Murray et al. [10] have firstly constructed an assessed phase diagram mainly based on the results published by Rath et al. [11], Pö tzschke and Schubert [12] and Tsyganova et al. [13], which is shown with dashed lines in Fig. 1. Due to large uncertainty in the experimental data, most phase boundaries were speculative. Some liquidus boundaries were strongly asymmetric, which is unlikely. The assessed phase diagram (Fig. 1) includes: (1) the liquid phase, L; (2) three terminal solid solutions, body-centered cubic [bcc(Hf)], close-packed hexagonal [cph(Hf)], and face-centered cubic [fcc(Al)]; and (3) seven intermediate compounds, AlHf₂, Al₂Hf₃, Al₃Hf₄, AlHf, Al₃Hf₂, Al₂Hf and Al₃Hf. The lattice parameter data are listed in Table 1.

Fig. 1

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	Fig. 1 Al-Hf phase diagram [16]

Fig. 2

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	Fig. 2 Al-rich portion of the Al-Hf phase diagram based on Rokhlin’ s results (points, solid lines) and the data in [11, 30] (dashed and dash- and dot-lines, respectively)

Table 1

Table 1

Table 1 Hf-Al lattice parameter data [10] Phase Composition (at.% Al) Pearson symbol Space group Strukturbericht designation Prototype References (Hf)a 0-33 cI2 Im 3¯ 3¯ m A2 W [Pearson2] (α Hf)b 0-27 hP2 P63/mmc A3 Mg [Pearson2] AlHf2 33.3 tI12 I4/mcm C16 Al2Cu [19] Al2Hf3 40 tP20 P42/mnm … Al2Zr3 [12, 20] Al3Hf4 42.9 hP7 P6 … Al3Zr4 [12, 21] AlHf 50 oC8 Cmcm Bf CrB [13, 22, 23] Al3Hf2 60 oF40 Fdd2 … Al3Zr2 [20, 21] Al2Hf 66.7 hP12 P63/mmc C14 MgZn2 [21, 24, 25] β Al3Hf 75 tI16 I4/mmm D023 AlZr3 [12, 21, 25] α Al3Hf ~75 tI8 I4/mmm D022 AlTi3 [12, 20, 21, 24, 25, 26, 27] (Al) 100 cF4 Fm 3¯ 3¯ m Al Cu [Pearson2] Metastable phase γ Al3Hf ~75 cP4 Pm 3¯ 3¯ m L12 AuCu3 [28, 29] aFrom 2231 to 1743 ° C at 0 at.% Al; bBelow 1743 ° C at 0 at.% Al

Table 1 Hf-Al lattice parameter data [10]

Kaufman and Nesor [14] have performed the calculation of the Al-Hf system in 1975 and proposed a calculated phase diagram that was quite different from the experimentally determined one [11]. However, the model-calculated phase diagram and the thermodynamic properties conducted by Wang et al. [15] are in good agreement with most of the experimental data that are shown with solid lines in Fig. 1. Because the experimental data used in the thermodynamic modeling are essentially the same as those used by Murray et al., the accuracy of the phase diagram must be confirmed. Okamato [16] redrew the Al-Hf phase diagram by preprinting of Murray and Wang’ s results. Special points of the system including the calculated invariant equilibrium data are listed in Table 2. The results of the enthalpies of formation for the Al-Hf intermetallic compounds are compiled in Table 3. The concentration dependence of mixing enthalpies at 0 < X_Hf < 0.2 and 1790 ± 5 K for the Al-Hf binary system has been established for the first time, and appropriate quantities for the entire concentration range have also been modeled by Sudavtsova and Podoprigora [17] based on Meshel’ s work [18].

Table 2

Table 2

Table 2 Comparison between selected and calculated invariant equilibrium data mainly from Wang et al. [15] and Murry et al. [10] Reaction Composition of the respective phase (at.% Al) Reaction type Temperature (K) References L ↔ bcc 0 Melting point 2504.15 bcc ↔ cph 0 Allotropic 2016.15 bcc ↔ cph + Al2Hf3 ~30 ~27 ~40 Eutectoid ~1723 [13] 28.1 27.2 40.0 1727 [15] cph + Al2Hf3 ↔ AlHf2 Peritectoid > 1273 [13] 19.8 40.0 33.3 1473 [15] L ↔ bcc + Al2Hf3 ~36 ~33 ~40 Eutectic 1803 [13] 34.7 31.0 40.0 1801 [15] L ↔ Al2Hf3 40 Congruent 1863 [13] 40.0 1840 [15] L ↔ Al2Hf3 + AlHf ~45 40 50 Eutectic 1823 [13] 41.0 40.0 50.0 1839 [15] Al2Hf3 + AlHf ↔ Al3Hf4 40 50 42.9 Peritectoid > 1223 [13] 40.0 50.0 42.9 1673 [15] L ↔ AlHf 50 Congruent ~2073 [13] 50.0 2034 [15] L + AlHf ↔ Al3Hf2 50 60 Peritectic 1913 [13] L ↔ AlHf + Al3Hf2 57.3 50.0 60.0 Eutectic 1911 [15] L ↔ Al3Hf2 60.0 Congruent 1929 [15] L ↔ Al3Hf2 + Al2Hf 60 66.7 Eutectic 1768 [13] 64.7 60.0 66.7 1879 [15] L ↔ Al2Hf 66.7 Congruent 1923 [13] 66.7 1886 [15] L ↔ Al2Hf + Al3Hf (β ) 66.7 ~75 Eutectic 1813 [13] 71.7 66.7 75.0 1842 [15] L ↔ Al3Hf (β ) ~75 Congruent ~1863 [13] 75.0 1856 [15] Al3Hf (β ) + L ↔ fcc ~75 99.93 99.81 Peritectic 935.3 [13] 938.15 [30] 75.0 99.94 99.76 934.8 [15] 934.15 [31] fcc + Al3Hf(β ) ↔ Al3Hf(α ) ~75 Peritectoid ~923 [13] 75.0 923 [15] L ↔ Al 100.0 Melting point 933.602

Table 2 Comparison between selected and calculated invariant equilibrium data mainly from Wang et al. [15] and Murry et al. [10]

Table 3

Table 3

Table 3 Comparison of the enthalpies of formation for the Al-Hf intermetallic compounds, ∆ fH2980 (kJ g-1 atom-1) AlHf2 Al2Hf3 Al3Hf4 AlHf Al3Hf2 Al2Hf Al3Hf Method Reference -41.0 -43.5 -44.4 -46.3 -47.5 -48.3 -41.8 [14] -46.3 -47.5 -48 -42 Phase diagram -39.9 ± 2.0 -43.8 ± 1.3 -40.6 ± 0.8 DSC* [32] -36.1 ± 4.3 -40.8 ± 2.6 -44.7 ± 2.4 Knudsen-effusion technique [33] 38.9 -45.0 -47.1 -50.3 -49.2 -44.7 -35.6 [15] -41.2 -48.9 -47.9 -45.2 -42.9 -41.7 -41.1 [15] -75 -72 -65 -51 Miedema’ s model * Direct synthesis calorimetry

Table 3 Comparison of the enthalpies of formation for the Al-Hf intermetallic compounds, ∆ fH2980 (kJ g-1 atom-1)

The Al-rich side of the Al-Hf phase diagram was studied by Rath et al. [11], Wang et al. [15], Zamotorin and Zamotorina [30] and Rokhlin et al. [31]. These studies indicated the peritectic character of the invariant reaction occurring in the Al-rich portion of the phase diagram at a temperature close to the melting temperature of pure aluminum, and the relative invariant reaction data are listed in Table 2. The solubility of Hf in both liquid and solid Al was determined and reported by three references [11, 30, 31], and the results are listed in Table 4. The solid solubility of Hf in aluminum at the peritectic temperature is approx. 0.5 wt%, which decreases as the temperature decreases below the peritectic reaction temperature, while the hafnium solubility in liquid aluminum increases gradually as the temperature increases above the peritectic reaction temperature. The Al-rich portion of the Al-Hf phase diagram is shown in Fig. 2.

Table 4

Table 4

Table 4 Maximum solubility of Hf in Al at peritectic temperature References Rath et al. [11] Zamotorin and Zamotorina [30] Rokhlin et al. [31] The solubility in liquid 0.075 at.% (0.49 wt%) 0.078 at.% (0.51 wt%) 0.065 at.% (0.43 wt%) The solubility in solid 0.186 at.% (1.22 wt%) 0.178 at.% (1.17 wt%) 0.153 at.% (1.00 wt%)

Table 4 Maximum solubility of Hf in Al at peritectic temperature

The Al-rich part of the Al-Hf-Sc ternary phase diagram was systematically studied by Rokhlin et al. [34], subsequently compiled by Raghavan [35]. The Al-Hf-Sc isothermal section at 600 ° C near Al corner is given in Fig. 3. The partial isothermal sections at 500 and 400 ° C were essentially resemblance with that at 600 ° C, which are not shown here.

Fig. 3

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	Fig. 3 Al-Hf-Sc isothermal section at 600 ° C near the Al corner redrawn by Raghavan [35] based on the results from Rokhlin et al. [34]

Using electrical resistivity measurements, optical microscopy and scanning electron microscopy with energy-dispersive X-ray spectrometry, the combined solubility of Sc and Hf and the phases in equilibrium in Al solid solution at 600, 500 and 400 ° C have been investigated. The results indicated that the Al solid-solution field in the Al-Hf-Sc phase diagram was contracted with decreasing temperature. Sc and Hf were shown to decrease the solubility of each other in a solid Al. The total solubility of Sc + Hf in a solid Al decreased gradually with increasing Sc/Hf ratio in the alloy.

Rokhlin et al. [36] also studied the Al-rich part of the Al-Hf-Zr ternary phase diagram. Using the similar method as for the Al-Hf-Sc, the obtained Al-Hf-Zr phase diagram showed an analogous character as the Al-Hf-Sc system, which could be due to the same group and similar chemistry of zirconium with scandium and hafnium. Taking into account the established extension of the Al single phase field and compositions of the ZrAl₃ and HfAl₃ compounds in equilibrium state, the partial isothermal sections of the Al-Hf-Zr phase diagram at 600, 500 and 400 ° C were constructed. Raghavan [37] redrew the Al-Hf-Zr isothermal section at 600 ° C near Al corner (Fig. 4), which represents the character of the sections at 500 and 400 ° C as well.

Fig. 4

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	Fig. 4 Al-Hf-Zr isothermal section at 600 ° C near the Al corner redrawn by Raghavan [37] based on the results from Rokhlin et al. [36]

As the Hf and Zr have limited solubility in solid Al, they could hardly dissolved in ternary Al-Hf-Zr system. Zr and Hf significantly decrease the solubility of each other in solid Al with contraction of the Al single phase field with decreasing temperature. In addition, there is an unexpected and remarkable result that the solubility of Zr in Al₃Hf and the solubility of Hf in Al₃Zr are insignificant because both Al₃Zr and Al₃Hf have the same crystal structure, similar constitution of the outer electron shells of their atoms and close atomic radius.

According to the binary phase diagram, primary Al₃Hf phase can be formed during solidification of all alloys with Hf content higher than approx. 0.5 wt%, i.e., higher than the peritectic composition.

The primary Al₃Hf phase has a tetragonal lattice of D0₂₃ type. Brodova et al. [48] studied the Al-1.4 wt% Hf alloy cast at the conditions of various overheating of initial melt above liquidus and different cooling rates during solidification. The primary Al₃Hf phase was observed in castings solidified with different cooling rates. Ryum [28] studied the Al-1.78 wt% Hf alloy casting from 1100 ° C in a copper chill mold placed on a water-cooled table. No primary intermetallics were observed within the grains, suggesting that hafnium was retained in solid solution during solidification. Hori et al. [29, 49, 50] have investigated the formation of primary Al₃Hf in Al-X wt% Hf series alloys, which were casted in chilling. Under the cooling rate of 3 × 10³ K/s, the primary Al₃Hf was not appeared until the content of Hf was up to 3.5 wt%. It is curious that the primary Al₃Hf phase was observed with angular structure in a splat cooled Al-6 wt% Hf alloy where the cooling rate was estimated to be 10⁷ K/s, while the Al-6.4 wt% Hf alloy showed the presence of only a supersaturated solid solution with identical cooling rate [51]. Therefore, it can be concluded that the formation of primary Al₃Hf phase in the Al-Hf alloys is dependent on both a cooling rate and an initial Hf content.

It was found by an electron microscope examination that angular structure did not consist of one phase but of a metastable Al₃Hf having an L1₂ structure and α -Al. The metastable phase had a fine needle-like shape parallel to one of < 111> _Al directions. In addition, the angular structure, which was surrounded by {100} plans and had eight processed orientations to < 111> _Al directions, had a cube shape. The morphology and structure of such phase are shown and illustrated in Fig. 6 [29].

Fig. 6

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	Fig. 6 Angular structure of Al-Hf alloy: a solid illustration, b-d cross sections of (100), (110) and (111), respectively

As described above, addition of hafnium often forms a supersaturated state in aluminum solid solution due to non-equilibrium solidification process. In particular, with a rapid cooling rate it can obtain quite high supersaturated Hf in solid solution. When the ingot is heat treated, supersaturated Hf will precipitate out from the solid solution and form new phase(s) together with Al and/or other alloying elements.

Discontinuous precipitation of the Al₃Hf phase from supersaturated solid solution was often observed in the Al-Hf binary alloys [29, 43, 49]. The mechanism of discontinuous precipitation (sometimes referred to as cellular precipitation) was commonly described as a decomposition of supersaturated solid solution into α -Al and Al₃Hf at a moving grain boundary [53].

As the grain boundary moves, it leaved behind a characteristic fan-shaped or dendritic-shaped array of precipitates [52]. One can get the general idea of the characteristic shaped array of precipitates from the schematic representation of interaction of angular structure and grain boundary reaction (Fig. 7) drawn by Hori et al. [29].

Fig. 7

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	Fig. 7 Schematic representation of interaction of angular structure and grain boundary reaction

Ryum [28] and Hori and Furushiro [50] observed only discontinuously precipitated precipitates in an Al-1.78 wt% Hf alloy annealed at 200 ° C and an Al-6 wt% Hf alloy at low temperature, respectively. This probably indicated that the diffusion of Hf in A1 was very slow, so that the precipitation took place at a measurable rate only in a discontinuous manner in which the Hf atoms diffuse in a grain boundary region [28]. After precipitation, the precipitates were very stable at 450 ° C over a long annealing time. Continuous and discontinuous precipitation of the L1₂-A1₃Hf phase in the Al-1.6 wt% Hf alloy aged at 300 ° C for 10 h is shown in Fig. 8.

Fig. 8

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	Fig. 8 Continuous and discontinuous precipitation of the L12-A13Hf phase in Al-1.6 wt% Hf alloy aged at 300 ° C for 10 h (centered dark field TEM image taken along [100]) [43]

In the Al-Hf case, the discontinuously precipitated Al₃Hf particles with a metastable L1₂ type was found to be completely coherent with the α -Al matrix and bored a closed orientation relationship with the matrix [28, 51]. No strain field existed around the discontinuous Al₃Hf in the Al-1.78 wt% Hf alloy which is different from that in the Al-Zr alloy [54].

Continuous precipitation of Al₃Hf is a bulk decomposition process of supersaturated Hf in Al solid solution. In the isothermal case, it can be characterized by three stages, i.e., nucleation, growth and coarsening. It may be described as a diffusional reaction in a multi-component system in which atoms are transported to grow nuclei by diffusing relatively large distances in the parent phase. Thus, the mean composition of the parent phase changes continuously toward its equilibrium value. Continuous precipitation is usually a desired precipitation mode to obtain a fine dispersion of homogeneously distributed precipitates with a spherical type. These precipitates are coherent with the Al matrix and usually gathered in cluster as shown in Fig. 9 [49].

Fig. 9

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	Fig. 9 Continuously formed spherical precipitates in chill cast Al-3.5 wt% Hf alloy aged at 450 ° C for 40 h

Hori et al. [49] were not able to observe any continuous precipitation of the Al₃Hf in an Al-1 wt% Hf alloy produced by splat cooling even after 2000 h aged at 450 ° C. This indicates that Al₃Hf precipitates were extremely difficult to homogeneously precipitate in binary Al-Hf alloys. The temperature-time-precipitation diagram of solution-treated Al-1 wt% Hf alloy and chill cast Al-3.5 wt% Hf alloy is shown in Fig. 10.

Fig. 10

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	Fig. 10 Temperature-time-precipitation diagram of solution-treated Al-1 wt% Hf alloy and chill cast Al-3.5 wt% Hf alloy (schematic)

In addition, the grain boundary mobility of the splat quenched Al-Hf alloy was so high that discontinuous precipitation caused by a grain boundary reaction preceded continuous precipitation within grains [29].

The transformation of the Al₃Hf phase including the structure and the morphology in the Al-Hf systems is dependent on annealing temperature and time. The decomposition of the supersaturated solid solution may thus be represented schematically in the following way [28]:

Decomposition of the supersaturated solid solution on annealing occurs by the formation of a metastable L1₂cubic Al₃Hf phase, which, during heat treatment, will transform in either equilibrium D0₂₂ or D0₂₃ structures. The equilibrium structure will be obtained depending on the temperature and the way of formation of a metastable Al₃Hf. The metastable L1₂-Al₃Hf would transform into D0₂₂ type if it was formed from casting alloy, while it would transform into D0₂₃ type if it was formed by the mechanical alloying [42, 55, 56]. It must be noted that Srinivasan et al. [42] observed the transformation of L1₂ into D0₂₃ at 750 ° C and did not observe the transformation of D0₂₃ into D0₂₂ even by heating at higher temperatures which was further studied by Colinet and Pasturel [41] using the first-principle total-energy calculations. In addition, the transformation of the Al₃Hf phases is quite different in the alloys with or without silicon.

Ryum [28] and Hori et al. [49] investigated the microstructure of the Al-1.78 wt% Hf alloy and Al-6 wt% Hf alloy with rapid solidification, respectively. They found that the metastable L1₂-Al₃Hf structure was firstly formed from decomposition of supersaturated solid solution, which was obtained by a rapid solidification. Such precipitate had a spherical morphology or fan shape and distributed within the dendrites. These precipitates partially transformed into D0₂₂ structure with plates, rods and laminated shape when the metastable L1₂-Al₃Hf was heated at 450 ° C for a long time. Some precipitates transforming into the laminated structure were developed along the < 110> directions of the matrix. It would be noted that in the Al-3.5 wt% Hf alloy all the precipitates hold the metastable Al₃Hf and no further structural change took place during the subsequent aging, which may be due to the low cooling rate of 3 × 10³ K/s. But pre-aging and pre-stressing were helpful for the transformation of L1₂ to D0₂₂ in the subsequent annealing of the alloy [49].

In addition, the imperfect D0₂₂ structure may be formed by a shear movement of a distance ½ < 110> on every other (001) plane of the L1₂ structure [28], and the perfect D0₂₂-Al₃Hf structure needed the slight movements of the Hf and Al out of the (100) planes [57].

Hori et al. [58] have studied the effect of Si on the precipitates of Al-Hf alloys containing 0.1-0.5 wt% Si isothermally aged at 350-500 ° C. A new kind of intermediate (H) phase was proposed in the phase transformation from a metastable L1₂ structure to an equilibrium D0₂₂ structure. The observed sequence of the transformation is schematically shown in Fig. 11. In addition, Hori et al. [49] and Pandey and Suryanarayana [51] also observed that the metastable L1₂-A1₃Hf phase discontinuously precipitated during the early stages of decomposition transforms directly into the equilibrium tetragonal D0₂₂ structure in the silicon-free alloys.

Fig. 11

Observed sequence of the transformation in the Al-3 wt% Hf-0.5 wt% Si alloy [49]

A possible mechanism of phase transformation of Al₃Hf from L1₂ to D0₂₂ during aging in a rapidly solidified Al-3 wt% Hf-0.3 wt% Si alloy was investigated by Furushiro and Hori [59]. The H phase was found to have a space group Pmmm (Fig. 12a). The transformation from one phase to the other could be explained by a periodic shear. Thus, a shear of 1/2[110](110)_L12 on every second plane led to the H phase which transforms to D0₂₂ by a shear of 1/2[010](101) on every second plane (Fig. 12b).

Fig. 12

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	Fig. 12 a Apparent reciprocal lattice of the H phase, b the larger symbol represents the stronger reflection, thesmallest circles of the characteristic spots are placed at ½ < 110> in the reciprocal lattice of the L12structure

In addition, it was found that the addition of Si in the alloys accelerated the continuous precipitation and decreased the time of age hardening, which was attributed to the acceleration of nucleation of spherical metastable particles by Si atoms within the grains [58]. On the other hand, Si in the alloys also suppressed the grain boundary reaction, i.e., depressing the discontinuous precipitation.

Hallem et al. also systematically investigated the dilute Al-Hf-Si alloys and found the similar results [53, 60]. Moreover, it was found that the addition of Si to the Al-Hf alloys leads a variation in grain size and precipitate morphology, which was dependent on the amount of Si addition. Relatively coarse and inhomogeneous AlHfSi particles with elongated shapes were formed in high Si-containing alloy at subsequent homogenization treatment. The formation of AlHfSi particles results in less Hf for the formation of small, coherent and spherical Al₃Hf precipitates. As a consequence, the Si content would be kept below 0.15 wt% in order to avoid the formation of AlHfSi-particle according to Hallem’ s research on the wrought aluminum alloys [53].

Most reported studies on hafnium in aluminum alloys have been focused on the wrought alloys. Jia and Arnberg [61] have investigated the microstructures of the Al-7 wt% Si-0.3 wt% Mg-0.5 wt% Hf-0.2 wt% Y cast alloy after solution treatment (Fig. 13). A novel phase was identified as Si₂Hf-type phase by combining high-resolution transmission electron microscopy (HRTEM) and energy-dispersive spectroscopy (EDS) analyses. This “ nanobelt” precipitate was observed after elevated temperature treatment of 560 ° C, with extremely large length/width or length/thickness ratio and high density. From this work, one could see more about the effect of Si on Hf-related phases in aluminum.

Fig. 13

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	Fig. 13 a Low-magnification bright-field TEM image of Al-7 wt% Si-0.3 wt% Mg-0.5 wt% Hf-0.2 wt% Y alloy. bHAADF-STEM image from the same alloy sample but different areas. Long nanobelt precipitates together with rectangular-shaped precipitates can be seen in both images [61]

Iron is one of additive elements or impurities in many commercial Al alloys, which may in some cases deteriorate or improve the properties of the alloys [62]. In the Zr-containing aluminum alloys, Fe acted as catalysts usually increases the rate of formation of Al₃Zr particles [63], while in the Hf-containing aluminum alloys Fe improves the driving force and kinetics of Al₃Hf precipitation [58].

The effect of iron on the Al-Hf alloys was systematically investigated by Hallem in his Ph.D. thesis work [60]. The amount of Fe in the range of 0.11-0.44 wt% did not show significant influence on the cast structure and the precipitation of Al-Hf alloys. Interestingly, the solubility of iron in aluminum was also increased from 0.02 wt% (according to the solidification model ALSTRUC) to 0.05 wt% with addition of Hf.

As mentioned in the section of ternary phase diagrams, considerable amount of Hf dissolved in the Al₃Sc phase and thus a more correct denotation of the precipitation is Al₃(Sc_1-x Hf _x ). In discussing the influence of the Sc content on the precipitation of Al₃Hf, one is therefore actually discussing the difference between Al₃Hf precipitation and Al₃(Sc_1-x Hf _x ) precipitation.

Harada and Dunand [64] studied the microstructure of Al₃Sc with Hf addition, leading to new ternary Al₃(Sc_1-x Hf _x ) precipitates where x = 0.10, 0.25, 0.50. When the Hf concentration increases to 0.50, a new ternary Al₃(Sc, Hf) phase is formed with D0₂₃ structure.

By using three-dimensional atom probe field ion microscopy (3D-APFIM), a Sc-rich cluster was found clearly in the Al₃(Sc_1-x Zr _x ) phase in the Al-Sc-Zr alloys, but no Zr-cluster was observed [65, 66]. Zakharov and Rostova [67] found that a Al₃(Sc_1-x Hf _x ) phase was formed when adding Hf to an Al-0.2 wt% Sc alloy. The dispersity of Al₃(Sc_1-x Hf _x ) was higher than that of Al₃Sc and less than that of Al₃(Sc_1-x Zr _x ). It is also concluded that hafnium more than 0.15 wt% would be added to gain a better or satisfying effect. Compared with the previously investigations, Hallem [60] also found Sc-clusters, but no Hf-clusters observed in Al-Hf-Sc at 290 ° C in the reconstructed 3D-volume from atom probe experiments, which revealed that Sc controlled the initial stage of precipitation. Rokhlin et al. [34] indicated the progressive decrease of the total solubility of Sc and Hf in solid Al with increasing Sc/Hf ratio and decreasing temperature.

Zr is always found together with Hf in nature and is very difficult to be separated from Hf. Both Zr and Hf show many similarities in chemical and physical properties. Srinivasan and Chattopadhyay [68, 69] found a new metastable phase formed on annealing, which had a crystal structure related to the equilibrium orthorhombic Si₂Zr. Gao et al. [70, 71, 72] found blocky AlZrSi intermetallic phase in the Al-Si-Zr alloy after annealing, respectively. Combined additions of Zr and Hf in Al alloys may form heterogeneously distributed Al₃(Hf, Zr) coarse precipitates, but not Al₃Hf precipitates, which improves the recrystallization temperature of aluminum alloys [73, 74]. Precipitation can actually be improved in Al-Hf-Zr alloys comparing with Al-Hf alloys [60]. The primary AlSi(Hf, Zr) phase formed during solidification was also found in Al-Si-Mg-Hf-Zr alloy in our unpublished work.

Rangel-Ortiz et al. [75] studied the microstructure evolution of the Al-1.2 wt% Li-0.8 wt% Hf alloys. The yield and ultimate tensile strength of the as-cast alloy were improved with the addition of hafnium and lithium. No A1₃(Li _x Hf_1-x ) precipitate in the as-cast materials was observed. Hf partly presented as an intermetallic precipitate improving the hardness of the as-cast Al-1.65 wt% Li-0.85 wt% Hf alloy [76]. According to Rangel-Ortiz et al. [77], the Hf-Li precipitates were more homogeneously distributed in Al-1.65 wt% Li-0.85 wt% Hf alloys and its size increased with increasing aging time.

Antipas et al. [78] studied the microstructure of spray formed Al-Hf and Al-Li-Hf alloys. Filamentary L1₂-Al₃Hf for the Al-Hf alloy and spherical/filamentary L1₂-Al₃(Li, Hf) for the Al-Li-Hf alloy were formed, respectively. The spherical particles were identified as the L1₂-Al₃(Li, Hf) metastable phase, formed continuously [79, 80], which was consisted of a darker L1₂-Al₃(Li, Hf) core surrounded by a lighter L1₂-Al₃Li envelope. Continuous and discontinuous precipitation of the α ′ -A1₃(Li _x Hf_1-x ) phase occurred in the Al-1.9 wt% Li-1.6 wt% Hf alloy during solution treatment at 450 ° C [79]. The α ′ -A1₃(Li _x Hf_1-x ) phase maintained a stable, fine distribution during solution treatment and controlled the strength of the alloy, while formed δ ′ -A1₃Li during aging homogeneously distributes within the matrix and at the α ′ -matrix interface and envelopes of the α ′ -phase [81].

Hallem [60] has investigated the evolution of the morphology and grain size in the dilute cast Al-Hf alloys. The equiaxed structure was observed in the Al-0.17 wt% Hf alloy, while the island grains and tendencies to the feather-shaped pattern typical for twinned columnar grains (TCGs) were observed in the Al-0.95 wt% Hf alloy. It was found that addition of Hf could refine grains. Table 6 shows that the grain size decreases from 917 to 475 μ m when the Hf content increases from 0.17 to 0.95 wt%. The conclusions are in agreement with the investigations conducted by Hori and Furushiro [50]. The remarkable grain refinement took place when the Hf content exceeded 4% (Fig. 14). In this case, the primary Al₃Hf-particles first formed acted as the nucleation sites for α -Al [43, 49]. In addition, Brodova et al. [48] have investigated the microstructure of the Al-1.4 wt% Hf alloy which was carried out with different overheating conditions of the initial melt above liquidus and various cooling rates. It was found that the increase of both overheating and cooling rate may efficiently decrease the mean grain size as shown in Fig. 15.

Table 6

Table 6

Table 6 Grain size measurements of the as-cast alloys [60] Alloy (wt%) Average grain size (μ m) Ax size (μ m) Min size (μ m) Rains measured (μ m) Al-0.17Hf 917 1967 353 68 Al-0.77Hf 574 1645 335 115 Al-0.82Hf 628 1704 277 73 Al-0.95Hf 475 1679 218 111

Table 6 Grain size measurements of the as-cast alloys [60]

Fig. 14

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	Fig. 14 Relation between grain size and Hf content in the cast alloy

Fig. 15

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	Fig. 15 Mean grain size in castings obtained at various cooling rates versus initial melt overheating above liquidus.Filled square V = 2 × 102 K/s, open square V = 4× 103 K/s, filled circle V = 104 K/s, open circleV = 2 × 104 K/s

Lattice mismatch is an important factor that can be used to predict coherency, or lack of it, between matrix and precipitates. We follow the scheme of Zedalis and Fine [73] for evaluating the lattices mismatch between the Al₃X intermetallics and aluminum. The overall mismatch δ was defined by the following equation, given by Zedalis and Fine [73] who studied the lattice parameter variation of Al₃(Ti, V, Zr, Hf) in Al-2 at.% (Ti, V, Zr, Hf) alloys

Norman and Tsakiropoulos [43] reported that hafnium increased the lattice parameter of α -Al at a rate of 0.0003 nm per wt% Hf, which is similar to the results from Hori et al. [29] (Fig. 16). Al₃Hf with the L1₂structure has the lowest the mismatch δ with the Al matrix compared with the mechanically alloyed Al₃Ti and Al₃Zr which was observed by Srinivasan et al. [42]. Harada and Dunand [64] have reported that the partial substitution of Sc-atoms by Hf leaded to a decrease in the lattice mismatch δ between matrix and precipitates. The lattice parameter of the L1₂ solid solution decreased linearly with increasing concentration of Group IVA metals including Hf, and this linear concentration dependence of the lattice parameter was found to correlate to the atomic size mismatch between Sc and the transition metal.

Fig. 16

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	Fig. 16 Plot of composition versus lattice parameter [43]. Reference here is come from Hori et al. [82]

Hori et al. [49] have studied the effect of hafnium content on Vickers hardness in Al-0-5 wt% Hf cast alloys. The increase of the hafnium content in the alloys generally increased the Vickers hardness of the alloy. When the Hf content exceeded 3.5 wt%, increase of hardness became even fast (Fig. 17). This may be due to the combination of grain refinement with the solid-solution hardening. Norman and Tsakiropoulo [43] also observed the microhardness improvement by 167.58 MPa per wt% Hf (17.1 kg/mm² per wt% Hf) by hafnium addition. The microstructure of the ternary trialuminide Al₃(Sc_1-yX _y ), where X is a transition metal from Groups IIIA (Y), IVA(Ti, Zr, Hf) or VA(V, Nb, Ta), was investigated by Harada and Dunand [64]. The conclusions were that the microhardness of the L1₂-type Al₃(Sc_1-yX _y ) phase increased linearly with increasing concentration of ternary elements. Dependence of hardness to concentration was strongest for Group VA metals and weakest for Group IVA metals.

Fig. 17

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	Fig. 17 Relation between Vickers hardness and Hafnium content in the cast alloy [49]

Electrical conductivity measurement is a suitable way to obtain information about the elements in solid solution and the occurrence of precipitation reactions during annealing. Seth and Woods [83] gave the description of the relationship between electrical conductivity and the solid-solution content for the investigated alloys by neglecting the temperature-dependent term in the Matthiessens rule:

where κ is the electrical conductivity (MS/m), p is the total resistivity (μ Ω cm/wt%), p₀ is the resistivity of the base material (Al-99.999 wt%), p _X is the contribution from each alloying element in solid solution and Sc_ss%, Zr_ss% Fe_ss%, Si_ss% and Hf_ss% represent the weight percent of Sc, Zr, Fe, Si and Hf in solid solution, respectively.

Rangel-Ortiz et al. [76] found that Hf was present as an intermetallic precipitate, improving the hardness of the as-cast Al-1.65 wt% Li-0.85 wt% Hf alloy. Hallem [60] has investigated the effect of Hf in solid solution on the conductivity. By using the equation above, p_Hf was found to be approximately 0.75 μ Ω cm/wt%. This value has subsequently been used to calculate the amount of Hf in solid solution in the Al-Hf alloys containing Si, Fe, Sc and Zr. Table 7 gives the measured and calculated values of resistivity in the alloys. It seems that all the alloying elements go into solid solution. However, some primary particles are still observed during the microstructure investigations.

Table 7

Table 7

Table 7 Calculated amounts of elements in solid solution from conductivity measurements in Al-Hf-(Sc)-(Zr) alloys [60] Alloy (wt%) Conductivity (% IACS) Resistivity (μ Ω m) Hfss% Scss% Zrss% Calculated resistivity (μ Ω m) Al-0.22Hf-0.15Sc 31.20 3.21 0.22 0.15 - 3.14 Al-1.1Hf-0.17Sc 25.20 3.97 1.10 0.17 - 3.84 Al-0.22Hf-0.11Zr 32.54 3.07 0.22 - 0.11 3.06 Al-1.0Hf-0.12Sc 27.32 3.66 1.00 - 0.12 3.66

Table 7 Calculated amounts of elements in solid solution from conductivity measurements in Al-Hf-(Sc)-(Zr) alloys [60]

A systematic creep study was undertaken for the binary intermetallic Al₃Sc and the ternary single-phase intermetallic Al₃(Sc_0.74Hf_0.26) by Harada and Dunand [84]. The activation energy of Al₃(Sc_0.74Hf_0.26) for creep deformation increased apparently. Jia and Arnberg [61] found a high density of Si₂Hf precipitates with the “ nanobelt” morphology after an appropriate heat treatment in an Al-7 wt% Si-0.3 wt% Mg-0.5 wt% Hf-0.2 wt% Y alloy. The unpublished experimental results show that such precipitate could improve evidently the high-temperature creep resistance, but less influence on hardness and strength of the material.