Thermal Expansion

This experiment is designed to test the student's experimental planning and experimental technique capabilities. Students will freeze an item of their choosing and measure dimensional changes. Consideration will be given to specimen composition and geometry, measurement techniques for both length and temperature, and accepted and calculated coefficients of thermal expansion (CTE).

α = δ / ΔT L = ε / ΔT = (L₁-L₂) / (T₁-T₂)L₁

Depending on the material, standard or accepted CTE values are provided in different temperature scales, so some conversion may be necessary.

T(^oF) = 1.8 T(^oC) + 32 = T(^oR) - 459.67
T(^oR) = 1.8 T(K)
T(^oC) = T(K) - 273.15

Temperature is a measure of the total kinetic energy of the atoms in the system.  In a solid, temperature is a measure of the vibrational energy of the atoms. (from matse.psu.edu/matse81/Spring%202003/LectureNotes)  In the crystal structure of a simple solid, we find that the atoms or ions are arranged in a regular three-dimensional array.  As the temperature of the crystal is raised more thermal energy is injected into the crystal, the ions vibrate with greater and greater amplitude, and the mean distance of separation of the ions increases.  Eventually the amplitudes become sufficiently large to overcome the restraining forces which hold the solid together, and the solid melts. (from Thermal Expansion, by Bernard Yates, Plenum Press, 1972, pp. 1-2)  The coefficient of thermal expansion is inversely proportional to the bond strength of the material: and hence to the melting point of the material.  Hence,

• Polymers, with weak, secondary, intermolecular bonds (low melting points) have very high expansion coefficients.
• Ceramics which are strongly bonded (i.e., ionic or network covalent) have low thermal expansion coefficients.
• Metals with high melting points (strong bonding) have low thermal expansion coefficients.  Low melting point metals have high thermal expansion coefficients.  (from matse.psu.edu/matse81/Spring%202003/LectureNotes)

Cracking due to volume changes may occur when there is a sudden change in temperature, particularly in brittle materials like glass and ceramics.  Thermal shock is a combination of (a) expansion or contraction constraints, (b) temperature gradients due to the thermal conductivity, and (c) phase transformations.  We do not expect thermal shock to be a problem in most metals; metals normally have sufficient ductility to permit deformation rather than fracture.  (from The Science and Engineering of Materials, 2nd Ed., by D.R. Askeland,1989, pp. 766-7)

Examples:

• Bridges
• Power Lines
• Train to Tibet
• Trans-Alaska Pipeline

ASTM Standards

Common CTE Values

Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-6 cm/cm oC)		Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-6 cm/cm oC)
Al	25		Yellow brass	18.9
Cu	16.6		Invar (Fe-36% Ni)	1.54
Fe	12		Polyethylene	100
Pb	29		Polystyrene	70
Mg	25		Polyethylene -- 30% glass fiber	48
Ni	13		Epoxy	55
Si	3		6,6-Nylon	80
Ti	8.5		6,6-Nylon -- 33% glass fiber	20
W	4.5		Fused quartz	0.55
1020 steel	12		Al2O3	6.7
Gray iron	12		Si3N4	3.3
Stainless steel	17.3		SiC	4.3
3003 aluminum alloy	23.2		Partially stabilized ZrO2	10.6

From The Science and Engineering of Materials, 2nd Ed., by D.R. Askeland,1989, p. 760.

Thermal Expansion Coefficients for Wood

αlateral = 3 x 10-6 to 5 x 10-6 per oC αradial = 56 G x 10-6 per oC αtangential = 81 G x 10-6 per oC

more on CTE for wood

Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-6 cm/cm oC)		Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-6 cm/cm oC)
Aluminum	24		Oak (perpendicular to grain)	54
Brass or Bronze	19		Oak (parallel to grain)	5
Ice	51		Pine (perpendicular to grain)	34
Glass	9		Pine (parallel to grain)	5
Brick	9		Steel	12
Granite	8		Iron	11

From Shortley and Williams, 1965.

Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-7 in/in oF)		Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-7 in/in oF)			Material	Linear Coefficient of Thermal Expansion at Room Temperature ( x 10-7 in/in oF)
Aluminum	128			parallel to grain	perpendicular to grain		Brick masonry	34
Brass	104						Concrete masonry	52
Bronze	101		Fir	21	320		Concrete	55
Copper	93		Maple	36	270		Granite	47
Iron, cast	59		Oak	27	300		Limestone	44
Iron, wrought	67		Pine	36	190		Marble	73
Lead	159		To find degrees Celsius, first subtract 32 from the degrees Fahrenheit and then multiply by 5/9.				Plaster	76
Nickel	70						Rubble masonry	35
Steel, carbon	65						Slate	44
Steel, Stainless	99						Glass	50

From Building Construction Illustrated, 3rd Ed by F.D.K. Ching and C. Adams, Wiley, 2000, p. 7.46.