Development of Materials Based on the NiAlCrMoCo System Reinforced with ZrO₂ Nanoparticles

Abstract

This paper describes thermodynamic modeling of the NiAl–CrMoCo system with the calculation of the equilibrium composition and thermodynamic parameters of the system. NiAl-Cr-Mo-Co alloy samples of equiatomic composition, including those with a small addition of zirconium oxide nanoparticles, were obtained by spark plasma sintering of mechanically alloyed powders. It was found that the material had a two-phase structure with wedge-shaped regions enriched in cobalt and molybdenum with a gradient distribution. In addition, in the regions enriched with (Cr, Mo) phase, a lamellar σ phase was found. Fractographic analysis showed a positive effect of the fine-grained wedge-shaped regions on the damping of crack propagation. The alloy with the addition of zirconium oxide nanoparticles had a bending strength and an elastic modulus of 611 MPa and 295 GPa at 25 °C, and 604 MPa and 260 GPa at 750 °C, respectively, when tested in vacuum.

1. Introduction

Nickel–aluminum materials are promising for the manufacture of parts for power plants and engines serving various purposes, operating at high temperatures and in an aggressive medium. Compared to nickel alloys, the NiAl intermetallic compound with a B2 structure has a high melting point (1911 K) and low density (5.7 g/cm³), high heat resistance of up to 1273 K, and good thermal conductivity (70–80 W/(m·K) at 300–1400 K) [1,2,3,4]. However, nickel–aluminum is non-ductile and brittle at room temperature, although it has high strength properties and creep resistance at elevated temperatures [5]. There are ways to improve the material characteristics using additives of transition, rare-earth and noble metals [6,7,8,9,10,11,12]. Eutectic materials in the NiAl–CrMoCo system have high thermodynamic stability [13,14]. Molybdenum-based intermetallics have high thermal stability and combine good physical and mechanical properties. In addition, nickel–molybdenum alloys are resistant to radiation and high-temperature corrosion in molten salts. In addition, molybdenum forms hardening precipitates with transition metals in alloys [15,16].

Metallic materials modified with small additions of nanoparticles of refractory compounds insoluble in the matrix are characterized by high mechanical characteristics [17].

The addition of nanoparticles to the powder matrix promotes various positive strengthening effects:

–

reducing the grain size, preventing the boundaries from growing and moving, increasing the yield strength and tensile strength, maintaining the distance between them and stabilizing the acquired structure at the stage of cold pressing. This is an obstacle to the movement of the dislocation front, since they retain incoherence at the grain boundary [18,19,20,21];

–

contributing to strengthening by the mechanism of double grain boundaries [20,22];

–

inhibiting creep along the grain boundaries, pressing into the matrix and turning during crack spreading [19,23];

–

limiting the formation, and promoting the annihilation, of vacancies, increasing the creep resistance along the grain boundaries [24];

–

preventing the diffusion of oxidant molecules by adsorbing them on its surface [18].

In this work alloys of the NiAl–CrMoCo system, modified by small additions of nanoparticles, were synthesized by spark plasma sintering of a mixture of NiAl, Cr, Mo, Co powders. However, in order to understand the processes of phase formation, we present an analysis of the literature on the phase features of alloys similar in composition. A number of studies were analyzed to understand the phase transformations in alloys carried out on similar compositions [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. For example, AlCoCrFeNi alloy powder was obtained by gas spraying in [26]. XRD analysis showed the presence of two phases: BBC and ordered BCC B2. Co was evenly distributed, Cr, Fe, Ni had small segregation, and Al had large segregation. Al–Ni-enriched areas were in the B2-phase, and Fe–Cr in BCC. The DSC curve had two exothermic peaks at 628 °C and 1376 °C, which corresponded to the formation of the FCC phase and melting, respectively [26]. The microstructure of the Al20Co20Cr20Fe20Ni20, Al10Co30Cr20Fe35Ni5 and Al15Co30Cr15Fe40Ni5 HEAs consisted of fine grains with sizes in the range of 50–500 nm, composed of AlNi–B2, BCC phase, FCC or BCC solid solutions and σ-sigma phase, respectively.

According to DTA data, the hunched area from 600 °C to 780 °C could be associated with the dissolution of the FCC-L12 phase, which was stable up to 500–620 °C, according to [27]. The peak at 1000 °C corresponded to the complete dissolution of the σ-phase. Chromium in the σ-phase was redistributed between the disordered solid solutions of the FCC–A1 and/or BCC–A2 phases. An alloy with a high aluminum content (Al15CoCrFeNi) did not have a dissolution peak of the σ-phase. The peak from 1200 °C to 1400 °C corresponded to the dissolution of the BCC and FCC solid solution, as well as early melting, when the solid solutions were in equilibrium with the liquid in [28]. Endothermic peaks from 1480 °C most likely corresponded to early phase melting.

The high-entropy alloy (HEA) CoCrFeMo_0.85Ni, studied by the authors during thermal analysis, had peaks at 1323 °C and 1331 °C, which corresponded to the solidus and liquidus temperatures, as well as at 800 °C and 1212 °C, which corresponded to the phase transitions FCC + μ + σ → FCC + σ → FCC [29].

In work [25] NiAl–13Cr–13Mo (wt.%) material was formed by spark plasma sintering. The main phases were NiAl–B2 and (Cr, Mo), and intermetallic compounds of the Al–Mo system. Cast alloys of the NiAl–Cr–Mo system in various compositions contained Cr–BCC, NiAl–B2, AlMo₃, MoNi, and oxide phases [30]. According to the work on modeling the Cr–Mo–Co diagram at 1373–1573 K in [31], the system contained the FCC, BCC, HCP, R, σ and μ phases.

HEA materials with similar composition with the material that was studied in this work also contained the following phases: Cr₂₃C₆–D84 [32,33], σ-CoCr [34], AlNi–B2 [29], Cr₇C₃ [35], σ–Co₂Mo₃ [36], Cr(Co)_e, Cr(Co,Mo) [37], and γ–Co (Ni) [38,39]. It should be noted that alloying elements that are added to NiAl-based materials are divided into three groups: Group VIII elements (Fe, Co, etc.); Cr, Mo, W, Re, V; elements of IIIB, IVB and VB subgroups. Iron and cobalt are highly soluble in the NiAl matrix and increase strength and ductility. Cr and Mo form pseudobinary eutectic phases, and increase fracture toughness and creep resistance [40,41]. A high content of Mo leads to embrittlement of the material, due to the formation of a hard phase of the sigma type. However, the presence of such a compound can increase the wear resistance of the material. Depending on the concentration, cobalt provides hardening, due to the formation of a continuous solid solution with NiAl and isostructural compounds. Alloys of the Ni–Al–Co system usually consist of several phases: β–NiAl, γ–Co(Ni) and γ’–Ni₃Al [21].

It is well known that σ, μ and other topologically close-packed (TCP) phases, separating in the form of plates (tapes), sharply reduce load resistance and plasticity at high temperatures. The atomic radii of the metals forming the σ phase differ slightly (no more than 8, less often 10–12%) from each other. However, the difference in the atomic radii of the elements that form the μ phase is quite large. They can exist as a single σ phase or decompose into a tetragonal σ phase, a rhombohedral μ phase, an orthorhombic ρ phase, and others, depending on the composition and atomic radius of the elements. These phases separate from the solid solution and are distinguished by an increased content of Cr, Mo, etc. compared to the alloy. These phases in multicomponent systems are electron compounds, because their structure is determined by the electron concentration e/a. This is the ratio of the number of valence electrons (e) to the number of atoms in a unit cell (a). In TCP phases, some atoms have electropositive properties (Cr, Mo), and others have electronegative (Ni, Co, Fe) properties. The tendency of the alloy to form TCP phases depends on the level of alloying and the concentration of elements. The microstructure of the σ-phase is close to the M₂₃C₆ structure in nickel alloys. If all carbon atoms are removed from the M₂₃C₆ lattice, then a very small shift in the mutual bracing of atoms would lead to the formation of the σ-phase. This is significant, because Cr₂₁Mo₂C₆ carbide contains many Cr and Mo atoms necessary for the formation of the σ phase. The same scheme is applicable to the formation of the μ-phase. Structurally, the μ phase is close to M₆C. In alloys containing M₆C and an excess of Cr and Mo, it is logical to expect a μ phase, instead of σ [42].

In [21], the formation of complex phases in the NiAl–15Mo–12Cr–6Co alloy of the Cr-based solid solution type Cr (Co, Ni, Al) residing between NiAl grains was established. In addition, Cr_0.8Mo_0.2 or Cr_0.5(Mo, Ni, Co)_0.5 solid solution phases were found in an alloy with Mo content up to 2.5% wt. According to [43], in the NiAl–14Co alloy, the main phases that appeared in the XRD pattern were γ’–Ni₃Al, β–NiAl, and NiAl–martensite. In [21], in the NiAl–Cr–Co–15Mo material, the main phases identified by XRD analysis were: NiAl, complex carbide (Ni, Cr, Co)₃Mo₃C, Ni₃Al, chromium-based solid solution, molybdenum-based solid solution.

In [44], an alloy. Co–Cr–Ni–Mo with an equiatomic ratio of the components, was studied. The main phases were σ, eutectic FCC, and eutectic σ. The study in [45] was devoted to a high-entropy alloy of the system (CoCrFeNi)₁₀₀ – _xMo_x (x = 1 − 3) and showed that the material consisted of FCC and σ phase.

In [46], new eutectic high-entropy alloys based on novel (Co_qCr_vFe_wMo_yNi_z)₁₀₀ – _xAl_x alloys contained FCC and B2 phases.

In [47], the chemical compositions of the CoCrFeNiMo_x (x = 0, 0.1, 0.11, 0.18, 0.2, 0.23 and 0.3, corresponding to 0, 2.44, 2.68, 4.31, 4.76, 5.44 and 6.96 at.%) alloy system were studied. It was found that with an increase in the amount of molybdenum, in addition to the FCC phase, σ and μ phases were detected.

In nickel superalloys, as a rule, TCP phases worsen ductility. However, it was reported in [23,47,48] that high-entropy alloys of the CoCrFeNiMo system had a good combination of strength and ductility after heat treatment, due to the formation of TCP σ and μ phases. In addition, an increase in the amount of Mo led to the formation of intermetallic compounds and deformation of the crystalline lattice of the alloy, which reduced the mobility of dislocations, leading to an increase in the strength of the alloy [49]. The authors of work [23] reported that the σ-phase was found to be a (Cr,Mo)-rich phase, corresponding to stoichiometric (Cr,Mo)(Co,Fe,Ni) composition, and the μ-phase was found to be a (Mo,Cr)-rich phase, corresponding to stoichiometric (Mo,Cr)₇(Co,Fe,Ni)₆. The solid–solution strengthening of the face-centered cubic matrix and the formation of the σ or σ + μ phases were the two main reasons for the strengthening of the alloy.

Table 1. Alloys based on transition metals, composition and properties.

Alloys Composition (HT—Heat Treated)	Material Type	Phase Structure	Preparation Method	Mechanical Properties at 25 °C	References
AlCrFe(0.6;1)CoNiMo0.5	HEA	BCC + σ	arc smelting	750 HV (Fe 0.6) 725 HV(Fe 1)	[50]
AlCrFeCo(1;1.5)NiMo0.5	HEA			780 HV(Co1) 730 HV(Co1.5)	[51]
AlCrFeCo2NiMo0.5	HEA	FCC + BCC + σ		600 HV	[51]
AlCr(1;1.5;2)FeCoNiMo0.5	HEA	BCC + σ		725 HV(Cr1) 810 HV(Cr1) 860 HV(Cr2)	[52,53]
AlCrCoFeMo0.5Ni(1.5;2)	HEA	FCC + BCC + σ		-	[53]
NiAl-28Cr-5.5Mo-0.5Hf at.%	eutectic alloy	Cr(Mo)—plates, NiAl, Ni2AlHf (Heusler)	induction melting	-	[54]
NiAl-20Cr-20Mo at.%	eutectic alloy	BCC-B2 NiAl, BCC-Cr, AlMo3, NiMo orth., oxide	arc melting	680 HV	[30]
NiAl-15Cr-25Mo at.%	eutectic alloy	BCC-B2 NiAl, BCC-Cr, NiMo orth.		650 HV
NiAl-28Cr-5.5Mo-0.5Zr at.%	eutectic alloy	NiAl, Cr(Mo)	SPS	YS 1321 MPa UCS 2360 MPa plasticity strain 0.313	[55]
NiAl-13Cr-13Mo, at.% (modified with 0.01 wt.% ZrO2)	eutectic alloy	NiAl, (CrMo), Al5Mo	MA + SPS	bending strength 210 MPa (at 20 °C) 475 MPa (at 700 °C).	[25]
Ni34.4Fe16.4Co16.4Cr16.4Al16.4 HT 750 °C (at.%)	HEA	cellular/“dendritic” eutectic, BCC-B2, FCC-A1	arc melting	flexural yield strength reached 1291 MPa; ultimate flexure strength 1968 MPa	[56]
NiAl–28Cr-5.5Mo-0.5Zr (at.%)	eutectic alloy	NiAl, Cr(Mo), Heusler	metallic powders were obtained by atomization technique, then hot pressing	UTS 405 MPa (at 1000 °C) 1300 MPa (25 °C)	[57]
Ni-29Al-28Cr-6Mo-4Ti HT at 1300 °C	eutectic alloy	NiAl, Cr(Mo), Ni2AlTi	vacuum arc melting	UCS 3430 MPa; YS 1549 MPa 340 MPa (at 1000 °C) YS 293 MPa 401HB εy 3.6% εu 27.71%	[58]
NiAl-5.5Co-11Cr-8 Mo at.%	eutectic alloy	NiAl, (Ni,Cr,Co)3Mo3C, Ni3Al, Cr(Mo)	centrifugal SHS casting	UCS 1728 MPa YS 1566 MPa degree of plastic deformation εpd 0.95%	[21]
CoCrFeNiMo0.3 HT 1173K, 5 h or 2 days	HEA	FCC + σ (5 h) FCC + σ+μ (2 days)	arc melting	UTS/YS/El% 709/305 MPa/49.3 (as cast) 1186/815 MPa/18.9 (1123 K, 1 h), 1042/646 MPa/32.5 (1173 K, 5 h)	[47]
CoCrFeMo0.85Ni	HEA powder alloy	FCC, μ, σ	gas atomization	-	[22]
CoCrFeNiMo0.85	HEA	FCC-A1, σ, μ-D85 (same as Co7Mo6)	arc melting	as the Mo content increases from 0 to 0.85, the yield stress and compressive strength rise from 136 MPa and 871 MPa to 929 MPa and 1441 MPa. fracture strain of 21 %,	[23]
AlCoCrFeNiMo0.5	HEA	Only simple BCC solid solution structure and α phase are identified.	arc melting	yield strength reached 2757 MPa when Mo content was 0.5; Compressive strength max (MPa) 3036, plastic strain 2.5%	[59]

shows the phase compositions and mechanical properties of alloys similar to the studied systems. As can be seen, an excess of nickel or cobalt promotes the formation of the FCC phase. An excess of chromium and molybdenum leads to the formation of TCP phases and BCC phases.

In areas enriched in aluminum, cobalt and nickel, three-phase alloys based on B2-CoAl intermetallic compound in the Co–Al–Ni system were formed [60]. B2 phase formed a continuous solid solution with NiAl of the same structure. Combination with B2 phase could result in a (Co,Ni) solid solution continuous from Co to Ni (phase diagram angles) and/or L12 phase, based on Ni₃Al. The L12 phase could be designated as (Ni,Co)₃Al. Ni served as a stabilizer of the FCC structure and prevented the cobalt FCC → HCP phase transition. Usually, ternary alloys with 0–35 at. % Ni had a B2 single-phase microstructure. As the amount of nickel increased towards the NiAl L12 angle, the phase began to form a second phase in the (Co,Ni) in the B2 matrix. In addition, it was found that aging an alloy with 21 at. % Ni at 1373 K for an hour led to the separation of lamellar phases of the solid solution (Co,Ni) in the B2 matrix [60].

The main objectives of this work were to obtain a material based on the NiAl–CrMoCo system with an equiatomic ratio of elementary components and to study the effect of a small amount of zirconium oxide nanoparticles on the structure and properties of the resulting material.

2. Materials and Methods

Alloys of the NiAl–CrMoCo system were synthesized by spark plasma sintering. The powders were mixed in steel containers with steel grinding media in a vibratory ball mill ‘MML’ (LLC “Vibrotekhnika”, Moscow, Russia). Powders of NiAl, as well as elemental Mo, Cr, and Co, in equiatomic concentrations, were mixed to obtain composite compositions.

The technology for nickel composites manufacturing included the preparation and mixing of initial powders (NiAl, PN70Yu30), JSC “Polema” (Tula, Russia)), Cr (98.5%, 150 µm, PH1S), JSC “Polema” (Tula, Russia)), Mo (99.5%, 5 µm, MPCh, LLC “Atomspecsplav”, St. Petersburg, Russia), Co (99.9%, 1 µm, OCHV (Moscow, Russia)), ZrO_2–8Y₂O₃ nanoparticles (Keldysh Research Center, Moscow, Russia) with specific surface area—25 m²/g. The appearance of powders was described in detail in [25]. Figure 1 shows the microstructure of the mixture of powders, obtained after vibromilling.

Mechanical alloying of the metal powders mixture was carried out in an Activator-2SL planetary mill (LLC «Zavod Himicheskogo Mashinostroeniya», Dorogino, Russia) in vacuum steel jars. Grinding balls (LLC «Zavod Himicheskogo Mashinostroeniya», Dorogino, Russia) made of stainless steel with a diameter of 5 mm were used. The ratio of powder to balls was equal to 1:10. Activation was carried out in isopropyl alcohol of chemical purity with the addition of a surface-active agent. Cubic zirconia nanoparticles were dispersed in isopropyl alcohol using a UPS 3600 Bandeline (BANDELIN electronic GmbH & Co. KG, Berlin, Germany) ultrasonic homogenizer for 3 min at a power level of 50% in pulsed mode. Nanoparticles were added to the matrix powder in isopropyl alcohol under low power ultrasound in an ultrasonic bath for 5 min, while stirring the solution with an overhead stirrer Eurostar digital (IKA^®-Werke GmbH & Co. KG, Staufen, Germany) at a speed of 400 rpm. Then, drying was carried out in a vacuum oven (Stegler, Moscow, Russia) at 250 °C for 10 h. After that, the powder was sintered by the spark plasma method on the FCT Systeme Gmbh machine (FCT Systeme Gmbh, Rauenstein, Germany) in the form of cylinders with a diameter of 30 mm and a height of 3 mm. The sintering was carried out at 1150 °C for 20 min in argon with the pressure 50 MPa. Samples with nanoparticle concentrations 0.01 wt.% and without nanoparticles were obtained.

The morphology and composition of the materials were studied by scanning electron microscope (SEM) Quanta 600 (FEI Company, Hillsboro, OR, USA) with TRIDENT XM4 energy-dispersive X-ray spectroscopy (EDX) equipment (). X-ray phase analysis (XRD) was performed in β-filtered cobalt radiation by a horizontal 2θ-θ X-ray diffractometer HZG-4 (LLC EDAX, Warrendale, USA). The phases were identified using the ICDD PDF-2 database (release 2003). The ultimate bending strength was determined by the three-point method on a Test Systems-VacEto universal mechanical testing machine (Keldysh Research Center, VacEto LLC, Moscow, Russia). The microhardness of the samples was determined by the Vickers method on a TM-40 hardness tester (Ultrakon, Kiev, Ukraine). Young’s modulus was measured by the ultrasonic method on the MUZA^® device (Vac-Eto, Moscow, Russia).

The NiAl–Mo–Cr–Co matrix powder sample was studied by differential scanning calorimetry (DSC), thermal gravimetric and differential thermal gravimetric analyses (DTG and TG) on a NETZSCH STA449F 1 Jupiter thermal analyzer (Netzsch-Gerätbau, Selb, Germany) in a corundum crucible in the temperature range from 25 °C to 1550 °C at a heating rate of 10°/min in an argon atmosphere.

Thermodynamic modeling of the system, namely the change in composition at temperature range 600–1200 °C, was carried out in the Terra^® software (v. 6.2 by Bauman Moscow State Technical University, Moscow, Russia). The method and algorithm for calculating the composition of phases in complex multi-element systems implemented in the Terra^® program performs a series of calculations with a variation in temperature and content of initial substances. Multiple calculations in a given temperature range for all possible ratios of the initial substances make it possible to find areas with the same sets of one-component condensed phases. Such calculations provide information that can limit the range of parameters for furthermore detailed studies or the assignment of technological conditions for the processes.

3. Results

3.1. Thermal Analysis

The results of DSC, TGA and TG the NiAl-Cr-Mo-Co matrix powder analyses are shown in Figure 2. In the temperature range from 240 °C to 390 °C, an insignificant weight loss of 0.34% occurred, while there were no peaks on DSC. The mass from 390 °C to the final heating temperature slightly increased by 0.2%. The peak in the region of 700–750 °C might correspond to the formation of the FCC phase. Starting from a temperature of 1464 °C, the DSC curve showed a several-stage overlapping endothermic process with observed peaks at temperatures of 1528 °C and 1543 °C, associated with the melting of various phases. There was nearly no overall weight change (slight loss of 0.14%).

3.2. Phase Composition

Figure 3 shows the result of X-ray phase analysis of a sample of the NiAl–CrMoCo matrix. It could be concluded that there were reflections of solid solutions of a complex composition with a different type of structure, similar to materials described in [16,29,36]. In addition, peaks of TCP phases (most likely, σ and μ), based on the Co–Mo system were visible and there was a halo of X-ray amorphous phases with all of the main elements.

3.3. Thermodynamic Modeling

The complexity of predicting the composition of multicomponent alloys containing an equiatomic number of elements lay in the development of many physicochemical processes, including competing ones, associated with selective dissolution, segregation of impurities, etc. In addition, the task was complicated by the fact that the samples were obtained under nonisothermal conditions of rapid heating and cooling, which were created during spark plasma sintering.

Thermodynamic modeling was carried out using the Terra^® software package for predicting phase evolution in new alloys [25]. In this work it was used to calculate the equilibrium composition of the NiAl–Cr–Mo–Co system. Data on the enthalpy of formation and heat capacity of a number of intermetallic compounds and various phases were taken from a number of verified sources [61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81].

The standard entropy, standard enthalpy, coefficients for the heat capacity polynomial were calculated according to known methods [82,83,84,85,86,87,88]. According to the recommendations of [83], one of the ways to estimate the value of the increment $H_{298}^0-H_0^0$ is to use the equation:

$$H_{298}^0-H_0^0=0.5\times c_{p,298}^0-298.15$$

(1)

The equation for the temperature dependence of the crystalline substances heat capacity in the range from 298 K to the melting temperature according to Mayer–Kelly was used in this work [89]:

C_p = a + 0.001 × b × T + 10⁵ × c × T⁻²

(2)

The heat capacity of intermetallic compounds of the A_xB_y type was calculated using the Neumann–Kopp method [90]:

C_p(A_xB_y) = xC_p(A) + yC_p(B)

(3)

Often the equation C_p = f(T) = a + bT for temperatures above 298 K is used to describe the temperature dependence of heat capacity. It quite rightly describes the change in the isobaric heat capacity not only of simple substances, but also of many compounds according to Perry and Green reference book [91].

The equation of standard heat capacity calculation is:

$$c_{p,298}^0={{\displaystyle \sum }}_i{m}_i{c}_{p,298}^0\left(i\right), \mathrm{J}/(\mathrm{mol}·\mathrm{K}),$$

(4)

where $c_{p,298}^0\left(i\right)$ is the standard heat capacity of the i-th simple substance, ${\displaystyle \sum }_i{m}_i$ is sum of moles of simple substances in solution,

The equation of standard entropy of intermetallic compound calculation is:

$$S_{298}^0\left(A_x{B}_y\right)=x{S}_{298}^0\left(A\right)+y{S}_{298}^0\left(B\right)$$

(5)

Terra^® software was previously successfully used to describe various multicomponent systems of alloys and composite materials, including those containing transition metals and non-metallic inclusions [25,92,93]. A feature of the methodology used in calculating the compositions of systems in the Terra software is that it is based on the principle of maximum entropy for an isolated equilibrium system, in contrast to the use of the concept of Gibbs energy, equilibrium constants and the principle of Guldberg and Waage of interacting masses [94].

The following assumptions are considered when using the methodology incorporated in the Terra^® software [95]:

–

closed and isolated thermodynamic systems are considered, where the boundaries are impenetrable for the exchange of matter, heat and energy with the environment;

–

systems are analyzed in a state of external and internal thermodynamic equilibrium (full or local);

–

it is considered that the system is heterogeneous, consisting of several homogeneous parts (phases) separated by visible boundaries;

–

the presence of the gas phase in the system is mandatory;

–

all gaseous individual substances (atoms, molecules, atomic and molecular ions, electron gas) are part of one gas phase;

–

the gas phase is described by the equation of state of an ideal gas;

–

surface effects at the phase boundary are not considered, the solubility of gases in condensed (liquid and solid) phases is absent; condensed matter may be absent;

–

condensed substances forming one-component immiscible phases are included in ideal condensed solutions;

–

individual substances that have the same chemical formula, but are included in different phases, are considered to be different components;

–

substances with the same chemical formula, which are in various polymorphic modifications, crystalline or liquid states, are considered as one component, in which the change in properties occurs abruptly at transformation temperatures;

–

the volume of condensed components is negligible.

The equilibrium of such systems, in accordance with the second law of thermodynamics, is characterized by a maximum of entropy relative to the thermodynamic degrees of freedom, which include the concentrations of the components of the equilibrium mixture (n, mol/kg), temperature T and pressure P.

$$S={\displaystyle \sum }_{i=1}^K\left[S_i^0\left(T\right)-R_0\mathit{ln}\frac{R_{0}T}{V}{n}_i\right]\times n_i+{\displaystyle \sum }_{c=1}^R{S}_c^0\left(T\right)n_c+{\displaystyle \sum }_N{\displaystyle \sum }_{m=1}^{N_m}\left[S_m^0\left(T\right)-R_0\mathit{ln}\left(\raisebox{1ex}{$n_m$}\!\left/ \!\raisebox{-1ex}{$n_{N_m}$}\right.\right)\right]\times n_m\Rightarrow S_{max}$$

(6)

where n_i, n_c, n_m, S_i⁰, S_c⁰, S_m⁰ are the number of moles and the standard entropy at temperature T and pressure 0.1 MPa in gas (i), condensed (c) phases and in solution (m), respectively; i, c, m—the number of gaseous, condensed components and solutions in the thermodynamic system, respectively. The value $n_{N_m}$ is the amount of substance in the m-th condensed solution; V—volume; R_i—the gas constant.

The specific volume V, as well as the internal energy U, remain independent variables, since the equilibrium conditions of the system, relative to the environment, can be expressed using the equalities:

dV = 0 and dU = 0 or V = const and U = const

(7)

Calculations of the equilibrium composition of the material in the temperature range of 873–1473 K at a pressure of 0.01 MPa showed that, in addition to solid solutions with the FCC and BCC structure from the main elements, intermetallic phases and TCP phases could form in the system. This approach to the calculation was adopted to consider the processes occurring under nonequilibrium conditions during SPS sintering of mechanically activated components. The impurity concentrations of C and O were considered in the calculations. Thermodynamic calculations determine the stability of certain phases in alloys with wide and narrow regions of homogeneity, including those accompanied by the formation of intermetallic compounds.

Since many intermetallic alloys and phases of transition metal solutions for which thermodynamic parameters are calculated were first considered using the Terra^® program, below we present the values of the polynomial coefficients for the reduced Gibbs energy of these substances, calculated according to the algorithms given in [95], in

Table 2. Thermodynamic properties of some substances used in the calculation.

Compound	Cp (T)			T, K	${\mathit{C}}_{\mathit{p},298}^0,$ J/(kg·K)	$\mathit{∆}{\mathit{H}}_{\mathit{f}, 298}^0$, J/mol	${\mathit{S}}_{298}^0$, J/(mol·K)	${\mathit{H}}_{298}^0-{\mathit{H}}_0^0,$ J/mol	${\mathit{G}}_{298}^{*}$, J/(mol·K)
	a	b	c
TCP-Co2Mo3	114.265	0.051	−6.314	1273–1893	113.94	−7000	146.2	15,586.5	325.078
TCP-Co7Mo6	292.796	0.145	−12.627	673–1783	290.106	−7000	382.5	41,135.9	385.316
Co9Mo2	240.41	0.141	−4.209	1285–1473	240.336	−3000	327.8	36,509.6	701.215
Co3Mo	13.3	32.4	−0.3	673–1498	88.7	−5000	118.8	13,220.5	-

and

Table 3. Coefficients of the polynomial of the reduced Gibbs energy (J/(mol K)).

Compound	Range of T, K	Φ = φ1 + φ2lnx + φ3x−2 + φ4x−1 + φ5x + φ6x2 + φ7x3, (x = T × 10−4, K)
		φ1	φ2	φ3	φ4	φ5	φ6	φ7
TCP-Co2Mo3	1273–1893	267.199	114.2652	−0.00316	13.0411	0.257	-	-
TCP-Co7Mo6	673–1783	878.350	292.7961	−0.006315	15.7826	0.727	-	-
Co9Mo2	1285–1473	580.361	240.41021	−0.00211	27.2862	0.708	-	-
Co3Mo	673–1498	112.05	13.3181	−0.030902	1.26433	162.003	5.02	666.8

.

Figure 4a shows the results of thermodynamic modeling for the interaction of components of the following composition, mole: (NiAl − 0.6) + (Cr − 0.3) + (Mo − 0.3) + (Co − 0.3) + (C − 0.01) + (O − 0.01) at 4 mol/kg constant concentration of the NiAl. The constancy was due to the fact that the main (“first”) stable phase in the material was precisely NiAl or a solution based on it with a small quantity of dissolved substances. The “second” phase was formed by alloying elements, the transformations of which, and the interaction with the “first” phase, affected its final composition. According to the results of thermodynamic modeling at a temperature near the sintering point (1170 °C), the main phases were BCC–CoCr(ss) and FCC–NiCo(ss) solid solutions, in addition to the “frozen” NiAl, as well as the close-packed TCP–CrMo. The molybdenum carbide Mo₂C content increased, and the amount of carbide (Cr₂₃C₆) decreased with temperature increasing. Aluminum and chromium oxides were also present. In work [22] pseudobinary diagram (Co, Cr, Fe, Ni)–Mox was simulated at 600–1500 °C. According to this work, with an increase in the amount of molybdenum (x) from 0.5 to 1 in the system, in the range from 600 °C to 1070 °C, there were three phases, FCC + μ + σ. In materials, aluminum and chromium oxides appeared, due to the presence of oxide layers on metal powder surfaces. Chromium and molybdenum are good carbide formers, so when graphite molds are used in spark plasma sintering, diffusing carbon atoms actively interact with these metals.

Figure 4b, c also shows the change in the total enthalpy and entropy of the calculated system. Both ascending curves had two inflections each, which corresponded to phase transitions. In particular, the first inflection was in the range 750–775 K, and the second inflection was in the range of 1125–1150 K. The first inflection corresponded to the appearance of TCP phases. The second one corresponded to an increase in one of the earlier appearing TCP phase concentration and amount of solid solution and molybdenum carbide.

3.4. Microstructure and Composition

Figure 5 shows the microstructure of alloy without nanoparticle additions before and after polishing. It contained two types of areas: light gray areas and duck particles of irregular form and with size up to 10 μm.

X-ray microanalysis mapping (Figure 6) showed that light gray areas contained mainly Cr, Mo, Co and duck particles—mainly Ni and Al. It was also noticeable that aluminum and oxygen were distributed along the grain perimeter of the dark gray particles, which was associated with the presence of an oxide film. It could be assumed that the light gray areas corresponded to BCC solid solution or mixed FCC–BCC structure, where large particles of B2 intermetallic compound, based on the NiAl phase, were located.

In addition, there were differently oriented nanoscale flat particles located inside the “matrix”. The light gray phase (Figure 5) was a solid solution of Cr–Mo–Co system, as well as a lamellar σ phase, which could be seen at a greater magnification (Figure 7). The spectrum referred to the high content acicular phase area. There was a predominance of molybdenum and chromium in this area.

Figure 8 shows the microstructure of the alloy with 0.01% addition of zirconium oxide nanoparticles. According to the elements distribution map, elongated wedge-shaped regions were enriched, on the one hand, with cobalt, and, on the other hand, with molybdenum, and also contained other elements of the matrix interspersed with nickel–aluminum particles.

This segregation was due to the features of mixing powders of various fractions, especially in the presence of nanoparticles. If one of the components is very small and the other is relatively large, it has been suggested that small particles can cover the surface of large particles. In this way, segregation does not occur, and it is possible to obtain a mixture that is more homogeneous than a random mixture [96,97], as shown in Figure 9. In this case, we had homogeneous zones in the sample. On the other hand, surface-active nanosized particles could combine with matrix particles with a higher surface energy compared to other larger matrix particles. The adhesion force of nanosized particles was 16 orders of magnitude less than for particles with a diameter of 10 µm. However, the relative adhesion force, considering the volume, for nanoparticles was 13 orders of magnitude greater than for non-nanosized ones. Thus, due to the size effect, the relative adhesion force of nanoparticles was significant and determined by an additional excess of surface energy [98]. Therefore, there were areas with gradient-sized particles in the sample. It was shown in [99,100] that, for systems of aluminum alloys, hardening with insoluble nanoparticles leads to the formation of elongated ellipsoidal regions, due to the segregation of nanoparticles. This effect prevents the growth of matrix grains. In this work, a similar effect was found. Nanoparticle additives formed such segregations due to their high surface energy and tendency to stick together with small particles of the matrix components, namely nickel–aluminum, chromium, molybdenum and cobalt (Figure 10). The height of such “wedges” was from tens to several hundred micrometers, and the width was several tens of micrometers.

Figure 11 shows the microstructure and distribution of elements in the wedge-shaped region in a sample with addition of nanoparticles. The region was enriched in cobalt and molybdenum, which was possibly associated with finer powders of these elements used in the matrix powder compared to chromium, for example. Moreover, the “wedges” were unevenly enriched in cobalt and molybdenum. The inter-wedge region seemed to be limited by sides with a high content of cobalt and molybdenum. Then there was a “partition” of areas with a large amount of molybdenum, and in the middle, there was a gradient of NiAl with molybdenum and chromium. The presence of Ni and Al in the same areas as Mo and Co showed the possibility of an intense interaction of Ni with Co and Mo, including the formation of TCP phases, and strong connections of Al with Ni.

Figure 12 shows an area with an increased content of the Co–Mo phase. Oxidized areas with high chromium content were clearly visible. There was an obvious area that contained an increased content of cobalt, in which nickel and chromium were dissolved, and another area, which was adjacent to the first, containing phases of the Co–Mo system.

Thus, the structure of the NiAl–CrMoCo alloy obtained in this work was a matrix containing nanoscale lamellar phases crossing each other. An acicular phase corresponded to the enriched phase (Cr, Mo) of the σ type. According to elements distribution maps, such elements as Cr, Mo, Ni segregated more intensively than Co and Al. At the same time, it was possible to distinguish areas enriched in the phase (Cr,Mo) with the plates of the σ type phase (Cr,Mo) inside. They were all located in the matrix, most likely, with the FCC and BCC–B2 structure. Iron was present in the alloy in an impurity amount due to milling during mechanical alloying in steel jars with steel grinding balls.

3.5. Fractographic Analysis

Bending strength studies were carried out using a three-point bending flexural test. Figure 13 shows the fracture structures of samples with nanoparticle additions. The destruction was predominantly brittle or ductile–brittle. Regions of a solid solution with a σ phase were visible, as well as regions of intermetallic grains, most likely the B2 BCC phase. In addition, a number of micrographs show areas with a fine-grained σ phase. Figure 13a shows how the crack was deflected and damped when passing through fine-grained and wedge-shaped regions. This effect increased the cracking resistance. The main difference in the fracture structure of the samples was that fine grain regions in a pure matrix were much rarer than in a sample modified with nanoparticles.

In Figure 13b, the areas of large pits are shown. Most likely they corresponded to NiAl phase grain before destruction. In the fracture, the cellular surface of the ‘CrMoCo’ phase was visible as was local ductile fracture initiated by the missing grain. The pores inside the large pits were probably where the NiAl grains presented.

The samples were characterized by brittle fractures, based on the areas of chips of the ‘CrMoCo’ phase. The material was destroyed mainly by a cleavage accompanied by microplastic deformation at the points of connection of the ‘CrMoCo’ phase with grains of the NiAl phase.

3.6. Mechanical Properties

Figure 14 shows the results of measuring the Vickers microhardness of various matrix material sample regions. The load was 25 g with an exposure of 20 s. The hardness of the matrix material phases regions enriched with chromium, NiAl and CrCoMo was measured. The region enriched with chromium had the highest hardness.

The results of measuring the bending strength of the alloy samples are shown in Figure 15 and Figure 16a. A sample with a crystalline matrix of NiAlCrMoCo with the addition of 0.01 wt. % nanoparticles of zirconium oxide had the highest strength of 611 MPa at room temperature and 604 MPa at 750 °C. The NiAlCrMoCo crystalline matrix sample had a strength of 504 and 474 MPa, at room temperature and 750 °C, respectively. Strength of single-crystal NiAl was about 305 MPa at room temperature and 429 MPa for heat-treated samples [1]. In [25] material NiAl-13at. % Cr-13at. % Mo-0.1 wt.% ZrO₂ prepared in a similar way had the bending strength of 201 MPa at room temperature, and 473 MPa at 700 °C.

The change in the elastic modulus of samples without and with nanoparticles, depending on temperature, is shown in the Figure 16b. The modulus of the material without nanoparticles at room temperature was in the range of 283–289 GPa, and 251–255 GPa at 750 °C. Young’s modulus of the material modified by zirconium oxide nanoparticles were in the range of 290–295 GPa at room temperature and 257–260 GPa at 750 °C. For comparison, the Young’s modulus of NiAl were in the range of 180–218 GPa at 25 °C [101].

The reason for increasing the strength of reinforced with zirconium oxide nanoparticle alloy was better adhesion between particles, due to the high surface energy of nanoadditives, preventing the movement of dislocations by the Orowan mechanism, and the formation of a composite structure with elliptical zones “enriched” with nanoparticles.

The modulus of elasticity was slightly higher for the material modified with nanoparticles, due to the high modulus of zirconium oxide nanoparticles and, according to the Obraztsov–Lurie–Belov theory, the formation of gradient zones of change in its value from particle to matrix [102].

4. Conclusions

Thermodynamic modeling of the equilibrium phase composition of the NiAl–Cr,Mo,Co system in an equiatomic ratio with a small amount of C and O impurities vs. temperature was found using Terra^® software. At sintering temperature, the main phases were NiAl, BCC–CoCr(ss) and FCC–NiCo(ss) solid solutions, as well as the close-packed TCP–CrMo phase. The amount of the Mo₂C phase increased and the content of Cr₂₃C₆ decreased with temperature increasing. The presence of aluminum and chromium oxides was also found.

The microstructure of spark plasma method sintered samples consisted of a phase enriched with NiAl and CrMo. The material modified with a small amount of zirconium oxide nanoparticles had wedge-shaped elongated fine-grained regions, enriched in cobalt and molybdenum in the main matrix structure.

The highest strengths at the level of 611 MPa at room temperature and 604 MPa at 750 °C were from a sample with a crystalline matrix of NiAlCrMoCo with the addition of 0.01 nanoparticles of zirconium oxide. A sample of the NiAlCrMoCo system without nanoparticle additions had strengths of 504 and 474 MPa, respectively, at room temperature and 750 °C. The Young’s modulus of the material without nanoparticles at room temperature was 286 GPa, and 253 GPa at 750 °C, and for the material with zirconium oxide nanoparticles, 292.5 GPa at room temperature and 258.5 GPa at 750 °C.