Thermal Conductivity

The thermal conductivity of a-alumina single crystals as a function of temperature is given in Table 16 (from [2, 23]). Heat is conducted through a nonmetallic solid by lat­tice vibrations or phonons. The mean free path of the phonons determines the thermal conductivity and depends on the temperature, phonon-phonon interactions, and scat­tering from lattice defects in the solid. At temperatures below the low temperature maximum (below about 40°K), the mean free path is mainly determined by the sample size because of phonon scattering from the sample surfaces. Above the maximum, the

Table 15 The pressure of AlO vapor and total vapor pressure in equilibrium with a-Al2O3 as a function of temperature, for reducing and neutral conditions

Temp. (K)

Log vapor pressure of AlO, P (bar) [29]

1,520

-15

1,630

-13

1,750

-11

1,900

-9

2,020

-7

2,290

-5

Temp. (K)

Log total vapor pres­sure, P (atm.) [2, 31]

2,309

-5.06

2,325

-4.99

2,370

-4.78

2,393

-4.77

2,399

-4.66

2,459

-4.42

2,478

-4.24

2,487

-4.04

2,545

-3.70

2,565

-3.89

2,605

-3.72

Table 16 Thermal conductivity of single crystal a-Al2O3

Temp. (K)

Conductivity (J s-1 mK-1)

Temp. (°C)

Conductivity (J s-1 mK-1)

0

0

25

36

10

1,200

100

29

20

3,800

300

16

40

5,900

500

10

50

5,000

700

7.5

60

2,300

900

6.3

80

790

1,100

5.9

100

400

1,300

5.9

200

100

1,500

5.4

1,700

5.9

1,900

6.3

From [2, 23]

conductivity decays approximately exponentially because of phonon-phonon interac­tions. At high temperatures (above about 800°C), the phonon mean free path is of the order of a lattice distance, and becomes constant with temperature. There is a much more detailed discussion of phonon behavior in ceramics and glasses in [23, 32]. The velocity v of a phonon or sound wave in a solid can be found from the formula

v2 = Elp (8)

in which E is Young’s modulus and p is the density, so this velocity in alumina is 10.1(10)3 m s-1 at 25°C. This result is close to the measured value of 10.845 m s-1.