Crystalline on Solids

What is a crystalline material?

A material in which atoms are arranged in a repeating pattern

What is the term for long-range order in a crystalline material?

Crystal structure

Which materials form crystalline structures under normal solidification conditions?

Metals, ceramic materials, and certain polymers

What is the term for materials that do not crystallize?

Noncrystalline or amorphous materials

What do the properties of crystalline solids depend on?

The crystal structure of the material

How many different crystal structures exist?

An extremely large number

What do we call the model where atoms are represented as solid spheres?

Atomic hard-sphere model

What is a lattice in the context of crystal structures?

A three-dimensional array of points coinciding with atom positions

What are small repeat entities in a crystal structure called?

Unit cells

What shape do most unit cells have?

Parallelepipeds or prisms with three sets of parallel faces

How are atom positions generated within a crystal structure?

By translations of the unit cell integral distances along each of its edges

What is the basic structural unit of a crystal structure?

The unit cell

How are parallelepiped corners positioned in relation to hard-sphere atoms?

Coincide with centers of the hard-sphere atoms

Can multiple unit cells be chosen for a particular crystal structure?

Yes

Which unit cell is generally used for a crystal structure?

The one with the highest level of geometrical symmetry

What type of atomic bonding is found in metallic crystal structures?

metallic

What are the characteristics of atomic packings in metallic crystal structures?

large numbers of nearest neighbors and dense atomic packings

What model is used to represent ions in metallic crystal structures?

hard-sphere model

What are the three common crystal structures found in most metals?

face-centered cubic, body-centered cubic, hexagonal close-packed

Which crystal structure has a unit cell with atoms at each corner and center of all cube faces?

face-centered cubic (FCC)

Which metals have the face-centered cubic crystal structure?

copper, aluminum, silver, gold

How many atoms per unit cell are there in the face-centered cubic crystal structure?

4

What is the coordination number for face-centered cubic crystals?

12

What is the atomic packing factor for face-centered cubic crystals?

0.74

Which crystal structure has a unit cell with atoms at all eight corners and a single atom at the center of the cube?

body-centered cubic (BCC)

Which metals have the body-centered cubic crystal structure?

chromium, iron, tungsten

How many atoms per unit cell are there in the body-centered cubic crystal structure?

2

What is the coordination number for body-centered cubic crystals?

8

What is the atomic packing factor for body-centered cubic crystals?

0.68

Which crystal structure consists of atoms only at the corners of a cube?

simple cubic (SC)

Which element has a simple cubic crystal structure?

polonium

Which crystal structure has a hexagonal unit cell with regular hexagons on top and bottom faces surrounding a single atom in the center?

hexagonal close-packed (HCP)

Which metals have the hexagonal close-packed crystal structure?

cadmium, magnesium, titanium, zinc

How many atoms per unit cell are there in the hexagonal close-packed crystal structure?

6

What is the coordination number for hexagonal close-packed crystals?

12

What is the atomic packing factor for hexagonal close-packed crystals?

0.74

What is the relationship between unit cell length (a) and atomic radius (R) in face-centered cubic crystals?

a = 2R√2

What is the relationship between unit cell length (a) and atomic radius (R) in body-centered cubic crystals?

a = 4R/√3

What is the relationship between unit cell length (a) and atomic radius (R) in hexagonal close-packed crystals?

c/a = 1.633

How are atoms shared among adjacent unit cells in face-centered cubic crystals?

Atoms at corners are shared by eight cells, atoms at faces are shared by two cells, and there are no interior atoms.

How are atoms shared among adjacent unit cells in body-centered cubic crystals?

Atoms at corners are shared by eight cells, and there is one interior atom per cell.

How are atoms shared among adjacent unit cells in hexagonal close-packed crystals?

Atoms at corners are shared by six cells, atoms at faces are shared by two cells, and there are three midplane interior atoms.

What is the formula to compute the theoretical density of a metallic solid?

𝜌 =(n*A)/(VC*NA)

What does n represent in the density computation formula?

number of atoms associated with each unit cell

What does A represent in the density computation formula?

atomic weight

What does VC represent in the density computation formula?

volume of the unit cell

What does NA represent in the density computation formula?

Avogadro’s number (6.022 × 1023 atoms/mol)

What is polymorphism?

The phenomenon of having more than one crystal structure

What is allotropy?

Polymorphism in elemental solids

What determines the prevailing crystal structure in polymorphism and allotropy?

temperature and external pressure

Give an example of polymorphism in carbon.

graphite and diamond

At what conditions is graphite the stable polymorph of carbon?

ambient conditions

At what conditions is diamond formed as a polymorph of carbon?

extremely high pressures

What is the crystal structure of pure iron at room temperature?

BCC (Body-Centered Cubic)

At what temperature does pure iron change its crystal structure to FCC (Face-Centered Cubic)?

912°C (1674°F)

How many different crystal systems are there based on unit cell geometry?

seven

What are the seven crystal systems based on unit cell geometry?

cubic, tetragonal, hexagonal, orthorhombic, rhombohedral, monoclinic, triclinic

Which crystal system has the highest degree of symmetry?

cubic

Which crystal system has the least symmetry?

triclinic

In which crystal system do FCC and BCC structures belong?

cubic

In which crystal system does HCP (Hexagonal Close-Packed) structure belong?

hexagonal

How many different Bravais lattices are there?

fourteen

What did Auguste Bravais discover about lattice structures?

There are only fourteen different lattice structures.

What method is used to determine the arrangement of atoms in a crystal?

X-ray Diffraction

What is X-ray Diffraction used for?

Determining the arrangement of atoms in a crystal

Who formulated Bragg's Law?

William Henry Bragg and William Lawrence Bragg

What does Bragg's Law calculate in X-ray Diffraction?

The diffraction of X-ray beams

What are crystallogic points, directions, and planes used for?

specifying locations and orientations in crystalline materials

How many numbers or indices are used to designate point locations, directions, and planes?

three

What is the basis for determining index values?

the unit cell with a right-handed coordinate system

Which crystal systems have axes that are not mutually perpendicular?

hexagonal, rhombohedral, monoclinic, triclinic

What are lattice position coordinates associated with?

x, y, and z axes

What is the notation for lattice position coordinates?

Px, Py, and Pz

How are lattice position coordinates determined?

multiplying point indices by unit cell edge lengths

What is a crystallographic direction defined as?

a line directed between two points or a vector

How many steps are used to determine directional indices?

five

What are equivalent directions in cubic crystals grouped into?

a family enclosed in angle brackets (〈〉)

Are equivalent directions in cubic crystals represented with the same order and sign of indices?

yes

How are crystallographic planes specified in all but the hexagonal crystal system?

by three Miller indices (hkl)

What is the procedure to determine the h, k, and l index numbers for crystallographic planes?

intersect or parallel each axis and take reciprocals of intercepts

Are planes parallel to each other equivalent and have identical indices?

yes

What is a family of planes designated by?

indices enclosed in braces ({})

In which crystal system do planes having the same indices irrespective of order and sign are equivalent?

cubic system

What is the favored indexing system for crystals with hexagonal symmetry?

the four-index (hkil) scheme

What is the relationship between directional equivalency and linear density?

For a specific material, equivalent directions have identical linear densities.

What is linear density (LD)?

The number of atoms per unit length whose centers lie on a specific crystallographic direction.

What are the units for linear density?

Reciprocal length (e.g., nm−1, m−1).

How can linear density be calculated?

Number of atoms centered on direction vector divided by the length of direction vector.

What is the linear density of the [110] direction in FCC?

1/2R

What is planar density (PD)?

The number of atoms per unit area that are centered on a particular crystallographic plane.

What are the units for planar density?

Reciprocal area (e.g., nm−2, m−2).

How can planar density be calculated?

Number of atoms centered on a plane divided by the area of the plane.

What is the planar density of the (110) plane in FCC?

1/(4R2√2)

What are linear and planar densities important considerations for?

The process of slip and metal plastic deformation.

What is slip?

The mechanism by which metals plastically deform.

What crystal structures have atomic packing factors of 0.74?

Face-centered cubic (FCC) and hexagonal close-packed (HCP) crystal structures.

How can FCC and HCP crystal structures be described in terms of close-packed planes?

The stacking of close-packed planes on top of one another.

What is the stacking sequence for FCC crystal structure?

ABCABCABC...

What is the stacking sequence for HCP crystal structure?

ABABAB...

Where are the centers of the third plane located in HCP crystal structure?

Directly above the original A positions.