0020-1685/03/3901- $25.00 © 2003

MAIK “Nauka

/Interperiodica”0043

Inorganic Materials, Vol. 39, No. 1, 2003, pp. 43–46. Translated from Neorganicheskie Materialy, Vol. 39, No. 1, 2003, pp. 49–53.Original Russian Text Copyright © 2003 by Gusev, Rempel’.

Nanostructure formation, having a significant effecton the physical properties of solids, is an important lineof research in designing materials for high technology[1]. The greatest advances in nanostructure formationhave been made via crystallization of Fe–Cu–Nb–Si–Band Al–Cr–Ce–M (M = Fe, Co, Ni, Cu) amorphousalloys [2, 3]. In this work, we report the preparation ofa stable nanostructure via decomposition of carbidesolid solutions.

In previous studies of

Zr

1 –

x

Nb

x

C

≡

(ZrC)

1

−

x

(NbC)

x

solid solutions containing less than 5 mol % ZrC, usingelectron microscopy, x-ray microanalysis, laser ioniza-tion mass spectrometry, and x-ray diffraction (XRD) [4,5], we observed for the first time spontaneous surfaceprecipitation of ZrC. Thermodynamic evaluation ofphase equilibria in the ZrC–NbC and Zr–Nb–C systemsand kinetic analysis of ZrC surface segregation in solidsolutions with a low ZrC content indicate that zirco-nium carbide precipitation is a consequence of the low-temperature solid-state decomposition of homoge-neous

(ZrC)

1

−

x

(NbC)

x

solid solutions [4, 5].

In this paper, we discuss the microstructure evolu-tion of decomposing solid solutions

(ZrC)

1 –

x

(NbC)

x

with

x

.

0.5. The solid solutions were prepared bysolid-state reactions in a vacuum of 0.001 Pa usingappropriate mixtures of NbC and ZrC or elementalmixtures. The highest sintering temperature was2300 K in the former case and 2500 K in the latter.

In choosing the temperatures and durations of solid-state sintering, we observed intermediate states accom-panying the formation of

(ZrC)

1 –

x

(NbC)

x

solid solu-tions with

x

.

0.5

. After vacuum sintering for 2 h at1070 K, 3 h at 1270 K, 3 h at 1470 K, 4 h at 1770 K, andfinally 4 h at 2200 K, the XRD pattern showed diffrac-tion peaks from two cubic phases with the

B

1

structure

and lattice parameters

= 0.4669

±

0.0002

nm and

= 0.4500

±

0.0003

nm, which are greater than thatof niobium carbide (0.4468 nm) and smaller than thatof zirconium carbide (0.4692 nm). Thus, sintering ledto partial dissolution of niobium carbide in zirconiumcarbide and, at the same time, of zirconium carbide inniobium carbide. Increasing the sintering duration andtemperature resulted in the formation of

(ZrC)

1 –

x

(NbC)

x

solid solutions with

x

.

0.5

. The XRD patterns of thesesolid solutions contained no split reflections.

The synthesized solid solutions (ZrC)

0.46

(NbC)

0.54

and (ZrC)

0.48

(NbC)

0.52

were vacuum-annealed at2300 K for 1 h and then cooled to 1300 K in 5 min andto 600 K in 3 h. The XRD patterns of the resultant mate-rials showed very broad reflections which could beindexed in the

B

1

structure with

a

B

1

= 0.4571 and0.4576 nm, respectively. As an example, Fig. 1 displaysthe XRD pattern of (ZrC)

0.46

(NbC)

0.54

. The diffractionpeaks, including those at large angles, are seen to beunsplit. To clarify why the reflections were unsplit, weanalyzed the diffraction profiles using the pseudo-Voi-ght function (linear superposition of Lorentzian andGaussian profiles)

(1)

where

c

is the relative contribution of the Lorentzian;

θ

L

and

θ

G

are parameters of the Lorentzian and Gaussiandistributions, respectively (the second moment of the

aB11( )

aB12( )

V θ( ) cA 1θ θ0–( )2

θL2

---------------------+

1–

=

+ 1 c–( )Aθ θ0–( )2

2θG2

---------------------– ,exp

X-ray Diffraction Study of the Nanostructure Resulting from Decomposition of (ZrC)

1 –

x

(NbC)

x

Solid Solutions

A. I. Gusev and S. V. Rempel’

Institute of Solid-State Chemistry, Ural Division, Russian Academy of Sciences, Pervomaiskaya ul. 91, Yekaterinburg, 620219 Russia

e-mail: gusev@ihim.uran.ru

Received May 6, 2002

Abstract

—Solid-state decomposition of nearly equimolar ZrC–NbC solid solutions was studied by x-ray dif-fraction. The results demonstrate that annealing broadens the diffraction peaks from the solid solutions. Anal-ysis of the peak width as a function of the diffraction angle indicates that the broadening is due to the decom-position of the solid solution into two coherent isostructural (

B

1) phases close in lattice parameter (0.4573 and0.4561 nm) and the formation of nanometer-sized (

.

70 nm) grains. The nanostructure remains stable duringlong-term (100 to 700 h) annealing between 670 and 1270 K.

44

INORGANIC MATERIALS

Vol. 39

No. 1

2003

GUSEV, REMPEL’

Lorentzian is

θ

L

/

, and that of the Gaussian is

θ

G

);

and

A

is an intensity normalizing factor. The resultsindicate that the width of all the diffraction peaks nota-bly exceeds the width of the instrumental profile of thediffractometer.

The observed broadening of diffraction peaks maybe due to chemical inhomogeneity, a small particle size,and lattice distortions. As shown previously [6], thebroadening

β

h

due to the inhomogeneity of an

Ä

1 –

x

Ç

x

solid solution (with

∆

x

varying in the range

x

±

∆

x

) isproportional to

sin

2

θ

/cos

θ

:

(2)

The particle-size contribution to broadening,

β

s

(2

θ

)

≡

2

β

s

(

θ

)

, is related to the average particle (grain, crystal-lite, or domain) size,

L

.

V

−

1/3

(where

V

is the particlevolume), by [7, 8]

(3)

where

K

hkl

is the Scherrer constant, dependent on theparticle shape and Miller indices (for cubic symmetry,

K

hkl

varies from 1 to 1.225, depending on

hkl

), and

λ

isthe wavelength of the diffracted radiation.

The contribution due to lattice distortions is givenby

(4)

where e is the lattice strain, i.e., the uniform strain aver-aged over the crystal [7, 8]. In formulas (2)–(4), β is inangular degrees.

3

βh θ( ) = 2.235 aB1' x( ) x x0=360

πλ h2 k2 l2+ +------------------------------------- θsin

2

θcos------------∆x.

βs θ( )90KhklλπL θcos-------------------,=

βd θ( ) 360/π( )e θ,tan=

Since βh, βs , and βd are proportional to sin2θ/cosθ,, and , respectively, the three contributions

can be separated.The observed full width at half maximum 2∆obs and

second moment θobs of each diffraction peak from(ZrC)0.46(NbC)0.54 and (ZrC)0.48(NbC)0.52 were deter-mined by fitting the diffraction profiles with Eq. (1).The full width at half maximum β of the intrinsic dif-fraction profile can be expressed through 2∆obs or θobs as

β = ≡ 2.235 , where θR

is the second moment of the instrumental profile of thediffractometer for the particular diffraction peak. Theangular dependence θR(θ) was determined in additionalmeasurements on annealed, large-grained materialspossessing no homogeneity range (large grains, insig-nificant lattice strain, and chemical homogeneityensure zero intrinsic broadening): a 6H-SiC singlecrystal and stoichiometric WC.

From the θobs(θ) and θR(θ) data, we found the angu-lar dependence β(θ). Analysis showed that the intrinsicbroadening was dominated by the inhomogeneity andparticle-size contributions, whereas the lattice-straincontribution was negligible. Therefore, the observedbroadening was a superposition of only two factors, βhand βs.

Figure 2 shows the plots of β vs. θ,

sin2θ/( cosθ), and Khkl for(ZrC)0.46(NbC)0.54. Since the intrinsic broadening is dueto two independent mechanisms, it can be found from theconvolution of the profiles related to the inhomogeneity

and particle size of the sample as β = . Our cal-culations demonstrate that the βh and βs contributions are

linear functions of sin2θ/( cosθ) andKhkl , respectively (Figs. 2a, 2b), which confirmsthat other contributions are negligible. Figure 2c showsthe angular dependences of βh and βs and compares theobserved intrinsic broadening β(θ) with the superposi-tion of these contributions. Using the βs and βh data andEqs. (2) and (3), we evaluated the average crystallitesize and inhomogeneity of the (ZrC)0.46(NbC)0.54 solidsolution: L = 70 ± 10 nm, ∆x = 0.041.

These results indicate that the annealed(ZrC)0.46(NbC)0.54 solid solution is an inhomogeneousnanostructured material. Its grains, measuring about70 nm in size, consist of isostructural cubic phases dif-fering in zirconium and niobium contents. In effect, thisnanostructured material is composed of coherent pre-cipitates of two isostructural cubic phases close in com-position: (ZrC)0.42(NbC)0.58 and (ZrC)0.50(NbC)0.50.Indeed, the diffraction peaks from (ZrC)0.46(NbC)0.54are well represented by the sum of two contributionsfrom (ZrC)0.42(NbC)0.58 and (ZrC)0.50(NbC)0.50 (Fig. 3).Similar results were obtained for (ZrC)0.48(NbC)0.52:

θsec θtan

2∆obs( )2 2∆R( )2– θobs2 θR

2–

h2 k2 l2+ + θsec

βh2 βs

2+

h2 k2 l2+ +θsec

20 40 60 80 100 120 140

Inte

nsity

2θ, deg

Fig. 1. XRD pattern of (ZrC)0.46(NbC)0.54 (aB1 = 0.45710 ±0.00005 nm) showing broad diffraction peaks.

INORGANIC MATERIALS Vol. 39 No. 1 2003

X-RAY DIFFRACTION STUDY OF THE NANOSTRUCTURE 45

∆x = 0.039, L . 75 nm. Note that the observed inhomo-geneity of the carbide solid solutions cannot beaccounted for by a nonuniform carbon distributionsince the carbon content of the two materials is close tothe stoichiometric value.

The decomposition of the solid solutions occursrather rapidly, taking slightly more than 3 h. Theabsence of superlattice reflections in the XRD patternstaken after decomposition indicates that the materialsundergo no ordering and that the composition fluctua-tions in the sample bulk are not modulated. This impliesthat the decomposition is not spinodal. The small crys-tallite size and the similar compositions of the resultantphases give grounds to believe that we observe the ini-tial stage of decomposition.

To assess the stability of the phase-separated(ZrC)0.46(NbC)0.54 and (ZrC)0.48(NbC)0.52 materials andexamine the possibility of further decomposition andequilibration of these materials, we carried out a seriesof anneals. Powder samples were annealed in silicatubes pumped down to 0.001 Pa. After annealing, thetube walls were clean, with no deposits. We used sev-eral annealing schedules: (I) 100 h at 1270 K followedby cooling to 670 K at 1 K/h; (II) 700 h at 1070 K;(III) 100 h at 870 K followed by heating to 970 K andannealing for another 100 h; (IV) 100 h at 670 K. Afterannealing at 1270, 1070, 870, and 670 K, the powdersshowed a deeper black coloration, but detailed chemi-cal analyses revealed no compositional changes.

The XRD patterns of the annealed solid solutionsdiffered little from those taken before annealing. Thesplitting of diffraction peaks, which might be inter-preted as evidence of further phase separation and theformation of two phases differing markedly in ZrC andNbC contents, was not detected. At the same time,annealing led to a minor increase in the width of thereflections, which could be attributed to a slightly stron-ger phase separation.

Thus, the results of long-term (100 to 700 h) anneal-ing in the range 670–1270 K demonstrate that thephase-separated state of the solid solutions with ∆x .0.5 is stable under the conditions examined. This exper-imental finding confirms the theoretical prediction thatZrC–NbC solid solutions must decompose [4, 9] andprovides insight into the real microstructure of thephase-separated solid solutions. In our experiments, wecould not determine the highest temperature at whichthe decomposition of the solid solution occurs. It seemslikely that the decomposition temperature is somewhathigher than the 1210 K predicted theoretically [9] andexceeds 1270 K. To accurately determine the highestdecomposition temperature, additional experimentalstudies are needed.

The Zr–Nb system is analogous to the pseudobinarycarbide system ZrC–NbC in that it also contains aregion of solid-state phase separation (T < 1260 K)[10−14]; that is, these systems are similar in low-tem-perature phase equilibria. It is reasonable to assume

0.1

10

0.1

1

0.1

0.1

0.2

0.3

0.4

0.2 0.3

β, deg

sin2θ/[(h2 + k2 + l2)1/2cosθ]

βobs

βh

(a)

(b)

(c)

βobs

βs

Khklsecθ2

0.2

0.3

0.4

βobs

θ, deg

0.2

0.3

0.4

20 30 40 50 60

βh

β = (βh2 + βs

2)1/2

βs

Fig. 2. Separation of contributions to the width of diffrac-tion peaks from the (ZrC)0.46(NbC)0.54 solid solution:

(a) plot of βobs vs. sin2θ/( cosθ) and the con-tribution of chemical inhomogeneity βh; (b) plot of βobs vs.

Khkl and the particle-size contribution βs; (c) plots ofβobs , βs, and βh vs. diffraction angle θ and comparison of

βobs with β = .

h2

k2

l2

+ +

θsec

βh2 βs

2+

46

INORGANIC MATERIALS Vol. 39 No. 1 2003

GUSEV, REMPEL’

that the decomposition of ZrC–NbC solid solutions isinherently related to the decomposition of Zr–Nb solu-tions. This implies that metal–metal interactions play aimportant part in the decomposition of ZrC–NbC solidsolutions.

ACKNOWLEDGMENTSThis work was supported by the Russian Foundation

for Basic Research, project no. 01-03-96510.

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polucheniya i svoistva (Nanocrystalline Materials: Prep-aration Techniques and Properties), Yekaterinburg: Ural.Otd. Ross. Akad. Nauk, 1998.

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3. Inoue, A., Preparation and Novel Properties of Nanoc-rystalline and Nanoquasicrystalline Alloys, Nanostruct.Mater., 1995, vol. 6, nos. 1–4, pp. 53–64.

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5. Rempel’, S.V. and Gusev, A.I., Surface Segregation ofZrC from Carbide Solid Solutions, Fiz. Tverd. Tela(S.-Peterburg), 2002, vol. 44, no. 1, pp. 66–71.

6. Gusev, A.I., Rempel, A.A., and Magerl, A.J., Disorderand Order in Strongly Nonstoichiometric Compounds:Transition Metal Carbides, Nitrides, and Oxides, Berlin:Springer, 2001.

7. Krivoglaz, M.A., Teoriya rasseyaniya rentgenovskikhluchei i teplovykh neitronov real’nymi kristallami (The-ory of X-ray and Thermal Neutron Scattering by RealCrystals), Moscow: Nauka, 1967, pp. 120–124.

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9. Rempel’, S.V. and Gusev, A.I., Phase Equilibria in theTernary System Zr–Nb–C, Zh. Fiz. Khim., 2001, vol. 75,no. 9, pp. 1553–1559.

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12. Abriata, J.P. and Bolcich, J.C., The Nb–Zr (Niobium–Zirconium) System, Bull. Alloy Phase Diagrams, 1982,vol. 3, no. 1, pp. 34–44.

13. Guilermet, A.F., Thermodynamic Analysis of the StablePhases in the Zr–Nb System and Calculation of thePhase Diagram, Z. Metallkd., 1991, vol. 82, no. 6,pp. 478–487.

14. Hari Kumar, K.S., Wollants, P., and Delaey, L., Thermo-dynamic Assessment of the Ti–Zr System and Calcula-tion of the Nb–Ti–Zr Phase Diagram, J. Alloys Compd.,1994, vol. 206, no. 1/2, pp. 121–127.

97 98 99 100

Background line

0.4561 nm

0.4573 nm

0.45706 nmIn

tens

ity

2θ, deg

Fig. 3. Decomposition of the observed 420B1 diffractionpeak from (ZrC)0.46 ± ∆x(NbC)0.54 ± ∆x with ∆x = 0.04 (solidline) into contributions from (ZrC)0.50(NbC)0.50 and(ZrC)0.42(NbC)0.58 (dashed lines).