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Equation of state of cubic hafnium(IV) nitride having Th3P4 -type structure
Solid State Communications 139 (2006) 255–258 www.elsevier.com/locate/ssc
Equation of state of cubic hafnium(IV) nitride having Th3P4-type structure Dmytro A. Dzivenko a,∗ , Andreas Zerr a,b , Reinhard Boehler c , Ralf Riedel a a Fachbereich Material- und Geowissenschaften, Technische Universit¨at Darmstadt, D-64287 Darmstadt, Germany b LPMTM-CNRS, Universit´e Paris Nord, F-93430 Villetaneuse, France c Max-Planck-Institut f¨ur Chemie, Saarstraße 23, D-55122, Mainz, Germany
Received 22 March 2006; accepted 14 June 2006 by C.H.R. Thomsen Available online 28 June 2006
Abstract Pressure dependence of the specific volume, V (P), of the recently discovered high-pressure compound Hf3 N4 having cubic Th3 P4 -type structure (c-Hf3 N4 ) has been measured at room temperature up to 43.9 GPa in a diamond anvil cell using energy-dispersive X-ray powder diffraction combined with synchrotron radiation. A least-square fit of the Birch–Murnaghan equation of state to the experimental V (P)-data yielded for c-Hf3 N4 the bulk modulus of B0 = 227 (7) GPa and its first pressure derivative of B00 = 5.3 (6). For B00 fixed at 4 the bulk modulus of c-Hf3 N4 was determined to be B0 = 241 (2) GPa. The obtained B0 -value is only insignificantly below that estimated in preliminary measurements. Existing theoretical predictions for B0 scatter around the present experimental data. The observation of a high bulk modulus of c-Hf3 N4 supports the suggestion that this compound could have high hardness. c 2006 Elsevier Ltd. All rights reserved.
PACS: 61.10.Eq; 62.20.Dc; 62.50.+p; 64; 64.30.+t Keywords: A. Cubic Hf3 N4 ; C. Bulk modulus; E. High pressure
1. Introduction Mononitrides of the group 4 elements having cubic NaCltype structure, δ-MN (M = Ti, Zr, Hf), are known as stiff and hard materials (Table 1) with high melting temperatures and outstanding chemical and thermal stability. They are used industrially for coating of cutting tools, turbine blades, window glass, etc. Coatings or diffusion layers of the mononitrides improve the products’ properties but also serve for decoration purposes [1]. In contrast to the mononitrides, examination of properties of the recently discovered nitrides of hafnium(IV) and zirconium(IV) with the cubic Th3 P4 -type structure, c-Zr3 N4 and c-Hf3 N4 , is in its infancy. These materials were first synthesized via a chemical reaction of the metals or their mononitrides with molecular nitrogen at high pressures
∗ Corresponding address: Fachgebiet Disperse Feststoffe, Fachbereich Material- und Geowissenschaften, Technische Universit¨at Darmstadt, Petersenstrasse 23, D-64287 Darmstadt, Germany. Tel.: +49 6151 16 6342; fax: +49 6151 16 6346. E-mail address: [email protected] (D.A. Dzivenko).
c 2006 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2006.06.020
and temperatures in a laser heated diamond anvil cell (LHDAC) [2]. The reported synthesis conditions were 18 GPa and 2800 K for c-Hf3 N4 and at 15.6–18 GPa and 2500–3000 K for c-Zr3 N4 . Preliminary measurements of the bulk modulus, B0 , of c-Zr3 N4 and c-Hf3 N4 yielded values of about 250 GPa and 260 GPa, respectively [2]. High values of B0 scattering between 200 and 300 GPa [3–5] were predicted for both compounds in subsequent theoretical calculations (Table 1). From the calculated shear modulus the Vickers hardness of cHf3 N4 was predicted to be about 21 GPa [4]. This value is close to that of β-Si3 N4 (Table 1) the well known hard material with high fracture toughness, wear resistance and thermal stability. More recently thin films of c-Zr3 N4 (about 1.2 µm in thickness) were deposited on carbides using a modified filtered cathodic arc (FCA) method [6]. Moreover, it was found that c-Zr3 N4 exhibits an exceptional wear resistance by milling of low carbon steel: It exceeded by almost one order of magnitude the wear resistance of δ-TiN. The hardness of the c-Zr3 N4 films, measured in that work using the nanoindentation technique with maximum applied load of 5 mN, was found to be about 36 GPa. This value exceeded considerably the nano-hardness of δ-ZrN
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Table 1 Experimental and theoretical values of bulk modulus, its first pressure derivative and hardness for c-Hf3 N4 , c-Zr3 N4 , δ-HfN, δ-ZrN and β-Si3 N4 Phase
B0 (GPa)
B00
Reference
HV (GPa)
This work This work [2] [3] [4] [5]
21.3/18.7c [4]
[2] [3] [4] [5]
19.7/17.5c [4]
36 (5 mN) [6]
Nanohardness (GPa)
c-Hf3 N4
227 (7) 241 (2) 260 283a , 215b 276a , 228b 268a
5.3 (6) 4-fixed 4-fixed
c-Zr3 N4
250 265a , 195b 262a , 218b 251a
4-fixed
δ-HfN
260 306a 313a , 270b
4-fixed
[7] [7] [3]
19.5 (0.49 N) [7] 15.5 (9.8 N) [7] 14.5 (10 N) [8]
25.2 (9 mN) [9] 27.4 (10–19 mN) [10]
δ-ZrN
248 285a
4-fixed
[7] [7]
17.4 (0.49 N) [7] 12.2 (9.8 N) [7] 12.5 (2 N) [11]
27 (5 mN) [6] 26 (2 mN) [12]
β-Si3 N4
233 259 273 (14)
4-fixed
[13] [14] [15]
20 (5 N) [16]
19–35d (4 mN) [17]
6.56
6.75
3.8 (1.6)
For hardness data we give in parentheses the indentation load values. a Theoretical bulk modulus calculated employing the local density approximation (LDA). b Theoretical bulk modulus calculated employing the generalized gradient approximation (GGA). c Estimation based on the assumption of a correlation between Vickers hardness (H ) and elastic shear modulus. The latter was obtained from the LDA/GGA V calculations. d Nanoindentation measurements on the β-Si N whiskers. The values vary due to significant hardness anisotropy of the material [17]. 3 4
films determined using the same technique to be 27 GPa [6]. These observations indicated that c-Zr3 N4 and, most probably, c-Hf3 N4 can be potentially used in industry for coating of cutting tools used for machining of ferrous alloys. In the present work we present the first accurate experimental data on the bulk modulus, B0 , and its first pressure derivative, B00 , for c-Hf3 N4 . The values were derived from the pressure dependence of its specific volume, V (P), measured to 43.9 GPa. Measurements were performed at quasihydrostatic load conditions in a diamond anvil cell (DAC) in combination with energy dispersive X-ray powder diffraction and synchrotron radiation. 2. Experimental details Similarly to the earlier work [2], the sample material was synthesized in a LH-DAC via a chemical reaction of hafnium mononitride, HfN (99%, Chempur), with molecular nitrogen at high pressures and temperatures: A platelet of the compacted mononitride powder, isolated from the lower diamond anvil by a thin layer of NaCl, was embedded in the nitrogen pressure medium, squeezed to about 19 GPa and heated up to 2850 K with the radiation of a Nd:YLF laser (wavelength λ = 1.053 µm, Quantronix 217D, continuous-wave, maximum power 55 W). After synthesis the polycrystalline sample of cHf3 N4 was recovered from the DAC, washed by dissolving NaCl in distilled water, and loaded again in a DAC for compression measurements. In the compression measurements we employed a DAC with bevelled anvils having culets of 350 µm in diameter. The
sample and the pressure transmitting medium were loaded in a hole in the preindented stainless steel gasket, which diameter decreased from initially ∼100 to ∼80 µm at the maximal pressure. As a quasi-hydrostatic pressure transmitting medium we used argon, which solidifies above 1.2 GPa e.g. [18,19]. The earlier measured equation of state of crystalline argon [19] was used to determine pressure. Samples were compressed in this work up to 43.9 GPa. The specific volumes of c-Hf3 N4 and of argon at high pressures were derived from the energy dispersive X-ray diffraction (EDXD) patterns, measured using polychromatic synchrotron radiation on the beamline F3 at the HASYLAB (DESY, Hamburg, Germany). In order to avoid diffraction from the gasket, the X-ray beam was collimated to 40×40 µm2 at lower and up to 30×30 µm2 at higher pressures. The EDXD-patterns were collected at the diffraction angles, 2θ, around 9◦ in the energy range from 13 to 63 keV using a Gedetector (IGP-25, Princeton Gamma-Tech) with tungsten slits open to 200 µm. The full-width-at-half-maximum resolution of the detector was about 120 eV. 3. Results and discussion At ambient and at high pressures we observed up to eight diffraction peaks for c-Hf3 N4 , namely (211), (220), (310), (321), (420), (332), (422) and (510). For crystalline argon we detected up to four peaks, (111), (200), (220) and (311). On compression, the intensities of the diffraction peaks of both c-Hf3 N4 and argon were affected by texture. Fig. 1 shows two EDXD-patterns measured at 11.1 GPa and 39.4 GPa. In comparing the patterns one should bear in mind that they were
D.A. Dzivenko et al. / Solid State Communications 139 (2006) 255–258
Fig. 1. EDXD-patterns of c-Hf3 N4 measured at 11.1 GPa and 39.4 GPa at the diffraction angles of 8.92◦ and 8.85◦ , respectively. K α2 - and K α1 - fluorescence peaks of hafnium at 54.61 and 55.79 keV (H) and of tungsten (the detector slits material) at 57.98 and 59.32 keV () were observed in all patterns. A broad peak ( ) is due to the diffraction from the gasket material. The (400) diffraction peak of c-Hf3 N4 was not observable due to the texture.
measured at diffraction angles of 8.92◦ and 8.85◦ , respectively. In the EDXD-patterns we observed also the K α2 - and K α1 fluorescence peaks of hafnium at 54.61 and 55.79 keV and of tungsten (the detector slits material) at 57.98 and 59.32 keV. A broad peak around 43 keV was due to the diffraction from the gasket material. By calculation of the specific volumes, the diffraction peaks of argon and of c-Hf3 N4 overlapping on increasing pressure with each other or with the X-ray fluorescence peaks were discarded from consideration. The lattice parameter of c-Hf3 N4 at ambient conditions was found ˚ [2]. In the present in earlier work to be a0 = 6.701 (6) A ˚ in good experiments a0 was determined to be 6.707 (9) A, agreement with the previous result. Accordingly, the latter value was used in our calculations to determine the ratios V /V0 , where V and V0 are the specific volumes of c-Hf3 N4 at high and ambient pressure, respectively. The results of our compression measurements on c-Hf3 N4 are shown in Fig. 2. As the uncertainty in the V /V0 -ratios of c-Hf3 N4 we chose their maximum difference for the observed diffraction peaks. Similarly, the pressure uncertainties correspond to the maximum difference in the pressure values calculated for each diffraction peak of argon. This was necessary because argon exhibits a significant elastic anisotropy on compression [20]. A small change of the specific volume by about 12% at the maximum pressure of 43.9 GPa indicated a high bulk modulus of c-Hf3 N4 . From the least-squares fit of the third-order Birch–Murnaghan equation of state (EOS) [21] −7/3 −5/3 ! 3 V V P = B0 − 2 V0 V0 ( " #) 3 V −2/3 0 × 1 − (4 − B0 ) −1 4 V0 to the experimental data we obtained for c-Hf3 N4 B0 = 227 (7) GPa and B00 = 5.3 (6). In Fig. 2 the result of the fit is represented by a solid line. For the second-order
257
Fig. 2. Relative volume V /V0 of c-Hf3 N4 at high pressures and room temperature. The experimental data are shown by solid squares. The solid line represents the least-squares fit of the third-order Birch–Murnaghan equation of state to the experimental data. The fit yielded B0 = 227 (7) GPa and B00 = 5.3 (6).
Fig. 3. Compression data of c-Hf3 N4 (squares) in terms of normalized pressure F and effective strain f . The solid and dashed lines represent the least-squares fit of the third- and second-order Birch–Murnaghan EOS, respectively.
Birch–Murnaghan EOS, with B00 having been fixed at 4, we obtained B0 = 241 (2) GPa. This value is similar to the previously reported preliminary result of B0 ≈ 260 GPa with B00 also fixed at 4 [2]. In Fig. 3 the experimental data and both fit results are shown on the F( f )-plot, where F = P/(3 f (1 + 2 f )5/2 ) is the normalized pressure, and f = (( V /V0 )−2/3 − 1)/2 the effective strain. The third- and second-order Birch–Murnaghan EOS are presented here by solid and dashed lines, respectively. The intercept of the line with the F-axis yields B0 and the slope corresponds to B00 . This form of representation is, in contrast to the V (P) plot in Fig. 2, very sensitive to the experimental uncertainties. It can be clearly recognised in Fig. 3 that all experimental data points agree, within the experimental uncertainties, with both fit results.
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In Table 1 our experimental data on B0 and B00 of cHf3 N4 are compared with results of earlier measurements and first-principles calculations obtained for both c-Hf3 N4 and c-Zr3 N4 , their mononitrides and for β-Si3 N4 . We also compare the available experimental and theoretical results on hardness of these compounds in Table 1. Since the measured hardness values depend on the applied indentation loads (see e.g. Ref. [22]) we split the collected data in two groups with strongly different load values: In one column we collected the Vickers microhardness data for loads in the Newton region. In the second one we present the so-called nanohardness data obtained for loads in the milli-Newton region. From the comparison of the hardness data for mononitrides of zirconium and hafnium we could expect that the hardness (and possibly wear resistance) of c-Hf3 N4 exceeds that of c-Zr3 N4 . We can further expect that nano- and microhardness of c-Hf3 N4 will significantly surpass that of δ-HfN. The latter follows from the reported considerable difference in nanohardness of c-Zr3 N4 (36 GPa) and δ-ZrN (27 GPa) measured for films deposited with the same technique [6]. As the experimental value of the bulk modulus of cubic Hf3 N4 is close to that of β-silicon nitride the hardness of c-Hf3 N4 could be comparable with or exceed that of β-Si3 N4 . This suggestion could be criticised since the correlation between bulk modulus and hardness is not straightforward and should be applied with care [23–25]. Our suggestion is supported, however, by a similar prediction based on the results of the first-principles calculations where the theoretical elastic shear modulus G of cHf3 N4 was used to estimate its Vickers hardness HV . The later was considered to be more reliable than to correlate hardness with the bulk modulus B0 [4]. Obviously, direct measurements of the hardness of c-Hf3 N4 and/or c-Zr3 N4 with loads in the Newton region are required. But this would be possible only after the successful synthesis of dense macroscopic bodies of these compounds. 4. Conclusion In this work the compressibility of c-Hf3 N4 was measured under quasi-hydrostatic load conditions at pressures up to 43.9 GPa. Measurements were performed in a DAC using energy dispersive X-ray diffraction combined with synchrotron radiation. The obtained bulk modulus B0 = 227 (7) GPa (B00 = 5.3 (6)) or B0 = 241 (2) GPa (with B00 fixed at 4) is only slightly below the preliminary estimated value [2]. Results of the first-principles calculations on B0 of c-Hf3 N4 [3–5] scatter around the present experimental value. The suggestions that c-
Hf3 N4 could exhibit high hardness [2,4] is supported by the observation of a high bulk modulus. Acknowledgements We thank the staff of the HASYLAB (DESY, Hamburg) for technical support. The financial support of the DESY and of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. A.Z. acknowledges the support of the AdolfMesser-Foundation. References [1] W. Lengauer, in: R. Riedel (Ed.), Handbook of Ceramic Hard Materials, Wiley-VCH, Weinheim, 2000, p. 202. [2] A. Zerr, G. Miehe, R. Riedel, Nature Mater. 2 (2003) 185. [3] P. Kroll, Phys. Rev. Lett. 90 (2003) 125501. [4] M. Mattesini, R. Ahuja, B. Johansson, Phys. Rev. B 68 (2003) 184108. [5] J.E. Lowther, Physica B 358 (2005) 72. [6] M. Chhowalla, H.E. Unalan, Nature Mater. 4 (2005) 317. [7] X.J. Chen, V.V. Struzhkin, Z.G. Wu, M. Somayazulu, J. Qian, S. Kung, A.N. Christensen, Y.S. Zhao, R.E. Cohen, H.K. Mao, R.J. Hemley, Proc. Natl. Acad. Sci. USA 102 (2005) 3198. [8] M. Desmaison-Brut, J. Montintin, F. Valin, M. Boncoeur, J. Eur. Ceram. Soc. 13 (1994) 379. [9] H.S. Seo, T.Y. Lee, J.G. Wen, I. Petrov, J.E. Greene, D. Gall, J. Appl. Phys. 96 (2004) 878. [10] H.A. Jehn, U. Kopacz, S. Hofmann, J. Vac. Sci. Technol. A 3 (1985) 2406. [11] N. Alexandre, M. Desmaison-Brut, F. Valin, M. Boncoeur, J. Mater. Sci. 28 (1993) 2385. [12] H. Spillmann, P.R. Willmott, M. Morstein, P.J. Uggowitzer, Appl. Phys. A 73 (2001) 441. [13] H.L. He, T. Sekine, T. Kobayashi, H. Hirosaki, I. Suzuki, Phys. Rev. B 62 (2000) 11412. [14] R. Vogelgesang, M. Grimsditch, J.S. Wallace, Appl. Phys. Lett. 76 (2000) 982. [15] Y.M. Li, M.B. Kruger, J.H. Nguyen, W.A. Caldwell, R. Jeanloz, Solid State Commun. 103 (1997) 107. [16] K. Tsukuma, M. Shimada, M. Koizumi, Am. Ceram. Soc. Bull. 60 (1981) 910. [17] J.C. Hay, E.Y. Sun, G.M. Pharr, P.F. Becher, K.B. Alexander, J. Am. Ceram. Soc. 81 (1998) 2661. [18] P.H. Lahr, W.G. Eversole, J. Chem. Eng. Data 7 (1962) 42. [19] P. Richet, J.A. Xu, H.K. Mao, Phys. Chem. Minerals 16 (1988) 207. [20] A. Zerr, L. Chudinovskikh, L. Zhang, H.-J. Reichmann, R. Boehler, HASYLAB Annual Report, HASYLAB at DESY, Hamburg 1993, p. 650. [21] F. Birch, J. Geophys. Res. 83 (1978) 1257. [22] V. Brazhkin, N. Dubrovinskaia, A. Nicol, N. Novikov, R. Riedel, R. Solozhenko, Y. Zhao, Nature Mater. 3 (2004) 576. [23] D.M. Teter, MRS Bulletin 23 (1998) 22. [24] A. Zerr, R. Riedel, in: R. Riedel (Ed.), Handbook of Ceramic Hard Materials, Wiley-VCH, Weinheim, 2000, p. XLV. [25] V.V. Brazhkin, A.G. Lyapin, R.J. Hemley, Philos. Mag. A 82 (2002) 231.
Equation of state of cubic hafnium(IV) nitride having Th3P4-type structure Dmytro A. Dzivenko a,∗ , Andreas Zerr a,b , Reinhard Boehler c , Ralf Riedel a a Fachbereich Material- und Geowissenschaften, Technische Universit¨at Darmstadt, D-64287 Darmstadt, Germany b LPMTM-CNRS, Universit´e Paris Nord, F-93430 Villetaneuse, France c Max-Planck-Institut f¨ur Chemie, Saarstraße 23, D-55122, Mainz, Germany
Received 22 March 2006; accepted 14 June 2006 by C.H.R. Thomsen Available online 28 June 2006
Abstract Pressure dependence of the specific volume, V (P), of the recently discovered high-pressure compound Hf3 N4 having cubic Th3 P4 -type structure (c-Hf3 N4 ) has been measured at room temperature up to 43.9 GPa in a diamond anvil cell using energy-dispersive X-ray powder diffraction combined with synchrotron radiation. A least-square fit of the Birch–Murnaghan equation of state to the experimental V (P)-data yielded for c-Hf3 N4 the bulk modulus of B0 = 227 (7) GPa and its first pressure derivative of B00 = 5.3 (6). For B00 fixed at 4 the bulk modulus of c-Hf3 N4 was determined to be B0 = 241 (2) GPa. The obtained B0 -value is only insignificantly below that estimated in preliminary measurements. Existing theoretical predictions for B0 scatter around the present experimental data. The observation of a high bulk modulus of c-Hf3 N4 supports the suggestion that this compound could have high hardness. c 2006 Elsevier Ltd. All rights reserved.
PACS: 61.10.Eq; 62.20.Dc; 62.50.+p; 64; 64.30.+t Keywords: A. Cubic Hf3 N4 ; C. Bulk modulus; E. High pressure
1. Introduction Mononitrides of the group 4 elements having cubic NaCltype structure, δ-MN (M = Ti, Zr, Hf), are known as stiff and hard materials (Table 1) with high melting temperatures and outstanding chemical and thermal stability. They are used industrially for coating of cutting tools, turbine blades, window glass, etc. Coatings or diffusion layers of the mononitrides improve the products’ properties but also serve for decoration purposes [1]. In contrast to the mononitrides, examination of properties of the recently discovered nitrides of hafnium(IV) and zirconium(IV) with the cubic Th3 P4 -type structure, c-Zr3 N4 and c-Hf3 N4 , is in its infancy. These materials were first synthesized via a chemical reaction of the metals or their mononitrides with molecular nitrogen at high pressures
∗ Corresponding address: Fachgebiet Disperse Feststoffe, Fachbereich Material- und Geowissenschaften, Technische Universit¨at Darmstadt, Petersenstrasse 23, D-64287 Darmstadt, Germany. Tel.: +49 6151 16 6342; fax: +49 6151 16 6346. E-mail address: [email protected] (D.A. Dzivenko).
c 2006 Elsevier Ltd. All rights reserved. 0038-1098/$ - see front matter doi:10.1016/j.ssc.2006.06.020
and temperatures in a laser heated diamond anvil cell (LHDAC) [2]. The reported synthesis conditions were 18 GPa and 2800 K for c-Hf3 N4 and at 15.6–18 GPa and 2500–3000 K for c-Zr3 N4 . Preliminary measurements of the bulk modulus, B0 , of c-Zr3 N4 and c-Hf3 N4 yielded values of about 250 GPa and 260 GPa, respectively [2]. High values of B0 scattering between 200 and 300 GPa [3–5] were predicted for both compounds in subsequent theoretical calculations (Table 1). From the calculated shear modulus the Vickers hardness of cHf3 N4 was predicted to be about 21 GPa [4]. This value is close to that of β-Si3 N4 (Table 1) the well known hard material with high fracture toughness, wear resistance and thermal stability. More recently thin films of c-Zr3 N4 (about 1.2 µm in thickness) were deposited on carbides using a modified filtered cathodic arc (FCA) method [6]. Moreover, it was found that c-Zr3 N4 exhibits an exceptional wear resistance by milling of low carbon steel: It exceeded by almost one order of magnitude the wear resistance of δ-TiN. The hardness of the c-Zr3 N4 films, measured in that work using the nanoindentation technique with maximum applied load of 5 mN, was found to be about 36 GPa. This value exceeded considerably the nano-hardness of δ-ZrN
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Table 1 Experimental and theoretical values of bulk modulus, its first pressure derivative and hardness for c-Hf3 N4 , c-Zr3 N4 , δ-HfN, δ-ZrN and β-Si3 N4 Phase
B0 (GPa)
B00
Reference
HV (GPa)
This work This work [2] [3] [4] [5]
21.3/18.7c [4]
[2] [3] [4] [5]
19.7/17.5c [4]
36 (5 mN) [6]
Nanohardness (GPa)
c-Hf3 N4
227 (7) 241 (2) 260 283a , 215b 276a , 228b 268a
5.3 (6) 4-fixed 4-fixed
c-Zr3 N4
250 265a , 195b 262a , 218b 251a
4-fixed
δ-HfN
260 306a 313a , 270b
4-fixed
[7] [7] [3]
19.5 (0.49 N) [7] 15.5 (9.8 N) [7] 14.5 (10 N) [8]
25.2 (9 mN) [9] 27.4 (10–19 mN) [10]
δ-ZrN
248 285a
4-fixed
[7] [7]
17.4 (0.49 N) [7] 12.2 (9.8 N) [7] 12.5 (2 N) [11]
27 (5 mN) [6] 26 (2 mN) [12]
β-Si3 N4
233 259 273 (14)
4-fixed
[13] [14] [15]
20 (5 N) [16]
19–35d (4 mN) [17]
6.56
6.75
3.8 (1.6)
For hardness data we give in parentheses the indentation load values. a Theoretical bulk modulus calculated employing the local density approximation (LDA). b Theoretical bulk modulus calculated employing the generalized gradient approximation (GGA). c Estimation based on the assumption of a correlation between Vickers hardness (H ) and elastic shear modulus. The latter was obtained from the LDA/GGA V calculations. d Nanoindentation measurements on the β-Si N whiskers. The values vary due to significant hardness anisotropy of the material [17]. 3 4
films determined using the same technique to be 27 GPa [6]. These observations indicated that c-Zr3 N4 and, most probably, c-Hf3 N4 can be potentially used in industry for coating of cutting tools used for machining of ferrous alloys. In the present work we present the first accurate experimental data on the bulk modulus, B0 , and its first pressure derivative, B00 , for c-Hf3 N4 . The values were derived from the pressure dependence of its specific volume, V (P), measured to 43.9 GPa. Measurements were performed at quasihydrostatic load conditions in a diamond anvil cell (DAC) in combination with energy dispersive X-ray powder diffraction and synchrotron radiation. 2. Experimental details Similarly to the earlier work [2], the sample material was synthesized in a LH-DAC via a chemical reaction of hafnium mononitride, HfN (99%, Chempur), with molecular nitrogen at high pressures and temperatures: A platelet of the compacted mononitride powder, isolated from the lower diamond anvil by a thin layer of NaCl, was embedded in the nitrogen pressure medium, squeezed to about 19 GPa and heated up to 2850 K with the radiation of a Nd:YLF laser (wavelength λ = 1.053 µm, Quantronix 217D, continuous-wave, maximum power 55 W). After synthesis the polycrystalline sample of cHf3 N4 was recovered from the DAC, washed by dissolving NaCl in distilled water, and loaded again in a DAC for compression measurements. In the compression measurements we employed a DAC with bevelled anvils having culets of 350 µm in diameter. The
sample and the pressure transmitting medium were loaded in a hole in the preindented stainless steel gasket, which diameter decreased from initially ∼100 to ∼80 µm at the maximal pressure. As a quasi-hydrostatic pressure transmitting medium we used argon, which solidifies above 1.2 GPa e.g. [18,19]. The earlier measured equation of state of crystalline argon [19] was used to determine pressure. Samples were compressed in this work up to 43.9 GPa. The specific volumes of c-Hf3 N4 and of argon at high pressures were derived from the energy dispersive X-ray diffraction (EDXD) patterns, measured using polychromatic synchrotron radiation on the beamline F3 at the HASYLAB (DESY, Hamburg, Germany). In order to avoid diffraction from the gasket, the X-ray beam was collimated to 40×40 µm2 at lower and up to 30×30 µm2 at higher pressures. The EDXD-patterns were collected at the diffraction angles, 2θ, around 9◦ in the energy range from 13 to 63 keV using a Gedetector (IGP-25, Princeton Gamma-Tech) with tungsten slits open to 200 µm. The full-width-at-half-maximum resolution of the detector was about 120 eV. 3. Results and discussion At ambient and at high pressures we observed up to eight diffraction peaks for c-Hf3 N4 , namely (211), (220), (310), (321), (420), (332), (422) and (510). For crystalline argon we detected up to four peaks, (111), (200), (220) and (311). On compression, the intensities of the diffraction peaks of both c-Hf3 N4 and argon were affected by texture. Fig. 1 shows two EDXD-patterns measured at 11.1 GPa and 39.4 GPa. In comparing the patterns one should bear in mind that they were
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Fig. 1. EDXD-patterns of c-Hf3 N4 measured at 11.1 GPa and 39.4 GPa at the diffraction angles of 8.92◦ and 8.85◦ , respectively. K α2 - and K α1 - fluorescence peaks of hafnium at 54.61 and 55.79 keV (H) and of tungsten (the detector slits material) at 57.98 and 59.32 keV () were observed in all patterns. A broad peak ( ) is due to the diffraction from the gasket material. The (400) diffraction peak of c-Hf3 N4 was not observable due to the texture.
measured at diffraction angles of 8.92◦ and 8.85◦ , respectively. In the EDXD-patterns we observed also the K α2 - and K α1 fluorescence peaks of hafnium at 54.61 and 55.79 keV and of tungsten (the detector slits material) at 57.98 and 59.32 keV. A broad peak around 43 keV was due to the diffraction from the gasket material. By calculation of the specific volumes, the diffraction peaks of argon and of c-Hf3 N4 overlapping on increasing pressure with each other or with the X-ray fluorescence peaks were discarded from consideration. The lattice parameter of c-Hf3 N4 at ambient conditions was found ˚ [2]. In the present in earlier work to be a0 = 6.701 (6) A ˚ in good experiments a0 was determined to be 6.707 (9) A, agreement with the previous result. Accordingly, the latter value was used in our calculations to determine the ratios V /V0 , where V and V0 are the specific volumes of c-Hf3 N4 at high and ambient pressure, respectively. The results of our compression measurements on c-Hf3 N4 are shown in Fig. 2. As the uncertainty in the V /V0 -ratios of c-Hf3 N4 we chose their maximum difference for the observed diffraction peaks. Similarly, the pressure uncertainties correspond to the maximum difference in the pressure values calculated for each diffraction peak of argon. This was necessary because argon exhibits a significant elastic anisotropy on compression [20]. A small change of the specific volume by about 12% at the maximum pressure of 43.9 GPa indicated a high bulk modulus of c-Hf3 N4 . From the least-squares fit of the third-order Birch–Murnaghan equation of state (EOS) [21] −7/3 −5/3 ! 3 V V P = B0 − 2 V0 V0 ( " #) 3 V −2/3 0 × 1 − (4 − B0 ) −1 4 V0 to the experimental data we obtained for c-Hf3 N4 B0 = 227 (7) GPa and B00 = 5.3 (6). In Fig. 2 the result of the fit is represented by a solid line. For the second-order
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Fig. 2. Relative volume V /V0 of c-Hf3 N4 at high pressures and room temperature. The experimental data are shown by solid squares. The solid line represents the least-squares fit of the third-order Birch–Murnaghan equation of state to the experimental data. The fit yielded B0 = 227 (7) GPa and B00 = 5.3 (6).
Fig. 3. Compression data of c-Hf3 N4 (squares) in terms of normalized pressure F and effective strain f . The solid and dashed lines represent the least-squares fit of the third- and second-order Birch–Murnaghan EOS, respectively.
Birch–Murnaghan EOS, with B00 having been fixed at 4, we obtained B0 = 241 (2) GPa. This value is similar to the previously reported preliminary result of B0 ≈ 260 GPa with B00 also fixed at 4 [2]. In Fig. 3 the experimental data and both fit results are shown on the F( f )-plot, where F = P/(3 f (1 + 2 f )5/2 ) is the normalized pressure, and f = (( V /V0 )−2/3 − 1)/2 the effective strain. The third- and second-order Birch–Murnaghan EOS are presented here by solid and dashed lines, respectively. The intercept of the line with the F-axis yields B0 and the slope corresponds to B00 . This form of representation is, in contrast to the V (P) plot in Fig. 2, very sensitive to the experimental uncertainties. It can be clearly recognised in Fig. 3 that all experimental data points agree, within the experimental uncertainties, with both fit results.
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In Table 1 our experimental data on B0 and B00 of cHf3 N4 are compared with results of earlier measurements and first-principles calculations obtained for both c-Hf3 N4 and c-Zr3 N4 , their mononitrides and for β-Si3 N4 . We also compare the available experimental and theoretical results on hardness of these compounds in Table 1. Since the measured hardness values depend on the applied indentation loads (see e.g. Ref. [22]) we split the collected data in two groups with strongly different load values: In one column we collected the Vickers microhardness data for loads in the Newton region. In the second one we present the so-called nanohardness data obtained for loads in the milli-Newton region. From the comparison of the hardness data for mononitrides of zirconium and hafnium we could expect that the hardness (and possibly wear resistance) of c-Hf3 N4 exceeds that of c-Zr3 N4 . We can further expect that nano- and microhardness of c-Hf3 N4 will significantly surpass that of δ-HfN. The latter follows from the reported considerable difference in nanohardness of c-Zr3 N4 (36 GPa) and δ-ZrN (27 GPa) measured for films deposited with the same technique [6]. As the experimental value of the bulk modulus of cubic Hf3 N4 is close to that of β-silicon nitride the hardness of c-Hf3 N4 could be comparable with or exceed that of β-Si3 N4 . This suggestion could be criticised since the correlation between bulk modulus and hardness is not straightforward and should be applied with care [23–25]. Our suggestion is supported, however, by a similar prediction based on the results of the first-principles calculations where the theoretical elastic shear modulus G of cHf3 N4 was used to estimate its Vickers hardness HV . The later was considered to be more reliable than to correlate hardness with the bulk modulus B0 [4]. Obviously, direct measurements of the hardness of c-Hf3 N4 and/or c-Zr3 N4 with loads in the Newton region are required. But this would be possible only after the successful synthesis of dense macroscopic bodies of these compounds. 4. Conclusion In this work the compressibility of c-Hf3 N4 was measured under quasi-hydrostatic load conditions at pressures up to 43.9 GPa. Measurements were performed in a DAC using energy dispersive X-ray diffraction combined with synchrotron radiation. The obtained bulk modulus B0 = 227 (7) GPa (B00 = 5.3 (6)) or B0 = 241 (2) GPa (with B00 fixed at 4) is only slightly below the preliminary estimated value [2]. Results of the first-principles calculations on B0 of c-Hf3 N4 [3–5] scatter around the present experimental value. The suggestions that c-
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