Materials can present many behaviours, such as how easily they conduct electricity or how much they can elongate without breaking. Many of these physical characteristics are known as ‘material properties’. Most of these properties depend on the behaviour of the atoms when they bond in a group.
Bulk properties of matter
When atoms or molecules bond together, their behaviour changes. The mechanical characteristics, which arise from how molecules or atoms respond to forces or energy exchanges when bonded, are known as bulk properties.
One example of mechanical properties in solids is when you extend a rubber band or scratch a diamond.
A rubber band consists of molecules forming long chains known as polymers. The chains are entangled and disordered, as shown in the figure below.
The long chains, known as polymers, which make up a rubber band, are entangled when no force acts to make the band tense
When stretched, the chains expand, allowing the band to increase its length without breaking. In this case, the force applied untangles the chains, as shown in the next figure.
When the rubber band is made tense, the chains that make up the rubber elongate and reorder
The chains can resist a certain amount of force without breaking or deforming. If the force applied to the band is small enough to not deform it permanently, it will go back to its initial length.
Here is another example:
Carbon atoms have four electrons in their outer shell. These electrons can bond freely with other elements. In the case of a diamond, the carbon atoms share these electrons with the other carbon atoms.
When the carbon is subjected to large pressure and temperatures, it will be compressed until the atoms form a crystal. The result thus is a compact crystalline structure without free electrons, which makes the diamond very hard and even gives it the ability to not react to acids.
Some important bulk properties include:
- Hardness.
- Electrical conductivity.
- Thermal conductivity.
- Elasticity.
- Density.
- Tensile strength.
Bulk properties of matter in mechanics
Some bulk properties are specifically related to the mechanical behaviour of a material. Hardness and elasticity are two examples. These characteristics are important to take into consideration, as we need to know the mechanical responses of materials to forces and loads. For instance, some materials need to be flexible, so they do not break when they are deformed, such as the frame of your glasses. Other important characteristics that help us classify materials are their density, tensile strength, and bulk modulus.
The characteristics of materials partially derive from the chemical bond between particles. In solid matter, metals have metallic bonds, polymers usually have covalent bonds, and ceramics have ionic bonds.
The type of bond in matter dictates not only the mechanical characteristics of the material but also its structural arrangement. You can think of this as a spring between atoms. Springs that connect metallic atoms are stiffer than those that connect a rubber band.
The elasticity of a material can be represented using the analogy of springs between the elements that make up the material. Each material features springs with different stiffness
Molecules in a rubber band are made of long entangled chains. When they are pulled by a force, their arrangement changes and they elongate.
When a rubber band tenses, its molecules untangle, allowing the band to expand
The main difference between a rubber band and diamonds or metals is that the latter two have a tight, linearly packed structure that does not allow them to elongate much.
The type of bond can also influence other bulk properties, such as the melting point. Materials with ionic, covalent, or metallic bonds have higher melting points, while hydrogen bonds, such as van der Waals’, have lower melting points.
Elasticity
Elasticity is the capacity of a material to elongate when a force is applied to it and regain its original shape when the force is removed. Elasticity is an important characteristic in science and industry where elastic materials are needed for certain types of work and applications. One example concerns the materials used in airbags, which during a crash must withstand powerful impacts and fast deformations while holding together.
The elasticity of a material is measured in Pascals. To perform the measurement, a mechanical test is needed, which is usually conducted by elongating a material using a force ‘F’, as shown in the image below.
Material properties, such as elasticity, can be measured by conducting mechanical tests, in which objects are exposed to forces that elongate them. The elongation causes a deformation δl by a force F
The material suffers ‘mechanical stress’ and changes its length. It then reverts back to its original length as long it has not passed its ‘elastic limit’. The more force the material can resist without deformation, the more elastic it is. An important property of elastic materials is known as Young’s modulus, which is measured in Pascals.
Young’s modulus
The Young modulus can be described as the proportion between the strain (deformation) of a material and the mechanical stress it is exposed to. See the stress vs strain graph below.
A material in a tensile test presents a deformation (strain), which depends on the force applied (mechanical stress). The resulting slope is equal to Young’s modulus
The red line in the figure indicates that the stress and the strain are proportional to each other. In the area labelled ‘elastic zone’, the material will revert to its original shape after having been deformed. The slope of the red line is known as the elastic modulus or Young’s modulus. This is different for different materials, as shown in the following table.
| Material | Young’s modulus (GPa) |
| Polystyrene | 3-3.5 |
| Aluminium | 68 |
| Glass | 50-90 |
| Copper | 117 |
| Diamond | 1220 |
To obtain the Young modulus from a stress and strain plot, we need to calculate the slope of the curve in the elastic zone. This can be done easily using the formula below if you know two points of the stress vs strain curve.
\[Modulus = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\sigma_2-\sigma_1}{\varepsilon_2-\varepsilon_1} = \frac{\Delta \sigma}{\Delta \varepsilon}\]
The tensile stress σ is defined as the force applied to deform the material divided by the cross-sectional area of the material, while the tensile strain ε is the increase in length divided by the original length. You can see this in the formulas below.
\[\sigma = \frac{F}{A}\]
\[\varepsilon = \frac{\delta I}{I}\]
A metal, i.e., a bar with the area A, is tested using a tension test. The applied force increases, producing an elongation in the elastic zone of the material. The data collected is shown in the table below. Find the Young modulus for this metal if the bar area is 4.2∙10-8 square metres with an initial length of 2 metres.
| Extension (mm) |
0 | 0 |
1 | 0.365 |
2 | 0.73 |
2.9 | 1.45 |
4 | 2 |
Plotting this data, you will find that the results are linear until 2.9N. Thereafter, you can use the difference between 0 to 2.9N, applying the tensile stress formula for F = 0N and F = 2.9N.
\[\sigma = \frac{F}{A} = \frac{2.9 N}{4.2 \cdot 10^{-8} m^2} = 6.9 \cdot 10^7 Pa\]
For F = 0, your result will be 0. Now, we calculate the elongation of the bar.
\[\varepsilon = \frac{1.45 \cdot 10^{-3}}{2} = 7.25 \cdot 10^{-4} m\]
For our first point, the result again will be 0. Finally, we divide both.
\[Modulus = \frac{\sigma}{\varepsilon} = \frac{6.9 \cdot 10^7 Pa}{7.25 \cdot 10^{-4}} = 9.517 \cdot 10^{10} Pa \approx 9.52 \cdot 10^{10} Pa\]
Hooke’s Law
The elastic zone of a material can be modelled using Hooke’s law. In this case, an analogy is useful. The force applied to the material is analogous to a weight pulled by gravity, and the material elasticity is a spring deformed by the weight.
In this case, the force is proportional to the elongation and the spring constant k.
Plasticity
When materials are elongated beyond their elastic zone, they enter their plastic zone, which indicates the area in which materials start to deform irreversibly as the force keeps pulling them. See the blue line in the following image.
A material in a tensile test presents a deformation (strain) that depends on the force applied (mechanical stress). The area in which the relationship between the tensile stress and the tensile strain is no longer linear is known as the plastic zone
The plastic zone begins where the proportion between tensile stress and tensile strains is no longer linear.
Hardness
Hardness, measured in Pascals, is the property of materials to resist penetration or scratches. For many materials, elasticity is inversely proportional to hardness. The molecules and atoms that allow a material to elongate also allow a force applied to a small portion of the surface to penetrate the material. Materials with low elasticity, such as metals and diamonds, are not elastic, as the strength of their bonds and structures resists penetration by a force trying to push them.
Density
Density, which is defined as the amount of mass existing in a unit of volume, is another important property of materials. Density is usually measured in SI units as kilograms per cubic metre. The density of a material varies depending on two factors:
- The atomic structure of the material.
- The element of which it consists.
It is well known that heavier elements weigh more. However, the atomic structure also plays an important role in density. Atoms of lighter elements that are heavily packed are denser than atoms of heavier elements with an atomic structure that incorporates more space.
The structure of a diamond consists of carbon atoms with a weight of 12.01 atomic mass units, while titanium weighs 47.867 atomic mass units. The weight of carbon is almost four times smaller than that of the titanium atom.
However, the structure of a diamond is much more densely packed, and the average density of diamonds can be around 3520 kilograms per cubic metre. Titanium, on the other hand, has a density of around 4420 kilograms per cubic metre.
Even though the difference between the masses of titanium and carbon is quite large, titanium’s density is only 25.6% more than that of carbon.
Bulk Properties of Solids - Key takeaways
- Bulk properties are mechanical properties that arise from the atoms or molecules acting together after bonding.
- Some important bulk properties include elasticity, tensile strength, density, hardness, electrical conductivity, and thermal conductivity.
- Elasticity and hardness respectively describe how bodies can be deformed and revert back to their original shape (elasticity) and how easy it is to penetrate or scratch them (hardness).
- The elastic limit is the point at which a material starts to deform so that it can no longer revert back to its original shape.
- When the material leaves its elastic zone, it enters its plastic zone, where it deforms irreversibly.
- Young’s modulus describes the ratio of mechanical stress and the deformation of the material.
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