Photoinduced Phase Transformations in Boron Nitride: New Polytypic

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Photoinduced Phase Transformations in Boron Nitride: New Polytypic Forms of sp3-Bonded (6H- and 30H-) BN Shojiro Komatsu,*,† Kazuaki Kobayashi,‡ Yuhei Sato,§ Daisuke Hirano,| Takuya Nakamura,⊥ Takahiro Nagata,† Toyohiro Chikyo,† Takayuki Watanabe,§ Takeo Takizawa,| Katsumitsu Nakamura,| and Takuya Hashimoto| AdVanced Electric Materials Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan, Computational Materials Science Center, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan, Department of EnVironmental Chemistry and Engineering, Tokyo Institute of Technology, 4259-G1-22, Nagatsuta, Midori-ku, Yokohama-shi, Kanagawa 226-8502, Japan, Graduate School of Integrated Basic Sciences, Nihon UniVersity, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan, and College of Humanities and Sciences, Nihon UniVersity, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan ReceiVed: March 31, 2010

New sp3-bonded polytypic forms of boron nitride (BN), namely, 6H-BN and 30H-BN, were prepared by plasma-assisted chemical vapor deposition (CVD) with an excimer laser at 193 nm being irradiated on the growing film surface. Only the 6H-BN was formed by postdeposition laser irradiation (PDL) of sp2-bonded BN precursor films prepared by plain plasma-assisted CVD. The PDL demonstrated direct photoinduced phase transformation from sp2-bonded BN into denser sp3-bonded BN here. Typical lattice constants a and c for 6H-BN determined by X-ray diffraction were 2.501 Å and 12.45 Å, respectively, while those for 30H-BN were 2.538 Å and 62.61 Å, respectively. The polytypic structures were analyzed in terms of “hexagonality” H and “close-packing” index D, and the “metastability” ∆E estimated by the first principles calculations. Linear relationships were found among the H, D, and ∆E for the polytypes of BN, AlN, and SiC, whose behavior proved to depend on the degree of ionicity in their iono-covalent bonds. The growth mechanism was discussed with regard to the “bond-strength initiative rule”, according to which the local thermodynamics at very early stage of growth should favor the formation of the strongest bond available (e.g., sp2-hybridized bonds in BN). Our conclusion that the ultraviolet laser irradiation induced the structural relaxation of the sp2-bonded “metastable” phase into more stable sp3-bonded phases at relatively lower temperatures (850 °C in our case) and below atmospheric pressure appears to be consistent with the recent pressure-temperature phase diagram of BN. Introduction Boron nitride (BN) is similar to carbon with respect to the crystal structures, i.e., it has hard and dense diamond-like sp3bonded phases as well as soft and white graphitic sp2-bonded phases.1 The dense sp3-bonded structures are prepared under high pressures (approximately a few GPa) and high temperatures, while the sp2-bonded ones are prepared under relatively moderate conditions in both cases of carbon2 and BN.3 Diamond and lonsdaleite (hexagonal diamond) find their counterparts, cubic and wurtzite BN, respectively,1 whereas R- and β-graphite correspond to hexagonal- and rhombohedral- BN, respectively.4 In view of stacking sequence of layers with densely packed sp3bonded atoms, diamond and cubic BN (c-BN) have ABCABC · · · periodicity along 〈111〉, while lonsdaleite and wurtzite BN have ABAB · · · sequence.4 They are classified as 3H (or 3C) and 2H, respectively, according to the Ramsdell notation * To whom correspondence should be addressed. E-mail: [email protected]. † Advanced Electric Materials Center, National Institute for Materials Science. ‡ Computational Materials Science Center, National Institute for Materials Science. § Tokyo Institute of Technology. | Graduate School of Integrated Basic Sciences, Nihon University. ⊥ College of Humanities and Sciences, Nihon University.

of polytypes,5 where 3 and 2 mean the periodicity whereas H and C denote hexagonal and cubic lattices, respectively. Incidentally, the densely packed sp2-bonded hexagonal layers of atoms show the periodic sequence of ABAB · · · in R-graphite, while β-graphite and rhombohedral BN have ABCABC · · · periodicity.4 Here, it should be noted that in hexagonal BN (hBN) the atoms of one layer are located directly above the atoms of adjacent layers with B · · · N contacts different from the R-graphite,4 thus it is more precisely described as AA′AA′ · · · rather than as ABAB · · · . Nevertheless, the above close structural correspondence between carbon and BN does not necessarily mean that the relative thermodynamical stability in the polymorphs is also similar, in opposition to Corrigan and Bundy in constructing their phase diagram of BN.6 That is, while it is recognized experimentally7,8 and theoretically9,10 that graphite is the most stable phase in carbon under the standard condition, sp3-bonded c-BN is now believed to be more stable than sp2-bonded h-BN at an atmospheric pressure and room temperatures.11–14 This implies that the appropriate methods for the growth of sp3bonded BN from vapor phase may be different from those for diamond. It is worth mentioning in the above context that a new 5H polytypic form of sp3-bonded BN (ref 15) was found to grow by chemical vapor deposition (CVD) method16 in which the

10.1021/jp1028728  2010 American Chemical Society Published on Web 07/14/2010

Photoinduced Phase Transformations in Boron Nitride growing film surface was simultaneously irradiated with an excimer laser at 193 nm. The crystal structure of 5H-BN proved to be unique as ABCBC with the space group of P3m1 (ref 17). Its electronic band structure was calculated by the firstprinciples method, and an indirect band gap was found therein.17 The polytypic sp3-bonded BN films were successfully doped as a p-type semiconductor, and a p-type BN/n-type Si heterojunction proved to work as a solar cell recently.18 Here we report newly found sp3-bonded polytypic forms of BN prepared by the plasma-assisted laser CVD (PLCVD) method. We also carried out “postdeposition laser irradiation” (PDL) of sp2-bonded precursor BN films, which were prepared by plain plasma-assisted CVD (PCVD) in advance, in order to elucidate the role of laser irradiation in forming the dense sp3bonded phases of BN. X-ray diffraction (XRD) of the film samples positively indicated photoinduced phase transformation from sp2-bonded BN into sp3-bonded BN. The lattice parameters obtained experimentally here were compared with those by first-principles calculations. The structural metastability of polytypic forms of BN was discussed in detail in comparison with SiC and AlN, in which we introduced the hexagonality H and close-packing index D to help the analysis. The growth mechanism is examined in terms of the “bond-strength initiative rule”, according to which we tried to reconcile the inconsistency between the recent pressure-temperature phase diagram of BN and the usual dominant growth of sp2-bonded BN from vapor phase. Experimental Section The experimental procedure for the deposition of BN films by PLCVD was almost the same as that reported previously19–22 except for some experimental parameters. The ArF excimer laser (193 nm) at the repetition rates of 2, 4, or 10 Hz was irradiated through optics including lenses and an optical attenuator onto the growing film surface of about 5 × 20 mm2 area at the substrate position with a pulse energy of 300 mJ/cm2. The substrate was a Si (100) disk (commercially available from Furuuchi-Kagaku, Japan) with n-type conductivity of 0.02 Ω cm, diameter 2.5 cm, and thickness 0.5 mm. Substrate temperature was kept constant at 850 °C during CVD for 30 min. Plasma gases were Ar 3 SLM (standard liters per minute), B2H6 2.5 sccm (standard cubic centimeters per minute), and NH3 20 sccm, while the process pressure was kept at 10 Torr. Radiofrequency (rf) power of 300 W at 15 MHz was inductively coupled with the plasma, where the rf-power was modulated with a square-wave signal at the same frequency of the laser pulses. The modulated plasma flow, or plasma packets, going down over the substrate surface, was synchronized with the laser-pulses by using computer-generated trigger signals. In the case of PCVD to prepare precursor BN films for the PDL experiments, the experimental conditions were the same as the above PLCVD only with an exception of no laser irradiation on the growing film surface. The conditions for PDL were the same as the corresponding PLCVD with the exception of no source gas (B2H6) for boron supplied, which excluded further deposition of BN. The BN films deposited on the Si substrates by PCVD in advance were used as target (precursor) material herewith. In this case, the modulation frequency of the plasma in PCVD was the same as that in the corresponding PDL. Crystal structures of BN film samples deposited on Si substrates were studied by using a fully computerized film XRD system (Bruker D8 Discover Super Speed) equipped with a “turbo X-ray source” at an acceleration voltage of 50 kV and a

J. Phys. Chem. C, Vol. 114, No. 31, 2010 13177 current of 100 mA. Incident beam optics included a Goebel mirror, a micro slit of 0.3 mm φ, a UBC collimator of 0.1-1.0 mm φ, and a monochromator of Ge (002). Diffracted beam optics consisted of a Hi-Star 2D detector (Bruker) and a scintillation counter. Chemical analyses of the BN films were done by energy dispersive X-ray spectroscopy using the EDAX Genesis, which was coupled with a scanning electron microscope (Keyence VE7800), at an acceleration voltage of 12 kV. As reported previously,16 using a high-purity sintered pyrolytic BN disk (BN N1-grade commercially available from Denka Co., Ltd., Japan) as a standard, the samples proved to have stoichiometric composition sometimes with a trace of oxygen impurity, which was supposed to reside on the surfaces. Results and Discussion New Polytypic Forms of sp3-Bonded BN; 6H- and 30HBN. In Figure 1a,b, XRD patterns for the sample prepared by PCVD at a plasma-modulation frequency of 10 Hz are shown. Patterns a and b were taken in lower and higher 2θ angles, respectively, sharing an overlapped area. From rather noisy and broad peaks that indicate low crystallinity, we picked up the positions of the peaks by referring to the digital data and numbered them (from 1 to 12) as shown in the figure. In the overlapped region, the numbers of the peaks corresponding to those of pattern a are primed in pattern b; XRD peaks are numbered in this way throughout this report. By examining the possibility of sp3-bonded nH-BN polytypes, where n ranges from 2 to 30, we could not find an appropriate one to fit the data. However, as shown in Table 1, a hexagonal unit cell with the lattice constants a ) 2.507 Å and c ) 101.6 Å proved to fit them completely within the error of 1%. This is best understood in terms of a crystal structure consisting of sp2-bonded 30 layers periodic along the c-axis based on the interlayer spacing of h-BN (3.33 Å) (ref 4). The lattice constant a (2.507 Å) is in good agreement with that of h-BN (2.504 Å) (ref 4). The 1.8% elongation of the interlayer spacing (3.387 Å) in this BN in comparison with h-BN seems to be reasonable considering the relatively metastable nature of this PCVD film with low crystallinity. If we are allowed to apply the notation method of Ramsdell5 here too, we may name this “sp2-bonded 30H-BN”. The precursor BN for the PDL was considered as the sp2-bonded 30H-BN consequently. Next we obtained XRD patterns for the sample prepared by PLCVD also at the plasma-modulation frequency of 10 Hz as shown in Figure 2a,b for lower and higher 2θ degrees, respectively. The pattern was totally different from that in Figure 1a,b. There appears to be two kinds of peaks, namely, the sharp and intense peaks (1-4) and the rather noisy and broad peaks (5-14). As will be shown, this is understood as originating from the coexistence of two phases of BN, i.e., sp3-bonded 6H-BN with high crystallinity and sp3-bonded 30H-BN with low crystallinity. As summarized in Table 2a, the whole peaks categorized as noisy and broad ones are consistent with a hexagonal unit cell with lattice constants a ) 2.538 Å and c ) 62.61 Å. This is understood as the 30H polytype of sp3-bonded BN. The interlayer spacing along the c-axis is 2.087 Å, which is in agreement with that of c-BN (2.088 Å) (derived from ref 23). The values of lattice constant a are to be discussed shortly with regard to the degree of close packing. The sharp peaks 1-4 in Figure 2a,b are completely consistent with a hexagonal unit cell with the lattice constants a ) 2.489 Å and c ) 12.44 Å. As shown in Table 2b, this structure is considered as sp3-bonded 6H-BN with regard to the interplane

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Figure 1. XRD patterns for the sample prepared by PCVD at a plasma-modulation frequency of 10 Hz. Patterns a and b were taken in lower and higher 2θ angles, respectively, sharing an overlapped area.

TABLE 1: Analysis of the XRD Patterns Shown in Figure 1 in Terms of the “sp2-Bonded 30H” Structure of BN in Which the Lattice Parameters a and c are 2.5070 and 101.60 Å, Respectively h

k

l

d (Å)

d (Å) (observed)

error (%)

peak

0 0 0 0 0 0 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0

18 20 21 24 34 45 6 19 38 45 50 53

5.6444 5.0800 4.8381 4.2333 2.9882 2.2578 2.1535 2.0116 1.6854 1.5650 1.4836 1.4370

5.6445 5.0392 4.8691 4.2303 2.9923 2.2562 2.1502 2.0128 1.6923 1.5536 1.4865 1.4419

0.00 0.80 -0.64 0.07 -0.14 0.07 0.15 -0.06 -0.41 0.73 -0.20 -0.34

1 2 3 4 5 6′ 7′ 8′ 9 10 11 12

distance of c-BN, where the interplane distance d was 0.65% shorter than that of c-BN. In ideal close-packed structures, the ratio of interplane distance h (h ) c/n, where c is the lattice constant and n is the periodicity along the c-axis in the Ramsdell notation) to the lattice constant a is (2/3)1/2, i.e., 0.8165 (ref 5). The deviation from this value, namely D (%), where D ) 100 [c/(na) (2/3)1/2]/(2/3)1/2, is regarded as an indicator of the degree of elongation (compression) of bonds along the c axis if the sign is plus (minus). For instance, diamond polytypes with n ) 3, 4, 6, 8, 10, which have no stoichiometric (ionic) polarity, show ideally close-packed structures with D ) 0% (ref 16). The only exception is 2H-diamond (lonsdaleite), where D is 0.12%, seemingly indicating its relatively metastable nature.16 However, polytypic compounds having ionic (stoichiometric) polarity such as BN and SiC may exhibit noticeable amounts of D. This is also the case for AlN, as will be discussed. Here we may name D the close packing index.

The D values are summarized in Table 3 for the data obtained here as well as for those calculated by the first-principles studies.24 Returning to the sp3-bonded 6H-BN and 30H-BN prepared by the PLCVD above, the D’s were +2.05% and +0.735%, respectively. Since the bond lengths in sp3-type tetrahedral coordination (and those in sp2-type planar coordination) are intuitively more meaningful, the bond lengths p (Å) are also tabulated in Table 3 (and the following Tables 4, 6, and 7). Generally speaking, since the unit cell is elongated (or compressed) along c-axis in comparison with ideal closepacking, the bond length in the sp3-type tetrahedral coordination is estimated as p ) (1/2)[h + a2/(3h)]; p ) (3/4)h for ideal close-packing where a ) (3/2)1/2h. Herein we assumed that the bond along the c-axis has an equal length with the remaining three bonds in the tetrahedral coordination, which may be strictly an approximation. In the case of sp2-type planar coordination, the bond length was estimated as p ) a/31/2. From the above results it was concluded that the PLCVD yielded a BN film consisting of two new phases of BN, namely, sp3-bonded 6H-BN with high crystallinity and sp3-bonded 30HBN with low crystallinity. In our previous result, sp3-bonded 5H-BN, which had very fine crystallite size (about 100 Å), was found to grow under similar experimental conditions by CVD only with the assistance of laser irradiation on the surface.16 Additional 100 sccm of hydrogen in the CVD process was also a factor different from the present case. Applying plasma in CVD seems to have improved the crystallinity in our present case. According to the first-principles calculations, the difference of thermodynamical stability (heat of formation) among polytypic forms of BN is subtle (a few tens of meV) as shown in Table 4. Hence we may suggest that kinetic factors rather than thermodynamical ones due to the different experimental conditions should have yielded the different polytypic forms here.

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Figure 2. XRD patterns for the sample prepared by PLCVD at a plasma-modulation frequency of 10 Hz. Patterns a and b were taken in lower and higher 2θ angles, respectively, sharing an overlapped area.

TABLE 2: (a) Analysis of the XRD Peaks (Numbers 5-14 in Figure 2) Categorized as Broad and Noisy, Which Was Done in Terms of the “sp3-Bonded 30H” Structure of BN with the Lattice Parameters a ) 2.5375 Å and c ) 62.6130 Å; (b) Analysis of the XRD Peaks (Numbers 1-4 in Figure 2) Categorized as Sharp and Intense, Which Was Done in Terms of the “sp3-Bonded 6H” Structure of BN with the Lattice Parameters a ) 2.4890 Å and c ) 12.444 Å (a) h

k

l

d (Å)

d (Å) (observed)

error (%)

peak

0 0 0 0 0 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0

11 12 15 18 21 6 11 12 13 23

5.6921 5.2178 4.1742 3.4785 2.9816 2.1504 2.0526 2.0277 2.0016 1.7099

5.6949 5.1674 4.1714 3.4797 3.0140 2.1591 2.0500 2.0291 2.0019 1.7022

-0.05 0.96 0.07 -0.03 -1.09 -0.41 0.13 -0.07 -0.01 0.45

5 6 7 8 9 10 11 12 13 14

(b) h

k

l

d (Å)

d (Å) (observed)

error (%)

peak

0 1 1 1

0 0 0 0

4 3 5 6

3.1110 1.9127 1.6294 1.4945

3.1063 1.9096 1.6293 1.5007

0.15 0.16 0.00 -0.41

1 2′ 3 4

Photoinduced Transformation of sp2-Bonded BN into sp3Bonded BN. At the end of the results section, we report that the XRD patterns for the sample prepared by PDL at 10 Hz

demonstrated the transformation of sp2-bonded BN into an sp3bonded one as shown in Figure 3a,b. Similarly to the PLCVD case, the XRD peaks in the figure are attributed to two components, i.e., sharp and intense peaks (1-5) and noisy and broad peaks (6-26). The sharp and intense peaks are in agreement with a hexagonal unit cell with lattice constants a ) 2.4927 Å and c ) 12.544 Å. Similar to the result of PLCVD, this also indicated sp3-bonded 6H-BN, as shown in Table 5a, and for which the D was +2.72% (Table 3). The rest of the peaks with low intensity (6-26) are attributed to a hexagonal unit cell with lattice constants a ) 2.5083 Å and c ) 101.434 Å: this is reasonably considered as the residual precursor BN film, i.e., sp2-bonded 30H-BN (Table 5b). A relatively large value of D (+2.72%) seems to indicate the higher metastability of the film prepared by PDL method, which is a direct transformation of an sp2-bonded phase into an sp3-bonded denser phase by an intense laser at 193 nm. Here we should distinguish two types of metastability; the first type is that of a polytypic structure itself relative to the most stable crystal form in the polytypes (e.g., cubic form in sp3-bonded BN), and the second type means that there remains room for further structural relaxation into a stable arrangement within the framework of the given polytype. In this case of D ) +2.72%, it seems that the both types of metastability contributed to the relatively large value. The second type of metastability in this case is considered to have originated from the coexistence of sp2- and sp3-bonded phases, in which the complexity of the texture to cause internal stress and strain is reasonably expected.

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TABLE 3: Summary of the Structural Data Obtained in This Study in Comparison with Theoretically Predicted Lattice Parameters bonding

structure

synthesis method

c (Å)

a (Å) ∆c1 (%) ∆c2 (%) ∆a1 (%) ∆a2 (%) D (%) p (Å) h (Å) n

sp3 sp3 sp3 sp3 sp3 sp3 sp3 sp3 sp3 sp3

6H 6H 6H 6H 6H 6H(ABCACB) 6H(ABCBCB) 30H 5H 5H(ABCBC)

PDL @ 2 Hz PDL @ 4 Hz PDL @ 10 Hz PLCVD @ 10 Hz [theoretical] [theoretical] PLCVD @ 10 Hz PLCVD @ 10 Hz [theoretical]

12.544 12.453 12.544 12.444 12.496 12.411 12.451 62.613 10.407 10.3490

2.4930 2.5013 2.4927 2.4890 2.4940 2.5220 2.5190 2.5375 2.5280 2.5220

sp2 sp2 sp2 sp2 sp2

30H 30H 30H 30H 30H

PDL @ 2 Hz PDL @4 Hz PDL @ 10 Hz PCVD @ 10 Hz

101.43 101.65 101.43 101.60 101.53

1.07 0.34 1.07 0.27 0.69

0.75 0.02 0.75 -0.06 0.36

0.56

-1.15 -0.82 -1.16 -1.31 -1.11

0.24

-1.03 -0.70 -1.04 -1.19 -0.99

2.71 1.63 2.72 2.05 2.28 0.45 0.89 0.74 0.84 0.51

2.5083 2.5010 2.5083 2.5070 2.5160

1.541 1.540 1.541 1.535 1.539 1.547 1.547 1.558 1.552 1.547

2.091 6 2.076 6 2.091 6 2.074 6 2.083 6 2.069 6 2.075 6 2.087 30 2.081 5 2.070 5

1.448 1.444 1.448 1.447 1.447

3.381 3.388 3.381 3.387 3.384

30 30 30 30 30

TABLE 4: Summary of Thermodynamical Metastability ∆E (Heat of Formation Relative to That for 3H(3C)), Hexagonality H, and Close Packing Index D in Polytypic Forms of sp3-Bonded BNa BN

c (Å)

a (Å)

D (%)

p (Å)

h (Å)

n

∆E (meV)

3H(ABC), 3C 10H(ABCABCABCB) 10H(ABCABCBACB) 6H(ABCACB) 5H(ABCBC) 10H(ABCABCABAB) 4H(ABCB) 10H(ABCBCACBCB) 6H(ABCBCB) 10H(ABCBCBCBCB) 2H(AB) h-BN

6.187 20.659 20.659 12.411 10.349 20.702 8.287 20.739 12.451 20.780 4.164 6.568

2.526 2.524 2.523 2.522 2.522 2.522 2.521 2.520 2.519 2.518 2.516 2.478

-0.01 0.25 0.28 0.45 0.51 0.53 0.65 0.79 0.89 1.07 1.35 62.31

1.547 1.547 1.546 1.547 1.547 1.547 1.547 1.547 1.547 1.548 1.548 1.431

2.062 2.066 2.066 2.069 2.070 2.070 2.072 2.074 2.075 2.078 2.082 3.284

3 10 10 6 5 10 4 10 6 10 2 2

0 12.5 12 20 26 29 31 39 46 57 75 126

3C(exp), 3H(ABC, exp) 30H(exp) 5H(exp) 2H(exp) 6H(exp) h-BN(exp)

6.263 62.613 10.407 4.220 12.440 6.656

2.557 2.538 2.528 2.553 2.500 2.504

0.00 0.74 0.84 1.22 1.57 62.78

1.566 1.558 1.552 1.570 1.539 1.446

2.088 2.087 2.081 2.110 2.073 3.328

3 30 5 2 6 2

H (%) 0 20 20 33 40 40 50 60 67 80 100 0 40 100 33 or 67

a h-BN is an exceptionally sp2-Bonded BN shown here for comparison. The upper 12 rows are for theoretically calculated structures, while the lower 6 rows exhibit experimental data for comparison.

In Table 3, the structural data for samples prepared by PDL at 2 and 4 Hz, whose original patterns are omitted here, are also added. They also proved to have both the highly crystalline sp3-bonded 6H-BN and the remaining sp2-bonded 30H-BN with lattice parameters slightly different from each other. Lattice parameters a and c averaged over the four samples of sp3-bonded 6H-BN are 2.494 Å and 12.50 Å, respectively. Correspondingly, the averaged a and c for sp2-bonded 30H-BN in the four samples are 2.516 Å and 101.5 Å, respectively. Structural data for sp3bonded 5H-BN and 6H-BN, which were optimized by the firstprinciples calculations,24 are also tabulated therein for comparison. It is known that there are only two ways of stacking sequences for 6H-BN, namely, ABCACB and ABCBCB (ref 24). In Table 3, ∆a1 and ∆c1 denote the deviation of observed values from theoretically predicted a and c for 6H(ABCACB), respectively. ∆a2 and ∆c2 are those for 6H(ABCBCB), correspondingly. From the averaged ∆ai and ∆ci (i ) 1, 2), it is found that 6H(ABCBCB) fits better than 6H(ABCACB) to the experimental data. The 6H(ABCBCB) will also be supported with regard to the relationship between close-packing index D and hexagonality H, later again. However, as shown in Table 4, 6H(ABCBCB) is thermodynamically less stable than 6H(ABCACB) by 26 meV according to the calculations. Although the above

discussion supports that the slightly more metastable phase was realized by our methods using intensive UV laser irradiation, it needs further studies to draw a conclusion. Structural Stability of Polytypes in Terms of Hexagonality H and Close-Packing Index D. It was previously pointed out that the hexagonality H (%) of BN polytypes was precisely related with their thermodynamical stability on the basis of theoretical calculations.24 The hexagonality in polytypes is defined as the ratio of wurtzite-type bilayers-sequences to those of cubic-type in a given unit cell, i.e., wurtzite BN has H of 100%, while c-BN 0% and the other polytypes between them.24 The hexagonality H for sp3-bonded BN is also tabulated in the Table 4 (and the following Tables 6 and 7). We notice that the order of the first type metastability indicated by ∆E, where the enthalpy (or the heat of formation) E is measured relative to that of c-BN, is precisely in agreement with the increasing order of H in sp3-bonded BN. The order of metastability also proved to be precisely in agreement with the increasing order of D in sp3-bonded BN. We have found here that the close-packing index D is quantitatively related with the metastability at least as far as theoretically obtained structural data are concerned. Phenomenologically speaking, it may be said that the structural factors D and H are closely linked and



Figure 3. XRD patterns for the sample prepared by PDL at 10 Hz. Patterns a and b were taken in lower and higher 2θ angles, respectively, sharing an overlapped area.

work together to realize metastable crystal structures, where a given H should result in an optimized D. The H is “chosen” most probably by kinetic (or dynamic) factors depending the deposition conditions. In order to further examine the validity of D as a measure of structural metastability, the data for AlN are also summarized in Table 6. We find an opposite tendency of H and D in relation with ∆E here. The higher the hexagonality is, the more stable the structure is, as was previously found.24 In addition, the higher the absolute value of D, the more stable the structure is. In contrast to BN, the minus sign of D indicates that compression along the c-axis with respect to close packing stabilizes the polytypic structures of AlN. Relatively large value of D (-1.8%) in 2H-AlN seems to justify fairly large value of D (+2.3%, the average in four samples) found for 6H-BN. It was pointed out that this opposite tendency between BN and AlN should be due to the different contribution ratio from ionic and covalent bonds.24 Here we express this point more quantitatively by using the Pauling’s degree of ionicity (ID) for ionocovalent bonds (Appendix A). Because the ID is comparatively large () 0.41) in AlN, the coupling of the third nearest neighboring Alδ+-Nδalong the direction of c-axis should substantially contribute to the structural stability.24 This kind of ionic coupling of Bδ+-Nδin the third nearest neighbor must not be so effective in BN where valency is comparatively influential over ionic bonding (ID ) 0.23). The compression along c-axis in AlN with respect to the D values is consistent with this point of view, where the stability is positively related with the degree of compression (the absolute value of D). To further inspect the validity of D as a structural measure for the metastability of polytypes, let us expand our scope to SiC (ID ) 0.09). In Table 7, the summary of structural data for

SiC (based on ref 24), which corresponds to Table 4 (for BN) and Table 6 (for AlN), is shown. In SiC, the linearity between ∆E and D (H) was not so definite. However, the increasing order of D is in agreement with that of H. Accordingly, it is found that the relationship between the hexagonality H and ∆E in SiC is classified as the same type as that of BN, in which the ionicity is not so dominant over the covalence. To summarize the above results, the relationships between H and D found in Tables 4, 6, and 7, for BN (closed circles), AlN (closed squares), and SiC (closed triangles), respectively, are plotted in Figure 4. Corresponding experimental data for BN (open circles), AlN (open squares), and SiC (open triangles) are also plotted. The data employed here for BN was those of PDL@4 Hz in Table 3 with the lowest value of D. Experimental data for sp3-bonded carbon, namely, polytypes of diamond (see Table 1 in ref 16) are also represented by open crosses, where 6H diamond is represented by both 6H(ABCACB) and 6H(ABCBCB), since we do not know which is correct. A linear relationship is found here, namely, D ) kH, where the constant k depends on the material. The experimental data agree satisfactorily with this theoretically predicted linearity in SiC and AlN. On the other hand, we notice that the 6H(ABCBCB) obeys the linear tendency much better than 6H(ABCACB) does, which suggests that the 6H-BN prepared here has the stacking sequence of ABCBCB. This is in agreement with the previous analysis made in Table 3. It is also noticed that k appears to depend on the ionicity ID. In the inset of Figure 4, k as a function of ID shows linearity for diamond, SiC, and BN, while k collapses into a negative value in AlN. This may suggest a threshold for ID to induce the compression along c-axis, by which the ionic coupling of

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TABLE 5: (a) Analysis of the XRD Peaks (Numbers 1-5 in Figure 3) Categorized as Sharp and Intense, Which Was Done in Terms of the “sp3-Bonded 6H” Structure of BN with the Lattice Parameters a ) 2.4927 Å and c ) 12.544 Å; (b) Analysis of the XRD Peaks (Numbers 6-26 in Figure 3) Categorized as Broad and Noisy with Low Intensity, Which Was Done in Terms of the “sp2-Bonded 30H” Structure of BN with the Lattice Parameters a ) 2.5083 Å and c ) 101.434 Å (a) h

k

l

d (Å)

d (Å) (observed)

error (%)

peak

0 1 1 1 1

0 0 0 0 0

4 3 5 6 7

3.1359 1.9182 1.6363 1.5008 1.3770

3.1362 1.9187 1.6357 1.5012 1.3715

-0.010 -0.028 0.038 -0.029 0.398

1 2 3 4 5

TABLE 7: Summary of Thermodynamical Metastability ∆E (Heat of Formation Relative to That for 4H), Hexagonality H, and Close Packing Index D in Polytypic Forms of SiCa polytype

∆E c (Å) a (Å) D (%) p (Å) h (Å) n (meV) H (%)

3H-SiC(ABC), 3C-SiC 7.466 3.048 0.00 1.867 2.489 6H-SiC(ABCACB) 14.948 3.047 0.14 1.867 2.491 5H-SiC(ABCBC) 12.461 3.046 0.21 1.867 2.492 4H-SiC(ABCB) 9.971 3.046 0.23 1.867 2.493 6H-SiC(ABCBCB) 14.966 3.045 0.33 1.867 2.494 2H-SiC(AB) 4.995 3.044 0.49 1.867 2.498

3 4.0 6 0.31 5 4.5 4 0 6 5 2 14.4

0 33 40 50 67 100

3C-SiC(Exp) 4H-SiC(Exp) 6H-SiC(Exp) 2H-SiC(Exp)

3 4 6 2

0 50 33 or 67 100

7.552 10.052 15.120 5.052

3.083 3.073 3.081 3.079

0.00 0.15 0.17 0.48

1.888 1.883 1.888 1.889

2.517 2.513 2.520 2.526

a The upper six rows are for theoretically calculated structures, while the lower four rows exhibit experimental data for comparison.

(b) h

k

l

d (Å)

d (Å) (observed)

error (%)

peak

0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

18 20 27 24 31 34 35 38 39 41 44 47 18 28 35 37 44 46 50 52 53

5.6352 5.0717 3.7568 4.2264 3.2721 2.9834 2.8981 2.6693 2.6009 2.4740 2.3053 2.1582 2.0269 1.8630 1.7382 1.7026 1.5810 1.5475 1.4827 1.4514 1.4360

5.6732 5.0278 3.7201 4.2264 3.2928 3.0120 2.8757 2.6504 2.5939 2.4921 2.3061 2.1690 2.0273 1.8626 1.7406 1.6946 1.5886 1.5484 1.4856 1.4467 1.4348

-0.67 0.87 0.98 0.00 -0.63 -0.96 0.77 0.71 0.27 -0.73 -0.03 -0.50 -0.02 0.02 -0.14 0.47 -0.48 -0.06 -0.20 0.32 0.08

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

TABLE 6: Summary of Thermodynamical Metastability ∆E (Heat of Formation Relative to That for 2H), Hexagonality H, and Close Packing Index D in Polytypic Forms of sp3-Bonded AlNa AIN

∆E c (Å) a (Å) D (%) p (Å) h (Å) n (meV) H (%)

2H(AB) 6H(ABCBCB) 4H(ABCB) 5H(ABCBC) 6H(ABCACB) 3C, 3H(ABC)

4.994 15.059 10.061 12.590 15.120 7.586

3.115 3.108 3.105 3.103 3.102 3.097

-1.82 -1.10 -0.79 -0.62 -0.50 0.00

1.896 1.896 1.896 1.896 1.896 1.897

2.497 2.510 2.515 2.518 2.520 2.529

2H(exp) 4H(exp) 3C(exp)

4.980 3.110 10.032 3.105 7.569 3.090

-1.94 -1.07 0.00

1.892 1.895 1.892

2.490 2 2.508 4 2.523 3

2 6 4 5 6 3

0 29 41 50 55 79

100 67 50 40 33 0 100 50 0

a The upper six rows are for theoretically calculated structures, while the lower three rows exhibit experimental data for comparison.

Alδ+-Nδ- along the c-axis can contribute to the energetic stability more efficiently. The metastability ∆E for BN, AlN, and SiC are plotted as a function of H in Figure 5, and of D in Figure 6. The linearity between ∆E and H are distinctive for BN and AlN, although the signs of the gradients are opposite (Figure 5). Similar tendency is also evident between ∆E and D for BN and AlN (Figure 6). Here the effects of D and H on ∆E proved to be

Figure 4. The theoretical close-packing index D plotted as a function of hexagonality H for BN (closed circles), AlN (closed squares), and SiC (closed triangles). Experimental values of D for BN (open circles), AlN (open squares), SiC (open triangles), and sp3-bonded carbon or diamond polytypes (crosses) are shown for comparison. The inset shows the gradients k (obtained by assuming D ) kH) for the four plots as a function of the ionicity ID, which were 0, 0.09, 0.23, and 0.41, for diamond, SiC, BN, and AlN, respectively. The linearity of k as a function of ID seems to collapse as the ionicity becomes predominant over covalence in AlN.

significant when ID was not negligible. In BN, the deviation from the isotropic 3C structure appreciably increased the metastability, while in AlN decreasing the isotropic nature increased the stability greatly. This tendency was not so substantial in SiC for which the ID was relatively small. This is relevant to the fact that the difference among polytypic metastability is small, and, accordingly, a larger number of polytypes has been found in the case of SiC. It seems reasonable that 3H- (H ) 0%) and 2H- (H is 100%) polytypes are the most stable structures in BN and AlN, respectively, in terms of H and ID according to the above discussion. A further extension of the above investigation of the polytypes in terms of H and D to the other compounds may be fruitful but should be done elsewhere. Growth Mechanism of BN from Vapor. It is seen from Table 4 that h-BN is less stable than sp3-bonded BN by about 100 meV with respect to the relative enthalpy (denoted by ∆E



6H(1.539 Å) < 5H(1.552 Å) < 30H(1.558 Å) < 3C(1.566 Å) < 2H(1.570 Å)

Figure 5. The metastability ∆E for sp3-bonded polytypes plotted as a function of hexagonality H for BN (closed circles), AlN (closed squares), and SiC (closed triangles).

Figure 6. The metastability ∆E for sp3-bonded polytypes plotted as a function of close-packing index D for BN (closed circles), AlN (closed squares), and SiC (closed triangles).

in the table). The D value for h-BN (in Table 4), which is more than +60%, means significantly roomy arrangement of the atoms. On the other hand, the significantly shorter interlayer bond length in sp2-bonded h-BN (1.446 Å) in comparison with more isotropic bond-length in sp3-bonded c-BN (1.566 Å) means the sp2-bonds are much stronger than sp3-bonds (see Appendix B for the relationship between the bond strength and bond length). This means that the bonding energy is localized in the intralayers in h-BN, and that is not “economic” with respect to the total thermodynamical stability. On the other hand, we may say that the bonding energy is more delocalized and distributed isotropically in sp3-bonded BN. The peculiarity of sp2-bonded BN shall be discussed in terms of molecular crystal later. Turning our attention to the bond lengths p in BN, AlN and SiC, we find that they do not show any significant difference among the polytypic forms as far as theoretical data are concerned. However, on the other hand, in reference to the experimental data of sp3-bonded BN, the increasing order of p is as follows:

Since 2H (wurtzite BN) is known to be less stable than 3C (c-BN), this order in the last part is acceptable, although the difference is subtle. The remaining part means that the 6H phase has the strongest bond among the sp3-bonded polytypes of BN. It is also worth mentioning that 6H, 5H, and 30H were obtained more preferably than 3C (c-BN) by our methods. In view of these facts, we propose the “bond-strength initiative rule” (abbreviated as the BSI rule here) in the crystal growth from vapor, where the initial nuclei should be characterized as still more molecular (possibly with dangling bonds and without periodicity) than crystalline due to their small size, in which the ratio of surface area to the bulk volume is still large. According to this rule, we suggest why sp3-bonded 6H-BN is preferred over c-BN in our processes as follows. It should be noted that the strongest bond in BN is the sp2bond (1.446 Å) and the preferential growth of sp2-bonded phases of BN is exclusively favored in usual pyrolytic CVD (and PCVD in our case). Since the growth of initial nuclei is a “local” event, the formation of the strongest sp2-bonds (i.e., the most stable bonds) should precede the thermodynamic stability of finally grown crystallites at the earliest stage of the crystal growth. In other words, from the kinetic point of view, the stronger sp2bonds should form fast due to lower activation energy than that for the formation of isotropic sp3-bonds during the growth reactions on the surface. While this formation dynamics puts priority in the lateral growth of sp2-bonded layers, the growth in stacking mode of these layers should also follow to yield the formation of sp2-bonded crystallites. However, with respect to the bulk crystals, the sp3-bonded phases should be more stable than the sp2-bonded one according to the theoretically predicted enthalpy24 (we defer the entropy for the moment); the recent developments on the relative stability of sp3-bonded c-BN and sp2-bonded h-BN under normal conditions also support this view.11–14 That is, the formation of sp2-bonded nuclei should be favored kinetically at the earliest stage of nucleation, while sp3-bonded phase should be thermodynamically preferable as the nucleus grows further. However, we suppose that the structure (bonding mode) of the initial nuclei tends to determine that of the following growth as a seed crystal. Accordingly, in most not-adequately far-from-equilibrium processes such as our plasma CVD and typical pyrolytic CVD, the sp2-bonded phase grows dominantly. On the other hand, in the processes exploiting far-fromequilibrium states such as our PL-CVD, the probability should be much enhanced to form the sp3-bonded entities at quite early stages of nucleation; the activation energy for the formation of sp3-bonded embryonic entities should be provided by the absorption of photons in our case. Similarly, the transformation of sp2-bonded BN into sp3-bonded ones in our PDL processes can be also understood within this framework as a relaxation of the “metastable” sp2-bonded phase into the truly stable sp3bonded phases with the help of appropriate activation by photon absorption at 193 nm. In the case of PDL, we understand that the initial nuclei of the sp3-bonded phase formed in the sp2-bonded matrix “choose” the 6H-polytypic structure in accordance with the BSI rule, and the structure of the following growth is directed under the influence of the initial embryonic “seed crystal” of 6H-BN, although the more fundamental question of why the slightly metastable polytypic periodicity is kept during the growth (by a long-range interaction?) still remains (ref 5). We are preparing to study this hypothetical process experimentally.

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The Role of Entropy Term in the Phase Selection. In the discussion above, we considered only the enthalpy (or heat of formation) term ∆H (denoted as ∆E in the tables) in the Gibbs free energy G (∆G ) ∆H - T∆S), which is the thermodynamical criterion for phase stability under a given set of temperature and pressure. Then let us try to look at the influence of the entropy term ∆S on the above discussion. As is experimentally known, sp3-bonded c-BN degrades into sp2-bonded h-BN at temperatures higher than 1600 °C in vacuum.25 This indicates that the T∆S term becomes significant at higher temperatures, with the entropy for sp2-bonded phase being higher than that for c-BN. The experimental values such as ∆H0 ) -16.2 ( 3.0 kJ mol-1 and ∆S0 ) -8.24 ( 0.11 J K-1 mol-1 are known,11 where ∆H0 (∆S0) means the difference of H (S) for c-BN from that for h-BN under the normal conditions. The degradation temperature is roughly estimated to be 1693 °C by employing these values, in fairly good agreement with the above observation. We may suppose that the entropy term is still less effective than the enthalpy term in our processes carried out at 850 °C, and the validity of the above discussion ignoring the entropy term is assured as far as the thermodynamical stability is concerned, accordingly. From the other point of view, it should be noted that the calculated values ∆E may be considered also as relative G () H - TS), since the difference of TS among the polytypes for a given compound must be negligible and should be canceled out by subtraction. Laser-Assisted Growth Mechanism of BN from Vapor under the Influence of Plasma. The activation energy for the formation of transitional states (most probably electronically excited states), which leads to the growth of sp3-bonded embryonic phases, is supposed to be supplied by the irradiation of the excimer laser at 193 nm (equivalent to 6.42 eV) in our processes (PLCVD and PDL). The definite energy needed for this activation is not known. However, in the case of carbon, we know that a carbon atom at the ground state (3P; 2s22p2) needs the energy of 0.66 eV so as to be excited to the valence state (5S; 2s12p3) (ref 26). Analogically, a few electron volts of energy is supposed to be needed for the activation of BN embryos, and which should be supplied by the laser in our case. The reaction coordinate for this structural transition may be defined as the interlayer distance along the c-axis. By the way, since the transitions from sp2-bonded phases to sp3-bonded ones are associated with the change of densities, it is formally a firstorder phase transition according to the classification by Ehrenfest. In contrast to the case of BN, there are several studies on the transformation mechanism from graphite to diamond induced by electronic (photonic) excitation, and which may allow us some analogical consideration for BN. An interesting experimental result on this subject by femtosecond-laser excitation at visible region was reported,27 and a theoretical model supported it28 recently. Their pseudo sp3-bonded nanoscale domain on carbon surface, namely, “diaphite”, was vulnerable and stayed for about 10 days, however.27 On the other hand, an ab initio calculation suggested that there might be some route in the potential energy surface at a C-1s (core level) excited state for rhombohedral graphite to transform into the diamond phase, which needs the energy of a soft X-ray, however.29 In the same paper, it was also shown theoretically that “doping” of holes in the valence band of rhombohedral graphite results in the shrinkage of the whole lattice and instability of the sp2-bonded structure, and which leads to the formation of diamond. The Auger decay process may achieve this “doping” of holes, for instance.

Komatsu et al. We may find the common principle from these that some kinds of electronic excitations in solids can be accompanied with a sort of “constructive deformation”, and which possibly leads to the transition from sp2-bonded structures to sp3-bonded ones. Although the allocation of appropriate excitation routes is not easy and depends on the case, we suppose that the irradiation of excimer laser at 193 nm brought about this kind of phenomenon effectively in our case. The formation of sp3-bonded 6H-BN found both in PLCVD and PLD seems to imply that the laser-induced phase transformation from sp2- to sp3-phases, which was evidently found in PDL, to proceed also in PLCVD. Here we notice that the pulsed excimer laser has a duration of about only 20 ns (at the repetition frequency of 2-10 Hz), while the CVD process takes place continuously. On the other hand, our past experiments illustrated the increased growth rates in PLCVD in comparison with PCVD, which indicated the photoinduced enhancement of CVD growth itself.22 These two effects by UV laser irradiation are supposed to be working in the PLCVD. The coexistence of two crystal structures with different crystallinity found in PLCVD is regarded as relevant in this instance. That is, we may suppose that sp3-bonded 6H-BN with high crystallinity was due to the direct phase transformation, while sp3-bonded 30H-BN was initiated and formed by photoenhanced CVD process. The precursor (sp2-bonded 30H-BN) for the former is supposed to be deposited during the absence of laser irradiation in the PLCVD process. It was pointed out earlier that charged particles such as ions and electrons supplied from the plasma should contribute to stabilize the sp3-bonded embryonic structures of BN according to molecular orbital calculations, where the structures of BN clusters being isoelectronic to the corresponding sp3-bonded carbon (diamond) clusters should inevitably require the introduction of charge(s) (ref 30). That is, they have to be ionic clusters. In our case here, this implies the importance of the plasma and/or ionized states, which was introduced in CVD and/or was generated by the intense laser irradiation on the surface. Optical emission spectroscopic studies on this phase of the growth mechanism are in progress in our research group. The Molecular- to Valence-Crystalline Transition: A New Category of Phase Transformation. Molecular crystals may be defined as the crystallization of molecules by weak interactions such as van der Waals force and dispersion force, while the constituent individual molecules are built through strong valence bonds. The coexistence of two different categories of bonds, that is, the weak physical bonds (or interaction) for crystallization and the strong chemical bonds for molecules, characterizes it. Fullerene crystal is an example of the molecular crystal.31 From this point of view, graphite and sp2-bonded h-BN might be considered as exceptional cases of molecular crystals, if we consider the graphene sheet (and sp2-bonded BN sheet) as a macromolecule. We say exceptional here because their low melting (or vaporization) temperatures also characterize molecular crystals, which is not the case in graphite and h-BN (ref 32). We may consider them as one-dimensional molecular crystals made of the macromolecular sheets, which allows the diversity in periodic stacking of the sheets. Accordingly, we become aware of the peculiarity of the phase transformation from sp2- to sp3-bonded crystals, which is associated not only with the change of atomic arrangements but also with the change of the nature of bonding. We suppose that the transition from the weak van der Waals force to the strong valence bonds requires substantially large activation energies.33 The intense



laser at 193 nm (equivalent to 6.42 eV) in our case is considered to have achieved this atypical phase transformation evidently in the PDL. Summary and Concluding Remarks (1) New sp3-bonded polytypic forms of BN, namely, 6H-BN and 30H-BN, were prepared by PCVD from diborane (B2H6) and ammonia (NH3) with an excimer laser at 193 nm being irradiated on the growing film surfacem, while only the 6HBN was formed by PDL of sp2-bonded BN precursor films prepared by PCVD. (2) The typical lattice constants a and c for 6H-BN determined by XRD were 2.501 Å and 12.45 Å, respectively, while those for 30H-BN were 2.538 Å and 62.61 Å, respectively. (3) The precursor BN for the PDL prepared by mere PCVD proved to be “sp2-bonded 30H-BN” with the lattice constants a ) 2.507 Å and c ) 101.6 Å by XRD. (4) The PDL demonstrated direct photoinduced phase transformation by a 193 nm excimer laser from sp2-bonded 30HBN into denser sp3-bonded 6H-BN. (5) On the basis of the metastability of the polytypes (∆E) estimated by the first principles calculations, their structures were studied in terms of “hexagonality” H and “close-packing” index D, in which the H and D proved to be closely linked with ∆E. A linear relationship D ) kH was found, where the constant k appeared to depend on the ionicity ID of material. The k as a function of ID shows linearity for diamond, SiC, and BN, while k collapses into a negative value in AlN. This may suggest a threshold for ID to induce the compression along the c-axis, by which the ionic coupling of Alδ+-Nδ- along the c-axis can contribute to the energetic stability more efficiently. (6) It should be pointed out that sp2-bonded BN is more metastable than sp3-bonded ones both theoretically and experimentally under ordinary conditions for CVD. This contradicts the dominant growth of sp2-bonded BN over sp3-bonded ones commonly seen in CVD. Then, the growth (and transformation) mechanism of the polytypic structures from the vapor with the assistance of a UV laser was discussed on the basis of the “BSI rule”, in which the local thermodynamics at very early stages of the growth should favor the formation of the strongest bond available (e.g., sp2-bonds in BN); this initial embryonic state should determine the bonding state and the structure of the following growth as a kind of seed crystal. According to this rule, the ordinary growth of sp2-bonded BN by pyrolytic (and plasma-assisted) CVD was explained. The UV laser was supposed to break this rule most probably by electronic excitations of the embryonic nuclei (a tiny cluster of BN), which should lead to a sort of constructive destruction into sp3-bonded states. (7) Our proposal that the UV laser irradiation should induce the structural relaxation of the sp2-bonded “metastable” phase into sp3-bonded truly stable phase at lower temperatures (at the substrate temperature of 850 °C in our case) appears to be consistent with the recent pressure-temperature phase diagram of BN. Appendix A In chemical bonds with intermediate nature between ionic and covalent bonds (ionocovalent bond), the degree of ionicity (ID) for two atoms X and A is evaluated by the following eq 1:

ID ) 1 - exp[-0.25(ENA - ENX)2]

(1)

TABLE 8: Degree of Ionicity (ID) ENA ENX ID

BN

AlN

SiC

2.051 3.066 0.23

1.613 3.066 0.41

1.916 2.544 0.09

where ENA and ENX are the electronegativity for the atoms A and X, respectively.34 By employing Pauling’s electronegativity values, the IDs for BN, AlN, and SiC were evaluated in Table 8. Ionicity is supposed to be dominant in AlN, less dominant in BN, and not influential in SiC according to the ID. Appendix B Analytical expressions for the bond strength s as a function of bond length R are proposed. Widely used ones are as follows:

s ) s0(R/R0)-N

(2)

s ) exp[(R0 - R)/B]

(3)

where s0, R0, N, and B are empirically derived parameters for a given pair of atoms.35 Although these parameters for B-N bonds do not seem to be available, it is evident from these equations that the bond strength is negatively and sensitively related to the bond length. References and Notes (1) Mishima, O.; Era, K. In Electric Refractory Materials; Kumashiro, Y., Ed.; Marcel Dekker: New York, 2000; p 495. (2) Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. AdVanced Inorganic Chemistry, 6th ed.; Wiley-Interscience: New York, 1999; p 209. (3) Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, 6th ed.; Wiley-Interscience: New York, 1999; p 168. (4) Greenwood, N. N. Earnshaw, A. Chemistry of the Elements; Elsevier Butterworth-Heinemann: Oxford, 2006; pp 275 and 208. (5) Verma, A. R. Krishna, P. Polymorphism and Polytypism in Crystals; John Wiley & Sons: New York, 1966; p 68. (6) Corrigan, F. R.; Bundy, F. P. J. Chem. Phys. 1975, 63, 3812–3820. (7) Hawtin, P.; Lewis, J. B.; Moul, N.; Phillips, R. H. Philos. Trans. R. Soc. London, A 1966, 261, 67–95. (8) Kleppa, O. J.; Hong, K. C. J. Chem. Thermodyn. 1978, 10, 243– 248. (9) Shirai, K.; Fujita, H.; Katayama-Yoshida, H. Phys. Status Solidi B 2003, 235, 526–530. (10) Thiel, M.; van and Ree, F. H. Int. J. Thermophys. 1989, 10, 227– 236. (11) Will, G.; Nover, G.; von der Goenna, J. J. Solid State Chem. 2000, 154, 280–285. (12) Albe, K. Phys. ReV. B 1997, 55, 6203–6210. (13) Solozhenko, V. L. Diamond Relat. Mater. 1994, 4, 1–4. (14) Solozhenko, V. L.; Turkevich, Z.; Holzapfel, W. B. J. Phys. Chem. B 1999, 103, 2903–2905. (15) ICCD #59-309, International Center for Diffraction Data, Newtown Square, PA. (16) Komatsu, S.; Okada, K.; Shimizu, Y.; Moriyoshi, Y. J. Phys. Chem. B 1999, 103, 3289–3291. (17) Kobayashi, K.; Komatsu, S. J. Phys. Soc. Jpn. 2007, 76, 113707 1–4. (18) Komatsu, S.; Sato, Y.; Hirano, D.; Nakamura, T.; Koga, K.; Yamamoto, A.; Nagata, T.; Chikyo, T.; Watanabe, T.; Takizawa, T.; Nakamura, K.; Hashimoto, T.; Shiratani, M. J. Phys. D: Appl. Phys. 2009, 42, 225107 (6 pp). (19) Komatsu, S. J. Phys. D: Appl. Phys. 2007, 42, 2320–2340. (20) Komatsu, S.; Okudo, A.; Kazami, D.; Golberg, D.; Li, Y.; Moriyoshi, Y.; Shiratani, M.; Okada, K. J. Phys. Chem. B 2004, 108, 5182– 5184. (21) Komatsu, S.; Kazami, D.; Tanaka, H.; Shimizu, Y.; Moriyoshi, Y.; Shiratani, M.; Okada, K. Appl. Phys. Lett. 2006, 88, 151914 1–3.

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(22) Komatsu, S.; Kazami, D.; Tanaka, H.; Moriyoshi, Y.; Shiratani, M.; Okada, K. J. Appl. Phys. 2006, 99, 123512 1–6. (23) ICDD #00-035-1365, International Center for Diffraction Data, Newtown Square, PA. (24) Kobayashi, K.; Komatsu, S. J. Phys. Soc. Jpn. 2008, 77, 084703 1–11. (25) Reference 1, p 502. (26) Reference 4, p 277. (27) Kanasaki, J.; Inami, E.; Tanimura, K.; Ohnishi, H.; Nasu, K. Phys. ReV. Lett. 2009, 102, 087402 1–4. (28) Ohnishi, H.; Nasu, K. Phys. ReV. B 2009, 79, 054111 1–6. (29) Nakayama, H.; Katayama-Yoshida, H. Jpn. J. Appl. Phys. 2002, 41, L817–L819. (30) Komatsu, S.; Yarbrough, Y.; Moriyoshi, Y. J. Appl. Phys. 1997, 81, 7798–7805.

Komatsu et al. (31) Rao, C. N. R. Seshardri, R. In Organic Molecular Solids Properties and Applications; Jones, W., Ed.; CRC Press: Boca Raton, FL, 1997; p 1. (32) Douglas, B.; Macdaniel, D. Alexander, J. Concepts and Models of Inorganic Chemistry, 3rd ed.; John Wiley and Sons: New York, 1994; p 200. (33) For the case of femtosecond-laser-induced formation of the pseudo sp3-bonded nanoscale domain on a carbon surface (ref 27), they state that only a few visible photons can trigger the transformation process (ref 28), however. (34) Ref 32, p 86. (35) Giacovazzo, C. Fundamentals of Crystallography, 2nd ed; Giacovazzo, C., Ed.; Oxford University Press: Oxford, 2002; p 526.

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