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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 |