Variation of microstructure by Ru additions in a single crystal Ni based superalloy

Abstract

The microstructural variation of three single crystal Ni based superalloys with various Ru contents has been investigated. The as cast, solid solution and fully heat treated microstructures were quantitatively analysed. The size of γ′ phase was decreased both in dendrite core and interdendritic regions with Ru additions after a solid solution heat treatment. Appropriate heat treatment schemes of three alloys were determined in terms of quantitative and qualitative microstructural characterisation. It was found that the size and volume fraction of γ′ phase were decreased, and the width of γ matrix channels was reduced in the dendrite core regions of fully heat treated microstructure with the additions of Ru. Moreover, the well known reverse partitioning occurred with increasing Ru content. The γ/γ′ lattice misfits changed from positive to negative and became more negative with Ru additions. The variation of γ/γ′ lattice misfit was caused by the changes of partitioning ratios of alloying elements via Ru additions.

Keywords

Ni based superalloy Ru Microstructure Misfit Partitioning

Introduction

Single crystal Ni based superalloys are used as high temperature structural materials for jet engines and gas turbines. It mainly consists of two phases, i.e. the disordered matrix of face centred cubic Ni rich γ phase and γ′ strengthening phase with L1₂ ordered structure embedded into them.^1,2 The temperature capability and creep properties of these alloys were substantially improved by removing grain boundaries, responsible for most deformation at high temperature in polycrystalline Ni based superalloys. In general, the cuboidal γ′ phase will finely disperse in the γ matrix in commercial single crystal Ni based superalloys. Their strengthening mechanisms include the solid solution strengthening, precipitation strengthening, coherency strengthening, antiphase boundary strengthening and others.^1,3,4 As the most important strengthening phase, the morphology, size, volume fraction and distribution of γ′ precipitates would determine the mechanical properties of superalloys. These morphological features are greatly dependent on the heat treatment process.

In order to progressively enhance the efficiency of gas turbines and reduce CO₂ emission, the turbine entry temperature must be further increased.⁵ This brings about a huge challenge for the temperature capability of superalloys. In recent years, several countries have developed the fourth or fifth generation of single crystal Ni based superalloys with higher temperature capability in comparison to previous third generation one. These new alloys all contain certain amount of Ru on composition in common.^6–8 Therefore, the effects of Ru additions on microstructure and mechanical properties have increasingly become one of the research concerns. It is known that creep resistance is the most important performance index, so the creep properties were extensively studied.^9–11 Furthermore, the creep properties of alloys would be greatly dependent on their heat treated microstructure. However, the relationship between microstructure and creep properties still remains debatable. It is reported that it has larger negative γ/γ′ lattice misfit, smaller γ′ size and more regular γ′ distribution in the microstructure of fourth or fifth generation of single crystal Ni based superalloys.^6,8,12 Despite some important progress achieved on microstructure and mechanical properties in Ru containing alloys, however, many Ru effects are required to be further understood. In particular, there are few studies on the heat treated microstructure in Ru containing alloys.^13,14

Experimental

Materials

Three single crystal Ni based superalloys with different Ru additions were employed in this present work. The nominal chemical compositions of the three alloys are listed in Table 1. The study was carried out on the MC–NG alloy (4Ru) and variants with lower (2Ru) and no (0Ru) ruthenium content. The master alloys were melted by vacuum induction technique and then directionally solidified into cylindrical bars (16 mm in diameter and 220 mm in height) in an investment casting cluster mould in a Bridgman furnace with a withdrawal rate of 6 mm min⁻¹. Conventional helical starters were utilised to initiate single crystal growth with <001> direction. Only the single crystal bars deviating from <001> within 15° by electron backscatter diffraction method were adopted.

Table 1

Nominal composition of three experimental alloys

		Ni	Al	Ti	Ta	Cr	Mo	W	Re	Ru
0Ru	wt-	Bal.	6	0·5	5	4	1	5	4	0
	at-	Bal.	13·3	0·6	1·7	4·6	0·6	1·6	1·3	0
2Ru	wt-	Bal.	6	0·5	5	4	1	5	4	2
	at-	Bal.	13·5	0·6	1·7	4·7	0·6	1·7	1·3	1·2
4Ru	wt-	Bal.	6	0·5	5	4	1	5	4	4
	at-	Bal.	13·6	0·6	1·7	4·7	0·6	1·7	1·3	2·4

Microstructural examination and analysis

A Nikon Eclipse ME600 optical microscope and a JMS-5800 scanning electron microscope (SEM) were used to observe the as cast and heat treated microstructures. The etchant is the Kalling's solution (3 g CuCl₂, 30 mL HCl and 70 mL ethanol). A CAMECA SX-100 electron probe microanalysis (EPMA) was employed to quantitatively determine the γ/γ′ partitioning ratios of all alloying elements. The accelerating voltage, current and beam size are 20 keV, 40 nA and 0·1 μm respectively. An attempt was made to precisely measure the composition of γ and γ′ phases, the special microstructure with larger γ and γ′ phases (5–10 μm) was obtained via a coarsening heat treatment, i.e. 1300°C/1 h+(1300–1150)°C/10 h, air cooling (AC). At least 10 measurement points for each γ and γ′ phase in the dendrite core regions in all three alloys were conducted. Image-Pro Plus 6·0 software was employed to quantitatively analyse the SEM images of γ/γ′ microstructure. Image segmentation was performed for γ and γ′ phases, and then, the size distribution and area fraction of γ′ particles will be obtained. The γ′ volume fraction can be defined as , where is the area fraction of γ′ phase.

Differential scanning calorimetry analysis

The liquidus, solidus and other phase transformation temperatures in as cast microstructure were analysed by a NETZSCH DSC 404C high temperature type differential scanning calorimeter (DSC). The major temperature interval ranges from 1000 to 1500°C and a 10°C min⁻¹ heating rate was chosen, as it yields the best combination of temperature accuracy and peak resolution. The cylindrical DSC samples (Φ4×2 mm) with ∼200 mg were prepared.

X-ray diffraction measurements

The X-ray diffraction (XRD) profiles were recorded by conventional Rigaku D/MAX 2500 X-ray diffractometer with Cu K_α radiation at 50 kV/300 mA. This instrument was set up for Bragg–Brentano geometry with a line focus and a graphite monochromator between specimen and detector. The intensity profiles of {004} reflection were collected to measure γ/γ′ lattice misfit. The step scans were made at 0·02° per step, and the counting time was adjusted to make sure the counts can up to 10⁴. The error of the absolute measurement of the lattice plane spacings in this diffractometer is Δd/d≈10⁻⁴. With Δ(2θ) = ±0·02°, Δδ = ±0·02 can be obtained. All the measurements were carried out at room temperature. The detailed diffraction techniques and peak fitting methods are depicted in Ref. 15.

Results

Heat treatment scheme and full heat treated microstructure

Figure 1 shows the typical dendritic microstructure with [001] orientation in the three alloys. The bright phase in the interdendritic regions is the γ/γ′ eutectics. To determine the heat treatment scheme, the so called ‘heat treatment window’, i.e. the temperature range between the γ′ solvus and incipient melting temperature, should be known. It is noted that the solid solution temperature should be chosen in the heat treatment window in order to ensure that γ′ precipitates could completely dissolve into γ matrix with the absence of incipient melting. As a result, the γ/γ′ eutectics would be eliminated and the homogenisation of alloying elements achieved. Two endothermic reactions can be observed from the DSC heating curves of three alloys. The γ′ solvus both in the dendrite core and interdendritic regions resulted in the first endothermic peak. The temperature at the beginning of the second endothermic reaction was linked with the melting temperature of the γ/γ′ eutectics in the interdendritic regions, i.e. the incipient melting temperature of alloy. The solidus could be obtained from the intersection point at the corner of the second endothermic reaction. Furthermore, the second endothermic peak was attributed to the melting of γ phase, which is the major endothermic reaction. The temperature at the second endothermic peak corresponds to the liquidus. Three exothermic peaks can be found in the DSC cooling curves of three alloys. The first one, namely the major exothermic reaction, resulted from the initial γ phase precipitation in the dendrite cores. The second one corresponds to the precipitation of γ/γ′ eutectics in the interdendritic regions. With the decreasing temperature, the precipitation of γ′ phase both in the dendrite core and interdendritic regions resulted in the third exothermic peak. The DSC results are listed in Table 2. It can be seen that the γ′ solvus and solidus were increased, the incipient melting temperature and liquidus were increased and then decreased, and the precipitation temperatures of γ/γ′ eutectics and γ′ phase were decreased with Ru additions. In addition, the incipient melting temperatures of three alloys are 1353, 1355 and 1345°C derived from the burning test. In practice, these temperatures are closer to the real case. The highest solution temperature was chosen to be lower than the incipient melting temperature by 5°C. This is able to maximise the efficiency of solid solution heat treatment and prevent the incipient melting, which may be caused by the temperature fluctuation during heating in the box furnace. Step type solid solution heat treatment ramp was employed in this present work. In terms of the comparison among the microstructures after different conditions, the solid solution heat treatment schemes were determined, as listed in Table 3. It is found from the solution heat treatment microstructure that the γ/γ′ eutectics have been eliminated. However, it still exhibits clear dendritic patterns due to the higher amount of refractory elements, such as Re, W, etc., in all three alloys. This may result in the obvious differences between dendrite core and interdendritic regions in the subsequent full heat treated microstructure. Figure 2 reveals the microstructure in the dendrite core and interdendritic regions in three alloys. The morphology of γ′ particles is less regular and their distribution non-uniform. The size of γ′ phase in the interdendritic region is larger in comparison to the dendrite core region. Moreover, the size of γ′ phase in the two regions is both reduced with the additions of Ru.

Table 2

Phase transformation temperatures for three alloys obtained from DSC heating and cooling curves/°C

Alloy	γ′ solvus	Incipient melting	Solidus	Liquidus	γ precipitation	Eutectic precipitation	γ′ precipitation
0Ru	1258	1352	1375	1421	1399	1346	1247
2Ru	1273	1354	1376	1424	1399	1346	1236
4Ru	1276	1342	1377	1420	1396	1344	1235

Table 3

Solid solution and aging heat treatment scheme of three alloys

Alloy	Solid solution	Primary aging	Secondary aging
0Ru	(1318–1348)°C/10 h+1348°C/15 h	1080°C/4 h	870°C/24 h
		1100°C/4 h
		1120°C/4 h
		1140°C/4 h
		1160°C/4 h
		1180°C/4 h
2Ru	(1320–1350)°C/10 h+1350°C/15 h	1080°C/4 h	870°C/24 h
		1100°C/4 h
		1120°C/4 h
		1140°C/4 h
		1160°C/4 h
		1180°C/4 h
4Ru	(1310–1340)°C/10 h+1340°C/15 h	1080°C/4 h	870°C/24 h
		1100°C/4 h
		1120°C/4 h
		1140°C/4 h
		1160°C/4 h
		1180°C/4 h

Numerous heat treatment experimental results indicate that the primary and secondary aging heat treatment would control the size and morphology of γ′ precipitates respectively.¹⁶ According to our previous heat treatment experience, the same secondary aging heat treatment was adopted in three alloys. In the range of 1080–1180°C, moreover, every 20°C was chosen as a primary aging heat treatment. The detailed heat treatment schemes are listed in Table 3. Figures 3 and 4 show the γ/γ′ microstructures after various heat treatments in dendrite core and interdendritic regions respectively. It should be emphasised that the size and volume fraction of γ′ phase are the two critical microstructural parameters evaluating the heat treated microstructure. In general, optimal γ′ size and volume fraction for a single crystal Ni based superalloy would probably exist. Furthermore, the arrangement and distribution of γ′ particles are also important aspects for microstructural characterisation. As known, the well arranged γ′ particles will be significantly beneficial to the mechanical properties of alloys. In addition, the width of γ matrix channels is extremely important. The precipitation of finer secondary γ′ particles should be avoided during the heat treatment process. This is due to the fact that the primary aging temperature is too high to result in the widening of γ channels, which is likely to be detrimental to the mechanical properties. Based on these criterions above, the γ′ size was firstly quantitatively analysed (as shown in Fig. 5). The size of γ′ phase in dendrite core regions was progressively increased with the primary aging temperatures. Once an aging temperature of 1160°C was reached, it exhibits evident widening of γ channels in all three alloys. Moreover, some amount of finer secondary γ′ particles appeared in the widened γ channels. In particular, the widening is most severe in alloy 0Ru; hence, its γ′ size starts to be decreased. However, the variation of γ′ size in interdendritic regions is irregular. The γ′ size in alloy 4Ru was gradually increased with aging temperature, while γ′ size was not obviously varied in alloy 0Ru and 2Ru. Under the same primary aging temperature, the γ′ size was decreased in dendrite core regions, while there was an increase followed by decrease in interdendritic regions with the additions of Ru. Overall, it reveals the smallest γ′ size in alloy 4Ru during the whole heat treatment process. Second, the γ′ volume fraction was quantitatively analysed (as seen in Fig. 6). The γ′ volume fractions in dendrite core and interdendritic regions were both increased and then decreased as the primary aging temperature rises, with a peak at 1140°C. The γ′ volume fraction was decreased beyond 1140°C due to the obvious widening of γ channels. Under the identical aging temperature, the γ′ volume fractions in dendrite core and interdendritic regions were both reduced with Ru additions. Finally, the arrangement and distribution of γ′ particles should also be qualitatively analysed. It can be clearly seen that there exist greater differences on γ′ size between the dendrite core and interdendritic regions in all three alloys when the aging temperature is <1140°C. Moreover, the γ′ particles are irregular and inhomogeneously arranged, and the γ/γ′ interfaces are not smooth. On the other hand, the γ/γ′ interfaces become smooth and straight when the aging temperature is >1140°C. However, the γ′ size distribution is extremely non-uniform because of the severe coarsening of γ′ phase.

In summary, the optimal primary aging temperatures are 1140°C for all three alloys unpredictably. Therefore, the final full heat treatment schemes are compiled in Table 4. The fully heat treated microstructures of three alloys were shown in Fig. 7. Furthermore, the γ′ size, γ′ volume fraction and γ channel width derived from image analysis were listed in Table 5. It is demonstrated that smaller γ′ phase, lower γ′ volume fraction and narrower γ channels were obtained in the dendrite core region with Ru additions. Unlike the dendrite core region, the γ′ size and γ channel width were slightly increased and then significantly decreased, and the γ′ volume fraction was reduced in the interdendritic region.

Table 4

Full heat treatment schedule of three alloys

Alloy	Solid solution	Primary aging	Secondary aging
0Ru	(1318–1348)°C/10 h+1348°C/15 h, AC^*	1140°C/4 h, AC	870°C/24 h, AC
2Ru	(1320–1350)°C/10 h+1350°C/15 h, AC	1140°C/4 h, AC	870°C/24 h, AC
4Ru	(1310–1340)°C/10 h+1340°C/15 h, AC	1140°C/4 h, AC	870°C/24 h, AC

Table 5

Microstructural parameters of three alloys in dendrite core and interdendritic regions

	Dendrite core			Interdendritic
	γ′ size/μm	γ′ volume fraction/	γ channel width/nm	γ′ size/μm	γ′ volume fraction/	γ channel width/nm
0Ru	0·46	64·3	58·7	0·44	72·0	61·4
2Ru	0·38	61·3	50·0	0·48	66·3	62·7
4Ru	0·29	56·7	42·0	0·30	59·5	50·6

γ/γ′ partitioning ratio

The microstructural features of single crystal Ni based superalloys would be highly dependent on the partitioning behaviour of each alloying element between the γ and γ′ phase. The γ/γ′ partitioning ratio was widely defined as follows 1 where and are the composition of γ and γ′ phase respectively. Figure 8 reveals the γ/γ′ coarsening microstructure of alloy 0Ru as an example. It is clear that the coarsened γ phase is adequately larger to measure its accurate composition by EPMA. Table 6 lists the average composition of γ and γ′ phase in the three alloys. In terms of equation (1), the γ/γ′ partitioning ratios of every alloying element were calculated and displayed in Fig. 9. It is indicated that Ru preferentially partition to γ phase, and its partitioning ratio is about 1·7–1·8. The partitioning ratios of Re, W, Mo and Cr were progressively decreased with the additions of Ru. On the contrary, they were gradually increased for Al, Ti and Ta. In the meanwhile, Ru's partitioning ratio was slightly raised. The partitioning ratios of Ni and W are close to unity, which means that they did not exhibit evident partition trend. Here, Ni's partitioning was basically not affected by Ru additions. Ru additions resulted in the so called ‘reverse partitioning’ phenomenon,¹⁷ namely the elements which are preferentially rich in γ (or γ′) phase would inversely more partition to γ′ (γ) phase. In particular, the driving force for topologically close packed (TCP) precipitation would be reduced, since the reverse partitioning of TCP forming elements, such as Re, W, Mo, Cr, etc., is able to lower the supersaturation of γ phase. This is considered as the major reason for the suppression of TCP phase by Ru addition.^7,18 However, there are increasing experimental results showing that the reverse partitioning did not occur by Ru addition.^19–22 It can be speculated that the reverse partitioning caused by Ru additions would probably be greatly influenced by the alloy series.

Table 6

Composition of γ and γ′ phases in three alloys measured by EPMA/at-

Alloy	Phase	Ti	Cr	Mo	Al	Re	Ni	Ta	W	Ru
0Ru	γ	0·347	8·740	0·990	7·667	2·953	77·043	0·510	1·753	N/A
	γ′	0·897	2·437	0·357	16·880	0·563	74·927	2·280	1·647	N/A
2Ru	γ	0·487	6·950	0·867	9·420	2·530	75·730	0·840	1·690	1·500
	γ′	0·898	2·505	0·328	16·375	0·613	74·573	2·220	1·638	0·863
4Ru	γ	0·495	6·903	0·820	10·513	2·495	72·603	1·010	1·653	3·023
	γ′	0·873	2·737	0·357	16·573	0·660	73·273	2·250	1·680	1·613

γ′ volume fraction and γ/γ′ lattice misfit

Image analysis and plotting methods were adopted to measure the γ′ volume fraction. According to the composition of γ and γ′ phases in Table 6, lines are plotted in Fig. 10, where C_γ, and C_n are the composition of γ phase, γ′ phase and overall alloy (at-). Consequently, its slope denotes the γ′ volume fraction. It can be seen that the slope was decreased with the additions of Ru, i.e. the γ′ volume fraction was reduced. The comparison of measurement results by these two methods is shown in Table 7. Despite a little difference existed, the γ′ volume fraction was reduced with Ru additions from both methods. It is found that the value of volume fraction obtained from the plotting method is relatively small. This may be due to the different analysing regions by these two methods.

Table 7

Comparison of γ′ volume fraction measured by image analysis and plotting for three alloys

Alloy	Image analysis/		Plotting/
Alloy	Dendrite core	Interdendritic	Plotting/
0Ru	64·3±0·2	72·0±1·1	62·7±1·2
2Ru	61·3±0·8	66·3±1·6	57·3±2·6
4Ru	56·7±1·5	59·5±0·4	52·0±1·7

There are several methods for measuring γ/γ′ lattice misfit, including XRD, convergent beam electron diffraction, interfacial dislocations analysis, theoretical calculation, etc.^6,23 The theoretical calculation method was firstly used to approximately estimate the misfit of three alloys at room temperature. In general, the γ/γ′ lattice misfit δ was defined as 2 where a_γ and are the lattice parameters of γ and γ′ phases respectively. In terms of the method proposed by Watanabe et al.,²⁴ the lattice parameters of γ and γ′ phases are able to be derived from the following equations 3 4 where and are the lattice parameters of pure Ni and Ni₃Al, V_i and are the Vegard coefficients of alloying element i in Ni and Ni₃Al, and C_i and are the atomic concentration of alloying element i in γ and γ′ phases respectively. According to Caron's work,⁶ the lattice parameters of γ and γ′ phases at room temperature can be estimated as 5 6

The composition of γ and γ′ phases in Table 6 was inserted into equations (5) and (6), and then the resulting lattice parameters were inserted into equation (2). Thus, the γ/γ′ lattice misfits are 0·077, −0·100 and −0·298 for alloy 0Ru, 2Ru and 4Ru respectively. It is worth noting that these misfits are the so called non-constrained lattice misfits, i.e. the lattice distortion was not taken into consideration. It is estimated that the γ/γ’ lattice misfit of alloy 0Ru is positive at room temperature. Ru additions made the misfit change from positive to negative and then become largely negative.

As known, it is significant to fit the overlapped γ/γ′ peaks precisely for the measurement of misfit by XRD method. The relevant experimental procedures can be seen in Ref. 15 in detail. The three-peak fitting model was employed for alloy 2Ru and 4Ru. It means that there exist two subpeaks of γ phase due to its obvious tetragonal lattice distortion. However, the two-peak fitting model was adopted for alloy 0Ru owing to its less γ lattice distortion. Figure 11 reveals that the peak fitting results are in good agreement with the experimental XRD profiles. Furthermore, the constrained γ/γ′ lattice misfits of three alloys are illustrated in Fig. 12. Likewise, the misfit was changed from positive to negative and became more negative by Ru additions. In addition, it is found that the misfits derived from theoretical calculation are basically consistent with those from XRD measurements. Nevertheless, a larger deviation appeared in alloy 4Ru (as seen in Fig. 12). This may probably due to the fact that the γ lattice distortion was not taken into consideration during the theoretical calculation. Consequently, the calculated misfit was overestimated.

Discussion

In practice, enhancement of the using temperature of single crystal Ni based superalloys was restricted by their solidus and liquidus. Therefore, it is desirable to improve the temperature capability via the increment of solidus and/or liquidus by the additions of alloying elements. Based on the Ni–X binary phase diagrams, most of the alloying elements will form low melting eutectics with Ni. As a result, the solidus and liquidus were greatly decreased. Only several alloying elements, such as Co, Re, W, Ru and Ir, were likely to be able to increase the solidus and liquidus.¹ It is found that Ru additions could slightly increase the solidus. There is only 1°C increment of solidus by every 2 wt-Ru addition. However, the liquidus was increased and then decreased with Ru additions, which is not in accordance with the results in Ref. 25. It is indicated that the influence of Ru on solidus and liquidus is extremely complicated. It seems to show various effects in different alloy series. Moreover, the incipient melting temperature was raised by ∼2°C with the addition of 2 wt-Ru. Nevertheless, 4 wt-Ru addition makes it fall by ∼10°C. It may be due to the fact that more Ru additions would promote the formation of low melting eutectics in the interdendritic regions.

There are two kinds of γ′ phase in the as cast microstructure, i.e. the primary eutectic γ′ phase and the secondary γ′ phase precipitated from the γ solid solution. The eutectic γ′ phase was completely dissolved after homogenisation heat treatment, while new γ′ phase would precipitate from the supersaturated γ solid solution coherently during the following cooling process. For the homogeneous nucleation in solids, the critical nucleus radius r* and activation energy barrier ΔG* will be given respectively by²⁶ 7 8 where Γ is the interfacial energy, ΔG_v is the volume free energy and ΔG_s is the elastic strain energy. For dilute solid solution, moreover, it exists , and , where ΔX and ΔT are the supersaturation and supercooling respectively. Since γ′ forming elements (Al, Ti, Ta, etc.) segregated into interdendritic regions, the supersaturation ΔX of γ solid solution is larger in interdendritic regions compared to dendrite core regions. Accordingly, ΔG_v becomes larger, and the nucleation and growth of γ′ phase will be easier in interdendritic regions. Thus, the γ′ size is larger in interdendritic regions than dendrite core regions after solid solution heat treatment. In addition, the γ′ precipitation temperature was decreased by Ru additions, which results in the larger ΔT and thus larger ΔG_v. As mentioned above, the magnitude of γ/γ′ lattice misfit was increased with Ru additions. ΔG_s would become larger; thus, the ΔG* was increased. It would cause the nucleation of γ′ phase to become difficult. It is therefore seen that the γ′ size was reduced both in dendrite core and interdendritic solid solution microstructure with Ru additions.

When Ru caused a small amount of γ forming elements to partition to γ′ phase, they might replace some γ′ forming elements in γ′ phase. Some γ′ forming elements, in the meanwhile, would enter γ phase. Thus, it is reasonable for either γ or γ′ forming elements to show the behaviour of reverse partitioning with Ru additions. As known, the γ/γ′ lattice misfit depends on not only the partitioning ratio but also the Vegard coefficients.¹ For example, Re does not have a large Vegard coefficient;¹ nevertheless, it has a larger partitioning ratio as shown in Fig. 9. Thus, Re acted as an effective element to make the γ/γ′lattice misfit more negative. The γ′ forming elements Ta, Ti and Al have obviously larger Vegard coefficients in γ phase than those of γ forming elements Re, W and Mo in γ′ phase (as seen in equations (5) and (6)), and Ru slightly preferentially partitioned to γ phase, it is therefore that the increment of γ lattice parameter would be larger than γ′ phase. Consequently, Ru additions are believed to make the misfit change from positive to negative and become more negative. It is demonstrated that the variation of γ/γ′ lattice misfit was caused by the changes of partitioning ratios of alloying elements via Ru additions.

The morphology of γ′ particles depends on both the interfacial energy and elastic strain energy, which are related to the interfacial area and volume of precipitate respectively.²⁶ Concerning the relationship among the morphology and distribution of γ′ particles and misfit, it can be seen elsewhere.¹² It is assumed that γ matrix is elastically isotropic, and the elastic modulus of γ matrix is equal to that of γ′ phase; therefore, the total elastic strain energy ΔG_s is not related to the morphology of γ′ particles. Thus²⁶ 9 where μ is the shear modulus of matrix, δ is the lattice misfit and V is the volume of γ′ particle. It can be known that the elastic strain energy is proportional to the square of lattice misfit and the volume of γ′ particle. Consequently, when the lattice misfit of the alloy is more negative, the volume of γ′ particle will be smaller, namely, the γ′ size is smaller. Moreover, the growth of γ′ phase belongs to diffusion process. It is thus that the final γ′ size would be dependent not only on the magnitude of misfit but also the diffusion of alloying elements. The alloying elements with low diffusion coefficients are able to effectively inhibit the continuous growth of γ′ phase during the aging heat treatment. It is found that Ru has a low diffusion coefficient²⁷ and more partition to γ matrix (see Table 6). Ru additions made the magnitude of misfit larger and inhibited the diffusion of alloying elements. Moreover, the optimal primary aging temperatures are all 1140°C for three alloys in this present work. As a result, it exhibits smaller γ′ size and more cuboidal morphology and regular arrangement of γ′ phase in Ru containing alloys.

At present, single crystal Ni based superalloys contain increasing amount of refractory elements. In particular, it has become the main purpose for solid solution heat treatment to fulfil the homogenisation of refractory elements instead of the elimination of eutectics because of the more additions of Re, Ru, etc. Hence, the increasingly higher solid solution temperature and longer heat treatment time were required. Nevertheless, it is extremely difficult to obtain the homogeneous microstructure. In this present work, for example the differences on the size and arrangement of γ′ phase in dendrite core and interdendritic regions are still evident. Under the fixed solidification condition and heat treatment technology, the segregation and γ/γ′ partitioning of refractory alloying elements would determine the final microstructural features for single crystal Ni based superalloys.

Conclusions

An obvious variation of microstructure in Ru free and Ru containing alloys was found in this present work. In the as cast microstructures, the solidus was slightly increased; the incipient melting temperature and liquidus were raised, and then dropped; the precipitation temperature of γ′ phase was decreased with the additions of Ru. Moreover, the size of γ′ phase was decreased both in dendrite core and interdendritic regions by Ru additions after solid solution heat treatment. In the fully heat treated microstructures, the size and volume fraction of γ′ phase were decreased, and the width of γ matrix channels was reduced in the dendrite core regions; however, the γ′size and γ channels width were slightly increased and then dramatically decreased, and the γ′ volume fraction was reduced in the interdendritic regions. Furthermore, the well known reverse partitioning occurred with increasing Ru contents. The γ/γ′ lattice misfits changed from positive to negative and became more negative with Ru additions. The variation of γ/γ′ lattice misfit was caused by the changes of partitioning ratios of alloying elements via Ru additions.

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