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Ti Pure Titanium
Ti Pure Titanium 1
Transitions, melting range (cph) -> (bcc) - T
tr
= 882 °C [1]
mp = 1668 °C [ 1 ]
2
Density (p) thermal expansion coefficient (a) p^soiid)
4540
=
kg m" [2]
a = 1 1 x 10'
3
6
K" [2] 1
The density-temperature relation is given in Figure 1. Density temperature relations for liquid Ti.have been recommended by Iida and Guthrie [2] (p = 4130 - 0.223(T - 1668 °C) kg m" ) and by Watanabe et al [3] (p = 4140 - 0.226 (T 1668 °C) kg m" ) by Vinet [13] (p = 4150 kg m' at the melting point). Mean values were used to derive the following equations: 3
3
3
p ( k g . m ) - 4540 - 0.150 ( T - 2 5 ° C )
(1)
p
(2)
-3
s
(kg.nT ) = 4140-0.225 (T-1668°C) 3
e
3
Density, P (Kg m" )
There is a 3.6% decrease in density at the melting point on the basis of the data given in Table 1.
1000
Temperature (°C)
Figure 1
Density of pure Ti as a function of temperature.
205
2000
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
3
Heat capacity (C ) enthalpy (H -H ) p
T
25
The heat capacity and enthalpy values are given in Figures 2 and 3 respectively, and in Table 1. Dinsdale [1] reported the following values: AH»
2
=
87 Jg"
1
295 JgAH fus 1668 = CJ£)
= 0.965 J g ' K
1
1.00 ~
0.95 1
y
0.90
00—o
D
Heat Capacity, C (
°> 0.85 | 0.80
1
1000 Temperature (°C)
Heat capacity of pure Ti as a function of temperature [1].
25
1
Enthalpy, Hy - H (J g" )
Figure 2
lemperature ("
Figure 3
Enthalpy of pure Ti as a function of temperature [1].
206
2000
Ti
4
PURE T I T A N I U M
Thermal conductivity (X) thermal diffusivity (a)
Thermal Conductivity, ^
34 1
2000
Temperature (°C)
Figure 4
Thermal conductivity of solid Ti as a function of temperature; - - Filippov [8]; Zinovyev [6]; Zinovyev [7]; value calculated from WFL Rule.
Thermal conductivity values for (3-phase solid Ti and liquid Ti [5-8] are given in Figure 4. The most recent investigation indicated a slight increase in conductivity on melting. Values calculated from electrical resistivity data and the WFL Rule are slightly lower and showed a small increase in X on melting. The values suggested by Mills et al [5] are adopted. A™ , =31 W m ^ K
- 1
:X™ = 31 W m ^ K "
1
Thermal diffusivity values shown in Figure 5 were calculated from recommended values of X, C and p.
(mV)
6
Thermal Diffusivity, 10 a
p
Figure 5
i
i
i
i
i
0
500
1000 Temperature (°C)
1500
2000
Thermal diffusivity of Ti as a function of temperature.
207
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
5
Viscosity (r|)
Iida and Shiraishi [10] recommend a value of r| = 2.2 mPas based on the measurements of A g a e v e t a l [11]. m
6
Surface tension (y)
Keene [12] collated the surface tension values for pure titanium and did not recommend a value of y" at the melting point since values varied between 1650 to 1390 mNm" . Vinet [13] reported a value 1525 mNm" using the drop weight method in a vacuum with a residual pressure of 10" mbar. Eustapopoulos et al [14] estimated a temperature coefficient of -0.28 mNm" K" . The principal problem is that titanium has a large solubility for oxygen and it is difficult to remove the oxygen from the metal. Consequently, it is difficult to recommend a value of y and (dy/dT) unless the soluble oxygen concentration is stated. 1
1
1
7
1
1
The value given by Vinet [13] is adopted but may be subject to significant error as a result of oxygen solubility. y
7
(mNm" ) = 1 5 2 5 - 0 . 2 8 ( T - 1 6 6 8 ° C ) 1
e
(3)
Emissivity
Shiraishi [15] reported the following values for the spectral emissivity, s smooth surface of Ti:
x
at 0.65
for a
T °C (e*): 750 (0.505): 1000 (0.485): 1200 (0.47): 1550 (0.45). Shiraishi [15] also reported the following values for the total normal emissivity Polished surface: Oxidised surface:
z
m
T °C (e ): 500 (0.20): 1000 (0.36) T °C (e ): 1000 (0.60) TO
TO
and Touloukian cites for a polished surface T °C ( s ) : 1300 to 1500 °C (0.42). w
References 1.
Dinsdale, A T: SGTE data for pure elements. CALPHAD 15 (1991) 317/425.
2.
Touloukian, Y S: Thermophysical properties of high temperature Vol 1 Elements, publ. Macmillan, New York (1967).
3.
Iida, T and Gurthrie, R I L: The physical properties of liquid metals. Clarendon Press, Oxford (1988).
208
solid
materials:
Ti
PURE T I T A N I U M
4.
Watanabe, S; Ogino, K and Tsu, Y: Handbook of physico-chemical properties at high temperatures, edited by Y Kawai and Y Shiraishi, publ. ISIJ, Tokyo (1988): Chapter 1.
5.
Mills, K C; Monaghan, B J and Keene, B J: Intl. Materials Review 41 (1996) 209/242.
6.
Zinovyev, V E: High temperature transport properties of metals, publ. Metallurgiya, Moscow (1984).
7.
Zinovyev, V E; Polev, V F; Taluts, S G; Zinovyeva, G P and Ilinykh, S A: Phys. Met. Metallog. 61 (6) (1986) 85/92.
8.
Filippov, L P: Intl. J. Heat Mass Transfer, 16 (1973) 865/885.
9.
Seydel, U and Fucke, W: J. Phys. F., Met. Phys. 10 (1980) L203/L206.
10.
Iida, T and Shiraishi, Y: as in ref 4, Chapter 4.
11.
Agaev, A D; Kostikov, V I and Bobkovski, Y N: Izv. Akad. Nauk SSSR, (1980) (3) 43.
12.
Keene, B J: Intl. Materials Review 38 (1993) 157/192.
13.
Vinet, B and Garandet, J P: Proc. Intl. Conf. on High Temperature Capillary held Smolenice Castle, May 1994, edited N Eustathopoulos, publ. Reproprint, Bratislava, 1995, pp 223-227.
14.
Eustapopoulos, N ; Drevet, B and Ricci, E: J. Crystal Growth, 191 (1998) 268/274.
15.
Shiraishi, Y: as in ref 4, Chapter 10.
209
METALLY
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
Table 1 Recommended thermophysical properties for pure Ti T
c
PT
°C 25 100 200 300 400 500 600 700 800 882 882 900 1000 1100 1200 1300 1400 1500 1600 1668 1668° 1700 1800 b
b
c
kgm' 4540 4529 4514 4499 4484 4469 4454 4439 4424 4412 4412 4409 4394 4379 4364 4349 4334 4319 4304 4294 4140 4133 4110
3
P
Jg K 0.522 0.549 0.580 0.601 0.622 0.643 0.661 0.685 0.703 0.718 0.612 0.614 0.626 0.641 0.662 0.689 0.708 0732 0.760 0.783 0.965 0.965 0.965 1
(H -H ) X
Jg 0 40 97 156 217 280 346 413 483 540 627 638 700 763 828 895 965 1037 1112 1189 1484 1515 1611
2 5
1
10 a m V 8.65 8.7 7.3 7.1 6.7 6.5 6.3 6.0 5.9 6.6 7.7 7.8 8.1 8.4 8.6 8.7 9.0 9.1 9.2 9.2 7.8 7.8 7.8 b
X Wm' K" 20.5 20 19.2 19 18.8 18.8 18.4 18.2 18.4 20.8 20.8 21 22.3 23.6 24.9 26.2 27.5 28.8 30.1 31 31 31 31
polished surface and X = 0.65 jam phase transition - density change assumed to be zero 0
melting temperature
210
1
1
TI
mPas
Y mNm"
1
0.50 0.50 0.49 0.49 0.49 0.48 0.47 0.46 0.46 0.46 0.45 2.2
1525 1516 1488
Transitions, melting range (cph) -> (bcc) - T
tr
= 882 °C [1]
mp = 1668 °C [ 1 ]
2
Density (p) thermal expansion coefficient (a) p^soiid)
4540
=
kg m" [2]
a = 1 1 x 10'
3
6
K" [2] 1
The density-temperature relation is given in Figure 1. Density temperature relations for liquid Ti.have been recommended by Iida and Guthrie [2] (p = 4130 - 0.223(T - 1668 °C) kg m" ) and by Watanabe et al [3] (p = 4140 - 0.226 (T 1668 °C) kg m" ) by Vinet [13] (p = 4150 kg m' at the melting point). Mean values were used to derive the following equations: 3
3
3
p ( k g . m ) - 4540 - 0.150 ( T - 2 5 ° C )
(1)
p
(2)
-3
s
(kg.nT ) = 4140-0.225 (T-1668°C) 3
e
3
Density, P (Kg m" )
There is a 3.6% decrease in density at the melting point on the basis of the data given in Table 1.
1000
Temperature (°C)
Figure 1
Density of pure Ti as a function of temperature.
205
2000
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
3
Heat capacity (C ) enthalpy (H -H ) p
T
25
The heat capacity and enthalpy values are given in Figures 2 and 3 respectively, and in Table 1. Dinsdale [1] reported the following values: AH»
2
=
87 Jg"
1
295 JgAH fus 1668 = CJ£)
= 0.965 J g ' K
1
1.00 ~
0.95 1
y
0.90
00—o
D
Heat Capacity, C (
°> 0.85 | 0.80
1
1000 Temperature (°C)
Heat capacity of pure Ti as a function of temperature [1].
25
1
Enthalpy, Hy - H (J g" )
Figure 2
lemperature ("
Figure 3
Enthalpy of pure Ti as a function of temperature [1].
206
2000
Ti
4
PURE T I T A N I U M
Thermal conductivity (X) thermal diffusivity (a)
Thermal Conductivity, ^
34 1
2000
Temperature (°C)
Figure 4
Thermal conductivity of solid Ti as a function of temperature; - - Filippov [8]; Zinovyev [6]; Zinovyev [7]; value calculated from WFL Rule.
Thermal conductivity values for (3-phase solid Ti and liquid Ti [5-8] are given in Figure 4. The most recent investigation indicated a slight increase in conductivity on melting. Values calculated from electrical resistivity data and the WFL Rule are slightly lower and showed a small increase in X on melting. The values suggested by Mills et al [5] are adopted. A™ , =31 W m ^ K
- 1
:X™ = 31 W m ^ K "
1
Thermal diffusivity values shown in Figure 5 were calculated from recommended values of X, C and p.
(mV)
6
Thermal Diffusivity, 10 a
p
Figure 5
i
i
i
i
i
0
500
1000 Temperature (°C)
1500
2000
Thermal diffusivity of Ti as a function of temperature.
207
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
5
Viscosity (r|)
Iida and Shiraishi [10] recommend a value of r| = 2.2 mPas based on the measurements of A g a e v e t a l [11]. m
6
Surface tension (y)
Keene [12] collated the surface tension values for pure titanium and did not recommend a value of y" at the melting point since values varied between 1650 to 1390 mNm" . Vinet [13] reported a value 1525 mNm" using the drop weight method in a vacuum with a residual pressure of 10" mbar. Eustapopoulos et al [14] estimated a temperature coefficient of -0.28 mNm" K" . The principal problem is that titanium has a large solubility for oxygen and it is difficult to remove the oxygen from the metal. Consequently, it is difficult to recommend a value of y and (dy/dT) unless the soluble oxygen concentration is stated. 1
1
1
7
1
1
The value given by Vinet [13] is adopted but may be subject to significant error as a result of oxygen solubility. y
7
(mNm" ) = 1 5 2 5 - 0 . 2 8 ( T - 1 6 6 8 ° C ) 1
e
(3)
Emissivity
Shiraishi [15] reported the following values for the spectral emissivity, s smooth surface of Ti:
x
at 0.65
for a
T °C (e*): 750 (0.505): 1000 (0.485): 1200 (0.47): 1550 (0.45). Shiraishi [15] also reported the following values for the total normal emissivity Polished surface: Oxidised surface:
z
m
T °C (e ): 500 (0.20): 1000 (0.36) T °C (e ): 1000 (0.60) TO
TO
and Touloukian cites for a polished surface T °C ( s ) : 1300 to 1500 °C (0.42). w
References 1.
Dinsdale, A T: SGTE data for pure elements. CALPHAD 15 (1991) 317/425.
2.
Touloukian, Y S: Thermophysical properties of high temperature Vol 1 Elements, publ. Macmillan, New York (1967).
3.
Iida, T and Gurthrie, R I L: The physical properties of liquid metals. Clarendon Press, Oxford (1988).
208
solid
materials:
Ti
PURE T I T A N I U M
4.
Watanabe, S; Ogino, K and Tsu, Y: Handbook of physico-chemical properties at high temperatures, edited by Y Kawai and Y Shiraishi, publ. ISIJ, Tokyo (1988): Chapter 1.
5.
Mills, K C; Monaghan, B J and Keene, B J: Intl. Materials Review 41 (1996) 209/242.
6.
Zinovyev, V E: High temperature transport properties of metals, publ. Metallurgiya, Moscow (1984).
7.
Zinovyev, V E; Polev, V F; Taluts, S G; Zinovyeva, G P and Ilinykh, S A: Phys. Met. Metallog. 61 (6) (1986) 85/92.
8.
Filippov, L P: Intl. J. Heat Mass Transfer, 16 (1973) 865/885.
9.
Seydel, U and Fucke, W: J. Phys. F., Met. Phys. 10 (1980) L203/L206.
10.
Iida, T and Shiraishi, Y: as in ref 4, Chapter 4.
11.
Agaev, A D; Kostikov, V I and Bobkovski, Y N: Izv. Akad. Nauk SSSR, (1980) (3) 43.
12.
Keene, B J: Intl. Materials Review 38 (1993) 157/192.
13.
Vinet, B and Garandet, J P: Proc. Intl. Conf. on High Temperature Capillary held Smolenice Castle, May 1994, edited N Eustathopoulos, publ. Reproprint, Bratislava, 1995, pp 223-227.
14.
Eustapopoulos, N ; Drevet, B and Ricci, E: J. Crystal Growth, 191 (1998) 268/274.
15.
Shiraishi, Y: as in ref 4, Chapter 10.
209
METALLY
RECOMMENDED VALUES OF THERMOPHYSICAL PROPERTIES FOR SELECTED COMMERCIAL ALLOYS
Table 1 Recommended thermophysical properties for pure Ti T
c
PT
°C 25 100 200 300 400 500 600 700 800 882 882 900 1000 1100 1200 1300 1400 1500 1600 1668 1668° 1700 1800 b
b
c
kgm' 4540 4529 4514 4499 4484 4469 4454 4439 4424 4412 4412 4409 4394 4379 4364 4349 4334 4319 4304 4294 4140 4133 4110
3
P
Jg K 0.522 0.549 0.580 0.601 0.622 0.643 0.661 0.685 0.703 0.718 0.612 0.614 0.626 0.641 0.662 0.689 0.708 0732 0.760 0.783 0.965 0.965 0.965 1
(H -H ) X
Jg 0 40 97 156 217 280 346 413 483 540 627 638 700 763 828 895 965 1037 1112 1189 1484 1515 1611
2 5
1
10 a m V 8.65 8.7 7.3 7.1 6.7 6.5 6.3 6.0 5.9 6.6 7.7 7.8 8.1 8.4 8.6 8.7 9.0 9.1 9.2 9.2 7.8 7.8 7.8 b
X Wm' K" 20.5 20 19.2 19 18.8 18.8 18.4 18.2 18.4 20.8 20.8 21 22.3 23.6 24.9 26.2 27.5 28.8 30.1 31 31 31 31
polished surface and X = 0.65 jam phase transition - density change assumed to be zero 0
melting temperature
210
1
1
TI
mPas
Y mNm"
1
0.50 0.50 0.49 0.49 0.49 0.48 0.47 0.46 0.46 0.46 0.45 2.2
1525 1516 1488