10.6 Lattice Structures in Crystalline Solids

There are different types of crystal defects.

By the end of this section, you will be able to: When the particles pack in the most efficient manner, the total intermolecular energy is minimized and the attractive interactions between particles are maximized.

The arrangement at an atomic level is often reflected at a macro level.
In this module, we will learn how to determine the structures of metallic and ionic crystallised objects.

We will begin our discussion by considering the basic elements of metal, which are 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- There is a repeating pattern of metal atoms in a pure metal.

The malleability and ductility of metals are largely due to having the same atoms in a regular pattern.
The different properties of one metal compared to another is dependent on the size of their atoms.
Four of the most common metal crystal geometries will be explored in the sections that follow.

lattice points represent the locations of atoms in the unit cell.

The locations of lattice points are shown in a unit cell.

The most basic unit cell and crystal lattice structure are what we will investigate first.

Imagine taking a large number of identical spheres, such as tennis balls, and arranging them uniformly in a container.

The lattice structure is called simple cubic when metal atoms are arranged with spheres in one layer directly above or below spheres in another layer.

The spheres are in contact.

The spheres are not packed as tightly as they could be, and they only fill about half of the container.

Only one metal (polonium, Po) can be seen in this arrangement.
The coordination number is six for a polonium atom.

The edge length of this cell is equal to two atomic radii, or one atomic diameter, because the atoms at the corners of the cell are 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- The parts of the atoms that make up a cell are referred to as a cubic unit cell.

One-eighth of an atom is within a specific unit cell, since an atom at a corner of a simple unit cell is contained by a total of eight unit cells.
There is 8 x 18 and one atom at each of the eight "corners" of a simple cubic unit cell.

A simple unit cell has one atom for each of its eight corners.

The unit cell of alpha polonium has an edge length of 336 pm.

The density of polonium can be determined by dividing the mass in a unit cell by the volume.

A unit cell has one Po atom for every eight corners.

The edge length of the unit cell is small.

Ni has a density of 8.90 g/ cm3.

Ni does not form a simple cubic structure because the density is not close to this.

One of the major types of unit cells are metal crystals.

There are seven different lattice systems, some of which have more than one type of lattice, for a total of 14 different types of unit cells.

The locations of lattice points and metal atoms in the unit cell are shown in the upper and lower figures.

The atoms in the corners of a cell don't communicate with each other but with the atom in the center.

A unit cell has two atoms, one at each of the eight corners and one at the center.
There are four atoms in the layer above it and four atoms in the layer below it.
The coordination number of an atom is eight.

The atoms in a specific layer do not touch each other.

Four atoms are in the layer above it and four atoms are in the layer below it.

The atoms are packed in a way that is more efficient than in a simple structure.

Isomorphous metals with aBCC structure include K, Ba, Mo, W, and Fe.

A FCC unit cell has four atoms, one for each of the eight corners and two for each of the six faces.

The atoms at the corners touch the atoms in the center of the cube.
The atoms have the same environments because they are on the same lattice points.

A face-centered solid has atoms at the corners and at the center of its unit cells.

The FCC arrangement has atoms packed as closely together as possible, with 70% of the volume occupied by atoms.

There are three layers of hexagonally arranged atoms.

Each atom has a coordination number of 12 in this arrangement.

There are three repeating layers of hexagonally arranged atoms.

A coordination number of 12 is the number of atoms that come in contact with each other.

By rotating our perspective, we can see that a unit cell with a face containing an atom from layer A at one corner, atoms from layer B across a diagonal, and an atom from layer C at the remaining corner is part of a CCP structure.
This is the same as a face-centered arrangement.

The atoms in most metals pack this way because it maximizes the attractions between them.

There are layers of hexagonally arranged atoms.
Each atom in the second layer is in contact with three atoms in the first layer in both types.

The third layer is positioned in two different ways.

The third layer is also type A, and the stacking consists of alternating type A and type B close-packed layers.
The third layer is type C and the stacking consists of alternating type A, type B, and type C close-packed layers.
Most of the metals are in close-packed array with coordination numbers of 12.
Cu, Ni, Pb, and Pt are some of the metals that can be found in a CCP structure.

atoms are packed as compactly as possible in both types of closest packing There are two alternating layers in the hatteral closest packing.

The packing consists of three layers.

There is a face-centered structure for calcium.

The unit cell's edge length is 558.8 pm.

The density of calcium can be determined by dividing the mass of the unit cell by the volume.

A face-centered Ca unit cell has one-eighth of an atom at each of the eight corners, and one-half of an atom on each of the six faces.

The FCC structure has silver in it.

The unit cell's edge length is 409 pm.

The axes are lengths between points in the space lattice.

Unit cell axes join points.

There are 14 different unit cells and seven different lattice systems.

There are two or more different kinds of ion that have different sizes.

The packing of these OpenStax book is more complex than the packing of metal atoms.

The attraction for the opposite charge of monatomic ion is the same in every direction.

Stable structures for ionic compounds result when the cations and anions are 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- The structures are determined by the relative sizes of the ion and the ratio of the numbers of positive and negative ion in the compound.

The anions are usually larger than the cations in simple ionic structures.

There are three anions in one plane and one anion in an adjacent plane.

There are two types of holes between anions.

Small cations and larger cations occupy the same holes.

The anions may adopt a more open structure if the cations are too large.
The larger cations can fit in the larger holes made possible by the more open spacing.

The shape of the hole occupied by the compound is related to the size of the cation.

There are two holes for each anion in the array.

A compound with a maximum cation:anion ratio of 2:1 can be filled with all of the tetrahedral holes.
Li2O, Na2O, Li2S, and Na2S are examples.
If the ionic sizes fit, compounds with a ratio of less than 2:1 will crystallise in a close-packed array of anions.
Some of the holes are empty in these compounds.

Zinc sulfide is an important industrial source of zinc and is also used as a white color in paint.

One-half of the holes in the structure of zinc sulfide are occupied by zinc ion.

There are two holes per anion and one-half of them are occupied by zinc ion.

The formula is ZnS.

There is a close-packed array of selenide ion with lithium ion in all of the holes.

The ratio of holes to anions in a structure is called Li2Se.

The maximum cation:anion ratio can be achieved by compounds with cations in holes in the anions.
All of the holes in NiO are filled.
When some of the holes are empty, the ratios are less than 1:1.

It is aluminum oxide.

Two-thirds of the holes in the aluminum oxide are filled with oxide ion.

The ratio of aluminum to oxygen must be 23 :1 because there is only one hole per anion.

The formula for the whole number ratio is Al2O3.

One-half of the holes in the titanium oxide are filled with titanium ion.

In a simple array of anions, there is one hole that can be occupied by a cation for each anion.

All of the holes in the compound are occupied.

Half of the holes are occupied by CaF2.

The structure of different types of ionic compounds can be determined by the relative sizes of their strontium and cations.

We will use ionic compounds to describe the general features of ionic structures.

A simple cubic structure is formed when an ionic compound is composed of cations and anions of the same size.

We can think of this as a unit cell with a chloride ion in the center, or a unit cell with a Cs+ ion in the middle.
Each unit cell has one cesium ion and one chloride ion.
There is no lattice point in the center of the cell, and CsCl is not a BCC structure because it is not the same as a chloride ion.

A simple cubic structure is formed by compounds with similar-sized cations and anions.

The unit cells have either cations at the corners or anions at the corners.

The location of lattice points is arbitrary.

There is an alternate description of the structure in which the lattice points are located.
The lattice points at the corners of the cell are where the cesium ion and the chloride ion are located.
The two cells describe the same structures.

Na+ and Cl- have a radii of 102 pm and 181 pm, respectively, as an example of this.

There are holes in the middle of the cell edges and in the center of the cell in Liquids and Solids FCC cell.

Along the cell edges, the sodium and chloride ion touch each other.

The unit cell has a mixture of both salt and chloride in it.

The FCC structure is formed by compounds with larger anions than cations.

FCC unit cells have cations in the holes.

The FCC unit cell contains zinc blende, a form of zinc sulfide, which can be seen in this structure.

The zinc ion is only 40% of the radius of the sulfide ion, so these small zinc ion are located in one half of the tetrahedral holes.
The empirical formula ZnS is given by the number of zinc and sulfide ion in the unit cell.

The zinc blende forms an FCC unit cell with zinc ion occupying half of the holes in the structure.

The cations are on the lattice points of the FCC cell, while the calcium ion are on the lattice points of the calcium fluoride unit cell.

The FCC array of calcium ion sites are occupied by fluoride ion.
The ratio of calcium to fluoride in a unit cell is required by the chemical formula, CaF2.

CaF2 forms an FCC unit cell with calcium ion and fluoride ion at the lattice points and all of the tetrahedral sites between them.

If we know the edge length of a unit cell and the position of the ion in the cell, we can calculate ionic radii for the ion in the compound.

The unit cell of LiCl has an edge length of 5.14 A.

The ionic radius for the chloride ion can be calculated if the lithium ion is small enough.

The length unit angstrom, A, is used to represent atomic-scale dimensions and is equivalent to 10 m.

The answer is 0.182 nm (1.82 A) for a Cl- radius.

The unit cell's edge length is 6.28 A.

Take anion-cation contact along the cell edge into account.
The chloride ion has a diameter of 1.82 A.

The ion's radius is 1.33 A.

It is important to realize that values for ionic radii calculated from the edge lengths of unit cells depend on many assumptions, such as a perfect spherical shape for ion, which are approximations at best.

The calculated values are themselves approximate and cannot be pushed too far.
The method has proved useful for calculating ionic radii from X-ray crystallographic determinations.

The wavelength of the X-rays is the distance between the neighboring atoms in the crystals.

When a beam of X-rays hits a crystal, it scatters its rays in all directions.

Light waves occupying the same space experience interference, combining to yield waves of greater (a) or lesser (b) intensity depending on the separation of their maxima and minima.

The figure on the left shows waves diffracted at the Bragg angle, while the figure on the right shows waves diffracted at a different angle.

The distance between the atoms is determined by the X-rays that are scattered by the atoms.

A diffracted wave of high intensity is depicted in the top image.
The low intensity diffracted wave is depicted in the bottom image.

You can explore the effect of each variable on the intensity of the diffracted wave by visiting this Bragg equation.

The Bragg equation can be used to calculate distances between atoms from such measurements.

In a diffractometer, X-rays with a wavelength of 0.1315 nm were used to produce a pattern for copper.

The diffracting planes are in copper.

A crystal with a wavelength of 0.147 is diffracts X-rays.

One of the great achievements in the history of science is the discovery of the structure of DNA.

Maurice Wilkins, who provided experimental proof of DNA's structure, was awarded the 1962 Nobel Prize in Physiology or Medicine.

Franklin's work in measuring X-ray images of DNA made a huge contribution to this monumental achievement.

The British war effort was helped by Franklin's research on the structure of coals.
After shifting her focus to biological systems in the early 1950s, Franklin and PhD student Raymond Gosling discovered that there are two types of DNA, a long, thin fiber formed when wet and a short, wide fiber formed when dried.
This OpenStax book is available for free at http://cnx.org/content/col11760/1.9 to find out the details of the double helix.
New information that changed the body of knowledge in the field was uncovered by Franklin's research on viruses and the RNA that contains their genetic information.
Franklin died of ovarian cancer at the age of 37.
The Chicago Medical School of Finch University of Health Sciences changed its name to the Rosalind Franklin University of Medicine and Science in 2004, and adopted an image of her famous X-ray diffraction image of DNA as its official university logo.

Franklin found an X-ray image similar to this one in her research.

The physical properties of liquid and solid matter can be explained in terms of the theory.

In a liquid, intermolecular attractive forces hold the molecule in contact with each other.

The van der Waals forces are responsible for the behavior of liquids and solids.

Dipole-dipole attractions are caused by the attraction of the partial negative end of one dipolar molecule for the partial positive end of another.
The London dispersion force can be caused by the temporary dipole that results from the motion of the electrons in an atom.
London forces increase in size.
When hydrogen bonds to one of the three most negatively charged elements, it's called a dipoledipole attraction.

Depending on the chemical identity of the molecule, the intermolecular forces between it and the liquid state can vary.

The elasticity of a liquid surface is determined by the cohesive forces between the molecule and the liquid.
Surface wetting and capillary rise are caused by the forces between the molecule of a liquid and different molecule in contact with it.

Liquids and Solids Phase transitions are processes that convert matter from one physical state to another.

The three phases of matter have six phase transitions.
Endothermic processes require heat to overcome intermolecular attractions.
Intermolecular attractive forces are established or strengthened during the transitions of freezing, condensation, and deposition.
The temperatures at which phase transitions occur are determined by the relative strengths of intermolecular attractions and are dependent on the chemical identity of the substance.

A phase diagram shows the temperature and pressure conditions at which a substance exists in solid, liquid, and gaseous states.

There are three pressure-temperature equilibrium curves: solid-liquid, liquid-gas, and solid-gas.
These curves show the relationship between temperatures and pressures.
The temperature and pressure at which all three phases are in equilibrium are represented by the point of intersection of all three curves.
A substance can't exist in the liquid state at pressures below the triple point.
The substance's critical point is the pressure and temperature above which a liquid phase cannot exist.

Some substances have an internal structure that is not ordered, while others have particles in a very organized structure.

The main types are ionic, metallic, covalent network, and molecular.
The types of particles, the arrangements of the particles, and the strengths of the attractions between them are some of the things that make up the properties of the different kinds of Crystalline Solids.
The particles in the same material experience the same attraction, so they melt over a range of temperatures.
There are defects in the pattern of the particles.
The physical properties of computer chips are affected by defects such as vacancies, atoms or ions not in the regular positions and impurities.

The packing of spheres can be described by the structures of simple ionic compounds.

Metal atoms can pack in hexagonal close-packed structures.

The spaces remaining between the anions in simple ionic structures are occupied by the cations.
A close-packed array of anions usually contains small cations.
Octahedral holes are usually occupied by larger cations.
A simple array of anions can hold larger cations.
The structure of a solid can be described by the size and shape of a unit cell.
The type of structure and dimensions of the unit cell can be determined by X-rays.

Pick substances, heating and cooling the systems, and changing the state.

The Ne atom can be moved on the right to see how the potential energy changes.

The Ne atom can be moved with the Total Force button.
You can move the Ne atom by selecting the Component Forces button.

The types of intermolecular forces in a substance are the same.

Both Neon and HF have the same mass.

Both butane and chloroethane have the same mass.

The differences in the boiling points of acetone and 1-propanol, which have the same molar mass, can be explained on the basis of dipole moments and hydrogen bonding.

Silane, phosphine, and hydrogen sulfide melt at different temperatures.

To show how two CH3COOH molecules are held together, draw a dimer of acetic acid.

A helix is a chain of amino acids that can be formed in a variety of arrangements.

The test tubes have the same amount of motor oils.

The metal spheres were dropped at the same time into each of the tubes, and a brief moment later, the spheres had fallen to the heights indicated in the illustration.

The values of the surface tension and viscosity are shown.

The table shows the surface tension and viscosity of water.

Refer to the example for the required information.

Water rises in a glass capillary tube.

CCl4 is no longer used as a dry cleaning solvent because it is cancer-causing.

The enthalpy of vaporization of CCl4 is 33.05 kJ/mol.

The normal boiling point for CCl4 can be estimated using this information.

There is no space for any vapor in a syringe filled with liquid ether at a temperature of 20 degrees.

The enthalpy of vaporization for liquid hydrogen fluoride is less than that for water because the molecule is more polar.

Excess heat is taken away from the body by sweating.

Some of the water may become sweat and evaporate.

The higher the pressure inside the pressure cooker, the faster the food will cook.

A pressure cooker has a safety valve that can be activated if the pressure reaches 3.4 atm.

Consider a cylinder with a mixture of liquid carbon dioxide and gaseous carbon dioxide at an initial pressure of 65 atm and a temperature of 20 degC.

Plot the change in the cylinder pressure with time as carbon dioxide is released at a constant temperature.

It is at a temperature of -78 degrees.

On the phase diagram, label the gas and liquid regions.

On the diagram, label the phase.

O2 forms a solid at very low temperatures.

As it cools, olive oil forms a solid over a range of temperatures.

Substance A has a melting point of 1135 degrees centigrade, is ionic, metallic, covalent network, or molecule, and conducts electricity well.

Substance B is brittle, does not conduct electricity as a solid, and has a melting point of 2072 degC.
Substance C is very hard, does not conduct electricity, and has a melting point.
Substance D has a melting point of 185 degrees.

Substance A is shiny and conducts electricity well.

Substance B does not conduct electricity and is hard.

There is a hexagonal closest packed structure.

The nickel metal is in a close packed structure.

The edge length of the cell is 3.165 A.

One half of the holes in a closest packed array of sulfide ion are occupied by Cadmium sulfide.

A compound containing zinc, aluminum, and sulfur has a close-packed array of sulfide ion.

One-third of the holes have zinc and aluminum in them.

Different ionities occupied the same cites in the crystals as minerals were formed from molten magma.

There is a difference in the charge on the minerals' iontes.

There is a rubidium ion in the center of the cell and a rubidium ion at the corners.

One of the various manganese oxides has a cell that has manganese ion at the corners and in the center.

The center of the unit cell is where the oxides are located.

The same crystal structure is found in NaH.

The edge length of the cell is 4.880 A.

The same structure is found in Thallium(I) iodide.

TlI's unit cell has an edge length of 4.20 A.

At the corners and at the center of each edge there are fluoride and manganese ion.

The diffracting planes are in this crystal.

A metal with spacing between planes equal to 0.4164 nm diffracts X-rays.

The wavelength is 1.54 A.

An X-ray is emitted when an electron falls from the L to the K shell.

The X-rays are diffracted by planes with a separation of 2.64 A.