Learn about the importance of Coefficient of Thermal Expansion (CTE) in ceramics—essential for predicting and managing thermal stresses in diverse applications. Explore factors influencing CTE, measurement techniques, and real-world examples showcasing its significance across industries.
3. The objective of this presentation is to explore the concept of Coefficient of
Thermal Expansion (CTE), its role in ceramic materials, and why it is crucial
for predicting and managing thermal stresses in ceramics. We'll discuss
the factors influencing CTE values in ceramics, measurement techniques
used, and the importance of matching CTE in various applications.
Additionally, we will examine real-world examples and challenges faced in
managing CTE, along with potential future directions in this field.
By the end of this presentation, you will have a comprehensive understanding of:
• What Coefficient of Thermal Expansion (CTE) is and why it matters in ceramics.
• How CTE influences the behavior of ceramics under thermal conditions.
• The importance of matching CTE for enhancing ceramic material reliability and
performance.
• Real-world applications and challenges related to CTE in ceramics.
The Key Takeaways
5. What is Coefficient of Thermal Expansion (CTE)?
When materials are heated, their size and volume increase in small increments, in a
phenomenon known as thermal expansion. The coefficient of thermal expansion
(CTE) refers to the rate at which a material expands with increase in temperature. More
specifically, this coefficient is determined at constant pressure and without a phase
change.
The coefficient of thermal expansion is the rate at which the size of a material changes
with respect to temperature change. Size considerations can be made by changes in
length, area or volume, and so there are coefficients derivable for linear, area and volume
expansions.
Volumetric coefficient of thermal expansion is given by
αV =
1
𝑉
𝜕𝑉
𝜕𝑇 𝑝 where 𝑝 = constant pressure, 𝑉 = volume, and
𝜕𝑉
𝜕𝑇
denotes the change in
volume with respect to temperature.
Linear, areal, and volumetric change
6. The pressure here is constant since we are dealing with ceramics but if we want to study
for gases its important to keep the pressure constant as gases will expand at constant
temperatures and reduced pressures.
The Unit
With an assumed constant pressure, linear expansion, area expansion and volume
expansion can be written more simply as:
α𝐿 =
1
𝐿
𝑑𝐿
𝑑𝑇
α𝐴 =
1
𝐴
𝑑𝐴
𝑑𝑇
αV =
1
𝑉
𝑑𝑉
𝑑𝑇
Where 𝐿, 𝐴 and 𝑉 are Length, Area and Volume, respectively, and 𝑇 is temperature.
The unit of measurement for thermal expansion coefficients is the inverse of temperature, oC-1 or K-1
However, extra dimensions such as cm/cm or mm2/mm2 are added to the unit so that it can be
inferred whether the coefficient is linear, area or volumetric.
7. The change in length with temperature for a solid material can be expressed as:
𝑙𝑓 − 𝑙0
𝑙0
= α𝐿 𝑇𝑓 − 𝑇0
∆𝑙
𝑙0
= α𝐿 ∆𝑇
α𝐿 =
1
𝑙
𝑑𝑙
𝑑𝑇
where 𝑙0 and 𝑙𝑓 represent the original and final lengths with the temperature change
from 𝑇0 to 𝑇𝑓. The parameter α𝐿 CTE and has units of reciprocal temperature (K–1) such
as µm / m · K or 10–6/K.
Unit Conversion Table
Representation of Coefficient of Linear Thermal Expansion
To Convert To Multiply by
10–6/K 10–6/oF 0.55556
10–6/oF 10–6/K 1.8
10–6/oC 10–6/K 1
(µm / m )/oF 10–6/K 1.8
(µm / m )/oC 10–6/K 1
9. Why is CTE Important in Ceramics?
The coefficient of thermal expansion indicates how much a material expands per 1℃ rise in
temperature. Fine Ceramics (also known as "advanced ceramics") have low coefficients of
thermal expansion — less than half those of stainless steels.
Ceramics possess low coefficients of thermal expansion, hence their distortion values, with
respect to changes in temperature, are low. The coefficients of thermal expansion depend on
the bond strength between the atoms that make up the materials.
Covalent materials such as diamond, silicon carbide and silicon nitride have strong bonds
between atoms, resulting in low coefficients of thermal expansion. In contrast, materials such
as stainless steel possess weaker bonds between atoms, resulting in much higher coefficients of
thermal expansion in comparison with Fine Ceramics.
10. When exposed to temperature changes, ceramics expand
or contract. If this expansion or contraction is restricted
(e.g., due to bonding with another material), it can lead to
internal stresses within the ceramic component.
• Prevention of Cracking: CTE helps predict and prevent thermal stresses that can
cause cracking or failure in ceramic components.
• Reliability and Durability: Matching CTE between different materials (e.g., ceramics
and metals) in composite structures enhances reliability and durability of the overall
system.
• Performance Optimization: By controlling CTE, we can optimize the performance of
ceramics in various applications, ensuring stability and longevity under different
thermal environments.
Impact of CTE
Thermal Stress in Ceramics
12. • Composition
The composition of the ceramic, especially the selection and design components, is
a major factor in CTE.
• Porosity
The porosity of the ceramic is another major factor in CTE.
• Glazes
The chemistry of the glaze is the main factor in thermal expansion. Other factors
include the degree to which the material particles are dissolved in the melt, the
degree to which the melt is homogeneous, and the degree to which phase
separation and crystallization occur during cooling.
• Metal-ceramic bond
The difference in CTEs between porcelain and metal is a major parameter in
predicting compatibility. In general, the alloy should have a higher CTE than the
porcelain to produce compressive stress in the porcelain when cooling.
14. How To Measure Coefficient of Thermal Expansion?
To determine the thermal expansion coefficient, two physical quantities (displacement and
temperature) must be measured on a sample that is undergoing a thermal cycle. Three of the
main techniques used for CTE measurement are dilatometry, interferometry, and
thermomechanical analysis. Optical imaging can also be used at extreme temperatures. X-ray
diffraction can be used to study changes in the lattice parameter but may not correspond to
bulk thermal expansion.
Mechanical dilatometry techniques are widely used. With this technique, a
specimen is heated in a furnace and displacement of the ends of the specimen
are transmitted to a sensor by means of push rods. The precision of the test is
lower than that of interferometry, and the test is generally applicable to
materials with CTE above 5×10–6/K (2.8×10–6/°F) over the temperature range
of –180 to 900 °C (–290 to1650°F). Push rods may be of the vitreous silica
type, the high-purity alumina type, or the isotropic graphite type. Alumina
systems can extend the temperature range up to 1600 °C (2900 °F) and
graphite systems up to 2500 °C (4500 °F). ASTM Test Method E228 (Ref 2)
cove the determination of linear thermal expansion of rigid solid materials using
vitreous silica push rod or tube dilatometers.
Dilatometry
Fig: Variation of expansion rate as a
function of temperature for a carbon
steel
15. Measurements are made with a thermomechanical analyzer consisting of a specimen holder
and a probe that transmits changes in length to a transducer that translates movements of the
probe into an electrical signal. The apparatus also consists of a furnace for uniform heating, a
temperature-sensing element, calipers, and a means of recording results. ASTM Test
Method E831 (Ref 4) describes the standard test method for linear thermal expansion of solid
materials by thermomechanical analysis. The lower limit for CTE with this method is 5 × 10–
6/K (2.8 × 10–6/°F), but it may be used at lower or negative expansion levels with decreased
accuracy and precision. The applicable temperature range is –120 to 600 °C (–185 to 1110 °F),
but the temperature range may be extended depending on instrumentation and calibration
materials.
With optical interference techniques, displacement of the specimen ends
is measured in terms of the number of wave lengths of monochromatic
light. Precision is significantly greater than with thermomechanical
dilatometry.
Interferometry
Thermomechanical analysis
17. 1. Managing Thermal Stress
In ceramics, managing thermal stress is crucial to prevent cracking and failure. One
effective strategy is to match the Coefficient of Thermal Expansion (CTE) of ceramic
materials with that of surrounding materials or components.
2. Significance of Matching CTE
a) Reducing Thermal Stress:
• Matching CTE between ceramic and metal components minimizes differential
expansion or contraction during temperature changes.
• This reduces the risk of mechanical stress buildup and subsequent cracking or
delamination.
b) Enhancing Reliability and Durability:
• When CTE is matched, it enhances the overall reliability and durability of ceramic-
based systems.
• Components maintain their structural integrity and functionality over prolonged use
and under varying thermal conditions.
18. 3. Examples of CTE Matching
a) Semiconductor Industry:
• Integrated circuits (ICs) require ceramic packages with closely matched CTE to ensure
reliable performance under thermal cycling.
b) Aerospace Applications:
• Ceramic thermal protection tiles on spacecraft are designed with CTE matching to withstand
extreme temperature changes during reentry into Earth's atmosphere.
c) Consumer Electronics:
• Ceramic substrates used in electronic devices (e.g., smartphones) require precise CTE
matching with semiconductor materials to prevent solder joint failures.
4. Strategies for CTE Matching
a) Material Selection:
• Choosing ceramic formulations and compositions with compatible CTE values for specific
applications.
b) Design Optimization:
• Engineering designs that minimize thermal stress by considering CTE matching between
different parts of a system.
20. 1. Semiconductor Industry
• Application: Integrated Circuit (IC) Packaging
• Importance of CTE: Ceramic packages with matched CTE prevent thermal stress on
ICs, ensuring reliability in electronic devices.
• Example: Ceramic ball grid array (BGA) packages for microprocessors and memory
chips.
2. Aerospace Engineering
• Application: Thermal Protection Systems
• Importance of CTE: Ceramic thermal tiles with controlled CTE protect spacecraft from
extreme temperatures during reentry.
• Example: Thermal protection tiles on space shuttles and reentry vehicles.
3. Consumer Electronics
• Application: Electronic Substrates
• Importance of CTE: CTE-matched ceramic substrates prevent solder joint failures in
electronic devices.
• Example: Ceramic substrates in smartphones and LED displays.
21. 4. Manufacturing and Industrial Applications
• Application: Ceramic Tools and Components
• Importance of CTE: CTE control ensures dimensional stability and performance in
high-temperature environments.
• Example: Ceramic cutting tools for machining operations in automotive and
aerospace industries.
5. Energy Industry
• Application: Thermal Insulation
• Importance of CTE: Ceramics with tailored CTE provide efficient thermal insulation in
power generation and distribution systems.
• Example: Ceramic insulators in gas turbines and power plants.
6. Biomedical Engineering
• Application: Dental and Medical Implants
• Importance of CTE: CTE-matched ceramics reduce stress on bone tissue, improving
longevity and biocompatibility of implants.
• Example: Dental crowns and orthopedic implants made from bioinert ceramics.
