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An analysis of carbide precipitation in V and Nb during aging and ion bombardment
270
Nuclear
Instruments
and Methods
in Physics Research
816 (1986) 270--2X3
North-Holland,
AN ANALYSIS OF CARBIDE PRECIPITATION DURING AGING AND ION BOMBARDMENT
Amsterdam
IN V AND Nb *
A.J. PEDRAZA Department
of Materials
Science and Engineering,
The Uniuersity
of Tennes.see, Knoxville, TN 37996-2200, USA
D. PEDRAZA Merdsand Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Carbide precipitation in vanadium and niobium is accompanied by a very large volume change ( =18$). A thermodynamic analysis of the V-C system and an estimate of the plastic energy required for accommodating that change is performed. The carbon concentrations for surface and for bulk precipitation are calculated. It is concluded that precipitation limited to the surface region can occur in high purity vanadium if an external carbon source is available. A similar conclusion is reached in the case of niobium, partly based on an estimate of the plastic energy required for accommodating the volume change due to carbide precipitation. These analyses provide a basis to distinguish between surface and radiation induced precipitates. Two main classes of behavior can arise during ion bomb~dment. When the highest damage region is very ctose to the surface, no internal precipitates are produced and radiation induced point defects enhance surface precipitate growth. When peak damage is produced farther from the surface, internal precipitates are formed and compete with the surface precipitates for carbon atom capture. The delicate balance between chemical driving force, transformation stresses and radiation effects may alter the precipitation pattern in both the surface and the damaged region.
Two fundamental changes occur during the ion implantation of a metal. First, atomic collisions result in radiation damage and second the injection of atoms causes, in many cases, a change in chemical composition which may extend further away from the damaged region. The distribution of solutes and impurities depends upon the interplay between those two processes. In fact, it is well known that under bomb~dment the stability of phases may be modified by allowing nucleation to occur at temperatures where it would not take place under thermal aging [1,2]. Also segregation of solute species may be induced due to annihilation of the irradiation produced point defects at the various sinks present in the metal. Although the role of the external surface as a point defect sink can be very important, other effects due to its presence should not be ignored. In this sense, it is
* Research sponsored in part by the Division of Materials Sciences, US Department of Energy, under contract DEACXX-84OR21400 with Martin Marietta Energy Systems, Inc. and in part by The University of Tennessee, Department of Materials Science and Energineering, Knoxville, TN, USA.
0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
worth emphasizing that the surface of a solid is the region where gas molecules may be adsorbed and eventually transferred to the bulk by a diffusion process. It is also the region where stresses can be more easily relaxed. Thus, the volume and shape changes that occur during the precipitation of a new phase can be more easily accommodated in the near surface region. During ion bombardment, the large fraction of point defects that are created provide additional means for accommodating these changes. The volume changes that occur during the precipitation of carbides in vanadium and niobium are particularly high, e.g., 18.4% change is involved in VzC fomation [3] and 17.4% in NbzC precipitation [4]. These carbides are observed to precipitate in the near surface region of alloys whose bulk carbon contents would cause no internal precipitates (5-71. We shall first analyse surface precipitation in vanadium during aging in order to show that it is a process that can be separated from bulk precipitation. This analysis will then be used for understanding the effects of ion irradiation upon carbide formation. Although data is much more limited, we have also treated the case of niobium. The competition for carbon capture by surface precipitates and irradiation induced precipitates will be evaluated. A brief experimental background is presented prior to the theoretical analyses.
271
A.J. Pedraza, D. Pedrara / Carbide precipitation in V and Nb 2. Experimental
relationship
background
2.1. Carbide precipitation
in vanadium
with the matrix given by
(011) ll(O~l)
during aging
In order to establish a reliable phase diagram of the V-C system in the vanadium rich end, Diercks and Wert [S] compiled the results obtained by various authors. The carbon solubility appears to be well below 1 at.% at 1273 K, whereas at higher concentrations the V,C phase precipitates. That compound is hexagonal and, in equilibrium, its lattice parameters are a = 0.2884 nm and c = 0.4565 nm [2]. At temperatures below 1073 K. the phase becomes slightly orthorhombic, possibly due to an ordering of the C atoms, the distortion from the hcp being 1.1% and the parameters, a = 0.257 nm (- 2aheX ) and c = 0.503 nm (= 3a,,,,) [8]. Diercks and Wert [8] observed two stages in the precipitation of carbides in supersaturated solid solution of = 0.2-0.4 at.% C in V. First, a coherent, plate-like precipitate forms, having a bee structure and a (310) habit plane. On further annealing, these precipitates appear to transform directly into the semicoherent V,C phase, which forms with either the hexagonal or the closely related orthorhombic structure. The VzC semicoherent phase eventually becomes incoherent and has an orientation
--[iii]ll[ii20] -[211]il[iioo] The volume change is not only very large but also highly anisotropic, viz., 9.98% in the [ill],
direction,
1.02% in the [ii2],
direction,
6.60% in the [ilo],,,
direction
and
There is a large deformation associated with the loss of coherency which produces dislocation loops and helices in the matrix. Fully developed V,C particles were observed after aging at 873 K for 1 h in samples containing 0.2 at.% C. Hexagonal V,C particles exhibiting the same orientation relationship have also been observed by Grabowski [7] as surface precipitates in thermally aged samples (nominal carbon content = 550 atppm) annealed in the range 523-973 K. These particles exhibit a three fold symmetry; when viewed in a (ill), surface, they appear elongated in three out of the six possible (112), directions. Some of Grabowski’s results are summarized in table 1. Fig. 1 illustrates the crystallography.
[00a, t .V-MATRIX
hl, [li,ol, I
o "v$'!-PRECIPITATE
32'
a
b
Fig. 1. (a) Star shaped precipitates on - (ill), surface of 975 K aged sample, (b) vanadium atom positions for observed orientation relationship between vanadium pointing in the [ii2], direction on (111) foil. The upward direction is [ilO], and Grabowski, Naval Research Laboratory, Washington DC)
matrix and a V,C precipitate, with star leg [OOOl],. (From ref. [7]). (Courtesy Dr. K.
IV. MICROSTRUCTURE
AND
PROPERTIES
212
A.J. Pedrara, D. Pedrara / Carbide precipitation
to a maximum value at = 770 K, then decreased mimimum at = 1023 K and again increased as the irradiation temperature was further increased. His results thus agree with those of Agarwal et al. [9], as table 2 shows. A comparison of the results after aging [8] and those with concurrent self-ion bombardment [7,9] seems to indicate that irradiation does, at least, not enhance the formation of V,C particles. The same surface precipitate morphology as that of V,C, i.e., a three bladed arrow driven into the specimen, was also observed in 150 keV H+- bombarded Nb in the range 975-1275 K by Thomas et al. [5,6]. This particle was identified as Nb,C and was seen to penetrate deeply into the irradiated samples, well beyond the ion range (- 1 pm). They observed a size increase with temperature of an order of magnitude when increasing the temperature from the lower to the higher limit of the studied range and a continuous increase of the average size with fluence, which did not exhibit any tendency towards saturation. It is important to note that Thomas and Bauer report the occurrence of precipitation only in the implanted area when samples were mechanically polished, in contrast to samples prepared by electropolishing which exhibited precipitates all over the sample surface.
Table 1 Amount of carbon measured after thermal aging alone and after concurrent ion bombardment, in the surface regions total irradiation and/or annealing time, f = lo4 s Temperature IKI
As prepared 523 723 823
Width times integrated amount of carbon after aging alone, ‘)
Width times integrated amount of carbon in the peak damage
2.55 x 2.40x 9.24~ 7.59 x
5.6x10-’ 4.5x10-3
lo- 3 lo-’ 10-a lo- .7
a) These values have been calculated by integrating the areas under the concentration profiles given in ref. [7], figs. 26 and 29, and substracting the values that correspond to the ‘as prepared’ sample.
2.2. Carbide precipitation
during ion bombardment
The effect of irradiation on carbide precipitation in vanadium has been studied by several authors [7,9-111. A coherent precipitate, similar to that observed by Diercks et al. [8], but with a different habit plane - a (210}, (8’ away from the closest {310),) - has been observed by Agarwal et al. [9,10] during 3 MeV 5’V+ ion bombardment of high purity vanadium and of vanadium with different carbon contents (see table 2). The V,C semicoherent or incoherent particles appeared at 973 K and higher temperatures only in the 0.4 at.% C alloy, after irradiation times equal to the aging times in the experiments of Diercks and Wert [8]. Grabowski [7] studied the precipitation behavior by measuring the depth distribution of carbon using ion beam analysis with neutron induced nuclear reactions. He measured a carbon content enhancement in the peak damage region which increased with temperature from 523 K to a
Table 2 Summary irradiation Irradiation temperature,
of the precipitate microstructures observed dose: 20 dpa, irradiation time: 3650 s
in vanadium
in V and Nb
3. The influence of the external surface During ion bombardment, phenomena that take place in the external surface can affect the radiation induced precipitation, because the damaged region is itself close to the bombarded surface. In particular, gas contamination from the surrounding atmosphere may contribute carbon to the surface region. Carbon adsorbed during sample preparation prior to irradiation and/or aging could be considered as an external solute source. Quantitative results of surface precipitation on aging were obtained by Grabowski [7] in the same atmosphere
and V-C alloys, at various
c
Vanadium
v-o.172
very high density of (012) precipitates no precipitates no precipitates fine precipitation on dislocations fine precipitation on dislocations and void surfaces
very high density of
irradiation
V-0.4%
temperatures
(from ref. 191)
c
IKI 923 973 1023 1073 1153
(012) precipitates dense (012) precipitates low density coarse (012)precipitates coarse (012) precipitates metastable carbide exhibiting displacement fringe contrast
very high density of {012) precipitates; no V,C V,C + (012) precipitates V,C + {012) precipitates V,C + some coarse (012) precipitates fine V,C on the surfaces of the specimen + V,C in bulk + some metastable carbide
A.J. Pedrara, D. Pedrazu / Carbide precipitarron
used for his ion irradiations. His data is therefore useful for evaluating the importance of the carbon external source vs possible bulk contributions. Measurements carried out in the temperature range from 523 to 823 K showed carbide precipitation limited to a surface layer of = 100 nm, the total carbon content apparently increasing from 523 to 723 K with no significant difference between 723 and 823 K. Let us first calculate how much carbon might be provided from the bulk material. We shall model the increase of precipitation as though it were a planar carbon sink (an interface) propagating inwards [12]. In that case, if we assume a local equilibriium at the advancing front and that the carbon concentration is lower than at the bulk (a hypothesis to be further discussed below), a simple estimate can be made using a linearized gradient approximation for solute balance. The amount of carbon per unit area, N,. provided by the bulk is given by
273
in V and Nb
4. Thermodynamics
and transformation stresses
As discussed in the previous section, surface contamination from the chamber atmosphere - even at very low CO partial pressures - can play a major role in surface carbide precipitation. For carbon to diffuse into the matrix, it is necessary that the crystal free energy decreases as carbon content increases. A simple reasoning suggests that carbon should enrich the matrix up to the solubility limit. But even then, it can be questioned whether precipitation may occur or not. In order to understand the precipitation dynamics, a detailed thermodynamic analysis is necessary. If we assume a regular approximation for the solid solution of C in vanadium and allow for an asymmetric miscibility gap. the enthalpy of mixing can be written as Hmi,=nx(l
-x)+/3,(1
-x)(2-x),
(2)
where x is the solute atomic fraction and (Yand p are constants. The free energy of the solution is then AC,,,
= (Yx(1 -x)+Px(l
-x)(2-x)
+RT{xInx+(l-x)ln(l-x)}+H,x, where D is the atomic volume of the crystal, x, and x,, are respectively the local equilibrium and the bulk concentrations, D is the carbon diffusion coeficient and t ib the annealing time. Although the diffusion coefficient of carbon in vanadium is high at the two highest temperatures of table 1, the bulk contribution is determined by the excess carbon content (xb - x,). If, for instance, this difference is of the order of 1 X lo-* at.%, the bulk contributions f?N, = 3.75
X
10m4 pm at 723 K
and
S?N, = 1.20 X 10P3 pm at 823 K, can be calculated, which are much lower than the measured surface contamination. The diffusion coefficient used was D=5.3X10m7
where H, is the enthalpy of bee carbon Kaufman and Nesor [13], H,, = 81594 - 14.6 T 5
t
i
as calculated
.
(3) by
(4)
The free energy of the intermetallic compound, AC,,,, was taken from the data by Hultgren et al. [14] for VC and adjusted for V,C by scaling with the melting temperatures. This yielded AC,,, = - 39626 J/mol at 1900 J/mol at 700 K. The chemical K, and AC,,, = -42803 potential for V,C and for the solid solution in equilibrium is given by Y=
Cl"mix ax
= a(1 - 2x,)
+ fi(2 -6x,
+ 3x;)
I,,
exp (5)
In the next section we show that the difference (xb - xc) is indeed of order lo-* and, therefore, that it is mainly an external source that provides carbon for surface precipitation. At 523 K, even if x, were zero, the diffusion distance is so short that no carbon build up can be supplied from the bulk by diffusion. In the experiments in niobium [5,6] and in those of Weber et al. in vanadium [ll], two sets of samples differing in their surface preparation were bombarded. In the set of samples where surface contamination was avoided or removed, the vacuum chamber atmosphere contributed most of the carbon. In the other set. both prior surface contamination and the vacuum chamber atmosphere acted as external sources.
equilibrium where x,, and xi”, are the corresponding concentrations. Taking the solubility limits given in the phase diagram by Mathews and Rowe [15] as the values at which precipitation starts, those should correspond to an available driving force of the right magnitude for allowing plastic deformation of the matrix as precipitation occurs. Taking this consideration into account, we have calculated the values reported in table 3. The calculations were made by first obtaining the coefficients a and p by fitting the high temperature solvus line of ref. [15]. Considering that ] AC,,, ] is much higher than (AC,,, 1 at the pertinent values of the concentrations, we have assumed that the value of y in eq. (6) is practically independent of temperature. Also, since at IV. MICROSTRUCTURE
AND
PROPERTIES
A.J. Pedrora, D. Pedraza / Carbide precipitation
274 Table 3 Thermodynamic
data for the V-C
system a)
xrnwl [at.%]
;a:.%]
Fat%]
523
5.00
0
573
5.14
0
723
5.56
0
823
5.85
1.7 x lo-”
1273
7.07
0.13
1859
8.61
0.90
0.08 0.20 0.08 0.20 0.25 0.08 0.20 0.25 0.08 0.20 0.25 0.08 0.50 1.00
a) o( - 1.052 x lo6 J/mol,
in V and Nb
71.48 1689 74.82 176.4 216.9 84.44 198.6 244.1 91.12 213.6 262.1 120.4 642.1 367
35.53 98.65 32.19 91.12 117.5 22.51 68.97 90.29 15.88 53.92 72.31 1.380 41.80 1.550
p = - 0.591 x lo6 J/mol
700 K one may expect that the straight line whose stope is y will pass almost through the origin (which was later confirmed), we have estimated y = - 133760 J/mol with xi”, = 0.32. Fig. 2a illustrates the calculated free energy curve for AGmix, together with a schematic plot of AG,,, 7 while fig. 2b gives a detail of AC,,, near the origin of X. In table 3 we have also included the values of x,,,~,, at which AGmi, has its minimum. If there is a carbon source available and there are no precipitates present, carbon enrichment will be favored because of the accompanying decrease of free energy. If the source is external, precipitation will start in the region adjacent to the free surface because the enrichment is higher there. Let us now analyze the role of the transformation stresses in the precipitation sequence. The observations of Diercks and Wert show that the precipitation of V,C is preceded by that of a coherent plate-like precipitate which, at a certain stage of growth, transforms directly into the semicoherent carbide. Khatchaturyan has calculated [16] the habit plane of a coherent plate-like precipitate in a cubic matrix by minimizing its elastic strain energy (which is a function of the habit plane). He considered the case of a bet host lattice (e.g., Nb) with interstitials that segregate to octahedral sites and produce a slight tetragonal distortion, #,_ Assuming that the elastic constants of precipitate and matrix are equal, he derived for Nb,O a habit plane close to either a {013} or a (012). Using the same approach as in [16] we have calculated for a coherent carbide precipitate in a vanadium matrix, assuming the same value of t, ‘and equal elastic constants for host and precipitate, a habit plane at 0.5” from a (012) and 8” from a (013). The latter is the habit plane of the coherent precipitate
reported after thermal annealing [9]. The 10123 habit has been obtained under self-ion bombardment (see table 2). Thus, from the point of view of minimizaton of elastic stresses, the habit plane for the coherent precipitate seems to be fairly well predicted. In the case of surface precipitation, not only the nucleation stage, but also the growth morphology reveal the effect of the large and anisotropic volume change. In this sense, a comparison with another phase transformation, quite different from that in V-C but with similar crystallographic features, helps to single out that effect. The equiatomic Ag-Zn alloy can undergo a diffusionless transformation p(/3’) -) lo, where matrix and precipitate have an orientation relationship similar to the V,C case. Clark et al. [17] observed copious surface nucleation of the [O-phase, and in a (lll)p, surface, three fold symmetric particles in the (112) directions, a morphology entirely analogous to that of the V,C precipitates. The authors concluded that the preferential surface nucleation is a clear result of the dimensional
Table 4 Energies required for plastic deformation at various temperatures a1Strain, z = 0.054
;rKl Vanadium 523 123 823 Niobium 1173 1273
+% lJlm4
~“&tl lJlm4
Plastic energy Plmoll
1826
2414
108
1170 961.4
1651 1375
71.1 50.1
438 221
731 656
25.1 12.5
‘) The data of the mechanical
properties
are from ref. 1181.
275
A.J. Pedrara. D Pedraza / Carbide precipitation in V and Nb
It can thus be suggested that the growth of V,C is limited by the plastic deformation necessary for accommodating the associated volume change. In this sense it is very illustrative to calculate the energy required to deform plastically the matrix by E = 5.4%, which is the average length change of V,C relative to the vanadium lattice. The energy that such a deformation would require was estimated using the yield strength, 5, the ultimate tensile strength, uU, and the elongation at the proper temperatures. The energy was then calculated as
125
100
-25
-50 0.0
0.2
0.4 ATOMIC
0.6
0.6
1.0
FRACTION
b
Where 52, is the molar volume of the matrix. The mechanical properties used [IS] are listed in table 4 together with the values of E, at various temperatures. The magnitude of eY and eU decrease in a very pronounced way with increasing temperature, indicating that at temperatures higher than = 1100 K the energy of plastic deformation is negligible. These results ensure the consistency of our thermodynamic calculations and the experimental diagram of Mathews and Rowe [15], as the solubility limits in the diagram do not become zero down to 723 K. The estimated plastic energies can next be used to determine the minimum concentration xo that will permit V,C to grow in the bulk, (7)
AC,, ( XG > ’ A$,
where AC,, is the chemical driving force and AC,, = E, is the excess energy required to accommodate the volume change by plastic deformation of the matrix. An inspection of tables 3 and 4 shows that xo should be around 0.2 at.% C at 523 < T< 823 K for the precipitates to grow, which is in very good agreement with the observations of Diercks and Wert [8]. I
I I
5. Surface
I I
-3
I I I
Xrninl
0.00
I
/
0.02
0.04
ATOMIC
I I 1 0.06
FRACTION
Fig. 2 Free energy diagram of the V-C solid solution and V,C intermetallic at 723 K. (a) Complete concentration range. (b) Detail near x = 0.
changes accompanying the transformation. The resulting morphology is basically determined by the way in which the matrix can accommodate those changes; when the direction of maximum volume change is normal to the external surface, nucleation is more copious than in any other case.
and radiation induced precipitation
In the presence of an external carbon source, continuing precipitation can occur in the surface region of high purity vanadium, regulated by the availability of carbon and by the possible presence of other competing sinks in the material. Although the system is open, we shall assume that local equilibrium is maintained at the precipitate/matrix interface. In the matrix, the free energy can be decreased if the carbon concentration increases (up to x,,,), as was shown in the previous section. This provides a supersaturated matrix that allows the nucleation and growth of precipitates. However, when the precipitate in question is V,C and growth is in the bulk, a considerable supersaturation is required in order to have the necessary driving force for the plastic deformation of the matrix that results from the accompanying volume change. For instance, at 723 K IV. MICROSTRUCTURE
AND PROPERTIES
216
A.J. Pedrara, D. Pedraza / Carbide precipitation
we have estimated that a carbon concentration of the order of 0.2 at.% yields the necessary driving force. In the experiments indicated in table 2, the vanadium matrix has a much lower concentration (2 5.5 x lo-* at.%) and the results do show indeed that in the matrix there is no carbon enrichment after thermal annealing. On the contrary, a slight depression of the carbon level is observed in the region adjacent to the surface layer having precipitates, indicating that the carbon equilibrium concentration is lower or of the order of 5 x 10P4. An inspection of table 3 shows that the driving force has been strongly reduced, indicating that the free surface does indeed accommodate a large fraction of the transformation strains. For this reason, the presence of the surface enables growth to proceed up to a limited depth where the transformatiion stresses can be relaxed. Furthermore, since the nucleation frequency is very sensitive to the available driving force, nucleation can be expected to occur only up to a very short distance from the surface. Under the constraints that we have just described, it is clear that the matrix around the precipitates cannot become very much depleted of carbon, as inward growth demands an increasing supersaturation. The external source of carbon in carefully controlled ion implantation experiments such as those in references [7] and [ll] involves a very low partial pressure of carbon containing molecules. The carbon content measured in the experiments with high purity vanadium referred to in table 1 is, according to our thermodynamic calculations, above x0 at the corresponding temperatures. However, that concentration is not sufficient _ as shown in table 3 - to cause precipitation in the bulk. But, during thermal aging, precipitation can occur in the surface region assisted in principle, by two sauces, viz., the atmosphere and the bulk. The balance of mass at any given time t can be expressed as:
LX, where [, is the precipitate fraction at time t in the near surface region of width S,, xP is the precipitate carbon concentration, J is the carbon flux available at the surface, averaged over time t. The second term in eq. (8) is negligible in the case we are considering. Assuming a spherical precipitate shape, we may next write SJ, = $rs3N,,
(9)
where r, is the precipitate radius and N, the number of precipitates per unit area. Grabowski found [7] at 973 K, N, = 1.2 X 1013rnm2, four times more than at 1153 K. Hence, this value is most likely a lower bound to the value of N, at 723 K. If we substitute for N, in eq. (lo), it yields r, - 61.7 nm,
in V and Nb
where we have included the total amount of precipitates. Considering now just the precipitate fraction that formed during aging time, the growth rate can be estimated if we next assume that J is approximately constant. Then, . c? - 6.23 x lo-‘nm/s, which reveals a very slow growth rate (about l/5 of the growth rate that would be obtained for diffusion controlled growth), and a size of the same magnitude as experimentally observed. The slow growth rate shows once more that, even for precipitates that are close to the surface, the volume change that accompanies their growth controls their kinetics. Two situations can be envisaged during ion bombardment. First, if the irradiaton produces internal precipitation, these precipitates can compete with the surface ones for carbon capture. Second, if no internal precipitates are generated, the annihilation of vacancies at the precipitate matrix interface can promote additional growth of the surface precipitates. Fig. 2 shows the damage profiles of 3 MeV V+ ions in V and of 150 keV H+ ions in Nb, which are instances where the above referred situations have been observed. In the case of vanadium, the half width of the damage profile extends from = 0.5 to 1.2 pm. Since under thermal aging surface precipitation extends up to = 0.5 pm inside the sample, a surface region of width 8, < 0.5 pm can be clearly distinguished from the highest damaged region of width a,, with 6, < 8: < 1.2 pm. In the irradiation experiments with niobium, the highest damage region is closer to the external surface and some superposition of surface and highest damage region exists. The ion bombardment experiments on vanadium yielded precipitate formation induced by self-ion bombardment in the region of highest damage [7]. As previously mentioned carbon diffusion does not control surface precipitation, but it may assist the precipitation processes in the damaged region. The experimental observations tend to suggest that precipitation takes place in the highest damaged region at temperatures below = 970 K, if carbon is available. Since the region of highest damage is adjacent to the subsurface region where precipitation occurs under thermal aging, the two regions can compete for carbon capture from the surface. This will only occur if precipitation in the damaged region depletes the local matrix of carbon and therefore carbon currents from a richer matrix at both sides of the region in question are established. The balance of mass at any time, t under irradiation can be written as SarQs=
(J-J,)tQ,
in the subsurface
00) region, and
(11)
A.J. Pedraza, D. Pedraza / Carbide precipitation in V and Nb
region. JS,. and SD are respectively the precipitate fractions in the surface region of width 8,. Jo is the carbon flux from the external source that is absorbed in the peak damage region. The second term in eq. (11) accounts for the carbon flux coming from the bulk toward an impoverished matrix of concentration s,. The data of table 1 can next be used for calculating the value of J,. Thus, at 723 K, when 1= lo4 S,
277
in the peak damage
J D = 2.52 x 10’6m-2s-’ and substituting ~scsr~PSs=
02)
into eq. (11) yields
5.70 X 10-‘3pm
1.0
0.8
0.6
0.4
0.2
(13) nn
which is in agreement with the value measured experimentally [7]. This result demonstrates that the damaged region is certainly a very efficient carbon sink whose presence decreases surface precipitate growth relative to thermal dging alone. The diffusional transport of carbon into the Irradiated region is demonstrated by the experiments at low temperature (523 K) where carbon enrichment is limited to the surface region while no enrichment occurs in the irradiated zone. Thus, the vacancy supersaturation alone, which is larger at the lower temperatures, is not sufficient for inducing precipitation. On the other hand, at higher temperatures e.g., = 970-1030 K, no precipitation occurs in high purity vanadium, showing that high diffusion rates alone are not sufficient either (see table 2). The experimental resufts show clearly that irradiation does induce precipitation. However, at variance with the surface phemonenon, the precipitates appear to be of a coherent nature. This fact together with the elastic calculations of Khatchaturyan [16] suggest that under irradiation carbon clustering is enhanced and this yields a very efficient mechanism of precipitation. In fact, if the results of AgarwaI et al. [9] and those of Diercks and Wert [8] are compared, the effect of irradiation is seen to promote the coherent precipitates in detriment of V,C. The nucleation process is clearly highly favored by irradiation. If carbon transport is small it should control the irradiation induced precipitatlon. However if the available amount is large, the clustering process will be controlling, which seems to happen in the experiments at 723 K. We thus differentiate two mechanisms that may follow a 4 law. One is that of diffusion and the other is that of point defect build up which must assist clustering. In fact, in the low sink strength regime, that build up is known to follow a 4; law [19]. The delicate balance discussed above involving chemical driving force, transformation stresses and radiation effects on precipitation is further demonstrated in the case of carbide formation in niobium. Assuming a simitar behavior as in the V-C system, carbon will enter the matrix, when an external source is available, be-
0.4
0.8
1.2
DEPTW (pm)
Fig. 3. Damage Profiles of 3 MeV Vf in V and 150 keV H+ in Nb. 8,: width of the subsurface region; 66: width of highest damage region in vanadium irradiated with 3 MeV V+ ions.
cause it decreases its free energy. The energy required for plastically deform the matrix is fairly low at the temperatures of the Bauer and Thomas experiments, as shown in table 4. However, the availability of carbon strongly influenced the precipitation pattern. Thus, when the external surface provided a large supersaturation, as was the case where an adsorbed layer was introduced during sample preparation, irradiation effects were negligible. When that source was absent, as was the case of mechanically polished surfaces, surface precipitation occurred only in the bombarded area. A quite different situation from that occurring in the V-C experiments of ref. [7] is seen when precipitates do not form in the highest damaged region. In this case, the vacancy supersaturation reaches the near surface precipitates allowing further growth inwards. Moreover, when the magnitude of AC+ is low, the precipitates that start growing in the surface are not limited to the sub-surface region and can continue growing while irradiation is applied and the carbon supply lasts. Not withstanding the possible effects of other differences such as the specific damage, there is clearly a simple reason related to the fact that preciptates do not form in Nb in separate associaton with the highest damaged region. As pointed out before and shown in fig. 3, the peak damage with 150 keV protons in niobium lies much closer to the external surface than that praduced in vanadium with 3 MeV Vi ions.
6. Conclusions 1) A carbon concentration of 0.2 at.% produces bulk precipitation of V,C in the range 523-823 K, while only = 0.05 at.% is necessary for surface precipitation. The mass balance equation shows that irradiation induced carbide precipitation in vanadium IV. MICROSTRUCTURE
AND
PROPERTIES
278
A. J. Pedraza, L). Pedraza / Carbide precipitation
depletes the matrix carbon concentration in its vicinity practically to zero. 2) Both habit planes (013) and f012) observed during aging and ion bombardment respectively seem to be consistent with the minimization of the elastic strain energy. 3) The mass balance equation shows that in vanadium irradiated with 3 MeV V’ ions the precipitates formed in the highest damage region compete with the surface precipitates for the capture of carbon coming from and external source. In contrast to surface precipitates that have practically only one carbon source, the butk can also contribute carbon atoms to the radiation induced matrix precipitates. 4) If the peak damage region is very close to the surface, as is the case with niobium bombarded with 150 keV H+, no internal precipitates are produced and radiation induced point defects enhance the growth of surface precipitates. balance between carbon availability, 5) The delicate transformation stresses and radiation effects may significantly alter the precipitation characteristics of both the surface and the internal damaged region, relative to thermal aging.
References [I] Phase stability under irradiation, eds., J.R. Holland, L.K. Mansur and D.I. Potter, conf. Proc. (TMS-AIME, 1981). [2] Phase transformation during irradiation, ed., F.V. Nolfi (Applied Science, New York, 1983).
in V and Nb
[3] E. Rudy, St. Wind&h and C.E. Brukl, Planseeber Puivermet. 16 (1968) 3. [4] N. Terao. Jpn. J. Appl. Phys. 3 (1964) 104. [S] W. Bauer and G. Thomas, Proc. First Topical Conf. on Fusion Reactor Technolgy, San Diego, CA (1973). [6] W. Batter and G. Thomas, J. Vat. Sci. Technol. 12 (1975) 490. [7] K. Grabowski, Ph.D. thesis, The University of Michigan, Ann Arbor (1980). [8] D.R. Diercks and C.A. Wert, Metal]. Trans. 3 (1972) 1699. [9] SC. Agarwai, D.I. Potter and A. Taylor, irradiation effects on the microstructure and properties of metals, ed., F.R. Schober, Symp., St. Louis, MO. (ASTM STP 611, 1976) p, 298. [lo] SC. Aganvai, D.I. Potter and A. Taylor, Metall. Trans. 9A (1978) 579. [ll] W.J. Weber, G.L. Kulcinski, R.G. Lott, P. Wilkes and H.V. Smith Jr, Radiation effects and tritium technology for fusion reactor, eds., J.S. Watson and F. Wiffen (CONF/750989, Oak Ridge 1976) p. I/130. [12] W. Jost, Diffusion (Academic Press, New York, 1952) 68. [13] L. Kaufman and H. Nesor, CALPHAD 2 (1978) 295. 1141 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelly, Selected values of the thermodynamic properties of binary alloys (American Society for Metals. 1973). [15] D.R. Mathews and EA. Rowe, US Bureau of Mines Rep. Invest. 6628 (1968). [16] A.G. ~atchatu~an, Theory of structural tr~sfromations in sohds (Wiley, New York, 1983). [17) H, Met. Clark, E.A. Merriman and C.M. Wayman. Acta Metall. 17 (1969) 719. [18] T.E. Tietz and J.W. Wilson, Behavior and properties of refractory metals (Stanford University, Stanford, CA 1965). [19] D.F. Pedraza, E.J. Savino and A.J. Pedraza, J. Nucl. Mater. 73 (1978) 151.
Nuclear
Instruments
and Methods
in Physics Research
816 (1986) 270--2X3
North-Holland,
AN ANALYSIS OF CARBIDE PRECIPITATION DURING AGING AND ION BOMBARDMENT
Amsterdam
IN V AND Nb *
A.J. PEDRAZA Department
of Materials
Science and Engineering,
The Uniuersity
of Tennes.see, Knoxville, TN 37996-2200, USA
D. PEDRAZA Merdsand Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Carbide precipitation in vanadium and niobium is accompanied by a very large volume change ( =18$). A thermodynamic analysis of the V-C system and an estimate of the plastic energy required for accommodating that change is performed. The carbon concentrations for surface and for bulk precipitation are calculated. It is concluded that precipitation limited to the surface region can occur in high purity vanadium if an external carbon source is available. A similar conclusion is reached in the case of niobium, partly based on an estimate of the plastic energy required for accommodating the volume change due to carbide precipitation. These analyses provide a basis to distinguish between surface and radiation induced precipitates. Two main classes of behavior can arise during ion bomb~dment. When the highest damage region is very ctose to the surface, no internal precipitates are produced and radiation induced point defects enhance surface precipitate growth. When peak damage is produced farther from the surface, internal precipitates are formed and compete with the surface precipitates for carbon atom capture. The delicate balance between chemical driving force, transformation stresses and radiation effects may alter the precipitation pattern in both the surface and the damaged region.
Two fundamental changes occur during the ion implantation of a metal. First, atomic collisions result in radiation damage and second the injection of atoms causes, in many cases, a change in chemical composition which may extend further away from the damaged region. The distribution of solutes and impurities depends upon the interplay between those two processes. In fact, it is well known that under bomb~dment the stability of phases may be modified by allowing nucleation to occur at temperatures where it would not take place under thermal aging [1,2]. Also segregation of solute species may be induced due to annihilation of the irradiation produced point defects at the various sinks present in the metal. Although the role of the external surface as a point defect sink can be very important, other effects due to its presence should not be ignored. In this sense, it is
* Research sponsored in part by the Division of Materials Sciences, US Department of Energy, under contract DEACXX-84OR21400 with Martin Marietta Energy Systems, Inc. and in part by The University of Tennessee, Department of Materials Science and Energineering, Knoxville, TN, USA.
0168-583X/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
worth emphasizing that the surface of a solid is the region where gas molecules may be adsorbed and eventually transferred to the bulk by a diffusion process. It is also the region where stresses can be more easily relaxed. Thus, the volume and shape changes that occur during the precipitation of a new phase can be more easily accommodated in the near surface region. During ion bombardment, the large fraction of point defects that are created provide additional means for accommodating these changes. The volume changes that occur during the precipitation of carbides in vanadium and niobium are particularly high, e.g., 18.4% change is involved in VzC fomation [3] and 17.4% in NbzC precipitation [4]. These carbides are observed to precipitate in the near surface region of alloys whose bulk carbon contents would cause no internal precipitates (5-71. We shall first analyse surface precipitation in vanadium during aging in order to show that it is a process that can be separated from bulk precipitation. This analysis will then be used for understanding the effects of ion irradiation upon carbide formation. Although data is much more limited, we have also treated the case of niobium. The competition for carbon capture by surface precipitates and irradiation induced precipitates will be evaluated. A brief experimental background is presented prior to the theoretical analyses.
271
A.J. Pedraza, D. Pedrara / Carbide precipitation in V and Nb 2. Experimental
relationship
background
2.1. Carbide precipitation
in vanadium
with the matrix given by
(011) ll(O~l)
during aging
In order to establish a reliable phase diagram of the V-C system in the vanadium rich end, Diercks and Wert [S] compiled the results obtained by various authors. The carbon solubility appears to be well below 1 at.% at 1273 K, whereas at higher concentrations the V,C phase precipitates. That compound is hexagonal and, in equilibrium, its lattice parameters are a = 0.2884 nm and c = 0.4565 nm [2]. At temperatures below 1073 K. the phase becomes slightly orthorhombic, possibly due to an ordering of the C atoms, the distortion from the hcp being 1.1% and the parameters, a = 0.257 nm (- 2aheX ) and c = 0.503 nm (= 3a,,,,) [8]. Diercks and Wert [8] observed two stages in the precipitation of carbides in supersaturated solid solution of = 0.2-0.4 at.% C in V. First, a coherent, plate-like precipitate forms, having a bee structure and a (310) habit plane. On further annealing, these precipitates appear to transform directly into the semicoherent V,C phase, which forms with either the hexagonal or the closely related orthorhombic structure. The VzC semicoherent phase eventually becomes incoherent and has an orientation
--[iii]ll[ii20] -[211]il[iioo] The volume change is not only very large but also highly anisotropic, viz., 9.98% in the [ill],
direction,
1.02% in the [ii2],
direction,
6.60% in the [ilo],,,
direction
and
There is a large deformation associated with the loss of coherency which produces dislocation loops and helices in the matrix. Fully developed V,C particles were observed after aging at 873 K for 1 h in samples containing 0.2 at.% C. Hexagonal V,C particles exhibiting the same orientation relationship have also been observed by Grabowski [7] as surface precipitates in thermally aged samples (nominal carbon content = 550 atppm) annealed in the range 523-973 K. These particles exhibit a three fold symmetry; when viewed in a (ill), surface, they appear elongated in three out of the six possible (112), directions. Some of Grabowski’s results are summarized in table 1. Fig. 1 illustrates the crystallography.
[00a, t .V-MATRIX
hl, [li,ol, I
o "v$'!-PRECIPITATE
32'
a
b
Fig. 1. (a) Star shaped precipitates on - (ill), surface of 975 K aged sample, (b) vanadium atom positions for observed orientation relationship between vanadium pointing in the [ii2], direction on (111) foil. The upward direction is [ilO], and Grabowski, Naval Research Laboratory, Washington DC)
matrix and a V,C precipitate, with star leg [OOOl],. (From ref. [7]). (Courtesy Dr. K.
IV. MICROSTRUCTURE
AND
PROPERTIES
212
A.J. Pedrara, D. Pedrara / Carbide precipitation
to a maximum value at = 770 K, then decreased mimimum at = 1023 K and again increased as the irradiation temperature was further increased. His results thus agree with those of Agarwal et al. [9], as table 2 shows. A comparison of the results after aging [8] and those with concurrent self-ion bombardment [7,9] seems to indicate that irradiation does, at least, not enhance the formation of V,C particles. The same surface precipitate morphology as that of V,C, i.e., a three bladed arrow driven into the specimen, was also observed in 150 keV H+- bombarded Nb in the range 975-1275 K by Thomas et al. [5,6]. This particle was identified as Nb,C and was seen to penetrate deeply into the irradiated samples, well beyond the ion range (- 1 pm). They observed a size increase with temperature of an order of magnitude when increasing the temperature from the lower to the higher limit of the studied range and a continuous increase of the average size with fluence, which did not exhibit any tendency towards saturation. It is important to note that Thomas and Bauer report the occurrence of precipitation only in the implanted area when samples were mechanically polished, in contrast to samples prepared by electropolishing which exhibited precipitates all over the sample surface.
Table 1 Amount of carbon measured after thermal aging alone and after concurrent ion bombardment, in the surface regions total irradiation and/or annealing time, f = lo4 s Temperature IKI
As prepared 523 723 823
Width times integrated amount of carbon after aging alone, ‘)
Width times integrated amount of carbon in the peak damage
2.55 x 2.40x 9.24~ 7.59 x
5.6x10-’ 4.5x10-3
lo- 3 lo-’ 10-a lo- .7
a) These values have been calculated by integrating the areas under the concentration profiles given in ref. [7], figs. 26 and 29, and substracting the values that correspond to the ‘as prepared’ sample.
2.2. Carbide precipitation
during ion bombardment
The effect of irradiation on carbide precipitation in vanadium has been studied by several authors [7,9-111. A coherent precipitate, similar to that observed by Diercks et al. [8], but with a different habit plane - a (210}, (8’ away from the closest {310),) - has been observed by Agarwal et al. [9,10] during 3 MeV 5’V+ ion bombardment of high purity vanadium and of vanadium with different carbon contents (see table 2). The V,C semicoherent or incoherent particles appeared at 973 K and higher temperatures only in the 0.4 at.% C alloy, after irradiation times equal to the aging times in the experiments of Diercks and Wert [8]. Grabowski [7] studied the precipitation behavior by measuring the depth distribution of carbon using ion beam analysis with neutron induced nuclear reactions. He measured a carbon content enhancement in the peak damage region which increased with temperature from 523 K to a
Table 2 Summary irradiation Irradiation temperature,
of the precipitate microstructures observed dose: 20 dpa, irradiation time: 3650 s
in vanadium
in V and Nb
3. The influence of the external surface During ion bombardment, phenomena that take place in the external surface can affect the radiation induced precipitation, because the damaged region is itself close to the bombarded surface. In particular, gas contamination from the surrounding atmosphere may contribute carbon to the surface region. Carbon adsorbed during sample preparation prior to irradiation and/or aging could be considered as an external solute source. Quantitative results of surface precipitation on aging were obtained by Grabowski [7] in the same atmosphere
and V-C alloys, at various
c
Vanadium
v-o.172
very high density of (012) precipitates no precipitates no precipitates fine precipitation on dislocations fine precipitation on dislocations and void surfaces
very high density of
irradiation
V-0.4%
temperatures
(from ref. 191)
c
IKI 923 973 1023 1073 1153
(012) precipitates dense (012) precipitates low density coarse (012)precipitates coarse (012) precipitates metastable carbide exhibiting displacement fringe contrast
very high density of {012) precipitates; no V,C V,C + (012) precipitates V,C + {012) precipitates V,C + some coarse (012) precipitates fine V,C on the surfaces of the specimen + V,C in bulk + some metastable carbide
A.J. Pedrara, D. Pedrazu / Carbide precipitarron
used for his ion irradiations. His data is therefore useful for evaluating the importance of the carbon external source vs possible bulk contributions. Measurements carried out in the temperature range from 523 to 823 K showed carbide precipitation limited to a surface layer of = 100 nm, the total carbon content apparently increasing from 523 to 723 K with no significant difference between 723 and 823 K. Let us first calculate how much carbon might be provided from the bulk material. We shall model the increase of precipitation as though it were a planar carbon sink (an interface) propagating inwards [12]. In that case, if we assume a local equilibriium at the advancing front and that the carbon concentration is lower than at the bulk (a hypothesis to be further discussed below), a simple estimate can be made using a linearized gradient approximation for solute balance. The amount of carbon per unit area, N,. provided by the bulk is given by
273
in V and Nb
4. Thermodynamics
and transformation stresses
As discussed in the previous section, surface contamination from the chamber atmosphere - even at very low CO partial pressures - can play a major role in surface carbide precipitation. For carbon to diffuse into the matrix, it is necessary that the crystal free energy decreases as carbon content increases. A simple reasoning suggests that carbon should enrich the matrix up to the solubility limit. But even then, it can be questioned whether precipitation may occur or not. In order to understand the precipitation dynamics, a detailed thermodynamic analysis is necessary. If we assume a regular approximation for the solid solution of C in vanadium and allow for an asymmetric miscibility gap. the enthalpy of mixing can be written as Hmi,=nx(l
-x)+/3,(1
-x)(2-x),
(2)
where x is the solute atomic fraction and (Yand p are constants. The free energy of the solution is then AC,,,
= (Yx(1 -x)+Px(l
-x)(2-x)
+RT{xInx+(l-x)ln(l-x)}+H,x, where D is the atomic volume of the crystal, x, and x,, are respectively the local equilibrium and the bulk concentrations, D is the carbon diffusion coeficient and t ib the annealing time. Although the diffusion coefficient of carbon in vanadium is high at the two highest temperatures of table 1, the bulk contribution is determined by the excess carbon content (xb - x,). If, for instance, this difference is of the order of 1 X lo-* at.%, the bulk contributions f?N, = 3.75
X
10m4 pm at 723 K
and
S?N, = 1.20 X 10P3 pm at 823 K, can be calculated, which are much lower than the measured surface contamination. The diffusion coefficient used was D=5.3X10m7
where H, is the enthalpy of bee carbon Kaufman and Nesor [13], H,, = 81594 - 14.6 T 5
t
i
as calculated
.
(3) by
(4)
The free energy of the intermetallic compound, AC,,,, was taken from the data by Hultgren et al. [14] for VC and adjusted for V,C by scaling with the melting temperatures. This yielded AC,,, = - 39626 J/mol at 1900 J/mol at 700 K. The chemical K, and AC,,, = -42803 potential for V,C and for the solid solution in equilibrium is given by Y=
Cl"mix ax
= a(1 - 2x,)
+ fi(2 -6x,
+ 3x;)
I,,
exp (5)
In the next section we show that the difference (xb - xc) is indeed of order lo-* and, therefore, that it is mainly an external source that provides carbon for surface precipitation. At 523 K, even if x, were zero, the diffusion distance is so short that no carbon build up can be supplied from the bulk by diffusion. In the experiments in niobium [5,6] and in those of Weber et al. in vanadium [ll], two sets of samples differing in their surface preparation were bombarded. In the set of samples where surface contamination was avoided or removed, the vacuum chamber atmosphere contributed most of the carbon. In the other set. both prior surface contamination and the vacuum chamber atmosphere acted as external sources.
equilibrium where x,, and xi”, are the corresponding concentrations. Taking the solubility limits given in the phase diagram by Mathews and Rowe [15] as the values at which precipitation starts, those should correspond to an available driving force of the right magnitude for allowing plastic deformation of the matrix as precipitation occurs. Taking this consideration into account, we have calculated the values reported in table 3. The calculations were made by first obtaining the coefficients a and p by fitting the high temperature solvus line of ref. [15]. Considering that ] AC,,, ] is much higher than (AC,,, 1 at the pertinent values of the concentrations, we have assumed that the value of y in eq. (6) is practically independent of temperature. Also, since at IV. MICROSTRUCTURE
AND
PROPERTIES
A.J. Pedrora, D. Pedraza / Carbide precipitation
274 Table 3 Thermodynamic
data for the V-C
system a)
xrnwl [at.%]
;a:.%]
Fat%]
523
5.00
0
573
5.14
0
723
5.56
0
823
5.85
1.7 x lo-”
1273
7.07
0.13
1859
8.61
0.90
0.08 0.20 0.08 0.20 0.25 0.08 0.20 0.25 0.08 0.20 0.25 0.08 0.50 1.00
a) o( - 1.052 x lo6 J/mol,
in V and Nb
71.48 1689 74.82 176.4 216.9 84.44 198.6 244.1 91.12 213.6 262.1 120.4 642.1 367
35.53 98.65 32.19 91.12 117.5 22.51 68.97 90.29 15.88 53.92 72.31 1.380 41.80 1.550
p = - 0.591 x lo6 J/mol
700 K one may expect that the straight line whose stope is y will pass almost through the origin (which was later confirmed), we have estimated y = - 133760 J/mol with xi”, = 0.32. Fig. 2a illustrates the calculated free energy curve for AGmix, together with a schematic plot of AG,,, 7 while fig. 2b gives a detail of AC,,, near the origin of X. In table 3 we have also included the values of x,,,~,, at which AGmi, has its minimum. If there is a carbon source available and there are no precipitates present, carbon enrichment will be favored because of the accompanying decrease of free energy. If the source is external, precipitation will start in the region adjacent to the free surface because the enrichment is higher there. Let us now analyze the role of the transformation stresses in the precipitation sequence. The observations of Diercks and Wert show that the precipitation of V,C is preceded by that of a coherent plate-like precipitate which, at a certain stage of growth, transforms directly into the semicoherent carbide. Khatchaturyan has calculated [16] the habit plane of a coherent plate-like precipitate in a cubic matrix by minimizing its elastic strain energy (which is a function of the habit plane). He considered the case of a bet host lattice (e.g., Nb) with interstitials that segregate to octahedral sites and produce a slight tetragonal distortion, #,_ Assuming that the elastic constants of precipitate and matrix are equal, he derived for Nb,O a habit plane close to either a {013} or a (012). Using the same approach as in [16] we have calculated for a coherent carbide precipitate in a vanadium matrix, assuming the same value of t, ‘and equal elastic constants for host and precipitate, a habit plane at 0.5” from a (012) and 8” from a (013). The latter is the habit plane of the coherent precipitate
reported after thermal annealing [9]. The 10123 habit has been obtained under self-ion bombardment (see table 2). Thus, from the point of view of minimizaton of elastic stresses, the habit plane for the coherent precipitate seems to be fairly well predicted. In the case of surface precipitation, not only the nucleation stage, but also the growth morphology reveal the effect of the large and anisotropic volume change. In this sense, a comparison with another phase transformation, quite different from that in V-C but with similar crystallographic features, helps to single out that effect. The equiatomic Ag-Zn alloy can undergo a diffusionless transformation p(/3’) -) lo, where matrix and precipitate have an orientation relationship similar to the V,C case. Clark et al. [17] observed copious surface nucleation of the [O-phase, and in a (lll)p, surface, three fold symmetric particles in the (112) directions, a morphology entirely analogous to that of the V,C precipitates. The authors concluded that the preferential surface nucleation is a clear result of the dimensional
Table 4 Energies required for plastic deformation at various temperatures a1Strain, z = 0.054
;rKl Vanadium 523 123 823 Niobium 1173 1273
+% lJlm4
~“&tl lJlm4
Plastic energy Plmoll
1826
2414
108
1170 961.4
1651 1375
71.1 50.1
438 221
731 656
25.1 12.5
‘) The data of the mechanical
properties
are from ref. 1181.
275
A.J. Pedrara. D Pedraza / Carbide precipitation in V and Nb
It can thus be suggested that the growth of V,C is limited by the plastic deformation necessary for accommodating the associated volume change. In this sense it is very illustrative to calculate the energy required to deform plastically the matrix by E = 5.4%, which is the average length change of V,C relative to the vanadium lattice. The energy that such a deformation would require was estimated using the yield strength, 5, the ultimate tensile strength, uU, and the elongation at the proper temperatures. The energy was then calculated as
125
100
-25
-50 0.0
0.2
0.4 ATOMIC
0.6
0.6
1.0
FRACTION
b
Where 52, is the molar volume of the matrix. The mechanical properties used [IS] are listed in table 4 together with the values of E, at various temperatures. The magnitude of eY and eU decrease in a very pronounced way with increasing temperature, indicating that at temperatures higher than = 1100 K the energy of plastic deformation is negligible. These results ensure the consistency of our thermodynamic calculations and the experimental diagram of Mathews and Rowe [15], as the solubility limits in the diagram do not become zero down to 723 K. The estimated plastic energies can next be used to determine the minimum concentration xo that will permit V,C to grow in the bulk, (7)
AC,, ( XG > ’ A$,
where AC,, is the chemical driving force and AC,, = E, is the excess energy required to accommodate the volume change by plastic deformation of the matrix. An inspection of tables 3 and 4 shows that xo should be around 0.2 at.% C at 523 < T< 823 K for the precipitates to grow, which is in very good agreement with the observations of Diercks and Wert [8]. I
I I
5. Surface
I I
-3
I I I
Xrninl
0.00
I
/
0.02
0.04
ATOMIC
I I 1 0.06
FRACTION
Fig. 2 Free energy diagram of the V-C solid solution and V,C intermetallic at 723 K. (a) Complete concentration range. (b) Detail near x = 0.
changes accompanying the transformation. The resulting morphology is basically determined by the way in which the matrix can accommodate those changes; when the direction of maximum volume change is normal to the external surface, nucleation is more copious than in any other case.
and radiation induced precipitation
In the presence of an external carbon source, continuing precipitation can occur in the surface region of high purity vanadium, regulated by the availability of carbon and by the possible presence of other competing sinks in the material. Although the system is open, we shall assume that local equilibrium is maintained at the precipitate/matrix interface. In the matrix, the free energy can be decreased if the carbon concentration increases (up to x,,,), as was shown in the previous section. This provides a supersaturated matrix that allows the nucleation and growth of precipitates. However, when the precipitate in question is V,C and growth is in the bulk, a considerable supersaturation is required in order to have the necessary driving force for the plastic deformation of the matrix that results from the accompanying volume change. For instance, at 723 K IV. MICROSTRUCTURE
AND PROPERTIES
216
A.J. Pedrara, D. Pedraza / Carbide precipitation
we have estimated that a carbon concentration of the order of 0.2 at.% yields the necessary driving force. In the experiments indicated in table 2, the vanadium matrix has a much lower concentration (2 5.5 x lo-* at.%) and the results do show indeed that in the matrix there is no carbon enrichment after thermal annealing. On the contrary, a slight depression of the carbon level is observed in the region adjacent to the surface layer having precipitates, indicating that the carbon equilibrium concentration is lower or of the order of 5 x 10P4. An inspection of table 3 shows that the driving force has been strongly reduced, indicating that the free surface does indeed accommodate a large fraction of the transformation strains. For this reason, the presence of the surface enables growth to proceed up to a limited depth where the transformatiion stresses can be relaxed. Furthermore, since the nucleation frequency is very sensitive to the available driving force, nucleation can be expected to occur only up to a very short distance from the surface. Under the constraints that we have just described, it is clear that the matrix around the precipitates cannot become very much depleted of carbon, as inward growth demands an increasing supersaturation. The external source of carbon in carefully controlled ion implantation experiments such as those in references [7] and [ll] involves a very low partial pressure of carbon containing molecules. The carbon content measured in the experiments with high purity vanadium referred to in table 1 is, according to our thermodynamic calculations, above x0 at the corresponding temperatures. However, that concentration is not sufficient _ as shown in table 3 - to cause precipitation in the bulk. But, during thermal aging, precipitation can occur in the surface region assisted in principle, by two sauces, viz., the atmosphere and the bulk. The balance of mass at any given time t can be expressed as:
LX, where [, is the precipitate fraction at time t in the near surface region of width S,, xP is the precipitate carbon concentration, J is the carbon flux available at the surface, averaged over time t. The second term in eq. (8) is negligible in the case we are considering. Assuming a spherical precipitate shape, we may next write SJ, = $rs3N,,
(9)
where r, is the precipitate radius and N, the number of precipitates per unit area. Grabowski found [7] at 973 K, N, = 1.2 X 1013rnm2, four times more than at 1153 K. Hence, this value is most likely a lower bound to the value of N, at 723 K. If we substitute for N, in eq. (lo), it yields r, - 61.7 nm,
in V and Nb
where we have included the total amount of precipitates. Considering now just the precipitate fraction that formed during aging time, the growth rate can be estimated if we next assume that J is approximately constant. Then, . c? - 6.23 x lo-‘nm/s, which reveals a very slow growth rate (about l/5 of the growth rate that would be obtained for diffusion controlled growth), and a size of the same magnitude as experimentally observed. The slow growth rate shows once more that, even for precipitates that are close to the surface, the volume change that accompanies their growth controls their kinetics. Two situations can be envisaged during ion bombardment. First, if the irradiaton produces internal precipitation, these precipitates can compete with the surface ones for carbon capture. Second, if no internal precipitates are generated, the annihilation of vacancies at the precipitate matrix interface can promote additional growth of the surface precipitates. Fig. 2 shows the damage profiles of 3 MeV V+ ions in V and of 150 keV H+ ions in Nb, which are instances where the above referred situations have been observed. In the case of vanadium, the half width of the damage profile extends from = 0.5 to 1.2 pm. Since under thermal aging surface precipitation extends up to = 0.5 pm inside the sample, a surface region of width 8, < 0.5 pm can be clearly distinguished from the highest damaged region of width a,, with 6, < 8: < 1.2 pm. In the irradiation experiments with niobium, the highest damage region is closer to the external surface and some superposition of surface and highest damage region exists. The ion bombardment experiments on vanadium yielded precipitate formation induced by self-ion bombardment in the region of highest damage [7]. As previously mentioned carbon diffusion does not control surface precipitation, but it may assist the precipitation processes in the damaged region. The experimental observations tend to suggest that precipitation takes place in the highest damaged region at temperatures below = 970 K, if carbon is available. Since the region of highest damage is adjacent to the subsurface region where precipitation occurs under thermal aging, the two regions can compete for carbon capture from the surface. This will only occur if precipitation in the damaged region depletes the local matrix of carbon and therefore carbon currents from a richer matrix at both sides of the region in question are established. The balance of mass at any time, t under irradiation can be written as SarQs=
(J-J,)tQ,
in the subsurface
00) region, and
(11)
A.J. Pedraza, D. Pedraza / Carbide precipitation in V and Nb
region. JS,. and SD are respectively the precipitate fractions in the surface region of width 8,. Jo is the carbon flux from the external source that is absorbed in the peak damage region. The second term in eq. (11) accounts for the carbon flux coming from the bulk toward an impoverished matrix of concentration s,. The data of table 1 can next be used for calculating the value of J,. Thus, at 723 K, when 1= lo4 S,
277
in the peak damage
J D = 2.52 x 10’6m-2s-’ and substituting ~scsr~PSs=
02)
into eq. (11) yields
5.70 X 10-‘3pm
1.0
0.8
0.6
0.4
0.2
(13) nn
which is in agreement with the value measured experimentally [7]. This result demonstrates that the damaged region is certainly a very efficient carbon sink whose presence decreases surface precipitate growth relative to thermal dging alone. The diffusional transport of carbon into the Irradiated region is demonstrated by the experiments at low temperature (523 K) where carbon enrichment is limited to the surface region while no enrichment occurs in the irradiated zone. Thus, the vacancy supersaturation alone, which is larger at the lower temperatures, is not sufficient for inducing precipitation. On the other hand, at higher temperatures e.g., = 970-1030 K, no precipitation occurs in high purity vanadium, showing that high diffusion rates alone are not sufficient either (see table 2). The experimental resufts show clearly that irradiation does induce precipitation. However, at variance with the surface phemonenon, the precipitates appear to be of a coherent nature. This fact together with the elastic calculations of Khatchaturyan [16] suggest that under irradiation carbon clustering is enhanced and this yields a very efficient mechanism of precipitation. In fact, if the results of AgarwaI et al. [9] and those of Diercks and Wert [8] are compared, the effect of irradiation is seen to promote the coherent precipitates in detriment of V,C. The nucleation process is clearly highly favored by irradiation. If carbon transport is small it should control the irradiation induced precipitatlon. However if the available amount is large, the clustering process will be controlling, which seems to happen in the experiments at 723 K. We thus differentiate two mechanisms that may follow a 4 law. One is that of diffusion and the other is that of point defect build up which must assist clustering. In fact, in the low sink strength regime, that build up is known to follow a 4; law [19]. The delicate balance discussed above involving chemical driving force, transformation stresses and radiation effects on precipitation is further demonstrated in the case of carbide formation in niobium. Assuming a simitar behavior as in the V-C system, carbon will enter the matrix, when an external source is available, be-
0.4
0.8
1.2
DEPTW (pm)
Fig. 3. Damage Profiles of 3 MeV Vf in V and 150 keV H+ in Nb. 8,: width of the subsurface region; 66: width of highest damage region in vanadium irradiated with 3 MeV V+ ions.
cause it decreases its free energy. The energy required for plastically deform the matrix is fairly low at the temperatures of the Bauer and Thomas experiments, as shown in table 4. However, the availability of carbon strongly influenced the precipitation pattern. Thus, when the external surface provided a large supersaturation, as was the case where an adsorbed layer was introduced during sample preparation, irradiation effects were negligible. When that source was absent, as was the case of mechanically polished surfaces, surface precipitation occurred only in the bombarded area. A quite different situation from that occurring in the V-C experiments of ref. [7] is seen when precipitates do not form in the highest damaged region. In this case, the vacancy supersaturation reaches the near surface precipitates allowing further growth inwards. Moreover, when the magnitude of AC+ is low, the precipitates that start growing in the surface are not limited to the sub-surface region and can continue growing while irradiation is applied and the carbon supply lasts. Not withstanding the possible effects of other differences such as the specific damage, there is clearly a simple reason related to the fact that preciptates do not form in Nb in separate associaton with the highest damaged region. As pointed out before and shown in fig. 3, the peak damage with 150 keV protons in niobium lies much closer to the external surface than that praduced in vanadium with 3 MeV Vi ions.
6. Conclusions 1) A carbon concentration of 0.2 at.% produces bulk precipitation of V,C in the range 523-823 K, while only = 0.05 at.% is necessary for surface precipitation. The mass balance equation shows that irradiation induced carbide precipitation in vanadium IV. MICROSTRUCTURE
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PROPERTIES
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A. J. Pedraza, L). Pedraza / Carbide precipitation
depletes the matrix carbon concentration in its vicinity practically to zero. 2) Both habit planes (013) and f012) observed during aging and ion bombardment respectively seem to be consistent with the minimization of the elastic strain energy. 3) The mass balance equation shows that in vanadium irradiated with 3 MeV V’ ions the precipitates formed in the highest damage region compete with the surface precipitates for the capture of carbon coming from and external source. In contrast to surface precipitates that have practically only one carbon source, the butk can also contribute carbon atoms to the radiation induced matrix precipitates. 4) If the peak damage region is very close to the surface, as is the case with niobium bombarded with 150 keV H+, no internal precipitates are produced and radiation induced point defects enhance the growth of surface precipitates. balance between carbon availability, 5) The delicate transformation stresses and radiation effects may significantly alter the precipitation characteristics of both the surface and the internal damaged region, relative to thermal aging.
References [I] Phase stability under irradiation, eds., J.R. Holland, L.K. Mansur and D.I. Potter, conf. Proc. (TMS-AIME, 1981). [2] Phase transformation during irradiation, ed., F.V. Nolfi (Applied Science, New York, 1983).
in V and Nb
[3] E. Rudy, St. Wind&h and C.E. Brukl, Planseeber Puivermet. 16 (1968) 3. [4] N. Terao. Jpn. J. Appl. Phys. 3 (1964) 104. [S] W. Bauer and G. Thomas, Proc. First Topical Conf. on Fusion Reactor Technolgy, San Diego, CA (1973). [6] W. Batter and G. Thomas, J. Vat. Sci. Technol. 12 (1975) 490. [7] K. Grabowski, Ph.D. thesis, The University of Michigan, Ann Arbor (1980). [8] D.R. Diercks and C.A. Wert, Metal]. Trans. 3 (1972) 1699. [9] SC. Agarwai, D.I. Potter and A. Taylor, irradiation effects on the microstructure and properties of metals, ed., F.R. Schober, Symp., St. Louis, MO. (ASTM STP 611, 1976) p, 298. [lo] SC. Aganvai, D.I. Potter and A. Taylor, Metall. Trans. 9A (1978) 579. [ll] W.J. Weber, G.L. Kulcinski, R.G. Lott, P. Wilkes and H.V. Smith Jr, Radiation effects and tritium technology for fusion reactor, eds., J.S. Watson and F. Wiffen (CONF/750989, Oak Ridge 1976) p. I/130. [12] W. Jost, Diffusion (Academic Press, New York, 1952) 68. [13] L. Kaufman and H. Nesor, CALPHAD 2 (1978) 295. 1141 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelly, Selected values of the thermodynamic properties of binary alloys (American Society for Metals. 1973). [15] D.R. Mathews and EA. Rowe, US Bureau of Mines Rep. Invest. 6628 (1968). [16] A.G. ~atchatu~an, Theory of structural tr~sfromations in sohds (Wiley, New York, 1983). [17) H, Met. Clark, E.A. Merriman and C.M. Wayman. Acta Metall. 17 (1969) 719. [18] T.E. Tietz and J.W. Wilson, Behavior and properties of refractory metals (Stanford University, Stanford, CA 1965). [19] D.F. Pedraza, E.J. Savino and A.J. Pedraza, J. Nucl. Mater. 73 (1978) 151.