TMA is a highly sensitive method for measuring how the coefficient of thermal expansion changes with temperature. It can also be used to measure volumetric expansion, thermal relaxation, stress relief, and dimensional changes due to phase transitions. Modulated TMA can be used to differentiate between the reversing and non-reversing effects due to temperature.

Typical Experimental Results:


Detection of Indium Melting Point


Thermal expansion of Silicon Nitride.


3-Point Bending Compression Contraction
Creep Analysis Distortion Temperature Dynamic TMA
Expansion Fiber Testing Film Penetration
Film Tensile Testing Glass Transition Isostrain Shrinkage Force
Mechanical Characterization Modulated TMA Multilayer Film Analysis
Softening Point Stress/Strain Behavior Stress Relaxation
Tension Thermal Expansion Viscoelastic Characterization


For more information please read our application notes:
Coefficient of Thermal Expansion Measurement using TMA


Instruments: TA Instruments Q400EM Thermomechanical Analyzer


Key Specifications:

Temperature Range -150 to 1000°C
Temperature Precision ± 1°C
Measurement Precision ± 0.1%
Displacement Resolution < 0.5 nm
Force Range 0.001 to 2 N
Force Resolution 0.001 N
Frequency Range 0.01 to 2 Hz
Atmosphere Inert, Oxidizing, or Reactive Gases


Coefficient of Thermal Expansion Measurement using TMA


When a material is heated, its physical dimensions will change. Typically when heated, the material will expand, although there are some rare exceptions. This expansion is due to increased movement of the constituent atoms at elevated temperature. Elevated temperature forces these atoms to maintain a greater average separation distance than they would at a lower temperature.


The coefficient of thermal expansion (CTE), α, describes how much the size of an object will change with temperature. While the CTE is normally given as just a single number, it will change depending on the temperature. The magnitude of a given materials CTE is strongly related to the bond energy between its constituent atoms. For example, metals and polymers have much higher CTE’s than ceramics. This can be illustrated using a schematic plot of bond energy vs. atomic separation, as seen in Figure 1.




As a material is heated, its constituent atoms gain more kinetic energy and vibrate with larger amplitudes. When there are many atoms in close proximity, they will spread out to accommodate the larger amplitude, causing the material to expand. The minimum in potential energy is much lower for ceramics than for polymers, increasing the amount of heat required to melt the material as well as reducing the change in interatomic spacing.


Knowing the precise amount of thermal expansion that will occur within a system is critical for many material applications. The components in an internal combustion engine will expand as the engine warms up to operating temperature. Supersonic jets will stretch during flight because of the heat generated by friction with the air. Casting molds will change dimensions as a molten metal is poured in. Any large-scale structures will experience large dimensional changes with small changes in temperature and must be designed to accommodate them.


Ebatco NAT Lab uses a Q400 Thermomechanical Analyzer (TMA) from TA Instruments to accurately measure the CTE of materials. This instrument uses a flat, quartz probe to measure the amount of linear expansion in a material as it is heated. With a displacement resolution of 0.5 nm and a temperature range of -150°C to 1000°C, it can measure the CTE of a wide variety of materials across a broad temperature range. The results from thermal expansion tests on aluminum and silicon nitride can be seen in Figures 2 and 3.







ASTM Number Title Website Link
E831-14 Standard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis Link
E2347-11 Standard Test Method for Indentation Softening Temperature by Thermomechanical Analysis Link
E2092-13 Standard Test Method for Distortion Temperature in Three-Point Bending by Thermomechanical Analysis Link
E1545-11 Standard Test Method for Assignment of the Glass Transition Temperatures by Thermomechanical Analysis Link
E1824-13 Standard Test Method for Assignment of the Glass Transition Temperatures Using Thermomechanical Analysis: Tension Method Link
E2769-15 Standard Test Method for Elastic Modulus by Thermomechanical Analysis Using Three-Point Bending and Controlled Rate of Loading Link
E1363-13 Standard Test Method for Temperature Calibration of Thermomechanical Analyzers Link
E2206-11 Standard Test Method for Force Calibration of Thermomechanical Analyzers Link
E2113-13 Standard Test Method for Length Change Calibration of Thermomechanical Analyzers Link
E2918-13 Standard Test Method for Performanc Validation of Thermomechanical Analyzers Link


ISO Number Title Website Link
11359 Plastics– Thermomechanical analysis (TMA) Link
12111 Metallic materials– Fatigue testing– Strain-controlled thermomechanical fatigue testing method Link