- Email: [email protected]
The hardness of NbB2 single crystals
Journal of the Less-Common Metals, 67 (1979) 485 - 492 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
THE HARDNESS
OF NbB,
485
SINGLE CRYSTALS*
K. NAKANO Government
Industrial
Research
Institute,
Nagoya (Japan)
I. HIGASHI The Institute
of Physical and Chemical Research,
Wako-shi, Saitama (Japan)
Summary
NbBa single crystals grown from an aluminium solution were characterized by an electron microprobe analysis, chemical etching and X-ray topography, and the hardnesses of the crystals were measured at room temperature. Single crystals have nearly stoichiometric compositions with slight impurities and high crystal perfections. The hardness measurements were made on the (0001) and (lOTO) planes with a Knoop indenter in various directions. The hardness was a maximum when the long axis of the indentation was in the tiOl0) direction and a minimum when the long axis was in the (1210) direction on the (0001) plane. The values of the hardness did not vary much in the (lOi0) plane. It was shown that in the single crystals two types of prismatic slip occurred at room temperature.
1. Introduction
NbBs is of considerable interest because of its use as a high temperature material owing to its high melting point and extreme strength at high temperatures. This material has a hexagonal C32 crystal structure like many other diborides [ 11.The hardness of NbBs crystals has been measured previously to some extent [ 2 - 51. However, we could find no details in the literature on hardness anisotropy. In this paper we describe the hardness anisotropy, the primary slip system and the characterization of NbBs single crystals grown by the method used previously [ 61.
*Paper presented at the 6th International Symposium on Boron and Borides, Varna, Bulgaria, October 9 - 12, 1978.
486
2. Experimental 2. I. Preparation of the single crystals and their characterization Single crystals were prepared in solutions (of atomic ratio Nb:B:Al = 1:1.6:35) which were cooled (10 “C h-l) from a maximum temperatu_re of 1570 “C. As-grown crystals had flat and mirror-like (0001) and (1010) planes (Fig. 1). The crystals were analysed by an electron microprobe analyser (Simazu model EMX-SM) and were examined by chemical etching (HF:H~O:HNOs = 4:4:1; 25 - 30 “C; 5 - 20 min) and Lang X-ray topography. The Lang topographs were obtained using Ag K, radiation (Rigaku Denki model A3 Lang camera; Rigaku Denki model RU-3H X-ray generator).
Fig. 1. NbBz single crystals grown from an aluminium solution (1 division is 1 mm): A, crystals with (0001) and {lOiO} faces; B, crystals with predominantly {lOiO} faces.
2.2. Hardness ~e~~re~e~ ts The hardnesses of the cleaned (0001) and (lO?O) planes of the same single crystal were measured with the Knoop diamond indenter at room temperature. The hardness me~~ernen~ were carried out by using the Akashi model MVK hardness tester under an applied load of 100 g for 15 s. The hardnesses were measured in the directions for which the long axis of the indenter pointed from [iOlO] to [l%O] every 10” on the (0001) plane and from [i2iO] to [OOOl] every 10” on the (lOTO) plane respectively. To obtain the hardness of each long axis direction on a plane, five to six readings were taken. In order to observe the slip lines, a load of 1000 g was applied to the Vickers diamond indenter on the two planes.
487
Fig. 2. The etching figure and the Lang topo~aph of the same area of the (lOi0) plane: (a) the etching figure (the length of the arrow is 200 m): the inset shows magnifications of shallow (A) and sharp (B) pits; (b) the Lang topograph (the direction of the diffraction vector, g = 0002, is indicated by the arrow, the length of which is 300 Mm).
3. Resufts 3.1. Charm terizu tion of the crystds A.n etching figure and a Lang topograph of the same area of the (lO?O)
plane are shown in Fig. 2(a) and Fig. 2(b) respe+vely. Etch pit arrays along the [OOOl] direction were observed on the {lOlO) plane. Shallow and sharp pits were observed and ma~ificatio~s of these are shown in Fig. 2(a), inset. Several sharp pits became shallow during the etching process. The shallow pits are considered to correspond not to line defects but to local defects such as ~pu~ties and vacancies. No precipices such as a second phase were observed, and the etch pit densities of the (lOi0) plane were of the order of 10’ cmq2. Grown crystals showed httle distortion and were relatively perfect, although the correspondence between the etching figure and the Lang topograph was not clear. Hexagonal or rounded etch pits were observed on the (0001) plane. Shallow and sharp pits were also observed on the (0001) plane, as on the (lOi0) plane. The etch pit densities of these planes
were lo3 - lo4 cme2. In the crystals we examined the ratio R of boron to niobium was 1.7 - 2.2 and the aluminium and silicon impurity contents were less than 0.01 wt.%. 3.2. Hardness of the crystals An example of the hardnesses in the (0001) and (lOi0) planes of the same single crystal is illustrated in Fig. 3. The angle 0 of the long axis of the indentation varied from-0 to 90” in both cases. In the (0001) plane, 0 = 0” corresponds to the [lOlO] direction and 0 = -90”- to the [1210] direction; in the (lOTO) plane, 0 = 0” corresponds to the [1210] direction and 0 = 90” to the [OOOl] direction. Another example of the hardnesses is shown in Fig. 4. In the examples in Figs. 3 and 4, R = 1.9 and the aluminium and silicon contents were less than 0.008 wt.%.
A-----(4
il
I
*nqic
. 0,
io
’
1ndcntatt0”
*
b
do
(deg)
(b)
6b
30 Anqle
0,
4 ndrntst
$2 I on
(drg)
Fig. 3. The hardnesses of (a) the (0001) and (b) the (lOi0) planes plotted against the angle 0 of the long axis of the indentation. 6 = 0” corresponds to the [ iOlO] direction and 0 = 90” to the [ 12101 direction on the (0001) plane; 0 = 0” corresponds to the [ i2iO] direction and 0 = 90” to the [OOOl] direction on the (lOi0) plane.
0
(4
AnpI.
Of
Ind,ntatlon
(deg)
60
x) Air’,l*
ot
,nd.ntat
90 ,on
(de@
(b)
Fig. 4. The hardnesses of another NbBz single crystal (which is similar to that in Fig. 3).
489
The hardnesses on the (0001) plane varied periodically with the angle 0, i.e. they had maximum values at 0 = 0 and 60” (the long axis of the indenter point was in the 8010) direction) and minimum values at 0 = 30 and 90” (the long axis of the indenter p_ointwas in the (1210) direction). In contrast, the hardnesses on the (1010) plane varied very little with 0. In general the hardnesses on the (0001) plane were higher than those on the (1010)plane. 4. Discussion NbBs single crystals grown from an aluminium solution were relatively perfect crystals. Most of the crystals had few impurities and the ratio R was in the diboride homogeneity range [ 71. The hardness values we measured were not so different as those previously reported for single crystals [4, 51. Consequently our hardness values might be acceptable. The hardness anisotropy of a single crystal depends strongly on the magnitude of the resolved shear stress on the active slip system when an indenter is applied. Brookes et al. [ 81 derived an expression for the effective resolved shear stress 7, on the active slip system by modifing the theory of Daniels and Dunn [ 91. F 7, = A coshcos@ $ (cosJ/ + siny)
(1)
where F is the applied force, A the area supporting F, h the angle between the F axis and the slip direction, 4 the angle between the F axis and the normal to the slip plane, 4 the angle between each facet of the indenter and the axis of rotation for a given slip system and y the angle between each facet of the indenter and the slip direction. Modifying eqn. (1) to 7, = (F/A)f(h, $, I/I,y), we obtained the factor f. The magnitude of l/f qualitatively corresponds to that of the hardness, i.e: the larger (smaller) value of l/f corresponds to the higher (lower) hardness. The primary slip systems of NbBz single crystals are thought to consist of a basal slip system (OOOl)Cll20) and a prismatic slip system (lO~O}Cl210>, as shown for group IVa diboride single crystals with the same crystal structure [ 10 - 141. However, NbBs crystals have an axial ratio (c/a = 1.06 as calculated from the data in ref. 6) that is near to unity. Therefore NbB2 single crystals may have another prismatic slip system (1010) [ OOOl] , as well as the two types mentioned above. When the indenter was applied to the (0001) and (1010) planes, we calculated the factor f asa function of t9for two indenter facets adjacent to each other; for this case, three types of slip system were active. In calculating this slip system, the largest value of f wasfound, because the largest effective resolved shear stress is the dominating factor in the plastic deformation to a first approximation. Next we determined the mean value f,,, of the two f values corresponding to the two indenter facets [ 151. These calculations were carried out by using a computer (Fujitsu model FACOM 270-30) and the results are shown in Fig. 5.
490
Two types of prismatic slip ({10~0}<1210>, {lOiO} [OOOl] ) were found, in agreement with the case where the f, values are at a minimum near 19= 0 and 60” and at a maximum near 0 = 30 and 90” on the (0001) plane (Fig. 5(a)). From Fig. 5(b), if either of these two slip systems is active, it can be seen that the hardness of the (lOTO) plane has a high anisotropy. However, if both slip systems are active, then the hardness of this plane has little anisotropy. The curve representing the mean values of fm,(reie~(l~~c) and ~III,(loi toooii ) is also shown in Fig. 5. When the indenter was applied on the (1010) plane, we can see from this curve that the average effective resolved shear stress on the active slip systems varies according to the indenter direction, i.e. the fact that this plane has little hardness anisotropy should be clearly predictable.
as-
04 __---
cloiolloooi)
04 .
0
(aI
30 AngM
01
rdml?.,I0”
,I Q4
Am$e
(deg)
of
ind.?n!Aon
(deg)
(b)
Fig. 5. The mean factor f, plotted against 8 in the case that the slip system becomes active (a) (0001) plane and (b) (lOi0) plane: curve x, mean value of fm,~~ol;o)(l~,-,)and fm. iloiOk[oooll *
These predictions coincide well qualitatively with the results of our experiments; the hardnesses had maximum values at 8 = 0 and 60” and minimum values at 0 = 30 and 90” on the (0001) plane and varied very little on the (ioio) plane. Consequently we concluded that the primary slip systems are { lOi0) (1210) and (lOi0) [ OOOl] when the indenter was applied on the crystal plane at room temperature. This was supported by observatio_ns of the slip lines around the Vickers indentations on the_~OOOl) and (1010) planes, as shown in Fig. 6; the slip lines along the (2110) di_rection on the (0001) plane and along the [OOOl] direction on the (1010) plane were clearly observed. From thesz observations we confirmed the fact that the primary slip planes were (1010).
491
Fig. 6. Slip lines around the Vickers indentations. The large arrows are 40 /.frn long; the small arrows indicate the slip lines (a) in the (0001) plane and (b) in th e (ioio) plane.
Acknowledgments The authors wish to thank Dr. A. Isogai, Toyota Central Research Laboratory, for the electron microprobe analyses and Mr. Y. Nishida and Mr. S. Ito, Government Industrial Research Institute, Nagoya, for the computer calculations.
492
References 1 B. Aronsson, T. Lundstrom and S. Lundqvist, Borides, Silicides and Phosphides, Methuen, London, 1965, p. 46. 2 H. Nowotny, F. BeneSovsky and R. Kieffer, 2. Metullkd., 50 (1959) 417. 3 J. F. Lynch, C. G. Ruderer and W. H. Duckworth, Engineering Properties of Selected Ceramic Materials, The American Ceramic Society, Columbus, Ohio, p. 5.1.3-7. 4 E. V. Clougherty and R. L. Pober, Nucl. Metall., 10 (1964) 423. 5 W. A. Sanders and H. B. Probst, J. Am. Ceram. Sot., 49 (1966) 231. 6 I. Higashi, Y. Takahashi and T. Atoda, J. Cryst. Growth, 33 (1976) 207. 7 F. A. Shunk, Constitution of Binary Alloys, McGraw-Hill, New York, 1969, Suppl. 2, p. 84. 8 C. A. Brookes, J. B. O’Neill and B. A. W. Redfern, Proc. R. Sot. London, Ser. A, 322 (1971) 73. 9 F. W. Daniels and C. G. Dunn, Trans. Am. Sot. Met., 41 (1949) 419. 10 S. A. Mersol, C. T. Lynch and F. W. Vahldiek, Anisotropy in Single Crystal Refractory Compounds, Vol. 2, Plenum Press, New York, 1968, p. 41. 11 J. S. Haggerty and D. W. Lee, J. Am. Ceram. Sot., 54 (1971) 572. 12 K. Nakano, T. Imura and S. Takeuchi, Jpn. J. Appl. Phys., 12 (1973) 186. 13 K. Nakano, H. Matsubara and T. Imura, Jpn. J. Appl. Phys., 13 (1974) 1005. 14 K. Nakano, H. Matsubara and T. Imura, J. Less-Common Met., 47 (1976) 259. 15 M. L. Tarkanian, J. P. Neumann and L. Raymond, The Science of Hardness Testing and Its Research Applications, American Society for Metals, Novelty, Ohio, 1973, p. 187.
THE HARDNESS
OF NbB,
485
SINGLE CRYSTALS*
K. NAKANO Government
Industrial
Research
Institute,
Nagoya (Japan)
I. HIGASHI The Institute
of Physical and Chemical Research,
Wako-shi, Saitama (Japan)
Summary
NbBa single crystals grown from an aluminium solution were characterized by an electron microprobe analysis, chemical etching and X-ray topography, and the hardnesses of the crystals were measured at room temperature. Single crystals have nearly stoichiometric compositions with slight impurities and high crystal perfections. The hardness measurements were made on the (0001) and (lOTO) planes with a Knoop indenter in various directions. The hardness was a maximum when the long axis of the indentation was in the tiOl0) direction and a minimum when the long axis was in the (1210) direction on the (0001) plane. The values of the hardness did not vary much in the (lOi0) plane. It was shown that in the single crystals two types of prismatic slip occurred at room temperature.
1. Introduction
NbBs is of considerable interest because of its use as a high temperature material owing to its high melting point and extreme strength at high temperatures. This material has a hexagonal C32 crystal structure like many other diborides [ 11.The hardness of NbBs crystals has been measured previously to some extent [ 2 - 51. However, we could find no details in the literature on hardness anisotropy. In this paper we describe the hardness anisotropy, the primary slip system and the characterization of NbBs single crystals grown by the method used previously [ 61.
*Paper presented at the 6th International Symposium on Boron and Borides, Varna, Bulgaria, October 9 - 12, 1978.
486
2. Experimental 2. I. Preparation of the single crystals and their characterization Single crystals were prepared in solutions (of atomic ratio Nb:B:Al = 1:1.6:35) which were cooled (10 “C h-l) from a maximum temperatu_re of 1570 “C. As-grown crystals had flat and mirror-like (0001) and (1010) planes (Fig. 1). The crystals were analysed by an electron microprobe analyser (Simazu model EMX-SM) and were examined by chemical etching (HF:H~O:HNOs = 4:4:1; 25 - 30 “C; 5 - 20 min) and Lang X-ray topography. The Lang topographs were obtained using Ag K, radiation (Rigaku Denki model A3 Lang camera; Rigaku Denki model RU-3H X-ray generator).
Fig. 1. NbBz single crystals grown from an aluminium solution (1 division is 1 mm): A, crystals with (0001) and {lOiO} faces; B, crystals with predominantly {lOiO} faces.
2.2. Hardness ~e~~re~e~ ts The hardnesses of the cleaned (0001) and (lO?O) planes of the same single crystal were measured with the Knoop diamond indenter at room temperature. The hardness me~~ernen~ were carried out by using the Akashi model MVK hardness tester under an applied load of 100 g for 15 s. The hardnesses were measured in the directions for which the long axis of the indenter pointed from [iOlO] to [l%O] every 10” on the (0001) plane and from [i2iO] to [OOOl] every 10” on the (lOTO) plane respectively. To obtain the hardness of each long axis direction on a plane, five to six readings were taken. In order to observe the slip lines, a load of 1000 g was applied to the Vickers diamond indenter on the two planes.
487
Fig. 2. The etching figure and the Lang topo~aph of the same area of the (lOi0) plane: (a) the etching figure (the length of the arrow is 200 m): the inset shows magnifications of shallow (A) and sharp (B) pits; (b) the Lang topograph (the direction of the diffraction vector, g = 0002, is indicated by the arrow, the length of which is 300 Mm).
3. Resufts 3.1. Charm terizu tion of the crystds A.n etching figure and a Lang topograph of the same area of the (lO?O)
plane are shown in Fig. 2(a) and Fig. 2(b) respe+vely. Etch pit arrays along the [OOOl] direction were observed on the {lOlO) plane. Shallow and sharp pits were observed and ma~ificatio~s of these are shown in Fig. 2(a), inset. Several sharp pits became shallow during the etching process. The shallow pits are considered to correspond not to line defects but to local defects such as ~pu~ties and vacancies. No precipices such as a second phase were observed, and the etch pit densities of the (lOi0) plane were of the order of 10’ cmq2. Grown crystals showed httle distortion and were relatively perfect, although the correspondence between the etching figure and the Lang topograph was not clear. Hexagonal or rounded etch pits were observed on the (0001) plane. Shallow and sharp pits were also observed on the (0001) plane, as on the (lOi0) plane. The etch pit densities of these planes
were lo3 - lo4 cme2. In the crystals we examined the ratio R of boron to niobium was 1.7 - 2.2 and the aluminium and silicon impurity contents were less than 0.01 wt.%. 3.2. Hardness of the crystals An example of the hardnesses in the (0001) and (lOi0) planes of the same single crystal is illustrated in Fig. 3. The angle 0 of the long axis of the indentation varied from-0 to 90” in both cases. In the (0001) plane, 0 = 0” corresponds to the [lOlO] direction and 0 = -90”- to the [1210] direction; in the (lOTO) plane, 0 = 0” corresponds to the [1210] direction and 0 = 90” to the [OOOl] direction. Another example of the hardnesses is shown in Fig. 4. In the examples in Figs. 3 and 4, R = 1.9 and the aluminium and silicon contents were less than 0.008 wt.%.
A-----(4
il
I
*nqic
. 0,
io
’
1ndcntatt0”
*
b
do
(deg)
(b)
6b
30 Anqle
0,
4 ndrntst
$2 I on
(drg)
Fig. 3. The hardnesses of (a) the (0001) and (b) the (lOi0) planes plotted against the angle 0 of the long axis of the indentation. 6 = 0” corresponds to the [ iOlO] direction and 0 = 90” to the [ 12101 direction on the (0001) plane; 0 = 0” corresponds to the [ i2iO] direction and 0 = 90” to the [OOOl] direction on the (lOi0) plane.
0
(4
AnpI.
Of
Ind,ntatlon
(deg)
60
x) Air’,l*
ot
,nd.ntat
90 ,on
(de@
(b)
Fig. 4. The hardnesses of another NbBz single crystal (which is similar to that in Fig. 3).
489
The hardnesses on the (0001) plane varied periodically with the angle 0, i.e. they had maximum values at 0 = 0 and 60” (the long axis of the indenter point was in the 8010) direction) and minimum values at 0 = 30 and 90” (the long axis of the indenter p_ointwas in the (1210) direction). In contrast, the hardnesses on the (1010) plane varied very little with 0. In general the hardnesses on the (0001) plane were higher than those on the (1010)plane. 4. Discussion NbBs single crystals grown from an aluminium solution were relatively perfect crystals. Most of the crystals had few impurities and the ratio R was in the diboride homogeneity range [ 71. The hardness values we measured were not so different as those previously reported for single crystals [4, 51. Consequently our hardness values might be acceptable. The hardness anisotropy of a single crystal depends strongly on the magnitude of the resolved shear stress on the active slip system when an indenter is applied. Brookes et al. [ 81 derived an expression for the effective resolved shear stress 7, on the active slip system by modifing the theory of Daniels and Dunn [ 91. F 7, = A coshcos@ $ (cosJ/ + siny)
(1)
where F is the applied force, A the area supporting F, h the angle between the F axis and the slip direction, 4 the angle between the F axis and the normal to the slip plane, 4 the angle between each facet of the indenter and the axis of rotation for a given slip system and y the angle between each facet of the indenter and the slip direction. Modifying eqn. (1) to 7, = (F/A)f(h, $, I/I,y), we obtained the factor f. The magnitude of l/f qualitatively corresponds to that of the hardness, i.e: the larger (smaller) value of l/f corresponds to the higher (lower) hardness. The primary slip systems of NbBz single crystals are thought to consist of a basal slip system (OOOl)Cll20) and a prismatic slip system (lO~O}Cl210>, as shown for group IVa diboride single crystals with the same crystal structure [ 10 - 141. However, NbBs crystals have an axial ratio (c/a = 1.06 as calculated from the data in ref. 6) that is near to unity. Therefore NbB2 single crystals may have another prismatic slip system (1010) [ OOOl] , as well as the two types mentioned above. When the indenter was applied to the (0001) and (1010) planes, we calculated the factor f asa function of t9for two indenter facets adjacent to each other; for this case, three types of slip system were active. In calculating this slip system, the largest value of f wasfound, because the largest effective resolved shear stress is the dominating factor in the plastic deformation to a first approximation. Next we determined the mean value f,,, of the two f values corresponding to the two indenter facets [ 151. These calculations were carried out by using a computer (Fujitsu model FACOM 270-30) and the results are shown in Fig. 5.
490
Two types of prismatic slip ({10~0}<1210>, {lOiO} [OOOl] ) were found, in agreement with the case where the f, values are at a minimum near 19= 0 and 60” and at a maximum near 0 = 30 and 90” on the (0001) plane (Fig. 5(a)). From Fig. 5(b), if either of these two slip systems is active, it can be seen that the hardness of the (lOTO) plane has a high anisotropy. However, if both slip systems are active, then the hardness of this plane has little anisotropy. The curve representing the mean values of fm,(reie~(l~~c) and ~III,(loi toooii ) is also shown in Fig. 5. When the indenter was applied on the (1010) plane, we can see from this curve that the average effective resolved shear stress on the active slip systems varies according to the indenter direction, i.e. the fact that this plane has little hardness anisotropy should be clearly predictable.
as-
04 __---
cloiolloooi)
04 .
0
(aI
30 AngM
01
rdml?.,I0”
,I Q4
Am$e
(deg)
of
ind.?n!Aon
(deg)
(b)
Fig. 5. The mean factor f, plotted against 8 in the case that the slip system becomes active (a) (0001) plane and (b) (lOi0) plane: curve x, mean value of fm,~~ol;o)(l~,-,)and fm. iloiOk[oooll *
These predictions coincide well qualitatively with the results of our experiments; the hardnesses had maximum values at 8 = 0 and 60” and minimum values at 0 = 30 and 90” on the (0001) plane and varied very little on the (ioio) plane. Consequently we concluded that the primary slip systems are { lOi0) (1210) and (lOi0) [ OOOl] when the indenter was applied on the crystal plane at room temperature. This was supported by observatio_ns of the slip lines around the Vickers indentations on the_~OOOl) and (1010) planes, as shown in Fig. 6; the slip lines along the (2110) di_rection on the (0001) plane and along the [OOOl] direction on the (1010) plane were clearly observed. From thesz observations we confirmed the fact that the primary slip planes were (1010).
491
Fig. 6. Slip lines around the Vickers indentations. The large arrows are 40 /.frn long; the small arrows indicate the slip lines (a) in the (0001) plane and (b) in th e (ioio) plane.
Acknowledgments The authors wish to thank Dr. A. Isogai, Toyota Central Research Laboratory, for the electron microprobe analyses and Mr. Y. Nishida and Mr. S. Ito, Government Industrial Research Institute, Nagoya, for the computer calculations.
492
References 1 B. Aronsson, T. Lundstrom and S. Lundqvist, Borides, Silicides and Phosphides, Methuen, London, 1965, p. 46. 2 H. Nowotny, F. BeneSovsky and R. Kieffer, 2. Metullkd., 50 (1959) 417. 3 J. F. Lynch, C. G. Ruderer and W. H. Duckworth, Engineering Properties of Selected Ceramic Materials, The American Ceramic Society, Columbus, Ohio, p. 5.1.3-7. 4 E. V. Clougherty and R. L. Pober, Nucl. Metall., 10 (1964) 423. 5 W. A. Sanders and H. B. Probst, J. Am. Ceram. Sot., 49 (1966) 231. 6 I. Higashi, Y. Takahashi and T. Atoda, J. Cryst. Growth, 33 (1976) 207. 7 F. A. Shunk, Constitution of Binary Alloys, McGraw-Hill, New York, 1969, Suppl. 2, p. 84. 8 C. A. Brookes, J. B. O’Neill and B. A. W. Redfern, Proc. R. Sot. London, Ser. A, 322 (1971) 73. 9 F. W. Daniels and C. G. Dunn, Trans. Am. Sot. Met., 41 (1949) 419. 10 S. A. Mersol, C. T. Lynch and F. W. Vahldiek, Anisotropy in Single Crystal Refractory Compounds, Vol. 2, Plenum Press, New York, 1968, p. 41. 11 J. S. Haggerty and D. W. Lee, J. Am. Ceram. Sot., 54 (1971) 572. 12 K. Nakano, T. Imura and S. Takeuchi, Jpn. J. Appl. Phys., 12 (1973) 186. 13 K. Nakano, H. Matsubara and T. Imura, Jpn. J. Appl. Phys., 13 (1974) 1005. 14 K. Nakano, H. Matsubara and T. Imura, J. Less-Common Met., 47 (1976) 259. 15 M. L. Tarkanian, J. P. Neumann and L. Raymond, The Science of Hardness Testing and Its Research Applications, American Society for Metals, Novelty, Ohio, 1973, p. 187.