The primitive, body-centred and face-centred cubic unit cells
Summary
TLDRThis video explores the structure of crystalline solids, focusing on how particles like atoms, ions, or molecules arrange in a regular array. It explains unit cells, the smallest portions that define crystal structures, and discusses the three types of cubic unit cells: simple, body-centered, and face-centered. Each cell type differs in particle arrangement and coordination number. The video highlights how stacking these unit cells leads to different packing efficiencies, which explains why certain crystal structures, like those of sodium chloride and zinc sulfide, are more common in nature due to their efficient space utilization.
Takeaways
- 🔍 The particles in a crystal, such as atoms, ions, or molecules, are arranged in a regular, close-packed array.
- 🧱 A unit cell is the smallest portion of a crystal that defines its structure, and repeating unit cells form the entire crystal.
- 🔲 Simple cubic unit cells have particles only at the corners, and the particles touch along the edges but not along the diagonals.
- 🧩 Each simple cubic unit cell contains one complete particle when considering particle portions from neighboring unit cells.
- 🔢 In a simple cubic structure, each particle has six nearest neighbors – one above, below, left, right, front, and back.
- 💠 Body-centered cubic unit cells have particles at each corner and one particle in the center, providing a total of two particles per unit cell.
- 🔺 In a body-centered cubic structure, each particle has eight nearest neighbors due to the particle in the center touching the corner particles.
- 🏛 Face-centered cubic unit cells have particles at each corner and in the center of each face, resulting in a total of four particles per unit cell.
- 🔗 The face-centered cubic structure gives each particle 12 nearest neighbors, four above, below, and around.
- 🌐 Cubic closest packing, based on the face-centered cubic structure, is the most efficient stacking, occupying 74% of available volume.
Q & A
What is a unit cell in a crystal structure?
-A unit cell is the smallest portion of a crystal structure that defines its overall structure. By stacking unit cells in all three directions, the entire crystal structure is formed.
What are the three types of cubic unit cells discussed in the script?
-The three types of cubic unit cells are: simple cubic, body-centered cubic (BCC), and face-centered cubic (FCC).
How do particles in a simple cubic unit cell interact?
-In a simple cubic unit cell, particles are located at the corners of the cube. They touch along the edges of the cube but not diagonally across the faces or through the body of the cube.
What is the coordination number in a simple cubic unit cell?
-The coordination number in a simple cubic unit cell is 6, meaning each particle has six nearest neighbors: one above, one below, one to the left, one to the right, one in front, and one in back.
What distinguishes a body-centered cubic (BCC) unit cell from a simple cubic unit cell?
-A body-centered cubic (BCC) unit cell has particles at each corner and one particle in the center of the cube. In contrast, the simple cubic unit cell only has particles at the corners.
What is the coordination number in a body-centered cubic (BCC) unit cell?
-In a body-centered cubic (BCC) unit cell, the coordination number is 8, meaning each particle has four nearest neighbors above and four below it.
What is the particle arrangement in a face-centered cubic (FCC) unit cell?
-In a face-centered cubic (FCC) unit cell, particles are located at each corner of the cube and in the center of each face, but there is no particle in the center of the cube.
What is the coordination number in a face-centered cubic (FCC) unit cell?
-The coordination number in a face-centered cubic (FCC) unit cell is 12, meaning each particle has 12 nearest neighbors: four around it, four above, and four below.
Why is the simple cubic unit cell rarely found in nature?
-The simple cubic unit cell is rarely found in nature because it uses space inefficiently, with only 52% of the available volume occupied by particles. More efficient structures like body-centered cubic (BCC) and face-centered cubic (FCC) are more common.
What structure does sodium chloride (NaCl) adopt, and how are the ions arranged?
-Sodium chloride (NaCl) adopts the rock salt structure, where face-centered cubic arrays of chloride ions and sodium ions interpenetrate. The smaller sodium ions fit into the spaces between the larger chloride ions.
Outlines
🔬 Understanding Crystal Structures and Unit Cells
The first paragraph introduces the concept of crystalline solids, where particles (atoms, ions, or molecules) are arranged in a regular array. It explains that the unit cell is the smallest portion of a crystal that defines its structure, and by stacking unit cells in all directions, a crystal is formed. The focus is on cubic crystal systems, which are common in many elements and simple compounds. The types of cubic unit cells—simple cubic, body-centered cubic, and face-centered cubic—are explored, emphasizing how particles are arranged at the corners of these cells. The concept of coordination number, which is the number of nearest neighbors a particle has, is introduced for each type of cubic unit cell.
🔶 Efficiency of Stacking in Crystals
The second paragraph discusses different ways of stacking particles to form crystal structures. It begins with the simple cubic unit cell, which has an inefficient use of space, occupying only 52% of the available volume. Next, the body-centered cubic unit cell is introduced, where better stacking leads to 68% volume occupancy, commonly seen in alkali metals. Finally, the most efficient stacking, cubic closest packing (based on the face-centered cubic unit cell), occupies 74% of the volume. This structure is adopted by many elements, compounds, and ionic compounds, such as sodium chloride and zinc sulfide. The paragraph explains how smaller ions fit into the gaps between larger ions, forming structures like sodium chloride (rock salt) and zinc blend, where ions are tetrahedrally arranged.
Mindmap
Keywords
💡Crystalline Solid
💡Unit Cell
💡Cubic Crystal System
💡Simple Cubic Unit Cell
💡Body-Centered Cubic Unit Cell
💡Face-Centered Cubic Unit Cell
💡Coordination Number
💡Packing Efficiency
💡Cubic Closest Packing
💡Sodium Chloride Structure
Highlights
Particles in a crystal structure are arranged in a regular, repeating array, though the spaces between particles are greatly exaggerated in illustrations.
The unit cell is the smallest portion of a crystal structure that defines its overall arrangement, with unit cells stacking in three dimensions to form the structure.
Many elements and compounds have unit cells derived from the cubic crystal system, which includes simple cubic, body-centered cubic, and face-centered cubic unit cells.
A simple (or primitive) cubic unit cell has particles only at the corners, with particles touching along the cube's edges but not along diagonals.
The simple cubic unit cell contains one particle in total, derived from the eight corners of the cube, each contributing 1/8 of a particle.
The coordination number in a simple cubic structure is six, meaning each particle has six nearest neighbors—one above, one below, one to the left, right, front, and back.
In the body-centered cubic unit cell, there is a particle at each corner and one in the center, which increases the number of particles per unit cell to two.
The coordination number in a body-centered cubic structure is eight, as each particle has four nearest neighbors above and four below.
A face-centered cubic unit cell has particles at each corner and in each face, resulting in a total of four particles per unit cell.
The coordination number in a face-centered cubic structure is twelve, as each particle has four nearest neighbors in three different layers (above, below, and surrounding).
The face-centered cubic structure is more efficient than the simple cubic and body-centered cubic, with particles occupying 74% of the available volume.
The simple cubic structure only occupies 52% of the available volume, making it an inefficient and rarely observed arrangement in nature.
The body-centered cubic arrangement improves efficiency with 68% of the available volume occupied, adopted by many metals including alkali metals.
Cubic closest packing, based on the face-centered cubic unit cell, provides the most efficient use of space, with spheres filling 74% of the volume.
Several compounds adopt the cubic closest packing structure, including sodium chloride (rock salt structure) and zinc sulfide (zinc blende structure).
Transcripts
if you could travel within a crystallin
solid you would see the particles atoms
ions or molecules arranged in a regular
array here the spaces are greatly
exaggerated but in reality the particles
are packed close together the unit cell
of a crystal structure is the smallest
portion that defines the structure
stacking unit cells next to each other
in all three directions gives the
structure many elements and simple
compounds have unit cells from the cubic
Crystal system let's examine the three
types of cubic unit
cells all cubic unit cells have
particles at the corners of a cube the
simple or primitive cubic unit cell has
particles at the corners
only in reality the particles lie as
close to each other as possible
note that the particles touch along the
cube edges but not along a diagonal in
the face or along a diagonal through the
body by slicing away parts that belong
to neighboring unit cells we see that
the actual unit cell consists of
portions of the
particles when the cells pack next to
each other in all three dimensions we
obtain the
crystal if we fade the others out you
can see the original group of eight
particles within the array and the unit
cell within that group we find the
number of particles in one unit cell by
combining all the particles portions in
the simple cubic unit cell eight Corners
Each of which is 1/8 of a particle
combined to give one
particle a key feature of a crystal
structure is its coordination number the
number of the nearest neighbors
surrounding each particle in a simple
cubic array any given particle has a
neighboring particle above below to the
right to the left in front and in back
of it for a total of six nearest
neighbors the body centered cubic unit
cell has a particle at Each corner and
one in the center which is colored pink
to make it easier to see with fullsize
spheres you can see that the particles
don't touch along the edges of the cube
but Each corner particle does touch the
one in the center the actual unit cell
consists of portions of the corner
particles and the whole one in the
center 88s give one particle and the one
in the center gives another for a total
of two
particles in this tiny portion of a body
centered cubic array you can see that
any given particle has four nearest
neighbors above and four below for a
total of eight nearest neighbors the
face centered cubic unit cell has a
particle at Each corner and in each face
which are colored yellow here but none
in the center the corner particles don't
touch each other but Each corner does
touch a particle in the face and those
in the faces touch each other as well
the actual unit cell consists of
portions of particles at the corners and
in the faces 88 at the corners gives one
particle and half a particle in each of
six phases gives three more for a total
of four
particles in this tiny portion of a face
centered cubic array notice that a given
particle has four nearest neighbors
around it four more above and four more
below for a total of 12 nearest
neighbors stacking spher shows how the
three cubic unit cells arise arrange a
layer of spheres in horizontal and
vertical rows note the large diamond
shaped space among the particles placing
the next layer directly over the first
gives a structure based on the simple
cubic unit cell those larger spaces mean
an inefficient use of space in fact only
52% of the available volume is actually
occupied by
spheres because of this inefficiency the
simple cubic unit cell is is seen rarely
in
nature a more efficient stacking occurs
if we place the second layer over the
spaces formed by the first layer and the
third layer over the space is formed by
the second that simple change leads to
68% of the available volume occupied by
the Spheres and a structure based on the
body centered cubic unit cell many
metals including all the alkali metals
adopt this
arrangement for the most efficient
stacking shift every other Row in the
first layer so the large diamond shaped
spaces become smaller triangular spaces
and place the second layer over them
then the third layer goes over the holes
visible through the first and second
layers in this Arrangement called cubic
closest packing spheres occupy 74% of
the volume note that it is based on the
face centered CBE unit cell many
elements calent compounds and as you'll
see in the next two examples ionic
compounds adopt cubic closest packing
sodium chloride adopts the sodium
chloride or rock salt structure as do
many other Alkali halides alkaline earth
oxides and sulfides and other ionic
compounds picture separate face centered
cubic arrays of chloride ions and sodium
ions ions as they approach and
interpenetrate each other the smaller
sodium ions fit in the holes between the
larger chloride ions and the NAC unit
cell zinc sulfide adopts the zinc blend
structure as do the copper one halides
and several other compounds if face
centered cubic arrays of zinc ions and
sulfide ions approach and interpenetrate
slightly offset from each other each ion
becomes surrounded tetrahedrally by four
of the other ions note the blinking zinc
ion and the four sulfides you can see
the relative positions in this slightly
expanded view of the zinc blend unit
cell
Weitere ähnliche Videos ansehen
Aula 10 – Estruturas Cristalinas Cúbicas de Face Centrada, Corpo Centrado e Hexagonal Compacta.
Cálculo do Fator de Empacotamento CFC e CS - Exercícios Resolvidos Callister (07)
CRYSTAL LATTICE AND UNIT CELL
Lecture 3 Part 1 - Crystal Structure - 2 (Unit Cell, Lattice, Crystal)
Solids, Its Properties, and the Intermolecular Forces | Crystalline Solids and Amorphous Solids
noc19-cy16 Lecture 06-Solid state Chemistry-Week 2 Lecture-1 Unit Cell
5.0 / 5 (0 votes)