Formation mechanism of stable NbC carbide phase in Nb-1Zr-0.1C (wt.%) alloy

Accepted Manuscript Formation mechanism of stable NbC carbide phase in Nb-1Zr-0.1C (wt.%) alloy B. Vishwanadh, A. Arya, R. Tewari, G.K. Dey PII:

S1359-6454(17)30950-3

DOI:

10.1016/j.actamat.2017.11.007

Reference:

AM 14178

To appear in:

Acta Materialia

Received Date: 11 August 2017 Revised Date:

30 October 2017

Accepted Date: 3 November 2017

Please cite this article as: B. Vishwanadh, A. Arya, R. Tewari, G.K. Dey, Formation mechanism of stable NbC carbide phase in Nb-1Zr-0.1C (wt.%) alloy, Acta Materialia (2017), doi: 10.1016/ j.actamat.2017.11.007. 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

NbC carbides with random orientation relationships in recrystallized sample

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500 µm

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Nb2C carbides In deformed sample

Nb2C carbides In as-solidified sample

100 nm

Nb α-Nb2C

NbC carbides with specific orientation relationship In heat treated as-solidified sample

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Nb α-Nb2C

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100 µm

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as-solidified sample heat treated without any prior deformation

ACCEPTED MANUSCRIPT Formation mechanism of stable NbC carbide phase in Nb-1Zr-0.1C (wt.%) alloy B. Vishwanadh, A. Arya, R. Tewari and G.K. Dey Materials Science Division, Bhabha Atomic Research Centre, Mumbai, India-400085

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ABSTRACT

In the present work, several long standing issues related to the formation of various carbides and transformation of Nb2C→NbC carbide in Nb-1Zr-0.1C alloy have been addressed. For this purpose, samples were processed by two routes. In the first route, as-solidified samples

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were extruded and recrystallized and in the second route, as-solidified samples were directly heat treated without imparting deformation. By combining detailed diffraction analyses and

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ab-initio calculations, identity of the Nb2C carbides in the as-solidified and extruded samples, among the various reported Nb2C crystal structures has been established as an orthorhombic crystal structure (α-Nb2C) having Pnma space group. Chemical analyses showed that the Nb2C carbides in extruded samples had higher Zr content as compared to the carbides formed in as-solidified samples. Experimental and theoretical results revealed that Zr destabilizes Nb2C phase which was shown as a possible reason for the precipitation of a more stable

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(Nb,Zr)C phase in recrystallized as well as in directly heat treated as-solidified samples. Detailed precession electron diffraction analysis of (Nb,Zr)C particles showed that if the nucleation of precipitates occurs prior to recrystallization and the growth of the precipitates

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occurs simultaneously with recrystallization, precipitates do not exhibit specific orientation relationship (OR) with the matrix phase. In contrast, if nucleation and growth of precipitates take place after recrystallization or in samples which do not undergo recrystallization, a

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specific (Baker-Nutting) OR is followed. Finally, by establishing atomic interrelationship by high resolution electron microscopy, the formation mechanisms of (Nb,Zr)C carbides in different morphologies in Nb alloy have been explained. 1. INTRODUCTION

Niobium carbides, due to their attractive properties such as high hardness, high elastic modulus, high melting point, chemical inertness, etc, have diverse engineering applications [1–4]. These carbides play a major role in increasing the strength of various alloy systems ranging from HSLA, Ni based alloys to Nb alloys, to name a few [5–8]. In addition, niobium carbides are widely used to strengthen composite materials, to refine grain size and to

ACCEPTED MANUSCRIPT improve wear resistance of materials [2]. In spite of having such wide applications, there are many aspects related to these carbides that are yet to be fully understood and requires further research work. In Nb-C system, under equilibrium conditions, mainly two types of carbides exist: Nb2C and NbC. The Nb2C carbide exists in three polymorphic forms, γ-Nb2C phase with disordered

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hexagonal structure (forms above 2500 °C), β-Nb2C with an ordered trigonal structure (exists in the temperature range between 1200 °C - 2500 oC), and α−Nb2C with orthorhombic structure (at temperatures below 1200 oC) [9–14]. Crystal structures and other information of these carbides are given in Table 1 [9–15]. Although plenty of literature on these carbides is

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available, some of the issues related to their formation are not well understood [9,10,16]. Some important and unresolved issues which are related to the formation of various niobium

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carbides could be summarised as following:

(a) Recently it has been shown that all the three forms of Nb2C phases (γ, β and α) are

structurally related [17]. On the basis of the crystallographic structural relationship, it was proposed that the difference among the phases lies in the ways carbon atoms decorate lattice sites in each phase [17]. Because of the close structural relationships,

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it is difficult to distinguish these three phases using the diffraction patterns. Therefore, establishing correct identity of the Nb2C carbide phase is a challenging task.

(b) There are at least four different crystallographic structures that have been reported for

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α-Nb2C [9–14] (Table 1) which suggest that the true structure of the α-Nb2C phase is not well identified. Most of the studies have reported that α-Nb2C has orthorhombic

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crystal structure. However, they differed in identifying the exact space group to which the α-Nb2C belongs within the orthorhombic crystal system (Table 1).

(c) Though in the binary Nb-C system, transformation of β-Nb2C to α-Nb2C have been

reported to occur at 1200 oC by Rudy et al.[11], the formation of α-Nb2C phase itself

is not well established [9]. It has been argued that the formation of the orthorhombic α-Nb2C phase is due to the presence of impurities such as O and N in the alloy [9,10,16]. The presence of O and N as low as 0.2 at.% and 0.5 at.%, respectively, can lead to the formation of α-Nb2C [9,10,16]. The α-Nb2C phase is, in fact, called as impurity stabilized phase. Therefore, in addition to the ambiguity in the lattice parameters, existence of the α-Nb2C phase is not yet clearly established.

ACCEPTED MANUSCRIPT (d) In Nb-Zr-C alloys, increasing aging time results in increase in the volume fraction of

NbC at the expense of Nb2C [18–20]. This is not consistent with the Nb-C phase diagram which shows Nb2C as a stable phase [21]. One pre-requisite for such a transformation would then be the dissolution of Nb2C phase into the matrix, the mechanism of which is not clear from the available literature.

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(e) The formation of NbC type of carbides in dilute alloys is still an unsolved problem. If it is a stable phase then the question arises why formation of Nb2C carbide occurs in the as-solidified condition and being a stable phase in dilute alloys, later on, why would it dissolves back to form NbC phase ?

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Titran and co-workers [18–20] have observed that in Nb-Zr-C alloy even after prolonged heat treatment (> 30,000 hrs at 1077 oC) there is no substantial change in the average particle size

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of (Nb,Zr)C carbide. Farkas et al. [22] have shown that thermodynamically the (Nb,Zr)C phase has lower free energy than Nb2C. This study has also indicated that addition of Zr in Nb-C alloy facilitates the formation of a stable NbC carbide phase. Similar transformation of Nb2C to NbC has been reported in Nb-Ti-C and Nb-Hf-C alloys [23–25]. Maksimovich et al. [26] and Khandarov et al. [27] recrystallized Nb alloy at 1400 oC and have shown formation of spherical morphology of NbC carbides exhibiting Kurdjumov-Sachs (K-S) orientation 111

// 101

, 011

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relationship (OR)

// 111

with Nb matrix phase. Titran

et al. [19] have also shown the formation of similar spherical morphology of NbC carbides in double annealed extruded Nb alloy samples. On the other hand, Toyohiko et al. [28] have reported formation of plate like morphology of NbC carbides in the creep tested Nb alloy.

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These carbides showed Baker-Nutting (B-N) OR with Nb matrix. Many such studies indicate that Nb-1Zr-0.1C alloy could be an ideal candidate for exploring answers to several

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unexplored questions. Firstly, niobium carbides play an important role in improving creep strength of the alloy without compromising its high resistance to liquid alkali metals corrosion, making this alloy suitable as high temperature structural material in aeronautical, space power and nuclear reactors [8,18,20,23,24,29–32]. Secondly, in the Nb-1%Zr-01%C alloy the presence of both the carbide phases, Nb2C and NbC, has been reported [9,19,20]. In the as-solidified condition, the formation of Nb2C phase with different crystal structures has been reported [10,11,16,17]. It has also been reported for the present alloy (Nb-1%Zr-0.1%C) that during heat treatment Nb2C phase dissolves and carbon re-precipitates as face centred cubic (Nb,Zr)C type of carbide [8,20,33]. Therefore, the alloy provides an excellent opportunity to explore the sequence of phase transformations within the Nb2C phase as well

ACCEPTED MANUSCRIPT as to study the formation mechanism of the NbC from Nb2C. In the present study, using this alloy, answers of the following issues are explored: 1. It is generally stated that the stability of γ-Nb2C phase extended up to room

temperature [16] and the formation of the α-Nb2C occurs only in the presence of interstitial impurities [9,10]. Therefore, in the present study formation of α-Nb2C

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carbide has been explored.

2. It has been shown that the formation of the NbC based carbide occurs after

dissolution of the stable Nb2C phase and that too in those alloys which have chemical composition beyond the phase boundaries of NbC phase. Therefore, the

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mechanism of formation of (Nb,Zr)C carbide in the Nb-Zr-C alloys has been studied in this work.

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3. NbC carbide has been reported to form in various morphologies [26–28]. It

appears that the morphology of the phase was influenced by the thermomechanical treatment. However, to the best of our knowledge, there exists no study which explained the morphological evolution of the carbide phase in the niobium alloys with changing thermo-mechanical processing conditions. The

morphologies.

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present study also looks into the rationale to the presence of different

2. EXPERIMENTAL WORK

The fabrication flow sheet for producing Nb alloy has been reported in our paper [31].

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Basically, there are three stages: 1) preparation of Nb-1Zr-0.1C (wt.%) alloy by electron beam melting using high purity Nb, Zr, C elements, 2) breaking the as-solidified structure by extrusion at 800 oC and (3) recrystallization of the deformed sample by heat treatment at

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1300 oC for 3 hrs. In order to check the homogeneity of the alloy, chemical analysis of samples collected from at least six different places of the ingot along its length was carried out. Composition of the alloy was verified by combustion extraction method for carbon and inductively coupled plasma method for zirconium and niobium. Typical chemical composition of the alloy is shown in Table 2. A thorough microstructural characterization of these three samples (as-solidified, extruded and recrystallized) was carried out in the present study. In order to compare the carbide phases present in the recrystallized samples with those formed in samples which were not subjected to any prior deformation, the as-solidified samples were directly heat treated at

ACCEPTED MANUSCRIPT 1300 oC for 3 hrs and 10 hrs. These samples are referred to as directly heat treated samples in the rest of the paper. Heat treatment of all the samples was carried out in a vacuum furnace at a vacuum of the order of 10-7 Pa and samples were wrapped in tantalum foil prior to heat treatment to further inhibit any possible oxidation. Characterization of all the samples was performed using X-ray diffraction (XRD),

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scanning electron microscopy (SEM), electron back scattered diffraction (EBSD), transmission electron microscopy (TEM) and precession electron diffraction (PED) techniques. Carbides particles were extracted from the alloy using 10% HCl + 90% methanol solution at 3V by employing centrifuge technique. These powder samples were also

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characterized using the above mentioned techniques. For all the types of characterization, samples were taken from the center region of the bulk samples to avoid surface effects. XRD

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was carried out using Rigaku operated at 40 kV, 30 mA with Cu-Kα source. Microstructural characterization by SEM was carried using Zeiss Auriga FIB system. For EBSD, final polishing of the samples was carried out using colloidal silica suspension for 1-2 hrs. Acquisition of EBSD patterns in SEM was done using Oxford EBSD detector. Analysis of the EBSD patterns was carried out using HKL software. Electron transparent samples for TEM were prepared using Technoorg Linda IV4 ion mill instrument operated at 6 kV/2 µA

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current. Final ion milling was performed at low KV (0.25 V) using Technoorg Linda gentle mill. TEM was carried out using aberration corrected TITAN 80-300 and JEOL 3010 transmission electron microscopes. Composition analysis of the carbides and matrix was carried out using Energy Dispersive Spectroscopy (EDS) in TITAN TEM in STEM (scanning

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transmission electron microscopy) mode at spot size 7 which corresponds to ~1 nm probe size. As quantitative analysis of carbon by EDS always associated with the large errors, the

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relative concentrations of Nb and Zr were estimated without considering carbon from the EDS profiles. Orientation mapping of carbides was also performed in TEM using NanoMegas precession electron diffraction (PED) attachment in JEOL 3010 instrument. Precession electron diffraction (PED) technique in TEM is a recently developed material characterization technique [34]. Using PED, orientation mapping can be carried out under TEM in a way similar to as EBSD carried out in SEM. In PED, based on the diffraction patterns, orientation of particles was determined. PED produces close to kinematical condition for diffraction. The major advantage of PED over EBSD is that it is possible to perform orientation mapping on particles which are even smaller than 100 nm using PED [35,36].

ACCEPTED MANUSCRIPT 2.1. Computational Procedure To examine the ground state stability hierarchy of Nb carbide phases including those doped with Zr, first principle calculations were performed using the plane wave-based Vienna ab-initio simulation package (VASP) [37,38] which is based on the density functional theory (DFT). In all our calculations, the exchange and correlation potential as parameterized

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by Perdew, Burke and Ernzerhof (PBE) under the generalized gradient approximation (GGA) was employed [39]. The projector augmented wave (PAW) potentials [40] were used for the ion–electron interactions.

The states 4p5s4d (for Nb), 2s2p (for C) and 4s4p5s4d (for Zr) were used as valence

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states for the three atomic species in our calculations. For each structure, optimization was carried out with respect to Ecutoff and k-point meshes to ensure convergence of total energy to

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within a precision of 0.2 meV/atom. First-order Methfessel and Paxton’s smearing method [40] with a temperature broadening parameter of 0.1 eV was used for structural relaxations and optimization of atomic positions. This temperature broadening parameter resulted in a very small entropy term (<0.05 meV/atom) in all the cases. The total energy of each structure was optimized with respect to volume (or lattice parameter), b/a, c/a ratio and atomic positions as permitted by the space group symmetry of the respective crystal structure. The

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structural relaxations (b/a, c/a ratio and atomic positions) were performed for each structure using the Davidson algorithm until the residual forces and stress in the equilibrium geometry were of the order of 0.005 eV/Å and 0.01 GPa, respectively. The final calculation of total

3. RESULTS

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electronic energy was performed using the tetrahedron method with Blöchl corrections [41].

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3.1. Characterization of As-Solidified Samples Fig. 1 shows SEM micrographs of typical as-solidified microstructure of the Nb-1Zr0.1C alloy. Presence of large grain size (1-1.5 mm) (Fig. 1a(i)) and needle morphology of precipitates at higher magnification (Fig. 1a(ii)) could be observed in the microstructures. When EBSD patterns were obtained from this microstructure using crystallographic data of γNb2C and Nb as input parameters (Fig. 1b(i)), nearly all the phases present in the microstructure could be successfully indexed in terms of these phases. The identification of the carbide phase as γ-Nb2C does not commensurate with the phase diagram of Nb-C. As per the binary Nb-C phase diagram and literature during cooling γ-Nb2C transforms to β-Nb2C at 2500 oC, which, in turn, transforms to α-Nb2C at 1200 oC. Therefore, at room temperature

ACCEPTED MANUSCRIPT some fraction of the α-Nb2C carbide phase is expected. As can be seen from Table 1, for the α-Nb2C phase, four different lattice parameters and space groups have been reported. These structures are marked as α-Nb2C-I, α-Nb2C-II, α-Nb2C-III and α-Nb2C-IV respectively (Table 1). Among all the four reported structures, as the crystallographic information for Nb2C-IV is unknown, it is not considered for further analysis. By taking into account the

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three remaining crystal structures of α-Nb2C listed in Table 1 EBSD data was reanalysed. Surprisingly, nearly all the carbides present in the sample could again be successfully indexed in terms of crystal structures of α-Nb2C-I and α-Nb2C-II (Fig. 1b(ii, iii)) whereas indexing was poor when crystal structure α-Nb2C-III was taken as input (Fig. 1b(iv)). Hence, α-Nb2Ccarbides with α-Nb2C-III are discussed later.

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III was also not considered for further analysis. The possible reasons for not indexing the

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As reported in an earlier paper [17], the basic unit cells of the α, β and γ - Nb2C carbides bear strong structural similarity (see in Table 1), which possibly makes it difficult to distinguish the three phases by EBSD. As ordering of the carbon atoms in the three phases is distinct and different, presence of super lattice reflections in X-ray or electron diffraction patterns can be used to distinguish the phases.

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Fig. 2a shows simulated XRD patterns of γ, β and α−Nb2C (with crystal structures I and II) phases. It may be noted that all of the high intensity peaks in γ, β and α-Nb2C-I with Pbcn space group superimpose on each other. But α-Nb2C-II having Pnma space group shows some additional superlattice peaks (marked in the Fig. 2a), which do not coincide with

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any of the other carbide phases. With the help of these additional peaks the presence of αNb2C-II could be easily identified. However, due to low magnitude of structure factors of the

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superlattice peaks, low volume fraction of carbides and probable texture effect due to the large grain size of as-solidified microstructure, these peaks get concealed even in the synchrotron XRD pattern [17] because of which the presence of α-Nb2C is not detected in the bulk as-solidified sample. To address issues related to the low volume fraction and texture effects, carbide particles were extracted from the sample using acidic solution and fresh XRD patterns were obtained from these carbide particles (Fig. 2b). When these XRD patterns were compared with the simulated XRD patterns, in addition to the common peaks, correspond to all the carbides, presence of extra peaks of α-Nb2C-II were observed. Therefore, it clearly confirmed that the as-solidified sample has α-Nb2C carbides. In the rest of the paper α-Nb2CII is written as α-Nb2C.

ACCEPTED MANUSCRIPT Fig. 3 shows the bright field STEM micrograph of the as-solidified sample and the inset figure shows the bright field TEM image of the extracted carbide particles. It shows that the carbides have needle morphology. The size and morphology matched with the carbides observed in SEM micrographs (Fig. 1a(ii)). Composition of the carbide particles and matrix obtained using EDS in TEM, tabulated in Table 3, shows that Zr has nearly equi-partitioned

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in the matrix (1.45±0.22 at.%) and carbide phases (1.52±0.20 at.%). This indicates that for all practical purposes, the carbides in as-solidified structure can be treated as a binary phase. 3.2. Characterization of Deformed and recrystallized Samples

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Deformed samples

Typical microstructures of extruded sample (Fig. 4) showed that the carbides aligned in the extrusion direction. EBSD micrographs (Fig. 4(b,c)) showed that as-solidified grains were

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severely fragmented and all the carbides present in the microstructure could be indexed in terms of the α-Nb2C carbide phase. Carbides were extracted by dissolving the matrix phase and XRD pattern was obtained (Fig. 5a). All the XRD peaks could be indexed in terms of the α-Nb2C phase. When XRD of the extruded sample was compared with the as-solidified XRD (inset Fig. 5a), a shift toward lower 2θ values in each peak was noticed indicating increase in

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the lattice parameters of Nb2C carbide phase present in the extruded sample. TEM examination showed needle morphology of the carbide phase (Fig. 5b). EDS analysis without considering carbon for the quantification showed that these carbides contained 18±0.26 at.% Zr (see Table 3) which is equivalent to 12 at.% Zr in the (Nb,Zr)2C phase. Stecher et al. [42]

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have shown that up to 9 at.% Zr2C can form solid solution with the Nb2C phase. In order to examine this aspect further, high intensity XRD peaks of extruded sample, which are

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common in both γ and α-Nb2C, were fitted with increasing lattice parameters of γ-Nb2C and based on the best fit lattice parameters of the phase were determined as a = 3.14 Å and c = 4.987 Å. These lattice parameters matched well with the solid solution of the Zr2C and Nb2C phases having 9 at.% Zr2C [42]. Hence, by combining results of EDS and XRD it can be deduced that carbides in the extruded sample have ~ 6 at.% Zr. The XRD, EBSD and TEM analyses showed that carbides present in the as-solidified and extruded samples are nearly similar, except that the carbides present in the extruded samples have higher concentration of zirconium. This indicates that during extrusion Zr got preferentially partitioned into the carbide phase.

ACCEPTED MANUSCRIPT Recrystallized Samples The extruded sample was heat treated at 1300 oC for 3 hrs to recrystallize the deformed microstructure. Typical EBSD micrograph of the heat treated sample (Fig. 6a) shows recrystallized grains of average size of 20 µm. In order to quantify the percentage of recrystallization in the sample, grain orientation spread (GOS) was calculated from the EBSD

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data. For a typical recrystallized grain, the value of GOS should be less than 1o [43]. Based on this criterion, it was estimated that 90% of the grains got recrystallized. EBSD image did not show the presence of any carbide precipitates in the recrystallized sample. However, in back scattered mode of SEM (Fig. 6b), at high magnification, presence of ~100 nm size of

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spherical morphology of precipitates in the matrix was noticed.

Detailed TEM examination of particles also showed typical ~ 100 nm size of

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spherical particles (Fig. 7a). In order to identify the crystal structure of these particles, set of diffraction patterns were collected by systematically tilting the sample (Fig. 7(b)). All the diffraction patterns could be successfully indexed in terms of fcc crystal structure with a lattice parameter of 4.5 Å. EDS analyses of these particles showed that the carbide particles have substantial amount of Zr (39.64±0.38 at.%) content (see Table 3). It corresponds to 30

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at.% Nb, 20 at.% Zr and 50 at.% C in the (Nb,Zr)C phase.

XRD patterns obtained from the carbides extracted from the recrystallized sample (Fig. 8) could also be successfully indexed as fcc crystal structure with its lattice parameter as 4.56 Å. This lattice parameter matched well with the lattice parameter of (Nb,Zr)C carbide

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phase [20]. The lattice parameters for NbC and ZrC carbide phases are 4.40 and 4.60 Å, respectively. Therefore, the lattice parameter determined in this study is in between the lattice

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parameters of NbC and ZrC phases suggesting the applicability of Vegard’s law [44]. Using this law, atomic percentages of Nb, Zr and C in the carbide phase were estimated as 27.5, 22.5 and 50 (at.%) respectively. The estimated lattice parameter matched well with those reported for the NbC carbide containing 25 at.% Zr [42]. These values of composition are not far from the values estimated by EDS and confirmed that the carbide present in the recrystallized sample is (Nb,Zr)C type of carbide phase. Since the size of the carbides is small (~100 nm) precession electron diffraction (PED) under TEM was done to get the details of the carbide. PED was carried out for carbides in the Nb matrix using precession angle of 1o. Before acquiring the orientation map of the recrystallized sample by PED, one of the carbides (marked as a) was brought to 100

ACCEPTED MANUSCRIPT zone axis. Fig. 9a shows the orientation map of the recrystallized sample. It shows that one of the carbides (marked as a) is at [100] orientation and the corresponding matrix is at 216 orientation. The other two carbides (marked as b and c in Fig. 9) had their 527 and 324 direction as zone axes. The fact that the three carbides had different crystallographic orientation relationships with their matrix (here matrix is a common grain for the three

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carbides) is manifested by different colours of the carbides in the orientation image in Fig. 9. These orientations of carbides could not be expressed in terms of any unique OR with the matrix phase.

In order to reconfirm absence of any unique orientation relationship between

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NbC particles and Nb matrix, EBSD was carried out on a bulk sample. For EBSD, sample was carefully polished using colloidal suspension to get the Kikuchi map from the carbide particles also. EBSD was carried out with a step size of 10 nm. Fig.9b shows

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the orientation image obtained by EBSD. It clearly shows the presence of different orientations (different colours) of NbC particles in a single grain of Nb matrix. In addition, the inverse pole figure also shows random orientations of NbC particles. Based on the orientation images obtained by PED in TEM as well as EBSD in SEM, it was concluded that the NbC carbides formed during annealing of the extruded

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samples have random orientation with respect to the Nb matrix. 3.3. Characterization of Directly Heat Treated Samples

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The formation of new carbides during each treatment raised questions regarding the stability and sequence of transformations in the carbide phase. The question that arises is that whether the sequence is unique or it depends on the treatments given to the alloy? In order to

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understand the carbide phase transformation, the as-solidified samples were directly heat treated to the same temperature and time (1300 oC for 3 hrs) as was used for the recrystallization of the extruded samples. This experiment allowed us to examine the precipitation of NbC type of carbide from alternative route. SEM micrographs of the directly heat treated sample did not show any noticeable changes in the microstructure and it remained similar to that of as-solidified microstructure. EBSD could index all the carbides as α-Nb2C which means that during the same heat treatment α-Nb2C did not transform to (Nb,Zr)C, unlike the case of recrystallized sample. In order to explore its ability to resist the transformation, heat treatment at the same temperature (1300 oC) was extended to 10 hrs. Fig. 10a(i) shows the SEM image of the sample heat treated for 10 hrs, in which the presence of

ACCEPTED MANUSCRIPT needle morphology of carbide phase can be observed. These carbides could again be indexed in terms of α-Nb2C, but this time volume fraction of the carbide phase was lower than the volume fraction of carbides observed in the as-solidified microstructure. When the sample was examined at higher magnification (Fig. 10a(ii)), it showed presence of needle morphology of precipitates of smaller size. These fine precipitates were further examined

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under TEM (Fig. 10b). Electron diffraction patterns from these precipitates confirmed that these carbides have fcc crystal structure with lattice parameter as 4.5 Å which is nearly same as that of the precipitates formed with spherical morphology in the recrystallized samples. EDS analysis of these precipitates also showed composition similar to that of spherical

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precipitates observed in the recrystallized sample (See Table 3).

Peaks of XRD patterns obtained from the carbides extracted from the directly heat treated

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sample (Fig. 11) could be indexed with fcc crystal structure having a lattice parameter of 4.56 Å, which is the same as that observed in the recrystallized sample. This indicates that the NbC carbides present in the recrystallized sample and in as-solidified heat treated samples are identical except that the morphologies are different in the two cases. Orientation map (Fig. 12a) obtained from PED carried out under TEM showed that all the carbides present within a single grain correspond to a single orientation (indexed with the

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same colour). For example, the orientation of all the carbides present in the Nb matrix ([001] grain) corresponds to <101> zone axis (shown in Fig. 12a). This unequivocally established the presence of a unique OR between Nb and NbC. Using orientation data of Fig. 12a, and

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composite SAED of Nb and NbC (Fig. 12b), OR has been derived and it can be written as: 001

⁄/ 001

110

⁄/ 100

110

⁄/ 010

This OR is similar to the Baker-Nutting (BN) OR [45]. It matches with the OR observed between NbC particles and Nb matrix in Nb-Mo system as well as with the OR published in several studies between fcc precipitates and bcc matrix [28,45,46]. It is worth mentioning here that in general bcc precipitates in the fcc matrix exhibit Nishyama-Wassermann (N-W) and Kurdjumov–Sachs (K-S) OR, whereas, fcc precipitates in bcc matrix exhibit BakerNutting (BN) OR [45,46].

ACCEPTED MANUSCRIPT 3.4. Estimation of relative stabilities of all the carbide phases using first principle calculations DFT based first principle calculations were performed to establish the stability of various carbide phases including those containing Zr atoms. For the γ-Nb2C phase which exhibits Csublattice disorder having 50% vacancies, a special quasirandom structures (SQS) with 32

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atoms supercell (having 8 vacancies) was employed to establish random configuration [47,48]. In SQS, the randomness is introduced by mimicking as closely as possible the most relevant nearest neighbour pair and multisite correlation functions of an infinite random solid solution within a finite supercell. For phases containing Zr, one or two Nb atoms were

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replaced by Zr atoms in the unit cell of the respective phases.

The calibration of various approximations in the DFT calculations were carried out by

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calculating ground state cohesive properties (lattice parameters and cohesive energies) of elemental Nb (bcc), C (graphite) and Zr(hcp). The cohesive energies are calculated by subtracting the corresponding atomic contribution from the total energies. The cohesive energy for Nb (bcc), C (graphite) and Zr (hcp) were calculated to be -7.0112, -4.0742 and 6.1618 eV/atom, respectively. It must be mentioned here that the cohesive energies are with respect to the true ground state electronic configurations of Nb, C and Zr atoms, respectively.

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Table 4 lists the optimized lattice parameters, deviation of lattice parameters from the experimental values (see Table 1) and formation energies for all the Nb2C and NbC carbide phases. The formation energy of a given phase has been determined by subtracting from its

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cohesive energy, the contributions from that of their constituent elemental solid in their respective ground states, viz., Nb (bcc), Zr (hcp) and C (graphite). The calculated lattice parameters for all the Nb2C and NbC carbides exhibit very good agreement with those

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determined experimentally except for the α-Nb2C-III carbide phase. The calculated equilibrium lattice parameters for α-Nb2C-III deviated substantially from the experimental values. When the formation energy of the same phase was calculated without geometry optimization, it showed positive formation energy (see Table 4). It indicates that this phase will not form in Nb-C system. When the crystallographic information was carefully observed, it was found that the Wyckoff (4a) positions for Nb atom reported in the literature [14] for the phase do not match with the positions given in the international crystallographic table [49]. According to the international crystallographic table the Wyckoff positions (4a) for the Pnma space group are (0,0,0), (1/2,0,1/2), (0,1/2,0), (1/2,1/2,1/2) which do not match with the reported atom positions in the literature. This could be a reason for not being able to index the

ACCEPTED MANUSCRIPT carbide particles with α-Nb2C-III in as-solidified condition (Fig. 1b(iv)). The same author Yvon et al. [13] who established α-Nb2C-III structure, later corrected crystallographic information in their paper and assigned it in terms of α-Nb2C-II. All the remaining Nb2C carbides exhibited negative formation energy indicating that formation of these carbides is thermodynamically feasible. Among all the Nb2C carbides, the

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α-Nb2C-II has the lowest formation energy and hence is the most stable. 4. DISCUSSION 4.1. Formation of α-Nb2C

In the present study, using EBSD images corresponding to the phase maps of Fig. 1b(i)

⁄/ 001

111

⁄/ 010

⁄/ 0001

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011

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and Fig. 1b(iii), the following ORs among α−Nb2C , γ−Nb2C and Nb matrix were estimated:

⁄/ 1120

The OR between γ-Nb2C and bcc-Nb shown here matched with the OR established in our earlier paper [17]. The structural similarity between α-Nb2C and γ-Nb2C phases can be illustrated from this OR. For example, when the unit cells of α and γ-Nb2C are arranged

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according to the deduced OR, all the atom positions of Nb in the α-Nb2C matched with the atom positions of Nb in the γ-Nb2C (Fig. 13a). Similarly, by overlapping the 001 plane of α-Nb2C on the 0001 plane of γ-Nb2C, it can be shown that the arrangement of Nb atoms in

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both the crystal structures match with each other (Fig. 13b). Similar conclusions were drawn when the unit cells of γ and β were arranged according to the determined OR [17]. A general picture that emerges out from this exercise is that while Nb atoms maintain nearly same

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configuration in all the three phases, carbon atoms are randomly arranged in γ-Nb2C and orderly arranged in the β and α-Nb2C. Such strong structural relationship among the three phases leads to misidentifications in some of the cases. The large differences between the atomic structure factors of Nb and C make the structure factors of super-lattice reflections nearly negligible. For example, intensity ratio between the fundamental reflection {211} and the super-lattice reflection {101} is ~200 (estimated from simulated XRD patterns). In most of the cases, including the present work, typical volume fraction of the Nb2C carbide phase remains less than 10% [8,16,18–20]. Because of which fundamental reflections of Nb2C carbides in XRD will fall below 10% of the matrix and super lattice reflections of the α-Nb2C

ACCEPTED MANUSCRIPT fall well below the back ground of the XRD pattern. It is, therefore, not possible to identify these super-lattice peaks and thereby the presence of the α-Nb2C in a bulk sample. Therefore while identifying the carbide phase extra care is needed to record and identify the weak reflections. Extraction of carbide by dissolving the matrix phase would be a good solution to capture weak reflections.

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Carbide particles in the as-solidified sample showed the presence of planar defects. These defects led to streaking perpendicular to (001) diffraction spot in the [120] zone axis of SAED pattern (see inset Fig. 3). Origin of these defects has been attributed to the occupancy of octahedral sites by carbon atoms during the formation of Nb2C [17]. When SAED patterns

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of carbide particles in the extruded sample were observed in the same zone axis [120], reduction in streaking has been noticed (see inset Fig. 5b). This indicates that the carbides in

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the extruded sample have lower concentration of defects suggesting that strain energy got relieved during the extrusion process. In addition to the relieving of strain, preferential partitioning of Zr into the carbide phase has also been observed in the extruded sample. Addition of Zr in the carbide phase, which has larger atomic radius (1.6 Å) [50] as compared to Nb (1.47 Å) [51], is expected to help in reducing the strain energy associated with the transformation. Increase in lattice parameter of the carbides in the extruded sample

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as compared to that of the carbides present in the as solidified sample could be taken as evidence for the same (Fig. 5a). In addition, dissolution of Zr in Nb2C can increase the configurational entropy of the system as well. Therefore, reduction in strain energy and

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increase in entropy provided necessary driving force for partitioning of Zr into the Nb2C phase of the extruded sample. Strain imparted during extrusion and presence of additional

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dislocations during warm working may have also enhanced the diffusion of Zr. First principle calculations performed by substituting Nb atoms with the Zr atoms in the Nb2C phase have shown that with increasing Zr content, stability of the Nb2C decreases (Table 4). Under these two opposing conditions, an unstable equilibrium concentration of Zr is attained in the Nb2C phase during extrusion. Increasing concentration of Zr in the carbide phase has eventually led to the formation of the (Nb,Zr)C carbides. 4.2. Formation Mechanism of (Nb,Zr)C Carbides Formation of the (Nb,Zr)C carbides in dilute Nb–Zr-C alloys has been reported in literature [8,16,18–20]. One possible reason is that in binary Zr-C system, there is no phase which is equivalent to Nb2C. However, in the case of NbC an isostructural ZrC phase exists

ACCEPTED MANUSCRIPT in equilibrium Zr-C phase diagram. It is, therefore, possible that partitioning of Zr may promote NbC type structure. The recrystallized as well as directly heat treated samples have shown that after heat treatment the Nb2C goes into the solution. As discussed earlier, increasing concentration of Zr in Nb2C makes it thermodynamically less stable. On the other hand, ab-initio calculations on the formation energy of the NbC phase (Table 4) showed that

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with increasing Zr content, stability of NbC phase increases. Therefore, subsequent to extrusion, when the alloy was subjected to heat treatment, difference between the formation energy of carbide phases provided the necessary driving force. This led to the dissolution of (Nb,Zr)2C in favour of (Nb,Zr)C phase. Farkas et al. [22] have calculated the free energy of

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formation of Nb2C, NbC and ZrC phases and have shown that (Nb,Zr)C carbide phase is more stable than the Nb2C in Nb-1%Zr-0.1%C alloy [52]. The present results are in good agreement with their results. However, the exact mechanism for the formation of (Nb,Zr)C

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from Nb2C is not known. To establish the mechanism, thermodynamic calculations were carried out which have shown that there are at least three possible ways by which NbC or ZrC phases may form in Nb-Zr-C alloy. These possibilities are shown in the form of following reactions:

(1)

Nb2C ⇋ Nb+NbC

(2)

2Nb2C+Zr ⇋ 3Nb+NbC+ZrC

(3)

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Nb2C+Zr ⇋ 2Nb+ZrC

The standard Gibbs free energies (∆Go) for all the reactions were calculated at

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different temperatures using Factsage thermodynamic software. Variation of ∆Go with temperature is plotted in Fig. 14. It shows that among all the above mentioned reactions,

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reaction (1) is thermodynamically feasible. But experimental results in the present study do not suggest formation of pure ZrC phase. Similarly, reaction (2), which shows the formation of pure NbC, is neither thermodynamically feasible nor in agreement with experimental results. Reaction (3) is the only reaction which shows simultaneous formation of both the carbides, but positive value of ∆Go for this reaction suggests that thermodynamically this reaction is also not feasible. However, according to experimental results, the resultant carbides are of (Nb,Zr)C type suggesting that instead of forming as separate entities these carbides formed as a solid solution of NbC and ZrC. This suggests that by decreasing the activities of NbC and ZrC

ACCEPTED MANUSCRIPT carbides further reduction in the free energy is possible. Considering this observation, free energy calculations for reaction (3) were repeated for decreasing activity values of NbC and ZrC and plotted in the Fig. 14. It can be noticed that when the activities of NbC and ZrC fall below 0.3, the reaction (3) becomes thermodynamically feasible at temperatures below 1300 o

C. Therefore, presence of Zr in the Nb2C carbide paved the way for the formation of the

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stable (Nb,Zr)C carbide phase. Finally, based on the ab-initio calculations, thermodynamic calculations and experimental results, it can be inferred that (Nb,Zr)C carbide phase in NbZr-C alloy can form according to the following modified reaction: Nb2C + Zr ⇋ Nb + (Nb,Zr)C

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To examine the importance of the Zr for the formation of (Nb,Zr)C, HAADF (High angle annular dark field) image of the carbide precipitate was obtained. EDS line scan carried

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out (Fig. 15a) across the carbide particle showed variation in the Zr concentration. Based on this variation at least three distinct regions could be identified. The first region with minimum Zr content corresponds to the Nb matrix, the second region with maximum Zr content corresponds to the interface region and the third region with intermediate Zr content corresponds to the core of the carbide phase. Distribution of Zr provides strong evidence that

next section.

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formation of (Nb,Zr)C phase depends on the availability of Zr [53,54]. This aspect is dealt in

4.2.1. Spherical Morphology of (Nb,Zr)C Carbides Three regions observed in the HAADF image needed further investigation and for this

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purpose HREM image of the spherical carbide, matrix and interface were obtained (Fig. 15b). Fast Fourier Transforms (FFT) obtained from various regions of the HREM image are shown

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as inset in the figure. These FFTs show that the matrix and the carbide particle are oriented along [111] and [101] zone axes, respectively. The interface between the particle and the matrix is broad and does not show any atomic matching, and therefore can be considered as an incoherent interface. Zr accumulates nearly uniformly across this incoherent interface leading to spherical morphology for NbC carbides. As in comparison to the Nb2C phase concentration of Zr is higher in (Nb,Zr)C phase, the growth of the (Nb,Zr)C carbide depends upon the supply of Zr from the matrix phase. Due to limited availability of Zr in the dilute alloy, growth of the (Nb,Zr)C get arrested, which explains why Titran et al. [18–20] have not observed any growth even after 30,000 hrs of aging.

ACCEPTED MANUSCRIPT As shown earlier, spherical (Nb,Zr)C carbides in the recrystallized sample did not show any specific OR with the Nb matrix. There are many incidences where precipitates formed during recrystallization do not maintain any OR with the matrix phase. For example, Matsukawa et al. [55] have shown that bcc precipitates (Zr rich and Nb-rich) in recrystallized Zr-2.5Nb did not follow any specific OR. Similarly, Fukino et al. [56] have also shown that

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austenite grains did not have any specific orientation relationships with the recrystallized ferrite grains in deformed Fe-8.5Ni alloy. One common finding of both these studies is that if the growth of the precipitates takes place along with recrystallization of the alloy, the particles do not follow specific OR. In line with this observation, it could be inferred that in

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the present study the (Nb,Zr)C particles nucleated before the onset of the recrystallization process and the growth of the precipitates occurred during recrystallization. As nucleation of the precipitates has taken place before recrystallization, the re-orientation of the grains due to

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recrystallization overwrites the OR between particle and matrix leading to random orientation of the carbide particles.

This conjecture can easily be verified by carrying out DSC and dilatometer where initial stages of precipitation could be successfully captured. However, due to the low volume fraction of carbide particles, sufficient signals could not be detected to show the temperature

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of nucleation and recrystallization events. Therefore, another approach was taken. If the above statement that re-orientation of the grains due to recrystallization overwrites the OR were true, then the formation of NbC carbide particles under the conditions where recrystallization process does not occur should exhibit a specific OR between the precipitates

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and the matrix phases. In order to verify the validity of this statement, as-solidified sample was heat treated at the same temperature (1300 oC) at which extruded sample was

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recrystallized.

4.2.2. Needle Morphology of NbC Carbides When the as-solidified samples were directly heat treated and characterized by SEM,

EBSD and TEM, (Nb,Zr)C carbide precipitates of needle morphology were observed. It has already been established that though morphologically these carbides are different from those observed in the recrystallized sample, compositionally and crystal structure point of view both the carbides are same. Another difference lies in the way these carbides are aligned with respect to the matrix phase. In contrast to the spherical carbides which were randomly oriented in the recrystallized matrix, the B-N OR was observed between the needle shaped

ACCEPTED MANUSCRIPT carbides and matrix in directly heat treated as-solidified sample. Presence of OR in the latter case validates our conjecture on the overriding effect of recrystallization texture on OR. HREM of the interface of carbide and matrix in latter case (Fig. 16) showed sharp interface with interplanar matching across it. This observation confirms coherency across the interface. Presence of OR not only explains the morphology but also provides a clue to

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understand the mechanism of formation of NbC from Nb. When both the lattices were arranged according to the B-N OR (Fig. 17a), positions of Nb atoms in the Nb lattice and in the NbC matched well along [100] and [010] directions but matching was relatively poor along the third [001] direction. It also showed that carbon atoms occupy the face and edge

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centred octahedral void positions in Nb lattice. The size of the octahedral void in Nb lattice is 0.04263 nm and is smaller than the size of the carbon atom (0.077 nm). In an octahedral void

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distances between two Nb atoms along 110 , 110 are 0.172 nm and 0.0355 nm along [001]. So, the carbon atom can be accommodated along <110> direction but not along [001]. Therefore, when carbon atoms occupy octahedral void positions in the Nb lattice to convert it to NbC lattice, the Nb lattice get expanded in [001] direction up to 38% and also leads to additional 4.2% compression strain along [010] direction. From HRTEM micrograph (Fig. 16a), it can be noticed that carbide grew along 031

direction and habit plane is 013

. It

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matches with the habit plane observed for NbC carbides in Nb-Mo system. Therefore, to minimize the strain (Nb,Zr)C precipitate tilted to 031

direction which is closely

perpendicular to the [001] direction (along which lattice get expanded) so that atomic and NbC 114

takes place (see Fig. 16b).

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matching between planes of Nb 013 5. CONCLUSIONS

To delineate the mechanism of formation of (Nb,Zr)C carbide phase in the Nb-1Zr-0.1C

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alloy and the factors affecting the formation, the alloy in four different conditions viz. assolidified, extruded, recrystallized and directly heat treated as-solidified samples without any deformation were examined in detail. Following conclusions can be drawn from the present study:

1. In the as-solidified condition, the alloy contained only α-Nb2C carbides, which remain stable under the conditions when Zr equi-partitioned in both the phases (Nb matrix and Nb2C phase). By extracting carbide particles, it has been shown that the αNb2C phase has Pnma space group.

ACCEPTED MANUSCRIPT 2. When the alloy was subjected to extrusion or heat treatment, Zr preferentially diffused into the α-Nb2C carbide phase, thereby rendering the phase unstable. The destabilizing effect of Zr was substantiated using ab-initio calculations. During subsequent annealing treatment, (Nb,Zr)C, a more stable phase, started precipitating out at the expense of the Nb2C carbides. to the following reaction: Nb2C + Zr ⇋ Nb + (Nb,Zr)C.

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3. It has been shown theoretically and experimentally that (Nb,Zr)C can form according

4. The morphology of the (Nb,Zr)C phase depends on the thermo-mechanical processing of the alloy. It can be either spherical or needle morphology. (Nb,Zr)C phase of

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spherical morphology exhibited random OR, whereas, (Nb,Zr)C of needle morphology exhibited a specific (Baker-Nutting) OR with respect to Nb matrix. 5. It has also been shown that if nucleation of the carbides takes place prior to

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recrystallization of the alloy and their growth takes place during recrystallization, then the carbides will have spherical morphology and maintain incoherent interface with the matrix. On the other hand, if nucleation and growth of the carbides take place without any recrystallization of the matrix, then the carbides show needle morphology and specific OR with the Nb matrix.

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ACKNOWLEDGEMENTS

The authors are grateful to Dr. Abhishek Mukherjee, MP&CED, BARC for his help in carrying out thermodynamic calculations. Special thanks to Mr. K.V. Ravikanth, Dr. K.V.

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Mani Krishna of Mechanical Metallurgy Division, BARC and Dr. A. Laik of Materials Science Division, BARC for critically reviewing the manuscript. The work was funded by

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Department of Atomic Energy, Government of India.

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[42] P. Stecher, F. Benesovsky, A. Neckel, H. Nowotny, Untersuchungen in den Systemen Titan (Zirkonium, Hafnium)-Niob-Kohlenstoff, Monatsh Chem. 95 (1964) 1630–1645. [43] V.D. Hiwarkar, S.K. Sahoo, I. Samajdar, A. Satpathy, K.V. Mani Krishna, G.K. Dey, D. Srivastav, R. Tewari, S. Banarjee, Defining recrystallization in pilgered Zircaloy-4 : From preferred nucleation to growth inhibition, J. Nucl. Mater. 412 (2011) 287–293. [44] L. Vegard, Die Konstitution der Mischkristalle und die Raumfüllung der Atome, Zeitschrift für Physik. 5 (1921) 17–26. [45] C. Barry Carter, D.B. Williams, Transmission Electron Microscopy: Diffraction Imaging, and Spectroscopy, 1st ed., Springer International Publishing, Switzerland, 2016. [46] H.W. Yen, C.Y. Chen, T.Y. Wang, C.Y. Huang, J.R. Yang, Orientation relationship transition of nanometre sized interphase precipitated TiC carbides in Ti bearing steel, Mater. Sci. Technol. 26 (2010) 421–430. [47] J.V. Pezold, A. Dick, M. Friák, J. Neugebauer, Generation and performance of special quasirandom structures for studying the elastic properties of random alloys : Application to Al-Ti, Phys. Rev. B. 81 (2010) 094203. [48] A. Zunger, S.H. Wei, L.G. Ferreira, J.E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65 (1990) 353–356. [49] International tables for crystallography Volume A: Space-group symmetry, Edited by Theo Hahn, 5th ed., Springer Netherlands, 2005. [50] D.G. Westlake, Stoichiometries and interstitial site occupation in the hydrides of ZrNi and other isostructural intermetallic compounds, J. Common Met. 75 (1980) 177–185. [51] W.E. Quist, R. Taggart, D.H. Polonis, The influence of iron and aluminium on the precipitation of metastable Ni3Nb phases in the Ni-Nb system, Metall. Trans. 2 (1971) 825–832. [52] V.B. Arzamasov, E.V. Vasil’eva, Phase composition of Nb-M-C alloys, Met. Sci. Heat Treat. 20 (1978) 291–293. [53] S.V. Rempel, A.I. Gusev, Surface segregation of ZrC from a carbide solid solution, Physics of the solid state. 44 (2002) 68–74. [54] O. Kubaschewski, C.B. Alcock, Metallurgical thermochemistry, Pergamon Press, New York, 1979. [55] Y. Matsukawa, I. Okuma, H. Muta, Y. Shinohara, R. Suzue, H.L. Yang, T. Maruyama, T. Toyama, J.J. Shen, Y.F. Li, Y. Satoh, S. Yamanaka, H. Abe, Crystallographic analysis on atomic-plane parallelisms between bcc precipitates and hcp matrix in recrystallized Zr-2.5Nb alloys, Acta Mater. 126 (2017) 86–101. [56] T. Fukino, S. Tsurekawa, Y. Morizono, In-situ scanning electron microscopy/electron backscattered diffraction observation of microstructural evolution during α to γ phase transformation in deformed Fe-Ni alloy, Metall. Mater. Trans. A. 42 (2011) 587–593.

ACCEPTED MANUSCRIPT Table 1. Crystallographic details of all the Nb2C and NbC carbide phases [9-15]. Structure

Lattice parameters (Å)

Space group

Atom positions

γ−Nb2C

Hexagonal

aH = 3.12, cH = 4.95

P63/mmc

2Nb in 2(c) 2C in 2(a) randomly distributed

β−Nb2C

Trigonal

a=5.4, b=4.95 (a ~ √3aH; c~ cH) a=4.95, b=6.24, c=5.4 (a~cH; b~2aH; c~√3aH)

Pbcn

Orthorhom bic

a=10.92, b=3.09, c=4.974 (a~2√3aH; b~aH; c~cH)

pnma

4Nb in 4(c) with x~1/24, z~3/4 4Nb in 4(c) with x~5/24, z~1/4 4C in 4(c) with x~3/8, z~0

III Orthorhom bic

a=10.9, b=4.974, c=3.09 (a~2√3aH; b~cH; c~aH)

Pnma

4Nb in 4(a) with x~1/24, y~3/4, z~0 4Nb in 4(a) with x~5/24, y~1/4, z~0 4C in 4(a) with x~3/8, y~0, z~0

IV Orthorhom bic

a=10.89, b=12.36, c=4.96

Not available

EP

Cubic

AC C

NbC

8Nb in 8(d) with x~1/4, y~1/8, 4C in 4(C) with y~3/8

TE D

II

Orthorhom bic

2C in 2(d) 1C in 1(a)

SC

I

6Nb in 6(k) with x~1/3,

31

M AN U

α−Nb2C

RI PT

Phase

4.4

3

Nb in 4(a) (0, 0, 0) C in 4(b) (0.5, 0.5, 0)

Table 2. Chemical composition of the as-solidified Nb alloy. Zr (wt.%)

C (wt.%)

Impurities (wppm)

Nb (wt.%)

0.9-1.2

0.1-0.13

H – 4 ppm N – 41 ppm O – 132 ppm

balance

ACCEPTED MANUSCRIPT Table.3. EDS analysis of the carbides and matrix present in as-solidified, extruded, recrystallized and as-solidified heat treated Nb-1Zr-0.1C alloy samples. Sample

Composition, wt. (at. %) with carbon content

Nb

Zr

Nb

Zr

C

matrix

98.55 ± 0.20 (98.52)

1.45 ± 0.22 (1.48)

98.37 ± 0.26 (97.17)

1.45 ± 0.22 (1.46)

0.18 ± 0.13 (1.37)

ppt

98.48 ± 0.24 (98.52)

1.52 ± 0.20 (1.48)

96.73 ± 0.30 (86.36)

1.49 ± 0.23 (1.36)

1.78 ± 0.20 (12.28)

matrix

99.06 ± 0.20 (99.04)

0.94 ± 0.18 (0.96)

91.53 ± 0.31 (60.52)

0.87 ± 0.18 (0.59)

7.60 ± 0.26 (38.89)

ppt

82.26 ± 0.24 (82.00)

17.74 ± 0.26 (18.00)

80.03 ± 0.27 (67.49)

17.25 ± 0.26 (14.82)

2.71 ± 0.11 (17.69)

matrix

99.10 ± 0.18 (99.08)

0.9 ± 0.22 (0.92)

98.94 ± 0.28 (97.88)

0.90 ± 0.18 (0.91)

0.16 ± 0.11 (1.21)

ppt

60.80 ± 0.44 (39.64)

39.20 ± 0.38 (39.64)

59.27 ± 0.44 (50.36)

38.21 ± 0.44 (33.07)

2.52 ± 0.15 (16.56)

matrix

98.82 ± 0.15 (98.80)

1.18 ± 0.15 (1.20)

98.80 ± 0.17 (98.67)

1.18 ± 0.15 (1.20)

0.02 ± 0.18 (0.13)

ppt

73.24 ± 0.35 (72.88)

26.76 ± 0.28 (27.12)

67.81 ± 0.26 (45.10)

24.78 ± 0.25 (16.78)

7.41 ± 0.32 (38.11)

Recrystallized

AC C

EP

TE D

As-solidified_ annealed

SC

Extruded

M AN U

As-solidified

RI PT

Without carbon content,

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Table.4. DFT-GGA optimized lattice parameters, and formation energies of Nb2C and NbC carbide phases. Lattice parameters after equilibration ( Å )

deviation from Formation experimental lattice energy parameters (eV/atom)

γ-Nb2C (SQS supercell)

α-Nb2C-I-Pbcn

a = b = 5.4242 c = 4.9565 a = 4.9671

0.0242 0.0005 0.0111

α-Nb2C-II-Pnma

b = 6.2408 c = 5.4292 a = 10.9502

0.0008 0.0292 0.0302

NbC

AC C

EP

Pnma

b = 3.0946 c = 4.9780 1 Zr atom a = 10.9660 b = 3.1289 c = 5.0247 2 Zr atoms a = 11.0464 b = 3.1524 c = 5.0596 after a= 17.2609 geometry b = 5.3306 optimization c = 5.3934 without a = 10.9000 geometry b = 4.9740 optimization c = 3.0900 no Zr atoms a = b = c = 4.4778 1 Zr atom a = b = c = 4.5271 2 Zr atoms a = c = 4.5847 b = 4.5712

TE D

α-Nb2C-III-

no Zr atoms

SC

M AN U

β-Nb2C

RI PT

Phase

0.0046 0.0040 0.046 0.0389 0.0507 0.1264 0.0624 0.0856 6.3609 0.3566 2.3034 0.0092 0.0585 0.1161 0.1026

-4.2270

-4.3691

-4.3704

-4.3794

-4.2977

-4.2208

-9.6222

32.0571

-2.527 -2.602 -2.681

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a(ii)

RI PT

a(i)

b(ii)

b(iii)

b(iv)

100 µm

AC C

EP

TE D

b(i)

M AN U

SC

Nb γ-Nb2C α-Nb2C-I_pbcn α-Nb2C-II_pnma

100 µm

100 µm

100 µm

Fig.1. (a) SEM micrographs of the as-solidified Nb-1Zr-0.1C alloy showing the presence of (i) large grain size (1-1.5 mm) and (ii) needle morphology of precipitates. (b) EBSD phase map of the fig.a(ii): matrix indexed with Nb and precipitates indexed with (i) γ-Nb2C, (ii) α-Nb2CI_Pbcn, (iii) α-Nb2C-II_Pnma and (iV) α-Nb2C-III_Pnma crystal structures (crystallographic data of all the Nb2C carbide phases are given in Table.1.). The carbides were successfully indexed with all the Nb2C crystal structures except with α-Nb2C-III structure.

TE D

50

(401)(211)

60

2θ (angle)

80

EP

40

100

AC C

20

120

(251)

(641)

(10 1 1)

(803) (423)

(213)

500

simulated pattern of α_Nb2C_II

γ-Nb2C

0

(214)

100

1000

extracted carbides of as-solidified sample

(612) (022) (801) (004) (802) (422)

β-Nb2C

(403)

150

1500

(610)

200

(020)

α-Nb2C-I_Pbcn

M AN U

Intensity

250

Intensity (a.u)

2000

(402) (212)

300

(002)

2500

α-Nb2C-II_Pnma

SC

350

3000

(400)(210)

(b)

400

(101)

(a)

RI PT

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0 20

40

60

80

100

120

2θ (angle)

Fig.2. (a) Simulated XRD patterns of all the Nb2C carbide phases showing the presence of similar peaks in all the patterns. In αNb2C-II_Pnma pattern, in addition to the common peaks additional reflections (marked in the fig) are present. (b) Experimental XRD pattern obtained from the extracted carbides of as-solidified sample. It matched with the simulated XRD pattern of α-Nb2CII_pnma carbide phase.

RI PT

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Nb matrix

AC C

EP

TE D

M AN U

SC

Extracted carbides

Fig.3. Bright field STEM micrograph of the as-solidified sample. The top inset figure shows bright field TEM image of the carbides extracted from the as-solidified sample. Both the images showing the presence of needle morphology of carbides in the sample. SAED pattern correspond to the carbide particle is shown as inset in the bottom of the fig. It is indexed with α-Nb2C carbide phase.

Extrusion direction b)

c)

M AN U

SC

a)

RI PT

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Nb α-Nb2C

TE D

ND

AC C

EP

Fig.4. (a) SEM micrograph of the extruded Nb alloy and corresponding (b) EBSD image and (c) Phase map. High magnification image of fig.c shows that precipitates are indexed with α-Nb2C phase. EBSD and phase map images showing that grains and carbides aligned along the extrusion direction.

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1500

(002)

1000

500 36.0

1500

36.5

37.0

37.5

38.0

38.5

Nb matrix

(251)

M AN U

500

(641)

(10 1 1)

(803) (423)

extruded sample (214)

(612) (022) (801) (004) (802) (422)

(403) (213)

(610) (020)

(402) (212)

1000

(400) (210)

2θ (angle)

(101)

Intensity (a.u)

2000

RI PT

Intensity (a.u)

(401) (211)

2500

Extracted carbides

(b)

SC

2000

as-solidified extruded

(211)

2500

(401)

3000

(002)

(a)

20

40

60

80

2θ (angle)

100

EP

0

TE D

simulated pattern of α_Nb2C_II

500 nm 120

AC C

Fig.5. (a) XRD pattern of the carbide particles extracted from the extruded sample showing that it matches with the simulated XRD pattern of α-Nb2C-II carbide phase. Inset figure in fig.a shows the comparison of XRD pattern of the extruded sample with as-solidified sample. It shows that XRD peaks of extruded sample shifted to low θ value which indicates increase in lattice parameters. (b) Bright field TEM image of the extruded alloy and extracted carbide particles (shown as top inset in fig.b) showing the presence of needle morphology of Nb2C carbides. The SAED pattern of the carbide precipitate shown as inset in the bottom of the fig.b is indexed with α-Nb2C carbide phase.

(b)

TE D

M AN U

SC

(a)

RI PT

ACCEPTED MANUSCRIPT

EP

ND

AC C

Fig.6. (a) EBSD and (b) BSE micrographs of the recrystallized sample showing the presence of recrystallized ~20 µm grains and spherical morphology of carbides, respectively.

(b)

EP

TE D

M AN U

SC

(a)

RI PT

ACCEPTED MANUSCRIPT

AC C

Fig.7. (a) Bright field TEM micrograph of the recrystallized sample showing the presence of spherical morphology of carbide precipitates. (b) SAED patterns of the carbide particles obtained at different zone axes by systematically tilting the sample. These SAED patterns are indexed with fcc crystal structure having lattice parameter of 4.5 Ao.

(110)

Recrystallized sample

800 600

0

40

AC C

20

EP

200

TE D

400

60

(400)

(222)

1000

(311)

M AN U

(220)

Intensity (a.u)

1200

(422)

1400

SC

(200)

1600

(331) (420)

1800

RI PT

ACCEPTED MANUSCRIPT

simulated NbC - 4.56 A

80

100

o

120

2θ (angle)

Fig.8. XRD pattern of the extracted carbide particles of the recrystallized sample. It matches with the simulated XRD pattern of (Nb,Zr)C-fcc with lattice parameter of 4.56 Ao.

ND

RI PT

ACCEPTED MANUSCRIPT

[001]-IPF

a

M AN U

SC

Nb

NbC 100 nm

a

b

TE D

c

c b

[001]-IPF

NbC

AC C

EP

Fig.9. (a) Orientation image of the recrystallized sample acquired by precession electron diffraction in TEM. Nb matrix oriented along 216 and carbide particles marked with ‘a’ corresponds to the orientation of [100], similarly ‘b’ and ‘c’ carbides oriented along 527 , 324 , respectively. (b) Orientation image obtained by EBSD of the selected region (marked in the inset SEM micrograph). Both the orientation images obtained by PED in TEM and EBSD in SEM shows that (Nb,Zr)C carbides randomly oriented with Nb matrix in recrystallized sample.

ACCEPTED MANUSCRIPT

(b)

RI PT

(a(ii))

AC C

EP

TE D

M AN U

SC

(a(i))

Fig.10. (a) BSE micrographs of the directly heat treated as-solidified alloy at 1300 oC for 10 h showing the presence of two types of carbides: (i) α-Nb2C carbides and (ii) small needle morphology of precipitates. (b) Bright filed TEM micrograph of the directly heat treated sample showing the presence of ~ 100 nm small needle morphology of precipitates. SAED pattern obtained from these precipitates is shown as inset in the figure. It is indexed with fcc crystal structure having lattice parameter of 4.5 Ao.

(200)

3000

RI PT

(110)

ACCEPTED MANUSCRIPT

SC

2500

M AN U

TE D

500

20

EP

0 40

60

(422)

(331) (420)

1000

(400)

(222)

1500

extracted carbide particles from as-solidified heat treated sample (311)

(220)

Intensity (a.u)

2000

o

standard NbC - 4.56 A

80

100

120

AC C

2θ (angle)

Fig.11. XRD pattern of the extracted carbides from the directly heat treated as-solidified sample at 1300 oC for 10 hrs. It matches with the simulated XRD pattern of (Nb,Zr)C carbides with lattice parameter of 4.56 Ao

ACCEPTED MANUSCRIPT

Orientation map (b)

SC

RI PT

(a)

M AN U

ND

AC C

EP

TE D

Inverse pole figure-[001]

Fig.12. (a) Orientation image of the directly heat treated as-solidified sample at 1300oC for 10 h acquired by precession electron diffraction in TEM showing the presence of specifically oriented (<100>Nb//<110>NbC) needle morphology of (Nb,Zr)C carbides. (b) Composite SAED pattern of the Nb matrix and needle morphology of NbC carbides showing the presence of B-N OR ([100]Nb//[110]NbC, (002)Nb//(002)NbC) between them.

ACCEPTED MANUSCRIPT

RI PT

(b)

SC

(a)

010

γ-Nb2C

Nb atoms in α-Nb2C C atoms in α-Nb2C Nb atoms in γ-Nb2C C atoms in γ-Nb2C

001

(001)α-Nb2C

TE D

α-Nb2C

001

(0001)γ-Nb2C

EP

001

AC C

001

M AN U

0001

/ 0001 , Fig.13. (a) crystal structures of α and γ-Nb2C are arranged according to the deduced OR: 001 010 / 1120 . (b) Schematic of the superimposed planes of (001)α-Nb2C and (0001)γ-Nb2C. Both the images showing a good match between Nb atoms of both the phases.

ACCEPTED MANUSCRIPT

Nb C ↔ N b+NbC---(2 2 )

50000

activ ity

2Nb C 2 + Z r ↔ 3N b of N +NbC+ bC + ZrC---( 3) ZrC for r eact ion ( 3) = 0 .5

SC

40000 30000 20000

M AN U

∆G (J/mole)

RI PT

60000

0.4

10000

0. 3

0

Nb C+Zr ↔ 2Nb+ ZrC ---(1) 2

TE D

-10000 -20000 -30000

0. 1

EP

-40000

0.2

0

200

AC C

-50000 400

600

800

1000

1200

1400

1600

o

Temperature ( C)

Fig.14. Free energy versus temperature plot of NbC and ZrC phases formed from Nb2C through different possible reactions. Free energy variation for the reaction.(3) at different activities of NbC+ZrC is also given in the figure.

ACCEPTED MANUSCRIPT

(a)

Nb

M AN U

SC

RI PT

(b)

TE D

NbC

Interface

Nb

AC C

EP

NbC

1.5 nm

Fig.15. (a) HAADF micrograph of the carbide particle showing the presence high concentration of Zr at the interface. (b) HRTEM micrograph of the interface between spherical morphology of (Nb,Zr)C carbide and Nb matrix along [101] and [111] orientation of carbide particle and matrix, respectively showing the presence of incoherent interface between them. Due to segregation of Zr, interface appears wider in the HREM image.

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

2 nm

Fig.16. HREM micrograph of the interface between needle morphology of (Nb,Zr)C carbide and Nb matrix showing the presence of coherent interface. The view of HREM is along the [110] zone axis of NbC which is parallel to [100] zone axis of the Nb matrix.

ACCEPTED MANUSCRIPT

(a)

(b)

RI PT

Habit plane 013

growth direction // 221

110

BCC-Nb

FCC-NbC

AC C

EP

TE D

001

M AN U

SC

031

// 114

110

Nb atoms in NbC C atoms in NbC Nb atoms in Nb

Nb

NbC

Fig.17. (a) Schematic picture of the Nb and NbC structures arranged according to established OR 001 // 001 , 110 // 100 between them and showing the occupancy of carbon atoms in edge and face centered octahedral voids in bcc Nb structure. (b) Schematic representation of the superimposed planes of Nb 013 and NbC 114 , a good matching of Nb atoms of two phases has been noticed.