11.7 Structures of Solids Zek Zhang Kevin Nash, *Matt Coleman¯\_( ツ )_/¯ *yeah were not racist, the non-white is not last

Types of Solids Crystalline Solid- a solid that has atoms, ions, or molecules in arrangements that are ordered and well-defined o usually have flat surfaces and definite angles o examples:  quartz  diamond o have definite melting points  after melting can sometimes cool to be amorphous solids Amorphous Solid-"without form" and have particles without orderly structure o usually made of big molecules that do not fit well together o examples:  glass  rubber o no definite melting point Quartz

The Unit Cell Deals with CRYSTALLINE solids Unit Cells are the smallest repeated segment in structure Crystal Lattice=3D array of points, which shows the structure of a crystalline solid o Points have identical conditions o Formed by putting together unit cells Unit cells=paralellpepids (usually) Described by angles and lengths of sides Lattice points: points where there are identical environments

What is the "unit cell"???

There are 7 different types of unit cells... Cubic Tetragonal Monoclinic Orthohombic Rhombohedral Hexagonal Triclinic

The Cubic Unit Cell All sides have equal lengths, all angles are 90 degrees 3 subtypes o Primitive or simple cubic  Lattice points at corners only o Body-centered cubic  Points at center and corners o Face centered cubic  Points on centers of faces and corners

The Number of Atoms in Each Unit Cell Fractions of atoms at each position: Center: 1 Face: 1/2 Edge: 1/4 Corner: 1/8 Applied to the cubic unit cell (single atom) Simple cubic o 8 corners x 1/8 = 1 atom Body-centered o (8 corners x 1/8) + 1 body = 2 atoms What about face-centered o ???-> Try it

The Crystal Structure of NaCl Na+ and Cl- ions centered on lattice points Is face-centered cubic, both Na or Cl can be centered on lattice pts Questions: Using your knowledge of a cube, how many of each ion are present LiF has the same arrangement as NaCl, and each side of its unit cell is 4.02 Angstroms, what is its density :O (hint: you need a periodic table...) *taken directly from textbook*

Answers 4 Na+ and 4 Cl- o Matches 1:1 ratio of NaCl o (.25 Na+s on edges x 12) + (1Na+ in center) = 4 total o (.125 Cl- on the corners x 8 corners) + (.5 on the faces x 6 faces) = 4 total 2.65 g/cm3 o 4 Lis and 4 Fs in each unit cell-> amu o 4.02 angstroms per side->divide by 10^8 to convert to cm  Cube for volume o Divide by 6.02 x 10^23 units of volume per gram

Close Packing of Spheres Crystaline Structures are made in order to bring their particles as close as possible to each other o Most cases that structure is spherical or approxiamately so Most efficient arrangement of a layer of equal-sized spheres is in hexagonal like shape Two main types of packing structure o Hexagonal Close Packing  (ABAB)  unit cell: hexagon o Cubic Close Packing  (ABCA)  unit cell: cube

Packing Structures Both structures have coordination number of 12 o 74% of total volume of structure is occupied by spheres o 26% empty space between spheres When unequal-sized spheres are packed into lattice o Large particles usually assume one of the close packing arrangements o Small particles fill the holes between larger particles

Outside Sources unitcell.php