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Thermal diffusivity of plasma sprayed alumina coatings
Mat. Res. Bull., Vol. 26, pp. 1363-1369, 1991. Printed in the USA. 0025-5408/91 $3.00 + .O0 Copyright (c) 1991 Pergamon Press plc.
THERMAL D I F F U S I V I T Y OF PLASMA SPRAYED ALUMINA COATINGS
A. Rudajevov~ Institute of Plasma Physics Czechoslovak Academy of Sciences Pod vod@renskou v6~i 4, 182 ll Prague 8, Czechoslovakia (Received July 9, 1991; Refereed) ABSTRACT It is demonstrated in the paper, that the determination of the parameter thermal diffusivity of plasma sprayed coatings from refractory oxides (type ZrO2, A12O 3) must involve the usually neglected partial contribution of photon mechanism of heat transfer by the coating. The influence of the partial transparency of the coating for impinging radiation on the values of thermal diffusivity determined by the flash method is discussed. Oefinitions are given of the intrinsic thermal diffusivity, which is a material constant, and effective thermal diffusivity, which depends, above all, on the coating thickness and impinging radiation wavelength. The relation between the mechanism of heat transfer by the coating and the value of thermal diffusivity was tested experimentally on two types of alumina coatings, namely A 99 and A 96. MATERIALS
INBEX:
alumina coatings
Introduction Plasma sprayed alumina coatings are used to protect a material against chemical and thermal effects. Like with other materials in use as a thermal protection, also in this case the knowledge of the thermal diffusivity values is needed. In plasma sprayed alumina coatings, the thermal diffusivity value is given first of all by porousness and phase composition. The study of the dependence of thermal diffusivity on these parameters has been given much attention (e.g. (1, 2)), but the relationship of thermal diffusivity and transmittance of alumina coatings for the impinging radiation has received little attention so far. The work to 1363
1364
A. RUDAJEVOV.4
Vol. 26, No. 12
be reported will deal with this problem. Plasma sprayed coatings of pure alumina belong to partly transparent materials. In partly transparent materials we define the so-called infinite thickness (3) i ~ , for which it applies 3~5
/i/
where ~ is the absorption coefficient, which strongly depends on the wavelength of the impinging radiation. Kingery (4) states that in the visible part of the spectrum the absorption coeffioiegt of partly transparent refractory materials is from 10 to 30 cm -±, i.e. in these materials the infinite thickness ranges from 0.1 to 0.3 cm. The infinite thickness is thus such a thickness when the material only reflects and uniformly absorbs the impinging radiation. As a rule, plasma sprayed alumina coatings are used in thick nesses smaller than the infinite thickness. This has to be borne in mind when we determine thermal diffusivity by the flash method as well as in our application of the thermal diffusivity parameter in practice. Experiment A l u m i n a c o a t i n g s were s p r a y e d by means of plasma g e n e r a t o r PAL 160 with water stabilization and a p e r f o r m a n c e of 160 kW. The a l u m i n a powder was a i r f e d i n t o t h e plasma i n an amount of 19 - 20 kg per h o u r . The s p r a y d i s t a n c e was 250 mm. Two s o r t s of a l u m i n a c o a t i n ~ were o b s e r v e d from s p r a y m a t e r i a l s A 99 and A 96, whose c o m p o s i t i o n i s g i v e n i n T a b l e 1. Thermal d i f f u s i v i t y was measured by t h e f l a s h method adapted to m e a s u r i n g two l a y e r s . The sample was i r r a d i a t e d by means of t h e Xe p u l s e g e n e r a t o r w i t h t h e p u l s e l e n g t h of 1.1 ms ( w a v e l e n g t h s up to 1 ~ m ) . The t h i c k n e s s of c o a t i n g s r a n ged from 0.18 to 0 . 8 2 , t h e t h i c k n e s s of t h e pad made o f corrosionresisting s t e e l was 2.5 mm. The a b s o r p t i v i t y of c o a t i n g s on the pad was e s t a b l i s h e d by t h e p r o c e d u r e d e s c r i b e d i n ( 5 ) . The c o a t i n g b l a c k i n g was made w i t h c a n d l e s o o t .
Results The coatings prepared from alumina A 99 are partly transparent for the impinging radiation. The transmittance is demonstrated in Fig. l, where the time dependence of the relative temperature measured on the rear side of the sample (metal pad) after the coating irradiation is plotted. Curve /1/ corresponds to the time dependence of the relative temperature for the metal pad without a coating, curve /2/ for unblackened surface of the coating with a pad, and curve /3/ for the same system but with blackened surface. In the flash method one of the characteristic parameters is the so-called half-life, which is a period, during which the temperature on the sample rear side grows to the maximum half. Figure 1 makes it evident that blackening the coating surface leads to a growth of the half-life. For coatings 0.18 - 0.27 mm thick we h~ve found a ratio of half-lives ( t , ~ ) b / ( t , ~ ) ~ 1.05, where (t,r b is the half-life for a coating o~ a p a d w l t h blackened surface, and (t~&) w is the half-life for the same system but without blackened surface. For other coating thicknesses this ratio has been found constant, namely, 1.14~ 2%. In Fig. 2 we plotted the dependence of thermal diffusivities of alumina coatings A 99
Vol. 26, No. 12
with blackened ings. Chemical
ALUMINA COATINGS
and unblackened
composition
surfaces
1365
on the thickness
TABLE I of sprayed powders
A1203 ( w t . % )
Materials
of coat-
A 99
min.
98.7
A 96
min.
95.5
admixtures Si02,Fe203,CaO TiO2,SiO2,Fe203~CaO
1
0.5
|
0
I
0.5
t[s]
FIG.
1
i
The time dependence of the relative temperature for the metal pad without a coating /i/, for unblackened surface of the coating with pad /2/ and for the same system with blackened surface /3/; T is temperature, t is time
Absorptivity Materials
TABLE II of plasma sprayed alumina coatings thickness
i /mm/
absorptivity
A 99
0.19 0.28 0.33 0.37 - 0.82
0.35 0.31 0.30 0.28 ~ 4%
A 96
0.50
0.86
-
0.70
~ 3%
1366
A. R U D A J E V O V ~
Vol. 26, No. 12
E u t~
0.03 0.02 0.01
v X
vX
~ --
X
..
y
.,,v
A"
2
I
0
0.5
I
][mm]
1
FIG. 2 The dependence of the thermal diffusivity ( a ) on the thickness of the coat ( 1 ); /i/ for unblackened surface and /2/ for bl-ackened surface Results of measurements of the radiation absorptivity (to l ~ m ) for the system coating-pad are presented in Table II. Alumina A 96 coatings 0.5 - 0.7 mm thick are not transparent for the impinging radiation, i.e. the thermal diffusivity of coatings with blackened and unblackened surfaces is identical. The temperature dependence of the thermal diffusivity of these coatings in a normal atmosphere is shown in Fig. 3. Oiscussion From the results it ensues that plasma sprayed alumina A 99 coatings are transparent for the impinging radiation (Fig. l). The solution of the heat conduction equation, on which the measurement of thermal diffusivity by the flash method is based, involves as one of the boundary conditions complete and instantaneous absorption of the radiation on the surface of the sample (6). In partly transparent alumina coatings this presumption is not satisfied unless the coating surface is blackened. Neglecting the transparency of the coating in the determination of thermal diffusivity by the flash method adapted to two layers leads to a distortion of the values found. The greater the distortion, the larger the portion of the coating transparent part. The flash
Vol. 26, No. 12
ALUMINA COATINGS
1367
0.01
l,j I,...I
!
0
SO0 FIG.
The dependence
I
of the thermal
T [ °C ]
I000
3
diffusivity
( a ) on the temperature
method can yield the so-called intrinsic thermal diffusivity, i.e. when the heat transfer mechanism is only of phonon nature. The intrinsic thermal diffusivity is a material constant, and as evident from Fig. 2, it does not depend on the coating thickness. Plasma sprayed coatings of pure alumina A 99 are most frequently used in the thickness domains smaller than the infinite thickness. Under these thicknesses, heat propagates in the coating due to radiation as well as conduction. The system of a partly transparent coating on a metal pad can be divided into three spheres. V 1 is the relative coating volume, where the energy transfer is due to both radiation and conduction, V 2 is the relative coating volume, where heat is transferred by conduction only, and V 3 is the relative volume of the metal pad. The surface sphere is characterized by thermal conductivity k I (thermal conductivity is equal to the product of thermal diffusivity, specific heat and density). In the respective sphere this value is not a material constant and depends on the layer thickness and the wavelength of the impinging radiation. The spheres of volume V2, where energy transfer is only due to conduction, can be characterized by thermal conductivity k 2. The sphere of the metal pad of relative volume V 3 has thermal conductivity k 3. If a perpendicular heat flow impinges on these three layers, then after (4) the value of the total thermal conductivity k is given by the relation:
klk2k 3 k =
Vlk2k3+V2klk3+V3klk2
1368
A. RUDAJEVOV,~
Vol. 26, No. 12
For the ratio of thermal conductivities of unblackened (k w) and blackened surfaces (k b) it holds:
kw kb
-
Vlklk 3
+
V2klk 3
+
V3klk 2
Vlk2k3
+
V2klk 3
+
V3klk 2
/3!
From the above relation it follows that the ratio of thermal conductivities of blackened and unblackened samples approaches 1 for extreme thicknesses, i.e. very thin, actually very thick coatings. Coatings of small thicknesses when a part of the radiation impinges directly on the metal pad and the ratio of half-lives of blackened and unblackened sample surfaces approaches i can be neglected from the viewpoint of heat conduction. In the thickness domains where the ratio of half-lives of blackened and unblackened sample surfaces is equal to 1.14, the total vaiue of thermal conductivity (diffusivity) depends on the portions of transparent and non-transparent parts of the coating. For the practically applied thickness domains of plasma sprayed coatings, the partly transparent layer makes and appreciable portion, which leads to an important conclusion: for practical purposes, plasma sprayed partly transparent coatings cannot be characterized by intrinsic thermal conductivity (diffusivity), but by effective thermal conductivity, which will depend on the coating thickness and the wavelength of the impinging radiation. After this value of effective thermal conductivity has been found, its application will be real only under the conditions it was determined. Transparency and absorptivity of the materials for radiation is given by their absorption coefficient, which depends on the sort and amount of admixtures. In contrast to alumina A 99 coatings, alumina A 96 coatings were not transparent for the impinging radiation. In a normal atmosphere, in the non-transparent coatings it was possible to find the temperature dependence of thermal diffusivity. It dropped with temperature to 750 o C. Conclusions In the present paper it was found that plasma sprayed A 99 alumina coatings were partially transparent, whereas A 96 alumina coatings were not trasparent for impinging radiation. The absorptivity of impinging radiation in A 96 alumina coatings was three times higher than in A 99 alumina coatings. In the partially transparent coatings two layers can be distinguished according to the mechanisms of heat transfer by the coating. In the first, surface layer energy transfer takes place by means of both photon and phonon mechanisms. In the second layer energy is only transferred by phonons. When the thickness of the surface partially transparent part of the coating is not negligible in comparison with the thickness of the non-transparent part of the coating, the following two conclusions are of importance: a) the flash method is not suitable for determining the thermal diffusivity, b) the value of intrinsic thermal diffusivity obtained by measurements is not applicabie to practical purposes.
Vol. 26, No. 12
ALUMINA COATINGS
1369
The partially transparent coatings should be characterized by the so-called effective thermal diffusivity, which is not a material constant and depends, above all, on the coating thickness and impinging radiation wavelength. The intrinsic thermal diffusivity of the alumina coatings of A 99 and A 96 is practically the same at room temperature. References 1. 2. 3. 4.
H.C.Fiedler, Mat.Res.Soc.Symp. Proc.30,173 (1984) G.F.Hurley and O.G.Frank, Am. Ceram. Soc. Bull.58,5 (1979) R.Gardon, J.Am.Ceram. Soc.39,378 (1956) W.O.Kingery, Property Measurements at High Temperatures p.93, John Wiley,Sons,Inc. New York (1959) 5. A.Rudajevov~, Silik@ty 3__3,61 (1989) 6. K.B.Larsen and K.Koyama, J.Appl.Phys.3__9,4408 (1968)
THERMAL D I F F U S I V I T Y OF PLASMA SPRAYED ALUMINA COATINGS
A. Rudajevov~ Institute of Plasma Physics Czechoslovak Academy of Sciences Pod vod@renskou v6~i 4, 182 ll Prague 8, Czechoslovakia (Received July 9, 1991; Refereed) ABSTRACT It is demonstrated in the paper, that the determination of the parameter thermal diffusivity of plasma sprayed coatings from refractory oxides (type ZrO2, A12O 3) must involve the usually neglected partial contribution of photon mechanism of heat transfer by the coating. The influence of the partial transparency of the coating for impinging radiation on the values of thermal diffusivity determined by the flash method is discussed. Oefinitions are given of the intrinsic thermal diffusivity, which is a material constant, and effective thermal diffusivity, which depends, above all, on the coating thickness and impinging radiation wavelength. The relation between the mechanism of heat transfer by the coating and the value of thermal diffusivity was tested experimentally on two types of alumina coatings, namely A 99 and A 96. MATERIALS
INBEX:
alumina coatings
Introduction Plasma sprayed alumina coatings are used to protect a material against chemical and thermal effects. Like with other materials in use as a thermal protection, also in this case the knowledge of the thermal diffusivity values is needed. In plasma sprayed alumina coatings, the thermal diffusivity value is given first of all by porousness and phase composition. The study of the dependence of thermal diffusivity on these parameters has been given much attention (e.g. (1, 2)), but the relationship of thermal diffusivity and transmittance of alumina coatings for the impinging radiation has received little attention so far. The work to 1363
1364
A. RUDAJEVOV.4
Vol. 26, No. 12
be reported will deal with this problem. Plasma sprayed coatings of pure alumina belong to partly transparent materials. In partly transparent materials we define the so-called infinite thickness (3) i ~ , for which it applies 3~5
/i/
where ~ is the absorption coefficient, which strongly depends on the wavelength of the impinging radiation. Kingery (4) states that in the visible part of the spectrum the absorption coeffioiegt of partly transparent refractory materials is from 10 to 30 cm -±, i.e. in these materials the infinite thickness ranges from 0.1 to 0.3 cm. The infinite thickness is thus such a thickness when the material only reflects and uniformly absorbs the impinging radiation. As a rule, plasma sprayed alumina coatings are used in thick nesses smaller than the infinite thickness. This has to be borne in mind when we determine thermal diffusivity by the flash method as well as in our application of the thermal diffusivity parameter in practice. Experiment A l u m i n a c o a t i n g s were s p r a y e d by means of plasma g e n e r a t o r PAL 160 with water stabilization and a p e r f o r m a n c e of 160 kW. The a l u m i n a powder was a i r f e d i n t o t h e plasma i n an amount of 19 - 20 kg per h o u r . The s p r a y d i s t a n c e was 250 mm. Two s o r t s of a l u m i n a c o a t i n ~ were o b s e r v e d from s p r a y m a t e r i a l s A 99 and A 96, whose c o m p o s i t i o n i s g i v e n i n T a b l e 1. Thermal d i f f u s i v i t y was measured by t h e f l a s h method adapted to m e a s u r i n g two l a y e r s . The sample was i r r a d i a t e d by means of t h e Xe p u l s e g e n e r a t o r w i t h t h e p u l s e l e n g t h of 1.1 ms ( w a v e l e n g t h s up to 1 ~ m ) . The t h i c k n e s s of c o a t i n g s r a n ged from 0.18 to 0 . 8 2 , t h e t h i c k n e s s of t h e pad made o f corrosionresisting s t e e l was 2.5 mm. The a b s o r p t i v i t y of c o a t i n g s on the pad was e s t a b l i s h e d by t h e p r o c e d u r e d e s c r i b e d i n ( 5 ) . The c o a t i n g b l a c k i n g was made w i t h c a n d l e s o o t .
Results The coatings prepared from alumina A 99 are partly transparent for the impinging radiation. The transmittance is demonstrated in Fig. l, where the time dependence of the relative temperature measured on the rear side of the sample (metal pad) after the coating irradiation is plotted. Curve /1/ corresponds to the time dependence of the relative temperature for the metal pad without a coating, curve /2/ for unblackened surface of the coating with a pad, and curve /3/ for the same system but with blackened surface. In the flash method one of the characteristic parameters is the so-called half-life, which is a period, during which the temperature on the sample rear side grows to the maximum half. Figure 1 makes it evident that blackening the coating surface leads to a growth of the half-life. For coatings 0.18 - 0.27 mm thick we h~ve found a ratio of half-lives ( t , ~ ) b / ( t , ~ ) ~ 1.05, where (t,r b is the half-life for a coating o~ a p a d w l t h blackened surface, and (t~&) w is the half-life for the same system but without blackened surface. For other coating thicknesses this ratio has been found constant, namely, 1.14~ 2%. In Fig. 2 we plotted the dependence of thermal diffusivities of alumina coatings A 99
Vol. 26, No. 12
with blackened ings. Chemical
ALUMINA COATINGS
and unblackened
composition
surfaces
1365
on the thickness
TABLE I of sprayed powders
A1203 ( w t . % )
Materials
of coat-
A 99
min.
98.7
A 96
min.
95.5
admixtures Si02,Fe203,CaO TiO2,SiO2,Fe203~CaO
1
0.5
|
0
I
0.5
t[s]
FIG.
1
i
The time dependence of the relative temperature for the metal pad without a coating /i/, for unblackened surface of the coating with pad /2/ and for the same system with blackened surface /3/; T is temperature, t is time
Absorptivity Materials
TABLE II of plasma sprayed alumina coatings thickness
i /mm/
absorptivity
A 99
0.19 0.28 0.33 0.37 - 0.82
0.35 0.31 0.30 0.28 ~ 4%
A 96
0.50
0.86
-
0.70
~ 3%
1366
A. R U D A J E V O V ~
Vol. 26, No. 12
E u t~
0.03 0.02 0.01
v X
vX
~ --
X
..
y
.,,v
A"
2
I
0
0.5
I
][mm]
1
FIG. 2 The dependence of the thermal diffusivity ( a ) on the thickness of the coat ( 1 ); /i/ for unblackened surface and /2/ for bl-ackened surface Results of measurements of the radiation absorptivity (to l ~ m ) for the system coating-pad are presented in Table II. Alumina A 96 coatings 0.5 - 0.7 mm thick are not transparent for the impinging radiation, i.e. the thermal diffusivity of coatings with blackened and unblackened surfaces is identical. The temperature dependence of the thermal diffusivity of these coatings in a normal atmosphere is shown in Fig. 3. Oiscussion From the results it ensues that plasma sprayed alumina A 99 coatings are transparent for the impinging radiation (Fig. l). The solution of the heat conduction equation, on which the measurement of thermal diffusivity by the flash method is based, involves as one of the boundary conditions complete and instantaneous absorption of the radiation on the surface of the sample (6). In partly transparent alumina coatings this presumption is not satisfied unless the coating surface is blackened. Neglecting the transparency of the coating in the determination of thermal diffusivity by the flash method adapted to two layers leads to a distortion of the values found. The greater the distortion, the larger the portion of the coating transparent part. The flash
Vol. 26, No. 12
ALUMINA COATINGS
1367
0.01
l,j I,...I
!
0
SO0 FIG.
The dependence
I
of the thermal
T [ °C ]
I000
3
diffusivity
( a ) on the temperature
method can yield the so-called intrinsic thermal diffusivity, i.e. when the heat transfer mechanism is only of phonon nature. The intrinsic thermal diffusivity is a material constant, and as evident from Fig. 2, it does not depend on the coating thickness. Plasma sprayed coatings of pure alumina A 99 are most frequently used in the thickness domains smaller than the infinite thickness. Under these thicknesses, heat propagates in the coating due to radiation as well as conduction. The system of a partly transparent coating on a metal pad can be divided into three spheres. V 1 is the relative coating volume, where the energy transfer is due to both radiation and conduction, V 2 is the relative coating volume, where heat is transferred by conduction only, and V 3 is the relative volume of the metal pad. The surface sphere is characterized by thermal conductivity k I (thermal conductivity is equal to the product of thermal diffusivity, specific heat and density). In the respective sphere this value is not a material constant and depends on the layer thickness and the wavelength of the impinging radiation. The spheres of volume V2, where energy transfer is only due to conduction, can be characterized by thermal conductivity k 2. The sphere of the metal pad of relative volume V 3 has thermal conductivity k 3. If a perpendicular heat flow impinges on these three layers, then after (4) the value of the total thermal conductivity k is given by the relation:
klk2k 3 k =
Vlk2k3+V2klk3+V3klk2
1368
A. RUDAJEVOV,~
Vol. 26, No. 12
For the ratio of thermal conductivities of unblackened (k w) and blackened surfaces (k b) it holds:
kw kb
-
Vlklk 3
+
V2klk 3
+
V3klk 2
Vlk2k3
+
V2klk 3
+
V3klk 2
/3!
From the above relation it follows that the ratio of thermal conductivities of blackened and unblackened samples approaches 1 for extreme thicknesses, i.e. very thin, actually very thick coatings. Coatings of small thicknesses when a part of the radiation impinges directly on the metal pad and the ratio of half-lives of blackened and unblackened sample surfaces approaches i can be neglected from the viewpoint of heat conduction. In the thickness domains where the ratio of half-lives of blackened and unblackened sample surfaces is equal to 1.14, the total vaiue of thermal conductivity (diffusivity) depends on the portions of transparent and non-transparent parts of the coating. For the practically applied thickness domains of plasma sprayed coatings, the partly transparent layer makes and appreciable portion, which leads to an important conclusion: for practical purposes, plasma sprayed partly transparent coatings cannot be characterized by intrinsic thermal conductivity (diffusivity), but by effective thermal conductivity, which will depend on the coating thickness and the wavelength of the impinging radiation. After this value of effective thermal conductivity has been found, its application will be real only under the conditions it was determined. Transparency and absorptivity of the materials for radiation is given by their absorption coefficient, which depends on the sort and amount of admixtures. In contrast to alumina A 99 coatings, alumina A 96 coatings were not transparent for the impinging radiation. In a normal atmosphere, in the non-transparent coatings it was possible to find the temperature dependence of thermal diffusivity. It dropped with temperature to 750 o C. Conclusions In the present paper it was found that plasma sprayed A 99 alumina coatings were partially transparent, whereas A 96 alumina coatings were not trasparent for impinging radiation. The absorptivity of impinging radiation in A 96 alumina coatings was three times higher than in A 99 alumina coatings. In the partially transparent coatings two layers can be distinguished according to the mechanisms of heat transfer by the coating. In the first, surface layer energy transfer takes place by means of both photon and phonon mechanisms. In the second layer energy is only transferred by phonons. When the thickness of the surface partially transparent part of the coating is not negligible in comparison with the thickness of the non-transparent part of the coating, the following two conclusions are of importance: a) the flash method is not suitable for determining the thermal diffusivity, b) the value of intrinsic thermal diffusivity obtained by measurements is not applicabie to practical purposes.
Vol. 26, No. 12
ALUMINA COATINGS
1369
The partially transparent coatings should be characterized by the so-called effective thermal diffusivity, which is not a material constant and depends, above all, on the coating thickness and impinging radiation wavelength. The intrinsic thermal diffusivity of the alumina coatings of A 99 and A 96 is practically the same at room temperature. References 1. 2. 3. 4.
H.C.Fiedler, Mat.Res.Soc.Symp. Proc.30,173 (1984) G.F.Hurley and O.G.Frank, Am. Ceram. Soc. Bull.58,5 (1979) R.Gardon, J.Am.Ceram. Soc.39,378 (1956) W.O.Kingery, Property Measurements at High Temperatures p.93, John Wiley,Sons,Inc. New York (1959) 5. A.Rudajevov~, Silik@ty 3__3,61 (1989) 6. K.B.Larsen and K.Koyama, J.Appl.Phys.3__9,4408 (1968)