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
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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.
M4 2 M4
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.
M4 – 3 – M4
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.
M4 – 5 – M4
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.
M4 – 7 – M4
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.
M4 – 9 – M4
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
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
62
0
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, Boltzmann’s constant
(1.381 1023
J K1
); T, absolute temperature (K); h, Planck’s 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.
{
{
{
M4 10 M4
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.
M4 – 11 – M4
M4 12 M4
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.
M4 – 13 – M4
For two non-polar molecules r apart with polarizability ,
Dispersion interaction energy, W, = 62
0
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.
M4 14 M4
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 Å.
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 Boltzmann’s constant, T is temperature, h is Planck’s 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 1015
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.
M4 – 15 – M4
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.
M4 16 M4
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 Å
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.
M4 – 17 – M4
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,
M4 18 M4
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 102–10
3 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.
M4 – 19 – M4
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 Dupré equation). Since, in equilibrium we have
cosLVSLSV
it follows that
cos1cos LVSLLVLVSLSLLVSVAW (YoungDupré 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, Young’s equation and the Dupré 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 YoungDupré 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’), ΔG° 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 ΔG°, which increases WA and decreases θ.
Reactions with the greatest negative values of ΔG° 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).
M4 20 M4
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.
M4 – 21 – M4
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:
M4 22 M4
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, πa2, is A.
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For purely elastic deformation Heinrich Hertz, ‘Ueber die Berührung fester elastischer Körper’ [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),
M4 24 M4
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 << 1, even for elastic contact. Hence, to a very good approximation, the ratio w/A is almost
constant.
From their models they were also able to deduce whether asperities made contact elastically or
plastically.
M4 – 25 – M4
M4 26 M4
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The important result from this work is that for most surfaces, i.e., for a given σ*, 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.
M4 28 M4
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.
M4 30 M4
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
M4 – 31 – M4
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.
M4 32 M4
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.
M4 – 33 – M4
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.
M4 36 M4
Viscosity Index (VI)
M4 – 37 – M4
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.
M4 – 39 – M4
Regimes of lubrication
Hydrodynamic (full film)
lubrication
ηU/W
Elasto-hydrodynamic
lubrication
Coefficient of
friction,
Boundary
lubrication
The Stribeck curve: the variation in the coefficient of friction with the dimensionless quantity ηU/W
for a lubricated bearing. Here, η is viscosity (dimensions of ML1
T1
), U is peripheral speed
(dimensions of LT1
), of the bearing and W the load (per unit width) (dimensions of MLT2
/L =
MT2
), carried by the bearing (after Hutchings, p. 65). A nice commentary on Stribeck’s 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 δW,
supported by an asperity, assumed to be circular in cross-section with a radius a, is
δW = Pπa2
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, δV, is a hemisphere sheared off from the
asperity, it follows that
δV = 2/3πa
3
This fragment is formed by the material having slid a distance 2a.
Hence, δQ, 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).
M4 42 M4
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.
M4 44 M4
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 Young’s 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 Grundriß 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, Tabor’s 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.
M4 – 59 – M4
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
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(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 0.25–0.6 mm. The depth of hardening is known as the ‘case’ depth.
Induction hardening
Radio frequency heating f = 3–500 Hz
Depth 0.5–5 mm.
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Laser hardening
High power (0.15–15 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 s
1
Cooling rate 104 K s
1
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 (1–10 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
M4 – 67 – M4
Thermochemical (solution)
Carburising (case hardening).
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Gas carburising
Atmosphere of CO/H2/N2 or CH3OH/N2 at 920–950 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 920–950 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 104
–102
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 580–610 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 Fick’s second law for a finite source of diffusing material
In one dimension, Fick’s 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:
M4 76 M4
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 < .
M4 – 77 – M4
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:
M4 78 M4
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
zxxxxxx
z
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 zxxz
z
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.
M4 – 79 – M4
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
M4 80 M4
M4 – 81 – M4
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 Å, b = 2.952 Å, c = 4.061 Å. Pnma, oP8,
average CTE = 23 106
K1
)
Inner layer Fe2B (a tetragonal phase with a = 5.110 Å, c = 4.249 Å. 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.
M4 82 M4
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. from a high chemical potential to a low
chemical potential, as in the schematic below taken from L.G. Yu, X.J. Chen, K.A. Khor and G.
Sundararajan, ‘FeB/Fe2B phase transformation during SPS pack-boriding: Boride layer growth
kinetics’, Acta Mater. 53, 23612368 (2005).
Under suitably long boriding times, depletion of boron in the boriding medium can allow the FeB
layer to shrink back and be eliminated, so that only a surface boride layer of Fe2B remains.
M4 – 83 – M4
Examples of boronising:
SEM micrographs for mild steel boronised at 850 °C for (a) 5 min, (b) 30 min, (c) 60 min, (d) 90
min, (e) 120 min and (f) 240 min from L.G. Yu, X.J. Chen, K.A. Khor and G. Sundararajan,
‘FeB/Fe2B phase transformation during SPS pack-boriding: Boride layer growth kinetics’, Acta
Mater. 53, 23612368 (2005).
M4 84 M4
Metallising
The general principle behind metallising is to induce a chemical reaction between the metal
being deposited on the surface and a component of the underlying substrate.
Chromising
Chromium is usually used to impart corrosion resistance to ferrous alloys (e.g. FeCr and FeNiCr
stainless steels), but if it reacts with carbon in steels, it forms a surface layer of chromium carbide (a
mixture of Cr23C6 and C7C3).
Chromising is achieved via a pack process (for example with Cr, an inert filler such as alumina and
a halide activator such as NH4Cl heated together for 34 hr at 1000 °C), gas phase (CrCl3) or salt
bath, with the principles as in the equivalent processes in carburising and carbonitriding. Typical
treatment temperatures are in the range 900–1000 C, so that the steel is in the austenitic phase
field.
A twelve hour heat treatment in this temperature range produces a 20 – 40 m thick chromium
carbide layer in steels of a suitable composition. The hardness of this layer is of the order of 1500
HV, i.e. 15 GPa and is retained to just below the eutectoid temperature for Fe-C steels.
For steels with > 0.35 wt% C, the chromising process produces both chromium carbides and also
chromium as a diffusion layer which also confers corrosion resistance. This is known as ‘hard
chromising’. For steels with < 0.35 wt% C, only a chromium diffusion layer is formed which leads
to excellent corrosion resistance, but does not confer wear resistance. This is known as ‘soft
chromising’.
Aluminizing
M4 – 85 – M4
Toyota Diffusion (TD) process
Developed at Toyota Central Research Laboratory for tool and die steels (i.e., steels with
> 0.7 wt% C). The process is a way of producing surface layers containing carbides of Cr, Nb, Ti
and V up to 10 m thick. Hardness > 3000 HV and abrasion-resistant.
A salt bath is used at 800–1000 C for up to 10 hr of the relevant carbide-forming metal.
Components are quenched direct from the salt bath.
Hard layers on non-ferrous alloys.
An example of a process suitable for producing hard layers on non-ferrous alloys is the Delsun
process (J.J. Caubet and J.C. Gregory, ‘Thermal and chemico-thermal treatments of non-ferrous
materials to reduce wear’, Tribology 4, 814 (1971)). This was designed to treat brasses and
bronzes.
A Sb/Cd/Sn alloy of proprietary composition is deposited on the metal substrate and then heat
treated to diffuse the alloy into the surface and react. This forms a 2030 m thick layer with
hardness 450–600 HV, substantially harder than the substrate brass alloy. However, a literature
search on this process draws a blank after 1971.
M4 86 M4
Ion Implantation
Accelerators are used to inject ions into surfaces at 50–100 kV. The process is therefore
expensive because of the need to use accelerators. Typical penetration depths are 0.5 m;
the profile is not sharp.
Ion Implanter
Typical doses are > 1021
ions m2
, enabling 1020 at% dose of the implanted species
relative to the native species of the substrate. Hence, the chemistry of the surface layer is
changed significantly.
It is a low temperature process, carried out at typically 200–300 C. While there is no
external heating, there is heating of the substrate layer from the kinetic energy transferred to
the surface layer from the implanted ions.
It is a ‘line of sight’ process so that simple geometries such as flat surfaces are amenable to
ion implantation, but not complex shapes.
It is possible to inject any atomic species into anything. Gas ions as sources are most easy to
use.
Neutral ions (e.g. Ar) can be used to drive ions deeper into a substrate than they would go
otherwise.
Displacement damage in a substrate gives high diffusion coefficients. Heating the substrate
after ion implantation enables chemical reactions to take place at temperatures lower than
might be expected because of the large number of vacancies being present as a consequence
of the ion implantation damage.
The extra volume of material injected into the surface produces surfaces with high
compressive stresses, leading to good fatigue resistance.
There is little dimensional change in the substrate as a result of the ion implantation process.
M4 – 87 – M4
Applications of Ion Implantation
.. but it must always be remembered that this is an expensive technique!
M4 88 M4
Physical Vapour Deposition
Evaporation method:
Vapour from a liquid (or solid) source evaporates and condenses onto the target.
(Only) useful for low melting point coatings, such as coatings on optical components such
as microscope lenses.
Adhesion is relatively weak because the atoms striking the substrate only have relatively low
thermal energy; there is little mixing between the substrate and the atoms in the evaporated
film This means that such a process is unsuitable for the deposition of a coating to improve
wear resistance of highly engineered components such as tool steels.
There are ‘line-of-sight’ problems when coating components with complex shapes. For
example, in the above figure the sides of the component will have a thinner coating than the
part of the component in the direct line-of-sight of the source.
It is an inexpensive process.
The process is very useful for relatively small objects.
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Sputtering deposition:
Argon gas introduced as the sputtering gas into the system forms a plasma. The gas is at low
pressure: 0.1–10 Pa. This plasma sputters atoms from the negatively charged source (the
sputtering target).
The sputtered atoms are accelerated towards the positively charged substrate (the target)
with a few kV, typically 0.5–5 kV.
Non-conductive sources can be used if an alternating voltage at radio frequency is used.
Reactive gases such as nitrogen, oxygen and methane can be introduced in the technique of
reactive sputtering. These produce nitrides, oxides and carbides respectively.
Atoms sputtered from targets have significantly higher energies than the thermal energies of
evaporated atoms, so there is stronger interdiffusion and mixing with the substrate in this
technique in comparison with evaporation, leading to coatings with stronger adhesion in
comparison with evaporated coatings.
The process is very useful for relatively small objects.
M4 90 M4
Ion plating method:
The substrate is negatively charged. In the schematic above for the deposition of titanium,
atoms evaporated from the titanium liquid become ionised in the plasma produced by the
hollow cathode discharge (HCD) source and are attracted to the target which is a few kV,
typically 0.5–5 kV, and negatively charged.
The shutter enables control of the process of deposition of the coating on the substrate.
Reactive gases can also be introduced into the process.
The deposition of Ti in a Ar/N2 atmosphere enables the deposition of TiN at 400 C onto
steels without affecting their temper characteristics (for the right type of steel, e.g. tool
steels). As we will see later in the course, TiN and its derivatives are a family of very useful
wear-resistant coating materials.
The process is very useful for relatively small objects of high value.
[‘TC’ in the above diagram is a temperature controller]
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Chemical Vapour Deposition
In chemical vapour deposition (CVD), reactant gases are passed over a heated substrate at low
pressures.
A chemical reaction occurs on the substrate.
Typical reaction conditions are:
0.1–1 m/hr deposition: i.e. fairly low deposition rates.
500–1000 C
1–10 m thick layers formed. Thicker layers would take too long.
Examples:
TiN/TiC
M4 92 M4
SiC
Diamond
One method is to deposit diamond coatings using a mixture of CH4/H2/O2 at about 600 C.
A microwave plasma is needed so that the H2 can etch away any graphite deposited to leave behind
diamond instead. It turns out there is a narrow composition window of CH4:H2:O2 in which
diamond is deposited, rather than sp2-coordinated carbon.
An example of a diamond thin film on silicon from the Bristol University CVD Diamond Group is
shown below:
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Plating and Anodising
Plating
Typically this is Cr or Ni on steel – thicknesses of tens of microns to several mm plated. For
decoration alone, the plating will be just tens of microns. Silver and gold are also often used for
electroplating – for example silver plated stainless steel cutlery (EPSS) and EPNS. (EPNS stands
for electroplated nickel silver – ‘nickel silver’ is actually an alloy of 60 wt% Cu, 20 wt% Ni and 20
wt% Zn. The plating layer is pure silver).
Hardness values:
Cr 850 – 1250 HV; Ni 400 HV.
In electroplating (electrolytic plating) of Cr and Ni, it is important that the electrochemical
conditions used do not give rise to hydrogen embrittlement. The Pourbaix diagram of the process
predicts H2 production, and so organic additions are made to the electrochemical solution to alter
the nucleation and growth of the coating and limit H2 production.
The metal to be deposited is the anode in the process and the object to be plated the cathode. The
metal of the anode releases ions into the electrolyte and these are then plated out at the cathode.
Electroless nickel plating can also be used. In this process nickel ions from the solution and a
reducing agent (hydrogen phosphate for example) are used together to plate out nickel and
phosphorus (mostly nickel) onto the item of interest.
For Ni and P in the solution, Ni – 10 wt% P coatings have hardness values of 500 HV.
For Ni and B in the solution, Ni – 5 wt% B coatings have hardness values of 700 HV.
Both electroplating and electroless plating can be adapted to include second phases in the deposited
film (e.g. hard diamond, alumina or SiC particles, or even a solid lubricant such as PTFE). In this
way the coating can be engineered to have good wear characteristics or low friction.
Copper is often used as a thin undercoat for the plating of other metals such as nickel or silver.
M4 94 M4
Anodising
This develops a thick (hydrated) oxide layer on alloys of a number of metals, e.g. Al, Ti, Hf, Ta,
Nb, Zr and Mg.
Examples of anodised layers on titanium are shown below. The essential reaction is an anodic
reaction in a solution such as H2SO4 or H3PO4 at and around ambient temperatures, e.g. 10 C to
+20 C.
Anodic film produced on a titanium alloy using 1.0 M H2SO4 at 150 V.
Anodised titanium produces an array of different colours without dyes, as found for example in
titanium jewellery:
2 m
M4 – 95 – M4
Colour can be imparted to aluminium anodised layers by incorporating dyes:
After impregnation with dyes the pores have to be sealed, e.g. immersion in boiling deionised water,
so that the anodic oxide is converted into its hydrated form and swells. Other methods of sealing are
described in MIL-A-8625 (a U.S. military specification on anodic coatings for aluminium and
aluminium alloys).
The porous nature of these layers means that such coatings can also be impregnated with solid
lubricants such as PTFE to form coatings on suitable alloys which have a combination of low
friction (from the PTFE) and high hardness (from the 25–150 m thick anodic coatings).
Hardness values achieved are up to 600 HV which is very soft for an oxide.
For aluminium alloys the process of anodising is only suitable for alloys with relatively low alloying
content, e.g. < 10 wt% Si or < 5 wt% Cu.
M4 96 M4
Suitable processing of the anodised layer can produce striking ordered arrays of pores:
Ordered pores in 120 m thick anodised layers of aluminium formed in (a), sulphuric acid, (b)
oxalic acid and (c) phosphoric acid, following by pore opening in phosphoric acid.
(A.P. Li, F. Müller, A. Birner, K. Nielsch and U. Gösele, ‘Hexagonal pore arrays with a 50420 nm
interpore distance formed by self-organization in anodic alumina’, J. Appl. Phys. 84, 60236026
(1998)).
These ordered arrays can be used as templates to produce nanosized structures, e.g. for the growth
of nanorod networks.
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Hardfacing – Weld coats
This is a process generally applied to steels. These are a form of ‘overlay’ coatings.
The coating is applied by standard welding methods using oxy-acetylene welding, arc welding, MIG
welding, TIG welding, etc. Hardfacing materials must be molten at the temperature of the welding
process.
Deposits are 1–50 mm thick, i.e. several mm.
Typical materials used as hardfacing materials:
Austenitic manganese steels (e.g. steels with 12 wt% Mn and 1.2 wt% C in which Mn
stabilizes the austenite phase down to room temperature. Such steels are generally known as
Hadfield steels, named after Sir Robert Hadfield).
Martensitic steels
Cast irons containing carbide formers
WC/Co cermets
Stellite (a range of cobalt chromium alloys containing complex mixed carbides).
It is generally used to apply ‘sacrificial’ hard material where there is high abrasive wear and is
almost exclusively applied to steels. The technique is particularly useful for components used in
mining and quarrying, e.g. for earthmoving equipment:
M4 98 M4
Thermal spraying processes
In these processes surface coatings are produced by molten droplets which have temperatures
significantly higher than the substrate on which they are deposited. The droplets solidify rapidly on
contact with the (initially at room temperature) substrate, so that the substrate temperatures remain
below 200 C typically.
The choice of materials to be deposited and choice of substrate to be used are much wider than for
hardfacing.
Flame spraying
As the name suggests, flame spraying involves spraying and a flame. The flame is usually an
oxyacetylene flame which melts either a metal wire or rod (as above), a ceramic rod, or a powder
feed of a refractory material, as below (e.g. a ceramic or WC/Co powder).
Typical flame temperatures are of the order of 3000 C. Typical droplet temperatures are of the
order of 2000 C.
Typical impingement speeds of the droplets on the substrate are 100 m s1
. By comparison, cruising
speeds of aircraft are 250 m s1
. Droplets ‘splat’ onto the substrate, rather than rain down gently on
it. The splat can be reheated by flame or radio frequency (r.f.) induction heating to remove porosity
in the coating, but of course this will of course also heat up the substrate.
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High Velocity Oxygen Fuel (HVOF) spraying
This technique is a variant on the flame spraying theme, the difference being that oxygen is used
with various gases to produce a flame into which powers are injected. Very high gas velocities can
be produced of the order of 2000 m s1
, so that the particles can be travelled at supersonic
velocities.
The advantage of this technique over conventional flame spraying is the relatively low porosity
level which can be produced in the coating.
Schematic of the thermal spraying process together with optical micrographs of sprayed layers
M4 100 M4
Plasma spraying
A schematic of the plasma spraying process in a controlled atmosphere is shown below, taken from
www.sulzer.com .
A vacuum plasma spray rig can be seen in the Process Laboratory in the Department. Powders are
the feedstock in this process which is particularly suitable for ceramics and other refractories.
Typical parameters for the process quoted by Sulzer are:
Plasma temperature of 16000 C.
Particle velocity 200 – 400 m s1
Deposition rate 35 – 100 g min1
As with flame spraying, the powder particles are heated up to a temperature of the order of 2000 C,
but, significantly for plasma spraying, the initially room temperature substrate is heated up to
around 400 C.
A controlled atmosphere (e.g. argon or vacuum) prevents oxidation.
The higher particle velocities in comparison with flame spraying lead to coatings with porosities of
the order of 1–10%, significantly lower than in flame spraying, where porosity levels can be as high
as 20%.
To obtain a ‘keyed’ surface, i.e. one where the coating does not delaminate from the substrate, grit
blasting is often used to clean and roughen the surface of the substrate prior to thermal spraying. In
addition, ‘bond coats’ such as Ni/Al are often used as an intermediate layer when spraying ceramic
powders.
M4 – 101 – M4
Case Studies of Surface Engineering
Glazing
Glazing is the process of covering a ceramic body with a thin layer of glass. For pottery, such as
porcelain, stoneware, bone china and terracotta, the thickness of the glaze is of the order of 100 m.
Advantages:
glazes are impervious coatings (particularly useful for porous bodies such as terracotta);
glazes have a high resistance to chemical attack;
glazes add mechanical strength to ceramic bodies through the sealing of surface flaws;
glazes are hygienic.
When choosing a glaze for a particular body the most important consideration is that of relative
thermal expansion.
We want g < b, so that the glaze is in compression after the ceramic has been cooled from the
firing temperature (which is typically > 1050 °C).
If g > b we get ‘crazing’, i.e., fine hair cracks in the glaze. These are useful in decorative pottery,
but not in tableware, because the cracks are potentially unhygienic.
M4 102 M4
M4 – 103 – M4
Other requirements:
choice of transparency, e.g., transparent, opaque or matt;
restrictions on toxic compounds, e.g., PbO. Lead is introduced into glazes through lead
bisilicate rather than lead oxide; lead oxide is readily soluble in stomach acids.
Nowadays, glazes on bone china are virtually all lead-free. The glazes of choice are alkali
borosilicate (ABS) glazes, typically containing significant amounts of CaO, Na2O as well as Al2O3,
SiO2 and B2O3. This change in practice from the former use of lead-containing frits has been driven
by legislation from the U.S.A. – the bone china market is very dependent on the U.S.A. for sales.
Lead-based glazes are still used in the hotelware and porous earthenware market sectors. The
advantages of lead-based glazes are that they melt at relatively low temperatures, flow easily and
impart shine to glazes through the increased refractive index of the glaze because of the presence of
the heavy lead ions.
Opaque and matt glazes are formed by introducing fine crystals into the glaze through controlled
nucleation and growth, much like in glass-ceramic production. Extreme variations of this are
crystalline glazes, in which the introduction of ZnO into the glaze formulation causes the
crystallisation of willemite, Zn2SiO4. Transition metal oxides introduced into the glaze can partition
between the SiO2-rich glaze and the willemite, producing dramatic colour effects.
Glazes are normally applied as a finely ground suspension of powder (≡ ‘slip’) to the body which is
then dried and fired, during which the glassy state is developed in the glaze.
Examples of crystalline glaze pots
M4 104 M4
Enamelling
Enamels are coatings typically applied to metals, in particular cast iron and steel. They are
essentially silicate glasses fired typically at 850 °C – 950 °C for short periods. Enamels tend to
contain a lot of defects at the microstructural level.
For good adhesion of enamels a chemical bond is required at the interface between the enamel and
the metal, but, in addition, reaction products at the interface and mechanical interlocking through
roughening the surface deliberately also lead to a mechanical bond.
The presence of CoO and/or NiO in the enamel formulation is usually beneficial to the adherence.
For example, pre-existing (native) FeO formed during heating of a steel substrate before fusing with
the enamel can react with CoO:
3 FeO + CoO Fe3O4 + Co
The molten glass can attack Fe3O4 more readily than FeO (B.W. King, H.P. Tripp and W.H.
Duckworth, ‘Nature of adherence of porcelain enamels to metals’, J. Am. Ceram. Soc. 42, 504525
(1959)), enabling the enamel to be in contact with the underlying metal. It is important that
saturation of FeO is then maintained at the metal-enamel interface to enable suitable adhesion of the
enamel to the underlying metal.
Intriguingly, the question about whether the adhesion is predominantly chemical or mechanical
interlocking in particular enamelling systems is still a matter of some debate in the literature.
Enamelling also occurs in the arts and crafts, e.g. the enamelling of silver jewellery, as in this
example below:
M4 – 105 – M4
Diamond-like carbon coatings
Terminology: diamond-like carbon, abbreviated as DLC. This includes
a-C:H amorphous hydrogenated carbon, a mixture of sp2- and sp
3-bonded carbon;
produced by plasma-assisted chemical vapour deposition (PACVD).
ta-C tetrahedral amorphous carbon, mostly (> 80%) sp3-bonded carbon; no hydrogen;
produced from pure carbon targets by filtered vacuum arc or pulsed laser
deposition (PLD). Typically, the carbon atoms have energies between 50 and
200 eV.
ta-C is harder than a-C:H. ta-C has a hardness of 3080 GPa, whereas a-C:H has a hardness of
1550 GPa.
Advantages of DLC coatings:
low coefficient of friction
low wear rates
very hard
The wear products are graphite-like which can transfer to the partner (softer) surface, forming a
transfer layer which acts as a lubricant and protects the softer surface from wear, as well as the
harder DLC coated surface.
Applications:
(1) Magnetic storage technology (hard disks)
coatings of read/write heads and computer hard disks, e.g. magnetic media protected by a
5 nm thick a-C:H overcoat; read/write heads protected by a 5 nm a-C:H overcoat.
In addition, the DLC overcoat bonds to a 12 monolayer thick fluorocarbon lubrication layer
deposited on top of it.
(2) Car and engine parts
e.g., gears, wrist pins, fuel injector parts, piston rings. For example, the now discontinued
and then bottom-of-the range VW Lupo (19992005) had a number of DLC-coated parts.
M4 106 M4
(3) Scratch-resistant sunglasses
e.g., Ray-Ban Survivors Collection sunglasses.
The Ray-Ban Survivors sunglasses were introduced in 1995. The literature accompanying the
product claimed that these sunglasses ‘feature a coating that offers 10 times the scratch-resistance of
conventional glass lenses’ – see http://www.sti.nasa.gov/tto/spinoff1996/43.html.
Unfortunately, they are no longer produced. The technology for these was developed by NASA.
Bausch and Lomb manufactured these before they were taken over by the Luxottica Corporation.
The glasses used a-C:H technology in which a hydrocarbon source was used.
M4 – 107 – M4
(4) Razor blades
This is a very interesting application of DLC coating technology.
Pioneered by Gillette and introduced in 1998. This technology underpins the ‘Mach 3’ series
of wet razors advertised in the U.K. by David Beckham, a former footballer.
This DLC coating technology for the Mach 3 series has superseded the previous technology, still
used in Sensor blade technology, where a Cr-rich PtCr alloy coating some 40 nm thick is used to
protect the underlying steel blade.
The steel used for razor blades is a FeCr stainless steel with low C, for example the Sandvik
13C26 steel, Fe13Cr0.68C0.7Mn0.4Si, with trace impurity levels of P of 0.025 max and S
0.01 max (all compositions in wt%) – see http://www.sandvik.com.
13C26 is a martensitic stainless chromium steel which has good grinding and honing properties,
making it useful for the manufacture of razor blade edges.
In its unhardened condition 13C26 is ferritic with finely dispersed carbides. Its corrosion resistance
is poor because the chromium is tied up in the carbides.
The carbides dissolve during the recommended heat treatment for the steel. After quenching and
tempering 13C26 has good corrosion resistance. Its microstructure consists of a martensitic matrix
with undissolved carbides and some retained austenite.
M4 108 M4
Mach 3 technology:
Detail from the Mach 3 patent of the edge region of a razor blade.
The stainless steel body is 50, the tip portion 52 (with a radius typically less than 50 nm), 54 and 56
are facets that diverge at an angle of 13°, 58 is a niobium layer, 60 is the DLC layer, and 62 and 64
are facets with an included angle of 80°. Further defined is the aspect ratio a defined as the ratio
between (i) the distance DLC tip 70 to 52 and (ii) the width of the DLC coating at tip 52. The layer
72 is PTFE telomer, described as having a substantial as-deposited thickness, but whose thickness is
reduced to monolayer thickness during initial shaving.
[A telomer is a polymer with a very small degree of polymerisation, e.g. 25 monomer units per
polymer chain.]
M4 – 109 – M4
Gillette has 66% of the male wet razor market and 70% of the female wet razor market and does
rather well from the mundane razor blade.
Blades in Gillette Fusion razors have the same basic technology underpinning the blades in Mach 3
razors – see for example US 6,684,513 B1 dated February 3 2004 and US20100319198 A1 dated 23
December 2010 for their construction.
M4 110 M4
Coatings for cutting tools
Examples of drills, reamers, shank cutters and taps that have undergone surface treatments (taken
from an article at http://www.azom.com overviewing surface coating technologies for tool steels).
Reasons for coatings:
Improvement of wear resistance
Increase of tool life
They enable cutting tools to be used at higher cutting speeds
Improved wear resistance arises from the high hardness, low and chemical inertness of the
coatings.
The first coating to be developed commercially, and still used today, was titanium nitride, TiN,
deposited by PVD or CVD, e.g., on high-speed steels (HSS).
M4 – 111 – M4
High-speed steels are high-alloy steels containing ~ 0.8–1.0 wt% carbon.
General purpose HSS contain W, Mo, V and Cr as alloying elements. Typical carbides occurring in
these steels through secondary hardening are W2C, WC, Mo2C, VC, Cr23C6 and Fe3W3C.
‘T’ grades such as T1 steels contain high levels of tungsten, while ‘M’ grades such as M2 either
have molybdenum with limited tungsten or similar levels of tungsten and molybdenum.
Cobalt-containing HSS contain W, Mo, V, Cr and Co as alloying elements. These more expensive
HSS are more brittle than non-cobalt types, but give better cutting performance on hard, scaly,
materials that are machined with deep cuts at high speed (Roberts et al., p. 289).
Cobalt is present in solid solution in the austenite and tempered martensite rather than being
introduced as a carbide former. Although it can produce Co3C and Co2C, it is at best a weak carbide
former. Instead, it helps to raise the solidus temperature of the HSS which is useful for high
temperature operation of these high-speed steels (Roberts et al., p. 283).
Examples of compositions of high-speed steels from the Timken Company based in Ohio:
M4 112 M4
TiN coating technology and physical properties of the coating:
M4 – 113 – M4
More recent PVD coating technologies:
‘TiCN’: titanium carbonitride (actually, TiCxN1x);
‘TiAlN’: titanium aluminium nitride (TixAl1xN)
These take advantage of the replacement of N by C, and Ti by Al, while still retaining the basic
NaCl mFm3 crystal structure in the coating.
TiAlN can oxidise during machining to form a very thin protective layer of Al2O3.
PVD vs CVD
PVD has a lower processing temperature, and produces a coating which is very smooth and
has a very fine grain structure.
CVD requires higher temperatures than PVD ( 1000 °C), which can cause brittle phases
(Co3W3C and Co6W6C) to form at the coating/substrate interfaces in coated WC/CO
cemented carbide tools as a result of carbon diffusion. MTCVD (MT = medium
temperature) produces coatings on cemented carbide cutting tool inserts without phases.
CVD coatings adhere well to substrates because of the high temperatures involved.
Multilayer coatings
TiC, TiCxN1x, TiN layering topped by TiN shows significantly longer life than a ‘simple’ TiN
coating for cutting tools. The aim in multilayer coatings is to provide a gradation of mechanical,
physical and chemical properties.
Multilayer coatings can be deposited either by PVD or CVD.
Other coating materials for cutting tools
CrN used for machining copper-based materials;
TiB2 used for machining hypoeutectic aluminium alloys and magnesium alloys;
Al2O3 deposited by CVD and used for machining cast irons;
Diamond used for coating cemented carbide (WC/Co) tools. Deposited by CVD onto
an etched WC/Co surface where WC grains are exposed before the coating
procedure is begun.
M4 114 M4
Self-cleaning window glass
This is used extensively in buildings. The coating enables the photocatalytic stripping of organic
contaminants from the surface of glass.
The coating needs to be hydrophilic, so that rain or other water contacting the surface will spread
over (wet) the surface and wash dirt away from it.
The coating tends to be comprised of titanium dioxide, TiO2.
Coating technology:
A solution containing a precursor of TiO2 is applied to a glass surface, forming a precursor film.
Heating to a high temperature calcines the film, so that the organic matter in the precursor film is
oxidised and TiO2 is crystallised.
The precursor can be a titanium tetraalkoxide, e.g.,
Ti(OCH(CH3)2)4, titanium tetraisopropoxide
The technology of the coating deposition is essentially that of sol-gel (solution-gelation) technology.
In such a technology, a colloidal solution acts as a precursor (in this case, the titanium tetraalkoxide
solution) for an integrated network (here, the precursor film), which when suitably heat treated
(here, calcined) produces the final titanium oxide film.
Photocatalytic activity:
Electron-hole pair generation occurs in the photocatalyst (e.g., TiO2) when it is illuminated by light
of a given frequency (usually UV light). The electron-hole pairs can react in humid air on the
surface of the semiconductor photocatalyst to form hydroxyl and peroxy radicals which oxidise
surface grime.
Suitable materials for use as photocatalysts have band gaps of about 3 eV.
Coatings for plastic optical lenses
These are particularly important for plastic lenses for glasses. For example, polycarbonate (PC)
lenses are coated on both sides with an anti-scratch coating to provide protection against normal
handling scratches. Other plastic lenses such as ones made from polymerised CR-39 monomer (a
poly(diethylene glycol bis allyl carbonate) patented in 1947) also need anti-scratch protection.
Such coatings tend to be silica-based, in which Si-O chemical groups are embedded in an organic
matrix. Sol-gel procedures are used to make the appropriate solution into which the lenses are
dipped and extracted at a controlled speed. After drying to allow solvent evaporation the coatings
are about 2 m thick.
M4 – 115 – M4
Surface modification in biomaterials
Biomaterials are used in:
Joint replacements
Bone plates
Bone cement
Artificial ligaments and tendons
Dental implants for tooth fixation
Blood vessel prostheses
Heart valves
Skin repair devices
Cochlear replacements
Contact lenses
In all cases, they must be compatible with the body. Often, there are biocompatibility issues which
need to be resolved before a product can be placed on the market and used in a clinical setting.
Therefore, it is usual to subject biomaterials to the same requirements as those for new drug
therapies.
The rationale for the surface modification of biomaterials is to retain the key physical properties of a
biomaterial while modifying the surface to influence the biointeraction.
M4 116 M4
Thus, for example, for artificial heart valves, such as the one illustrated below, pyrolytic carbon is
used widely. However, it is a brittle material, and so can fail by crack propagation under load. An
alternative material for heart valves is a titanium alloy, e.g. Ti – 6 wt% Al – 4 wt% V.
Patients with both types of heart valves have to take anti-coagulation drugs to prevent blood clots
inside blood vessels, i.e. thrombosis.
Potential biocompatible coatings which can both extend the life of artificial heart valves and also
reduce the need to take anti-coagulation drugs are (CN)x, TiN, DLC, TiO and duplex TiN/TiO
coatings.
The nature of the TiO coatings depends on the oxygen : titanium ratio used to make the coatings:
for example if titanium is deposited as a plasma and oxygen is introduced into the plasma stream,
the oxygen : titanium ratio can be 2 : 1, as in rutile and anatase, but it can be as low as 1.4 : 1, so a
general chemical form of the TiO coatings is TiO2x.
M4 – 117 – M4
Materials used in joint replacements
Typical properties
Material Young’s
modulus (GPa)
Ultimate tensile
strength (MPa)
KIc
(MPa m1/2
)
GIc
(J m2
)
Alumina 365
Hydroxyapatite 85 40100
Cobalt-chromium alloy (ASTM
F75 standard)
230 4301028 100 50,000
304 Austenitic stainless steel 200 2071160 100 50,000
Ti – 6wt%Al – 4 wt%V 105 7801050 80 10,000
Cortical bone 725 50150 212 6005,000
Cancellous bone 0.11
PMMA bone cement 2–3 1.5 400
Polyethylene 0.52 2030 12 6,000
Notes:
ASTM F75 specifies an alloy of composition 27–30 wt% Cr, 5–7 wt% Mo, balance Co, with no
more than 0.5 wt% Ni.
304 austenitic stainless steel is 17.5–20 wt% Cr, 8–11 wt% Ni, < 2 wt% Mn, < 0.08 wt% C.
An alternative stainless steel suitable for biocompatible situations is 316L which contains 16.5–
18.5 wt% Cr, 10–13 wt% Ni, 2–3 wt% Mo , < 2 wt% Mn, < 0.08 wt% C.
M4 118 M4
Coating on materials used in joint replacements
Macro- or meso-porous coating processes on (pre-formed) implants
M4 – 119 – M4
Coatings for hip implants
Hip prostheses are examples of successful clinical implants in which a massive foreign body is
inserted into the human body. These implants are designed to last as long as possible after the
operation, but in practice lifetimes are often limited to only 15 years.
The lifetimes are principally constrained by the wear debris created at the articulating surface which
can migrate down to the bone/implant interface. Corrosion products in the form of particles and ions
can irritate the local cells and cause an adverse biological response.
Coating technology is therefore an active area of research for hip implants.
M4 120 M4
Examples of coatings advocated and used for hip prostheses:
Hydroxyapatite coatings for stems, e.g., by plasma spraying.
Diamond-like carbon coatings for articulating surfaces, e.g., deposited by CVD.
Hydroxyapatite coatings have the advantage of having new bone growth being able to integrate with
the coatings, particularly relevant for young patients requiring hip implants.
Other coatings suggested in the literature for the articulating surfaces:
Chromium carbonitride, CrCN
Chromium nitride, CrN
Titanium nitride, TiN
However, PVD TiN coatings have had poor long-term clinical results – these coatings have been
shown to produce unacceptable levels of wear debris (M.K. Harman, S.A. Banks and W.A. Hodge,
‘Wear analysis of a retrieved hip implant with titanium nitride coating’, J. Arthroplasty, 12,
938945 (1997)), due to the nature of the PVD coating process and the nonuniformity of the
resultant defect-containing coating. Titanium droplets which do not become an integral part of the
TiN coating during the deposition process can be removed during final polishing to leave micron-
sized voids in the TiN coatings. Partial delamination of the coating around these voids leads to the
unacceptable level of wear.
All coatings have to protect the underlying substrate from corrosion (note that the human body is a
very corrosive environment for hip implant materials) and must not delaminate during service.
M4 – 121 – M4
Coatings for ceramic fibres in ceramic matrix composites
These are required to enable matrix-fibre interfaces to be relatively weak in shear, so that the
toughness of ceramic matrix composites (CMCs) can be increased relative to monolithic ceramics.
Finally, we could have looked at many other coating technologies. The ones I have chosen for these
case studies are to some extent arbitrary, but demonstrate the range of surface engineering
technologies available commercially and demonstrate the reasons for their use.
M4QS PART III MATERIALS SCIENCE AND METALLURGY M4QS
Course M4: Tribology and Surface Engineering
KMK/LT15
Question Sheet
1. What is the physical origin of the van der Waals forces between two non-polar materials?
The van der Waals interaction energy, W, per unit area between two parallel surfaces a
distance D apart takes the form
212 D
AW
where the negative sign denotes that it is attractive if A, the Hamaker constant is greater than
zero.
For two macroscopic isotropic dielectric phases 1 and 2 interacting across a thin (15 nm
thick) isotropic dielectric medium 3, A can be presumed to take the form
2/1 23
22
2/1 23
21
2/1 23
22
2/1 23
21
23
22
23
21
3231
3231132
28
3
00 00
00 00
4
3
nnnnnnnn
nnnnh
TkA
e
B
where kB is Boltzmann’s constant, T is temperature, e is the common characteristic
absorption frequency for all three materials (3 1015
s1
), h is Planck’s 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.
For non-polar materials (0) n2 + where << n
2. For polar materials (0) >> n
2 because
of relaxation polarisation mechanisms which operate at frequencies less than the frequency of
visible light.
(i) Evaluate the terms
28
3 and
4
3 eB
hTk
for T = 298 K. Hence determine which of the two terms contributing to A132 is likely to
be the larger for typical values of n1, n2 and n3 all between 1 and 2.5, if the three
materials under consideration are all non-polar materials.
(ii) Deduce the conditions under which the van der Waals force is repulsive.
(iii) Evaluate A132 for the system air – water – air at 298 K. Will air bubbles be attracted to
one another in water? What will A132 be for water – air – water at 298 K?
(iv) Evaluate A132 for the system silica – liquid helium – air at 1.38 K. On the basis of this
calculation, how might you expect liquid helium to behave at 1.38 K in a beaker made
out of silica glass?
[Data: for air, n = 1 and (0) = 1; for water n = 1.33 and (0) = 80; for silica n = 1.448 and
(0) = 3.8; for liquid helium n = 1.028 and (0) = 1.057.]
M4QS – 2 – M4QS
2. Show how a simple model for wear due to the relative sliding of two surfaces leads to the
Archard equation
QKW
H
where Q is the volume of material removed per unit sliding distance, W is the load normal to
the surfaces and H is the indentation hardness of the softer surface.
In a tribological test, a medium carbon steel pin containing 0.5 wt% C is loaded against the
surface of a small hard steel disc rotating at 6 revolutions per second in air. The pin has a
small cross-section and the wear track has a diameter of 50 mm. The hardness of the pin is
240 Hv, i.e., 240 kg f mm2
(1 kg f = 9.81 N). Over a test duration of 1 hour at a normal load
of 1.0 N, the mass of the pin falls by 0.4 mg. The wear debris is found to be oxide. Calculate
the wear coefficient, K, of the pin, assuming that the density of the carbon steel is 7.8 Mg m3
.
The test is then repeated with fresh specimens at a load of 10 N. After only 1 minute the pin
was found to lose 10 mg in mass. A third test was performed at a load of 50 N. After an hour
the mass loss from the pin was 22 mg. Discuss these observations, suggest reasons for them,
and indicate how you could establish whether your reasons were correct.
How and why would you expect the results of this series of experiments to differ if they were
repeated (i) with a pure iron pin and (ii) with an austenitic stainless steel pin?
3. Suggest reasons for the following:
(a) for steel sliding on copper in air, a transition occurs between mild wear and relatively
low friction at low loads and severe wear and relatively high friction at high loads.
(b) a square PTFE slider rubbing for the first time on a clean smooth metal surface exhibits
a coefficient of friction, , of 0.1. For subsequent sliding in the same direction on the
same track, drops to 0.03. After rotation of the slider by 90° about an axis normal to
the track, rises to 0.1 for the next pass in the same direction on the same track.
4. Describe the mechanisms of lubrication at both low and high sliding speeds.
A system in which a steel sphere slides on a steel plane is well lubricated at 25 °C with a
hydrocarbon oil containing a small quantity (0.5 wt%) of stearic acid, a boundary lubricant.
Indicate how and why the behaviour of the system would be different at (i) 100 °C and (ii)
200 °C. What would happen if the oil did not contain stearic acid?
An agricultural gearbox operates satisfactorily at a oil temperature of 60 °C, with gear teeth of
surface roughness, Ra, equal to 0.5 m. To make the gearbox work more efficiently for a new
model of gearbox, the manufacturers wish to raise the operating temperature of the gearbox to
80 °C and, in order to market the gearbox globally at a cost-effective price, they also want to
install gears with a tooth roughness, Ra, equal to 1 m. Indicate how these two changes might
affect the choice of lubricant for the new model of gearbox.
M4QS – 3 – M4QS
5. A slab of material yields in uniaxial compression against a rigid plane surface at a yield stress
po. Show that if instead a compressive stress p1 (a negative quantity) and a shear stress are
both applied, so that the state of stress is the stress tensor
p1 0
0 0
0 0 0
then yield according to the Tresca criterion occurs when
W F A p2 2 2 24 o
if p1 = W/A and = F/A, where W is the normal load on the slab, F is the tangential force and
A is the area of contact.
The above formalism can be used to model the contact behaviour of asperities against a hard
plane surface during frictional sliding. As the shear force on the contact between the asperity
and the plane surface increases, the area of contact, A, increases.
The maximum possible tangential force, Fmax, is given by
Fmax = i Amax
when A has reached its maximum value, Amax, and where the surface is presumed to fail at
shear stress i because of the presence of a weak interfacial film between the slab and the
surface.
The coefficient of friction will then be
W
Fmax
On the Tresca criterion determine the relation between po and o, where o is the bulk shear
yield stress. Hence show on the Tresca yield criterion that the coefficient of friction will be
given by the formula
2/1 2io 1/2
1
Plot the dependence of on the ratio (i/o) for 0 < (i/o) < 1.
6. Thermochemical treatments are often used in order to change the surface properties of a
material while retaining its bulk properties. With reference to ferrous alloys, explain how such
treatments are accomplished with respect to the use of:
(i) interstitial elements;
(ii) substitutional elements;
(iii) the formation of hard reaction products.
M4QS – 4 – M4QS
7. Answer the following:
(a) Explain briefly why the wear rate of engineering ceramics depends on both their
hardness and fracture toughness.
(b) In order to increase the tool life of a high-speed steel cutting tool, it is proposed to coat
the tool. What coating material would you recommend, and why? How would you
suggest that the coating material be deposited on the high-speed steel?
(c) In an abrasive wear situation, suppose that there are N identical hard abrading particles
per unit area abrading a softer material each carrying the same normal load w in a
situation where the applied load is W. If the particles each have a linear dimension d,
show by considering each particle as an indenter of the softer material that N is
proportional to 1/d2.
(d) In a model to predict the wear of engineering ceramics due to abrading particles as a
function of the total load W, the wear Q was found to obey an equation of the form
rqp KHWQ c
where H is the hardness of the ceramic, Kc is its fracture toughness, is a material-
independent dimensionless constant and p, q, and r are power coefficients. If Q is
predicted to be proportional to H 1/2
, how is Q expected to depend on W and Kc?
Experiments were undertaken to examine the above equation using both SiC (hardness
20 GPa, fracture toughness 3 MPa m1/2
) and Si3N4 (hardness 15 GPa, fracture toughness
6 MPa m1/2
). What would you expect the wear rate of SiC to be relative to Si3N4 for a
particular set of abrading particles where lateral fracture is produced?
8. Coatings are an attractive method for protecting otherwise vulnerable surfaces from the effects
of wear, fatigue and corrosion. Explain the processes involved in:
(i) the electroplating of metal coatings;
(ii) anodising;
(iii) chemical vapour deposition (CVD).
For each of the above types of surface coating indicate for which forms of degradation the
treatment might be most appropriate.
Spraying of powdered materials is also an option for the production of a coating. Outline the
main features and advantages to be gained by using the high velocity oxy-fuel (HVOF)
process for applying a ceramic coating to a metal substrate.
9. The surfaces of engineering alloys can be modified in a variety of ways. For each of the
following, outline methods by which the surfaces of iron-based alloys can be modified,
describe the surfaces that are produced, and suggest possible applications for the final product.
(i) surface modifications which do not change the alloy composition;
(ii) surface modifications which change the alloy composition;
(iii) overlay coatings (hardfacing).
M4QS – 5 – M4QS
10. Answer the following:
(a) Outline the main methods used to treat metallic surfaces with boron compounds and
explain the advantages of such treatments.
(b) Indicate the microstructural phases formed in such treatments and any problems that
might be encountered.
(c) Outline the properties of the surface layers formed and suggest possible applications of
the treated materials.
(d) An iron component is treated in a boronising medium for 2 h at 940 C. The surface
concentration of boron is assumed to be maintained at a constant 25 wt%.
Using a suitable solution of the diffusion equation for boron diffusing through iron in
the absence of any chemical reactions, estimate the depth at which the boron
concentration in the iron drops to that of the boron compound formed with the lowest
concentration of boron during boronising.
In practice, the depth of the surface layers formed after this heat treatment is found to be
85 m when the surface is saturated in boron. Comment.
[For boron diffusion in austenite, data from P.E. Busby, M.E. Warga and C. Wells,
‘Diffusion and solubility of boron in iron and steel’, Trans. AIME, 197, 14631468
(1953) give values of the pre-exponential D0 = 2 107
m2 s1
and the activation energy
Q = 88 kJ mol1
.]
Previous Tripos Questions: 2005: 4(f), 18
2006: 4(f), 12
2007: 4(f), 12
2008: 4(f), 12
2009: 4(f), 11
2013: 19
2014: 20
Note that for the 20052009 Tripos questions, all of the 4(f) questions and all of the ‘EITHER’
questions are relevant, but not all of the ‘OR’ questions are relevant to the current course.
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