Los textos de las corporealidades: ( Una ) metodología de análisis

Unlike all the other binary systems considered in this thesis, iron and cobalt are miscible even under equihbrium conditions, with a small negative heat of mixing of -1 kJ/mol [100]. This is to be expected as they occupy neighbouring positions in

IRON-COBALT-SILVER J 35

the periodic table, have similar atomic sizes (metallic radii of 0.126 mn and 0.125 mn respectively for atoms with coordination number of 12 [106]) and similar chemical and magnetic properties. The main difference between the elements is structural, with iron atoms forming a bcc lattice and cobalt an hcp/fcc, as described earlier. Thus, in order for alloying to occur, a structural transformation is required on the part of one of the elements, as was the case with iron-copper.

Structural Properties

The structural phase diagram of the resulting alloy, when prepared from the melt, is well established [40, 107]. For iron concentrations above 25 at.% the lattice is bcc and for concentrations below 10 at.% it is fee, with a mixed phase region between these values. The results for mechanically alloyed material should be similar to this, although it is possible that high milling intensities could introduce changes, particularly in the mixed phase transition region. To investigate these questions more fully, samples were prepared with varying Fe:Co ratio, and using both stainless steel and Syalon containers.

Significant differences were observed between samples of the same composition that were prepared using different milling containers. Firstly, an approximate halving of the container density from steel to Syalon led to a doubling of the time required for complete alloy formation, from 10 hours to 20 hours in the case of FesoCoso- This would be expected, since a change in density would result in a corresponding change in the respective impact energies. Additionally it was apparent, whichever containers were used, that milling times were generally significantly lower than those for the immiscible alloy systems considered in the previous chapter. As a comparison, FcsoCoso milled in stainless steel alloyed within 10 hours, whereas Fe^oCu^o imder the same conditions required 30 hours. (It should be noted that it is not always easy to make precise time measurements, as this requires the preparation of a large number of samples.)

A second piece of evidence for a variation in impact energy between the two container materials was provided by a comparison of the respective compositional phase diagrams. The first set of results, from samples milled in Syalon, corresponded to what was expected from the equilibrium phase diagram, in terms of structure as a function of composition, whereas the set of results from the steel milled samples showed significant differences.

136 Ch a p t e r 6 In the Syalon based alloys, as with the equilihrium material, a two phase region was found for iron concentrations between 20 - 25 at.%, within which it was impossible to form a single phase alloy even at extended milling times up to 200 hours (figure 6.6). It was, however, noticeable from the x-ray scans that, whilst the ratio of bcc to fee material fluctuated during milling, it ultimately settled at values related to the distance of the sanqile from the pure bcc or fee zone. For example, Fe22Co7 8, which is close to

the pure fee region, contained a larger proportion of fee material than did Fe25Co?5.

Additionally, within the single phase regions the required milling times for alloying increased substantially on approaching the border with the two phase zone. For example, FeigCogz took 70 hours to fully alloy and Fe2oCogo took 120 hours, rather than

the more usual 20 hours. This is likely to be a result of a steady increase in the enthalpy of formation as the composition tends towards the critical values. Once the iron concentration rises above 20 at.% or falls below 25 at.% the energy required becomes greater than that available from the milling process.

Fe Co (fee) c/3 5 .e Fe Co (mixed)

8

3

Fe Co 50 ‘ (bee) 40 45 35 15 20 25 30

20 (Degrees)

Figure 6.6 X-ray dififraction patterns of selected Fe-Co alloys milled in Syalon containers, showing the change in structure with composition.

IRON-COBALT-SILVER ₁₃₇ However, in stainless steel containers, as stated before, the total impact energy is greater. Thus in samples milled in steel this transition region disappears, and the compositional phase diagram looks significantly different. The bcc region extends down to an iron concentration level of 10 at.%, with the remaining samples being fee. The explanation for this formation of single phase alloys across the composition range follows as a logical extension of that given for the immiscible systems such as iron- copper and copper-silver. Within this two phase region a metastable single phase alloy can be formed as a result of the extra energy imparted by the milling process. The enthalpy of formation is again measurably greater in this region, with samples such as Fe9oCoio requiring 20 hours rather than 10 hours milling.

It should be noted that when using steel, the actual transition point between bcc and fee phases is disturbed somewhat as a result of the addition of iron impurities during milling. However, as typical milling times for these experiments are only 10 hours, compared with 70 hours in the previous chapter, the final sample composition showed an increase of no more than 3 at.% iron. The corresponding Mossbauer spectra displayed httle evidence of chromium impurities, with for example the Fe-Cr sextet occupying only 9.0 % of the total area in FezoCogo, shown in figure 4.7. Given the results for chromium percentage against spectral area obtained in chapter 4, this imphes a total chromium impurity level of approximately 0.4 at.% and thus a total steel impurity level of 2.2 at.% in this sample. Extended milling, however, resulted in the further addition of chromium and the consequent distortion in the Mossbauer spectrum.

FeggCogg 10 h o u rs 0.0 ^ § 0.5 FegnCoon 60 h o u rs g 0.0 "ww ^ 0.5 1.0 2 4 6 —4 —2 0 - 6 Velocity (mm/s)

Figure 6.7 Mossbauer spectra of FeaoCogo miUed in steel containers for 10 and 60 hours. Alloy formation was complete after 10 hours, with the addition of minimal chromium impurities.

138 Ch a p t e r 6 Thus in summary, it can be seen that differences exist in structure between the iron- cobalt alloys formed in steel and those made in Syalon. These differences can be related to the impact energy of the mill, which in turn is shown to be dependent upon the density of the milling tools. Mechanical alloying using stainless steel generates higher impact energies than equivalent experiments in Syalon, though even these should be considered as non-equihbrium processes, given the narrowing in extent of the observed dual phase region.

Magnetic Properties

The magnetic properties as well as the structural properties of iron-cobalt alloys have been the subject of close investigation. The variation of the saturation magnetisation is described by the Slater-Pauling curve, [5] which gives the mean magnetic moment per atom as a function of the number of 3d electrons per atom (fractional in the case of alloys since the electron density is averaged). The complete curve extends from chromium with 5 3d electrons to copper with 10, but the region of interest here is in the centre, between iron and cobalt. There is a maximum in the curve of approximately 2.4|Tb, at a composition of FeyoCoso. This is the point at which there is the greatest imbalance between spin up and spin down electrons in the 3d band. (This is explained using the itinerant electron model by considering the 3d band as two parts; the upper part capable of holding 4.8 electrons and the lower part 5.2. In chromium, for example, the lower part of the band is full, with the electron spins evenly paired, and the upper band empty, so there is no net spin imbalance and no magnetic moment [5]. In FeyoCoso, on the other hand the lower band is again filled, but additionally the spin up states in the upper band are occupied, resulting in a large magnetic moment. The addition of further electrons as the cobalt concentration increases fills the spin down part of the upper band reducing the imbalance and net moment.)

Magnetisation measurements on the mechanically alloyed samples using a VSM gave values for the saturation magnetisation which varied with sample composition as expected from the Slater-Pauling curve, although the absolute values in terms of ps were on average some 10-20 % lower. This is probably a result of the presence of non­ magnetic Syalon impurities and the lack of complete saturation in the 0.75 T field, although it may also be that the contribution to the magnetisation from the many atoms

IRON-COBALT-SILVER _{1 3 9} at grain boundary sites is less than that of those in the standard bulk environment [100]. The variation of the magnetic properties of Fe-Co alloys along the Slater-Pauling curve can also be seen through the parallel change in the Mossbauer hyperfine field [108, 109]. The change in Bhf occurs, via the Fermi contact interaction (see chapter 3), because the systematic variation with composition in the density of unpaired 3d conduction electrons affects in turn the spin density of the core s electrons at the nucleus and thus changes the effective magnetic field at the Fe nucleus [108, 110].

Most of the original experiments were conducted on solid alloys prepared using standard techniques such as arc melting rather than powders, although some work has been done on mechanically alloyed systems [99-101], giving similar results. To obtain more information on this variation in the mechanically alloyed Fe-Co system, spectra were collected for the full range of compositions, using both steel and Syalon containers and paying particular attention to alloys in the structural transition region. The resulting plot of Bhf as a function of composition with Syalon containers is shown in figure 6.8. In general terms it resembles that given by Johnson [108], with it being noticeable, for example, that the maximum in Bhf occurs for a composition of FegoCo2o, which is a

higher iron content material than that with the maximum saturation moment. However, there are a couple of significant differences to be commented on.

H m 100

Co

Fe

Co at.%

bcc ^nuxed^ f ^

Figure 6.8 Plot showing the variation in Mossbauer hyperfine field with composition for Fe-Co samples milled for 60 hours in Syalon. The lattice structure of the resulting alloy is also marked.

140 Ch a p t e r 6 Firstly, the average Bhf values o f the alloys are approximately 0.5 T lower than those observed by Johnson, but are consistent with those found by Briining et al. for mechanically alloyed samples [99]. As with the VSM results, this could be due to the presence in the nanocrystalline powder o f a large number o f grain boundary atoms which have a lower net magnetisation and Bhf [68, 100]. However, unlike in the VSM data where unreacted impurity particles contributed to the reduction in observed magnetisation (as they were included in the total mass of the system), it should be noted that the unreacted impurities will not affect the magnitude o f the measured hyperfine field. This explains why the discrepancy is less in the Mossbauer data than it was in the magnetisation data. Additionally, a small discontinuity in the Bhf curve was seen in the structural transition region, which is explainable if the hyperfine field experienced by an iron nucleus in a magnetic fee lattice is slightly larger than that in a bcc lattice. Alternatively, as the effect is small enough to be within experimental error.

Where there is a sufficient difference in the mean Bhf between the final Fe-Co alloy and the initial unmilled material (in which Bhf = 33.0 T for a-Fe), the change in the Bhf distribution with milling time can be used as an accurate method o f monitoring the progress o f alloy formation. An exan^le o f a hyperfine field distribution plot is shown in figure 6.9, for a sample of FesoCoso in Syalon, at milling times o f between one and 60 hours. Each profile is produced by fitting the Bhf parameter o f the Mossbauer spectrum to a histogram distribution containing 50 bins o f equal width in the hyperfine field range of 30-40 T.

The plots contain two features; a narrow peak centred at 33.0 T due to undisturbed a-Fe, and a second, broader feature due to the emerging Fe-Co alloy. With time, the alloy peak grows in area at the expense o f the a-Fe, and the final plot at 60 hours shows a single, symmetric peak centred at 34.6 T due to the Fe^oCojo solid solution. The broadness o f this feature relative to that o f a-Fe results from the fact that the alloy, being a disordered solid solution, is inhomogeneous on the atomic scale. Each iron atom will be surrounded by a different combination o f iron and cobalt nearest and next nearest neighbours, although the material will have an average composition o f FesoCoso- As the plot in figure 6.8 showed, this variation in composition affects the measured hyperfine field. Any iron atoms which sense a local environment with composition similar to that of a FcyoCoso alloy, for example, will experience a hyperfine field o f

IRON-COBALT-SILVER ₁₄₁

^0! hours -

5 hovirs

2 hoiirs

1 hour

30 32 34

Hyperfine Field (T)

38 36 40

Figure 6.9 Variation in hyperfine field distribution with milling time for Fe^oCO)

35.6 T rather than the expected 34.6 T of FesoCoso [99]. Supporting evidence for this explanation comes from the fact that the distribution o f fields in the alloyed FesoCoso sample is broader than that in, for example FeisCogs (ABhf = 1.6 T and 1.2 T respectively). The former alloy is in an area o f the Slater-Pauling curve where Bhf changes rapidly with composition, whereas the latter lies in a region with less variability. Thus any atomic scale composition fluctuations will not produce as noticeable a change in the hyperfine field (see figure 6.10 and table 6.1).

This variation in Bhf aroimd the 50:50 composition zone accounts for a second effect observed in the plot o f Bhf distribution as a fimction of time, namely that in the early stages of milling, the mean Bhf o f the alloy peak is higher than expected, and slowly tends towards the final value over time. Since the interdiffusion process occurs gradually, in the initial stages of alloy formation the iron atoms in the interfacial regions

1 4 2 Ch a p t e r 6 0.0 2.0 4.0

«

0.0 0.5 2 4 6 - 2 0 - 6 - 4

Velocity (mm/s)

Figure 6.10 Mossbauer spectra of FesoCoso and Fe^Cogg milled for 60 hours in Syalon, illustrating the differences in the respective linewidths.

will interact with only a limited number o f cobalt atoms. With fewer than 50 % cobalt nearest neighbours, the measured hyperfine field of these atoms will in the majority of cases be higher than the final 34.6 T (according to figure 6.8). With time, however, the number o f cobalt neighbours increases to the ultimate value o f 50 %, and the mean hyperfine field decreases towards 34.6 T. Similar effects were seen by Briining et al. [99]. It is more likely that the fcc/hcp cobalt will diffuse into the bcc-iron lattice than vice versa, as the diffusion coefficient for this process is the larger and the final structure is bcc-Fe type rather than fcc-Co type. The absence o f features in the Bhf distribution graph in the 31-32 T region confirms that, during all stages of milling few isolated iron atoms diffuse into the cobalt lattice.

Thermal Properties

Given the high degree of miscibihty of iron and cobalt, the structural changes that are observed in the alloy on heating should be less dramatic than those seen in the metastable Fe-Cu-Ag system in the previous chapter. Indeed, whilst the Fe-Cu-Ag samples decomposed after moderate annealing at 200-300 °C, the Fe-Co alloys are known to be stable up to the respective melting points of the elements at around

IRON-COBALT-SILVER ₁₄₃ 1500 °C [40]. However, it has been shown that the alloys formed during ball milling differ from those produced under equihbrium conditions in that they consist of small, highly strained crystaUites. Thus, identical behaviour to the equihbrium ahoy during annealing cannot be assumed and at the least it is expected that thermal treatment would be accompanied by a degree o f lattice recovery and recrystaUisation.

0.25 0.2 0.05 200 3 0 0 400 Temperature (°C) 500 600

Figure 6.11 DSC thermogram for FcisCogs milled for 60 hours in Syalon.

The occurrence of recovery and recrystaUisation processes is confirmed by DSC measurements, an example of which is shown in figure 6.11, for FeisCogs- The behaviour o f the Fe-Co aUoy is similar to that seen for the milled iron in the previous chapter. Since both iron and cobalt have similarly high melting points, the aUoy lattice is able to store substantial energy during milling, in this case 9 kJ/mol, which is then graduaUy released on heating to 600 °C. The most intense exotherm is in the 400-500 °C temperature span, which is the region identified in the last chapter as that in which recrystaUisation processes occur. There is httle heat released below 350 °C, indicating that there is no low temperature phase segregation and thus implying that the aUoy remains stable on heating.

This point can best be iUustrated by examining the Mossbauer spectra in figure 6.12 of FeyoCoso before and after heating. This composition was chosen as it hes at the top of the Slater-Pauling curve and thus has a hyperfine field that is the most visibly different from that of standard a-Fe (35.7 T compared with 33.0 T). It can be seen that as

144 Ch a p t e r 6 3.0 300 °C 0.0 (/} :< 3.0

^

6.0 0.0 3.0 - 6 - 4 - 2 0 2 4 6

Velocity (mm/s)

Figure 6.12 Mossbauer spectra of the Pe7oCo3o alloy, as milled and after heating in the DSC to 300 and 600 °C. The sohd lines are least-squares fits to the data, as discussed in the text.

heating progresses the hyperfine field of the main sextet remains constant, with no appearance o f an a-Fe component and therefore no segregation. The linewidth also remains broad (with a very shght decrease in ABhf fi'om 1.5 T to 1.4 T), not because of structural disorder but because the alloy is a random substitutional sohd solution. The iron atoms thus have different arrangements o f iron and cobalt nearest neighbours which results in a distribution o f Bhf values as described earlier. The structural changes on heating are evident fi'om the decrease in area o f the second magnetic component, which was modelled to take into account the presence o f iron atoms in a non-cubic environment. These could be atoms at grain boundaries or distorted lattice sites, but in either case the heating process can be seen to reduce their number due to the

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