What is Coefficient of Linear Expansion? Formula, Units & More

Posted on September 21st, 2023 by

Temperature affects the behavior of materials, causing them to expand or contract. However, not all materials respond to temperature variations in the same way. Some materials, like metals, tend to expand when heated, while others, like water, show a more complex behavior, with expansion occurring at specific temperatures.

This property is crucial in predicting how a material will respond to temperature changes. This coefficient, represented by the Greek letter alpha (α), describes how much a material expands per unit length for each degree of temperature rise. Understanding this concept helps engineers make accurate predictions and design structures that can withstand temperature fluctuations.

Learn about other thermal coating properties, like thermal conductivity and glass transition temperature

Formula for Calculating the Coefficient of Linear Expansion

The coefficient of linear expansion (α) can be calculated using the following formula:

α = ΔL / (L₀ × ΔT)


α is the coefficient of linear expansion

ΔL is the change in length

L₀ is the original length

ΔT is the change in temperature

Units used for expressing the coefficient

The coefficient of linear expansion is typically expressed in units of length per unit temperature, such as millimeters per degree Celsius (mm/°C) or inches per Fahrenheit (in/°F). These units emphasize the linear dimensions and temperature change required to induce a specific change in length. By using consistent units, scientists and engineers can easily compare and analyze the behavior of different materials.

Measurement and Units

Accurately measuring values is essential in understanding how materials respond to changes in temperature. Several experimental techniques are commonly employed to measure the coefficient of linear expansion. The most widely used method is known as the thermal expansion apparatus. This apparatus consists of a rod or sample material, which is heated or cooled while its length changes are recorded. By carefully analyzing the recorded data, researchers can calculate the coefficient of linear expansion for the material.

The interferometric method utilizes interference patterns created by light passing through a material. This technique accurately measures the changes in length resulting from thermal expansion.

Additionally, some advanced techniques like dilatometry, which involves measuring volume changes, and strain gauges, which record dimensional changes, are used for highly precise measurements of the coefficient of linear expansion.

Relationship between the Coefficient of Linear Expansion and Thermal Expansion

Thermal expansion refers to the increase in size or volume of a material as its temperature rises. This expansion occurs because heat causes the atoms and molecules within the material to move more rapidly, increasing their average spacing. As a result, the material takes up more space and expands.

Meanwhile, the coefficient of linear expansion represents the change in length per unit length per unit change in temperature.

The relationship between the coefficient of linear expansion (α) and thermal expansion can be expressed using the following formula:

Thermal expansion = coefficient of linear expansion × Original length × Change in temperature

This formula allows engineers to calculate a material’s dimensions change when its temperature changes.

Factors Influencing the Coefficient 

Several factors can influence the coefficient of linear expansion in materials. These factors can affect how much a material expands or contracts when subjected to changes in temperature.

 Crystal Structure, Bonding Types, and Impurities

The crystal structure of a material heavily influences the coefficient of linear expansion. Different crystal structures can lead to variations in the coefficient. The type of bonding between atoms in a material can also affect its coefficient. For example, materials with stronger intermolecular forces tend to have lower coefficients, while those with weaker ones tend to have higher ones.

Impurities in a material can also impact its coefficient of linear expansion. Their presence can disrupt the regular arrangement of atoms, causing changes in the expansion behavior.

External Factors

External factors such as pressure, magnetic fields, and electric fields can also influence this value. Pressure can alter the arrangement of atoms in a material, affecting its expansion behavior. Similarly, magnetic fields and electric fields can cause changes in the alignment and movement of atoms, leading to variations in the coefficient.

Material Selection

This property is highly dependent on the material properties of a substance. Different materials exhibit different coefficients due to their unique structures and bonding arrangements. For example, materials with stronger intermolecular forces tend to have lower values because their particles are held tightly together, making them less likely to expand significantly with temperature changes.

Material properties such as elasticity, rigidity, and thermal conductivity also play a significant role in determining this value. Elastic materials can return to their original shape after being subjected to deformation caused by thermal expansion. On the other hand, rigid materials are less prone to significant expansion due to their stiffness and resistance to deformation.

Additionally, materials with high thermal conductivity tend to have higher values. High thermal conductivity allows for faster heat transfer, leading to greater expansion or contraction in response to temperature changes.

When dimensional stability is critical, materials with low coefficients are preferred to minimize undesired expansions or contractions. On the other hand, materials with higher coefficients may be utilized in applications where controlled expansion is desired.

Engineers can make informed decisions regarding material selection, product design, and manufacturing processes by understanding how different materials expand or contract with temperature changes. This knowledge helps create efficient and durable structures, products, and systems. If you are looking for a coating material to suit your application needs, please contact our engineers to discuss DFM. Or, learn more about thin film protection capabilities, such as optical properties like transparency and index of refraction.

Mallory McGuinness

As a veteran writer with over a decade of writing experience, Mallory McGuinness has spent the last two years at HZO learning about coating technology from the best minds in the industry. Professionally, Mallory is especially interested in the process of problem-solving and watching how the engineering team develops solutions that ensure business requirements are met. In her free time, you can find Mallory walking her dog Ebbie, fueling up on coffee, watching the Simpsons, and referencing the Simpsons.

All of Mallory’s blogs are reviewed for accuracy before publication.

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