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# MSE Ch 3

### Atomic and Ionic Arrangements

Term | Definition |
---|---|

What are the 3 types of atomic or ionic arrangements? | no order, short-range order (SRO), long-range order (LRO), |

___ display no order. | Monatomic gases |

Steam would be an example of ___ order. | short-range |

A material displays SRO if ___. | the special arrangement of atoms extends only to the nearest atoms. |

A material displays LRO if ___. | the special arrangement of atoms extends over 100 nm. |

___ order materials form a regular repetitive, grid-like pattern in 3 dimensions. We refer to them as ___ materials. | Lon-range, crystalline |

Single crystal materials consist of ___. | one large crystal |

An example of a single crystal is ___. | silicon used for computer chips |

A ___ material is comprised of many small crystals with varying orientations in space. | polycrystalline |

Borders between crystals of polycrystalline materials are called ___. | grain boundaries |

Many properties of polycrystalline materials depends on ___. | physical and chemical characteristics of grains and grain boundaries |

Many properties of single crystal materials depends on ___. | chemical composition and specific direction within the crystal called crystallographic directions |

___ are polymorphic materials that behave as amorphous materials in one state with regions of crystal when some outside force like electricity is provided. | Liquid crystals |

What are the 4 types classifications of materials based on type of atomic order? | monatomic gases, amorphous materials, liquid crystals, crystalline materials |

T or F? Liquid crystals can exhibit both short and long range order. | True |

Most materials want to naturally form periodic arrangements since this configuration maximizes the ___ of the material. | thermodynamic stability |

Glasses are crystalline structures that are ___ and plastics are ___. (organic/inorganic) | inorganic, organic |

The result of nucleating ultrafine crystals into amorphous glasses is ___. | glass-ceramics |

Some glass-ceramics can be made optically transparent by ___. | keeping the size of crystals very small (~<100 nm) |

T or F? Plastics naturally have polymers that are disorganized and tangled. | True |

When adding forces to plastics such as blow-stretch forming, some polymer chains are untangled causing ___. | stress-induced crystallization |

T or F? Metals tend to form crystalline materials rather easily. | True |

To prevent crystallization of metals and instead form metallic glasses, metals must be ___ very quickly at a rate of ___ in a process called ___. | quenched, >10^6°C/s, rapid solidification |

The natural tendency for amorphous materials is to ___. | crystallize |

A lattice is a collection of points called ___, which are arranged in a periodic pattern so that the surrounding of each point in the lattice are ___. | lattice points, identical |

A lattice may be one, two, or three ___. | dimensional |

A group of one or more atoms, located in a particular way with respect to each other and associated with each lattice point, is known as the ___ or ___. | motif, basis |

___ = lattice + basis. | Crystal structure |

The ___ is the subdivision of a lattice that still retains the overall characteristics of the entire lattice. | unit cell |

There are ___ unique arrangements of lattices known as ___. | 7, crystal systems |

The 7 crystal systems are ___. | cubic, tetragonal, orthorhombic, hexagonal, rhombohedral (trigonal), monoclinic, triclinic |

Among the 7 crystal systems there are ___ arrangements known as ___. | 14, Bravais lattices |

There are ___ cubic lattices, ___. | 3, simple cubic (SC), face-centered cubic (FCC), body-centered cubic (BCC) |

There are ___ tetragonal lattices, ___. | 2, simple, body-centered |

There are only one of ___, ___, and ___ lattices. | hexagonal, rhombohedral (trigonal), triclinic |

There are ___ orthorhombic lattices, ___. | 4, simple, body-centered, base-centered, face-centered |

There are ___ monoclinic lattices, ___. | 2, simple, base-centered |

___, which describe the size and shape of the unit cell, include the dimension of the sides and the angles. | Lattice parameters |

1 nm = ___ cm. | 10^-7 |

1 nm = ___ angstroms. | 10 |

1 angstrom = ___ cm. | 10^-8 |

A lattice point at a corner of one unit cell is shared by ___ adjacent unit cells and thus has only ___ in each cell. So for a SC cell each one would have total of ___. | 7, 1/8, 1 |

In most metals, ___ atoms/s is/are located at each point. | one |

Each BCC cell contains ___ total atom/s. | 2 |

Each FCC cell contains ___ total atom/s. | 4 |

Directions in a unit cell where atoms are in continuous contact are called ___ directions. | close-packed |

For SC cells, a = ___, where r = atomic radius. | 2r |

For BCC cells, a = ___. | 4r/√3 |

For FCC cells, a = ___. | 4r/√2 |

In BCC the <111> direction is the equation ___. | (√3)a |

In FCC the <011> direction is the equation ___. | (√2)a |

In BCC 4r = ___. | a√3 |

In FCC 4r = ___. | a√2 |

The ___ is the number of atoms touching a particular atom, or the number of nearest neighbors of that atom. | coordination number |

For ionic solids, the coordination number of cations is defined as the number of nearest ___ and vice versa. | anions |

The coordination number for SC is ___. | 6 |

The coordination number for BCC is ___. | 8 |

The coordination number for FCC is ___. | 12 |

The packing factor is the ___. | space occupied by atoms in a unit cell |

Packing factor = ___. | ((# of atoms in a cell)(volume of each atom))/(volume of the cell) |

Volume of a sphere is calculated by ___. | (4πr³)/3 or (4/3)πr³ |

For FCC, PF = ___. | (4*(4/3)πr³)/a³ (which equals .74) |

A ___ structure is the highest possible PF. | close-packed |

FCC cells have a PF of ___, BCC is ___, and SC is ___. Which is close-packed? | .74, .68, .52, FCC |

T or F? Hexagonal and FCC can have the same PF. | True |

Metals have a close-packed arrangement if ___. | only metallic bonds are present |

Density = ___. (using properties of crystal structure) | ((# of atoms per cell)(atomic mass))/((Vol. of cell)(6.02x10^23)) |

In hexagonal close-packed (HCP) a = ___ and c = ___. | 2r, 1.633a |

The maximum packing factor you can get is π/√18. This is known as ___. | Kepler's conjecture |

In metals with an ideal HCP structure, the a and c axes are related by the ratio ___. | c/a = 1.633 |

Materials that can have more than one crystal structure are called ___ or ___. | allotropic, polymorphic |

The term allotropy is normally reserved for ___. | pure elements |

The term polymorphism is normally reserved for ___. | compounds |

T or F? As temperature increases more symmetric crystal structures become less stable. | False. They become MORE stable. |

Adding dopants such as ___ stabilize the cubic phase of zirconia. | yttria (Y_2O_3) |

Specific volume is the inverse of ___. The formula is ___. | density, sV = 1/D |

The volume of a tetragonal cell is given by the formula ___. | v = a²c |

The percent change in volume is given by the formula ___. | (final volume - initial volume)/(initial volume) * 100 |

Directions in a unit cell are described by ___. | Miller indices |

To determine the index for a direction subtract the ___ from the ___. | tail, head |

Indices for directions are enclosed in ___. The is called ___ form. | [], vector |

Negative number in Miller indices are noted with ___. | a bar above them |

Directions that are ___, are identical. | parallel |

T or F? [100] = [-100] (NOTE: using (-) is non-standard) | False. They go in opposite directions. |

T or F? [100] = [200] | True. They are parallel so they are identical. |

[100] is ___ to [010]. | equivalent |

[100] is ___ to [200]. | identical |

Groups of equivalent directions are known as ___ and are enclosed in ___. | directions of a form, ‹› |

[110], [011], and [101] are all directions of the form ___. | ‹110› (NOTE: there are 12 total) |

Directions of a form are made by ___. | redefining the coordinate system |

___ is the distance between lattice points along a direction. | Repeat distance |

___ is the number of lattice points per unit length along a direction. | Linear density |

Linear density is the reciprocal of the ___. | repeat distance |

Linear ___ is the fraction covered by atoms. | packing fraction |

What are the steps of determining a direction? | 1. determine 2 points on the direction. (If a plane passes through the origin the origin MUST BE MOVED) 2. subtract the tail from the head. 3. clear fractions and reduce to lowest integers if needed. |

When writing Miller indices of planes we enclose them in ___. | () |

Planes of a form are enclosed in ___. | {} |

What are the steps of determining a plane? | 1. identify points where they intercept axes. 2. take the reciprocals of the intercepts. 3. clear fractions, but DO NOT reduce to lowest integers. |

(020) and (0-20) are ___. (NOTE: using (-) is non-standard) | identical |

T or F? (100) is equivalent to (200). | False, Planes and their multiples are not identical. |

Planar density is ___. | the number of atoms per unit area whose CENTERS lie on the plane |

Planar packing fraction is ___. | the fraction of the area of a plane that is covered by atoms |

Planar D = ___. | # of atoms/area of the plane |

Planar PF = ___. | area of atoms on the plane/area of the plane |

Area of an equilateral triangle is given by the formula ___. | A = (√3/4)s², where s = the length of a side |

Area of a circle is ___. | πr² |

What is the coordination number for an HCP point? | 12 |

What is the coordination number for an FCC point? | 12 |

What is the stacking sequence of FCC? | ABCABC |

What is the stacking sequence of HCP? | ABABAB |

What are the spaces called among cells? | interstitial sites |

Cubic interstitial sites have a coordination number of ___. | 8 |

Tetrahedral interstitial sites have a coordination number of ___. | 4 |

Octahedral interstitial sites have a coordination number of ___. | 6 |

T or F? Atoms that are slightly smaller than the interstitial site fill the site. | False. They are slightly larger and "squeeze" into the site. Smaller atoms are not allowed. |

In ionic materials such as ceramics, ___ form the Miller-Bravais structure and ___ fill the interstitial sites. | anions, cations |

The ratio of the sizes of ionic radii of anions and cations is the ___ and is abbreviated ___. | radius ratio, r/R |

As a general rule, __ions are larger than __ions. | an-, cat- |

The coordination of ions is the number of ___. | oppositely charged ions |

What is the range of r/R for a linear interstitial site? | 0-0.155 |

What is the range of r/R for a center of triangle interstitial site? | 0.155-0.225 |

What is the range of r/R for a center of tetrahedron interstitial site? | 0.225-0.414 |

What is the range of r/R for a center of octahedron interstitial site? | 0.414-0.732 |

What is the range of r/R for a center of cube interstitial site? | 0.732-1 |

What structure is CsCl? | SC, but the cube is formed by the cation |

What structure is NaCl? | FCC |

What structure is ZnS (zinc blende)? | FCC, but only half of the interstitial sites are filled with S-² |

What structure is CaF_2 (fluorite)? | FCC, with all interstitial sites filled |