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Wear 271 (2011) 2477– 2484

Contents lists available at ScienceDirect

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ear mechanism study of exhaust valve system in modern heavy dutyombustion engines

. Forsberg ∗, P. Hollman, S. Jacobsonepartment of Engineering Sciences, The Ångström laboratory, Uppsala University, Sweden

r t i c l e i n f o

rticle history:eceived 1 September 2010eceived in revised form8 November 2010ccepted 29 November 2010

a b s t r a c t

The increasing demands from environmental legislations are changing the conditions that the valvesystem is exposed to in heavy duty engines. Increased pressures, higher temperatures and lower amountsof soot which can build up a protective film are some of the increasing challenges which the system hasto endure.

Three pairs of valves and valve seat inserts with the same material and design properties but withdifferent service condition have been analyzed with a variety of analytical instruments to gain information

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of how the wear occurs.The wear mechanisms found were a combination of oxidation, where many different oxides were

found, adhesive wear, which was seen both in form of material transfer and flow lines. On top of SampleMild and Hard there were tribo films of thickness varying from 1 to 5 �m consisting of Ca, O, P, S and Zn.The film has in all cases protected the underlying surface from wear but in some cases seems to have a

dhesive corrosive impact instead.

. Introduction

The exhaust valve system of modern combustion engines expe-iences a very complex contact situation including frequent impactnvolving micro sliding, high and varying temperatures, complexxhaust gas chemistry and possible particulates. The wear rate haso be extremely low, and the individual wearing events operate at

very minute scale that is hard to detect even in scanning elec-ron microscope. These difficulties have resulted in that very littles known about why present well-working systems really work. Theurrent system configurations are based on extensive testing andecades of gradual development rather than on knowledge-basedesign.

The tribological situation in the exhaust valve system isxpected to be severe for engines that will follow the Euro 6 emis-ion regulation, which is briefly compared to earlier legislations inig. 1. Due to enhanced combustion and cleaner fuels, almost noombustion products are formed that might ease the wear condi-ions. The wear of the contact surfaces is thus expected to become

ore aggressive, which in the case of the exhaust valve could lead tohange in the combustion conditions and increasing emission lev-

ls. Obviously, this sharpens the requirements for reduced wear,o keep the emissions low throughout the life of the engine, andresents a great challenge.

∗ Corresponding author. Tel.: +46 18 471 6376; fax: +46 18 471 35 72.E-mail address: peter.forsberg@angstrom.uu.se (P. Forsberg).

043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2010.11.039

© 2011 Elsevier B.V. All rights reserved.

The wear mechanisms of valves are not easy to investigate. Theyhave been described to include a combination of abrasive, adhe-sive and oxidative wear [1,2]. Simultaneously, thin tribofilms areformed on the surfaces, composed from material from the valvesand residues from the combustion, acting as a solid lubricant. Alarge part of the residues is soot. Soot is a relatively good lubri-cant for the valves but will become strongly reduced with the newregulations.

One of the biggest steps in valve seat inserts (VSI) developmentwas in 1970 when the Clean Air Act prescribed the introduction ofcatalytic converters to the market in an attempt to reduce vehicleemissions. The proper operation of the catalysts required the leadcontent in the fuel to be removed, to avoid lead poisoning. How-ever, in the 70s the lubricating role of lead in the valve seat/valvecontacts was not known. The removal resulted in heavy wear, espe-cially on the exhaust side. Research proved that the lead reacted andformed complex lead oxides on the valve and seat surfaces, thesehad beneficial friction properties and protected the surfaces [3,4].In absence of the lead, a brittle iron oxide formed. This oxide flakedduring operation, directly leading to accelerated oxidative wear andfurther to abrasion in other locations where the hard particles gotstuck [5,6]. For several years, a common solution to counteract thiswear was to harden the seat surface [4]. However, new designsusing valve seat inserts made from alternative materials solved the

problem.

Many test rig designs have been employed to simulate the con-tact situation, some involving real valve and valve seats [1,2,7–10]but also some with simplified simulated contact situations [11–13].

2478 P. Forsberg et al. / Wear 271 (2011) 2477– 2484

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Table 1Material composition for used samples.

Valve [%] VSI [%]

C 1.75 0.80–1.30Co Bal 15.0–22.0Cr 25.5 3.5–5.5Cu – 10.0–20.0Fe Max 1.5 BalanceMn 0.5 0.3–1.5Mo 0.6 9.0–14.0Ni 22.5 –S 0.15–0.75Si 1.1 0.5–2.0V – 1.3–2.3W 12 2.5–4.5Others <3

Fig. 2. Valve seat and insert, both with a contact angle of 45◦ . Contact surfacesmarked grey in the magnification.

Fig. 3. Typical microstructure of the tested samples before testing imaged with

a welded hard face consisting of Stellite F. Stellite F is a cobaltchromium based alloy with a microstructure shown in Fig. 3. TheNi content is higher than in the other members of the Stellite fam-ily. The alloy is specifically designed for combustion engine valve

Table 2Sample descriptions.

ID Origin Operated condition

Sample Mild Consumer truck 440,000 km mildlydriven

Sample Hard Consumer truck 210,460 km relatively

Fig. 1. Accepted emission of sot (PM) and NOx depending on legislation.

he wear mechanisms found in these studies include adhesiveear in form of micro welding and material transfer. The trans-

erred material have in some cases resulted in abrasive wear as thealve rotates and the protruding material meets a non-matchingurface.

Large adhesive forces have induced shear forces and deforma-ion in the material and in some cases created flow lines which cane seen in cross sections. In some cases there have been crackingf the valve due to high stresses due to misalignment and materialefects [1,2].

Lewis et al. [7] have composed the following list of designhanges tested through the years with successful results andeduced wear; hardening of seat, increased seat width, weldingaterial onto valve seating face, greater rigidity of valve mecha-

ism, improved cooling of cylinder head bottom, greater rigidityf valve head, positive rotation of valve, use of hardened valveeat inserts, reducing speed of valve impact, lubrication of contactetween valve and seat, reduction in seating face angle. The latteras been reported to be very effective; a change from 45◦ to 30◦ may

ead to a wear reduction of up to 75% due to decreased frictionalovement [14].To sum up the different tests, a number of factors should be

onsidered when minimizing the wear. The two major mechani-al factors are; impact force of the valve on the seat insert duringalve closing and sliding of the valve on the seat insert during thection of the combustion pressure [15]. The impact due to closingan be, and nowadays is, greatly reduced with clever design of theamshaft. Other factors that influence the wear; impact resistancef the seat insert material, lubricity of the seat insert material underry running conditions, combustion load, flexibility of the valveead, machining tolerances of the seat insert and valve guide, seat

nsert and valve guide concentricity, uniformity of cylinder headooling, temperature, etc.

The main objective of the present investigation is to analyse theear mechanism of some typical exhaust valves that have oper-

ted under different conditions. The valves and valve materialsre investigated using several analytical instruments, both on theurface and in cross sections.

. Experimental

Three pairs of valves and valve seat inserts (VSI) have been ana-yzed. All pairs are made from the same material combination, listed

n Table 1, and they share the same geometry with a contact anglef 45◦, see Fig. 2.

The valve head and stem consists of austenitic and marten-itic stainless steel, respectively (Table 2). The contact surface has

BSE-SEM on polished cross sections. To the right is the Stellite F and to the left is theAR20. Material composition marked. Note the different magnifications of the twomaterials.

hard drivenSample Engine cell Engine cell tested 723 h (equals 400,000

hard km or 800,000mild km)

P. Forsberg et al. / Wear 271 (2011) 2477– 2484 2479

Fig. 4. Showing examples of analyses performed on the valve contact surface. SEMoverview image to the left and a surface topography overview map to the right. Asurface profile plotted from the bottom up in the surface map. Note the stronglyexaggerated y-axis which is magnified 40 times in comparison to the x-axis.

Fig. 5. Wear depth is measured via image processing of optical microscope. Pro-file from picture in white compared to an unworn reference. Grey area representsremoved material. Wear depth is marked with white arrow.

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Fig. 6. Surface characterisation of the valve from Sample Mild. SEM overview imageto the left and a surface topography map in the middle. The chart to the right shows

The valve surface appeared spotty, with bright and darker areas,as shown in Fig. 6. The dark areas correspond to a thin tribofilm on

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ard facing. It has a slightly higher hardness and better resistanceo erosion and corrosion compared to Stellite 6.

The valve seat is made of a sintered material with brand nameovofer AR20, produced by Bleistahl. This is a high speed steel

ncorporating intermetallic phases and high temperature solidubricants. A typical microstructure is shown in Fig. 3. To enhancehe thermal conductivity, which is of great importance since about5% of the heat from the valve is transported via the VSI to the cool-

ng channels [11], the majority of the pores are filled with copper.Each pair has run under different service condition. One has been

art of a highway truck engine and has therefore experienced a rel-tively mild load. The second has been driven relatively hard withots of high load on the engine, but has a lower mileage, and thehird was tested in an engine test cell. The third pair is from a dif-erent engine model of a later design, resulting in less combustionesidues. The test cycles in the engine cell are cycled between max-mum load, and sometimes even above, and back to idle in order totress the engine hard, so the wear can be expected to alter some-hat from ordinary use. Each cylinder has two pairs of exhaust

alves and VSI (back and forward), for this analysis we chose the

ack pair from each cylinder.

ig. 7. Cross section of the valve surface in Sample Mild. SEM to the left. EDX maps to theigher element concentration in that area.

the surface profile along the red line (from bottom and up) in the topography map.(For interpretation of the references to color in this sentence, the reader is referredto the web version of the article.)

3. Analysis

Surfaces and polished cross sections were analyzed with sev-eral instruments. Scanning electron microscopes (SEM) were usedfor imaging. SEM with backscatter detector in composition mode(BSE) and energy dispersive X-ray spectroscopy (EDX) was usedto get compositional information. The distribution of all elementsdetected was mapped, while only the most interesting are pre-sented in Section 4.

3D topography measurement was performed using white lightinterference microscopy (WYCO). Due to the rotation of the valves,the wear scars become almost uniform all around the contact. The3D topography scanning was performed over a 0.9 mm wide trackalong the sliding direction of the valve and VSI, as shown in Fig. 4.

The Focused Ion Beam (FIB) was used to create small scale, well-polished cross sections. The ion beam is very mild to the surface,which reduces the composition changes, smearing, etc. comparedto the conventional grinding/polishing process. Prior to preparingthe cross section, a thin layer of Pt is deposited to protect the outer-most surface from the milling ion beam. These Pt-layers, depositedin two steps, are visible in the cross sections as a light upper layerwith a slightly darker layer beneath, with a total thickness of about0.5–0.8 �m.

An optical microscope was used to estimate the wear depth oneach sample. Cross section pictures were processed to show onlythe contours of the samples. The contours were compared to anunworn reference Sample and the wear was measured, see Fig. 5.

4. Results

4.1. Valve from Sample Mild

the surface while the bright areas indicate bare valve material. The

right illustrate the signal strength for different elements. Brighter areas represent

2480 P. Forsberg et al. / Wear 271 (2011) 2477– 2484

Fig. 8. Cross section of the valve surface where the deformed microstructure revealsplastic flow on the outermost layer. The flow pattern is pointing towards the outerradius of the valve. On top of the affected microstructure there is a thin oxide ofabout 1.5 �m. BSE SEM.

Fig. 9. Cross section showing a 0.5 �m thick tribofilm with embedded carbon par-ticles. FIB SEM cross section.

Fig. 10. Surface characterisation of the valve seat insert from Sample Mild. SEMoverview image to the left and a surface topography map in the middle. The chartto the right shows the surface profile along the red line (from bottom and up) in thetopography map. (For interpretation of the references to color in this sentence, ther

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Fig. 12. Surface characterisation of the valve from Sample Hard. SEM overviewimage to the left and a surface topography map in the middle. The chart to the right

surface with some circular spots, which are residues from the clean-ing agent, see Fig. 15. The surface has a smoothly rounded elevation,roughly 5 �m high. The wear depth is estimated to 50 �m. No oxide

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eader is referred to the web version of the article.)

ribofilm consists mainly of Mo and O, see Fig. 7. No scratches can beeen on the surface. The topography is characterised by pits with aepth of a couple of micrometers in an otherwise smooth plateau,ee Fig. 6. The outermost micrometers of the valve are stronglyeformed, showing flow lines pointing towards the outer rim, seeig. 8.

FIB cross section shows a dark coating which contains Ca, O, P, and Zn. The coating include black embedded particles consisting

f carbon residues resulting from poor combustion, see Fig. 9.

ig. 11. Cross section of the seat surface in Sample Mild. SEM to the left. EDX maps to theigher element concentration in that area.

shows the surface profile along the red line (from bottom and up) in the topographymap. (For interpretation of the references to color in this sentence, the reader isreferred to the web version of the article.)

4.2. Valve seat insert from Sample Mild

The valve seat insert from Sample Mild shows a very smoothsurface, both in the SEM and in the topography image in Fig. 10.The wear depth is estimated to 20 �m. The valve surface appearsslightly darker in the middle section, which can be seen as anelevation in the corresponding topography image. The elevationis some 5 �m above the bottom of the wear scar. The dark linesacross the SEM image are machining grooves, which indicates thatthis area is almost unworn. A surface film covers parts of the seat.It has a thickness of a few �m and consists of Mo, Si and O, seeFig. 11.

4.3. Valve from Sample Hard

The valve from Sample Hard is mainly characterised by itssmooth appearance with a layer including small scattered pits, seeFigs. 12 and 13. The pit appears brighter in the SEM which indi-cates a heavier/denser material than the coating. The close-up inFig. 13 shows one of the pits in the smooth surface layer and theelement maps confirm that the pits expose the bare valve material.The smooth surface coating consists of Ca, O, P, S and Zn. EDX alsoshows that the darker regions in the pits are depositions of carbon.A rough estimated based on image processing of the overview SEMpicture gives an approximate value of 10% bare metal on the sur-face. The EDX cross section in Fig. 14 further identifies the tribofilm,as a 5 �m thick film and made up by Ca, O, P, S and Zn on top of theseemingly unaffected valve material.

4.4. Valve seat insert from Sample Hard

The valve seat insert from Sample Hard shows a very smooth

layer was detected by EDX analysis of a cross section in an area

right illustrate the signal strength for different elements. Brighter areas represent

P. Forsberg et al. / Wear 271 (2011) 2477– 2484 2481

Fig. 13. Surface overview and composition analyse of the valve in Sample Hard from area marked by white rectangle in Fig. 12. The small pits are areas where the surfacefilm has flaked off and exposes the underlying metal.

Fig. 14. Cross section of the valve surface in Sample Hard. A smooth, 5 �

Fig. 15. Surface characterisation of the valve seat insert from Sample Hard. SEMoverview image to the left and a surface topography map in the middle. The chartto the right shows the surface profile along the red line (from bottom and up) in thetopography map. (For interpretation of the references to color in this sentence, thereader is referred to the web version of the article.)

Fig. 16. FIB cross section of the valve seat insert from Sample Hard. The outermostbright layer is the deposited protective platinum. The tribofilm is around 1 �m andthe oxide up to 2 �m thick.

m thick tribofilm covers the seemingly unaffected valve material.

close to the outer edge of the valve seat. The FIB cross section inFig. 16 reveals two layers on top of the original microstructure. Theoutermost layer is a dark smooth tribofilm composed of Ca, O, P, Sand Zn that covers the entire surface. Beneath this layer, in the left

part of this section, there is layer of iron oxide with a rough, almostetched-like surface. Severe cracks have developed in the valve seat,as revealed by Fig. 17. The cracks appear to propagate towards theinner radius.

Fig. 17. Optical micrograph of a polished cross section of the valve seat insert fromSample Hard showing large cracks that have propagated towards the inner radiusof the VSI.

2482 P. Forsberg et al. / Wear 271 (2011) 2477– 2484

Fig. 18. Surface characterisation of the valve from Sample Engine Cell. SEM overviewimage to the left and a surface topography map in the middle. The chart to the rightsmr

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Fig. 19. Cross section of the valve from Sample Engine Cell prepared at the position

hows the surface profile along the red line (from bottom and up) in the topographyap. (For interpretation of the references to color in this sentence, the reader is

eferred to the web version of the article.)

.5. Valve from Sample Engine Cell

The valve from Sample Engine Cell deviates from the others byhowing a much sharper profile, see Fig. 18. Several ridges, out ofhich the largest is about 20 �m high, continue around the valve.

his ridge consists of fine grained material that seamlessly trans-orms to the original Stellite structure beneath, see Fig. 19. Thene-grained ridge is covered by a thin darker coating. The inter-

ace to this coating is very rough. The EDX-analyse in Fig. 20 is fromhe foot of the ridge where the adhered material is thinner. At theurface there is an oxidised film which is built up by two layers ofxides. On the outermost surface there is a ∼300 nm layer of copperxide. Beneath this layer there is a thicker layer of iron oxide with

thickness of about 700 nm. There are no evident wear depths thatan be measured on the valve, however the edges of the valve crossection are rounded off.

.6. Valve seat insert from Sample Engine Cell

The valve seat insert from Sample Engine Cell shows very simi-ar, but inverted, surface profile to that of the mating valve, compare

ig. 21 with Fig. 18. The highest ridge on the valve has a matchingrench in the valve seat, and so on. The trenches are also visiblen the SEM image as darker patterns in the rotating direction. The

ear depth is estimated to 80 �m.

ig. 20. Cross section of the valve in Sample Engine Cell. SEM to the upper left. EDX maepresent higher element concentration in that area.

of the 20 �m ridge seen in Fig. 18. The original Stellite structure is covered by a layerof finer structure, with a thickness that matches the height of the ridge. An oxidelayer has formed on top of the ridge. SEM-BSE.

The microstructure is largely unaffected although the surface isnot totally smooth, and no tribofilm could be detected, see Fig. 22.

5. Discussion

The two valve seat inserts from the customer trucks (samplesMild and Hard) have similar surface characteristics. They are bothsmooth and have a darker elevated middle part of the contact sur-face. Based on the present investigations, the surface can be said tobe covered by a smooth surface film containing Ca, O, P, S and Znwhich for some reason has a more beneficial situation and becomesthicker in the centre. If this is due to difference in oxide growth,wear, difference in pressure distribution, sliding distance, gas flowconditions or something else is not revealed by the present anal-yses The composition of the surface film contains elements whichare common in the additive packages in engine oil (zinc dithiophos-

ps to the right illustrate the signal strength for different elements. Brighter areas

phate, calcium sulfonates, etc.) and is presumably partly residuesfrom evaporated oil.

No evidence of abrasive wear in the sliding direction was found.The sliding distance in the contact between the valve and the insert

P. Forsberg et al. / Wear 27

Fig. 21. The valve seat insert from Sample Engine Cell is relatively rough with deeptrenches and raised ridges. Note that the surface profile of the valve seat matchesthat of the valve in Fig. 18. SEM overview image to the left and a surface topographymap in the middle. The chart to the right shows the surface profile along the red line(from bottom and up) in the topography map. (For interpretation of the referencesto color in this sentence, the reader is referred to the web version of the article.)

Fig. 22. Cross section of the valve seat insert in Sample Engine Cell. SEM to the left.EDX maps to the right illustrate the signal strength for different elements. Brightera

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reas represent higher element concentration in that area.

as been estimated from several to tens of �m [1]. If abrasive wearas a dominant factor, scratches with a length of the same magni-

ude as the sliding length should likely have been detected.Many different oxides with varying thickness and different dis-

ribution across the surface were found. Due to the limited insight inhe history and tribological conditions for the different valve pairs,t cannot be said how and why they form other than that it appearso be very random. It is worth mentioning that the different crossections have been made on parts of the valve and VSI that appeareds most interesting to investigate. This selection gives just a smallmage of the total surface.

Obviously, the tribofilms found on many of the surfaces con-ain Ca, O, P, S and Zn and have a protective effect for the materialeneath. Apparently the tribofilms sometimes locally flake off andxpose the bare metal beneath. Depending on the situation forhe exposed metal, it either forms an oxide by oxidising itself, orecomes covered by a new layer of tribofilm based on residues fromhe combustion. A rough estimation from image processing giveshat surface films cover somewhere in the vicinity of 90% of the con-act surface on the valves. The remaining parts are exposed metalhere the film has been removed. This probably represents a steady

tate situation, where the film forms, flakes off and rebuilds.On the Sample Engine Cell pair there is no sign (except local

races on the surface) of the film consisting with Ca, O, P, S and Zn.nstead there are much thinner oxide layers on the surface of thealve. Further, the surfaces are noticeably rougher and have coarserrofiles than the other two sample pairs. The matching surfacerofiles in Figs. 18 and 21 can be explained by following mecha-isms; Plastically deformed material on the valve which leads to

rain refinement and hardening of the surface. The hard rough sur-ace leads to accelerated wear on the VSI due to lack of protectingribofilms and stress concentration. There are also evidents thatopper is transferred from the VSI to the valve. From these samples

1 (2011) 2477– 2484 2483

it cannot be said if the lack of tribofilm is due to the cleaner runningconditions or due to the variation in between the engine cell andnormal service conditions.

C.A. Mantey describes a similar finding when investigating dif-ferent material combinations for a Liquefied petroleum gas (LPG)application. In a LPG engine there is very little exhaust residueswhich can build up a protecting film and hence have an atmospherethat is comparable to that of future diesel engines. For a materialcombination similar to the one investigated here, he observed that“during operation, very small portions of the VSI are pulled fromthe seat and deposited on the valve face due to adhesive deposi-tion”. This resulted in an accelerated abrasive wear of the VSI asthe deposited material on the valve came in contact with new VSIsurfaces due to rotation of the valve. The reduced VSI area leadto decreased heat transfer possibilities and therefore also largerthermo related stresses. Before the wear and deposits have gonethe whole rotation and creating a symmetrical pattern, which iteventually will, the valve will also suffer from bad valve sealingand higher local peak loads due to poor load distribution [10].

Several occurrences of corrosive wear on the surfaces were iden-tified. Especially in the FIB cross section in Fig. 16, the corrosiveaction has not only etched the outermost surface on the oxide butalso etched out a piece of the VSI material. It looks like one of thephases of the material has been left whereas the material aroundit has been consumed. Since Mo often is added to counteract thecorrosion a qualified guess is that this is from within an area of highMo content and it is the Mo-phases that have been spared. Whetherthis corrosion has taken place before the tribofilm was formed or ifit is the forming process of the tribofilm itself that has caused thecorrosion is hard to determine.

The valves on Samples Mild and Hard show no measurable wearalthough there are signs of plastic deformation. This is probably dueto the well covering tribofilms that protect the surfaces. In SampleEngine Cell the edges of the valves have become rounded. It is hardto establish if this is due to that the engine cell test procedure differsfrom ordinary engine use, an effect of cleaner exhausts or highercompression pressures.

An interesting observation is that the microstructure of the valveseat inserts never seems to be affected. There are no evidences thatthe VSI material has been plastically deformed.

Regarding the cracks in Fig. 17, it should be noted that these wereonly observed in one sample and in one cross section of that sample.More cross sections of the same sample were prepared withoutfinding any trace of cracks. Thus, it seems to be a rare phenomenon.Nevertheless, if these cracks had been left to propagate, which onecan assume they would, they would eventually have lead to largespalling of the VSI material and finally to valve leakage and failure.It is possible that the cracks originate from the disassembly. As theinserts are shrunk into the cylinder head they have to be pulledout when disassembled. This can result in large bending forces andcrack formation.

When the combustion process gets more optimised, fewerresidues are left that can create a soot layer on the bottom ofthe valve. Moreover, the combustion temperatures are increasing.These two factors will lead to higher temperatures in the valve [15]and thereby also require a higher heat flow through the valve/VSIcontact, which could be expected to further aggravate the wearsituation. A solution for this could perhaps be to add an isolatingcoating which would protect the valve, or perhaps just polish thebottom of the valve to enhance its reflective properties.

6. Conclusions

Based on the analyses performed and information given in pub-lished papers it can be concluded that:

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The dominant wear mechanism of the VSI material is oxidationand formation of a tribofilm.There are no signs of abrasive wear on any part of the studiedsystems.The valves did not wear for the samples where the tribofilm wasfound.For the cleaner engine – Sample Engine Cell – the combustionresidues have not been sufficient to build up a protective layer,which has lead to material transfer and rougher surfaces.

cknowledgements

This project is supported by FFI–Strategic vehicle research andnnovation through contract no. 2009-01208. Staffan Jacobson waslso supported by the Swedish Foundation for Strategic Research,hrough the programme Technical advancement through con-rolled tribofilms.

The authors wish to thank Åsa Gustafson at Scania CV AB, Mate-ials Technology, Basic Engine, Dominique Debord, Daniel Lindbergnd Petter Kylefors at Scania CV AB, Engine development, Valve sys-em for their comments on the draft manuscript, for sharing theirnowledge and for supplying the samples studied.

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[

[

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