# 9.2: The Solid State of Matter

Skills to Develop

• Define and describe the bonding and properties of ionic, molecular, metallic, and covalent network crystalline solids
• Describe the main types of crystalline solids: ionic solids, metallic solids, covalent network solids, and molecular solids
• Explain the ways in which crystal defects can occur in a solid

When most liquids are cooled, they eventually freeze and form crystalline solids, solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern. It is also possible for a liquid to freeze before its molecules become arranged in an orderly pattern. The resulting materials are called amorphous solids or noncrystalline solids (or, sometimes, glasses). The particles of such solids lack an ordered internal structure and are randomly arranged (Figure $$\PageIndex{1}$$).

Figure $$\PageIndex{1}$$: The entities of a solid phase may be arranged in a regular, repeating pattern (crystalline solids) or randomly (amorphous).

Metals and ionic compounds typically form ordered, crystalline solids. Substances that consist of large molecules, or a mixture of molecules whose movements are more restricted, often form amorphous solids. For examples, candle waxes are amorphous solids composed of large hydrocarbon molecules. Some substances, such as silicon dioxide (Figure $$\PageIndex{2}$$), can form either crystalline or amorphous solids, depending on the conditions under which it is produced. Also, amorphous solids may undergo a transition to the crystalline state under appropriate conditions.

Figure $$\PageIndex{2}$$: (a) Silicon dioxide, SiO2, is abundant in nature as one of several crystalline forms of the mineral quartz. (b) Rapid cooling of molten SiO2 yields an amorphous solid known as “fused silica”.

Crystalline solids are generally classified according the nature of the forces that hold its particles together. These forces are primarily responsible for the physical properties exhibited by the bulk solids. The following sections provide descriptions of the major types of crystalline solids: ionic, metallic, covalent network, and molecular.

## Ionic Solids

Ionic solids, such as sodium chloride and nickel oxide, are composed of positive and negative ions that are held together by electrostatic attractions, which can be quite strong (Figure $$\PageIndex{3}$$). Many ionic crystals also have high melting points. This is due to the very strong attractions between the ions—in ionic compounds, the attractions between full charges are (much) larger than those between the partial charges in polar molecular compounds. This will be looked at in more detail in a later discussion of lattice energies. Although they are hard, they also tend to be brittle, and they shatter rather than bend. Ionic solids do not conduct electricity; however, they do conduct when molten or dissolved because their ions are free to move. Many simple compounds formed by the reaction of a metallic element with a nonmetallic element are ionic.

Figure $$\PageIndex{3}$$: Sodium chloride is an ionic solid.

## Metallic Bonding

In the early 1900's, Paul Drüde came up with the "sea of electrons" metallic bonding theory by modeling metals as a mixture of atomic cores (atomic cores = positive nuclei + inner shell of electrons) and valence electrons. Metallic bonds occur among metal atoms. Whereas ionic bonds join metals to non-metals, metallic bonding joins a bulk of metal atoms. A sheet of aluminum foil and a copper wire are both places where you can see metallic bonding in action.

Metals tend to have high melting points and boiling points suggesting strong bonds between the atoms. Even a soft metal like sodium (melting point 97.8°C) melts at a considerably higher temperature than the element (neon) which precedes it in the Periodic Table. Sodium has the electronic structure 1s22s22p63s1. When sodium atoms come together, the electron in the 3s atomic orbital of one sodium atom shares space with the corresponding electron on a neighboring atom to form a molecular orbital - in much the same sort of way that a covalent bond is formed.

The difference, however, is that each sodium atom is being touched by eight other sodium atoms - and the sharing occurs between the central atom and the 3s orbitals on all of the eight other atoms. Each of these eight is in turn being touched by eight sodium atoms, which in turn are touched by eight atoms - and so on and so on, until you have taken in all the atoms in that lump of sodium. All of the 3s orbitals on all of the atoms overlap to give a vast number of molecular orbitals that extend over the whole piece of metal. There have to be huge numbers of molecular orbitals, of course, because any orbital can only hold two electrons.

The electrons can move freely within these molecular orbitals, and so each electron becomes detached from its parent atom. The electrons are said to be delocalized. The metal is held together by the strong forces of attraction between the positive nuclei and the delocalized electrons (Figure $$\PageIndex{4}$$).

This is sometimes described as "an array of positive ions in a sea of electrons". If you are going to use this view, beware! Is a metal made up of atoms or ions? It is made of atoms. Each positive center in the diagram represents all the rest of the atom apart from the outer electron, but that electron has not been lost - it may no longer have an attachment to a particular atom, but it's still there in the structure. Sodium metal is therefore written as $$\ce{Na}$$, not $$\ce{Na^+}$$.

Example $$\PageIndex{1}$$: Metallic bonding in magnesium

Use the sea of electrons model to explain why Magnesium has a higher melting point (650 °C) than sodium (97.79 °C).

Solution

If you work through the same argument above for sodium with magnesium, you end up with stronger bonds and hence a higher melting point.

Magnesium has the outer electronic structure 3s2. Both of these electrons become delocalized, so the "sea" has twice the electron density as it does in sodium. The remaining "ions" also have twice the charge (if you are going to use this particular view of the metal bond) and so there will be more attraction between "ions" and "sea".

More realistically, each magnesium atom has 12 protons in the nucleus compared with sodium's 11. In both cases, the nucleus is screened from the delocalized electrons by the same number of inner electrons - the 10 electrons in the 1s2 2s2 2p6 orbitals. That means that there will be a net pull from the magnesium nucleus of 2+, but only 1+ from the sodium nucleus.

So not only will there be a greater number of delocalized electrons in magnesium, but there will also be a greater attraction for them from the magnesium nuclei. Magnesium atoms also have a slightly smaller radius than sodium atoms, and so the delocalized electrons are closer to the nuclei. Each magnesium atom also has twelve near neighbors rather than sodium's eight. Both of these factors increase the strength of the bond still further.

Note: Transition metals tend to have particularly high melting points and boiling points. The reason is that they can involve the 3d electrons in the delocalization as well as the 4s. The more electrons you can involve, the stronger the attractions tend to be.

Bulk properties of metals

Metals have several qualities that are unique, such as the ability to conduct electricity and heat, a low ionization energy, and a low electronegativity (so they will give up electrons easily to form cations). Their physical properties include a lustrous (shiny) appearance, and they are malleable and ductile. Metals have a crystal structure but can be easily deformed. In this model, the valence electrons are free, delocalized, mobile, and not associated with any particular atom. This model may account for:

• Conductivity: Since the electrons are free, if electrons from an outside source were pushed into a metal wire at one end (Figure $$\PageIndex{5}$$), the electrons would move through the wire and come out at the other end at the same rate (conductivity is the movement of charge).
• Malleability and Ductility: The electron-sea model of metals not only explains their electrical properties but their malleability and ductility as well. The sea of electrons surrounding the protons acts like a cushion, and so when the metal is hammered on, for instance, the overall composition of the structure of the metal is not harmed or changed. The protons may be rearranged but the sea of electrons with adjust to the new formation of protons and keep the metal intact. When one layer of ions in an electron sea moves along one space with respect to the layer below it, the crystal structure does not fracture but is only deformed (Figure $$\PageIndex{6}$$).
• Heat capacity: This is explained by the ability of free electrons to move about the solid.
• Luster: The free electrons can absorb photons in the "sea," so metals are opaque-looking. Electrons on the surface can bounce back light at the same frequency that the light hits the surface, therefore the metal appears to be shiny.

However, these observations are only qualitative, and not quantitative, so they cannot be tested. The "Sea of Electrons" theory stands today only as an oversimplified model of how metallic bonding works.

In a molten metal, the metallic bond is still present, although the ordered structure has been broken down. The metallic bond is not fully broken until the metal boils. That means that boiling point is actually a better guide to the strength of the metallic bond than melting point is. On melting, the bond is loosened, not broken. The strength of a metallic bond depends on three things:

1. The number of electrons that become delocalized from the metal
2. The charge of the cation (metal).
3. The size of the cation.

A strong metallic bond will be the result of more delocalized electrons, which causes the effective nuclear charge on electrons on the cation to increase, in effect making the size of the cation smaller. Metallic bonds are strong and require a great deal of energy to break, and therefore metals have high melting and boiling points. A metallic bonding theory must explain how so much bonding can occur with such few electrons (since metals are located on the left side of the periodic table and do not have many electrons in their valence shells). The theory must also account for all of a metal's unique chemical and physical properties.

## Expanding the Range of Bonding Possible

Previously, we argued that bonding between atoms can classified as range of possible bonding between ionic bonds (fully charge transfer) and covalent bonds (fully shared electrons). When two atoms of slightly differing electronegativities come together to form a covalent bond, one atom attracts the electrons more than the other; this is called a polar covalent bond. However, simple “ionic” and “covalent” bonding are idealized concepts and most bonds exist on a two-dimensional continuum described by the van Arkel-Ketelaar Triangle (Figure $$\PageIndex{7}$$).

Bond triangles or van Arkel–Ketelaar triangles (named after Anton Eduard van Arkel and J. A. A. Ketelaar) are triangles used for showing different compounds in varying degrees of ionic, metallic and covalent bonding. In 1941 van Arkel recognized three extreme materials and associated bonding types. Using 36 main group elements, such as metals, metalloids and non-metals, he placed ionic, metallic and covalent bonds on the corners of an equilateral triangle, as well as suggested intermediate species. The bond triangle shows that chemical bonds are not just particular bonds of a specific type. Rather, bond types are interconnected and different compounds have varying degrees of different bonding character (for example, polar covalent bonds).

Using electronegativity - two compound average electronegativity on x-axis of Figure $$\PageIndex{7}$$.

$\sum \chi = \dfrac{\chi_A + \chi_B}{2} \label{sum}$

and electronegativity difference on y-axis,

$\Delta \chi = | \chi_A - \chi_B | \label{diff}$

we can rate the dominant bond between the compounds. On the right side of Figure $$\PageIndex{7}$$ (from ionic to covalent) should be compounds with varying difference in electronegativity. The compounds with equal electronegativity, such as $$\ce{Cl2}$$ (chlorine) are placed in the covalent corner, while the ionic corner has compounds with large electronegativity difference, such as $$\ce{NaCl}$$ (table salt). The bottom side (from metallic to covalent) contains compounds with varying degree of directionality in the bond. At one extreme is metallic bonds with delocalized bonding and at the other are covalent bonds in which the orbitals overlap in a particular direction. The left side (from ionic to metallic) is meant for delocalized bonds with varying electronegativity difference.

The Three Extremes in bonding

In general:

• Metallic bonds have low $$\Delta \chi$$ and low average $$\sum\chi$$.
• Ionic bonds have moderate-to-high $$\Delta \chi$$ and moderate values of average $$\sum \chi$$.
• Covalent bonds have moderate to high average $$\sum \chi$$ and can exist with moderately low $$\Delta \chi$$.
Example $$\PageIndex{2}$$

Use the tables of electronegativities (Table A2) and Figure $$\PageIndex{7}$$ to estimate the following values

• difference in electronegativity ($$\Delta \chi$$)
• average electronegativity in a bond ($$\sum \chi$$)
• percent ionic character
• likely bond type

for the selected compounds:

1. $$\ce{AsH}$$ (e.g., in arsine $$AsH$$)
2. $$\ce{SrLi}$$
3. $$\ce{KF}$$.

Solution

a: $$\ce{AsH}$$

• The electronegativity of $$\ce{As}$$ is 2.18
• The electronegativity of $$\ce{H}$$ is 2.22

Using Equations \ref{sum} and \ref{diff}:

\begin{align*} \sum \chi &= \dfrac{\chi_A + \chi_B}{2} \\[4pt] &=\dfrac{2.18 + 2.22}{2} \\[4pt] &= 2.2 \end{align*}

\begin{align*} \Delta \chi &= \chi_A - \chi_B \\[4pt] &= 2.18 - 2.22 \\[4pt] &= 0.04 \end{align*}

• From Figure $$\PageIndex{4}$$, the bond is fairly nonpolar and has a low ionic character (10% or less)
• The bonding is in the middle of a covalent bond and a metallic bond

b: $$\ce{SrLi}$$

• The electronegativity of $$\ce{Sr}$$ is 0.95
• The electronegativity of $$\ce{Li}$$ is 0.98

Using Equations \ref{sum} and \ref{diff}:

\begin{align*} \sum \chi &= \dfrac{\chi_A + \chi_B}{2} \\[4pt] &=\dfrac{0.95 + 0.98}{2} \\[4pt] &= 0.965 \end{align*}

\begin{align*} \Delta \chi &= \chi_A - \chi_B \\[4pt] &= 0.98 - 0.95 \\[4pt] &= 0.025 \end{align*}

• From Figure $$\PageIndex{4}$$, the bond is fairly nonpolar and has a low ionic character (~3% or less)
• The bonding is likely metallic.

c: $$\ce{KF}$$

• The electronegativity of $$\ce{K}$$ is 0.82
• The electronegativity of $$\ce{F}$$ is 3.98

Using Equations \ref{sum} and \ref{diff}:

\begin{align*} \sum \chi &= \dfrac{\chi_A + \chi_B}{2} \\[4pt] &=\dfrac{0.82 + 3.98}{2} \\[4pt] &= 2.4 \end{align*}

\begin{align*} \Delta \chi &= \chi_A - \chi_B \\[4pt] &= | 0.82 - 3.98 | \\[4pt] &= 3.16 \end{align*}

• From Figure $$\PageIndex{4}$$, the bond is fairly polar and has a high ionic character (~75%)
• The bonding is likely ionic.
Exercise $$\PageIndex{2}$$

Contrast the bonding of $$\ce{NaCl}$$ and silicon tetrafluoride.

$$\ce{NaCl}$$ is an ionic crystal structure, and an electrolyte when dissolved in water; $$\Delta \chi =1.58$$, average $$\sum \chi =1.79$$, while silicon tetrafluoride is covalent (molecular, non-polar gas; $$\Delta \chi =2.08$$, average $$\sum \chi =2.94$$.

## Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms Figure $$\PageIndex{8}$$. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties. All exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many are very hard and quite strong. Because of their malleability (the ability to deform under pressure or hammering), they do not shatter and, therefore, make useful construction materials. The melting points of the metals vary widely. Mercury is a liquid at room temperature, and the alkali metals melt below 200 °C. Several post-transition metals also have low melting points, whereas the transition metals melt at temperatures above 1000 °C. These differences reflect differences in strengths of metallic bonding among the metals.

Figure $$\PageIndex{8}$$: Copper is a metallic solid.

## Covalent Network Solids

Covalent network solids include crystals of diamond, silicon, some other nonmetals, and some covalent compounds such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds. The atoms in these solids are held together by a network of covalent bonds, as shown in Figure $$\PageIndex{9}$$. To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically characterized by hardness, strength, and high melting points. For example, diamond is one of the hardest substances known and melts above 3500 °C.

Figure $$\PageIndex{9}$$. A covalent crystal contains a three-dimensional network of covalent bonds, as illustrated by the structures of diamond, silicon dioxide, silicon carbide, and graphite. Graphite is an exceptional example, composed of planar sheets of covalent crystals that are held together in layers by noncovalent forces. Unlike typical covalent solids, graphite is very soft and electrically conductive.

## Molecular Solids

Molecular solids, such as ice, sucrose (table sugar), and iodine, as shown in Figure $$\PageIndex{10}$$, are composed of neutral molecules. The strengths of the attractive forces between the units present in different crystals vary widely, as indicated by the melting points of the crystals. Small symmetrical molecules (nonpolar molecules), such as H2, N2, O2, and F2, have weak attractive forces and form molecular solids with very low melting points (below −200 °C). Substances consisting of larger, nonpolar molecules have larger attractive forces and melt at higher temperatures. Molecular solids composed of molecules with permanent dipole moments (polar molecules) melt at still higher temperatures. Examples include ice (melting point, 0 °C) and table sugar (melting point, 185 °C).

Figure $$\PageIndex{10}$$: Carbon dioxide (CO2) consists of small, nonpolar molecules and forms a molecular solid with a melting point of −78 °C. Iodine (I2) consists of larger, nonpolar molecules and forms a molecular solid that melts at 114 °C.

## Properties of Solids

A crystalline solid, like those listed in Table $$\PageIndex{1}$$ has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Thus, the attractions between the units that make up the crystal all have the same strength and all require the same amount of energy to be broken. The gradual softening of an amorphous material differs dramatically from the distinct melting of a crystalline solid. This results from the structural nonequivalence of the molecules in the amorphous solid. Some forces are weaker than others, and when an amorphous material is heated, the weakest intermolecular attractions break first. As the temperature is increased further, the stronger attractions are broken. Thus amorphous materials soften over a range of temperatures.

Table $$\PageIndex{1}$$: Types of Crystalline Solids and Their Properties
Type of Solid Type of Particles Type of Attractions Properties Examples
ionic ions ionic bonds hard, brittle, conducts electricity as a liquid but not as a solid, high to very high melting points NaCl, Al2O3
metallic atoms of electropositive elements metallic bonds shiny, malleable, ductile, conducts heat and electricity well, variable hardness and melting temperature Cu, Fe, Ti, Pb, U
covalent network atoms of electronegative elements covalent bonds very hard, not conductive, very high melting points C (diamond), SiO2, SiC
molecular molecules (or atoms) IMFs variable hardness, variable brittleness, not conductive, low melting points H2O, CO2, I2, C12H22O11

Graphene: Material of the Future

Carbon is an essential element in our world. The unique properties of carbon atoms allow the existence of carbon-based life forms such as ourselves. Carbon forms a huge variety of substances that we use on a daily basis, including those shown in Figure $$\PageIndex{11}$$. You may be familiar with diamond and graphite, the two most common allotropes of carbon. (Allotropes are different structural forms of the same element.) Diamond is one of the hardest-known substances, whereas graphite is soft enough to be used as pencil lead. These very different properties stem from the different arrangements of the carbon atoms in the different allotropes.

Figure $$\PageIndex{11}$$: Diamond is extremely hard because of the strong bonding between carbon atoms in all directions. Graphite (in pencil lead) rubs off onto paper due to the weak attractions between the carbon layers. An image of a graphite surface shows the distance between the centers of adjacent carbon atoms. (credit left photo: modification of work by Steve Jurvetson; credit middle photo: modification of work by United States Geological Survey)

You may be less familiar with a recently discovered form of carbon: graphene. Graphene was first isolated in 2004 by using tape to peel off thinner and thinner layers from graphite. It is essentially a single sheet (one atom thick) of graphite. Graphene, illustrated in Figure $$\PageIndex{12}$$, is not only strong and lightweight, but it is also an excellent conductor of electricity and heat. These properties may prove very useful in a wide range of applications, such as vastly improved computer chips and circuits, better batteries and solar cells, and stronger and lighter structural materials. The 2010 Nobel Prize in Physics was awarded to Andre Geim and Konstantin Novoselov for their pioneering work with graphene.

Figure $$\PageIndex{12}$$: Graphene sheets can be formed into buckyballs, nanotubes, and stacked layers.

## Crystal Defects

In a crystalline solid, the atoms, ions, or molecules are arranged in a definite repeating pattern, but occasional defects may occur in the pattern. Several types of defects are known, as illustrated in Figure $$\PageIndex{13}$$. Vacancies are defects that occur when positions that should contain atoms or ions are vacant. Less commonly, some atoms or ions in a crystal may occupy positions, called interstitial sites, located between the regular positions for atoms. Other distortions are found in impure crystals, as, for example, when the cations, anions, or molecules of the impurity are too large to fit into the regular positions without distorting the structure. Trace amounts of impurities are sometimes added to a crystal (a process known as doping) in order to create defects in the structure that yield desirable changes in its properties. For example, silicon crystals are doped with varying amounts of different elements to yield suitable electrical properties for their use in the manufacture of semiconductors and computer chips.

Figure $$\PageIndex{13}$$: Types of crystal defects include vacancies, interstitial atoms, and substitutions impurities.

## Summary

Video $$\PageIndex{2}$$: An overview of solids.

Some substances form crystalline solids consisting of particles in a very organized structure; others form amorphous (noncrystalline) solids with an internal structure that is not ordered. The main types of crystalline solids are ionic solids, metallic solids, covalent network solids, and molecular solids. The properties of the different kinds of crystalline solids are due to the types of particles of which they consist, the arrangements of the particles, and the strengths of the attractions between them. Because their particles experience identical attractions, crystalline solids have distinct melting temperatures; the particles in amorphous solids experience a range of interactions, so they soften gradually and melt over a range of temperatures. Some crystalline solids have defects in the definite repeating pattern of their particles. These defects (which include vacancies, atoms or ions not in the regular positions, and impurities) change physical properties such as electrical conductivity, which is exploited in the silicon crystals used to manufacture computer chips.

## Glossary

amorphous solid
(also, noncrystalline solid) solid in which the particles lack an ordered internal structure
covalent network solid
solid whose particles are held together by covalent bonds
crystalline solid
solid in which the particles are arranged in a definite repeating pattern
interstitial sites
spaces between the regular particle positions in any array of atoms or ions
ionic solid
solid composed of positive and negative ions held together by strong electrostatic attractions
metallic solid
solid composed of metal atoms
molecular solid
solid composed of neutral molecules held together by intermolecular forces of attraction
vacancy
defect that occurs when a position that should contain an atom or ion is vacant