Surface Engineering

Natural Sciences Tripos Part III

MATERIALS SCIENCE

III

MATERIALS SCIENCE

M4: Surface Engineering

Dr K. M. Knowles

Lent Term 2014 15

Name............................. College..........................

Lent Term 2014-15

M4 PART III MATERIALS SCIENCE AND METALLURGY M4

Module M4: Tribology and Surface Engineering

KMK/LT15

12 Lectures KMK

Overview (1 lecture)

Consideration of the need to engineer surfaces in terms of the provision of essential properties,

protection, and processing or service issues. Examples of surface engineering at the nanoscale and

the macroscale.

Physical characteristics of the surfaces of materials (5 lectures)

Chemical bonding and intermolecular forces. Interactions between solid surfaces at the molecular

level. Surface energies. Wetting behaviour. Adhesive contact.

Contacts between macroscopic surfaces. Friction and lubrication. Sliding wear. Abrasive and

erosive wear behaviour. Use of dimensional analysis for formulating wear rate equations.

Hardness testing (1 lecture)

The need for hardness testing. Spherical indentation. Scaling laws in indentation. Vickers

indentation. Berkovich indentation. Knoop indentation. Nanoindentation. ISO 14577.

Surface engineering processing techniques (3 lectures)

Surface modification with chemical composition unchanged: shot peening, blasting, transformation

hardening, surface melting.

Surface modification with chemical composition changed for ferrous alloys: carburising,

carbonitriding, nitriding, nitrocarburising, boronising. Revision of relevant solutions of the

diffusion equation to describe the physical processes involved in these technologies.

Metallised layers, e.g. chromising. Ion implantation. Physical vapour deposition. Chemical vapour

deposition. TiN, TiC, SiC and diamond CVD formation. Plating. Anodising. Hardfacing. Thermal

spray processes.

Case studies of surface engineering (2 lectures)

Inorganic glazes for traditional ceramics. Residual stresses in surface coatings and their effects.

Enamelling, titanium nitride coatings, diamond-like carbon coatings, coatings for cutting tools, self-

cleaning window glass, coatings for plastic optical lenses, Surface modification in biomaterials.

Coatings on materials used in joint replacements, coatings for ceramic fibres in ceramic matrix

composites.

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Book List

ASM Handbook, Volume 5, Surface Engineering, ASM International, 1994 R122

A.C. Fischer-Cripps, Nanoindentation, 3rd Edition, Springer, 2011 Kf36

W.F. Gale and T.C. Totemeier, Smithells Metals Reference Book, 8th Edition,

Elsevier, 2004 R202 (Ref)

K. Holmberg and A. Matthews, Coatings Tribology, Elsevier, 1994 NpT123

R.J. Hunter Foundations of Colloid Science, 2nd Edition, Oxford University Press, 2001 Pf64

I.M. Hutchings, Tribology: friction and wear of engineering materials,

Edward Arnold, 1992. NpT115

J.N. Israelachvili, Intermolecular and Surface Forces, 3rd Edition. Academic Press, 1992. La51a

A.J. Kinloch, Adhesion and Adhesives: Science and Technology, Chapman and Hall, 1987 Np186

M.J. Neal (ed.), Tribology Handbook, Butterworths, 1973 NpT2

M.B. Pearson and W.O. Winer, Wear Control Handbook, Am. Soc. Mech. Engrs., 1980. NpT56

E. Rabinowicz, Friction and Wear of Materials, 2nd Edition, John Wiley and Sons, 1995 NpT131

G.A. Roberts, G. Krauss and R.L. Kennedy, Tool Steels, 5th Edition,

ASM International, 1998 De95

W.S. Robertson, Lubrication in Practice, 2nd Edition. Macmillan Press, 1983 NpT72

D. Tabor, The Hardness of Metals, Clarendon Press, Oxford, 1951 Kg4

K.-H. Zum Gahr, Microstructure and Wear of Materials, Elsevier, 1987 NpT82

In addition there are a number of web sites, conference proceedings and journals in the

Departmental library in the general area of surface engineering where there is material relevant to

this course.

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The need to engineer surfaces

1. Where the surface property is the primary function

Bulk is the carrier, e.g. it provides the strength, the ductility, etc., while the surface provides essential properties.

Examples:

Brake pads

Primary properties: high coefficient of friction and low rate of wear over a wide range of

temperatures.

Secondary properties: ductile and formable to shape.

Machine tools

Primary properties: these are the properties needed for cutting at high temperature. It is evident that

abrasion resistance and oxidation resistance are primary properties.

Secondary properties: the need to make to the correct shape (e.g. for cermets).

Mirrors

Primary properties: the need to provide reflective surfaces.

Secondary properties: supportive strength.

Semiconductor substrates

Primary properties: the need to be very smooth and free of defects.

Secondary properties: the substrate may have to have different electrical properties from the

material to be deposited.

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2. Where the surface will provide protection

The surface might be designed to be corrosion-resistant.

The surface might be designed to be wear-resistant.

The surface might be treated chemically to gain the required level of protection.

Examples:

Corrosion-resistant coatings and surface treatments

Diffusion coatings.

Precipitation treatments.

Surface hardening for wear and fatigue resistance

e.g., martensitic layers.

Polishing of surfaces increases component fatigue life by removal of surface defects.

Erosion-resistant layers

Hard layers to resist particle impingement.

Hard layers require a brittle versus ductile compromise.

Polishing surfaces for fatigue resistance and strength

e.g., ceramics.

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3. Where the surface property has changed as a result of processing or service

For example, cutting of a metallic material introduces dislocations in its surface, as a result of

which the surface is hardened. We may then need to re-engineer the surface.

Examples

Machining, grinding and polishing processes

After primary processing, e.g. casting of metallic alloys, we may only reach near-net shape of a component. If so, we need to machine.

Damage to surface caused by machining, grinding or polishing will require further processing.

Surface oxide layers

Temperatures of processing are usually high, and so the degree to which surfaces are oxidised needs to be taken into consideration. Vacuum treatment might be necessary for

metals, but this is expensive.

Stainless steels are often annealed in H2/H2O to ensure pO2 < pO2,crit for oxidation, such as the process of bright annealing in which a highly reducing furnace running under hydrogen,

dissociated ammonia or nitrogen/hydrogen atmospheres is used to minimise surface

oxidation. [If an atmosphere containing N2 is used, there is the risk of nitrogen pick up in the

surface.]

Surface work-hardened layers

Fatigue initiation

Surface defects.

Corrosion

Different chemical compositions at surface to provide corrosion resistance.

Erosion and Wear

All these considerations lead to the rationale for the field of surface engineering.

The aim of this course is to achieve an understanding of the variety of ways in which this can be

achieved and how quantitative data can be obtained to validate surface engineering treatments in

terms of improved performance in the product under consideration.

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Surface Engineering

This is defined by practitioners as:

The modification or coating of a surface in order to achieve a combination of properties in both

the surface and the underlying bulk which could otherwise not be achieved.

The properties can be

Mechanical (e.g., low wear properties, low friction properties).

Chemical (e.g., corrosion and oxidation-resistant coatings).

Thermal (e.g., thermal barrier coatings for nickel-based superalloys).

Biomedical (e.g., coatings for hip implants to bond to the surrounding bone).

Functional (coatings for electronic, optical and magnetic applications).

Most generally, surface engineering as a discipline can be widened in scope to include topics such

as

Interface adhesion

since coatings need to adhere to bulk substrates in components for the timescale over which the

component is deemed to be fit-for-purpose. The definition of surface engineering should also be widened in scope to include emerging disciplines such as:

Nanotechnology;

Synthesis of nanoparticles;

Interactions at the atomic and molecular level between particles and surfaces

Colloid science is concerned with both the synthesis of nanoparticles and interactions at the atomic

and molecular level between particles and surfaces, and can therefore be regarded as a branch of

surface engineering in this wider scope.

This is surface engineering at the nanoscale.

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Another example of this is the technology of computer hard disks, such as in the schematic below of

the slider head / hard disk interface.

Protective overcoats and careful control of the disk surface roughness enable the spacing, h,

between the recording head and the disk media to be less than 10 nm. The disk rotates at speeds of

up to 550 m s1 relative to the head.

Conventional disk technologies typically consist of an Al or glass substrate, a NiP undercoat and a

Cr alloy underlayer upon which a Co/Cr magnetic recording layer is deposited. This is then

protected by the carbon layer, so that the disk has good wear and corrosion resistance. Finally a thin

layer of lubricant (e.g. perfluoropolyether) is deposited to reduce friction between the head and disk

and to reduce the wear of the carbon overcoat. The head is also protected by a thin layer of carbon.

Future decreases in h will be necessary for increased magnetic storage densities and increased

capacities of hard disk drives. For recording densities of 1 Terabit per square inch, values of h

approaching 23 nm are required.

Contact-induced friction is therefore a serious challenge to the design of these ultra-low flying

magnetic storage slider-disk interfaces. Contact can lead to high flying height modulation, bouncing

vibration and wear of the recording head (A.Y. Suh, C.M. Mate, R.N. Payne and A.A. Polycarpou,

Experimental and theoretical evaluation of friction at contacting magnetic storage sliderdisk interfaces, Tribology Letters 23, 177190 (2006)).

Head substrate

Protective layer of carbon ( 10 nm thick)

Protective layer of carbon ( 25 nm thick)

Magnetic medium ( 20 nm thick)

Lubricant film ( 2 nm thick)

Disk substrate

h < 10 nm

Read/Write

element

Schematic of a head/hard disk surface.

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Offshore wind turbines

At the other end of the size spectrum for surface engineering of objects, coatings on offshore wind

turbine blades are designed to enable the glass-reinforced plastic (GRP) blades avoid the build-up of

salt and ice. These coatings are nanoengineered self-cleaning, water-repellent coatings.

We begin by considering chemical bonding and intermolecular forces, building up a picture of

surface and surface interactions from the atomic level to the macroscopic level, where we will

consider the important topics of friction, lubrication and wear.

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Common types of interactions between atoms, ions and molecules in vacuum

(after Israelachvili, 2nd Edition, p. 28)

Type of interaction Interaction energy w(r)

Covalent, metallic

Chargecharge

Chargedipole

Dipoledipole

Chargenon-polar

Dipolenon-dipolar

Two non-polar molecules

Hydrogen bond

Complicated, short range

r

QQ

0

21

4 (Coulomb energy)

204

cos

r

Qu

420

22

46 kTr

uQ

3

0

112121

4

cossinsincoscos2

r

uu

620

22

21

43 kTr

uu

(Keesom energy)

420

2

42 r

Q

620

22

42

cos31

r

u

620

2

4 r

u

(Debye energy)

620

2

44

3

r

h

(London dispersion energy)

Complicated, short range, energy

approximately proportional to 1/r2

w(r) is the interaction energy (in J); Q, electric charge (C); u, electric dipole moment (C m); electric

polarizability (F m2); r, distance between interacting atoms or molecules (m); k, Boltzmanns constant

(1.381 1023 J K1); T, absolute temperature (K); h, Plancks constant (6.626 1034 J s); , electronic

absorption (ionization) frequency (s1

); 0, dielectric permittivity of free space (8.854 1012

F m1

). The

force is obtained by differentiating the interaction energy w(r) with respect to r.

{

{

{

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Types of chemical bonding

The main types of chemical bonding are summarised in the Table on page 9. The strongest bonds

are covalent bonds and metallic bonds.

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In addition we can have:

Van der Waals dispersion forces

These are forces between non-polar molecules arising from the non-zero average value of the square of the temporary dipole moment due to charge density fluctuations arising from

the instantaneous positions of electrons in an atom or molecule.

The forces are termed dispersion forces because these forces are related to the dispersion of light in the visible and UV regions of the electromagnetic spectrum (discussed in M7:

Electronic Ceramics in connection with polarization mechanisms).

Dispersion forces are always present in forces between atoms and molecules and feature in a

number of surface phenomena: adhesion, surface tension, wetting, the flocculation of particles in

liquids and the behaviour of thin films.

For example, work by F.W. DelRio, M.P. de Boer, J.A. Knapp, E.D. Reedy, P.G. Clews and

M.L. Dunn, The role of van der Waals forces in adhesion of micromachined surfaces, Nature Materials 4, 629634 (2005) has shown that the adhesion of micromachined surfaces, such as those found in microcantilevers in microelectromechanical systems (MEMS), arises from van der Waals

dispersion forces acting across extensive non-contacting areas when the surfaces are very smooth.

At larger roughness values, the primary contributors to adhesion are van der Waals dispersion

forces at contacting asperities.

Important features of van der Waals dispersion forces:

They are long-range forces effective from interatomic spacings to relatively large distances (> 10 nm).

They can be attractive or repulsive.

They are quantum mechanical in origin.

They are non-additive: the dispersion interaction of two bodies is affected by the presence of other bodies nearby.

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For two non-polar molecules r apart with polarizability ,

Dispersion interaction energy, W, = 620

2

44

3

r

h

where is the orbiting frequency of an electron orbiting around a proton in the Bohr atom model.

For small atoms and molecules such as argon and methane, the dispersion interaction energy is a

few kT at room temperature significantly less than the strength of covalent and ionic bonds, but not entirely negligible, and certainly not zero.

Larger molecules such as hexane and higher molecular weight hydrocarbons are liquids or solids,

held together solely by dispersion forces. Such molecules are useful as lubricants, as we will see

later in the course.

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At low T molecules such as neon, krypton and argon are solid and form close-packed crystal

structures with 12 nearest neighbours per atom, all because of the existence of these dispersion

forces. For example, solid krypton has the c.c.p. crystal structure at 82 K with a = 5.68 .

D

Between two parallel surfaces D apart (e.g., as might be encountered in MEMS),

W = 212 D

A

per unit area

where A is known as the Hamaker constant.

For dielectric or non-conducting materials, A is a function of the absorption frequencies of the

media under consideration and the refractive indices of the media.

For two macroscopic isotropic dielectric phases 1 and 2 interacting across a thin (15 nm thick) isotropic dielectric medium 3 where all three materials have a common characteristic absorption

frequency, e , A takes the form

2/1 23

22

2/1 23

21

2/1 23

22

2/1 23

21

23

22

23

21e

3231

3231B132

28

3

00 00

00 00

4

3

nnnnnnnn

nnnnh

TkA

where kB is Boltzmanns constant, T is temperature, h is Plancks constant, n1, n2 and n3 are the refractive indices of the three materials and 1(0), 2(0) and 3(0) are the static dielectric constants of the three phases. Typically e 3 10

15 s1

.

Optical frequencies are relevant, hence n1, n2 and n3 in the above expression, because of the

characteristic times of vibrations of bound electrons and, where appropriate, vibrating molecules.

For silica air silica, important when considering direct wafer bonding of silicon wafers,

A 6.5 1020 J = 65 zJ (zeptojoules)

For silica water silica,

A 0.83 1020 J = 8.3 zJ

The refractive index of water is greater than that of air and closer to that of silica. The effect of this

is to lower A for silica water silica relative to silica air silica.

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Hamaker constants are of particular interest when considering the stability of thin intergranular

films at grain boundaries in engineering ceramics such as Si3N4 and SiAlON: such grain boundaries

tend to contain thin intergranular silica-rich films. The equilibrium thickness of such films is

determined by a force balance between the attractive dispersion forces and repulsive steric forces.

(steric: relating to the spatial arrangement of atoms in a molecule (Oxford English Dictionary)).

A gecko

Van der Waals forces are also important in the adhesion of geckos to smooth surfaces such as

vertical window glass. Recent work by Kellar Autumn and colleagues in the U.S.A. has studied this

adhesion in some detail.

Tiny foot-hairs of the gecko known as setae adhere to surfaces through van der Waals forces (K.

Autumn, M. Sitti, Y.A. Liang, A.M. Peattie, W.R. Hansen, S. Sponberg, T.W. Kenny, R. Fearing,

J.N. Israelachvili and R.J. Full, Evidence for van der Waals adhesion in gecko setae PNAS 99, 1225212256 (2002)).

Sliding against a surface enables the setae, and therefore the gecko, to adhere to the surface. Geckos

can peel their toes from a surface by hyperextending the toes. The size and shape of the tips of the

setae determine the magnitude of van der Waals forces for adhesion with a particular surface, and

therefore the ability of the geckos to adhere and detach from a surface.

The actual adhesion is not that strong geckos need to be able to attach and detach their feet from the surface, and a strong adhesive force would clearly slow the gecko down. In practice geckos can

run up a vertical wall at a velocity of more than 1 m s1

.

Gecko adhesion has inspired a lot of interest in the media, not least due to the popularity of the

Spiderman films. The paper, Towards a Spiderman suit: large invisible cables and self-cleaning releasable superadhesive materials, J. Phys.: Condens. Matter 19, 395001 (2007) by Nicola Pugno is a particular example.

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Surface energies

Non-hydrogen-bonding solids and liquids

Surface energies of non-hydrogen-bonding solids and liquids are determined from the van der

Waals dispersion interaction energy between two surfaces.

For such materials, the surface energy, , is of the form

A20105

where is in units of mJ m2 and A is in J (so that the constant has dimensions m2). is the energy needed to separate two flat surfaces from contact to infinity where there is a finite contact

separation between the centres of atoms of adjacent surfaces when the flat surfaces are in contact.

Hence, for PTFE, for which A for PTFE air PTFE is 3.8 1020 J, 19 mJ m2.

Hydrogen-bonded substances

For substances such as water, where hydrogen bonding dominates dispersion interactions, the

surface energy is significantly higher than for materials like PTFE where van der Waals forces

dominate:

A for water air water is 3.7 1020 J, while 73 mJ m2.

Metals and ceramics

Metallic bonding causes for metals to be between 400 and 4000 mJ m2. In essence, short-range, non-additive electron exchange interactions arising between metal surfaces at separations below 5

are responsible for the metallic bonding and the high . Similar considerations apply to ceramic materials: is much higher than for hydrogen-bonded or van der Waals-bonded materials.

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Wetting and Adhesion

Surface energies, , are determined by intermolecular forces. These are the same forces which determine other properties of materials such as boiling point and latent heat.

Therefore, we can reasonably expect substances with high melting points (e.g., metals) to have high

values of . This is also true for ceramics where there is strong covalent or ionic bonding.

Surface energies are important in the context of joining ceramics using metal brazes. For the metal

braze to be effective, it has to wet the ceramic:

S

L

V

SL SV

LV

From the above, in equilibrium,

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Alternatively, in the so-called moly-manganese process, a powder consisting of mixed glass, molybdenum and manganese is coated onto the ceramic, sintered at 1500 C in a wet hydrogen

atmosphere, and then nickel plated and resintered at 950 C in a hydrogen atmosphere.

A wet hydrogen atmosphere is one in which pH2O is significant, e.g. a partial pressure of 102103 Pa

or even higher. A dew point of 20 C corresponds to 1.8% of air being composed of water vapour at the equilibrium condition where the rate of liquid water droplet formation is the same as the rate

of evaporation of water into air. This corresponds to a pH2O of 1.8 103 Pa.

The moly-manganese process produces a metallization layer interfaced to an outer layer of

molybdenum adhered to the nickel plate.

The surface can then be brazed using conventional AgCu eutectic braze without added Ti.

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Work of adhesion

S

L

V

SL SV

LV

The work of adhesion per unit area, WA, required to pull away the liquid leaving an equilibrium-

adsorbed film (i.e., a layer of vapour of the liquid assumed to be one molecule thick) is

SLLVSVA W

(the Dupr equation). Since, in equilibrium we have

cosLVSLSV

it follows that

cos1cos LVSLLVLVSLSLLVSVAW (YoungDupr equation)

If the surface energy of the liquid does not change appreciably on cooling, this equation is also

relevant to solidsolid interfaces if shrinkage stresses can be ignored.

The relevance of this equation is that for a given LV low values of increase AW , i.e. the metal

will adhere to the ceramic, and so in the absence of other factors, a strong bond can reasonably be

expected to form.

In reality for joining engineering ceramics, Youngs equation and the Dupr equation are an over-simplication because they do not take into account any chemical reactions which might occur

between the metal and ceramic. If a reaction takes place, a new compound can form, which may

well enhance wetting and adhesion. To take account of this possibility, the YoungDupr equation can be modified. One such modification takes the form

GCWA SRLV )cos1(

where the subscript SR indicates the interfacial energy between the substrate (S) and the reaction layer (R), G is the Gibbs free energy of formation of the reaction product in J m3 and C is a constant in units of metres, determined by the volume of reaction product formed for unit extension

of the drop on the solid (equation (6) of F.G. Yost and A.D. Romig, Thermodynamics of wetting by liquid metals, MRS Proceedings 108, 385390 (1988)).

A spontaneous reaction is characterised by a negative G, which increases WA and decreases .

Reactions with the greatest negative values of G will be thermodynamically most favourable, but such considerations must recognise that in practice reactions may be hindered kinetically due to the

formation of diffusion barriers.

Wetting of engineering ceramics in the context of joining them to other materials is discussed by

J.A. Fernie, R.A.L. Drew and K.M. Knowles, Joining of engineering ceramics, Int. Mater. Rev. 54, 283331 (2009).

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Mechanisms of Adhesion

These are the various types of intrinsic forces which can operate across an adhesive/substrate

interface (A.J. Kinloch, pp. 56100; B.G. Yacobi, S. Martin, K. Davis, A. Hudson and M. Hubert, Adhesive bonding in microelectornics and photonics, J. Appl. Phys. 91, 62276262 (2002)).

There are in essence four main mechanisms:

Mechanical interlocking

Interdiffusion

Electrostatic forces arising from electron transfer

Lifshitz van der Waals forces

Of these the main mechanism is normally assumed to be Lifshitz van der Waals forces, e.g., the London dispersion forces, and, if relevant, the Keesom and Debye interaction contributions from

dipole dipole and dipole non-polar interactions.

Mechanical interlocking is not of wide applicability (although it is the principle behind how Velcro

works), although it is common practice to roughen surfaces before applying adhesives. However,

this is because surface pretreatments can remove weak surface layers and improve interfacial

contact through increasing the bonding area available. For polymer-based adhesives, surface

pretreatments also help to promote plastic deformation in the adhesive.

Diffusion is relevant in the context of bonding ceramics using metal brazes and in any high

temperature deposition process for coatings such as chemical vapour deposition (CVD). It is also

relevant for polymers: adhesion of adhesives arises through mutual diffusion of polymer molecules

across the polymer adhesive interface. This process occurs in the solvent welding of plastics. The solvent is usually applied to one surface. After a short time interval, this is applied to the other

surface and held under pressure, with heat being supplied to the interfacial zone (Kinloch, p. 72).

Electrostatic forces arising from electron transfer are particularly important in the adhesion of

charged particles to planar surfaces, e.g., as in the Xerox process. In this process, charged particles,

referred to as toner, are attracted to an electrostatic image on a photoconductor and subsequently

electrostatically transferred to paper. Hence, the adhesive properties of the toner are very important.

A nice description of the Xerox process can be found at http://howstuffworks.com/photocopier.htm.

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Contacts between macroscopic surfaces

Up to now we have only considered contact at the molecular level. However, for most industrial

applications at present where the term surface engineering is used, the behaviour of surfaces in contact with one another is an important consideration.

This leads to the subject of tribology the study of the friction, lubrication and wear of materials.

Not all engineered materials need have low friction and low wear rates. High friction between shoes

and the floor is desirable when walking. High wear rates using coarse SiC grit is beneficial in

metallographic specimen preparation (e.g., the Part IB artefact). However, in most cases, wear is

detrimental to component performance, e.g., in cutting tools.

We begin by considering surface topography:

Flat surfaces polished to a mirror finish are not truly flat on an atomic scale:

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Contact between macroscopic flat surfaces

Contact initially occurs at only a few points called asperities, as in the circled regions in the above

schematic. These cover a very small fraction of the total surface area typically < 1%, even for very high loads on metals.

Frictional force and wear originates at these asperities. Therefore, an examination of asperity

behaviour is a useful place to start when developing theories of friction and wear.

Deformation of a single spherical asperity pressed against a plane surface:

Deformation of a sphere of radius r pressed against a plane surface under a load w. The radius of

contact is a. The area of contact, a2, is A.

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For purely elastic deformation Heinrich Hertz, Ueber die Berhrung fester elastischer Krper [On the contact of solid elastic solids], J. reine angewandte Mathematik 92, 156171 (1881) showed that

For perfect plastic deformation (e.g., when the asperity has yielded),

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Multiple asperity contact:

Extending the principles found in single asperity contacts to multiple asperities, J.A. Greenwood

and J.B.P. Williamson, Contact of nominally flat surfaces, Proc. Roy. Soc. Lond. A 295, 300319 (1966) developed a statistical theory of multiple asperity contact by two rough surfaces.

They found

1wA

with

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The important result from this work is that for most surfaces, i.e., for a given *, r and surface density of asperities, the deformation mode (elastic or plastic) cannot be altered by changes in the

load.

Thus, the previously widespread belief prior to the work of Greenwood and Williamson of elastic

contact at low load and plastic contact at high load was shown to be wrong.

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Friction:

F

W

N

For the above block to be able to slide to the right, the applied horizontal force must be greater than

the frictional force, F.

Now, NF

where N is the normal load and is the coefficient of friction.

When sliding occurs, F = N. More generally, on the point of sliding = S, the static coefficient of friction, and during sliding = D, the coefficient of dynamic friction.

Experimentally, the frictional force is proportional to N over a load factor of 106, as shown below.

Note that the value of of 1.25 is typical of values seen for unlubricated sliding conditions for metals.

Experimental data showing the invariance of the coefficient of friction over a wide range of normal

loads for the unlubricated sliding of steel on aluminium in air (Hutchings, p. 24; from F.P. Bowden

and D. Tabor, Friction and Lubrication of Solids, 1950).

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The coefficient of friction is also independent of the apparent area of contact:

Experimental data showing the invariance of the coefficient of friction with the apparent area of

contact for wooden sliders on an unlubricated steel surface (Hutchings, p. 24; from E. Rabinowicz,

Friction and Wear of Materials, 1965).

The variation of the coefficient of friction with applied normal load for copper sliding against

copper in air, unlubricated. At low loads, the two metal surfaces are separated by thin oxide films

on the two surfaces. At high loads, metallic contact occurs between copper asperities and the oxide

films are penetrated (Hutchings, p. 37; from J.R. Whitehead, Surface deformation and friction of metals at light loads, Proc. Roy. Soc. Lond. A201, 109124, 1950). A high coefficient of friction results because of the plastic deformation of the contacting metallic surfaces.

Typically, 0.41.5 for metallic materials sliding against other metallic materials.

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The higher, the value of , the steeper the slope can be for a metal object to remain on a slope, rather than slide down the slope:

N

W

F

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Further features of the coefficient of friction:

The behaviour of the coefficient of friction as a function of normal load for steels sliding against

themselves in air, unlubricated. Results are shown for two different low carbon steels with

compositions in wt% (Hutchings, p. 39; from Wilson, 1952). Note the differences seen in steels of

very similar compositions.

The stratified nature of the oxides on iron accounts for the difference in behaviour in comparison

with the rubbing of copper surfaces against one another the upper most layer of the oxide is Fe2O3, below which are layers of Fe3O4 and finally FeO in contact with the metal itself. Relatively

small changes in chemical composition can change the frictional properties of an alloy appreciably,

e.g., through the tendency of trace additions to oxidise or to segregate to the surface see Hutchings, p. 39 for a discussion.

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The effect of sliding speed on the coefficient of friction for pure bismuth and pure copper sliding

against themselves (Hutchings, p. 42; from F.P. Bowden and D. Tabor, The Friction and

Lubrication of Solids, Part II, 1964). At very high speeds, the dissipation of frictional work can

raise the temperature at the interface to beyond the melting point of the material involved. Sliding

then takes place under hydrodynamic lubrication conditions.

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Theory of friction

The coefficient of friction, , is determined by the behaviour of asperity contacts. Adhesive forces which develop at asperity contacts and deformation forces which are needed to plough the asperities

of the harder surface through the softer surface are important. However, these two forces are not

sufficient to explain the observed values of .

To account for observed values of , we need to take account of the stress system at the contact areas and how this changes as the frictional force is applied.

Simple model of friction for metals

In a simple model of metal-metal contact, we can imagine that at each asperity contact there is an

area of contact, a, that acts like a hardness indentation, with an indentation pressure, P, equal to the

hardness, H, of the asperity material. The normal force on the contact, w, is then w = aH.

Summing over all asperity contacts between two surfaces, the total normal force, W = AH where A

is the true area of contact (not the nominal area of contact). We can assume that, to a good

approximation, H = y, the uniaxial yield stress.

Using the Tresca criterion, the yield stress in pure shear, k, is half the uniaxial yield stress, y.

Hence, when sliding is just about to occur, the total shear force, F, is such that

63222 y

yyy WW

H

WAF

and so since W is a normal force, we predict that

6

1

This simple model gives the correct order of magnitude for a coefficient of friction between two

metal surfaces. It also shows that the frictional force is independent of nominal area and

proportional to the load, W, because of the way in which the true area of contact varies as a function

of nominal area and applied load.

If there were a thin interfacial contaminant layer with shear yield stress i at the contact regions, then a straightforward modification of the above analysis would predict that

y

i

3

Note that this model is not relevant to either polymers or ceramics. For polymers, asperities are soft

and elastic, so at high contact pressures the true area of contact can approach the nominal area of

contact. For ceramics, fracture can arise at the asperity tops, and so the plastic flow model is not

appropriate.

M4 34 M4

A more sophisticated theory of friction

A consequence of either the simple model or the more sophisticated model of friction is that films

of low shear strength deliberately interposed between the surfaces lower considerably this is of course the principle behind lubrication.

M4 35 M4

Lubrication:

Types of Lubricants

Mineral Oils

Lubricants have been used since Ancient Times, e.g., in Ancient Greece and Ancient Egypt. These

were all organic products, such as vegetable oils, animal oils, fats and waxes. Olive oil and soap are

good examples of such lubricants. Greases can also act as lubricants, e.g., petroleum jelly marketed

as Vaseline.

Commercial mineral oils (petroleum oils) used for lubricating machinery parts are based on several

different hydrocarbon species with mean molecular weights between 300 and 600. Two such types

are paraffins and naphthenes.

Paraffins are long-chained hydrocarbons with either straight or branched chains.

Naphthenes are cycloalkanes, in particular those based on cyclopentane (C5H10, a nearly planar

molecule with bond angles of 108) and cyclohexane (C6H12, a non-planar molecule because of the

need for the carbon atoms to be in sp3 tetrahedral co-ordination) with attached side-chains.

Pariffinic oils have a predominance of paraffin chain-like species and have high pour points (the

temperature at which an oil stops flowing in given conditions), high viscosity indices (so that the

rate of change of viscosity with temperature is relatively low) and good resistance to oxidation.

Naphthenic oils have a relatively high proportion of carbon atoms in ring formation and have low

pour points, relatively low viscosity indices and relatively low oxidation stability.

The advantages of mineral oils are:

their low cost;

their suitability for a wide range of load, speed and temperature conditions encountered in a wide variety of situations where lubrication is needed;

the low friction they produce;

their effectiveness at carrying away heat from bearing surfaces.

Synthetic Oils

These oils have few impurities in comparison with mineral oils, but are significantly more

expensive. They are used when it would not be sensible to use mineral oils, such as when relatively

high or relatively low temperatures or relatively high loads are to be experienced in service

conditions, or if it is vital that the lubricants have low flammability.

Examples:

Synthetic hydrocarbon oils (SHCs);

Polyglycols (PAGs);

Ester oils;

Silicones.

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Viscosity Index (VI)

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Additives

Additives either improve the lubricating properties of an oil (e.g. by increasing its viscosity index,

either preventing the oil from becoming too thin at high temperatures and/or too greasy at low temperatures) or prolong its life, or do both. Examples:

Viscosity-index improvers;

Extreme pressure (EP) additives and anti-wear additives;

Boundary lubricants (e.g., stearic acid, C17H35COOH or hexadecanol, C16H33OH);

Pour-point depressants, e.g., complex long-chain polymers.

Viscosity-index improvers are oil-soluble long-chain polymers which increase the VI by decreasing

the viscosity at low temperatures (acting as pour-point depressants) and increasing the viscosity at

high temperatures. Oils with VI improvers are termed multigrade oils.

EP additives react with the sliding surfaces under the severe conditions experienced in service to

give compounds with low shear strength which behave as thin lubricating films separating

asperities on adjacent surfaces and preventing them from welding together.

EP additives usually contain sulphur, phosphorus or chlorine to facilitate the chemical reactions

required at the high pressures and high temperatures experienced by the lubricant. Examples are

zinc dialkyl dithiophosphate (ZDDP) and tricresyl phosphate (TCP).

ZDDP and TCP are relatively mild EP additives and are also referred to as anti-wear additives. By contrast, full EP additives function by removing metal from the asperities. Fortunately, as surface finish improves, such additives are not required by the lubricant, and the EP action is not triggered

because the temperatures experienced by the lubricant will be less than for a rough surface.

Pour-point depressants improve the flow properties of oils when cold so that they are no longer

waxy at the temperature of interest, preventing the oil from thickening.

Other additives to oils (in the general sense) are detergents, antioxidants and dispersants. Detergents

are used to clean and neutralize oil impurities which would normally cause deposits (also known as

oil sludge) on vital engine parts. Antioxidants prevent oils from oxidising, while dispersants

prevent contaminants in the oil from coagulating or aggregating into larger groupings that would

hinder the flow of the oil.

See http://en.wikipedia.org/wiki/Oil_additive for more details.

M4 38 M4

Solid Lubricants

These can be used to produce self-lubricating systems which do not need an external source of lubrication during the lifetime of the system. Examples of solid lubricants are graphite, MoS2,

diamond-like carbon, soft metals such as silver, tin, indium and gold, and PTFE. Suitable solid

lubricants have chemical structures that enable low values of friction to be obtained under certain

conditions. A recent review of solid lubricants is T.W. Scharf and S.V. Prasad, J. Mater. Sci. 48,

511531 (2013).

Solid lubricants are particularly useful in vacuum technology because they do not evaporate away.

The same considerations are relevant for space applications. Solid lubricants are also particularly

important in food-processing machinery.

The crystal structures of two common solid lubricants: (a) graphite and (b) molybdenum disulphide.

Boundary lubricants

EP additives are examples of lubricants with boundary lubricating properties. Boundary lubricants

operating under less extreme conditions of pressure and temperature do not react chemically with

the surfaces, but instead adsorb onto the surfaces being lubricated:

Polar end-groups on the hydrocarbon chain bond to the surfaces, providing layers of lubricant

molecules which reduce direct contact between the asperities on the two surfaces.

Typical examples are long-chain carboxylic acids (fatty acids) such as stearic acid (octadecanoic

acid, C17H35COOH) and hexadecanol, C16H33OH. These are added at 0.1% to 1% concentration

levels.

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Regimes of lubrication

Hydrodynamic (full film)

lubrication

U/W

Elasto-hydrodynamic

lubrication

Coefficient of

friction,

Boundary

lubrication

The Stribeck curve: the variation in the coefficient of friction with the dimensionless quantity U/W for a lubricated bearing. Here, is viscosity (dimensions of ML1T1), U is peripheral speed (dimensions of LT

1), of the bearing and W the load (per unit width) (dimensions of MLT

2/L =

MT2

), carried by the bearing (after Hutchings, p. 65). A nice commentary on Stribecks work can be found in B. Jacobson, The Stribeck memorial lecture, Tribology International 36, 781789 (2003).

Under the most favourable circumstances can be very low (e.g., 0.001), so lubrication is certainly beneficial in reducing wear of materials.

M4 40 M4

Sliding wear:

This is the wear which occurs when two solid bodies slide over each other.

A simple model for sliding wear is the Archard equation. For asperity contact, the local load W, supported by an asperity, assumed to be circular in cross-section with a radius a, is

W = Pa2

where P is the yield pressure for the asperity, assumed to be deforming plastically. As assumed

when developing a theory of friction, P will be close to the indentation hardness, H, of the asperity

(which will be an asperity on the softer surface).

As sliding proceeds, wear will arise from the continuous formation and destruction of asperity

contacts.

If, for a particular asperity, the volume of wear debris, V, is a hemisphere sheared off from the asperity, it follows that

V = 2/3a3

This fragment is formed by the material having slid a distance 2a.

Hence, Q, the wear volume of material produced from this asperity / unit distance moved is simply

H

W

P

Wa

a

VQ

3332

2

making the approximation that P H.

However, not all asperities will have had material removed in a sliding operation. The total volume

of wear debris produced per unit distance moved, Q, will therefore be lower than the ratio of the

total normal load, W, to 3H. It is convenient to write this dimensionless constant of proportionality

as a constant K with the factor 3 subsumed into K, giving the so-called Archard equation:

H

KWQ

M4 41 M4

Heavy

mechanical

damage

Sliding velocity

Low interface

temperature

Normal

load

Slight

mechanical

damage

Isothermal Adiabatic

High interface

temperature

Graph illustrating the combined influences of load and sliding speed

on the process of sliding wear in metals (after Hutchings, p. 93).

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An example of a wear regime map for the unlubricated sliding of steel on steel in the pin-on-disc

test (from S.C. Lim and M.F. Ashby, Overview no. 55. Wear-mechanism maps, Acta Metall. 35, 124 (1987)). Eight distinct regimes are identified in this map:

Regime I: Gross seizure of the surfaces: catastrophic growth of the asperity junctions occurs,

leading to the real area of contact becoming equal to the apparent area.

Regime II: Penetration of the native surface oxide film occurs at asperity contacts, leading to

high wear rates and metallic debris.

Regime III: Mild wear because only oxide debris is formed by removal of particles from the

native oxide layer.

Regime IV: Melting occurs. The wear rate is high, with metal being removed in the form of

metallic droplets.

Regime V: Surface oxidation occurs (the conditions are not sufficiently extreme to cause

local melting). Wear regime is mild because the wear debris is oxide debris.

Regime VI: Thermal effects begin to play a role. Hot-spots at asperity contacts cause local

oxide growth. Wear debris is from this oxide layer through spalling.

Regime VII: Metallic contact occurs at asperities (despite the ability of oxide to grow), leading

to severe wear through the formation of metallic debris.

Regime VIII: Martensite forms at the interface through local heating of asperities followed by

quenching through heat conduction into the bulk. This provides local mechanical

support of the oxide film because martensite has a high strength, helping to reduce

the degree of wear. Wear occurs by the formation of oxide debris.

M4 43 M4

Abrasion and erosion

In abrasive wear (Hutchings, p. 132), material is removed or displaced from a surface by hard particles, or sometimes by hard protuberances on a counterface, forced against and sliding along the

surface. Examples of two-body and three-body abrasion are shown below.

In erosion, wear is caused by hard particles striking the surface, either carried by a gas stream or

entrained in a flowing liquid (Hutchings, p. 133).

Erosive wear is relevant to many geological processes the wear of a river bed by hard particles flowing in the river is an example. Coastal erosion is another well-known erosive wear process.

Wear by hard particles abrasion and erosion. In two-body abrasion, wear is caused by hard protruberances on the counterface (e.g., as in the wear of drill bits cutting rock), while in three-body

abrasion the hard particles are free to roll and slide between the two surfaces.

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Two-body abrasion resistance of various materials as a function of hardness (Zum Gahr, 1987;

Hutchings, p. 157).

The above diagram is relevant for when abrasive particles are hard compared to the material being

abraded, i.e. the material being abraded is less hard than the abradent.

Materials with the same hardness can have widely different values of abrasive wear resistance.

Thus, in the above diagram, for the same value of hardness, ceramics have a lower resistance to

abrasion than martensitic steels. Austenitic steels have higher resistance to abrasion than martensitic

steels.

Models of abrasion recognise that abrasive wear can arise either from (i) plastic deformation

forming a groove in a material or (ii) abrasive wear by brittle fracture (c.f. Part II C13 Ceramics

course in which indentation of ceramics by sharp indenters was considered). In abrasive wear by

brittle fracture, lateral cracks formed beneath a plastic groove produce chips which are subsequently

removed from the surface by the abrasive process.

Schematics of abrasive wear of (a) ductile material and (b) a material which is brittle.

M4 45 M4

Materials such as white cast irons and ceramics which have a decrease in wear resistance with

increasing bulk hardness can be understood in terms of their propensity to exhibit brittle fracture.

In general, materials with high hardness have low toughness, and visa-versa, so that maximum wear

resistance will arise through a combination of intermediate values of hardness and toughness.

This accounts for the diagram below:

Relationship between fracture toughness and wear resistance for metals and ceramics under severe

abrasion conditions (after Zum Gahr, 1987; Hutchings, p. 159). Under such conditions fracture is

likely to occur.

Under severe abrasion conditions metals, which are tougher but less hard, such as tool steels, tend

to have good abrasive wear resistance and suffer abrasive wear by plastic deformation in contrast to

ceramics, which are less tough, but harder, and suffer abrasive wear by brittle fracture.

Ceramics Metals

M4 46 M4

For abrasive wear where there is negligible plastic flow, material removal will be dominated by

brittle fracture. This can be modelled through an analogy with indentation fracture of brittle

materials by sharp indenters. Under such circumstances the fracture toughness, Kc, is also relevant.

Depending on the model, the Youngs modulus, E, of the abraded material can also be relevant.

If the variables assumed are W, H and Kc, so that

rqp KHAWQ

c

with Q being the volume wear rate per unit sliding distance for a constant A, and with W, H and Kc

raised to powers of p, q and r respectively, it follows from the units of Q, W, H and Kc that

(1) rqp (equating units in Newtons)

(2) 443 qr (equating units in length)

and so in this case dimensional analysis cannot be used to formulate suitable equations. Importantly,

the models used for predicting wear rates where brittle fracture is involved predict wear rates higher

than would be expected due to plastic mechanisms.

These models also predict

An increase in wear rate with the size of the abrading particles;

An inverse correlation between fracture toughness (raised to some power) and wear rate, to the extent that fracture toughness rather than hardness is a more important material

parameter;

A threshold load below which wear by brittle fracture will not occur.

M4 47 M4

Erosive Wear

As we have noted on page 43, in erosion, wear is caused by hard particles striking the surface,

either carried by a gas stream or entrained in a flowing liquid.

In erosive wear, variables which a simple model would expect to affect the volume of material, V,

removed from an eroding surface of a plastically deforming material are the velocity, U, of the

particles impinging on a surface and the mass, m, of the particles (together in a kinetic energy term)

and the hardness, H, of the material being eroded.

M4 48 M4

M4 49 M4

Hardness testing

Everyday experience reminds us that some materials are harder than others. For example, hardened

steel blades can be used to scratch or cut pure annealed copper, but not the reverse.

The Mohs scale of hardness was devised by Carl Friedrich Christian Mohs (17731839), known as Friedrich Mohs, a German mineralogist, in 1822 (not 1812 as it states in Wikipedia) in his two

volume work Grundri der Mineralogie which translates as Treatise on Mineralogy. This is a scale of hardness from 1 to 10 based on the principle of scratch hardness the ability of one solid to be scratched by another.

The (non-examinable) scale of Mohs hardness is shown below. It is noteworthy that the material

with the highest value of hardness of 10 is diamond.

Mohs hardness scale

Material Hardness

Talc (Mg3Si4O10(OH)2) 1

Gypsum (CaSO4) 2

Calcite (CaCO3) 3

Fluorite (CaF2) 4

Apatite (Ca5(PO4)3(OH,F,Cl)2) 5

Orthoclase (KAlSi3O8) 6

Quartz (SiO2) 7

Topaz (Al2SiO4(F,OH)2) 8

Corundum (Al2O3) 9

Diamond (C) 10

The scale is not linear, and so is not suitable for quantitative comparison of the hardness values of

different materials.

A logical development of scratch hardness is ranking of materials by indentation hardness.

Quantitative methods of measuring indentation hardness were developed during the nineteenth

century (see, for example, the recent review by Stephen Walley, Historical origins of indentation hardness testing, Materials Science and Technology 28, 10281044 (2012)).

The technology behind hardness testing continues to evolve with the advent of nanoindentation

techniques. These are of particular relevance to thin films, and therefore relevant to surface

engineering, where a substrate may be coated with a wear-resistant hard coating whose mechanical

properties need to be established.

M4 50 M4

Types of indenters

Spherical

An idealised situation is shown here. In the Brinell hardness test developed by the Swedish engineer

Johan August Brinell in 1900, the ball of diameter D produces an indentation of diameter d. The

Brinell hardness number (BHN) is defined as the ratio of the load W on the spherical indenter (the

ball) to the curved surface area of the indentation formed.

Hence, if the load is W, BHN is defined as

22

2BHN

dDDD

W

W

M4 51 M4

In a real situation the indenter causes a permanent change not only below the indenter itself, but

also in the surrounding material being indented: plastic flow takes place in the vicinity of the

indentation, so that sinking in can arise.

This will happen in annealed metals in which material around the indentation is left at a lower level

than the material farther away from the indenter and where material flow to the surface from well

beneath the indenter produces the sinking-in. In reality the surface has a small disc of piling up at some distance from centre of the indenter.

Piling up can also arise close to the indenter, in which material displaced by the indenter flows out to the surface (e.g. as in the consideration of indentation in C12, Plasticity and Deformation

Processing in Part II).

The schematic cross-section below shows the two effects for a spherical indenter (and see also

Tabor, p. 15):

In this diagram, h is the depth at maximum load, s is the pile-up depth, hc the contact depth for a spherical indenter of radius R. The two idealised situations of pile-up and sink-in are shown.

A little thought about the definition of BHN shows that this is not the mean pressure over the

surface of the indentation. Instead, as Tabor explains in his book, The Hardness of Metals,

(Clarendon Press, Oxford, 1951), p. 7, the mean pressure, P, is

2

4

d

WP

i.e., it is the ratio of the load applied to the projected area of the indentation. As we shall see, this is

also true for pyramidal indenters. This quantity, P, is known as the Meyer hardness for spherical

indenters. For a particular d/D, the BHN is simply the Meyer hardness multiplied by a geometrical

factor.

M4 52 M4

The proof that 2

4

d

WP

is straightforward:

M4 53 M4

Further consideration of spherical indenters shows that the Meyer hardness is a function of the

diameter of the residual impression, d. An empirical relationship of the form

nkdW

is found (see for example, Tabors book and the book by Anthony Fischer-Cripps.)

n is generally greater than 2 and typically is between 2 and 2.5 for metals. Importantly, it is also

found to be almost independent of D. Knowledge of the value of n enables balls of different

diameters to be used since it is found experimentally that for two different diameters of balls D1 and

D2, and two constants k1 and k2,

2

222

11nn

DkDk

where is a constant, so that n is, to a sufficiently good approximation, almost independent of D, and, in general,

2nkD

so that k decreases as D increases to conform to this equation. Hence, substituting for k, we find

M4 54 M4

Vickers indenter

This shown in the above diagram. It has the shape of a square pyramid with opposite faces making

an angle of 136 with one another.

The choice of this indenter shape was based on an analogy with the Brinell test for a ball with a

diameter D producing an indentation with a diameter 0.375D. Simple geometry shows that when

tangents are drawn from the points of contact of a spherical impression with 0.375D as a diameter,

the included angle is 136 to three significant figures.

Vickers hardness, HV, is defined as the ratio of the load applied to the surface area of the

indentation, so that for a load W and diagonal of length d measured from corner to corner on the

residual impression in the specimen surface,

228544.1

2

136sin

2HV

d

W

d

W

The load W divided by the projected area is actually the pressure P (the Meyer hardness), so that

2

2

d

WP

and so

P9272.0HV

As might be expected from a consideration of the behaviour of spherical indenters, the impressions

left by Vickers indenters can have shape distortion depending on whether piling-up or sinking-in

occurs around the impression.

M4 55 M4

Berkovich indenter

This is the indenter used routinely for nanoindentation as Fischer-Cripps observes in his book on p. 27. Made out of diamond, it is more easily fashioned to a point than the Vickers indentation

geometry.

A nanoindentation produced by a Berkovich indenter is shown below:

It has the shape of an equilateral triangle shown in the above diagram. In the modified Berkovich

geometry, the angle a between the axis of the indenter and one of the pyramid flats, as shown, is

65.27. [The equivalent angle defined for the Vickers indentation geometry would be 68].

For nanoindentation, it is the custom to use the mean contact pressure as a definition of hardness in

nanoindentation, which is why the angle a is 65.27, so that a Berkovich indenter with this geometry has the same ratio of projected area to indentation depth as a Vickers indenter.

M4 56 M4

Knoop indenter

This indenter makes an indentation in which one of the diagonals is approximately seven times the

length of the other.

Knoop hardness (Hk) is defined as the ratio W/A where A is the projected area of the indentation left

in the sample. For the above geometry, if the length of the longer diagonal is d, then

2

130tan

2

5.172cot

2H

2k

d

W

It is evident from the above that care must be taken when defining hardness of a material. This is true for both conventional hardness tests with macroindentation and microindentation (where, in

the latter case, the loads may be as low as 2 N), but is particularly true for nanoindentation.

M4 57 M4

Nanoindentation

In nanoindentation, the load-displacement curve can be measured throughout the test.

A typical loaddisplacement curve for an indenter penetrating the surface of an elasticplastic solid and causing a residual impression in the solid after removal of the indenter is shown below, taken

from the 1992 Oliver and Pharr paper on this topic in J. Mater. Res. 7, 1564

Here, P is the applied load (not pressure) and h the displacement of the surface being indented

relative to its initial position.

On loading, a permanent hardness impression is formed by the indenter, with the gradient of the

slope dP/dh increasing. As the indenter penetrates the surface, it becomes increasingly difficult to

continue penetration because of the concept of constraint even though a plastic region is formed underneath the indentation, it is constrained by the surrounding elastic material of the material

being indented.

During unloading, it can be assumed that only elastic displacements are recovered: consequently,

there is a depth hf which defines the permanent depth of penetration after the indenter is fully

removed.

Key parameters in this curve are Pmax, hmax, hf and the slope S = dP/dh at (hmax, Pmax).

M4 58 M4

A very important aspect to analysing the response of a material to indentation is to recognise what

happens during loading and unloading. A suitable schematic to consider is the one shown below,

also from Oliver and Pharr, and also with P as load.

When using nanoindentation as a method for determining the hardness of thin films, the obvious

problem which arises is that the depth of penetration of the indenter (spherical or blunt) can be

comparable to both the surface roughness of the thin film and also its depth.

Residual stress in thin films can also affect the apparent hardness value.

However, the main experimental problem is arriving at a reliable estimate of S = dP/dh at (hmax,

Pmax) and, crucially, the depth of the circle of contact between the indenter and the specimen at

(hmax, Pmax), hc (see diagram above) because the hardness value, H, determined is inversely

proportional to hc2.

Underestimates of hc will lead to overestimates of the true value of H.

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ISO 14577

ISO 14577 is an international standard in four parts covering indentation in materials across the

load spectrum from macroindentation to nanoindentation. In this standard, indentation hardness,

HIT, is defined as the ratio of the maximum load, Wmax, to the projected area of contact, Ap, at that

load. [Note that I am deliberately using W for load here rather than P, as Oliver and Pharr used.

Others use F for load, e.g. Fischer-Cripps. It can be confusing!]

and so for a given maxW , an underestimate in ch leads to an overestimate in HIT.

In essence, this is the reason behind controversy in the literature on hardness measurements in

superhard thin films see for example, A.C. Fischer-Cripps, S.J. Bull and N. Schwarzer, Critical review of claims for ultrahardness in nanocomposite coatings, Phil. Mag. 92, 16011630 (2012).

M4 60 M4

Surface engineering methods

Surface modification: chemical composition unchanged

Mechanical, e.g. shot peening, etc. In the technique of shot peening, small steel, glass or ceramic particles bombard a surface, such as for example 3 mm diameter steel balls. The

procedure work hardens the surface. Hard particles are needed, but the procedure itself is

cheap. There are problems with line-of-sight, so that holes for example can be difficult to shot peen to the same degree as flat surfaces.

Transformation as a result of heating: oxy-acetylene flame; induction coils used to heat surface. The transformations in this sense can be phase transformations.

Surface melting, e.g. via laser, electron beam, metal inert gas (MIG), tungsten inert gas (TIG) welding. MIG welding uses consumable wire connected to an electrode current; the

more expensive TIG welding process uses a non-consumable tungsten electrode to provide

the electric current.

Surface modification: chemical composition changed

Thermochemical via solution, e.g. carburising, particularly in steels. Carburising can be achieved via solid carbon (graphite), a liquid carbon-containing phase (cyanide-based) and

carbon-containing gas phase (CO, CO2, CH4). After carburising, the steel will be quenched.

The assumption in a thermochemical heat treatment is that there is no chemical reaction

during the deposition stage. Thus, at the temperatures used for carburising, the steel is in the

austenite phase of the phase diagram and the level of carbon introduced does not exceed the

solubility limit of carbon in austenite at that temperature.

Thermochemical via reaction, e.g. nitriding and metallising. In nitriding, nitrogen goes into solid solution but primarily it reacts to form FexNy precipitate-hardening phases.

Ion implantation. As the name implies, a material is bombarded with ions to modify the surface. Afterwards, the surface has to be heated to allow ions to diffuse. The technique is

expensive.

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Surface modification: chemical composition unchanged

(i) Mechanical Methods

M4 62 M4

(ii) Transformation hardening

Steels

Heat surface into austenite range in a furnace, and then quench, naturally or with extra cooling

(water quenching spray or bath)

This produces both martensite and retained austenite.

Controlled quenching in oil baths is also an option.

Flame hardening

Oxy-acetylene or oxy-propane flames

Depth 0.250.6 mm. The depth of hardening is known as the case depth.

Induction hardening

Radio frequency heating f = 3500 Hz

Depth 0.55 mm.

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Laser hardening

High power (0.1515 kW) continuous beam CO2 laser (23 mm spot size) scanned over surface by mirrors.

Surface can be coated with an absorbent such as graphite powder or iron oxide (Fe3O4) powder to

absorb the laser light.

Heating rate 106 K s1

Cooling rate 104 K s1

Surface is quenched by thermal conduction into the bulk of the material.

Very high cooling rates over the period of 1 sec can give martensite even in steels with low C

content.

The quenching by thermal conduction into the bulk of the material minimises distortion and also

avoids quench cracking the formation of cracks in steels which can happen when quenched by immersion into water or oil.

Higher power densities can lead to melting (laser glazing). This is used for AlSi alloys where very fine microstructures can be obtained.

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Electron beam hardening

High power (110 kW cm2).

An electron beam with a 23 mm spot size is scanned over the surface by electromagnetic deflection.

No surface coating is required.

Very schematically, we have the following comparison:

Laser /e-beam

Laser melting

Induction / Flame

hardening

Power

density

(W cm2

)

on a log10

scale

106

s 1 s

Interaction time (log10 scale)

102

s 104

s

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Surface melting

Main effect is grain refinement (e.g. AlSi alloys), although steels can transform.

It needs high input power density which can be supplied by

Electron beam

Laser

Tungsten inert gas (TIG) welding

Good for

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Surface composition changed

Principally for ferrous alloys. Two thermochemical treatments are used: solution hardening and

chemical reaction.

Solution hardening

Interstitial elements (C, N) diffused into surface. Cyanides (CN) can be used in one process, that of salt bath carbonitriding.

The ferrous alloy is hardened by the solutes introduced.

For example, the surface C content can be raised to make it easier to obtain martensite on the surface by quenching after the thermochemical heat treatment. This has to be tempered

to make the surface of the component less brittle and more ductile. There is a trade-off

between ductility and yield strength, which can be represented (very schematically!) in the

following diagram:

Reaction hardening

Interstitial elements (C, N, B) and substitutional elements (e.g. chromium) diffused into the surface. Chemical elements such as V, Ti and W can be in the bulk ferrous alloy.

Hardening can be achieved through the formation of very fine hard reaction products such as TiC, VN, etc. which increase the strength by precipitation hardening.

Alternatively, a hard layer of reaction product is produced on the surface of the ferrous alloy, e.g. the hard white layer arising from the formation of -Fe2(C,N).

In both solution and reaction thermochemical heat treatments it is possible to obtain surfaces with

graded strength by varying diffusion depths and concentrations.

Ductility

Yield

strength

Yield

strength;

ductility

Time at temper temperature

Working

stress

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Thermochemical (solution)

Carburising (case hardening).

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Gas carburising

Atmosphere of CO/H2/N2 or CH3OH/N2 at 920950 C, but can be as high as 1000 C to shorten reaction times.

Pack carburising

Pack in box with charcoal and an energiser such as BaCO3 at 920950 C. The energiser helps to create gas to obtain good coverage of the surface with carbon.

C + residual O2 CO

C + CO2 2CO

Pack carburising can last for many hours if required (e.g. > 1 day). Typical carburising times

of 236 hrs at 920940 C are quoted in Smithells Metals Reference Book, Eighth Edition, p. 29-45.

Vacuum carburising

Components are heated in low pressures of CH4 or C5H12 at 1050 C. Heating at higher temperatures gives shorter times for carburisation. An enriched thin surface layer is

achieved.

Subsequent heat treatment of the enriched surface layer enables drive-in diffusion of the

carbon into the component.

Plasma carburising

This can be used to form small components. The components are heated in a low pressure of CH4 at 1050 C. Glow discharge deposits C on the negatively charged surface.

Subsequent heat treatment of the enriched surface layer enables drive-in diffusion of the

carbon into the component.

Parts that are subjected to high pressures and sharp impacts are still commonly case hardened.

Examples include firing pins, rifle bolt faces and engine camshafts. In these examples, the surfaces

requiring the hardness may be hardened selectively, leaving the bulk of the part in its original tough

state.

A further example is that of self-drilling screws. For these, mild steel screws are first fabricated.

These are then carburised to obtain a high C content on their surface, quenched and tempered to

give a hard, tough outer layer.

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A comparison of hardness depth profiles for 0.18 wt% C steels carburised by three different methods for similar carburising times. Atmosphere carburising is the least expensive; plasma

carburising the most expensive.

[Source reference: Fig. 4 from W.L. Grube and J.G. Gay, High rate carburizing in a glow-discharge methane plasma, Metallurgical Transactions A 9, 14211429 (1978)).]

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Carbonitriding

A little thought about the level of nitrogen uptake in the carbonitrided layer shows that steels that

have nitride-forming elements in their chemical composition (e.g. those containing Cr or Mo for

example) can produce nitrides within the carbonitrided layer during the cooling and post-processing

procedure after the carbonitriding process has been completed, or even during the carbonitriding

process itself.

Controlled nitride formation is beneficial in helping to increase the surface hardness after post-

processing. It also reduces the possibility of distortion of the steel.

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Thermochemical (surface reactions)

Nitriding

The formation of particles, in this case nitrides as fine particles (precipitates) which harden the ferrous alloy as a consequence of nitriding.

In steels containing Al, Cr, Mo, Ti, V or W, all of which are nitride-forming elements, nitrogen is

diffused into the steels to form fine nitrides. This is carried out at 400 C, i.e. in the ferritic regime for carbon steels, rather than the austenite regime (as for carburising).

Like carbon, nitrogen diffuses interstitially, but the solubility level of nitrogen in ferrite is low:

0.1 wt% N. Nitrogen will react with the solute elements.

Some thought about the temperature used will recognise that, at a temperature of 400 C, a medium carbon steel with 0.4 wt% C will temper at the nitriding temperature since carbon can diffuse at this

temperature as well. This can be a problem for some steels.

Nitriding hardens the steel. Hardness levels are retained up to 500 C. Compressive stresses are produced in the steel, which are good for fatigue resistance.

Nitriding is achieved either by gas nitriding (heating in ammonia), for which 34 days are needed to achieve a 500 m layer, or plasma/ion nitriding.

In plasma/ion nitriding, the component to be nitrided is used as a cathode at 5001000 V in a H2/N2 mixture at 10

4102 atm (10 to 1000 Pa). The plasma is produced in the form of atomic N and heats the surface of the component to enable the nitrogen to diffuse three times faster than in gas

nitriding. It is, however, expensive. It can be used at a lower temperature of 350 C, so it is useful to steels which are particularly sensitive to tempering, such as tool steels.

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A possible undesired consequence of nitriding is the formation of a white layer containing the iron nitrides Fe2N and Fe4N (a consequence of the low solubility of N in -Fe). The FeN phase diagram is shown below.

[Note that 850 K = 577 C: nitrogen is a -stabiliser, decreasing the eutectoid temperature.]

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Nitrocarburising (Ferritic nitrocarburising)

Nitrocarburising involves the deliberate formation of a white layer on the surface of a ferrous alloy,

usually a low alloy or mild steel. The white layer is -Fe2(C,N). This layer is thin (20 m thick for example, formed after 2 hours at 580610 C) and is formed as nitrogen is diffused into a low carbon alloy. It is a cheap and fast process, but the layers can be brittle.

Traditional processes such as Tufftriding use a molten salt bath of NaCN and NaOCN (nowadays supplanted by more environmentally friendly compounds).

More modern processes use adapted gas or plasma nitriding processes the process is essentially a modified nitriding procedure.

Typical applications:

Bodycote, one of the companies which offers nitrocarburising as a process, states the following on

their web page about their proprietary Lindure process which is carried out at 570 C (and

therefore in the ferritic phase of iron):

Ferritic nitrocarburising is applied to a wide range of engineering components, such as textile gears, rocker arm spacers, cylinder blocks, pumps and jet nozzles, which are treated for wear

resistance properties. Crankshafts and drive shafts are treated to enhance fatigue properties.

Common applications include spindles, cams, dies, hydraulic piston rods, and powdered metal

components.

Highlights of successful applications:

Automotive washers

Races and cones for commercial-grade bearings

Various types of tooling, including dies

Lindure can be applied on low carbon, low alloy steels, medium and high-carbon steels,

tool steels, cast and ductile irons

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Exponential solution to Ficks second law for a finite source of diffusing material

In one dimension, Ficks second law can be written as

2

2

x

cD

t

c

where c is concentration, x is distance and t is time. The appropriate solution depends on the

boundary conditions, i.e., the values of c(x,t) at particular positions x and t.

One possible solution relevant for the diffusion of a finite source (thin film) into a material is that

Dt

x

t

Ac

4 exp

2

2/1

for a constant A. Looking at the left hand side of the diffusion equation, we have:

2

22

2/1

2

2

2

2/1

2

2/3 42

1

4 exp

4 exp

44 exp

2

1

Dt

x

tDt

x

t

A

Dt

x

Dt

x

t

A

Dt

x

t

A

t

c

Looking at the right hand side of the diffusion equation, we have:

Dt

x

Dt

x

t

A

x

c

4 exp

4

2 2

2/1

Dt

x

Dt

x

t

A

Dt

x

Dtt

A

x

c

4 exp

4

2

4 exp

4

2 22

2/1

2

2/12

2

2

22

2/12

2

42

1

4 exp

Dt

x

tDt

x

t

A

x

cD

and so we have shown that this is a solution of the diffusion equation.

The form of the solution (which is of course a Gaussian) is sketched below:

t2 > t1

t1

x

c t = 0 ( function)

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Note: for Dtx 2 the composition has fallen to e

1 of its value at x = 0.

Deposition and drive-in diffusion

When applying this form of the solution to a real process, we can consider a process where we first

deposit an amount of material, Q, per unit area, on the surface of another material and then allow

heat to drive in the deposited atoms into the second material. For this reason, the process is known as deposition and drive-in diffusion. It is a process which is applied to achieve reasonably uniform levels of the dopant in the material.

We can use the form of solution of the diffusion equation that we have just shown, noting that the

diffusion can be in one direction only (say + x).

x

c

Since diffusion is only one dimensional, the total amount of solute summed over all columns of

thickness x and of unit cross-sectional area going into the sample must always equal the amount, Q, deposited initially on unit area before the drive-in process.

Hence, as x 0, we have

0

2

2/1d

4 exp x

Dt

x

t

MQ

where M is to be determined.

To evaluate this integral, we can make the substitution Dt

xu

4

22 , so that

uDtx 2 ; uDtx d 2d

whence

0

2

0

2

2/1d exp 2d 2 exp uuDMuDtu

t

MQ

We can now substitute in a standard result that was derived in IA Mathematics for Natural Sciences:

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2

d exp

0

2

xx

so that we find

DMQ

Thus we can specify the parameter M in terms of the amount deposited, Q:

D

QM

and so the composition at depth x and time t is given by:

Dt

x

Dt

Qc

4 exp

2

which in words is one half of a Gaussian distribution for 0 < x < .

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Error function solution

A second physical situation is one where two different materials of different concentrations are

placed together so that solute diffuses from the higher concentration to the lower concentration and

the surface concentration remains constant.

P

0

c0

x

d

At t = 0, c = c0 for x 0 and c = 0 for x > 0 (e.g., two long metal bars in contact,

one pure iron and one a steel with a carbon concentration level of c0,

or alternatively pure iron in contact with a carburising atmosphere).

Consider the initial extended distribution to be a semi-infinite number of line sources.

To calculate the contribution to the concentration at P at time t: due to source of thickness d at distance from P, note that the initial amount in the source is M = c0d.

Thus, the contribution to the concentration at P, c(x,t) from the source of thickness d at distance from P is:

DtDt

ctxc

4 exp

2

d,

20

The extra factor of 2 in the denominator arises because from x = 0 to x = we have a solid and the region from x = 0 to x = is a solid, liquid or gas, but we are only interested in that component which physically reaches .

The total concentration at x at time t, c(x,t), is then obtained by integrating over from x to . [Note that because of the way we have set out the problem, is measured from right to left on the figure above.]

Hence,

xDtDt

ctxc d

4 exp

2,

20

Again, we make a substitution to simplify the exponent:

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Dt4

22 , so that 2 Dt ; d 2d Dt

so that

Dt

x

ctxc

2

20 d exp,

This is an example of a solution of the diffusion equation related to the Error Function.

THE ERROR FUNCTION (erf z ) AND THE ERROR FUNCTION COMPLEMENT (erfcz )

Definition

Error Function z

xxz

0

2 d exp2

erf

It follows at once that erf z = erf (z), erf (0) = 0 and erf () = 1.

It also follows that

zxxxxxxz

z

erf1d exp2

d exp2

d exp2

0

2

0

22

and this is defined as the error function complement, erfc z.

Error Function Complement zxxzz

erf1d exp2

erfc 2

Hence the solution already derived for two regions with different initial and uniform concentrations

can be written:

Dt

xctxc

2 erfc

2, 0

Simple extensions of this methodology enable solutions for (1) diffusion from a constant infinite

source of concentration c1 into an infinite medium with an initial concentration of c0 (e.g., to model

carburisation, covered in Part IB Materials Science), and (2) interdiffusion between two semi-

infinite blocks with initial concentrations of c1 and c0 respectively.

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In general this form of the solution of the diffusion equation takes the form

Dt

xBAtxc

2erf ),(

To persuade ourselves of this from an alternative point of view, we note that in general

z

uuz

0

2 d exp2

erf

and so it follows that

2 exp2 erfd

dzz

z

and 2

2

2

exp 4

erfd

dzzz

z

If we let

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Boronising

This procedure also produces wear-resistant surfaces.

In general, boron is diffused into the surface of a ferrous alloy to produce an iron boride layer

consisting of:

Outer layer: FeB (an orthorhombic phase with a = 5.506 , b = 2.952 , c = 4.061 . Pnma, oP8,

average CTE = 23 106 K1)

Inner layer Fe2B (a tetragonal phase with a = 5.110 , c = 4.249 . I4/mcm, tI12,

average CTE = 7.85 106 K1)

The outer FeB layer has mean coefficient of thermal expansion, T, noticeably greater than that of either Fe2B or Fe; on cooling this is put into tension, and so careful process control is needed to

avoid cracking.

The hardness values achieved are 1500 HV (Vickers hardness) which is in units of kg mm2; this equates to a hardness of 15 GPa, a value useful for abrasive wear.

The most common process for boronising is similar to that of pack carburising the material to be boronised is surrounded in a mixture of B4C (as a source of boron to continue the reaction once it

starts), an inert diluent such as SiC or Al2O3 and an activator such as KBF4 which vaporises, decomposes onto the steel surface and enables boron to diffuse into the steel.

Reaction of K and F vapour with B4C reforms KBF4 to enable the boron to be extracted from the

boron carbide. The vaporisation of KBF4 then enables the boron to be continuously formed in the

gas phase and be transported to the steel surface.

A typical boronising process quoted by Hutchings in his book on Tribology is 6 hr at 900 C. This produces a boron layer 150 m thick in total.

Boronising can also be achieved via molten salt baths (e.g. 60 wt% borax (Na2B4O7.10H2O), 20

wt% boric acid (H3BO3) and 20 wt% ferrosilicon (Fe70wt% Si) held at 800 950 C for 37 hr) or plasma processing using BCl3. It can also be applied to WC/Co cermets and titanium alloys.

In WC/Co cermets a variety of boride-containing phases are formed in the hard outer surface: CoB,

Co2B, Co3B, W2(C,B)5 and W(C,B)2. In titanium alloys, TiB and Ti2B constitute the boride-containing layer.

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Boron is insoluble in Fe as far as the above phase diagram is concerned. In boronising, B atoms

diffuse through the surface FeB/Fe2B layer to the iron, i.e. f