Effect of microalloying constituents–A novel approach to ordering phenomenon

Accepted Manuscript Effect of microalloying constituents–A novel approach to ordering phenomenon Shubhadeep Maity, Subhabrata Chakraborty, Bijay Kumar Show, Supriya Bera PII:

S0925-8388(18)32892-5

DOI:

10.1016/j.jallcom.2018.08.018

Reference:

JALCOM 47106

To appear in:

Journal of Alloys and Compounds

Received Date: 15 January 2018 Revised Date:

31 July 2018

Accepted Date: 2 August 2018

Please cite this article as: S. Maity, S. Chakraborty, B.K. Show, S. Bera, Effect of microalloying constituents–A novel approach to ordering phenomenon, Journal of Alloys and Compounds (2018), doi: 10.1016/j.jallcom.2018.08.018. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Effect of microalloying constituents–A novel approach to ordering phenomenon

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Department of Metallurgical and Materials Engineering, National Institute of Technology, Durgapur -713209, India.

Department of Chemical Engineering, National Institute of Technology, Rourkela -769008,

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India.

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Shubhadeep Maity1, Subhabrata Chakraborty2, Bijay Kumar Show1, Supriya Bera1*

Abstract:

A conscientious study by X-Ray diffractometry has been done to determine long-range order parameter, the lattice constant, and crystallite size of B2 NiAl (Cu) as a function of Ni

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concentration. Addition of Zr and Ti as micro-alloying elements enhances the lattice parameter as well as ordering behavior, particularly at higher Ni concentration in the alloys.

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Our present investigation shows that a broad concentration range of Ni content is suitable for the formation of B2 structure. Ordering behavior in NiAl is explained by the formation of the

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antiphase boundary based on the data of transmission electron microscopy (TEM) study and enthalpy of formation of the corresponding compositions.

Keywords: Ordered alloys, Long range parameter, Micro-alloying, Site occupancy, XRD

*

Author for correspondence: [email protected], [email protected];Ph:

+91-343-2754711; FAX: +91-343-2547375

ACCEPTED MANUSCRIPT 1. Introduction: Ordered intermetallic alloys (specific chemical compositions) with low ordering (Tc) and high disordering temperature exhibit many unique properties. These alloys are widely studied due to their interesting properties such as high specific strength, high melting point, good

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oxidation resistance, low density and decent thermal conductivity. The atomic packing density of the ordered alloys results in high frictional stress which restraints pair dislocation motion at high temperatures. Consequently, ordered intermetallics show high strength at

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elevated temperature. Restriction in atomic mobility suppresses the diffusion process to enhance creep resistance of the ordered materials. Therefore, ordered alloys have a wide

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range of high-temperature applications such as in advanced aerospace structures, propulsion, power generation turbines (e.g., rotor blades and stator vanes) and in high-temperature environmental coatings [1-3]. Despite such attractive properties, low ductility/plasticity and poor toughness at ambient temperature restrict the use of the ordered intermetallic alloys

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(e.g., FeAl, NiAl, Fe3Al, Ni3Al, CoAl, TiAl, and Ti3Al, etc.). In ordered alloys, the extrinsic brittleness comes from impurities as observed in ordered aluminide materials. In contrast, weak grain boundary cohesion leads to intrinsic brittleness [4-5]. Different types of dopants

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are used to enhance the cohesive strength at grain boundaries [6-7]. Furthermore, the addition

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of micro-alloying elements like boron, carbon, and zirconium suppresses moisture induced environmental brittleness by the reduction of hydrogen diffusivity along the grain boundaries [8]. The cohesive strength at the grain boundaries is enhanced when dopants generate covalent bonds with the host atom. Elements with a lower electronegativity (with higher atomic radii) can provide additional bonding at the grain boundaries by creating the homopolar bonds [7]. However, considering a wide range of the ordered alloys, the improvement in strength is insignificant. Additionally, due to their brittle nature, the ordered intermetallics are difficult

ACCEPTED MANUSCRIPT to produce. Therefore, the primary challenge for ordered materials is to increase the ductility/plasticity to make them suitable for industrial applications. Among different types of ordered alloys, NiAl has attractive characteristics such as simple crystal structure, wide compositional homogeneity range, highly ordered crystal structure and reversible shape

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memory effect. Thus, NiAl alloys are suitable for electronic applications in advanced semiconductor heterostructures, optical emissivity in devices, magnetoresistance and magnetic susceptibility measurements [3].However, like other ordered alloys, NiAl shows

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poor ductility and toughness [9] due to a weak grain-boundary cohesion. <100> slip system of NiAl provides only three slip systems. Thus, the criteria of five independent slip systems

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cannot be fulfilled which is a prerequisite to improve the ductility of polycrystalline materials (the von Mises criterion) [10-12]. Researchers have tried several techniques like grain refinement [13, 14], the addition of micro-alloying elements [15-17] and oxide dispersion [18, 19] to overcome the lacuna and improve the mechanical strength of NiAl. The micro-

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alloying elements are important due to their interatomic bonding with dislocation core. Furthermore, they decrease antiphase boundary energy thus promoting the easy formation of necessary slip system in particular direction. Several elements were used as the micro-

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alloying constituents to improve the plasticity/ductility of NiAl. Addition of Fe increases

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valence electron density in the grain boundary region [20] and results in a homogenized distribution of cohesion-bonds, thus, increasing the ductility. Elements with larger atomic radius than Al/Ni can create structural heterogeneity in NiAl ordered structure [21] and facilitate dislocation movement. Kogachiet al. [22] found that vacancy formation in off-stoichiometric compositions and addition of third elements improves the strength of NiAl. A precise understanding of strengthening mechanism requires the knowledge of site occupancy of constituent atoms, constitutional vacancies, and effects of micro-alloying element/elements. Incidentally, the

ACCEPTED MANUSCRIPT concept of site occupancy plays an important role to determine the degree of long-range ordering (long-range order parameter). Therefore, it is essential to determine the long-range order (LRO) parameter to understand the deformation mechanism of ordered alloys. NiAl ordered phase can be synthesized by mechanical alloying [17, 23, 24]. Solid state

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synthesis mechanism of NiAl has been explained by several researchers [25, 26]. In 1988, Atzmon et al. [25] proposed that stoichiometric NiAl could be formed by explosive exothermic reaction and self-propagating high-temperature reaction. Then in 1992, Zbiral et

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al. [26] suggested a theory on the diffusion of constituent elements depending on their equilibrium solid solubility. Later, Pabi et al. [27] described the formation mechanism by

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“discontinuous additive mixing” based on a prerequisite critical grain size. Our prime objective of the present investigation is to understand the role of the primary constituents (Al/Ni) and effect of microalloying elements on the formation of NiAl superstructure. We chose Al-Cu-Ni alloys for the present study due to their high strength and

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ductility (both compressive and tensile) at elevated temperatures [28]. It is known that Zr and Ti have lower electronegativity values as compared to Al, Ni, and Cu [7]. Consequently, they can improve grain boundary cohesion and introduce local structural heterogeneity [9, 21].

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Thus, Zr and Ti were also chosen as microalloying elements. We intended to carry out a

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detailed and precise microstructural characterization through extensive XRD analysis with complementary TEM investigation for this study. 2. Site preference and theoretical background: The mechanism of B2 NiAl formation in Al (Cu) Ni alloys with the addition of Zr and Ti as micro-alloying elements is very complicated compared to the simple binary NiAl alloys. The effect of Cu addition on the formation of B2 NiAl has been studied by Lipson and Taylor [29]. Binary NiAl alloys follow the electron to atom ratio of 1.5 according to HumeRothery’s rule for ideal stoichiometric configuration (50%-50%). It is assumed that the ratio

ACCEPTED MANUSCRIPT is 1.48 when Fermi surface first touches the Brillouin zone. However, the ratio is more than 1.5 for off-stoichiometric configuration (for Al-rich alloys) [30]. In NiAl, while Al has three valence electrons, Ni has filled-up“d” shell. It leads to an electron to atom ratio of 1.5. Values, greater than 1.5 indicate in excess electron inside the inscribed sphere of Brillouin

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zone. Consequently, the energy of the electron increases rapidly [31]. For Al-rich alloys, number of valence electron increases and the number of atoms per unit cell diminishes in such a waythat the electron to unit cell ratio (standard 3 electrons per unit cell) and the

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number of electrons to be accommodated in Brillouin zone remains constant. In Al (Cu) Ni system, the number of electrons per unit cell in Brillouin zone increases only due to the

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addition of Cu atoms [31]. In Al-rich alloys, vacancies are formed in the Ni sublattice to maintain the stoichiometry. When Cu is added, it replaces those vacancies as Cu atoms are supposed to occupy in Ni sublattice [32, 33]. There are very few evidences of Al antistructure atom’s existence [32, 34, 35]. However, the more acceptable perception is that the excess Al

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atoms does not occupy Ni sublattice; instead, it creates vacancies [32, 33]. Lipson and Taylor [29] proposed the concept of placing TM (Transition Metal)-atoms into the Ni sublattice by forming vacancies. However, a more detailed analysis by Jiang [33] suggests that, in Al-rich

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system, Cu occupies Ni sublattice, whereas Ti and Zr occupy Al sublattice as the "d" shell

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electron occupancy in Ti and Zr is much lower than in Cu [36-37]. Fig. 1 schematically shows the preferred site occupancy of the constituent elements in the proposed alloy. 3. Materials and Methods: Nanocrystalline B2 NiAl was synthesised by mechanical alloying (MA) of elemental aluminium (99.9%), nickel (99.9%), copper (99.9%), zirconium (99.9%) and titanium (99.9%) powders. Ternary [Al (85-x) Cu15Nix], quaternary [Al (85-x) Cu10 Nix Zr5] and quinary [Al (85-x) Cu10 Nix Zr2.5Ti2.5] [x=5, 10, 15 and 30] alloys were studied. Milling was carried out in a Retsch PM200 planetary ball mill.During all experiments, 15 g powder blends (according

ACCEPTED MANUSCRIPT to the composition) were canned together with 150 g tungsten carbide (WC) balls of 10mm diameter into WC vial. Milling was carried out for 100 hrs at a rotational speed of 300 rpm. Toluene was used as a process control agent (PCA) to prevent excessive cold welding. To avoid undesired heating, one hr milling was followed by 30 minutes cooling period. Samples

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were collected and characterized at the selected duration of milling.

Phase evolution of the alloys was studied by X-ray diffraction (XRD) using Philips PANalytical X-Ray diffractometer. Cu-Kα (λ= 0.154078 nm) radiation generated at

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45kV/40mA was used with a step size of 0.04 degree and 1.35 s per step. Particularly, for quantitative analysis (determination of lattice parameters and long-range order [LRO]

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parameter) precise scanning (step size of 0.02 degree and 2.5s per step) was performed. LRO parameter was calculated usingXRD line profile analysis by comparing the observed and theoretical intensities of (100) superlattice and (110) fundamental reflections as per the following equation [38]. ( )

(

) ( ) ( )

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LRO parameter (S ) = ( ) (

) ( ) ()

………………………………...…………...……….. (1)

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The precise lattice parameter of the alloys was determined from the intercept of calculated lattice parameter vs. Nelson-Riley (NR) parameter (cos2θ/sinθ +cos2θ/θ) plot to avoid

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possible instrumental offset. Crystallite size was calculated using Williamson-Hall (W-H) method [39].W-H equation for uniform deformation model (UDM) is expressed as

β cos θ =

 

+ 4ε sin θ..................................................................................................... (2)

A graph was plotted taking 4sinθ along the x-axis and βhklcosθ along the y-axis. The crystallite size (D) and lattice strain (ε) were obtained from the intercept on the Y-axis and the slope, respectively. The instrumental error in the full-width half maxima of any reflection (βhkl) was rectified by the following method [40].

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β = [(β )& '()*+(, − (β )& ./)0+*(/0 ]2 ……………………………..……..…….. (3) 

Microstructural and compositional analysis of the milled alloys were carried out in detail by High-Resolution Transmission Electron Microscope (HRTEM) (TECNAI T F 30 G2SUPER

TWIN Made by FEI) equipped with FISCHIONE High Angle Annular Dark Field (HAADF)

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detector (Model M-3000). The powdered alloys were first sufficiently ultrasonicated in ISO Propyl alcohol. A small drop from the well mixed solution was put on carbon-coated copper

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grids of 300 mesh size and then dried for TEM analysis.

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4. Results:

Fig.2 shows the XRD patterns of selected milled alloys for different milling duration (1, 10, 40, 70 and 100hrs). The XRD patterns of all one hr milled alloys show the presence of every constituent element of the corresponding compositions. With gradual increase of the milling time, the characteristic reflection peaks of the alloys are broadened and intensity of the peaks

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reduces due to the increasing lattice strain, lattice defects and decreasing grain size [14]. Fig.2 depicts that, at 40 hrs of milling, single phase B2 NiAl is evolved. Detailed phase

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analysis using XRD data reveals the formation of NiAl at 40 hrs of milling in all the ternary, quaternary and quinary alloys with Ni=30 at. %. The superlattice reflection ((100), 2θ=30.9⁰)

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is indicated by arrow (Fig. 2). As Ni content decreases, elemental Al remains undissolved (Fig. 2(d)), even after 100 hrs of milling.

Fig. 3 exhibits parametric phase diagrams which suggest suitable milling criteria for the formation of superlattice structure in the present ternary, quaternary, and quinary alloys. Quaternary and quinary alloys show contrasting and somewhat contradicting results in comparison to ternary alloys. In general, the similar type of NiAl superlattice formation is observed during milling for most of the quaternary and quinary alloys. However, both

ACCEPTED MANUSCRIPT quaternary and quinary alloys with 5 at. % Ni show single phase solid solution instead of superlattice NiAl, even after 100 hrs of milling. It seems addition of Ti and Zr deteriorates the evolution of ordered structure in Al (Cu) Ni alloys. Superlattice phase forms again when Ni

kinetics of superlattice formation further.

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content is ≥ 10 at. %. It is observed that in quinary alloys, the addition of Ti decreases the

For precise calculation of LRO parameter, slow scan XRD has been done. Slow scan XRD with corresponding SAED pattern is shown in fig. 4.LRO parameters of the alloys at different

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milling time are calculated from slow scan XRD patterns and are enlisted in table 1. With gradual milling, LRO parameters increase monotonously. Most surprisingly, both quaternary

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and quinary alloys with 30 at. % Ni possess significantly higher LRO parameters than their ternary alloy counterpart. This suggests that the addition of both Zr and Ti increases LRO parameter, thus, assists superlattice formation. This contradicts our previous observation that (at lower Ni content (5 at. %)) addition of both Zr and Ti deteriorates ordered phase

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formation. This apparent fallacy is explained in the discussion section with further in-depth analysis and a possible thermodynamic justification. Figs. 5 (a) and (b) show the variation in lattice parameters and lattice expansion (%)as a

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function of milling time and alloy composition (Ni%), respectively. Ni30alloys show higher

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lattice parameter expansion than the alloys with lower Ni concentration.Ni30 quaternary alloy possesses highest lattice parameter (0.2906 nm) which is significantly higher than the commercial NiAl powder (0.2883 nm, Alfa Aesar 99.9 % purity) and stoichiometric NiAl composition (0.2887 nm) [3]. Fig. 5 (c) exhibits the average crystallite size of 100 hrs milled alloys. Average crystallite size reduces to below 20 nm after 100 hrs of milling. It is worthwhile to mention that crystallite size decreases to a nanometric range (< 100 nm) at the time of NiAl ordered phase formation (40 hrs of milling). More interestingly, no significant grain refinement is observed with further milling up to 100 hrs. HRTEM analysis of few

ACCEPTED MANUSCRIPT selected samples was carried out to corroborate the XRD line profile analysis by W-H method. Both results are comparable with each other. For example, grain size distribution of 100 hrs milled ternary Ni30 alloy (Fig. 5(d)) is fitted well with the average grain size calculated by W-H method (8-12 nm).

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Furthermore, in-depth TEM analysis confirms the presence of NiAl phase and helps to understand the mechanism of superlattice formation during milling. Fig. 6 (a, b and c) shows the bright and dark field TEM images of 100 hrs milled Al55Ni30Cu15 alloy with elemental

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mapping. Scanning Transmission Electron Microscope (STEM) with the aid of high angle annular dark field (HAADF) detector provides the Z contrast images of selected ternary,

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quaternary and quinary alloys (Fig. 6d, 6e and 6f). The selected Area Electron Diffraction (SAED) patterns of 100 hrs milled Al55Ni30Cu15 alloy show all reflections (weak and fundamental) of NiAl phase (Fig. 7a). The HRTEM images (Fig. 7b) of same alloy exhibit corresponding lattice fringes of (110) planes. Inverse Fourier Filtered Image of (b) shows

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antiphase boundaries (APB) (marked by arrows) and dislocations (with “

5. Discussions:

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7c).

”symbols) (Fig.

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5.1. XRD analysis:

Mechanical alloying (MA) of the present alloys results in the evolution of ordered Ni-Al phase, except for quaternary and quinary alloys containing 5 at. % Ni. Powder blends after 10 hrs of milling exhibit traces of undissolved elements. Further milling reduces the grain size to a nanometric range (Fig. 2) and significantly increases the grain boundary free energy. Subsequently, free energy of the alloys increases and it provides the driving force for alloying [41, 42]. Our results indicate that possible Ni composition range, which results in ordered

ACCEPTED MANUSCRIPT NiAl, can be extended more towards Al rich side than previously reported data (up to 25at. % Ni compared to 45at. %Ni) [27]. Several earlier studies also show that addition of third element (Fe/Cr/Ti) results in reduced Ni concentration (20-42 at. %) compared to a stoichiometric composition, which can evolve

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NiAl alloy [45-47]. Our work indicates that addition of Cu/Zr/Ti [table 2] provides further flexibility in Ni concentration range considering the evolution of NiAl ordered phase in low Ni containing alloys. Therefore, it can be concluded that not only binary off-stoichiometric

in the Ni sublattice than in the Al sublattice [3, 43].

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composition but also ternary, quaternary and quinary alloys exhibit more vacancy tolerance

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In the present investigation, ball milling was carried out in a normal atmosphere under toluene. Gradual surface oxidation of the particles occurs with continuous milling. These oxide coated particles result in slowing down the diffusion process, which decelerates the system kinetics and hinders the explosive reaction [48]. The reaction is specified as

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discontinuous additive mixing [27] where both constituents Ni and Al rapidly intermix with each other and involve a moving boundary process to form NiAl. Interestingly, NiAl phase

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nano size region.

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formation is triggered up by the reduction of Al and Ni grain size below a certain level in a

5.2. TEM analysis:

The bright and dark field TEM images along with elemental mapping ensure that the constituent elements are homogeneously distributed within ultrafine grains of NiAl (average size ∼ 10nm). For example, fig. 6 (a) and (b) show the bright and dark field TEM images of 100 hrs milled Al55Ni30Cu15 alloy, respectively. The images indicate ultrafine alloy grain size. Corresponding elemental mapping (Fig. 6 c) shows the homogeneous distribution of Al, Ni and Cu. The HAADF images of selected ternary (Fig. 7a), quaternary (Fig. 7a) and

ACCEPTED MANUSCRIPT quinary (Fig. 7a) alloys show compositional variation in the form of atomic contrast imaging (image contrast depends on atomic no (Z) of constituents). Presence of heavier atoms (higher atomic number) looks brighter as scattering intensity is directly proportional to Z2. Quaternary alloys exhibit bright contrast ensuring the presence of heavy element enriched

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zones. In other words, it indicates regions with relatively higher electron density distribution [49, 50].Understandably, the quaternary alloys contain the maximum amount of Zr (possesses highest atomic number among five constituent elements), thus, looks brighter than ternary

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and quinary alloys. It is believed that homogeneous distribution of constituent elements with regions of high electron density results in higher LRO parameter.

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The Selected Area Electron Diffraction (SAED) patterns (Fig. 4(b) and 7(a)) confirm the formation of ordered NiAl. The figures show both fundamental reflections (110, 200, 211, 220 and 310) and superlattice reflections (100, 111, 210 and 221). Fig. 7(b) illustrates the HRTEM image of 100 hrs milled Al55Ni30Cu15 alloy. Calculated interplanar spacing (nm)

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indicates,(110) plane which is the most intense reflection in XRD pattern (Fig.4a) and diffracted ring in SAED pattern (Fig. 7a). Inverse Fourier Filtered Image (Fig. 7(c)) of fig. 7(b) further resolves several antiphase boundaries (APB) (marked by arrows). Noticeably, the

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APBs are surrounded by edge dislocations (both positive and negative).

5.3. Factors influencing the long-range order parameter: 5.3.1. Theoretical assumption: NiAl contains two sublattices of Al and Ni, where both of these sublattices interpenetrate each other. It is assumed that while the cube-centre contains Al atom, Ni atoms occupy the corner sites of the unit cell. In the present investigation, the theory described in ref [22, 51, 52] for Ni-Al, Co-Al and Fe-Al alloys is used to understand the variation of LRO parameter in Al-rich ternary, quaternary and quinary alloys.

ACCEPTED MANUSCRIPT According to a statistical possibility,

N4/6 + N7+/6 + N89/6 + N:/6 +N;9/6 = N;9/< + N=*/< + N4/< + N:/< = N........... (4)

The above equation is rearranged as

N(4>7+>89)/6 + N:/6 +N;9/6 = N(;9>=*)/< + N4/< + N:/< = N.................................... (5)

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HereN4/6 , N7+/6 , N89/6 , N;9/6 and N:/ 6 are Al, Zr, Ti and Ni atoms and vacancy in the Al

sublattice, respectively. Ni, Cu and Al atoms and vacancy in the Ni sublattice are represented as N;9/< , N=*/< , N4/< and N:/< . This is in accordance with site preferences for all atoms

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as described earlier. N4/< and N;9/6 denote Al anti site defect and Ni anti site defect,

respectively.

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C C If the total amount of atom fraction in Al and Ni sublattice are x4 , x;9 , respectively then

C C x4 + x;9 + x: = 1................................................................................................................. (6)

x: is the total vacancy fraction in both sublattices.

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Now according to the site occupancy, atomic fractions in particular sublattices are described below.

C x4 = x4 + x7+ + x89 ............................................................................................................. (7)

C x;9 = x;9 + x=* ...................................................................................................................... (8)

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Wherex4 ,x;9 , x=* , x7+ and x89 are the fractions of Al, Ni, Cu, Zr and Ti atoms respectively. The effective fractions of Al and Ni atoms are given below.

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C 2x4 = N(4>7+>89)/6 + N4/< ............................................................................................... (9)

C 2x;9 = N(;9>=*)/< + N;9/6 ................................................................................................. (10)

LRO parameters are expressed in term of two independent variables, S1 and S2 which are expressed as.

C S1=2[N(;9>=*)F − x;9 ]....................................................................................................... (11) ;9

C ] ................................................................................................... (12) S2=2[N(4>7+>89)F − x4 4

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C C For a perfect ordered state S1= S2 = 1, where x;9 =x4 =

G &

andHI = 0. The above LRO

parameters would reach maximum for arbitrary compositions only if the following equations are satisfied.

C C SG = 2(1 − x;9 ), S& = 2x4

When x;9 ≥ & (Ni-rich composition).................................................................................... (13)

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G

C C SG = 2x;9 , S& = 2(1 − x4 )

When x4 > (Al-rich composition).................................................................................... (14) G

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&

The present investigation is based on Al-rich composition. Therefore, LRO parameter of

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NiAl will achieve highest possible value when all additional atoms (Cu, Zr, Ti) occupy their preferential sites (as mentioned earlier) and extra Al atoms will fill the positions in Ni sublattice (antisite defect) without any vacancy to maintain positional number balance. The equations (13 and 14) are based on the above assumption. Furthermore, according to structure factor calculation

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FN = {(Y;9/< )f;9 + (Y=*/< )f=* } + {(Y4/6 + Y4/< )f4 + (Y7+/6 )f7+ + (Y89/6 )f89 }......... (15) For fundamental reflection, (h +k + l) = even And

;9

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;9

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F) = {(Y;9F )f;9 + (Y=*F )f=* } − {(Y4F − Y4/< )f4 + (Y7+/6 )f7+ + (Y89/6 )f89 }......... (16) 4

For superlattice reflection, (h +k + l) = odd.

Here f4 , f;9 , f=* , f7+ and f89 represent atomic scattering factor of Al, Ni, Cu, Zr and Ti,

respectively. For each diffracted peak integrated intensity (I )9,( is

I = K U V)9/2 Y.WX) Y[ . e]&' |F|&.......................................................................................... (17) G>WX)2 &Y

Where F is the structure factor, p is the multiplicity factor, V)9/2Y.WX) Y[ is the LorentzG>WX)2 &Y

polarization factor, K is the scale factor (independent of reflecting planes) and e]&' is the

ACCEPTED MANUSCRIPT temperature factor. For particular (100) and (110) reflection, predicted intensity is expressed as (

) _ `abcd _

=

efgh2 i )b l2m |nh |2 }( ) hjk2 i.fgh i 2 2 efgh i {( 2 )b l2m onp o }( ) hjk i.fgh i

{(

................................................................................... (18)

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To measure the LRO parameter, the present investigation followed the JCPDS to calculate the ideal intensity ratio. The present investigation has ~5-6 % error in LRO parameter calculation as compared to analytical assumption. Based on the theory (and related

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equations), the apparent fallacy regarding the variation of LRO parameter of the ternary,

compositions is explained.

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quaternary and quinary alloys and reduced kinetics of NiAl phase formation in certain

i) In all the alloys as Ni concentration decreases the composition becomes more and more off-stoichiometric. Obviously, it creates more vacant sites in Ni sublattice; thus, reduces the kinetics of NiAl formation. Particularly, in quaternary and quinary alloys, Zr and Ti further

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occupy the position of Al sublattice and push the system towards more off-stoichiometric position. Therefore, the addition of Zr/Ti in lower Ni (5 at. %) content alloys restricts the formation of NiAl. The above regulation can be explained in detail by the theory of electron

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to unit cell ratio proposed by Lipson and Taylor [29]. In the extreme off-stoichiometric situation (Ni 5 at. %), ternary alloy accommodates itself with the suitable electron per unit

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cell ratio (standard 3:1) by omitting Ni atoms. Addition of Zr and Ti in quaternary and quinary alloys enhances the number of valence electron per unit cell. Except of 5 at. % Ni composition, all other quaternary and quinary alloys maintain standard electron to unit cell ratio by the omission of Ni atoms. Perhaps, such omission of Ni atoms in low Ni content (5 at. %) alloys (quaternary and quinary) reduces standard electron to unit cell ratio and consequently restricts the formation of ordered NiAl.

ACCEPTED MANUSCRIPT ii) Ordering behaviour depends upon atomic size mismatch. In the present investigation, atomic radius of microalloying elements are higher than replaced element (rZr>rTi>rCu). Addition of bigger atoms like Zr and Ti in low Ni content quaternary and quinary alloys reduces the rate of vacancy formation [28], thus, retards NiAl formation. At higher Ni

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concentration, strong bond formation between Zr-Ni and Ti-Ni atoms overshadows this and facilitates NiAl formation. Furthermore, the minor variation in the LRO parameters of quaternary and quinary alloys arises perhaps due to the difference in the atomic radius of Zr

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and Ti.

iii) Atomic scattering factor plays an important role in LRO variation among the alloys.

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Higher electron density distribution of Zr is responsible for higher atomic scattering factor (qrs ).Probably, quaternary alloys (containing 30 at. % Ni) show highest LRO for the same reason which is corroborated by atomic contrast images (Fig. 6(d, e and f).

9 iv) ∆Hmix of Zr-Ni and Ti-Ni are more negative than Cu-Ni (∆u(;9]=*) =

35 kJ/mol) [53]. Therefore, substituting Cu with

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9 9 ∆u(;9]7+) = 49 kJ/mol, and ∆u(;9]89) =

4 kJ/mol,

Zr/Ti in the quaternary and quinary alloys makes the alloys more stable and favours the

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formation of NiAl. Further analysis on the thermodynamic feasibility of NiAl formation is discussed in the next section.

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5.3.2. Thermodynamic analysis on the formation of NiAl phase: We analyse the effect of composition on the theoretical feasibility of NiAl formation in all alloys studied in the present investigation. Enthalpy of formation (∆H) as a function of Ni concentration is calculated using extended Miedema’s model [54-56]. Detailed calculation is given elsewhere [55]. Fig. 8 shows the variation of ∆H of the ideal solid solution and ordered phase as a function of Ni concentration in (a) ternary, (b) quaternary and (c) quinary alloys, respectively. In all alloys, the ordered phase exhibits lower ∆H than the ideal solid solution and the difference in ∆H between ordered phase and random solid solution increases with

ACCEPTED MANUSCRIPT increasing Ni concentration (makes ordered phase more stable). It is quite understandable, that increasing Ni content pushes the system towards more stoichiometric condition. However, in the model [55] there is no scope to consider the site preference of the constituent elements (and vacancy sites in the unit cell as its obvious consequence). To understand the

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effect of site preference and vacant site (in Ni sublattice), the model is modified (given in the appendix). Consequently, ∆H of the ordered phase is recalculated. It is found that (Fig. 8), the vacancies increase the ∆H of ordered phase and make the ideal solid solution more stable.

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However, as Ni concentration increases, the ∆H of ordered phase decreases more rapidly than

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that of the ideal solid solution. Strikingly, this effect is more prominent in quaternary and quinary alloys than ternary alloys. Therefore, higher Ni containing alloys favour the formation of the ordered phase. A possible justification for the previously observed apparent discrepancy can be given based on this thermodynamic analysis. At lower Ni concentration (more off-stoichiometric composition), addition of Zr/Ti results in a more significant increase

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in ∆H as it creates more vacancies in Ni sublattice, thus, restricting the formation of ordered phase. However, when the alloys are close to stoichiometric (higher Ni concentration) composition, this effect becomes insignificant. Instead, the addition of Zr/Ti favours ordered

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phase formation as ∆H becomes more negative. Higher LRO parameters of the quaternary

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and quinary alloys with higher Ni content are in agreement with such a behavior. 5.3.3. Formation of Antiphase Boundary (APB): Table 1 indicates that degree of NiAl ordering (expressed in terms of S parameter) increases with milling time. Fig. 3 shows that NiAl formation is initiated at 40th hrs of ball milling. The corresponding values of S are increasing with further milling, apparently due to the atomic migration throughout the APB. Inverse Fourier filter image of (110) lattice plane (fig. 6c) shows interruption of lattice regularity by a formation of a huge number of dislocations (generated during milling due to severe plastic deformation) which are surrounded by APB

ACCEPTED MANUSCRIPT faults. During MA, strain (induced by high energy milling) triggers the atomic migration which in turn enhances APB mobility. Consequently, two neighbouring domains absorb each other to reduce APB, increasing LRO [57].In this regard, addition of Zr and Ti in the alloys close to more stoichiometric composition possibly decreases APB (as both atoms form strong

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bonds with Ni atoms) and increases LRO parameter.

In addition to the factors mentioned above (stoichiometry, vacancy, and electron to atom ratio, size mismatch, atomic scattering factor and enthalpy of formation), few other

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parameters like heat generation due to continuous milling can trigger thermally activated reordering phenomenon and enhancement of LRO parameter [58]. However, the effect is

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minute compared to the other factors as the present milling sequence (in toluene; 1 hr milling followed by 30 min cooling) does not allow excessive heating. 5.4 Crystallite size and lattice parameter:

Fig. 5(c) exhibits the crystallite size of 100 hrs milled alloys as a function of Ni

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concentration. It can be seen from this figure that, crystallite size decreases with increasing content of Ni. According to Hellsternet et al. [59], crystallite size reduces by the reduction of LRO with progressive milling since a single monolayer of atoms near grain boundaries does

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not take a part in ordering behaviour of the material. Thus, LRO parameter should

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continuously decrease with the reduction of crystallite size as the number of atoms increases in the grain boundaries as compared to the remaining atoms in the grain. Therefore, our results reflect discrepant behaviour with Hellstern et al. [59]. However, Schropf et al. [60] had reported similar trend as that of the present investigation. In principle, crystallite size depends on the full width half maxima (FWHM) of the XRD pattern. FWHM is same for (100) and (110) reflections, but, different for remaining peaks [60]. Thus, LRO parameter seems to be independent of crystallite size [60].

ACCEPTED MANUSCRIPT Furthermore, the crystallite size decreases with milling time (Fig. 2) as the alloys acclimatize to drastic defect density. The ultrafine grains (with large grain boundary area) reduce the inter particle distance and accelerate atomic diffusion [14]. However, after certain milling period dislocations are reluctant to move through the lattice due to the formation of antiphase

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boundary and reduction of grains to the nano-meter range and thus restricting further refinement [61]. Mechanical alloying of current alloys exhibits similar findings as insignificant grain refinement occurs after 40 hrs of milling. For example, while all 40 hrs

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milled alloys (containing 30 at. % Ni) show ∼ 15 nm grain size, further milling to 100 hrs reduces the grain size to ∼ 10 nm only. In contrast to insignificant grain refinement after 40

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hrs of milling, lattice parameter shows considerable increase with gradual milling. Perhaps atomic diffusion during the milling results in such an expansion of the lattice parameters. Lattice parameter increases with increasing Ni concentration as well (Fig.5 (a)). In general, stoichiometric NiAl possesses the highest unit cell size. Reduction of lattice expansion is

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observed at lower Ni content compositions due to the formation of vacancies in Ni sublattices [22, 32 and 62]. Furthermore, it suggests the presence of minute Al antisite defects in the present alloys as Al antisite defects enhance the lattice parameter [59]. Lattice parameters of

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the ternary alloys are higher than the lattice parameter of the stoichiometric NiAl composition

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due to the presence of large Cu atoms (0.128 nm atomic radii in comparison to 0.124 nm atomic radii of Ni) [62]. Lattice parameter increases further in quaternary and quinary alloys as Zr (0.160 nm) and Ti (0.147 nm) replace Cu. In addition to this, simultaneous increase in both lattice parameter and LRO parameter with gradual milling corroborates the enhancement of ordering behaviour by mechanical milling.

6. Conclusions:

ACCEPTED MANUSCRIPT Mechanical alloying of Al-Cu-Ni alloys promotes ordered B2 NiAl phase formation. Addition of Zr and Ti as micro-alloying elements in Al-Cu-Ni alloys shows two clear contrasting results. It retards the kinetics of ordered phase formation in off-stoichiometric compositions. Therefore, unlike the ternary alloys, quaternary and quinary alloys restrict

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phase field flexibility, probably due to retention of the standard electron to unit cell ratio. In more stoichiometric composition, addition of Zr and Ti has a propensity to enhance the ordering behaviour as reflected by LRO parameter. Zr and Ti have lower electronegativities

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than the host atoms (Al and Ni) and have high electron density which impinges the ordering phenomenon of the alloys. The concept of electron density suits well with the theory of

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atomic scattering factor and HAADF images. Enthalpy of formation of the alloys with the consideration of preferential site occupancy of constituent elements further justifies the above mentioned contrasting results. Most importantly, the concept developed in this study can be applied to predict the effect of alloying elements on ordering behaviour of any stoichiometric

structures. It matches with that.

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Acknowledgement:

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compound. Thus, this will help to select proper alloying elements to obtain the desired

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Partial financial support from NPIU (through Centre of excellence in advanced materials under TEQIP-II) is gratefully acknowledged. We acknowledge the fruitful technical discussion with Dr. Arijit Sinha, Assistant Professor, IIEST Shibpur.

ACCEPTED MANUSCRIPT Appendix: Thermodynamic calculations A thermodynamic calculation was carried out to determine the enthalpy of formation (∆H) for solid solution and for intermetallic using extended Miedema model [54-56]. ∆H, according to Miedema’s original model [56], is expressed as

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∆H = ∆H= + ∆Hw + ∆Hx ..................................................................................................... (19)

Where ∆HC, ∆HE and ∆HS are the chemical, elastic and structural contributions, respectively. The structural contribution is insignificant in comparison to the first two terms [63]. Thus,

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∆H ≅ ∆H= + ∆Hw................................................................................................................. (20)

Now, ∆HC can be estimated as

4 9/ { ∆HxX { 9/ 4 ∆HxX

=~ =~

2F

:6 

lF (/€ )6‚ 2F

:‰ 

lF (/€ )6‚

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4 9/ { { 9/ 4 ∆H= = X4 X{ |f{4 ∆HxX + f4{ ∆HxX }.............................................................................. (21) ]GF

ƒ [−P(∆φ)& + Q(n‡x ˆ )& ]................................................................... (22) ]GF

ƒ [−P(∆φ)& + Q(n‡x ˆ )& ]................................................................... (23)

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Where Š is the effective chemical potential, nWS represents the electron density at the

boundary of the Wigner-Seitz (WS) cell, V expresses the molar volume and P and Q are empirical constants. f{4 ‹Œ f4{ can be calculated by the following equations.

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f{4 = C{ [1 + y(C4 C{ )]......................................................................................................... (24)

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f4{ = C4 [1 + y(C4 C{ )]......................................................................................................... (25)

Here y = 5 for solid solution and y = 8 for intermetallic (order material for the present investigation), respectively. The concerned coefficients (CA or CB), say CB can be expressed as C{ =

2F

‰ :‰ 

2F

2F

‰ :‰  >6 :6 

................................................................................................................ (26)

To estimate ∆H as per Eq. 20, ∆HE can be calculated as

∆Hw = X4 X{ |f{4 ∆E(4 9/ { + f4{ ∆E({ 9/ 4 }............................................................................... (27)

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Where, ∆’b“ `” • is the size mismatch contribution to the enthalpy of solution of A in B per

mole of A. It is estimated as, ∆E(4 9/ { =

&6 –6 (:‰ ]:6 ) ˆ6 :‰ >—–6 :6

....................................................................................................... (28)

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∆H of the ternary, quaternary and quinary alloys is calculated with the ∆H values of all possible binary combinations between the constituent elements according to a modified approach [54]. The vacancy is considered as an additional constituent and ∆H values of the

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binary mixtures with vacancy are taken as 0.

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[41] T.D. Shen, K.Y. Wang, M.X. Quan, J.T. Wang, Amorphous phase formation in the FeW System induced by mechanical alloying, Mater. Sci. Forum 88-90 (1992) 391-398. [42] S. Bera, I. Manna, Synthesis of CuCr and CuCrAg alloy with nano-ceramic dispersion

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Fe-Al at room temperature, Acta. Metall. Mater. 43 (1995) 391-396. [52] H. Xiao, I. Baker, Long range order and defect concentrations in NiAl and CoAl, Acta. Metall. Mater. 42 (1994) 1535-1540.

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heat of mixing and period of constituent elements and its application to characterization of the main alloying element, Mater. T. Jim 46 (2005) 2817–2829. [54] S. Bera, S. Mazumdar, M. Ramgopal, S. Bhattacharyya, I. Manna, Prediction of enthalpy of formation and Gibbs energy change in pseudo-binary (Ti–Zr)(Fe–Cr)2 and pseudo-ternary (Ti–Zr)(Fe–Cr)2-H system using extended Miedema model, J. Mater. Sci. 42 (2007) 3645–3650.

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Ohio, 1993.

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mechanically alloyed (NixFe1-x) Al alloys, Scripta Metall. Mater. 30 (1994) 1569-1574. [61] M.F. Ashby, P.J. Ferreira, D.L. Schodek, Nanomaterials, Nanotechnologies and Design, Butterworth-Heinemann, Burlington, USA, 2009.

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B2 intermetallics, Acta. Mater. 45 (1997) 3709-3719. [63] J.M. López, J.A. Alonso, L.J. Gallego, Determination of the glass-forming concentration range in binary alloys from a semi-empirical theory: Application to Zrbased alloys, Phys. Rev. B 36 (1987) 3716-3719.

ACCEPTED MANUSCRIPT Table 1: LRO parameters of all ternary, quaternary and quinary alloys at different milling duration. 40 hrs

70 hrs

100 hrs

Al55-(Ni30)-Cu15

0.584

0.640

0.695

Al70-(Ni15)-Cu15

0.527

0.576

0.669

Al75-(Ni10)-Cu15

0.454

0.528

Al80-(Ni5)-Cu15

-

-

Al55-(Ni30)-Cu10-Zr5

0.611

0.750

Al70-(Ni15)-Cu10-Zr5

0.475

0.553

Al75-(Ni10)-Cu10-Zr5

0.450

0.567

0.719

Al80-(Ni5)-Cu10-Zr5

-

-

-

Al55-(Ni30)-Cu10-Zr2.5-Ti2.5

0.634

0.713

0.824

Al70-(Ni15)-Cu10-Zr2.5-Ti2.5

-

0.561

0.654

Al75-(Ni10)-Cu10-Zr2.5-Ti2.5

-

-

0.585

Al80-(Ni5)-Cu10-Zr2.5-Ti2.5

-

-

-

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System

0.576

0.884

0.720

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0.454

Table 2: Range of Ni concentration (in which ordered NiAl phase forms successfully) in various alloys.

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Composition/Ingredients

Product

Ni composition

Reference

range (at. %) NiAl

25-65

[27]

Ni-Al alloy powder+ Al/Ni

NiAl

10-68

[44]

Elemental Al and Ni powder

Al and Ni

10-68

[44]

Elemental Al, Ni and Ti powder

NiAl

20-65

[45]

Elemental Al, Ni and Fe powder

NiAl

40

[46]

Elemental Al, Ni and Cr powder

NiAl

42

[47]

Elemental Al, Ni and Cu powder

NiAl

5-30

Present work

Elemental Al, Ni, Cu and Zr powder

NiAl

10-30

Present work

Elemental Al, Ni, Cu, Zr and Ti powder

NiAl

10-30

Present work

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Elemental Al and Ni powder

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Graphical abstract:

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List of Figure Captions

Fig.1: Schematic diagram of B2 NiAl structure with preferred cite occupancy of constituent

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elements (Al, Cu, Ni, Zr and Ti).

Fig.2: XRD patterns showing the evolution of nanocrystalline NiAl during MA in (a)

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Al55Ni30Cu15 (b) Al55Ni30Cu10Zr5 (c) Al55Ni30Cu10Zr2.5Ti2.5 systems. (d) XRD patterns of ternary [Al (85-x) Cu15Nix] [x=5, 10, 15 and 30] alloys. NiAl superlattice reflections are marked by the arrows.

Fig.3: Parametric phase diagrams show (a) NiAl (Cu) (b) NiAl (Cu, Zr) (c) NiAl (Cu, Zr, Ti) formation during MA of ternary, quaternary and quinary powder blends, respectively. Al, Ni, Cu, Zr and Ti signify elemental forms and Al (ss) indicates solid solution phase. NiAl (Cu), NiAl (Cu, Zr), NiAl (Cu, Zr, Ti) represents single NiAl phase with complete dissolution of the elements shown in bracket.

ACCEPTED MANUSCRIPT Fig.4: (a) Slow scan XRD patterns of 100 hrs ball milled ternary, quaternary and quinary alloys with composition of 30 at.% Ni. Respective LRO parameters are measured and indicated. (b) Selected Area Electron Diffraction (SAED) pattern of the quaternary alloy shows the superlattice reflection ring.

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Fig.5: (a) Lattice parameter variation of ternary alloys as a function of milling time. (b) Lattice parameter expansion of 100 hrs milled alloys as a function of composition (Ni %). (c) Average crystallite size of 100 hrs milled alloys as a function of Ni concentration. (d) TEM

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image shows grain size distribution of 100 hrs milled ternary alloy with 30 at.% Ni. [Error in measurements: While there is an error of 0.02 % in lattice parameter calculation ∼2%

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deviation occurs in crystallite size determination.]

Fig.6: TEM images of 100 hrs milled Al55Ni30Cu15alloy in (a) bright and (b) dark field mode. (c) elemental mapping of the aforesaid alloy shows distribution of Al, Ni and Cu. Scanning Transmission Electron Microscope (STEM) images of (d) Al55Ni30Cu15 (e)

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Al55Ni30Cu10Zr5 and (f) Al55Ni30Cu10Zr2.5Ti2.5 alloys.

Fig.7: (a) Selected Area Electron Diffraction (SAED) pattern of 100 hrs milled Al55Ni30Cu15 alloy shows all reflection rings of NiAl phase. (b) HRTEM image of the same

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alloy exhibits (110) lattice planes. (c) Inverse Fourier Filtered Image of (b) shows antiphase

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boundary (APB) (marked by arrows) and dislocations (with “

”symbols).

Fig.8: Variation of enthalpy of formation (∆H) of ideal solid solution, ordered phase and order phase with vacancy as a function of Ni concentration in (a) ternary, (b) quaternary and (c) quinary alloys, respectively.

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Figures

Fig.1: Schematic diagram of B2 NiAl structure with preferred cite occupancy of constituent

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elements (Al, Cu, Ni, Zr and Ti).

ACCEPTED MANUSCRIPT Fig.2: XRD patterns showing the evolution of nanocrystalline NiAl during MA in (a) Al55Ni30Cu15 (b) Al55Ni30Cu10Zr5 (c) Al55Ni30Cu10Zr2.5Ti2.5 systems. (d) XRD patterns of ternary [Al (85-x) Cu15Nix] [x=5, 10, 15 and 30] alloys. NiAl superlattice reflections are marked

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by the arrows.

Fig.3: Parametric phase diagrams show (a) NiAl (Cu) (b) NiAl (Cu, Zr) (c) NiAl (Cu, Zr, Ti)

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formation during MA of ternary, quaternary and quinary powder blends, respectively. Al, Ni, Cu, Zr and Ti signify elemental forms and Al (ss) indicates solid solution phase. NiAl (Cu), NiAl (Cu, Zr), NiAl (Cu, Zr, Ti) represents single NiAl phase with complete dissolution of the elements shown in bracket.

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Fig.4: (a) Slow scan XRD patterns of 100 hrs ball milled ternary, quaternary and quinary alloys with composition of 30 at.% Ni. Respective LRO parameters are measured and indicated. (b) Selected Area Electron Diffraction (SAED) pattern of the quaternary alloy

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shows the superlattice reflection ring.

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Fig.5: (a) Lattice parameter variation of ternary alloys as a function of milling time. (b) Lattice parameter expansion of 100 hrs milled alloys as a function of composition (Ni %). (c) Average crystallite size of 100 hrs milled alloys as a function of Ni concentration.(d) TEM

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image shows grain size distribution of 100 hrs milled ternary alloy with 30 at.% Ni. [Error in measurements: While there is an error of 0.02 % in lattice parameter calculation ∼2%

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deviation occurs in crystallite size determination.]

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Fig.6: TEM images of 100 hrs milled Al55Ni30Cu15alloy in (a) bright and (b) dark field mode. (c) elemental mapping of the aforesaid alloy shows distribution of Al, Ni and Cu. Scanning Transmission Electron Microscope (STEM) images of (d) Al55Ni30Cu15 (e)

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Al55Ni30Cu10Zr5 and (f) Al55Ni30Cu10Zr2.5Ti2.5 alloys.

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Fig.7: (a) Selected Area Electron Diffraction (SAED) pattern of 100 hrs milled Al55Ni30Cu15 alloy shows all reflection rings of NiAl phase. (b) HRTEM image of the same alloy exhibits (110) lattice planes. (c) Inverse Fourier Filtered Image of (b) shows antiphase

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boundary (APB) (marked by arrows) and dislocations (with “

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Fig.8: Variation of enthalpy of formation (∆H) of ideal solid solution, ordered phase and order phase with vacancy as a function of Ni concentration in (a) ternary, (b) quaternary and

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(c) quinary alloys, respectively.

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ACCEPTED MANUSCRIPT Highlights:
B2 ordered NiAl (Cu) alloys (without and with Zr/Ti addition) has been synthesized
Degree of ordering is governed by the preferred site occupancy of the solutes
Standard electron to unit cell ratio has further controls the ordering

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Developed philosophy will help to select proper alloying elements for an ordered alloy