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Hafnium carbide growth behavior and its relationship to the dispersion hardening in tungsten at high temperatures
Materials Science and Engineering, A160 (1993) 159-167
159
Hafnium carbide growth behavior and its relationship to the dispersion hardening in tungsten at high temperatures Mingqui Liu and John Cowley Department of Physics, Arizona State University, Tempe, AZ 85287-1504(USA) (Received August 5, 1992; in revised form September 18, 1992)
Abstract The growth behavior of dispersed hafnium carbide particles and its relationship to the strength of a tungsten-rhenium alloy at temperatures above 2200 K have been examined with transmission electron microscopy. From 2200 to 2600 K, HfC particles grow homogeneously with a relatively slow growth rate. In this temperature region, the activation energy for HfC particle growth is determined to be 50.2 + 1.0 kcal mol- ~. The coarsening of HfC particles is a bulk diffusioncontrolled process and hafnium is the less stable element in the HfC decomposition and growth process. Rapid particle growth occurs at temperatures above 2600 K. A bi-modal particle size distribution is observed at 2800 and 3000 K and selective particle growth takes place along dislocation lines and at grain boundaries, indicating that dislocation and boundary enhanced diffusion mechanisms are involved in the HfC particle coarsening process above 2600 K. Based upon the studies on the growth behavior of HfC particles, An Ashby-Orowan dispersion strengthening model is applied to the HfC hardened tungsten. Good agreement is obtained between the calculated resolved shear stress and experimental results.
1. Introduction
2. Experimental procedures
Tungsten (W) has the highest melting temperature among all metals and hence has been one of the most important metals for high temperature applications. Hafnium carbide (HfC) possesses the highest melting temperature among the metallic compounds and is considered as the most effective second-phase particle in strengthening tungsten at high temperatures. To our knowledge, W-HfC alloy appears to be the strongest high temperature metallic material [1-3]. Because the high temperature mechanical properties of a dispersion alloy depend upon the thermal stability of second-phase particles, the excellent strength of W-HfC alloy at high temperatures is directly related to the size and distribution of HfC particles in tungsten matrix. The present study is to examine the HfC particle growth behavior in a temperature range of 2200 to 3000 K by using transmission electron microscopy (TEM). The purpose of the present study is to determine the HfC particle size and distribution at individual temperatures, to understand the growth mechanism of dispersed HfC particles, and to explain the exceptional high strength of HfC-hardened tungsten at high temperatures.
The material used in the present study was an arcmelted tungsten-3.6 wt.% rhenium-0.35 wt.% hafnium carbide provided by NASA Lewis Research Center, Cleveland, OH. The physical properties and crystal structures of tungsten, rhenium, and hafnium carbide are given in Table 1. The addition of rhenium (Re) was to increase the ductility and fabricability of tungsten at room temperature [4-6]. According to the W-Re phase diagram, rhenium has a solubility of 30 wt.% in tungsten at temperatures greater than 2200 K [7]. It was therefore assumed that in the present study rhenium atoms were completely dissolved into tungsten and formed a W-Re solid solution. Plate-type specimens were heated to a temperature of 2200, 2400, 2600, 2800, and 3000 K in a UHV chamber which maintained a vacuum below 1 x 10-6 Pa. The specimen heating was conducted by self-resistance heating in which an adjustable direct current was passed through the specimen. The heating rate was approximately 10 K per second. The test temperature was measured with a micro-optical disappearing filament pyrometer calibrated to a standard tungsten strip lamp provided by the National Institute of Standards
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M. Liu, J. Cowley /
160
Hafnium carbide growth behavior 200
TABLE 1. Physical properties and crystal structure of alloy components Component
Tungsten
Rhenium
Hafnium carbide
Melting point (K) Density (g cm -3 ) Crystal structure Lattice parameter (A )
3683 19.25 b.c.c, 3.165
3453 21.04 h.c.p. a/2.760;c/4.458
4163 12.20 NaC1 4.641
and Technology, Gaithersburg, MD. The maximum uncertainty of the temperature measurement was + 8 K in the entire temperature range employed. In order to examine the HfC particle growth behavior, each specimen was held at a given temperature for 2 h, and then plastically deformed at this temperature in order to determine the relationship between the yield strength and HfC particle size. After a plastic elongation of 5% was obtained, the specimen was rapidly cooled down to room temperature at a cooling rate greater than 200 K s-~ to maintain the high temperature substructure. The TEM samples were cut from the gage section of heated and deformed specimens, first thinned by the ion milling, and then thinned electrochemically in a 2.0% NaOH solution. All TEM samples were examined with a JEOL-2000FX high resolution transmission electron microscope operated at 200 kV.
Arc MeltedW-Re-HfC
i • 160 .o "O
0
1800
i
t
i
i
i
|
2000
2200
2400
2600
2800
3000
3200
Temperature, K Fig. 1. Dispersion-hardening of HfC particles on tungsten at high temperatures.
3. Results
Figure 1 shows the yield stress of W-Re-HfC alloy after two hours of heating, together with the yield stress of arc-melted pure tungsten [2]. It can be seen that dispersion-hardened tungsten has a much greater strength than pure tungsten at high temperatures. With respect to the stress magnitude, this figure can be divided into two temperature regions. The first one is temperature region of 2200 to 2600 K within which the stress decreases slowly with increasing test temperature and there is an approximately linear relationship between the yield stress and temperature. No significant stress decrease is found at temperatures up to 2600 K, indicating the dispersion hardening is dominant up to this temperature. In the second temperature region (2600-3000 K) yield stress decreases rapidly with increasing temperature, indicating that a significant particle coarsening occurs so that the HfC precipitates can no longer effectively pin up dislocations. The substructure of as-received W-Re-HfC alloy is shown in Fig. 2. It was characterized by low dislocation density and approximately uniform HfC particle size. Most HfC particles were not in touch with the disloca-
Fig. 2. Substructure of as received W-Re-HfC alloy.
tion lines. The average HfC particle diameter of asreceived alloy was determined to be approximately 330A. Figures 3-5 show the substructure of W-Re-HfC after heating and deformation at 2200, 2400, and 2600 K respectively. The plastic deformation introduced a high density of dislocations, as well as dislocation networks. A strong interaction between the HfC particles and dislocations was observed. Dislocation lines are securely pinned by HfC particles, resulting in a significant decrease in dislocation mobility. Therefore, dispersion hardening is the dominant strengthening mechanism in this temperature region. Even though a slow HfC particle growth occurred after 2 h of heating at high temperatures, the particle size is still relatively small up to 2600 K. No significant particle coarsening is observed up to this temperature. Particle size
M. Liu, J. Cowley /
Hafnium carbide growth behavior
161
measurements showed that in this temperature region HfC particle diameters are scattered in a range of approximately 400-500/k., depending upon the individual test temperatures. In order to determine the relationship between the HfC particle size and test temperature, the particle size distribution at each temperature was examined. The diameters of more than 300 HfC particles were measured for each individual test temperature specimen. Figures 6-8 show the volume percentage of different size of HfC particles at given temperature. It is noted that in the temperature region of 2200 to 2600 K, the HfC particle growth is a homogeneous process. With increased temperature, the peak representing the majority particles continuously shifts from small diameter to large diameter. For given annealing time, Fig. 3. Substructure of W-Re-HfC alloy at 2200 K. 28
Q 24 01 4)
P 16
4) O. Q
12
i= 8
0 •
4 0
250
300
350
400
450
500
550
600
650
Particle Diameter, A Fig. 4. Substructure of W-Re-HfC alloy at 2400 K.
Fig. 6. HfC panicle size distribution a~er 2 h of beating at 2200 K.
I-
•
:
O1 t~ 4) O Q. 4)
E m
O
250
300
350
400
450
500
550
600
650
700
Particle Diameter, ,A. Fig. 5. Substructure of W-Re-HfC alloy at 2600 K.
Fig. 7. HfC panicle size distribution a~er 2 h of heating at 2400 K.
162
4)
M. Liu, J. Cowley /
Hafnium carbide growth behavior
24
o) oo '~ 20 c 4) tj k..
16
4) I1. 4)
E ~ O
~
12
8
4 0
250
300
350
400
450
500
S50
000
650
700
Particle Diameter, A Fig. 8. HfC panicle size distribution a~er 2 h of heating at 2600 K.
Fig. 10. Substructure of W-Re-HfC alloy at 3000 K.
4) m
t4) o 4) Q. 4)
E m
O
v
200
400
600
800
1000 1200 1400 1600 1800 2000 2200
Particle Diameter, A Fig. 9. Substructure of W-Re-HfC alloy at 2800 K.
the HfC particle size basically obeys a statistical distribution. Significant HfC particle growth was found at 2800 K, corresponding to 0.67 Tm (melting temperature of HfC), and higher temperatures. The substructures of W - R e - H f C after heating and plastic deformation at 2800 K and 3000 K are shown in Figs. 9 and 10. Inhomogeneous particle growth is observed at such high temperatures. The substructure is characterized by extremely large HfC particles surrounded by numerous small ones. There are no intermediate size particles identified from the T E M micrographs, as illustrated by Figs. 11 and 12. The HfC particle diameter is either smaller than 8 0 0 / ~ or greater than 1400 A, indicating that there is a selective particle growth. The large particles appear to grow rapidly by consuming the small ones.
Fig. 11. HfCparticle size distribution a~er 2 h of heating at 2800 K.
Q
~
2o
~ le ~. 4) +2 I~ = e O 4 0
200 400 600 800 10001200140016001110020002200240026002800
Particle Diameter, A Fig. 12. HfC particle size distribution after 2 h of heating at 30O0 K.
M. Liu, J. Cowley / Hafnium carbide growth behavior 4.
Discussion
4.1. HfC particle growth behavior Because of the scatter in the size of HfC particles, it is necessary to find the average particle diameter at individual temperatures based upon the particle size distributions determined from transmission micrographs. A weighted average method was used in determining the average particle size by using the following formula ~I= Z dip, • 100
(1)
where d is the weighted average HfC particle diameter at given temperature, d i is the individual particle diameter, and Pi is the volume percentage of each size group of particles. The average particle size was calculated from Figs. 6-8, 11, and 12 by using eqn. (1). The result is shown as a function of temperature in Fig. 13. From Fig. 13, it can be seen that the particle size is relatively stable up to 2600 K. When temperature is increased from 2200 and 2600 K, the HfC panicle diameter increases from 4 2 1 / k to 516/k. The growth rate is less than 0.25 /k K -t. Significant particle coarsening occurs at temperatures greater than 2600 K. In the temperature region of 2600 to 3000 K, HfC particle rapidly coarsens at a growth rate of approximately 4.0 ,/k K - 1. This is believed to be the dominant reason causing the rapid decrease of the yield stress of a W-Re-HfC alloy at temperatures above 2600 K. In the temperature region of 2200 to 2600 K, the particle size distribution shows a single maximum moving to a larger diameter with increasing temperature, indicating that the particle coarsening is most likely a bulk diffusion-controlled process. In the TEM studies of the HfC panicle morphologies, it was found ,<¢
2400
0,) 2O0O
E 1600
o
m
._+,2 1200 13.
8O0
0
m
4OO
O~
>
0 2000
.
2 2 , o0 .
2 4 ,0 0
,
2 6 ,0 0
,
2 8 , 00 ,
3 0 , ,0,
3200
Temperature, K Fig. 13. Weightedaverage HfC particle diameter as a function of temperature.
163
that most particles were spherical. For the ideal case of spherical particle-growth due to the bulk diffusioncontrolled transfer of solute in the matrix, the most acceptable equation used to predict the particle size is the cubic equation [8]:
3 3 8pDCeVm 2 r - ro t 9RT
(2)
where r 0 is the onset particle radius, r is the panicle radius at time t, p is the free energy of the particle-matrix interface, D is the diffusivity of the rate-limiting solute in the matrix, C e is the concentration of solute in the matrix in equilibrium with a particle of infinite size, Vm is the molar volume of dispersed particles, R is the universal gas constant, and T is the absolute temperature. Since the p value of HfC particles in tungsten is not available in the literature, eqn. (2) can not be used to calculate the particle size as a function of temperature and time. But eqn. (2) may be rewritten in another form: (3)
where C is a temperature-independent constant, Q is the activation energy for the bulk diffusion-controlled particle growth process, and g(r, T,t) is a particle growth parameter given by:
g(r, T, t) = ( r 3 -- ro 3) T t
(4)
Because r, r0, T, and t are all known, the value of g(r, T, t) at each individual temperature can be calculated by using eqn. (4). The activation energy for HfC particle growth is hence found by a logarithmic plot of g(r, T, t) vs. reciprocal temperature, as shown in Fig. 14. From the slope in Fig. 15, the activation energy for HfC particle growth over the temperature range of 2200 to 2600 K is found to be 50.2_+ 1.0 kcal mol-~. Comparing this magnitude with the activation energies for bulk diffusion of hafnium and carbon in tungsten at high temperatures [8, 9], it is found that this magnitude within the experimental error is fairly close to the activation energy for carbon diffusion in tungsten (53.5 kcal mo1-1) and the activation energy for hafnium diffusion in tungsten (47.2 kcal mol-1), indicating that the HfC growth in tungsten in the temperature range of 2200 to 2600 K is a bulk diffusion-controlled process. Since the coarsening of HfC panicles results from the bulk diffusion process occurring in the region adjacent to the particles from 2200 to 2600 K, it is hence necessary to examine the diffusivity of hafnium
M. Liu, J. Cowley / Hafnium carbide growth behavior
164 10"16
10.5
i
i
i
w
w
,
,
,
,
2300
2400
2500
.~W 10"6 ~
~1~ 10"7
|0-17
0
a
,~10" "~ 10.9
I-- 10.18 . ~ 1 0 "1° 10-11 ,
10-19 0.35
.
.
.
.
.
.
.
.
0.40
0.45
,
0.50
Reciprocal Temperature, 10 3/K
10-12 2100
2200
:,n.,C
2600
2700
Temperature, K
Fig. 14. Temperature dependence of HfC growth rate in the temperature region of 220"0to 2600 K.
Fig. 16. Diffusivities of hafnium and carbon in tungsten and in I-IfC at high temperatures.
tungsten. Therefore, hafnium should diffuse at a much faster rate in tungsten matrix at high temperatures. The same is true for the diffusivity of hafnium and carbon in HfC compound. The diffusivity of hafnium in HfC was determined to be [10]: D--1.48 x 10s cm 2 s-1 exp (
182.8 kcal mol-1) RT
(7)
And the diffusivity of carbon in HfC is given by [11]: ( 130.3 kcal mol-l) D =6.3 x 101 cm 2 s -1 exp RT
Fig. 15. Grown HfC particle and its microdiffraction pattern.
and carbon in tungsten in this temperature region. The diffusivity of hafnium in tungsten was determined by Dainyak and Kostikov [9] and could be expressed by: D = 7 . 2 × 1 0 -3 c m 2 s -1 exp(
47.2 kcalmol-J // ~-~-
(5)
The diffusivity of carbon in tungsten in this temperature region was also determined [9]: D =8.91 x l 0 -3 cm 2 s -~ e x p ( ' 53.5 kcal mo1-1) RT
(6)
Comparing eqn. (5) with eqn. (6), it can be easily seen that even though the pre-exponential factors are similar but the activation energy for hafnium diffusion in tungsten is approximately 12% less than carbon in
(8)
The diffusivities of hafnium and carbon in tungsten and in HfC are calculated in the temperature region of 2200 K to 2600 K. The results are given in Fig. 16. It is noted that the diffusivity of hafnium in tungsten is approximately one order of magnitude greater than that of carbon over the entire temperature range. The diffusivity of hafnium in HfC is also significantly larger than for carbon. It is one order of magnitude greater than the diffusivity of carbon in HfC at 2200 K and two orders of magnitude greater than that of carbon at 2600 K. It is therefore concluded that hafnium is the less stable element in HfC compound. During the particle growth process, hafnium and carbon atoms in small HfC particles are dissolved into the tungsten-rhenium matrix, diffused through the matrix to the large particles, and recombined to form even greater particles. Because of its great diffusivity in HfC and in tungsten, hafnium atoms are supposed to be the first ones dissolved into the matrix and reach to the large particles. This is confirmed by examining the crystal structure of grown HfC particles. The crystal structure of HfC has been determined by Cotter and Kohn [13]. It is
M. Liu, J. Cowley / Hafnium carbide growth behavior
found that HfC has a NaCl structure with a lattice parameter a 0 equal to 4.641 A. In the present study, electron microdiffraction is used to examine the crystal structure of HfC particles coarsened at high temperatures. Figure 15 shows a grown HfC particle and its microdiffraction pattern. The lattice parameter of grown HfC particles is found to be 4.56 /~, approximately 2% smaller than the lattice parameter of pure HfC. Cotter and Kohn [13] have found that the lattice parameter of HfC decreases with excess hafnium. Therefore, the result obtained by microdiffraction indicates that the coarsened particles are hafnium-rich HfC particles. This is, certainly, because hafnium has a greater diffusivity than carbon in tungsten at high temperatures. At temperatures above 2600 K the growth rate of HfC particles increases rapidly and there are two peaks appearing on the particle size distribution (Figs. 11 and 12). This indicates that some other diffusion mechanisms are involved in the particle coarsening process at extremely high temperatures. Comparing Figs. 3-5 with Figs. 9 and 10, two interesting facts are found. First, the number of HfC particles in the dislocationfree zone decreases with increasing temperature, indicating there is a selective diffusion from the particles not touched with dislocations to those located on the dislocation lines. Second, the majority of the grown particles in the temperature region of 2800 to 3000 K are located at the dislocation lines, surrounded by some very small particles that are also attached to the dislocations. Therefore, diffusion along dislocation "pipes" is most likely to be one of the reasons responsible for the observed bi-modal particle size distribution. The growth of the large particles on dislocation lines are accomplished by consuming the near-by intermediate ones touched to the dislocation "pipes". The great diffusivity of solute atoms along dislocations causes a rapid coarsening of selective large particle, and at the same time, results in a size decreasing of its neighboring particles. The intermediate particles are hence not observed in the size distribution. Grain-boundary diffusion could be another mechanism responsible for the bi-modal size distribution of HfC particles. Very large particles are often seen at grain boundaries, especially at boundary triple joints (Fig. 15). In the present material, the grain size is relatively large, approximately 130/~m determined by the intercept method. Considering the limited boundary area and the fact that the boundary diffusion rate increases not as fast as the bulk and dislocation diffusion rates when temperature is raised [14], the contribution of boundary diffusion to the rapid coarsening and bi-modal size distribution of HfC particles at extremely high temperatures is not as significant as the dislocation diffusion.
165
4.2. HfC dispersion hardening It has been shown that the solid-solution hardening of rhenium in tungsten is negligible at temperatures above 2200 K [3, 15]. The HfC dispersion hardening was assumed to be responsible for the exceptionally high strength of W-Re-HfC alloy in the temperature range employed in the present study. For the case of non-shearable second-phase particles, the most acceptable dispersion-hardening theory is the one proposed by Orowan [16]. According to Orowan's mechanism, the yield stress is determined by the shear stress required to bow a dislocation line between two particles separated by a distance 2p. This mechanism was later modified by Ashby with considerations on the dislocation line tension, dislocation energy, and random particle spacing [17]. The Ashby-Orowan dispersion-hardening model has the following form:
Gb d Ar=2--~p In ~
(9)
where A r is the resolved shear stress necessary to overcome the effects of particles, G and b are the shear modulus and the burgers vector of the matrix respectively, and ;tp is the planar interparticle spacing. Because the volume fraction of dispersion particles, f, is given by:
3 f = ,~,p2d
~d 2 -- 6~.p2
(10)
The planar interparticle spacing 2p can be calculated from known average particle diameter d and given particle volume fraction f:
2p =
fl/2
(11)
In the present case, the volume fraction f of HfC particles is 5.53 x 10 -3. The weighted average HfC particle diameter t~ at each test temperature is determined from transmission electron micrographs (Fig. 13). The magnitude of the burgers vector b of dislocation in tungsten is 2.741 A. The shear modulus of tungsten, G, is a decreasing function of temperature and is calculated based upon the following formula [18]: G = 1.5893 x 105- 1.4733 x 101( T - 273) - 2.448 x 10-3( T - 273) 2 MPa
(12)
By using eqn. (11) and Ashby-Orowan model, the shear stress A r resulting from the dispersionhardening of HfC particles in tungsten was calculated in the entire temperature region from 2200 to 3000 K.
166
M. Liu, J. Cowley /
Hafnium carbide growth behavior
TABLE 2. Comparison of the calculated resolved shear stress increment A r with the experimental value A 3' T (K)
d(A)
G (MPa)
Ar (MPa)
At' (MPa)
Deviation (%)
2200 2400 2600 2800 3000
421 470 516 1556 2072
121 116 111 106 100
56.1 49.5 44.0 17.3 12.9
61.8 52.7 45.4 19.2 13.1
-9.2 - 6.1 - 3.1 - 9.9 -1.4
449 518 391 067 548
deforming particles and the soft matrix. The formation of a cell structure introduces a strong dislocation interaction between the dislocation lines and hence, the dislocation mobility is decreased. But in the AshbyOrowan dispersion-hardening model, only particledislocation interaction has been considered. Because the contribution of dislocation-dislocation interaction to the yield stress is not counted in Ashby-Orowan model, it is therefore expected that this model would give an underestimate of the stress.
5. Conclusions
Fig. 17. Dislocation cell structure in 2400 K heated specimen.
The results are given in Table 2. For comparison, the experimentally determined shear stress increment At' is also shown in this table. Comparison of the calculated values with the experimental data indicates that the Ashby-Orowan model is successful in explaining the strength property of HfC particle hardened tungsten at high temperatures. It was noted that the stresses calculated based upon this model are slightly smaller than the experimental values over the entire temperature region, especially at 2200 and 2800 K where the calculated stress is approximately 10% smaller than the experimentally determined stress. This is attributed to two causes. One may be the error introduced in neglecting the contribution of rhenium to the strength of tungsten. Even though the solid-solution hardening effect of rhenium is very small at temperatures greater than 2200 K, the contribution of dissolved rhenium to the strength is certainly not zero. Another factor may be the dislocation cell structure around the dispersion particles. As shown in Fig. 17, the dislocation cell structure is formed by the generation of dislocations due to the necessity for retaining continuity between the non-
(i) HfC particle size is relatively stable after 2 h of heating in the temperature region 2200-2600 K. In this temperature region, the activation energy for HfC particle growth is determined to be 50.2+ 1.0 kcal mol-1 and the coarsening of HfC particles is a bulk diffusion-controlled process. (ii) Rapid particle growth occurs at temperatures above 2600 K. A bi-modal particle size distribution is observed at 2800 and 3000 K and selective particle growth takes place along dislocation lines and at grain boundaries, indicating that the mechanisms of dislocation and boundary enhanced diffusion are involved in the HfC particle coarsening process in this temperature region. (iii) Analysis on the diffusivity data shows that hafnium has a much faster diffusion rate than carbon at high temperatures and the grown particles are found to be hafnium-rich HfC particles. Hafnium is hence the less stable element in the HfC decomposition and growth process. (iv) The strength property of W - R e - H f C alloy at high temperatures basically depends upon the HfC particle size stability. The hardening effect of HfC particles in tungsten-rhenium matrix decreases with increased particle size. (v) The A s h b y - O r o w a n model is successful in explaining the dispersion hardening of HfC in tungsten at high temperatures. Good agreement is obtained between the calculated resolved shear stress and experimental results in the temperature region 2200-3000 K.
Acknowledgment This work was supported by National Science Foundations (NSF) grant D M R 90-14975 and made use of the T E M specimen preparation equipment at the Facility for High Resolution Electron Microscopy supported by NSF D M R 89-13384. The authors would like to thank the Electron Microscopy Labora-
M. Liu, J. Cowley
/
Hafnium carbide growth behavior
tory of Material Science and Engineering Program at A r i z o n a State University for using the microscope. T h e authors would also like to thank Dr. A. L u o and Dr. D. L. Jacobson for the assistance in performing the mechanical tests and the reviewer from Materials Science a n d Engineering A for the astute comments which have been integrated in this final version.
References 1 W. D. Klopp and W. R. Witzke, Mechanical properties of a W-23.4%Re-0.27%HfC alloy, J. Less-Common Met., 24 (1971) 427-443. 2 A. Luo, D. L. Jacobson and K. S. Shin, Tensile properties of tungsten-3.6% rhenium-0.4% hafnium carbide above 0.5 Tm Scr. Metall., 23 (1989) 397-401. 3 K.S. Shin, A. Luo, B. L. Chela and D. L. Jacobson, High temperature properties of particle-strengthened tungsten, J. Met., 42(1990) 12-17. 4 E L. Raffo, Yielding and fracture in tungsten and tungsten-rhenium alloys, J. Less-Common Met., 17 (1969) 133-149. 5 J. R. Stephens and W. R. Witzke, Alloy softening in group VIA metals alloyed with rhenium, J. Less-Common Met., 23 (1971)325-341. 6 A. Luo, D. L. Jacobson and K. S. Shin, Solution softening mechanism of iridium and rhenium in tungsten at room temperature, Int. J. Refractory Met. Hard Mater., 10 (1991) 107-114.
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7 M. Hansen, Constitution of Binary Alloys, McGraw-Hill, New York, 1958, pp. 766-777. 8 I.M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solution, J. Phys. Chem. Solids, 19 (1961)35-50. 9 B. A. Dainyak and V. I. Kostikov, Chem. Metal., 11 (1976) 15-18. 10 A. Y. Nakonechnikov, L. V. Pavlinov and V. N. Bokov, Fiz. Metal. Metalloved., 22(1966) 234-239. 11 R.A. Andrievskii, V. V. Klimenko and Y. E Khormove, Selfdiffusion of Hf in Group IV and V transition metal carbides, Fiz. Metal. Metalloved, 28(1969), 214-221. 12 R.A. Andrievskii, V. V. Klimenko and Y. E Khormove, Selfdiffusion of C in Group 1V and V transition metal carbides, Fiz. Metal. Metalloved, 28(1969) 298-303. 13 E G. Cotter and J. A. Kohn, Industrial diamond substitutes: I, physical and X-ray study of hafnium carbide, J. Am. Ceram. Soc., 37(1954) 415-420. 14 L. A. Girifalco, Atomic Migration in Crystals, Blaisdell Publishing, New York, 1964, pp. 117-130. 15 A. Luo, K. S. Shin and D. L. Jacobson, High temperature tensile properties of W-Re-ThO 2 alloys, Mater. Sci. Eng., A148(1991) 229-233. 16 E. Orowan, Internal Stresses in Metals and Alloys, Institute of Metals, London, 1948, pp. 451-477. 17 M. E Ashby, The theory of critical shear stress and working hardening of dispersion-hardened crystals, in G. S. Ansell, ed., Oxide Dispersion Strengthening, Proc. 2nd Bolton Landing Conf., Gordon and Breach Science Publishers, New York, 1968, pp. 143-205. 18 R. Lowrie and A. M. Gonas, Dynamic properties of polycrystalline tungsten, J. Appl. Phys., 36 (1965) 2189-2192.
159
Hafnium carbide growth behavior and its relationship to the dispersion hardening in tungsten at high temperatures Mingqui Liu and John Cowley Department of Physics, Arizona State University, Tempe, AZ 85287-1504(USA) (Received August 5, 1992; in revised form September 18, 1992)
Abstract The growth behavior of dispersed hafnium carbide particles and its relationship to the strength of a tungsten-rhenium alloy at temperatures above 2200 K have been examined with transmission electron microscopy. From 2200 to 2600 K, HfC particles grow homogeneously with a relatively slow growth rate. In this temperature region, the activation energy for HfC particle growth is determined to be 50.2 + 1.0 kcal mol- ~. The coarsening of HfC particles is a bulk diffusioncontrolled process and hafnium is the less stable element in the HfC decomposition and growth process. Rapid particle growth occurs at temperatures above 2600 K. A bi-modal particle size distribution is observed at 2800 and 3000 K and selective particle growth takes place along dislocation lines and at grain boundaries, indicating that dislocation and boundary enhanced diffusion mechanisms are involved in the HfC particle coarsening process above 2600 K. Based upon the studies on the growth behavior of HfC particles, An Ashby-Orowan dispersion strengthening model is applied to the HfC hardened tungsten. Good agreement is obtained between the calculated resolved shear stress and experimental results.
1. Introduction
2. Experimental procedures
Tungsten (W) has the highest melting temperature among all metals and hence has been one of the most important metals for high temperature applications. Hafnium carbide (HfC) possesses the highest melting temperature among the metallic compounds and is considered as the most effective second-phase particle in strengthening tungsten at high temperatures. To our knowledge, W-HfC alloy appears to be the strongest high temperature metallic material [1-3]. Because the high temperature mechanical properties of a dispersion alloy depend upon the thermal stability of second-phase particles, the excellent strength of W-HfC alloy at high temperatures is directly related to the size and distribution of HfC particles in tungsten matrix. The present study is to examine the HfC particle growth behavior in a temperature range of 2200 to 3000 K by using transmission electron microscopy (TEM). The purpose of the present study is to determine the HfC particle size and distribution at individual temperatures, to understand the growth mechanism of dispersed HfC particles, and to explain the exceptional high strength of HfC-hardened tungsten at high temperatures.
The material used in the present study was an arcmelted tungsten-3.6 wt.% rhenium-0.35 wt.% hafnium carbide provided by NASA Lewis Research Center, Cleveland, OH. The physical properties and crystal structures of tungsten, rhenium, and hafnium carbide are given in Table 1. The addition of rhenium (Re) was to increase the ductility and fabricability of tungsten at room temperature [4-6]. According to the W-Re phase diagram, rhenium has a solubility of 30 wt.% in tungsten at temperatures greater than 2200 K [7]. It was therefore assumed that in the present study rhenium atoms were completely dissolved into tungsten and formed a W-Re solid solution. Plate-type specimens were heated to a temperature of 2200, 2400, 2600, 2800, and 3000 K in a UHV chamber which maintained a vacuum below 1 x 10-6 Pa. The specimen heating was conducted by self-resistance heating in which an adjustable direct current was passed through the specimen. The heating rate was approximately 10 K per second. The test temperature was measured with a micro-optical disappearing filament pyrometer calibrated to a standard tungsten strip lamp provided by the National Institute of Standards
0921-5093/93/$6.00
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M. Liu, J. Cowley /
160
Hafnium carbide growth behavior 200
TABLE 1. Physical properties and crystal structure of alloy components Component
Tungsten
Rhenium
Hafnium carbide
Melting point (K) Density (g cm -3 ) Crystal structure Lattice parameter (A )
3683 19.25 b.c.c, 3.165
3453 21.04 h.c.p. a/2.760;c/4.458
4163 12.20 NaC1 4.641
and Technology, Gaithersburg, MD. The maximum uncertainty of the temperature measurement was + 8 K in the entire temperature range employed. In order to examine the HfC particle growth behavior, each specimen was held at a given temperature for 2 h, and then plastically deformed at this temperature in order to determine the relationship between the yield strength and HfC particle size. After a plastic elongation of 5% was obtained, the specimen was rapidly cooled down to room temperature at a cooling rate greater than 200 K s-~ to maintain the high temperature substructure. The TEM samples were cut from the gage section of heated and deformed specimens, first thinned by the ion milling, and then thinned electrochemically in a 2.0% NaOH solution. All TEM samples were examined with a JEOL-2000FX high resolution transmission electron microscope operated at 200 kV.
Arc MeltedW-Re-HfC
i • 160 .o "O
0
1800
i
t
i
i
i
|
2000
2200
2400
2600
2800
3000
3200
Temperature, K Fig. 1. Dispersion-hardening of HfC particles on tungsten at high temperatures.
3. Results
Figure 1 shows the yield stress of W-Re-HfC alloy after two hours of heating, together with the yield stress of arc-melted pure tungsten [2]. It can be seen that dispersion-hardened tungsten has a much greater strength than pure tungsten at high temperatures. With respect to the stress magnitude, this figure can be divided into two temperature regions. The first one is temperature region of 2200 to 2600 K within which the stress decreases slowly with increasing test temperature and there is an approximately linear relationship between the yield stress and temperature. No significant stress decrease is found at temperatures up to 2600 K, indicating the dispersion hardening is dominant up to this temperature. In the second temperature region (2600-3000 K) yield stress decreases rapidly with increasing temperature, indicating that a significant particle coarsening occurs so that the HfC precipitates can no longer effectively pin up dislocations. The substructure of as-received W-Re-HfC alloy is shown in Fig. 2. It was characterized by low dislocation density and approximately uniform HfC particle size. Most HfC particles were not in touch with the disloca-
Fig. 2. Substructure of as received W-Re-HfC alloy.
tion lines. The average HfC particle diameter of asreceived alloy was determined to be approximately 330A. Figures 3-5 show the substructure of W-Re-HfC after heating and deformation at 2200, 2400, and 2600 K respectively. The plastic deformation introduced a high density of dislocations, as well as dislocation networks. A strong interaction between the HfC particles and dislocations was observed. Dislocation lines are securely pinned by HfC particles, resulting in a significant decrease in dislocation mobility. Therefore, dispersion hardening is the dominant strengthening mechanism in this temperature region. Even though a slow HfC particle growth occurred after 2 h of heating at high temperatures, the particle size is still relatively small up to 2600 K. No significant particle coarsening is observed up to this temperature. Particle size
M. Liu, J. Cowley /
Hafnium carbide growth behavior
161
measurements showed that in this temperature region HfC particle diameters are scattered in a range of approximately 400-500/k., depending upon the individual test temperatures. In order to determine the relationship between the HfC particle size and test temperature, the particle size distribution at each temperature was examined. The diameters of more than 300 HfC particles were measured for each individual test temperature specimen. Figures 6-8 show the volume percentage of different size of HfC particles at given temperature. It is noted that in the temperature region of 2200 to 2600 K, the HfC particle growth is a homogeneous process. With increased temperature, the peak representing the majority particles continuously shifts from small diameter to large diameter. For given annealing time, Fig. 3. Substructure of W-Re-HfC alloy at 2200 K. 28
Q 24 01 4)
P 16
4) O. Q
12
i= 8
0 •
4 0
250
300
350
400
450
500
550
600
650
Particle Diameter, A Fig. 4. Substructure of W-Re-HfC alloy at 2400 K.
Fig. 6. HfC panicle size distribution a~er 2 h of beating at 2200 K.
I-
•
:
O1 t~ 4) O Q. 4)
E m
O
250
300
350
400
450
500
550
600
650
700
Particle Diameter, ,A. Fig. 5. Substructure of W-Re-HfC alloy at 2600 K.
Fig. 7. HfC panicle size distribution a~er 2 h of heating at 2400 K.
162
4)
M. Liu, J. Cowley /
Hafnium carbide growth behavior
24
o) oo '~ 20 c 4) tj k..
16
4) I1. 4)
E ~ O
~
12
8
4 0
250
300
350
400
450
500
S50
000
650
700
Particle Diameter, A Fig. 8. HfC panicle size distribution a~er 2 h of heating at 2600 K.
Fig. 10. Substructure of W-Re-HfC alloy at 3000 K.
4) m
t4) o 4) Q. 4)
E m
O
v
200
400
600
800
1000 1200 1400 1600 1800 2000 2200
Particle Diameter, A Fig. 9. Substructure of W-Re-HfC alloy at 2800 K.
the HfC particle size basically obeys a statistical distribution. Significant HfC particle growth was found at 2800 K, corresponding to 0.67 Tm (melting temperature of HfC), and higher temperatures. The substructures of W - R e - H f C after heating and plastic deformation at 2800 K and 3000 K are shown in Figs. 9 and 10. Inhomogeneous particle growth is observed at such high temperatures. The substructure is characterized by extremely large HfC particles surrounded by numerous small ones. There are no intermediate size particles identified from the T E M micrographs, as illustrated by Figs. 11 and 12. The HfC particle diameter is either smaller than 8 0 0 / ~ or greater than 1400 A, indicating that there is a selective particle growth. The large particles appear to grow rapidly by consuming the small ones.
Fig. 11. HfCparticle size distribution a~er 2 h of heating at 2800 K.
Q
~
2o
~ le ~. 4) +2 I~ = e O 4 0
200 400 600 800 10001200140016001110020002200240026002800
Particle Diameter, A Fig. 12. HfC particle size distribution after 2 h of heating at 30O0 K.
M. Liu, J. Cowley / Hafnium carbide growth behavior 4.
Discussion
4.1. HfC particle growth behavior Because of the scatter in the size of HfC particles, it is necessary to find the average particle diameter at individual temperatures based upon the particle size distributions determined from transmission micrographs. A weighted average method was used in determining the average particle size by using the following formula ~I= Z dip, • 100
(1)
where d is the weighted average HfC particle diameter at given temperature, d i is the individual particle diameter, and Pi is the volume percentage of each size group of particles. The average particle size was calculated from Figs. 6-8, 11, and 12 by using eqn. (1). The result is shown as a function of temperature in Fig. 13. From Fig. 13, it can be seen that the particle size is relatively stable up to 2600 K. When temperature is increased from 2200 and 2600 K, the HfC panicle diameter increases from 4 2 1 / k to 516/k. The growth rate is less than 0.25 /k K -t. Significant particle coarsening occurs at temperatures greater than 2600 K. In the temperature region of 2600 to 3000 K, HfC particle rapidly coarsens at a growth rate of approximately 4.0 ,/k K - 1. This is believed to be the dominant reason causing the rapid decrease of the yield stress of a W-Re-HfC alloy at temperatures above 2600 K. In the temperature region of 2200 to 2600 K, the particle size distribution shows a single maximum moving to a larger diameter with increasing temperature, indicating that the particle coarsening is most likely a bulk diffusion-controlled process. In the TEM studies of the HfC panicle morphologies, it was found ,<¢
2400
0,) 2O0O
E 1600
o
m
._+,2 1200 13.
8O0
0
m
4OO
O~
>
0 2000
.
2 2 , o0 .
2 4 ,0 0
,
2 6 ,0 0
,
2 8 , 00 ,
3 0 , ,0,
3200
Temperature, K Fig. 13. Weightedaverage HfC particle diameter as a function of temperature.
163
that most particles were spherical. For the ideal case of spherical particle-growth due to the bulk diffusioncontrolled transfer of solute in the matrix, the most acceptable equation used to predict the particle size is the cubic equation [8]:
3 3 8pDCeVm 2 r - ro t 9RT
(2)
where r 0 is the onset particle radius, r is the panicle radius at time t, p is the free energy of the particle-matrix interface, D is the diffusivity of the rate-limiting solute in the matrix, C e is the concentration of solute in the matrix in equilibrium with a particle of infinite size, Vm is the molar volume of dispersed particles, R is the universal gas constant, and T is the absolute temperature. Since the p value of HfC particles in tungsten is not available in the literature, eqn. (2) can not be used to calculate the particle size as a function of temperature and time. But eqn. (2) may be rewritten in another form: (3)
where C is a temperature-independent constant, Q is the activation energy for the bulk diffusion-controlled particle growth process, and g(r, T,t) is a particle growth parameter given by:
g(r, T, t) = ( r 3 -- ro 3) T t
(4)
Because r, r0, T, and t are all known, the value of g(r, T, t) at each individual temperature can be calculated by using eqn. (4). The activation energy for HfC particle growth is hence found by a logarithmic plot of g(r, T, t) vs. reciprocal temperature, as shown in Fig. 14. From the slope in Fig. 15, the activation energy for HfC particle growth over the temperature range of 2200 to 2600 K is found to be 50.2_+ 1.0 kcal mol-~. Comparing this magnitude with the activation energies for bulk diffusion of hafnium and carbon in tungsten at high temperatures [8, 9], it is found that this magnitude within the experimental error is fairly close to the activation energy for carbon diffusion in tungsten (53.5 kcal mo1-1) and the activation energy for hafnium diffusion in tungsten (47.2 kcal mol-1), indicating that the HfC growth in tungsten in the temperature range of 2200 to 2600 K is a bulk diffusion-controlled process. Since the coarsening of HfC panicles results from the bulk diffusion process occurring in the region adjacent to the particles from 2200 to 2600 K, it is hence necessary to examine the diffusivity of hafnium
M. Liu, J. Cowley / Hafnium carbide growth behavior
164 10"16
10.5
i
i
i
w
w
,
,
,
,
2300
2400
2500
.~W 10"6 ~
~1~ 10"7
|0-17
0
a
,~10" "~ 10.9
I-- 10.18 . ~ 1 0 "1° 10-11 ,
10-19 0.35
.
.
.
.
.
.
.
.
0.40
0.45
,
0.50
Reciprocal Temperature, 10 3/K
10-12 2100
2200
:,n.,C
2600
2700
Temperature, K
Fig. 14. Temperature dependence of HfC growth rate in the temperature region of 220"0to 2600 K.
Fig. 16. Diffusivities of hafnium and carbon in tungsten and in I-IfC at high temperatures.
tungsten. Therefore, hafnium should diffuse at a much faster rate in tungsten matrix at high temperatures. The same is true for the diffusivity of hafnium and carbon in HfC compound. The diffusivity of hafnium in HfC was determined to be [10]: D--1.48 x 10s cm 2 s-1 exp (
182.8 kcal mol-1) RT
(7)
And the diffusivity of carbon in HfC is given by [11]: ( 130.3 kcal mol-l) D =6.3 x 101 cm 2 s -1 exp RT
Fig. 15. Grown HfC particle and its microdiffraction pattern.
and carbon in tungsten in this temperature region. The diffusivity of hafnium in tungsten was determined by Dainyak and Kostikov [9] and could be expressed by: D = 7 . 2 × 1 0 -3 c m 2 s -1 exp(
47.2 kcalmol-J // ~-~-
(5)
The diffusivity of carbon in tungsten in this temperature region was also determined [9]: D =8.91 x l 0 -3 cm 2 s -~ e x p ( ' 53.5 kcal mo1-1) RT
(6)
Comparing eqn. (5) with eqn. (6), it can be easily seen that even though the pre-exponential factors are similar but the activation energy for hafnium diffusion in tungsten is approximately 12% less than carbon in
(8)
The diffusivities of hafnium and carbon in tungsten and in HfC are calculated in the temperature region of 2200 K to 2600 K. The results are given in Fig. 16. It is noted that the diffusivity of hafnium in tungsten is approximately one order of magnitude greater than that of carbon over the entire temperature range. The diffusivity of hafnium in HfC is also significantly larger than for carbon. It is one order of magnitude greater than the diffusivity of carbon in HfC at 2200 K and two orders of magnitude greater than that of carbon at 2600 K. It is therefore concluded that hafnium is the less stable element in HfC compound. During the particle growth process, hafnium and carbon atoms in small HfC particles are dissolved into the tungsten-rhenium matrix, diffused through the matrix to the large particles, and recombined to form even greater particles. Because of its great diffusivity in HfC and in tungsten, hafnium atoms are supposed to be the first ones dissolved into the matrix and reach to the large particles. This is confirmed by examining the crystal structure of grown HfC particles. The crystal structure of HfC has been determined by Cotter and Kohn [13]. It is
M. Liu, J. Cowley / Hafnium carbide growth behavior
found that HfC has a NaCl structure with a lattice parameter a 0 equal to 4.641 A. In the present study, electron microdiffraction is used to examine the crystal structure of HfC particles coarsened at high temperatures. Figure 15 shows a grown HfC particle and its microdiffraction pattern. The lattice parameter of grown HfC particles is found to be 4.56 /~, approximately 2% smaller than the lattice parameter of pure HfC. Cotter and Kohn [13] have found that the lattice parameter of HfC decreases with excess hafnium. Therefore, the result obtained by microdiffraction indicates that the coarsened particles are hafnium-rich HfC particles. This is, certainly, because hafnium has a greater diffusivity than carbon in tungsten at high temperatures. At temperatures above 2600 K the growth rate of HfC particles increases rapidly and there are two peaks appearing on the particle size distribution (Figs. 11 and 12). This indicates that some other diffusion mechanisms are involved in the particle coarsening process at extremely high temperatures. Comparing Figs. 3-5 with Figs. 9 and 10, two interesting facts are found. First, the number of HfC particles in the dislocationfree zone decreases with increasing temperature, indicating there is a selective diffusion from the particles not touched with dislocations to those located on the dislocation lines. Second, the majority of the grown particles in the temperature region of 2800 to 3000 K are located at the dislocation lines, surrounded by some very small particles that are also attached to the dislocations. Therefore, diffusion along dislocation "pipes" is most likely to be one of the reasons responsible for the observed bi-modal particle size distribution. The growth of the large particles on dislocation lines are accomplished by consuming the near-by intermediate ones touched to the dislocation "pipes". The great diffusivity of solute atoms along dislocations causes a rapid coarsening of selective large particle, and at the same time, results in a size decreasing of its neighboring particles. The intermediate particles are hence not observed in the size distribution. Grain-boundary diffusion could be another mechanism responsible for the bi-modal size distribution of HfC particles. Very large particles are often seen at grain boundaries, especially at boundary triple joints (Fig. 15). In the present material, the grain size is relatively large, approximately 130/~m determined by the intercept method. Considering the limited boundary area and the fact that the boundary diffusion rate increases not as fast as the bulk and dislocation diffusion rates when temperature is raised [14], the contribution of boundary diffusion to the rapid coarsening and bi-modal size distribution of HfC particles at extremely high temperatures is not as significant as the dislocation diffusion.
165
4.2. HfC dispersion hardening It has been shown that the solid-solution hardening of rhenium in tungsten is negligible at temperatures above 2200 K [3, 15]. The HfC dispersion hardening was assumed to be responsible for the exceptionally high strength of W-Re-HfC alloy in the temperature range employed in the present study. For the case of non-shearable second-phase particles, the most acceptable dispersion-hardening theory is the one proposed by Orowan [16]. According to Orowan's mechanism, the yield stress is determined by the shear stress required to bow a dislocation line between two particles separated by a distance 2p. This mechanism was later modified by Ashby with considerations on the dislocation line tension, dislocation energy, and random particle spacing [17]. The Ashby-Orowan dispersion-hardening model has the following form:
Gb d Ar=2--~p In ~
(9)
where A r is the resolved shear stress necessary to overcome the effects of particles, G and b are the shear modulus and the burgers vector of the matrix respectively, and ;tp is the planar interparticle spacing. Because the volume fraction of dispersion particles, f, is given by:
3 f = ,~,p2d
~d 2 -- 6~.p2
(10)
The planar interparticle spacing 2p can be calculated from known average particle diameter d and given particle volume fraction f:
2p =
fl/2
(11)
In the present case, the volume fraction f of HfC particles is 5.53 x 10 -3. The weighted average HfC particle diameter t~ at each test temperature is determined from transmission electron micrographs (Fig. 13). The magnitude of the burgers vector b of dislocation in tungsten is 2.741 A. The shear modulus of tungsten, G, is a decreasing function of temperature and is calculated based upon the following formula [18]: G = 1.5893 x 105- 1.4733 x 101( T - 273) - 2.448 x 10-3( T - 273) 2 MPa
(12)
By using eqn. (11) and Ashby-Orowan model, the shear stress A r resulting from the dispersionhardening of HfC particles in tungsten was calculated in the entire temperature region from 2200 to 3000 K.
166
M. Liu, J. Cowley /
Hafnium carbide growth behavior
TABLE 2. Comparison of the calculated resolved shear stress increment A r with the experimental value A 3' T (K)
d(A)
G (MPa)
Ar (MPa)
At' (MPa)
Deviation (%)
2200 2400 2600 2800 3000
421 470 516 1556 2072
121 116 111 106 100
56.1 49.5 44.0 17.3 12.9
61.8 52.7 45.4 19.2 13.1
-9.2 - 6.1 - 3.1 - 9.9 -1.4
449 518 391 067 548
deforming particles and the soft matrix. The formation of a cell structure introduces a strong dislocation interaction between the dislocation lines and hence, the dislocation mobility is decreased. But in the AshbyOrowan dispersion-hardening model, only particledislocation interaction has been considered. Because the contribution of dislocation-dislocation interaction to the yield stress is not counted in Ashby-Orowan model, it is therefore expected that this model would give an underestimate of the stress.
5. Conclusions
Fig. 17. Dislocation cell structure in 2400 K heated specimen.
The results are given in Table 2. For comparison, the experimentally determined shear stress increment At' is also shown in this table. Comparison of the calculated values with the experimental data indicates that the Ashby-Orowan model is successful in explaining the strength property of HfC particle hardened tungsten at high temperatures. It was noted that the stresses calculated based upon this model are slightly smaller than the experimental values over the entire temperature region, especially at 2200 and 2800 K where the calculated stress is approximately 10% smaller than the experimentally determined stress. This is attributed to two causes. One may be the error introduced in neglecting the contribution of rhenium to the strength of tungsten. Even though the solid-solution hardening effect of rhenium is very small at temperatures greater than 2200 K, the contribution of dissolved rhenium to the strength is certainly not zero. Another factor may be the dislocation cell structure around the dispersion particles. As shown in Fig. 17, the dislocation cell structure is formed by the generation of dislocations due to the necessity for retaining continuity between the non-
(i) HfC particle size is relatively stable after 2 h of heating in the temperature region 2200-2600 K. In this temperature region, the activation energy for HfC particle growth is determined to be 50.2+ 1.0 kcal mol-1 and the coarsening of HfC particles is a bulk diffusion-controlled process. (ii) Rapid particle growth occurs at temperatures above 2600 K. A bi-modal particle size distribution is observed at 2800 and 3000 K and selective particle growth takes place along dislocation lines and at grain boundaries, indicating that the mechanisms of dislocation and boundary enhanced diffusion are involved in the HfC particle coarsening process in this temperature region. (iii) Analysis on the diffusivity data shows that hafnium has a much faster diffusion rate than carbon at high temperatures and the grown particles are found to be hafnium-rich HfC particles. Hafnium is hence the less stable element in the HfC decomposition and growth process. (iv) The strength property of W - R e - H f C alloy at high temperatures basically depends upon the HfC particle size stability. The hardening effect of HfC particles in tungsten-rhenium matrix decreases with increased particle size. (v) The A s h b y - O r o w a n model is successful in explaining the dispersion hardening of HfC in tungsten at high temperatures. Good agreement is obtained between the calculated resolved shear stress and experimental results in the temperature region 2200-3000 K.
Acknowledgment This work was supported by National Science Foundations (NSF) grant D M R 90-14975 and made use of the T E M specimen preparation equipment at the Facility for High Resolution Electron Microscopy supported by NSF D M R 89-13384. The authors would like to thank the Electron Microscopy Labora-
M. Liu, J. Cowley
/
Hafnium carbide growth behavior
tory of Material Science and Engineering Program at A r i z o n a State University for using the microscope. T h e authors would also like to thank Dr. A. L u o and Dr. D. L. Jacobson for the assistance in performing the mechanical tests and the reviewer from Materials Science a n d Engineering A for the astute comments which have been integrated in this final version.
References 1 W. D. Klopp and W. R. Witzke, Mechanical properties of a W-23.4%Re-0.27%HfC alloy, J. Less-Common Met., 24 (1971) 427-443. 2 A. Luo, D. L. Jacobson and K. S. Shin, Tensile properties of tungsten-3.6% rhenium-0.4% hafnium carbide above 0.5 Tm Scr. Metall., 23 (1989) 397-401. 3 K.S. Shin, A. Luo, B. L. Chela and D. L. Jacobson, High temperature properties of particle-strengthened tungsten, J. Met., 42(1990) 12-17. 4 E L. Raffo, Yielding and fracture in tungsten and tungsten-rhenium alloys, J. Less-Common Met., 17 (1969) 133-149. 5 J. R. Stephens and W. R. Witzke, Alloy softening in group VIA metals alloyed with rhenium, J. Less-Common Met., 23 (1971)325-341. 6 A. Luo, D. L. Jacobson and K. S. Shin, Solution softening mechanism of iridium and rhenium in tungsten at room temperature, Int. J. Refractory Met. Hard Mater., 10 (1991) 107-114.
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7 M. Hansen, Constitution of Binary Alloys, McGraw-Hill, New York, 1958, pp. 766-777. 8 I.M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solution, J. Phys. Chem. Solids, 19 (1961)35-50. 9 B. A. Dainyak and V. I. Kostikov, Chem. Metal., 11 (1976) 15-18. 10 A. Y. Nakonechnikov, L. V. Pavlinov and V. N. Bokov, Fiz. Metal. Metalloved., 22(1966) 234-239. 11 R.A. Andrievskii, V. V. Klimenko and Y. E Khormove, Selfdiffusion of Hf in Group IV and V transition metal carbides, Fiz. Metal. Metalloved, 28(1969), 214-221. 12 R.A. Andrievskii, V. V. Klimenko and Y. E Khormove, Selfdiffusion of C in Group 1V and V transition metal carbides, Fiz. Metal. Metalloved, 28(1969) 298-303. 13 E G. Cotter and J. A. Kohn, Industrial diamond substitutes: I, physical and X-ray study of hafnium carbide, J. Am. Ceram. Soc., 37(1954) 415-420. 14 L. A. Girifalco, Atomic Migration in Crystals, Blaisdell Publishing, New York, 1964, pp. 117-130. 15 A. Luo, K. S. Shin and D. L. Jacobson, High temperature tensile properties of W-Re-ThO 2 alloys, Mater. Sci. Eng., A148(1991) 229-233. 16 E. Orowan, Internal Stresses in Metals and Alloys, Institute of Metals, London, 1948, pp. 451-477. 17 M. E Ashby, The theory of critical shear stress and working hardening of dispersion-hardened crystals, in G. S. Ansell, ed., Oxide Dispersion Strengthening, Proc. 2nd Bolton Landing Conf., Gordon and Breach Science Publishers, New York, 1968, pp. 143-205. 18 R. Lowrie and A. M. Gonas, Dynamic properties of polycrystalline tungsten, J. Appl. Phys., 36 (1965) 2189-2192.