the lattice: …ABABABAB... “ A ” layer “ B ” layer Repeat “ A ” layer

20 20 Ceramics Characteristics –Hard –Brittle –Heat- and corrosion-resistant Made by firing clay or other minerals together and consisting of one of more metals in combination with one or more nonmetals (usually oxygen)

21 21 Nomenclature The letter a is added to the end of an element name implies that the oxide of that element is being referred to: SiO 2 - silicaSi 4+ + 2(O 2- ) Al 2 O 3 - alumina 2(Al 3+ ) + 3(O 2- ) MgO - magnesia Mg 2+ + O 2- Positively charged ions cations example: Si 4+, Al 3+, Mg 2+ Negatively charged ions - anions example: O 2- Charge balanced

22 22 Closed Packed Lattices The Basis for Many Ceramic Crystal Structures Ionic crystal structures are primarily formed as derivatives of the two simple close packed lattices: face center cubic (FCC) and hexagonal close packed (HCP). Most ionic crystals are easily derived from these by substituting atoms into the interstitial sites in these structures.

23 23 Closed Packed Lattices The larger of the ions, generally the anion, forms the closed-packed structure, and the cations occupy the interstices. –We will often consider the anion to be oxygen (O 2- ) for convenience since so many important ceramics are oxides. However, the anion could be a halogen or sulfur. –In the case of particularly heavy cations, such as zirconium and uranium, the cations are larger than the oxygen and the structure can be more easily represented as a closed packed arrangement of cations with oxygen inserted in the interstices.

24 24 Location and Density of Interstitial Sites

25 25 The interstitial sites exist between the layers in the close-packed structures There are two types of interstitial sites –tetrahedral –octahedral These are the common locations for cations in ceramic structures Interstitial Sites

26 26 Each site is defined by the local coordination shell formed between any two adjoining close-packed layers –the configuration of the third layer does not matter –the nearest neighbor configuration of oxygen atoms around the octahedral and tetrahedral cations is independent of whether the basic structure is derived from FCC or HCP FCC and HCP have the same density of these sites Interstitial Sites

27 27 Interstitial sites Octahedral: 3-6-7-b-c-f –3 from the A layer and 3 from the B layer –an octahedron has eight sides and six vertices –the octahedron centered between these six atoms, equidistant from each - exactly half way between the two layers 31 2 4 5 6 7 89 10 abc d e f g h i j Numbers = A sites lower case letters = B sites

28 28 Interstitial sites The octahedral site neither directly above nor directly below any of the atoms of the A and B layers that surround the site –The octahedral site will be directly above or below a C- layered atom (if it is FCC) –These octahedral sites form a hexagonal array, centered exactly half-way between the close-packed layers 31 2 4 5 6 7 89 10 abc d e f g h i j Numbers = A sites lower case letters = B sites

29 29 Interstitial sites Tetrahedral: 1-2-5-a and e-h-i-9 –1 negative tetrahedron –1 positive tetrahedron – three of one layer and one of the second layer –3A and 1B – one apex pointing out of the plane of the board –3B and 1 A – one apex pointing into the plane of the board 31 2 4 5 6 7 89 10 abc d e f g h i j Numbers = A sites lower case letters = B sites

30 30 Interstitial sites Tetrahedral: 1-2-5-a and e-h-i-9 –For both tetrahedral sites the center of the tetrahedron is either directly above or below an atom in either the A or B layers –The geometric centers are not halfway between the adjacent oxygen planes but slightly closer to the plane that forms the base of the tetrahedron 31 2 4 5 6 7 89 10 abc d e f g h i j Numbers = A sites lower case letters = B sites

31 31 Octahedral sites in the FCC Unit Cell o o o o o o o o o o o o The FCC cell contains four atoms six faces that each contribute one half and atom eight corners that each contribute one-eighth an atom FCC cell contains four octahedral sites 12 edges each with one quarter of a site one site in the center o One octahedral site halfway along each edge and one at the cube center The ratio of octahedral sites to atoms Is 1:1

32 32 Tetrahedral sites in the FCC Unit Cell One tetrahedral site inside each corner Eight tetrahedral sites The ratio of tetrahedral sites to atoms is 2:1 t t t tt t t t

33 33

34 34 T 2n O n X n T – Tetrahedral sites O – Octahedral sites X – Anions General Structural formula for close-packed structures

35 An Example Applying the Formula 35 A 2n B n X n A = tetrahedral sites B = octahedral sites X = anions MgAl 2 O 4 If fully occupied A 8 B 4 X 4 Mg in tetrahedral sites - 1/8 of the sites occupied Al in octahedral sites - 1/2 of the sites occupied

36 36 Nobel Prize in Chemistry 1954 –“ for his research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances ” Nobel Peace Prize 1962 Born in 1901 and died in 1994 We may use Pauling ’ s rules to predict the tendency for a specific compound to form a specific crystal structure Linus Pauling

37 37 Pauling ’ s rules are based on the geometric stability of packing for ions of different sizes and simple electrostatic stability arguments. –These geometric arguments treat the ions as hard spheres which is an over implication Pauling ’ s Rules

38 38 Ionic radii (as defined by interatomic spacings) do vary from compound to compound –they tend to vary most strongly with the valance state of the ion and the number of nearest neighbor ions of the opposite charge We may consider an ionic radius to be constant for a given valance state and nearest-neighbor coordination number Ionic crystal radii

39 39 stable unstable Pauling ’ s Rule 1 The radius ratio rule: r c /r a

40 40 CNDisposition of ionsr c /r a about central atom 8 corners of  0.732 a cube 6 corners of  0.414 an octahedron 4 corners of  0.225 a tetrahedron 2 corners of  0.155 a triangle 1 linear  0 When the radius ratio is less than this geometrically determined critical value the next lower coordination is preferred

41 41 NaCl, KCl, LiF, MgO, CaO, SrO, NiO, CoO, MnO, PbO –for all of these the anion is larger than cation and forms the basic FCC lattice The lattice parameter of the cubic unit cell is “ a o ” and each unit contains 4 formula units aoao Rocksalt

42 42 NiO -rocksalt structure a = 4.1771 Å space group Fm3m AtomOxWyxyz Ni+24a000 O-24b0.50.50.5  n ’ (∑M Ni +∑M O ) V unit cell N AV 4(58.69 + 15.999) g/mol ((4.1771 x 10 -8 cm) 3 )(6.022 X 10 23 atom/mol) = g/mol cm 3 x molecules/mol = 6.81 g/cm 3 Calculating density

43 43 Corundum Structure x x - empty site x xx O Al

44 44 Corundum Structure A A A A B B B x x x x x - empty site O Al [0001] Columns of face-sharing octahedra

45 45 Cubica = b = c  =  =   Hexagonala = b  c  =  =      Tetragonala = b  c  =  =   Rhombohedral a = b = c  =  =   Orthorhombica  b  c  =  =   Monoclinica  b  c  =  =     Triclinica  b  c      Seven Crystal Systems

46 VESTA and the American Mineralogist Crystal Structure Database 46

47 47 tal.html FCC – Fractional atoms Rocksalt – Fractional atoms Building Crystal Structures from Legos Let’s build!

48 Crystal Jars – Prototype 1 Contents: Mason jar, ½ cup Borax, two pipe cleaners, popsicle stick, 18 inches of dental floss

49 Costs 60 Crystal Jars for approximately $70 All supplies purchased at the grocery store

50 Trial Run 1 Pre-prototype 1 Materials Processing students were given a ½ cup of Borax and a pipe cleaner and asked to grow crystals Several students experimented with cooling rates (green tetrahedron placed in freezer) and stirring (purple blob used stirring rod)

51 Trial Run 2 – Gadget Girls Adventures in STEM A collaborative effort between the Girl Scout Council of the Southern Appalachians and the University of Tennessee, Knoxville Attracted more that 150 middle school girls from southwest Virginia, eastern Tennessee, and northern Georgia – each girl that attended our session received a crystal jar to take home 14 STEM activities and growing crystals using Borax was among the activities they enjoyed the most

52 The Results Hi Claudia, Please find attached 2 pics of Natasha's borax crystals that she grew. Rather than boil water on the stove in a kettle, she decided to use our electric teapot. She placed the borax in the canning jar, brought the water to boil in the teapot, then poured boiling water into the jar and stirred it with a chopstick until the liquid was clear. As you can see by the picture, she decided to use the wonderful shape of a circle again. We were surprised and delighted to see one small crystal form on the end of the floss. I suggested that this was probably due to the fact that there wasn't much wax on the cut end. Natasha really enjoyed your presentation and thought it was great fun to bring a "science kit" home to be able to do it on her own. Thank you and your staff for taking time to spend the day opening the doors of science a little wider for girl scouts. Sincerely, Paige L. Long

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