Composition Dependence of Lattice Parameter, Thermal and Electrical Properties in ZrCx Compounds

Hiroyuki Nakayama1,*, Kimihiro Ozaki1, Takuji Nabeta2 and Yasushi Nakajima2

1Magnetic Powder Metallurgy Research Center (Mag Met), National Institute of Advanced Industrial Science and Technology (AIST), Nagoya 463–8560, Japan2Daiichi Kigenso Kagaku Kogyo Co. Ltd., Osaka 559–0025, Japan

The lattice parameter, thermal conductivity and electrical resistivity in off-stoichiometric ZrCx compounds were investigated and com-pared with previous research results. The change in the lattice constant as a function of carbon content in the present study was clearly different compared to results from previous studies. In the present study, the lattice constant decreased with the decrease in carbon content. In contrast, the lattice constant exhibited a maximum value at x =  0.8 in the previous studies. Moreover, the lattice constants obtained in this study were smaller than that of the previous studies at the same carbon contents. The changes in the thermal and electric properties as a function of carbon content and temperature exhibited the same trends in the present and previous studies. However, the values of the thermal conductivity at the same carbon content were different. The values in the present study were higher than those of the previous studies. [doi:10.2320/matertrans.M2016283]

(Received August 18, 2016; Accepted March 10, 2017; Published April 14, 2017)

Keywords:　 pulsed current sintering, thermal conductivity, electrical resistivity, vacancy

1.　 Introduction

Zirconium carbide (ZrC) exhibits a high melting tempera-ture (3700 K)1), high hardness (25.5 GPa), low electrical re-sistivity (45  ±  10  ×  10−6 Ωcm) and thermal conductivity (20.5 W/m K) at around stoichiometric composition of ZrCx (x <  1), and high chemical resistance to acids2). Hence, ZrC is a candidate for applications of thermal barrier coatings and cutting tools. Moreover, ZrC is an interesting material from the viewpoints of metallography and crystallography. ZrC has a NaCl (B1) structure with wide composition ranges on the Zr-rich side between ZrC0.55 to ZrC0.99

1). Although there are signi�cant defects due to carbon de�ciency, it is well-known that these defects can strongly affect the thermal and electrical properties in the conductive material. Therefore, in the ZrC phase, the effect of carbon de�ciency on the lattice parameter, thermal and electrical conductivities was investi-gated several decades ago3–14). Recently, however, continued research of the basic properties in ZrC has not been conduct-ed; thus, the property data of ZrC measured from the 1960s to the 1970s are still used, and these data have wide distribu-tions, even at the same composition15,16). Hence, in this study, we reinvestigate the lattice parameter, electrical and thermal properties of ZrC and compare them with the previous data.

2.　 Experimental Procedure

Zirconium carbide powders supplied from Daiichi Kigenso Kagaku Kogyou Co., Ltd. were used in this study. The sup-plied ZrC contained a free carbon; thus the actual composi-tion of the powder was ZrC1.07. For the fabrication of off-stoi-chiometric ZrC compounds, the ZrC powder was manually mixed with pure zirconium powder using an agate mortar. The powder mixture was sintered at 2073 K for 600 s under an 80 MPa uniaxial pressure in a vacuum using a pulsed cur-rent sintering method. For sintering, a carbon mold (ϕ30 × 

ϕ10 ×  h30 mm) and punches (ϕ10 ×  h20 mm) were used. The temperature was monitored at the surface of the mold using a radiation thermometer. Crystalline analysis of the sintered ZrC was performed by X-ray diffraction (XRD) using Cu Kα1 radiation. Microstructural observation was carried out using scanning electron microscopy (SEM). The electrical re-sistivity of the samples was measured by the four-terminal method at ambient temperature and the four-probe DC tech-nique in the temperature range of 300 K to 750 K under a He atmosphere. The thermal conductivity of the samples was measured by the laser �ash method in the temperature range of 323 K to 523 K in air. The specimen dimensions were ϕ10 mm with thickness of 1–2 mm. For the reference materi-al, alumina or Inconel was used. The carbon and oxygen con-tent of the sintered samples was measured using a carbon and oxygen analyzer, respectively.

3.　 Results and Discussion

The sample compositions used in this study are listed in the Table 1. The impurity of oxygen was detected. Other impuri-ties of nitrogen and metal elements were below the detection limits with the instrument used.

Figure 1 shows the change in XRD patterns with various compositions. The source ZrC powder showed the peaks for

* Corresponding author, E-mail: hiro-nakayama@aist.go.jp

Table 1　Carbon and oxygen content of the ZrCx compounds.

Sample C (mass%) O (mass%) Comment

ZrC0.82 9.71 not measured with free carbon

ZrC0.74 8.84 0.67

ZrC0.61 7.47 not measured

ZrC0.52 6.41 0.38

ZrC0.42 5.26 0.42 with Zr

ZrC0.41 5.06 not measured with Zr

- Nitrogen : < 20 ppm- Metallic impurity : < 0.5 at%

Materials Transactions, Vol. 58, No. 6 (2017) pp. 852 to 856 ©2017 The Japan Institute of Metals and Materials

ZrC phase and graphite because the composition of source powder was carbon-rich ZrC1.07. In the sintered samples, the carbon peak disappeared by decreasing the carbon content. The added pure Zr compensated the free-carbon and formed the ZrC phase during sintering; however, small peaks for Zr oxide (ZrO2) appeared. The excess addition of Zr led to an exclusive Zr phase in the sample with x =  0.41.

The change in the lattice parameter of the sintered samples is plotted as a function of carbon content as shown in Fig. 2. The lattice parameters were calculated from the peak posi-tions of the XRD patterns. For the calibration of the peak po-sitions, pure Si was used. As a comparison, the previous data are plotted by open symbols11–14,17). In the present case, the lattice parameter decreased linearly with a decrease in the carbon content of the ZrC samples without a coexisting of carbon or zirconium phase. The relationship between the lat-tice parameter, a, and the ZrCx composition, x, is expressed by:

a = 4.620 + 0.084x (1)

The sample containing free carbon exhibited a departure from the regression line. This suggested that the actual ZrC composition was more Zr-rich in these samples. The change in the lattice parameter of the present study exhibited a dis-tinctly different trend compared with the previous results. In the previous study, the lattice parameter exhibited a maxi-mum at around x  =  0.8 and gradually decreased thereafter with a decrease in the carbon content. Moreover, the lattice parameters were larger than that of the present study at the same carbon content. However, in the case of titanium car-bide, which is also a transition metal group IV carbide and has the same crystal structure as the ZrC phase, the change in the lattice constant exhibited a similar trend with that in the present study, i.e., the lattice constant decreased with a de-crease in the carbon content18,19). Hence, the linear decrease in the lattice constant observed in this study seemed to be reasonable result. The reason for the difference of the lattice constant between the present and previous studies was pre-sumed to be due to the amount of the impurities in the ZrC phases. In fact, the previously reported ZrC0.75 contained 8100 ppm oxygen and 1.4 mass% sulfur with a lattice param-eter of 4.715 Å14). The ZrCx compounds used in this study (Table 1) contained lower oxygen level comparing to the above mentioned sample. However, the oxygen level of the several previous samples was lower than that of this study14). Hence, to verify the cause for this discrepancy, the further investigation would be required.

The SEM images of the sintered ZrC with various compo-sitions are shown in Fig. 3. The free carbons originally con-tained in the source powders are seen in (a). The free carbon disappeared in (b)–(d) due to the formation of the ZrC phase by the reaction of carbon and added Zr. In addition, the grain size of the sintered ZrC increased with a decrease in the car-bon content, x. This increase indicated the increase in the self-diffusion rate of the ZrC phase due to the introduction of carbon vacancies and the decrease in the melting point of ZrC. The excess Zr phases were observed, as indicated by arrows, at the grain boundary and triple junction of ZrC in the

Fig. 2　Change in the lattice parameter of ZrCx as a function of carbon con-tent. The previous reported parameters are potted by open symbols.

Fig. 1　(a) XRD results of the ZrCx compounds. (b) is an enlarged view of (a).

853Composition Dependence of Lattice Parameter, Thermal and Electrical Properties in ZrCx Compounds

sample with x =  0.41.The change in the electrical resistivity at room temperature

as a function of composition is shown in Fig. 4. Here, the compositions of samples with coexisting carbon or Zr were corrected to the actual ZrC compositions using eq. (1). The dotted line is the empirical �tting of a previous study at room temperature derived by Storms and Wagner14).

ρ = 1/ 0.00382 +1

(55 + 950(1 − x)) (2)

In the present study, the electrical resistivity rapidly in-creased with a decrease in the carbon content. It can be in-ferred that carbon de�ciency, i.e., carbon vacancy, affected the electron transport properties. This trend agrees with that found in previous research.

Figure 5 shows the temperature dependence of the electri-cal resistivity in ZrC0.61. The temperature dependence of the resistivity is linearly �tted here, similar to the previous re-

ports7). In previous research, the linear dependence in the near stoichiometric ZrC0.93 was �tted as follows:

ρ = 0.437 + 0.00073T (3)

and, in the present case (ZrC0.61), the temperature dependence is expressed by:

ρ = 1.658 + 0.00023T (4)

The temperature dependence in the lower carbon content compound was weaker than that in the higher carbon content compound. In previous research, similar results were ob-tained. The temperature dependences of the electrical resis-tivities of ZrC and NbC showed positive correlations, and their gradients became smaller with the decrease in carbon content20,21). This composition dependence of the gradient can be well-explained by Matthiessen’s rule by considering the composition dependence of the carrier concentration20).

The temperature dependence of thermal conductivities in the sintered ZrCx is shown in Fig. 6. In all samples, the ther-

Fig. 3　SEM images of sintered ZrCx for x =  (a) 0.82, (b) 0.74, (c) 0.52, and (d) 0.41.

Fig. 4　Change in the electrical resistivity at room temperature as a function of carbon content. The dotted line is the empirical �tting derived by Storms and Wagner14).

Fig. 5　Temperature dependence of the electrical resistivity in ZrC0.61. As a comparison, the temperature dependence in ZrC0.93 is also shown.

Fig. 6　Temperature dependence of the thermal conductivity in ZrCx. For the reference material, alumina or Inconel was used.

854 H. Nakayama, K. Ozaki, T. Nabeta and Y. Nakajima

mal conductivity increased with the increase in temperature and decreased with the decrease in carbon content. The tem-perature dependence exhibited a typical semi-metallic behav-ior, and the trend agrees with previous research and band cal-culations12,22).

Figure 7 is a plot of the thermal conductivity at room tem-perature as a function of carbon content. To consider the in-�uence of oxygen impurity, the thermal conductivities of ZrC0.74, ZrC0.52 and ZrC0.42 were replotted to the Zr(C+O)x by open triangles with arrows, because the oxygen impurity re-sides on a carbon vacancy14). For a comparison, plots ob-tained from previous research are also shown14). From the �gure, it is clear that the oxygen impurity shifts the thermal conductivity to the higher x value. However, this in�uence becomes small with decrease in carbon content. In the lower carbon region (x <  0.52), the thermal conductivity is almost constant; thus the apparent oxygen effect is not observed. This means that oxygen in�uence of the sample with lower carbon content is negligible in this study. In previous re-search, the thermal conductivity rapidly decreased from a stoichiometric composition and later became saturated by a decrease in the carbon content. This tendency is in agreement with the present data. However, the present study exhibited a higher conductivity than previous research at the same ZrC composition. In the samples of previous research, the relative densities of the samples were low (ρ: 75–98%)14). Hence, po-rosity correction was carried out. In contrast, the relative den-sities of the present studies were more than 98% as estimated from image analysis; thus, porosity corrections were not car-ried out, and the raw values were used. The high-density specimens would show more intrinsic properties of the ther-mal conductivity. Therefore, there is a possibility that the ac-tual thermal conductivities of the ZrC were slightly higher than that of previous reports. The smaller thermal conductiv-ities in the previous studies might be due to the impurity of the sintered samples as inferred from the lattice constant (Fig. 2). However, the detailed reason has not been clari�ed.

The thermal conductivity, κ, is given by the simple sum of electronic contribution, κe, and lattice contribution, κph, κ = 

κe +  κph. The κe can be estimated using the Wiedemann-Franz law:

κe =L0

ρT (5)

where L0 is the Lorenz number, ρ is the electrical resistivity, T is the absolute temperature, and e is the elementary electric charge. Using eq. (5) and Fig. 4, the thermal conductivities in Fig. 7 can be divided into κe and κph as shown in Fig. 8. The theoretical Lorenz number is 2.44 ×  10−8 (V/K)2. However, in actual materials, the number varies from the theory. In this study, the actual Lorenz number was not clear, thus the theo-retical value was used and the calculated κe and κph were not precise for showing a qualitative composition dependence. For comparison, the previously reported thermal conductivity was also divided into κe and κph using eqs. (2), (5), and Ref. 14), and the empirical �tting for κph is expressed as fol-lows:

κph =0.82

(1 − x)0.9x < 1 (6)

In the present study, κe decreased with the decrease in car-bon content for x >  0.6, and then it became saturated. On the other hand, κph showed a rather modest dependence of the carbon content as compared to κe. κph gradually decreased with the decrease in carbon content. This suggested that the change in κe was dominant in the composition dependence of κ for x >  0.6. In a previous report, κe and κph gradually de-creased in the 0.6 <  x <  0.8 region, and these values were comparable to or smaller than those of the present study. However, rapid decreases of κe and κph were observed in the near stoichiometric region (x >  0.9). First principle calcula-tions revealed that carbon vacancies were stable in the carbon de�cient ZrC23). Hence, from the present and previous stud-ies, carbon vacancies appeared to affect κe and κph around the stoichiometric composition, but the introduction of a large amount of vacancies had little in�uence on the κe and κph.

Fig. 7　Change in the thermal conductivity of ZrCx at room temperature as a function of carbon content. The compositions of samples with coexisting carbon or Zr were corrected to the actual ZrC compositions using eq. (1).

Fig. 8　Electronic (κe), and lattice (κph) contributions of the thermal conduc-tivity as a function of carbon content at room temperature. The broken line is κph calculated from eq. (6), and the dashed line is κe calculated from eqs. (2) and (5).

855Composition Dependence of Lattice Parameter, Thermal and Electrical Properties in ZrCx Compounds

4.　 Conclusions

The thermal and electrical properties in off-stoichiometric ZrCx were investigated and compared with data from previ-ous reports. The lattice constant decreased lineally with the decrease in carbon content. This trend was different from that reported in previous studies. In the previous reports, the lat-tice constant exhibited a maximum at around x =  0.8. In addi-tion, the lattice constants observed in this study were smaller than those of the previous studies at the same carbon content. The electrical resistivity showed a linear temperature depen-dence, as previously reported. The qualitative changes in the electrical and thermal conductivities as functions of carbon content and temperature exhibited the same tendencies as that shown in previous research. However, the thermal conductiv-ity observed in this study was higher than that from previous research at the same carbon composition. One of the reasons for these observed differences could be the amount of impu-rity presumed in the ZrC phase. However, this reason behind this discrepancy was not veri�ed in this study; hence, further investigation is warranted.

REFERENCES

1) P. Villars, editor-in-chief; H. Okamoto and K. Cenzual, section editors, ASM Alloy Phase Diagrams Database, http://www1.asminternational.org/AsmEnterprise/APD, ASM International, Materials Park, OH, (2006).

2) Hugh O. Pierson, Handbook of refractory carbides and nitrides (prop-

erties, characteristics, processing and application), Chapter 4 (1996). 3) L.N. Grossman: J. Am. Ceram. Soc. 48 (1965) 236–242. 4) C.H. Hinrichs, M.H. Hinrichs and W.A. Mackie: J. Appl. Phys. 68

(1990) 3401–3404. 5) F.A. Modine, M.D. Foegelle, C.B. Finch and C.Y. Allison: Phys. Rev. B

40 (1989) 9558–9564. 6) L.G. Radosevich and W.S. Williams: Phys. Rev. 181 (1969) 1110–

1117. 7) R.E. Taylor: J. Am. Ceram. Soc. 45 (1962) 353–354. 8) E.K. Storms and P. Wagner: High Temp. Sci. 5 (1973) 454–462. 9) M.M. Mebed, R.P. Yurchak and L.A. Korolev: High Temperature 11

(1973) 380–381. 10) V.B. Fedorov and I.N. Aleinikov: High Temperature 9 (1972) 984–985. 11) R.V. Sara: J. Am. Ceram. Soc. 48 (1965) 243–247. 12) B.H. Morrison and L.L. Sturgess: Rev. Int. Hautes Tempér. et Réfract.

7 (1970) 351–358. 13) E.K. Storms and J. Grif�n: High Temp. Sci. 5 (1973) 291–310. 14) E.K. Storms and P. Wagner: High Temp. Sci. 5 (1973) 454–462. 15) W.S. Williams: JOM 50 (1998) 62–66. 16) Y. Katoh, G. Vasudevamurthy, T. Nozawa and L.L. Snead: J. Nucl. Ma-

ter. 441 (2013) 718–742. 17) Powder diffraction �le #01-071-5535. 18) Y.X. Li, J.D. Hu, H.Y. Wang, Z.X. Guo and A.N. Chumakov: Mater.

Sci. Eng. A 458 (2007) 235–239. 19) R. Chaim, L. Kleiner and S. Kalabukhov: Mater. Chem. Phys. 130

(2011) 815–821. 20) W. S. Williams, “Progress in Solid State Chemistry,” 6 (1971) Chapter

3. 21) Y. Ishizawa, S. Otani, H. Nozaki and T. Tanaka: J. Phys. Condens. Mat-

ter 4 (1992) 8593–8598. 22) H. Ihara, M. Hirabayashi and H. Nakagawa: Phys. Rev. B 14 (1976)

1707–1714. 23) S. Kim, I. Szlufarska and D. Morgan: J. Appl. Phys. 107 (2010) 053521.

856 H. Nakayama, K. Ozaki, T. Nabeta and Y. Nakajima