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Ž . Wear 237 2000 253–260 www.elsevier.comrlocaterwear Chemical contribution to friction behavior of sintered hexagonal boron nitride in water T. Saito a, ) , F. Honda b a Toyoda Machine Works, Technical R & D Center, Asahi, Kariya 448-8652, Japan b Toyota Technological Institute, Nagoya 468-8511, Japan Received 12 May 1999; received in revised form 20 October 1999; accepted 25 October 1999 Abstract Ž . Sliding characteristics of sintered hexagonal boron nitride hBN are investigated in water. The friction coefficient of sintered hBNrhBN decreases to 0.06 in distilled water, whereas it is 0.23–0.25 in dry air. As the result of tribochemical reactions, ammonia was formed during sliding in water, and its amount was determined quantitatively for tribochemical reactions and the wear mechanism investigation. The percentage of NH rtotal worn nitrogen was observed to be as high as 20% in regions of low wear rate, while it was 3 around 2% in almost all of the tested regions of hBN. The percentage chemical wear was proposed as an index to distinguish the Ž . Ž . dominant wear process: chemical or mechanical wear process. On the slid surface, X-ray diffraction XRD analysis revealed that 002 crystal orientation of hBN was dominant, which corresponds to the sliding plane of the hBN film transferred onto the steel surface. The Ž . Ž . sintered hBN with CaO additive hBN–CaO had a higher frictional force and a lower specific wear rate than sintered pure hBN p-hBN . Ž . Ž . Surface analysis of hBN–CaO revealed that Ca OH condensed on the slid surface and a Ca OH film covered hBN to reduce ammonia 2 2 formation as well as the chemical wear ratio of hBN–CaO. The minor component CaO additive was proven to take an important role in the characteristics of hBN in water. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Nitride; hBN; Water; Wear; Chemical reaction; Ammonia; Sintering additive; Layer 1. Introduction Several nitrides including Si N , TiN and CrN, are 3 4 considered useful materials in tribology. Since Si N r 3 4 Si N slid in water is reported to produce silica and 3 4 w x ammonia 1,2 , the friction characteristics of nitrides are expected to be strongly related to chemical reactions oc- curring on the nitride surface. Ž . Another nitride, hexagonal boron nitride hBN , is used as a solid lubricant, similar to MoS and graphite. Several 2 reports concerning the friction characteristics of hBN in w x water are available 3,4 . Self-lubrication of hBN was explained in terms of sliding of the low-index crystal plane wx 5 ; however, the lubrication layer on the slid surface somehow influences the tribological behavior. We also confirmed that hydroxides or hydrates exist on the sliding wx wx surfaces of silicon nitride 6 and carbon steel 7 . Ammonia was produced from silicon nitride slid in wx water 2 . On the other hand, hBN is also assumed to ) Corresponding author. E-mail: [email protected] produce ammonia by sliding in water; however, no quanti- tative analysis of ammonia from sliding the hBN has been reported so far. Quantitative analysis of ammonia is neces- sary for the elucidation of the tribochemical reaction. From the quantity of ammonia produced, the chemical influence on the wear of Si N rSi N in distilled water was calcu- 3 4 3 4 wx lated to be 20–60% in a previous report 8 , and an apparently strong chemical influence on Si N sliding was 3 4 confirmed. Discussion of the chemical influence is also significant for hBN sliding. hBN is fabricated by several industrial methods. Sinter- wx ing is one of the commercial methods 9 , and sintered hBN contains some sintering additives in general. The influence of sintering additive on the friction behavior has been ignored, although the sintered material has been widely used for sliding parts. In this report, we carried out sliding tests of hBN pin on hBN plate in water, and primarily describe the friction characteristics of sintered hBN in water, and discuss the influence of sintering additives. Furthermore, the chemical influence on hBN wear is estimated by a quantitative 0043-1648r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. Ž . PII: S0043-1648 99 00346-4

Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

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Page 1: Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

Ž .Wear 237 2000 253–260www.elsevier.comrlocaterwear

Chemical contribution to friction behavior of sintered hexagonal boronnitride in water

T. Saito a,), F. Honda b

a Toyoda Machine Works, Technical R&D Center, Asahi, Kariya 448-8652, Japanb Toyota Technological Institute, Nagoya 468-8511, Japan

Received 12 May 1999; received in revised form 20 October 1999; accepted 25 October 1999

Abstract

Ž .Sliding characteristics of sintered hexagonal boron nitride hBN are investigated in water. The friction coefficient of sinteredhBNrhBN decreases to 0.06 in distilled water, whereas it is 0.23–0.25 in dry air. As the result of tribochemical reactions, ammonia wasformed during sliding in water, and its amount was determined quantitatively for tribochemical reactions and the wear mechanisminvestigation. The percentage of NH rtotal worn nitrogen was observed to be as high as 20% in regions of low wear rate, while it was3

around 2% in almost all of the tested regions of hBN. The percentage chemical wear was proposed as an index to distinguish theŽ . Ž .dominant wear process: chemical or mechanical wear process. On the slid surface, X-ray diffraction XRD analysis revealed that 002

crystal orientation of hBN was dominant, which corresponds to the sliding plane of the hBN film transferred onto the steel surface. TheŽ . Ž .sintered hBN with CaO additive hBN–CaO had a higher frictional force and a lower specific wear rate than sintered pure hBN p-hBN .

Ž . Ž .Surface analysis of hBN–CaO revealed that Ca OH condensed on the slid surface and a Ca OH film covered hBN to reduce ammonia2 2

formation as well as the chemical wear ratio of hBN–CaO. The minor component CaO additive was proven to take an important role inthe characteristics of hBN in water. q 2000 Elsevier Science S.A. All rights reserved.

Keywords: Nitride; hBN; Water; Wear; Chemical reaction; Ammonia; Sintering additive; Layer

1. Introduction

Several nitrides including Si N , TiN and CrN, are3 4

considered useful materials in tribology. Since Si N r3 4

Si N slid in water is reported to produce silica and3 4w xammonia 1,2 , the friction characteristics of nitrides are

expected to be strongly related to chemical reactions oc-curring on the nitride surface.

Ž .Another nitride, hexagonal boron nitride hBN , is usedas a solid lubricant, similar to MoS and graphite. Several2

reports concerning the friction characteristics of hBN inw xwater are available 3,4 . Self-lubrication of hBN was

explained in terms of sliding of the low-index crystal planew x5 ; however, the lubrication layer on the slid surfacesomehow influences the tribological behavior. We alsoconfirmed that hydroxides or hydrates exist on the sliding

w x w xsurfaces of silicon nitride 6 and carbon steel 7 .Ammonia was produced from silicon nitride slid in

w xwater 2 . On the other hand, hBN is also assumed to

) Corresponding author. E-mail: [email protected]

produce ammonia by sliding in water; however, no quanti-tative analysis of ammonia from sliding the hBN has beenreported so far. Quantitative analysis of ammonia is neces-sary for the elucidation of the tribochemical reaction. Fromthe quantity of ammonia produced, the chemical influenceon the wear of Si N rSi N in distilled water was calcu-3 4 3 4

w xlated to be 20–60% in a previous report 8 , and anapparently strong chemical influence on Si N sliding was3 4

confirmed. Discussion of the chemical influence is alsosignificant for hBN sliding.

hBN is fabricated by several industrial methods. Sinter-w xing is one of the commercial methods 9 , and sintered

hBN contains some sintering additives in general. Theinfluence of sintering additive on the friction behavior hasbeen ignored, although the sintered material has beenwidely used for sliding parts.

In this report, we carried out sliding tests of hBN pin onhBN plate in water, and primarily describe the frictioncharacteristics of sintered hBN in water, and discuss theinfluence of sintering additives. Furthermore, the chemicalinfluence on hBN wear is estimated by a quantitative

0043-1648r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved.Ž .PII: S0043-1648 99 00346-4

Page 2: Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

( )T. Saito, F. HondarWear 237 2000 253–260254

analysis of ammonia produced by hBN slid in water. Fromthe estimated chemical influence on the wear rate, the lowfriction coefficient of hBN is discussed. The crystal struc-ture of hBN is also discussed for the investigation of theslipping layer under a mechanical force. The influence ofwater on the wear mechanisms of nitrides under water-lubricated conditions is also discussed.

2. Experimental

2.1. Apparatus and specimens

Friction and wear experiments were conducted using apin-on-plate testing device in which a rotating hBN platewas contacted with an upper stationary hBN pin in dis-tilled water. A schematic diagram of the equipment, to-gether with the specimen dimensions, is shown in Fig. 1. Anormal load was applied to the stationary pin, and fric-tional force was continuously measured by a strain gauge.The change in water temperature was negligible and hence,was ignored.

Ž .The test specimens used in this report were: a sinteredŽ . Ž .pure hBN without sintering additives p-hBN ; and b

sintered hBN with 1.5 wt.% CaO and 2.5 wt.% B O2 3Ž .sintering additives hBN–CaO . Material properties of their

specimens are shown in Table 1. The specimens hadŽ .hemispherical 4 mm in diameter ends and the plates were

30=30 mm2 and 4 mm thick. hBN pin ends and hBNplate surfaces were finished by grinding to 1.2 mm R .a

Ž .Only for X-ray diffraction XRD analysis of the hBNcrystal structure of the transferred film were sliding testscarried out on low-carbon steel plate replacing the hBN

Fig. 1. Schematic of wear tester and dimensions of specimens.

Table 1Material properties of hBN specimens

Specimen p-hBN hBN–CaO

Sintering additives no additive 1.5 wt.% CaO;2.5 wt.% B O2 3

3Ž .Density grcm 1.85 1.90Ž .Bending strength MPa 40 40

Thermal conductivity 40 18Ž .Wrm k

plate to eliminate the diffracted signals from the substratehBN plate.

2.2. Procedure

The specimens were slid in distilled water at a speed of0.13 mrs, and a constant load between 3 and 33 N. Thevolume of distilled water was chosen to be 200 ml topreserve the slid surface under water, and the slidingdistance was fixed at 700 m. After the experiments, thespecimens were stored in a vacuum desiccator to minimizefurther oxidation.

The reaction products and wear debris formed on theslid surfaces were analyzed by an electron probe microana-

Ž .lyzer EPMA , operated at 15 kV acceleration voltage and1 mm beam diameter. The amount of ammonia formedtribochemically in water was quantitatively determined bya conventional spectrophotometric method using Nessler’s

w xreagent 10 . The worn surfaces of the plates were ob-Ž .served by scanning electron microscopy SEM and the

surface profile was measured by a highly sensitive stylusprofilometer to calculate the specific wear rate.

3. Experimental results and discussion

3.1. Friction behaÕior of hexagonal boron nitride

Fig. 2 shows the friction coefficient of p-hBN andhBN–CaO sliding against itself in distilled water. The

Fig. 2. Friction coefficient of p-hBN and hBN–CaO sliding againstthemselves in distilled water.

Page 3: Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

( )T. Saito, F. HondarWear 237 2000 253–260 255

Fig. 3. Specific wear rate of p-hBN and hBN–CaO sliding againstthemselves in distilled water.

friction coefficient of p-hBN in water was 0.06–0.12,whereas it was 0.23–0.25 in dry sliding. A friction coeffi-cient of as low as 0.06 was obtained from p-hBN at loadsunder 10 N. At a load of 10 N or lower, the friction

coefficient of p-hBN is significantly lower than that ofhBN–CaO, but, above a load of 15 N, the friction coeffi-cient of p-hBN increases obviously up to the same levelwith hBN–CaO.

A significant increase is also observed in the specificwear rate, as shown in Fig. 3, where p-hBN and hBN–CaOare almost on the same level at loads lower than 10 N;however, the specific wear rate of p-hBN increases drasti-cally and exceeds that of hBN–CaO.

3.2. Determination of calcium compound film on the slidsurface of sintered hBN–CaO

Since the difference in the friction behavior betweensintered p-hBN and hBN–CaO is expected to depend onthe interfacial layer of the slid surface, the latter wasanalyzed by means of EPMA.

Fig. 4 shows the SEM and images of characteristicX-rays of boron, calcium and oxygen on a slid platesurface of sintered hBN–CaO in water, at a load of 11.4 Nand a speed of 0.13 mrs. Analytical results revealed that a

Fig. 4. Electron probe microanalysis of hBN–CaO sliding surface in distilled water.

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( )T. Saito, F. HondarWear 237 2000 253–260256

calcium compound, which is due to the sintering additive,formed an interfacial film on the slid surface. The slidsurface had a roughness of 0.2 mm R or less after slidinga

in water, compared to a roughness of 1.2 mm R beforea

sliding.Fig. 5 shows the correlation between the relative inten-

sities of X-ray from calcium and oxygen on the slidsurface in water. It indicates that enrichment of calciumand oxygen is observed on the slid surface, especially at aload of 10–20 N. The enriched concentration of calciumand oxygen suggests that small amounts of sintering addi-tives in hBN may have a large influence on the frictionbehavior of the sintered material. Furthermore, the amountsof calcium and oxygen show a high correlation coefficientR of 0.85 in water, compared to R 0.03 for dry sliding.Such a high correlation indicates that calcium exists as anoxide or a hydroxide on the slid surface. In contrast,calcium and oxide are only detected at the edges of thetrack slid in air; calcium and oxygen do not cover the slidsurface, and the distribution of calcium and oxygen doesnot show constancy in their relative abundances.

From the regression line in Fig. 5, the weight ratio ofŽ .oxygenrcalcium OrCa is calculated and shown as a

function of load in Fig. 6. The OrCa ratio of sinteringadditive CaO is 0.4 and that on the surface before slidingwas approximately 3, which are reasonable values for thecompound and the complex oxidized surface. A low OrCaratio of 1.3–1.5 is observed on the slid surface at a load of5–20 N in water. This value is quite similar to that of

Ž .Ca OH , which has a theoretical ratio of 0.8. Therefore,2

the chemical form of Ca on the slid surface was estimatedŽ .to be Ca OH .2

Additional analysis by EPMA was expected to elucidatethe chemical state of calcium on the slid surface using CaKa spectra. Since Ca Ka spectra showed a shift due to

Ž .the chemical state of calcium, CaO and Ca OH were2

Fig. 5. Correlation of oxygen with calcium on the hBN–CaO slid surfaceby electron probe microanalysis.

Fig. 6. Ratio of oxygen to calcium on hBN–CaO in distilled water.

distinguishable by comparison of their spectra. Spectralanalysis revealed that the peak position of the slid surface

Ž .in water matches that of standard Ca OH but not that of2

CaO. This indicates that the calcium compound on the slidŽ .surface in water is Ca OH which appears to form a film2

on the slid surface and is assumed to change the frictionbehavior.

( )3.3. Mechanism and role of Ca OH film produced on the2

slid surface

Ž .The Ca OH film obviously has a strong influence on2

the friction behavior and the chemical reaction of sinteredhBN. On the slid surface of hBN–CaO, the hBN pin

Ž .contacts the Ca OH film, leading to the observation of2Ž .an apparently higher friction coefficient of hBNrCa OH .2

A lower friction coefficient is observed from the boronhydrate or hydroxide on the surface that calcium hydroxidefilm formation interrupts the smooth sliding of hBN. On

Ž .the other hand, Ca OH film on the sliding surface has a2

high wear resistance that protects hBN underneath it fromŽ .wear loss. Ca OH film therefore works as a protective2

layer but not as a lubricant, such that lower wear loss andhigher friction coefficient are observed.

The mechanism involved in CaO condensation is con-sidered as follows. The sintering additive, CaO, is hydrated

Ž . Ž .easily and produces Ca OH according to reaction 1 :2

CaOqH O™Ca OH . 1Ž . Ž .22

Another oxide B O , which is present in the sintering2 3

additive and also produced by sliding, is easily hydrated tow xform H BO 11 :3 3

B O q3H O™2H BO . 2Ž .2 3 2 3 3

The solubility of H BO is 2.6 wt.% at 208C; thus, it is3 3

readily soluble in water, in contrast with the solubility 0.17Ž .wt.% of Ca OH . H BO is preferentially dissolved in2 3 3

Ž .water and the residual condensation of Ca OH is re-2Ž .tained on the slid surface. A residual Ca OH film is2

Page 5: Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

( )T. Saito, F. HondarWear 237 2000 253–260 257

Fig. 7. Boron oxide formation on p-hBN slid surface in distilled water.

produced especially at the load of 10–20 N, which is thelow wear loss region of hBN–CaO.

3.4. Chemical contribution to the wear of sintered hBN inwater

The ammonia and oxides formed by tribochemical reac-Ž .tion 3 were analyzed on the slid surface of sintered hBN:

BNq3r2H O™1r2B O qNH . 3Ž .2 2 3 3

Boron oxide formation on the p-hBN sliding surface isshown in Fig. 7. Fig. 8 shows the quantity of ammoniaformed in the test water, which was determined quantita-tively by a spectrophotometrical method. Ammonia forma-tion is therefore confirmed to proceed as a function of

Ž .load, following reaction 3 .From p-hBN and hBN–CaO, amount of ammonia in-

creases with increasing load at load regions lower than 20N, and from hBN–CaO, a maximum appeared at 25 N of

Ž .load. The influence of sintering additives CaO, B O on2 3

Fig. 8. The quantity of ammonia in test water produced from sinteredhBN sliding.

ammonia production is distinct over the load of 20 N. At aload of 20 N or higher, hBN becomes rather mechanically

Ž .worn than chemically worn following reaction 3 , so thata smaller amount of ammonia is formed. For example, asmaller amount of ammonia, which corresponds 1r3 ofthat produced by p-hBN, is observed in the case of hBN–

Ž .CaO by the presence of the Ca OH film, which worked2

as a protective layer against the formation of ammoniaŽ Ž ..reaction 3 .

The ammonia formed also increases the pH of the testwater, as shown in Fig. 9. The pH of water increases to 8.2with increasing amount of ammonia formed. The alkalinesolution is believed to have an influence on the corrosivereaction of oxide material. The pH of test water forhBN–CaO is higher than that of test water for p-hBN, aftersliding at a constant sliding distance, although the amountof ammonia formed by hBN–CaO is lower than thatformed by p-hBN. A higher pH was attained from hBN–CaO due to the dissolution of Ca2q into the test water. Onthe other hand, for p-hBN, B O contacts with H O to2 3 2

Fig. 9. pH of water after sliding test on sintered hBN.

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( )T. Saito, F. HondarWear 237 2000 253–260258

Fig. 10. Chemical wear loss of sintered hBN in water, shown in units ofmoles.

form and acidic H BO , which dissolves in water to lower3 3

the pH.

3.5. Chemical wear ratio of hBN slid in water

The production of ammonia is associated with chemicalinfluence on wear; therefore, a quantitative measurementof the ammonia produced may provide information on themechanism involved in wear.

To estimate the chemical influence on wear, two as-sumptions are made. First, the total wear loss in waterW is assumed to comprise mechanical wear loss Wtotal me

and chemical wear loss W . Mechanical wear is definedc

here as wear due to mechanical force. On the other hand,chemical wear is defined here as the ammonia formation

Ž .from nitrogen following reaction 3 . The degree of chemi-cal wear was calculated from the amount of ammoniaproduced:

W sW qW . 4Ž .total me c

The second assumption is that ammonia is producedŽ .from reaction 3 alone. Undefined reactions involved in

the formation of nitrogen-containing compounds are notŽ .considered here. From reaction 3 , 1 mol of hBN is

required for the production of 1 mol of NH . Chemical3

wear loss is calculated from the quantity of ammoniaconsumed as follows:

W skM . 5Ž .c NH 3

Ž . Ž .In Eq. 5 , k is the reactant coefficient of reaction 3 .Chemical wear loss of sintered hBN is shown in Fig.

10. The total chemical and mechanical wear losses areshown as a function of total wear loss, which is shown inunits of cubic millimeters. Fig. 10 shows that the chemicalwear loss of hBN increases as the total wear loss increases,and the fraction of chemical wear is lower in the high totalwear loss region. On the other hand, mechanical wear lossincreases in the high total wear loss region. In the high

wear loss region, mechanical wear becomes dominantrather than chemical wear.

To estimate the chemical influence unambiguously, theratio of chemical wear loss to total wear loss is defined bythe chemical wear ratio CR:

w xCR % s100=W rW . 6Ž .c total

Fig. 11 shows the chemical wear ratios of hBNrhBN slidin distilled water. A low chemical wear ratio of 2–20% isobserved at hBNrhBN in water, whereas that ofSi N rSi N in water is reported to be as high as 20–60%3 4 3 4w x8 . A high chemical wear ratio is observed for p-hBN atlow wear volume. A high chemical wear ratio indicatesthat the wear of hBN proceeds chemically. This resultindicates that chemical influence on the wear of hBN islarge in the lower wear region, and mechanical influence islarge in the higher wear region. Furthermore, the higherchemical wear region corresponds to the low friction re-gion of ms0.06, and the low friction coefficient ofp-hBN is chemically influenced. The chemical effect ap-pears in the form of oxidation or hydration of boron, andsignificant boron oxide is detected on the slid p-hBNsurface.

Low wear ratio obviously indicates that the wear ofhBN proceeds mechanically in hBN–CaO. In the lowerwear region, the slid surface is covered sufficiently with

Ž .Ca OH film so that hBN and H O do not contact2 2

effectively. In other words, chemical influence of H O to2

hBN is reduced due to a low amount of CaO additives.The chemical wear ratio of hBN is as low as 2–20%;

therefore, additional mechanical influence on the frictionbehavior was examined. An important mechanical influ-ence on hBN is the presence of its layered crystal structurew x12 , which is considered to slip easily under low frictionalforce.

The slid surface of p-hBN in water was observed withan SEM and shown in Fig. 12. SEM observation revealsthat the slipped plane was retained on the wear track. The

Fig. 11. Chemical wear ratio of sintered hBN slid in distilled water,shown in units of moles.

Page 7: Chemical contribution to friction behavior of sintered hexagonal boron nitride in water

( )T. Saito, F. HondarWear 237 2000 253–260 259

Fig. 12. SEM observation of p-hBN slid in distilled water.

slipped plane could be confirmed from the preferentialorientation of the layers, using XRD analysis as follows.

From this object, we replaced hBN plate to a steel plateof the sliding experiments. The crystal structure of thehBN thin transferred film was almost undetectable on hBNplate, but was detectable on a slid surface of hBNrsteel.At the sliding test of hBNrsteel in water, hBN film isformed on the steel surface and the friction coefficient is0.12. XRD analysis of the hBN film transferred to steelwas made without any interference from X-ray signals ofthe substrate.

Ž .Fig. 13. XRD analysis of a hBN film transferred to sliding surface forŽ .hBNrsteel in water and b hBN surface before sliding.

Fig. 13 shows XRD results of slid surface ofhBNrlow-carbon steel, and indicates that the transferred

Ž . Ž . Ž .hBN film shows preferred 002 , 004 and 006 orienta-tions. The orientation indicates the importance oflayerrlayer sliding on the friction behavior of hBN. Theslipping between these layers is more dominant duringmechanical wear than during chemical wear of hBN.

The sliding between hBNrtransferred hBN film pro-duces a friction coefficient 0.12, but the low frictioncoefficient of 0.06 in water could not be interpreted onlyby the XRD results. Furthermore, the surface films of

Ž .Ca OH and boron oxides have some influence on the2

friction coefficient.

4. Conclusion

Ž .1 Wear mechanism of hBN was investigated and it isconcluded that 2–20% of wear is chemical wear that leadsto the formation of ammonia and that the remainder ismechanical wear.

Ž .2 Lower chemical wear ratio is observed for hBN–CaO, due to the limited reaction of hBN with H O by the2

Ž .Ca OH film on the slid surface.2Ž .3 Friction coefficient of p-hBN is minimum at 0.06

for a load of 6–8 N, and that of hBN–CaO is 0.1 orhigher.

Ž .4 At high loads, wear of hBN–CaO is less than that ofŽ .p-hBN due to the presence of the Ca OH protective film.2

Ž .5 The transferred film of hBN on steel has a strongŽ .and preferential 002 orientation, and influence of sliding

between the crystal plane is confirmed. The orientationindicates a significant role of the sliding plane on thefriction behavior of hBN.

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( )T. Saito, F. HondarWear 237 2000 253–260260

Acknowledgements

We would like to thank Emeritus Professor K. Naka-jima of Toyota Technological Institute for his helpfulsuggestions. We would also like to thank Dr. Y. Mizutaniof Toyota Central R&D Laboratories for instructive sup-port, as well as Mr. K. Nakamura, Mr. T. Abe, Mr. Y.Imai, Mr. T. Sibukawa, Dr. Y. Inaguma, Mr. K. Sugiyama,Mr. T. Teramura and Mr. H. Fukami of Toyoda MachineWorks for their warm encouragement. Toyoda MachineWorks is acknowledged for the financial support of thiswork.

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