spacer spacer Go to Kaye and Laby Home spacer
spacer
spacer spacer spacer
spacer
spacer
spacer
spacer spacer

You are here:

spacer

Chapter: 2 General physics
    Section: 2.3 Temperature and heat
        SubSection: 2.3.5 Thermal expansion

spacer
spacer

spacer

« Previous Subsection

Next Subsection »

Unless otherwise stated this page contains Version 1.0 content (Read more about versions)

Version 1.1
Updated: 2 December 2010
Previous versions


 

2.3.5 Thermal Expansion

Coefficients of expansion

Coefficients of thermal expansion are normally described either as the increase in length (or volume, esp. for liquids) per unit length at a given temperature, known as the expansivity, α. = (l/L)(dL/dT), or as the mean expansion coefficient over a temperature range, = (1/L0)(ΔLT), where L is the instantaneous length, L0 is an initial length, T is temperature, and ΔL and ΔT are changes in length referenced to a temperature at which L0 was measured. The latter form is more common than the former in engineering texts. Significant differences in numerical data can arise between the two methods. In this section, expansivity data only are given. The latter form can be determined from the former by integration over ΔT. To a first approximation, cubical or volume expansivities of solids are three times the linear expansivity.



Coefficients of cubical expansion of liquids

The following table gives values for the cubical (volume) expansivity (l/V) (dV/dT) at T = 293 K (20 °C). Generally, the expansivity increases with increasing temperature.

Liquid

α/10−5K−1

Liquid

α/10−5K−1

 

 

 

 

Acetic acid

107

            Ethyl bromide

141

Acetone

143

            Ethylene glycol

  57

Alcohol, methyl

118

            Glycerol (glycerine)

  49

Alcohol, ethyl

109

            Mercury*

     18.2

Aniline

  85

            Methyl iodide

120

Benzene

121

            n-Pentane

158

Bromine

112

            Sulphuric acid (100%)

  56

Carbon disulphide

119

            Toluene

107

Carbon tetrachloride

122

            Turpentine

  96

Chloroform

127

            m-Xylene

  99

Ether

163

            Water**

  21

 

 

 

 


      *   See also section 2.2.1 (Density of mercury).
      ** See also section 2.2.1 (Density of water).




Coefficients of linear expansion of solids
The expansivities of the majority of solid materials increase with increasing temperature, and can be represented by an equation of the form α = a + bT + cT2 over limited temperature ranges. The tables in this section cover elements, metal alloys, ceramics and miscellaneous materials.

Many materials exhibit anisotropic thermal expansion behaviour. When single crystals are in common use, data in the respective principal directions are given. Otherwise a homogeneous isotropic polycrystal-line solid is assumed. High levels of anisotropy and/or phase changes can lead to microcracking and thermal expansion hysteresis. Complex multiphase materials possess thermal expansion characteristics which are related to the expansion coefficients and elastic moduli of the individual components. Only approximate ranges can be cited. Further, more detailed data can be obtained from Touloukian et al., (1971).




Elements

α/(10−6 K−1

100 K

200 K

293 K

500 K

800 K

1100 K

1500 K

 

 

 

 

 

 

 

 

Aluminium

12.2

20.3

23.1

26.4

34.0

 –

  –

Antimony*

  9.1

10.5

11.0

11.7

11.7

  –

  –

Beryllium*

  1.3

  7.1

11.3

15.1

19.1

21.6

23.7

Bismuth*

12.3

13.1

13.4

12.7

 –

  –

  –

Boron

–  

–  

  4.7

  5.4

  6.2

  6.8

  –

Cadmium

26.9

29.8

30.8

36.0

 –

  –

  –

Carbon, vitreous

–  

–  

  3.1

  3.3

  3.6

  4.0

  4.6

Carbon, diamond

0.05

  0.4

  1.0

  2.3

  3.7

  4.7

  5.6

Carbon, graphite, polycrystalline**

–  

–  

  7.1

  7.5

  8.1

  8.6

  9.3

Carbon, pyrolytic, para. deposition

–  

–  

23.1

24.4

25.9

27.2

28.6

                            perp. deposition

–  

–  

−0.6

  0.6

  0.8

  1.7

  2.5

Chromium

  2.3

  5.3

    4.9a

  8.8

10.8

12.3

14.9

Cobalt*

  6.8

11.5

13.0

 15.0b

15.2

17.0

  –

Copper

10.3

15.2

16.5

18.3

20.3

23.7

  –

Germanium

  2.4

  4.9

  5.7

  6.5

  7.2

  7.8

  –

Gold

11.8

13.7

14.2

15.4

17.0

19.7

  –

Indium*

25.4

28.1

32.1

  –

  –

  –

Iridium

  4.4

  5.9

  6.4

  7.2

  8.1

  8.5

  9.4

Iron

  5.6

10.1

11.8

14.4

16.2

 16.7c

  23.3c

Lead

25.6

27.5

28.9

33.3

  –

  –

  –

Magnesium*

13.5

 21.4

 24.7

28.9

35.2

  –

  –

Molybdenum

  2.8

 4.6

  4.8

  5.1

  5.7

  6.5

  7.5

Nickel

  6.6

11.3

13.4

15.3

16.8

17.8

20.3

Niobium

  5.2

  6.8

  7.3

  7.8

  8.2

  8.7

  9.3

Palladium

  8.0

10.7

11.8

13.2

14.5

16.3

  –

Platinum

  6.6

  8.5

  8.8

  9.6

10.3

11.1

12.8

Rhodium

  5.0

  7.3

  8.2

  9.3

10.8

12.5

14.8

Silicon

−0.4

  1.5

  2.6

  3.5

  4.1

  4.5

  4.7

Silver

14.2

17.8

18.9

20.6

23.7

27.1

  –

Tantalum

  4.8

  6.0

  6.3

  6.8

  7.2

  7.4

  7.8

Thallium*

25.2

28.0

29.9

34.7

  –

  –

  –

Tin*

16.5

19.6

22.0

27.2

  –

  –

  –

Titanium*

  4.5

  7.4

  8.6

  9.9

11.1

  11.7d

12.9

Tungsten

  2.6

  4.1

  4.5

  4.6

  5.0

  5.3

  5.5

Uranium*

10.0

13.4

13.9

16.9

 24.3e

 22.9e

  –

Vanadium

  5.1

  7.1

  8.4

  9.9

10.9

12.0

14.1

Zinc*

24.5

28.6

30.2

32.8

  –

  –

  –

 

 

 

 

 

 

 

 


     * Crystallographically anisotropic. Data are for isotropic polycrystalline bodies. For anisotropic bodies, data vary.
   ** Data for isotropic POCO Grade AXM-5Q isotropic graphite. Most polycrystalline graphites are anisotropic.
       a Phase change at 311 K.
     b Phase change at 690 K.
       c Phase changes at 1 185 K and 1 667 K.
       d Phase change at 1 156 K.
       e Phase change at 941 K and 1 048 K.



Metal alloys
(Approximate compositions in mass %)

α/(10−6 K−1)

100 K

200 K

293 K

500 K

800 K

1 100 k

 

 

 

 

 

 

 

Aluminium bronze (90 Cu + 5 Al + 4.5 Ni)

12–14

15.9

18.1

20.3

Brass (67 Cu + 33 Zn)

17.5

20.0

22.5

Bronze (85 Cu + 15 Sn)

17.3

19.3

21.9

Cast iron (Fe + 3 C + 2 Si)

11.9

13.1

14.5

Constantan (65 Cu + 35 Ni)

11.2

15.0

17.4

19.2

Cupro-nickel (65 Ni + 30 Cu + 1.5 Fe + 1 Mn)

  9.8

12.7

15.4

18.2

Dural (94 Al + 4 to 5 Cu)

13.1

21.6

27.5

30.1

Inconel

  8.7

11.6

14.4

17.6

Nickel–iron alloys*

 

 

 

 

 

 

      (64 Fe + 36 Ni, Invar)

  1.4

  0.53

   0.13

  5.1

17.1

      (63 Fe + 32 Ni + 4 Co, Super Invar)

  0.0

      (50 Fe + 50 Ni)

  9.9

10.2

13.7

17.3

Phosphor bronze

17.0

20.0

Stainless steel

 

 

 

 

 

 

      ferritic type (14-20 Cr, <1 Ni, e.g. AISI 430)

  -

  -

10.7

10.6

13.3

19.3

      austenitic type (16-22 Cr, 8-20 Ni, e.g. AISI 304)

 11.8

 13.1

14.1

16.2

18.3

19.9

Steel, carbon (0.7–1.4 C)

  6.9

10.7

13.7

16.2

Stellite (65 Co + 20–30 Cr + 6–15 W)

  6.9

  9.3

11.2

14.6

17.2

17.4

Tungsten carbide cermets (4–11 Co)

  3.7

  4.3

  4.8

  5.5

 

 

 

 

 

 

 

     * Note that Ni–Fe–Co alloys have low expansivities below the gamma to alpha phase transformation and high expansions above this temperature. Expansivities and the transition temperature depend critically on the proportions of the major as well as minor elements; see for example. Partridge (1949) or ASM Metals Handbook (1981).



Ceramics, glasses, semiconductors

α/(10−6 K−1)

100 K

200 K

293 K

500 K

800 K

1 100 K

1 500 K

 

 

 

 

 

 

 

 

Alumina (Al2O3)

0.6

3.3

5.5

7.8

8.5

  9.4

10.2

Beryllia (BeO)

5.5

8.0

9.5

10.6

12.4

Boron nitride:

 

 

 

 

 

 

 

     para. hot pressing

0–2

0–2.3

0–3

0–4

1–8

4–9

     perp, hot pressing

~1    

0–1

0–1

0–1

1–2

1–2

Cordierites (Mg2Al4Si5O18)

~0   

~1.0

1–2

Forsterites (Mg2SiO4)

  9.0

10.3

11.8

13.2

Glasses:*

 

 

 

 

 

 

 

     Borosilicate, Pyrex

1.5

2.7

  2.8

  3.3

  5.0

     Borosilicate, crown

7–8

     Dense flint

8–9

     Fused silica

−0.53

  0.13

    0.49

    0.63

   0.47

   0.35

     Soda-lime (Float)

  7.5

Glass–ceramics:*

 

 

 

 

 

 

 

     Corning 9606

  1.9

  3.6

  4.1

  4.6

     Corning 9608

1–2

1–3

1–4

2–5

     Macor machinable

~8

~9

~11

~14

     Zerodur

<0.1

<0.1

  –

Magnesia (MgO)

2.2

  7.6

11.0

13   

15.2

16.2

Magnesium fluoride:

 

 

 

 

 

 

 

    para. c-axis

3.9

14.5

17.0

19.2

    perp. c-axis

1.4

  9.5

11.5

15.8

    polycrystalline

2.2

11.1

13.3

16.8

Mullites (Al6Si2O13)

–   

  3.0

  4.4

  5.2

  6.0

6.5

Porcelains:

 

 

 

 

 

 

 

    aluminous

–   

3–6

4–7

5–8

7–10

    chemical

–   

2–4

    quartz

–   

3–6

4–7

5–8

7–10

Pyrophillite, fired 1 250°C**

–   

2–3

3–4

3–4

Quartz single crystal:

 

 

 

 

 

 

 

    para. c-axis

4.0

  5.2

  6.8

11.4

31.4

    perp. c-axis

9.1

10.3

12.2

19.5

37.6

Sapphire single crystal:

 

 

 

 

 

 

 

    para. c-axis

3.6

  4.1

  4.8

  7.9

  8.9

  9.8

10.9

    perp. c-axis

3.3

  2.2

  6.6

  7.4

  8.3

  9.1

10.0

Semiconductors:

 

 

 

 

 

 

 

    gallium arsenide

1.9

  5.7

  6.5

  7.1

– 

    gallium phosphide

–   

  4.7

  5.5

  6.0

– 

    indium antimonide

2.8

  5.0

  6.1

– 

Silicon carbides

  0.14

  3.3

  4.2

  4.9

  5.5

  6.1

Silicon nitrides

–   

  2.5

  2.7

  3.2

  4.0

  4.5

Steatites (MgSiO3)

–   

6–9

6–9

6–9

Titania (TiO2)

6.5

7.1

  7.5

  8.4

  9.3

  9.8

Zirconia (ZrO2, stabilised)

–  

8–9

9–10

11–13

13–15

13–15

 

 

 

 

 

 

 

 

     *   Glasses and glass–ceramics have expansion coefficients tailorable by varying compostion.
   
 ** May be anisotropic. Expansivity is a strong function of firing temperature.
      Further data on ceramic materials can be found in Morrell (1985).


Miscellaneous materials

α/(10−6 K−1)

293 K

 

 

Building materials:

 

     Brick

3–10

     Cement/concrete

7–14

     Granite

4–7  

     Limestone, marble

8–12

     Portland stone

~3

     Sandstone

~10  

     Slate

5–12

Plastics and plastic composites:

 

     (see also section 3.11.1)

 

     CFRP (cross-ply)

0–3

     GRP (cross-ply)

12–20

     PTFE

525

 

 

Woods:

 

     along grain

3–6

     across grain

35–60

 

 




References

R. Morrell (1985) Handbook of Technical and Engineering Ceramics, Part 1, An Introduction for the Engineer and Designer, HMSO.
Metals Handbook (1990), tenth edition, Vol 1: Properties and selection: Irons, steels and high performance alloys, ASM International, Materials Park, Ohio, USA.
J. H. Partridge (1949) Glass-to-metal seals, Society of Glass Technology, Sheffield.
Y. S. Touloukian et al., (eds.) (1971) Thermophysical Properties of Matter, vols 12 and 13, IFI Plenum, NewYork.

R.Morrell

spacer


spacer
spacer
spacer spacer spacer

Home | About | Table of Contents | Advanced Search | Copyright | Feedback | Privacy | ^ Top of Page ^

spacer

This site is hosted and maintained by the National Physical Laboratory © 2017.

spacer