Materials Science Course F Materials unders extreme conditions

Prévia do material em texto

Natural Sciences Tripos Part IA 
MATERIALS SCIENCE 
Course F: Materials Under Extreme Conditions 
 
Dr Jess Gwynne 
Easter Term 2013-14 
IA 
Name............................. College.......................... 
FH1 Course F: Materials under Extreme Conditions FH1 
 
 
INTRODUCTION 
So far this year, you have had lecture courses about the atomic structure and microstructure of 
materials, device materials, mechanical properties, and biomaterials. In this course, we will 
explore a number of aspects of materials and their performance under extreme conditions. 
We will begin by considering the effect of high pressure on the structures of materials. We will 
then investigate materials at high temperatures, including melting and creep resistance (which 
is the resistance of a material to shape change under the combined effect of stress and 
temperature) and we will cover the superalloys used in the hottest part of jet engines. We will 
then look at the effect of radiation (in particular neutron radiation) on the structure and 
properties of materials and we will finish the course with a short section about life under 
extreme conditions. 
The aims of this course are to introduce you to new concepts and materials, but also to revise 
and build on material covered in the previous courses. 
Additional Resources 
Since this course builds on the earlier courses, and explicitly incorporates elements of revision, 
the books and web resources for earlier courses remain relevant. Some resources of particular 
relevance for this course are as follows: 
Web resources – DoITPoMS TLPs: 
 Creep Deformation of Metals: 
http://www.doitpoms.ac.uk/tlplib/creep/links.php 
 Materials for Nuclear Power Generation: 
http://www.doitpoms.ac.uk/tlplib/nuclear_materials/index.php 
Useful books: 
M.F. Ashby & D.R.H. Jones: “Engineering Materials Parts 1 and 2” 
D.A. Porter, K.E. Easterling & M.Y. Sherif, “Phase Transformations in Metals and Alloys” 
K.F. Kelton & A.L. Greer, “Nucleation in Condensed Matter” 
R.C. Reed, “The Superalloys: Fundamentals and Applications” 
K.L. Murty & I. Charit, “An Introduction to Nuclear Materials” 
FH2 Course F: Materials under Extreme Conditions FH2 
 
 
Contents 
1. Pressure 3 
1.1 Definition; scale and units 3 
1.2 Free energy (some revision from course C) 4 
1.3 Pressure as a thermodynamic variable 5 
1.4 Pressure-temperature phase boundaries: the Clausius-Clapeyron equation 6 
1.5 Experimental determination of P-T phase diagrams 8 
1.6 Calculation of P-T phase diagrams 10 
1.7 What can we expect at high pressure? 11 
1.8 Reconstructive phase transitions 12
 
2. Temperature 16 
2.1 Melting 16 
2.2 Mechanical performance at high temperature: Creep 21 
2.3 Superalloys for jet engines 26 
2.4 Thermal barrier coatings 34 
2.5 Ice 37 
 
3. Radiation damage 41 
3.1 Introduction 41 
3.2 The displacement cascade 42 
3.3 Damage rates 43 
3.4 Principal types of damage 44 
 
4. Life under extreme conditions 47 
4.1 Extremophiles 47 
4.2 Tardigrades 48 
4.3 Applications of extremophiles 49 
 
Glossary 52 
Abbreviations 55 
Symbols, quantities and units 56 
 
 
 
 
 
FH3 Course F: Materials under Extreme Conditions FH3 
 
 
1. Pressure 
The role of temperature in phase transformations and the development of microstructure was 
covered in course C. Temperature affects the kinetics of a transformation (typically occurring 
faster at higher temperatures) and is also a thermodynamic variable. Likewise, pressure affects 
both the kinetics (typically slower at higher pressures) and the thermodynamics of a 
transformation, the latter being our focus in this section. Pressure-induced transformations can 
be exploited for materials synthesis and are of interest in a wide range of other contexts, 
notably geology. 
1.1 Definition; scale and units 
The pressure of a gas is defined in terms of the force acting per unit area. In a solid, it is 
possible to have different forces acting on different surfaces, giving complicated stress states. 
Any such state, however, can be decomposed into components, one of which is the hydrostatic 
pressure: this is isotropic, with the same force per unit area acting normal to any surface. 
 
At zero temperature, the pressure P can be defined as the change in internal energy dU due to a 
change in volume dV: 
d
d
 
U
P
V
 
Note that the negative sign arises because application of a positive pressure reduces the 
volume. 
 
The SI unit of pressure is the pascal (1 Pa 

 1 N m
-2
). Standard atmospheric pressure (1 atm) is 
101325 Pa (

 1.01325 bar), i.e. approximately 10
5
 Pa. Some other values: 
 
under a stiletto heel ~ 7  106 Pa 7 MPa 
in the deepest ocean trench ~ 10
8
 Pa 100 MPa 
at the centre of the Earth ~ 3.8  1011 Pa 380 GPa 
maximum steady pressure in experiment ~ 5.6  1011 Pa 560 GPa 
at the centre of Saturn ~ 10
12
 Pa 1 TPa 
in pulsed-laser experiments ~ 10
16
 Pa 10 PPa 
at the centre of the Sun ~2.5  1016 Pa 25 PPa 
 
Note that we can also have negative pressures (as in tensile stress, but isotropic). 
 
FH4 Course F: Materials under Extreme Conditions FH4 
 
 
1.2 Free energy (some revision from course C) 
The Gibbs free energy G plays a central role in the interpretation of phase transformations: 
 G H TS
 
where H is the enthalpy, T is the temperature and S is the entropy. Usually the extensive 
variables (G, H, S) are expressed per mole of formula units. 
The stable phase at any pressure or temperature is that with the lowest free energy. It is often 
useful to formulate the thermodynamic functions in terms of differentials: 
TSSTPVqTSSTHG dddδdddd 
 
where q is the heat supplied to the system, V is the volume and P is the pressure. 
From the second law of thermodynamics (CH16), for reversible changes: 
STq dδ 
 
which gives the standard differential form of the Gibbs free energy: 
TSPVG ddd 
 
 
1.2.1 Phase transformations at constant pressure 
Phase changes as a result of changing temperature (at constant pressure) were considered in 
detail in Course C. From the differential form of G, it follows that at constant pressure 
(dP = 0): 
S
T
G
P








 
At low temperatures the entropy tends to zero, so the slope of the free energy curve must be 
zero at zero temperature. The slope is negative otherwise (i.e. positive entropy), and is 
increasingly negative at higher temperature, giving the characteristic form of the G curves. 
In the example below, the α phase has a lower enthalpy at zero temperature and hence is the 
stable phase at low temperatures. The β phase has a higher entropy at all temperatures (hence 
the slope of G is greater), and at a certain temperature the two curves cross. This defines the 
temperature of the phase transition. The phase of higher entropy is favoured by higher 
temperature. 
FH5 Course F: Materials under Extreme Conditions FH5 
 
 
 
 
1.3 Pressure as a thermodynamic variable 
We can now extend the treatment in course C by consideringthe effects of changing the 
pressure as the temperature is held constant (dT = 0). From the differential form of G: 
V
P
G
T








 
In the example below, at low pressures the β phase has the lower free energy and is the stable 
phase. On increasing the pressure, the free energy of the phase with the higher volume 
increases faster. If the volume of the β phase is higher than that of the α phase, increasing the 
pressure eventually causes the free energy of the β phase to rise above that of the α phase, and 
above this pressure the α phase is the stable phase. The phase of lower volume is favoured by 
higher pressure. 
 
 
F
re
e 
en
er
g
y
Temperature
Transition 
temperature
α
β
F
re
e 
en
er
g
y
Pressure
Transition 
pressure
α
β
FH6 Course F: Materials under Extreme Conditions FH6 
 
 
1.3.1 Pressure-temperature phase diagrams 
For a given phase, the variation of G with T and P is represented in a 3D plot by a curved plane. 
The G planes for two phases intersect on a line. The projection of that line onto the P−T plane 
gives the phase boundary between the phases on the pressure-temperature phase diagram. Such 
boundaries are approximately straight, as discussed in section 1.4. 
 
 
1.4 Pressure-temperature phase boundaries: the Clausius-Clapeyron equation 
Consider the phase boundary between the  and  phases of a material: 
 
At all points along the phase-boundary line, the two phases are in equilibrium, and they 
therefore have the same free energy: Gα = Gβ. 
We can use the differential form of the free energy (giving the infinitesimal changes in G that 
arise from infinitesimal changes in T or P): 
d d d G V P S T
 
P
re
ss
ur
e,
 P
Temperature, T
α
β
P
re
ss
ur
e,
 P
Temperature, T
α
β
Gα=Gβ
dP
dT
FH7 Course F: Materials under Extreme Conditions FH7 
 
 
For a small step along the phase boundary, given by dT and dP in the figure above, we have: 
TSPVG ddd ααα 
 
TSPVG ddd βββ 
 
  TSPVG ddd 
 
The fact that dGα = dGβ along the phase boundary implies that 
  0d  G
, giving the final 
result: 
d Δ
d Δ

P S
T V
 
This is known as the Clausius–Clapeyron equation (sometimes shortened to the Clapeyron 
equation). 
It relates the slope of the phase boundary simply to the differences in entropy and volume of 
the two phases. Since the crystalline solids in a given system have similar specific heat 
capacities and compressibilities, S and V are to reasonable approximation independent of 
temperature and pressure. In that case, the phase boundary is a straight line, which is the case 
for many phase transformations. 
To predict the equation of a phase boundary we need to know one point on the phase boundary 
and values for ΔS and ΔV. In analytical treatments, we assume throughout that ΔS and ΔV are 
independent of T and P. 
 
FH8 Course F: Materials under Extreme Conditions FH8 
 
 
1.5 Experimental determination of P-T phase diagrams 
The usual method of determining a phase diagram is to identify the stability fields of different 
phases in samples at a variety of temperatures and pressures. There are two ways of doing this: 
 One is to hold a sample under a given temperature and pressure until it has 
equilibrated, and then to identify the phase in situ. 
 The other way is to equilibrate the sample at a given temperature and pressure, quench 
it to room temperature, let the pressure down to ambient level, and then identify the 
phase at ambient temperature and pressure. Since reconstructive transformations (see 
section 1.8) are often slow, the quench preserves the structure obtained under the P−T 
conditions of the anneal. This approach cannot be applied for kinetically fast 
transformations, e.g. for displacive transitions and many order-disorder transitions. 
Even for reconstructive transitions, the degree to which they can be prevented by a 
quench can be open to doubt. 
High pressures and temperatures can be obtained by a variety of methods that vary widely in 
the conditions that can be attained, the sample size that can be processed, and the ease with 
which crucial property and structure measurements can be made in situ. 
1.5.1 Piston-and-cylinder devices 
The first high-pressure devices used simple piston 
arrangements. The piston is pushed into the cylinder by 
an external press. The materials of which the press is 
constructed determine how much of the applied force can 
be translated into pressure on the sample. Heating of the 
sample is straightforward. 
 
1.5.2 Opposed-anvil devices 
Anvils can be used to concentrate the force onto a 
small area, effectively magnifying the pressure. The 
gasket applies external constraint, avoiding extrusion 
of the sample from the sides. A good gasket material 
should be able to flow without fracture. A belt ring 
supports the gasket. 
 
Applied force
Sample
Sample
Gasket
Supporting 
belt
FH9 Course F: Materials under Extreme Conditions FH9 
 
 
This type of device can be used with diffraction equipment at a neutron or synchrotron X-ray 
source, and heating can be achieved by insertion of a heating element such as graphite. This 
type of device was used in the first synthesis of diamond (see section 1.8.3). 
1.5.3 Multi-anvil devices 
In a multi-anvil press, the sample is squeezed within an 
arrangement of several truncated tungsten carbide or sintered 
diamond anvils, and then pressed in a large loading frame with 
a resistance heater incorporated in the sample assembly. 
Relatively large sample sizes can be used (up to 100 mg, 
depending on pressure) and good control of temperature and 
pressure can be achieved. However, it is difficult to observe 
samples in situ. Modern devices typically use 4, 6 or 8 anvils. 
 
1.5.4 Diamond-anvil cell 
In a diamond-anvil cell, the sample is squeezed between opposed 
diamonds and heated with an infra-red laser focused on the sample 
for high temperatures, or an external heater for moderate 
temperatures. Sample sizes are limited by the size of the diamonds 
and are typically less than 50 mg. It is difficult to calibrate exact 
temperatures, but these can be very high. It is possible to perform in 
situ measurements such as X-ray diffraction and spectroscopy. 
 
1.5.5 Pulsed-laser implosion 
Facilities such as the National Ignition Facility (USA, with 192 laser beams) or Orion (UK, 12 
laser beams) are capable, with pulsed beams for very short times, of creating temperatures and 
pressures (> 1 PPa) similar to those in the cores of stars and giant planets. Achieving nuclear 
fusion in the laboratory is at the heart of the studies using such facilities. 
 
 
Tungsten 
carbide 
anvil
Gasket Sample 
assembly
32 mm
Gasket
FH10 Course F: Materials under Extreme Conditions FH10 
 
 
1.6 Calculation of P-T phase diagrams 
In many cases it may not be possible to determine phase diagrams by direct experiment. For 
example, it may not be possible to reach the necessary pressures and/or temperatures. In such 
cases it may be necessary to extrapolate from thermodynamic measurements made under not-
so-extreme conditions. The Clapeyron equation is then very useful for calculating the 
equilibrium boundary between two phases. 
ΔV can be measured for the two phases at room temperature using X-ray diffraction. The 
experimentaldetermination of ΔS is not so straightforward, but it can be achieved by two 
methods: 
 One approach is to determine S directly from calorimetric measurements of the 
enthalpy change (latent heat) for the transition at its equilibrium temperature 
eqT
, using: 
eqT
H
S


 
 Alternatively, the absolute entropy of each phase can be determined by measuring the 
heat capacity from 0 K up to the required temperature 
1T
, and then integrating. Since 
T
S
TC
d
d
P 
 
we have: 
  








i
i
T
T
H
T
T
C
TS d
1
0
P
1
 , 
taking account of the latent heats 
iH
 of any transitions. (According to the third law of 
thermodynamics, 
 K 0TS
 is zero.) 
Experimental measurements and thermodynamic analysis are usually supported with computer 
modelling. With modern computational methods, it is now possible to calculate phase 
properties sufficiently well to permit prediction of P-T phase diagrams. 
 
 
FH11 Course F: Materials under Extreme Conditions FH11 
 
 
1.7 What can we expect at high pressure? 
At high pressure, lower volumes can be achieved by higher packing density, whether of 
atoms/ions, or of coordination polyhedra. 
Pressure may also force changes in local bonding configuration, or in the nature of the bonding 
(e.g. graphite-diamond). 
On pushing molecules together, the point must be reached where the distances between ‘non-
bonded’ atoms are very similar to the distances between atoms within the molecules 
themselves; this provokes a loss of molecular identity as intermolecular electrons are 
delocalised between molecules, either locally (forming polymers, e.g. polymeric CO and CO2 
under high pressure), or completely (forming metals). 
There is particular interest in forming metallic states. For example, the crystal structure of solid 
iodine at ambient pressure has the I2 molecules packed in a herringbone pattern. However, 
under pressure, the molecules dissociate and the new phase is metallic. Metallisation has even 
been achieved for hydrogen, at pressures exceeding 250 GPa (it has the hcp structure). 
Setting aside such extreme examples, the application of more modest pressures has proved to 
be exceptionally useful in generating a wide variety of novel structures with potentially 
exploitable properties (mechanical and electronic). These include: 
 artificial diamond, cubic BN, and other super-hard materials 
 new superconductors (clathrates, nitrides etc) 
 new organometallic compounds 
 nitride semiconductors 
 thermoelectrics. 
 
FH12 Course F: Materials under Extreme Conditions FH12 
 
 
1.8 Reconstructive phase transitions 
Many phase transitions that occur under pressure are between two structures that are not 
closely related. Such transitions are reconstructive and are in contrast to the displacive phase 
transitions met in Course B (BH29). 
 Because the structures of the two phases involved are dissimilar, the transition involves 
breaking and re-forming of bonds. The phase transition is discontinuous and there is a sharp 
boundary between the phases during the transition. 
 Reconstructive transitions are thermally activated, and it is possible for one phase to remain 
as a metastable state even under P−T conditions where the other phase should be stable. The 
metastable state of diamond at ambient pressure and temperature, where graphite is the 
thermodynamically stable phase, provides a good example. 
 Reconstructive transitions require nucleation and growth of the new phase; many of the 
concepts used to describe precipitation (Course C) apply in this case also (coherence, TTT 
diagrams, supercooling for nucleation, preferential sites for nucleation such as grain 
boundaries and triple lines, diffusion for growth). 
 The kinetics of reconstructive phase transitions are important in analysing many pressure-
induced effects. 
 
1.8.1 NaCl-MgO at high pressures 
At ambient pressure both NaCl and MgO adopt the rocksalt f.c.c. structure (for which NaCl of 
course is the classic example). In this structure, each ion has 6 nearest neighbours of the 
opposite type. However, at higher pressures, both materials adopt the cubic P CsCl structure, in 
which there is a denser packing with each ion having 8 nearest neighbours of the opposite type. 
 
 
 
FH13 Course F: Materials under Extreme Conditions FH13 
 
 
1.8.2 The reconstructive transformation in Mg2SiO4 
At ambient pressure, rocks are brittle, which is consistent with occurrence of earthquakes. 
However, some earthquakes originate deep in the Earth’s mantle where the high temperature 
and pressure mean that the rock flows plastically rather than failing in a brittle manner. 
Therefore, these deep-focus earthquakes cannot be caused by brittle fracture of the rocks, and 
are instead likely to be caused by a pressure-induced phase transition. 
The Earth is composed of distinct layers of different materials and densities. The inner core 
consists of an iron-rich solid phase, the outer core consists of an iron-rich liquid phase, and the 
mantle layers consist of various silicates, mainly (Mg0.9Fe0.1)2SiO4. 
In the uppermost layer, at lowest pressures, 
olivine is the stable phase. However, it 
undergoes a reconstructive phase transformation 
to the spinel phase as the pressure is raised (at 
about 400 km depth in the Earth). 
Each of these phases (or polymorphs) has a 
structure composed of SiO4 tetrahedra and 
MgO6 octahedra. 
 
In both structures, the Si cations are in tetrahedral sites, and the Mg cations are in octahedral 
sites. In olivine (below left, viewed down [100]), the oxygen atoms are in an approximately 
hcp arrangement, and the crystal structure is orthorhombic. In spinel (below right, viewed 
down [001]), the oxygen atoms are in an approximately ccp arrangement and the crystal lattice 
is cubic F. Note that Mg atoms are shown as circles and SiO4 tetrahedra are shaded. 
 
 
The large kinetic barrier to the transformation from olivine to spinel means that olivine exists 
metastably far beyond its equilibrium range, finally transforming to spinel at depths greater 
than 600 km, rather than in the range 300-400 km. A significant implosion shock results from 
the volume contraction of 8%, which causes the deep-focus earthquakes. 
P
re
ss
u
re
 (
G
P
a
)
at 1000 C
FH14 Course F: Materials under Extreme Conditions FH14 
 
 
1.8.3 The graphite-diamond transformation 
Diamond is thermodynamically metastable under ambient conditions, but there is no risk of it 
transforming to the stable polymorph graphite (“diamonds are forever”). Transformation from 
diamond to graphite is extremely sluggish because a complete reconstruction of the bonding is 
required (sp
3
 in diamond, sp
2
 in graphite) and the activation energy is therefore very high. 
This sluggishness applies equally, of course, to the more desirable transformation from 
graphite to diamond. In the upper mantle, the temperature-pressure profile (the geothermal 
gradient) is such that diamond becomes thermodynamically stable at sufficient depth and 
natural diamonds form over millions of years at a depth of ~300 km. They are found in the 
necks of extinct volcanoes where they have been brought nearer to the surface (and also at 
meteorite impact sites). 
The most famous site is the Kimberley 
“big hole” in South Africa, which has 
yielded around 14.5 million carats of 
diamonds. At this site,deep-Earth 
materials were thrust upwards sufficiently 
quickly that the diamonds did not revert to 
graphite. 
 
 
On the P−T phase diagram for 
carbon, the equilibrium boundary 
between graphite and diamond is 
extremely difficult to determine 
directly, because the transformation 
(in either direction) is so sluggish. 
However, the boundary can be 
readily calculated from measured 
quantities such as heats of 
combustion or of solution. 
 
There has long been an interest in the production of artificial diamonds. This first achieved 
commercial success in 1954-5 with the “high-pressure high-temperature” (HPHT) process. 
This uses a liquid metallic solvent (Ni, Co, Fe) at ~ 5 GPa, ~ 1500°C into which graphite 
dissolves, and from which diamond precipitates (possibly on natural diamonds used as seeds). 
geothermal
gradient
FH15 Course F: Materials under Extreme Conditions FH15 
 
 
Mostly small (dis)coloured stones are produced, suitable for most uses except gemstones. 
Nitrogen impurity, for example, accelerates diamond growth, but gives a yellow/brown 
discolouration. However, since the 1970s, it has been possible to synthesise gem-quality 
stones. 
Similar methods can be used to synthesise other superhard materials. A good example is cubic 
boron nitride, the second hardest substance known. At ambient temperature and pressure, the 
stable form of BN is hexagonal and has a similar structure to graphite (below left), but the 
cubic phase has the sphalerite structure (below right), which is analogous to diamond. 
 
 
Cubic boron nitride is widely used as an abrasive and has the advantage over diamond that it is 
much more chemically inert. For example, it is insoluble in metals such as steels, whereas 
diamond is soluble and forms carbides (which can cause embrittlement). 
 
 
 
FH16 Course F: Materials under Extreme Conditions FH16 
 
 
2. Temperature 
We have seen that crystal structures, particularly when not closely packed, can be rather 
susceptible to change under pressure. We will now explore the behaviour of solids as the 
kinetic energy of their atoms is changed. As the temperature is lowered from ambient values, 
there can be interesting and important effects on physical properties, for example the onset of 
superconductivity and the appearance of exotic types of magnetic ordering, but the structural 
effects on solids are limited. As the temperature is raised, there can be phase transitions to 
other crystal structures, but our initial focus will be the stability of the crystalline state itself. 
Some temperature values: 
lowest temperature achieved in a laboratory 0.1 nK 
cosmic microwave background (temperature in space) 2.7 K 
boiling temperature of nitrogen N2 (at atmospheric pressure) 77 K 
standard room temperature (25°C) 298.15 K 
blue Bunsen flame 1870 K 
calculated melting point of diamond at atmospheric pressure 3823 K 
surface of the sun 5800 K 
core of the sun 13.6 MK 
plasma in a Tokamak fusion reactor 0.5 GK 
 
2.1 Melting 
2.1.1 Asymmetry between freezing and melting 
In course C, we saw that when a liquid is cooled, there is a distinct barrier to nucleation of the 
crystal (CH49). As a result, the liquid may be significantly supercooled below its equilibrium 
freezing temperature before solidification occurs. Significant changes in behaviour can be 
achieved by initiating freezing by using heterogeneous nucleants (e.g. CH52−CH53 and 
EH51‒EH52). 
In marked contrast, common experience suggests that there is no similar nucleation barrier to 
melting. This clear asymmetry is of interest to analyse. 
 
FH17 Course F: Materials under Extreme Conditions FH17 
 
 
2.1.2 Theories of melting 
Lindemann theory: The first attempt to predict the bulk melting point of crystalline materials 
was made in 1910 by Frederick Lindemann. He suggested that melting occurs when the 
average amplitude of the atomic vibrations reaches a critical fraction of the interatomic spacing 
– at this point, the atoms start to collide with their neighbours, making the structure 
mechanically unstable and initiating the melting process. Experimentally, that fraction seems to 
be 0.15 to 0.30. Lindemann’s simple model works reasonably well, but cannot explain why the 
structure of a solid breaks down within such a narrow temperature range. 
Born theory: Another theory of bulk melting was formulated by Max Born in 1939. He 
suggested that melting occurs when one of the elastic shear moduli of the crystal goes to zero. 
This would constitute a rigidity catastrophe or mechanical melting in which the entire crystal 
lattice collapses, making a continuous transition into the liquid state. 
Actual melting, however, is not uniform throughout the solid, but typically begins at the solid 
surface and progresses inward. At the melting/freezing temperature, the solid and the liquid 
coexist with a well-defined interface between them. Importantly, although shear moduli do 
decrease with increasing temperature, at the melting temperature the solid is still rigid with 
non-zero moduli. 
 
2.1.3 Surface melting 
For most crystals, some form of surface melting can be found at temperatures significantly 
below the bulk melting temperature. This can be simply interpreted in terms of interfacial 
energies. It is usually the case that the solid-vapour interfacial energy exceeds the sum of the 
liquid-solid and liquid-vapour interfacial energies: 
sv ls lvγ γ γ 
 
(Here 
ls
 is the quantity simply labelled  on CH49‒50.) In that case, the crystal is wetted by 
its own melt (i.e. the contact angle of the liquid on the solid surface is zero, CH52) and a thin 
layer of liquid should coat the solid even below Tm. This of course explains why there is no 
nucleation barrier for melting. Below Tm, the liquid layer must remain very thin because the 
bulk liquid is not thermodynamically stable, but its thickness diverges as Tm is approached on 
heating. 
 
 
FH18 Course F: Materials under Extreme Conditions FH18 
 
 
2.1.4 Melting of small particles 
If the inequality above is satisfied, then any particle of a 
crystal would be coated by a thin layer of liquid if close 
enough to the macroscopic melting temperature. If we take a 
spherical particle of radius r, then the crystal-liquid interface 
between the particle and its surface liquid is analogous to the 
surface of a critical nucleus (CH49). 
 
The critical radius for stability of that nucleus r* is given by (CH50): 
ls ls
V V
2 2
*
Δ Δ Δ
γ γ
r
G S T
   
 
where 
VS
 is the entropy of freezing per unit volume (a negative quantity) and T is the 
supercooling (a positive quantity, 
mΔT T T 
). 
Well below Tm, the crystal is of course stable. The critical radius r* below which the crystal 
hypothetically would melt is much less than the actual particle radius (the crystal is 
“postcritical” and would naturally grow if it could). As the temperature is raised, however, the 
supercooling T decreases, the driving free energy for crystallisation 
VG
 decreases, and 
correspondingly r* increases. 
When r* equals and then exceeds the actual radius of the particle, it is suddenly preferable for 
any liquid coating to grow into the particle: i.e. the particle melts. We predict that this melting 
occurs below the bulk equilibrium melting temperature at a supercooling T given (from 
rearranging the above equation) by: 
*
2
V
ls
rS
T



 
The supercoolingis therefore inversely proportional to the particle radius. Such depressions of 
the melting temperature are measurable and very significant for nanoparticles, as shown in the 
data below for particles of gold. It is evident that common phenomena such as melting can be 
radically altered in the nanoscale regime. Note that for bulk gold, Tm = 1338 K. 
FH19 Course F: Materials under Extreme Conditions FH19 
 
 
 
2.1.5 Suppression of surface melting and attainment of superheating 
If surface melting could be suppressed, then it would be possible to test how much the bulk 
crystal could be superheated above its own melting temperature. This can be achieved by 
arranging that the interior of the crystal is hotter than its surface, for example by focusing 
radiation inside a sample. 
Internal melting was first observed and analysed by 
Tyndall (1858) who noted the appearance of 
“flower-shaped figures” in Alpine ice exposed to 
sunlight. These dendrites of water show the six-fold 
symmetry of the ice within which they form, and can 
take up essentially identical faceted shapes as ice 
crystals. Just as dendritic crystals can only form in a 
liquid with sufficient supercooling, the dendritic 
melting can occur only with sufficient superheating 
(in the example of ice shown this is 0.15 K). 
 
Surface melting can also be suppressed by coating the crystal with a material of higher melting 
point, i.e. by embedding in a solid matrix. Recent experiments have used extreme confinement 
within fullerene shells. The limit to the stability of the crystal appears to be the point at which 
the liquid manages to nucleate within the crystal, either homogeneously, or heterogeneously on 
crystal defects such as dislocations. As nucleation is a kinetic process, its onset can be delayed 
by faster heating (using methods such as shock-wave loading, intense laser irradiation and 
electrical pulse heating) at rates up to 10
12
 K s
-1
. Using these methods, large superheatings can 
be attained. These show that crystal lattices under normal melting conditions are in fact 
internally very stable — it’s just that they have a higher free energy than a neighbouring liquid. 
 
Simple theory
FH20 Course F: Materials under Extreme Conditions FH20 
 
 
The table below shows the maximum temperatures reached by crystalline solids in a range of 
experiments and the corresponding superheats and relative superheats: 
Material Melting temp. 
Tm (K) 
Maximum temp. 
Tmax (K) 
Superheat ΔT 
=Tmax−Tm (K) 
Relative superheat 
ΔT/Tm 
Bulk single crystals 
SiO2 (quartz) 1698 > 2148 > 450 > 0.27 
Embedded nanoparticles and layers 
Ag 
(coated with Au) 
1234 1259 25 0.02 
Sn (in fullerene) 505 > 770 > 265 > 0.52 
Sn (in Sn/Si 
multilayer) 
505 > 720 > 215 > 0.43 
Pb (in Al matrix) 601 673 72 0.12 
Ultra-fast heating (~10
12
 K s
−1
): laser irradiation 
H2O (ice) 273 330 57 0.21 
Al 933 1300 367 0.39 
GaAs 1511 2061 550 0.36 
 
 
 
 
 
 
FH21 Course F: Materials under Extreme Conditions FH21 
 
 
2.2 Mechanical performance at high temperature: Creep 
In many engineering applications, components need to maintain their strength and their shape 
over long times at high temperature. To preserve shape, it might be thought sufficient to ensure 
that the applied stress stays below the (temperature-dependent) yield stress of the component 
material, but it is found that materials do show permanent shape changes at stresses well below 
their yield stress. This is creep, more evident at higher temperatures and longer times. 
2.2.1 Creep: basic characteristics 
Creep is defined as time-dependent permanent deformation (i.e. plastic, not elastic) of a 
material under the action of a stress applied, the magnitude of which is less than the 
macroscopic yield stress 
y
. 
The creep rate depends on: 
 the material 
 the applied stress 
 the temperature: standard creep behaviour is seen at elevated temperatures: 
T > 0.3 
mT
 for pure metals 
T > 0.4 
mT
 for alloys and ceramics 
For macroscopic samples, creep shows three regimes: 
 
The primary and tertiary stages of creep are often quite short. We focus on secondary or 
steady-state creep, in which the strain rate is approximately constant and is given by an 
equation of the form: 
nA
t


 
d
d
 
where 

 is the strain rate, σ is the stress, A is a constant, and n is the stress exponent, which 
reveals two regimes: 
FH22 Course F: Materials under Extreme Conditions FH22 
 
 
Dislocation (power-law) creep is seen at high stress, n ≈ 3−10, and is analysed in terms of 
dislocation motion. 
Diffusion (linear, viscous) creep is seen at low stress, n ≈ 1, and is analysed in terms of atomic 
diffusion. 
 
2.2.2 Dislocation (power-law) creep 
So far we have met dislocation motion in the form of glide on slip planes, which occurs on 
application of an applied stress. Obstacles (precipitate particles, tangles of other dislocations, 
etc.) on the slip plane may block dislocation glide and contribute to the observed yield strength. 
If dislocations could migrate onto a different slip plane they could move past obstacles and in 
this way creep could occur below the yield stress. The key event is this “climb”, but the 
sample’s deformation is due entirely to the subsequent glide. 
 
The process of migration to a different slip plane is climb, a process distinct from glide. Unlike 
glide, climb occurs entirely by the diffusive transport of atoms. 
The process is most readily visualised for edge dislocations, for which the dislocation line is 
effectively the end of an extra half-plane of atoms (although note that screw and mixed 
dislocations do also show climb). Removal of atoms from, or their addition to, the dislocation 
line itself clearly moves the line to a different slip plane. The dislocation line marks the 
location of the dislocation core, which is acting as a source or sink for atoms (which of course 
diffuse by exchanging with vacancies): 
 
FH23 Course F: Materials under Extreme Conditions FH23 
 
 
Either positive or negative climb may assist a dislocation in avoiding obstacles. The climb is 
driven by local forces as the dislocations meet obstacles; these forces on the dislocations have 
components acting perpendicular to the slip plane. 
The climb can be such as to move a limited segment of dislocation line to a different slip plane. 
The climbed segment remains linked to the original dislocation by so-called jogs. 
 
The dominant path for diffusion of atoms to or from the dislocation core is dependent on 
temperature: 
 Bulk diffusion dominates at higher temperatures, when there is enough mobility in the 
bulk lattice around the dislocations for the atoms to join or leave the dislocation core 
via the surrounding lattice. 
 Core diffusion dominates at lower temperatures, when the only significant diffusion is 
along the dislocation cores themselves. 
That atomic diffusion might be 
involved in creep is revealed by the 
close link between the activation 
energies (and therefore the temperature 
dependences) of creep and diffusion. 
In this example, data for bulk lattice 
diffusion are compared with data for 
dislocation creep at high temperature. 
 
 
FH24 Course F: Materials under Extreme Conditions FH24 
 
 
Taking the temperature dependence of the creeprate to derive entirely from that of the relevant 
diffusivity D, we can express the strain rate as: 
exp
 
     
 
n n n Qε Aσ A σ D A σ
RT
 
where A, 
A
 and 
A
 are constants, Q is the activation energy for diffusion and R and T have 
their usual meanings. 
 
2.2.3 Diffusion (linear, viscous) creep 
The diffusion of atoms, when biased in direction by an applied stress, enables grains to change 
shape, for example to elongate in response to tension. 
Again, there are two regimes, dependent on temperature: 
 Nabarro-Herring creep is that seen at higher temperatures when diffusion within the 
bulk lattice is dominant. 
 Coble creep is that seen at lower temperatures when diffusion is predominantly along 
grain boundaries. 
 
The creep strain rate in diffusion creep (for either of the above cases) must depend on the 
average grain diameter d of the polycrystalline material. We can express it as: 
2 2
exp
  
   
 
Dσ B σ Q
ε B
d d RT
 
where B and 
B
 are constants, D is the relevant diffusivity, and Q is its activation energy. 
 
 
FH25 Course F: Materials under Extreme Conditions FH25 
 
 
2.2.4 Summary of creep behaviour: Deformation-mechanism map 
As developed by Ashby, diagrams of stress  (normalised by the shear modulus G) versus 
homologous temperature (
mTT
) are useful in permitting the display of regimes in which 
different deformation mechanisms dominate. This is a simplified map that shows the creep 
mechanisms discussed in this course. 
 
 
2.2.5 Designing creep-resistant alloys 
To minimise creep rates, it would be desirable to have: 
 a high-melting point system (since atomic diffusion relates to homologous temperature 
T/Tm) 
 minimal dislocation motion at elevated temperatures 
 stable precipitates (no coarsening) 
 controlled grain size and grain orientations: 
- grain size: desirable to have large grains 
- grain boundaries (if present): should control orientation & pin them to prevent 
sliding. 
 
FH26 Course F: Materials under Extreme Conditions FH26 
 
 
2.3 Superalloys for jet engines 
2.3.1 Efficiency of an engine: the need for high temperatures 
The performance of a heat engine can be measured in terms of a thermodynamic cycle of its 
operating gas. The best known is the idealised Carnot cycle. This consists of two isothermal 
(constant temperature) stages and two adiabatic stages (in which the entropy is constant, as no 
heat is exchanged with the surroundings). 
There are two heat reservoirs, hot (T = TH) from which heat is extracted, and cold (T = TC) into 
which waste heat is lost. 
 Stage 1: isothermal expansion of the gas at TH, with heat flowing in from the hot 
reservoir 
 Stage 2: adiabatic expansion of the gas, during which it cools to TC 
 Stage 3: isothermal compression at TC, with heat flowing out to the cold reservoir 
 Stage 4: adiabatic compression of the gas, during which it heats back to TH. 
 
This is a cycle in pressure and volume of the gas, but it is most readily analysed on the T−S 
diagram. 
Bearing in mind that 
STq dδ 
, the total heat absorbed in stage 1 must be 
 ABH SST 
, while 
the heat lost in stage 3 is 
 ABC SST 
. 
The difference between these two quantities would appear to increase the internal energy of the 
system with every clockwise cycle, but the system in fact returns to the same internal energy 
because of the work done, which is therefore 
  ABCH SSTT 
. 
The efficiency is 
  
  H
C
ABH
ABCH 1
inputheat total
donework 
T
T
SST
SSTT




 
 
FH27 Course F: Materials under Extreme Conditions FH27 
 
 
The cycle for a gas turbine looks a little different, but ideally, there are still four stages: 
 Stage 1: Adiabatic compression of fresh air on entering the engine (S = constant) 
 Stage 2: Heating in the combustion chambers (P = constant) 
 Stage 3: Adiabatic expansion, with the turbine extracting work (S = constant) 
 Stage 4: Dissipation of hot gases (P = constant). 
 
 
2.3.2 The materials challenge 
A schematic diagram of a jet engine is shown below. 
 
(from Wikimedia commons) 
The blades at the hot end of an aeroengine operate under very challenging conditions, requiring 
strength, creep resistance, toughness and oxidation resistance. 
 The temperature of the blade material may exceed 75% of its melting temperature. 
 At 10,000 revolutions per minute, the blade tip velocity is 330 m s-1 (1200 km/h). The 
stresses are largely centrifugal and are nearly 200 MPa at the root of the blade. 
 A typical lifetime is 3 years of use, equating to 5 million miles (200 Earth 
circumferences). 
FH28 Course F: Materials under Extreme Conditions FH28 
 
 
 The complete disc of ~100 blades extracts energy from the hot gas at a rate (power) of 
about 50 MW, i.e. each blade extracts ~500 kW, enough for >1000 homes at the 
average rate of household consumption (400 W). 
The graph below shows that the turbine entry temperature (TET) has risen dramatically over 
the years, by more than 700 K, using Rolls-Royce civil aeroengines as examples. 
 
Since the introduction of superalloys in the 1940s, the 
temperature at which turbine blade materials can operate 
(i.e. when they have adequate creep resistance) has risen 
by more than 300 K, but there has been a strong incentive 
to push operating temperatures even higher. 
In modern engines the TET exceeds (by > 400 K) the 
temperature at which the superalloy would have adequate 
creep resistance. The blades are kept cooler than the 
surrounding gas by passing cold air through them from 
the inside. This requires the casting of blades with 
complex internal channels, as shown on the right. 
Additionally, the blades are coated with a thin layer of a 
ceramic with a low thermal conductivity (a thermal 
barrier coating – see section 2.4). 
 
Obviously, these measures increase manufacturing costs. The need for materials with 
dramatically better temperature capabilities is very clear, but the search for such materials has 
proved very difficult. 
FH29 Course F: Materials under Extreme Conditions FH29 
 
 
2.3.3 Possible materials 
Blades in an aeroengine need to be tough. With present technologies, ceramics are not 
sufficiently tough throughout the temperature range from start-up to operation, so for high-
temperature blades, metallic alloys are the only option. 
We have already seen that all types of creep are related to atomic diffusion, and in general 
terms, the rates of diffusion and creep at a given temperature are lowered by choosing a 
material of higher melting temperature Tm. The present materials of choice for high-
temperature aeroengine blades are alloys based on nickel (Tm = 1728 K). 
However, there are metals with much higher melting points, so why are they not used? 
Potential problems include: 
(i) Polymorphism: Blades cycle through wide temperature ranges and repeated 
changes of phase (e.g. bcc ↔ ccp in iron) would not be acceptable. 
(ii) Intrinsic diffusivity: Typical atomic diffusivities at a given homologous 
temperature vary with crystal structure. Of the simple metallic structures, the 
diffusivity at Tm is in the sequence ccp < hcp < bcc. Thus ccp metals are favoured. 
(iii) Brittleness: Some metals are intrinsically too brittle. 
(iv) High density: It is never desirable to increase the weightof aeroengine components, 
but it is especially bad to use a high-density material in rotating parts as centrifugal 
forces are thereby increased, making creep more difficult to resist. 
(v) Poor oxidation resistance is a problem for several metals. 
(vi) Cost: Even for a high-technology product such as a turbine blade, the cost of the 
main constituent metal may be an issue. 
Two metals that, because of high Tm values, might be considered attractive for high-
temperature use are tungsten (Tm = 3660 K) and tantalum (Tm = 3253 K). They do not show 
polymorphism, but their structure is bcc, giving relatively high diffusion rates (at a given 
homologous temperature), and that they also suffer from every other problem in the above list. 
Nickel is ccp and this phase is very stable in the presence of alloying additions. It has no 
serious problem with any of the items in the above list, and is the base metal of choice. 
 
 
FH30 Course F: Materials under Extreme Conditions FH30 
 
 
2.3.4 Nickel-based superalloys 
2.3.4.1 Composition and microstructure 
With many decades of development, rather complex compositions have evolved, designed to 
improve strength, creep resistance, oxidation resistance, etc. As an example, one of the first 
generation of alloys designed for use in single-crystal blades (see section 2.3.4.2) was 
PWA1480, which consists of nickel as the base metal, plus the following alloying additions (in 
weight %): 
 10.0 Cr 5.0 Co 4.0 W 5.0 Al 1.5 Ti 12.0 Ta 
 
Nickel-based superalloys essentially consist of a dense 
dispersion of precipitates (often faceted) in a matrix, the 
so-called 
γ-γ 
 (gamma/gamma prime) microstructure, 
as shown on the right. 
Gamma: the nickel-based ccp solid solution. 
Gamma prime: is a closely related phase based on an 
ordering of solute-atom sites. The archetype is Ni3Al. 
The 
AlNi3
 structure has the Al atoms not randomly occupying Ni-atom sites (as would be true 
in a ccp solid solution), but instead located only at the corners of the unit cell: 
The  unit cell: The 
γ
 unit cell: 
 
 cubic F lattice, ccp structure 
 1 atom per lattice point 
 On average, each lattice site has the 
overall alloy composition. 
 Cubic P lattice 
 4 atoms (3 Ni + 1 Al) per lattice point 
 The structure is fully ordered. There 
are no Al-Al nearest neighbours. 
 
2 m 
FH31 Course F: Materials under Extreme Conditions FH31 
 
 
In real superalloys, the Al sites are occupied also by Ti and Ta atoms, so 
γ
 can be represented 
as 
 Ta Ti, Al,Ni3
. The solute atoms partition between the  and 
γ
 phases, mildly affecting the 
lattice parameter of each. It is possible for the lattice parameters of the  and 
γ
 phases to 
match very closely, in which case the 
γ-γ 
 interface can be fully coherent (CH55). This is 
highly desirable, as fully coherent interfaces have very low interfacial energy, and therefore 
provide very low driving force for the detrimental coarsening of precipitates. 
2.3.4.2 Single-crystal blades 
Analysis of creep (FH21−FH25) shows that grain boundaries can contribute to atomic 
diffusion, and their presence also degrades creep resistance in other ways. The detrimental 
influence of grain boundaries on creep life is minimised when they are parallel to the main 
tensile stress (i.e. parallel to the length of the blade). Directional solidification can give blades 
with grain boundaries aligned in this way. It is then a short step to control the solidification a 
little more and to make single-crystal blades: 
In this picture, solidification starts from the bottom, where 
many grains are formed, and proceeds through the liquid-
filled mould towards the top. 
Growth of the solid through the helical path (pig-tail grain 
selector) leads to just one grain growing into the main blade 
cavity. This grain is oriented with the 
100
 preferred growth 
direction parallel to the blade length. 
The single-crystal nature of the blades is checked on the 
production line by back-reflection X-ray photography. 
 
 
 
FH32 Course F: Materials under Extreme Conditions FH32 
 
 
2.3.4.3 Order hardening 
As noted above in section 2.3.4.1, superalloy compositions are selected so that the 
γ-γ 
 
interface is fully coherent. While this is desirable (in inhibiting coarsening), it means that the 
interfaces themselves offer no extra resistance to the passage of dislocations. However, the 
γ
 
precipitates do have a strong hardening effect, so the hardening effect in superalloys is of 
particular interest to analyse. 
The Burgers vector of a dislocation must be a lattice vector, and is generally the shortest 
possible. 
In the ccp  phase the slip systems are of the type 
2
a  111011
. 
However, in the 
γ
 
AlNi3
 structure vectors of the type 
2
a 011
 are no longer lattice vectors. 
If a dislocation with such a Burgers vector were to glide 
through the 
γ
 phase, it would move Al atoms to Ni-
atom sites and some Ni atoms to Al-atom sites, and 
create some Al-Al nearest neighbours (which are 
forbidden in the ordered 
γ
 structure). 
The slip plane would be a boundary between two 
γ
 
structures that are out of step with each other. This is an 
anti-phase boundary (APB), shown schematically here. 
In Ni3Al, APBs have rather high energies of ~ 0.1 J m
-2
. 
In 
γ
, the shortest lattice vectors are 
100a
, but the phase in fact deforms as compatibly as 
possible with the deformation of , according to the slip systems 
 111011a
. In this way, the 
same dislocations mediate the deformation of both phases. 
 phase: 
γ
 phase: 
 
b = 
2
a  011
 b = 
 011a
 
FH33 Course F: Materials under Extreme Conditions FH33 
 
 
A dislocation with a b = 
2
a 011
 entering a 
γ
 
precipitate must create an APB. 
In consequence, it feels a strong resistance (drag). 
The passage of a second dislocation with the same 
Burgers vector restores the undefected 
γ
 structure 
(i.e. removes the APB). 
Accordingly the dislocations move in pairs, the first 
meeting great resistance, and the second not, giving 
rather characteristic shapes of the dislocation lines 
as shown here. 
The pair of dislocations has an effective Burgers vector 
011a
 and constitutes a perfect 
dislocation for 
γ
. This is called a superdislocation; each individual dislocation is a 
superpartial. As the pair of dislocations moves through 
γ
, the APB exists only on the ribbon 
of slip plane between them. 
The energy dissipation and associated dislocation drag from creating APBs gives order 
hardening, and this is by far the dominant contribution to hardening in superalloys. 
 
 
 
FH34 Course F: Materials under Extreme Conditions FH34 
 
 
2.4 Thermal barrier coatings 
Despite the increased hardness and creep-resistance of nickel-based superalloys, turbine blades 
require additional protection from the high temperatures, because (as mentioned in section 
2.3.2), the temperatures inside jet engines exceed the temperature at which the superalloy 
would have sufficient creep resistance, by several hundred Kelvin. Cold air is passed through 
internal channels within the blade, and they are additionally protected from the high 
temperatures by thermal barrier coatings. 
The main requirements for a thermal barrier coating are: 
 a low thermal conductivity a high melting point and maximum service temperature 
 adequate strength 
The main component in a thermal barrier coating is a layer of the ceramic zirconia, ZrO2 (in the 
form of yttria-stabilised zirconia). 
As seen in the materials selection maps below, the technical ceramics are the materials with the 
best combination of strength and maximum service temperature, and of these, the material with 
by far the lowest thermal conductivity is zirconia. 
 
Selection map showing yield strength against maximum service temperature. 
Technical ceramics are in the top right corner. 
ZrO2
FH35 Course F: Materials under Extreme Conditions FH35 
 
 
 
Selection map showing thermal conductivity against thermal diffusivity. 
Most technical ceramics are in the top right corner, but zirconia is significantly lower. 
However, in order to make a good thermal barrier coating, the ceramic needs to adhere well to 
the turbine blade. The blade surface must therefore first be coated with a thin bond coat, which 
is an alloy of Ni-Cr-Al-Y and essentially acts as a glue between the blade and ceramic coating. 
One potential problem is that oxygen diffuses readily through YSZ (see BH48), which would 
make the superalloy liable to undergo oxidation. To overcome this problem, a thin dense layer 
of alumina (which has a low oxygen mobility) is added between the bond coat and the zirconia. 
Another potential problem is that zirconia has a lower coefficient of thermal expansion than the 
nickel-based superalloy from which the blades are manufactured, which would induce thermal 
stresses and cause cracking of the zirconia on heating and cooling. To overcome this, the 
ceramic layer is grown such that it has a columnar structure perpendicular to the surface of the 
blade. When the blade heats and expands, the columns are able to separate very slightly, but 
not enough for a significant amount of hot gas to penetrate to the surface of the blade. 
ZrO2
FH36 Course F: Materials under Extreme Conditions FH36 
 
 
 
(From http://www.bren.ucsb.edu/facilities/MEIAF/images.html) 
Thermal barrier coatings therefore have a relatively complex 4-layer structure, as illustrated 
schematically below. 
 
(adapted from J. Mater. Chem., 2011, 21, 1447-1456) 
 
 
YSZ layer (250–500 μm)
Dense alumina layer (3–10 μm)
Bond coat (75–150 μm)
Nickel-based superalloy
FH37 Course F: Materials under Extreme Conditions FH37 
 
 
2.5 Ice 
Ice covers a significant fraction of the Earth’s surface and plays a role in regulating climate. 
Very unusually for materials under normal conditions, ice is always at a temperature close to 
its melting point. 
Ice also has the unique feature that it remains profoundly brittle right up to its melting 
temperature, a property that can be explained in terms of its structure. Other materials that we 
think of as brittle, such as ceramics, are all a long way from their melting point: when these 
materials approach their melting point, they become ductile, but this is not the case for ice. 
 
2.5.1 Structure, bonding and proton disorder 
The H2O molecule has a bond angle close to the tetrahedral 
angle of 109.47°. Hydrogen bonding to other water 
molecules is in a tetrahedral format, with each oxygen 
covalently bonded to two hydrogens in the same molecule 
and hydrogen-bonded to two further hydrogens in 
neighbouring molecules. 
 
The most common crystal structure of ice is Ih, 
which is stable under ambient conditions. 
This is a tetrahedrally linked framework of 
hexagonal symmetry, the arrangement of 
oxygens being equivalent to that of the Zn and S 
atoms in wurtzite (BH28). The water molecules 
remain intact, but at a given tetrahedral centre 
(i.e. O) there are up to six possible orientations 
of the molecule: 
 
 
The neighbouring orientations are related because the ice rules must be obeyed: 
 there must be two hydrogens adjacent to each oxygen 
 there is only one hydrogen per bond. 
hydrogen
bonds
FH38 Course F: Materials under Extreme Conditions FH38 
 
 
Even with these constraints, the positions of the hydrogens are not determined throughout the 
structure. The limited degree of disorder (proton disorder) has a profound effect on the 
properties of ice Ih. 
Ice exhibits a number of phases, as illustrated in the pressure-temperature phase diagram 
below. All phases have a network of tetrahedrally coordinated oxygen atoms, sometimes with 
and sometimes without proton disorder. In high-pressure phases, the H atom may become 
equidistant from both O neighbours, blurring the distinction between water molecules. 
Tetrahedral coordination gives low packing densities. The highest pressure phases increase 
their density while keeping the 4-fold coordination by means of two interpenetrating networks. 
 
2.5.2 Mechanical properties 
As previously mentioned, ice is brittle all the way up to its melting point (at normal strain 
rates). This behaviour arises because of the proton disorder described above. 
This diagram shows a layer of the ice Ih 
structure projected on to the (100) plane. The 
proton disorder disrupts the translational 
symmetry and greatly impedes dislocation 
motion. 
 
 
[001]
[010]
FH39 Course F: Materials under Extreme Conditions FH39 
 
 
However, because temperatures are typically so 
close to the melting point, it is possible for ice to 
undergo creep (usually power-law creep). 
Large ice masses deform under their own weight, 
resulting in phenomena such as glacier flow, which 
has significantly shaped the Earth’s land surface. 
 
 
 
2.5.3 Surface melting 
As noted earlier (in section 2.1.3), crystals can show some degree of surface melting even 
below the macroscopic melting temperature. We nearly always encounter ice in the extreme 
condition close to its melting point there is significant melting of the surface layers. Computer 
simulations have shown that this starts at about −33°C: the liquid-like layer is 12 nm thick at 
−24°C and 70 nm at −0.7°C. 
This surface melting can account for: 
 the low coefficient of friction of ice (exploited, for example in skating) 
 the high adhesion of ice surfaces 
 the ease of compaction of ice (compared to a normal powder). 
When two ice surfaces touch (for example two ice cubes), the liquid-like layer between them 
solidifies. 
 
2.5.4 Regelation 
The ice Ih to liquid phase boundary (unusually) has a negative slope, which can be explained 
using the Clausius-Clapeyron equation: 
d Δ
d Δ

P S
T V
 
Since ice is less dense than water, ΔV is negative for melting, whereas ΔS is positive (as usual). 
Therefore, as pressure increases, the melting point of the ice decreases. 
 
FH40 Course F: Materials under Extreme Conditions FH40 
 
 
 
This effect is exploited in the phenomenon of regelation, in which a material melts under 
pressure but refreezes when the pressure is reduced. It can only occur in materials whose 
densities decrease when they melt (if the density increases, the slope of the phase boundary is 
positive, meaning that the melting point increases as pressure increases). 
Regelation can be clearly demonstrated in an experiment in which weights are hung from a thin 
wire looped over a cylinder of ice. The pressure exerted by the wire lowers the melting point of 
the ice, causing it to melt and the wire to pass through the ice. The ice abovethe wire then 
refreezes once the pressure is removed and eventually, the wire will have passed the whole way 
through the ice cylinder, leaving it intact. 
(Note that it is actually slightly more complicated than this because the wire will absorb heat 
from the room and conduct it through the wire, which also contributes to the melting of the ice) 
Apart from creep, regelation is another factor that contributes to the movement of glaciers. 
They can undergo basal sliding, in which the movement of a glacier is lubricated by the 
presence of liquid water created by the high pressure exerted by the weight of the glacier above 
it. 
 
 
FH41 Course F: Materials under Extreme Conditions FH41 
 
 
3. Radiation Damage 
3.1 Introduction 
Radiation damage refers to microscopic defects produced in materials due to irradiation, and 
results in changes to their physical, chemical and mechanical properties. Of course, many types 
of radiation are possible (using ion accelerators, for example), but here we will focus on 
neutrons. Nuclear fission produces fast neutrons with energies of approximately 1 MeV. In 
fusion, neutrons with energies as high as 14 MeV are produced. 
The main components of a fission reactor are: 
 The fuel (usually uranium or uranium dioxide), which absorbs neutrons and undergoes 
fission, in which the nucleus splits into two smaller nuclei but also releases neutrons to 
keep the chain reaction going. 
 The cladding (usually austenitic stainless steel, or a zirconium alloy), which surrounds 
the fuel, protecting it from corrosion and giving it structural integrity. 
 Control rods, which absorb neutrons and can be raised or lowered to control the chain 
reaction (or lowered completely in an emergency to stop the reaction). 
 The coolant, which removes heat generated during fission and is used to produce steam 
to drive turbines for electricity generation. 
There are many types of nuclear fission reactor, but the most common type is the Pressurised 
Water Reactor (PWR). 
 
Schematic of a Pressurised water reactor (from Wikimedia Commons) 
 
FH42 Course F: Materials under Extreme Conditions FH42 
 
 
3.2 The displacement cascade 
Radiation damage in crystals has been widely studied because of its importance in structural 
components in and near the cores of nuclear reactors. 
The damage follows the sequence: 
1. An energetic incident particle (such as a fast neutron) strikes an atom in the crystal 
2. The transfer of kinetic energy to the atom is large enough to displace it from its position 
in the lattice and it becomes a primary knock-on atom, or PKA, leaving behind a 
vacant site 
3. The PKA moves through the lattice, creating further knock-on atoms in a displacement 
cascade; the mean free path between displacement collisions depends on the energy of 
the knock-on atoms, but is typically in the range 1 nm to 1 m 
4. The PKA and other knock-on atoms eventually come to rest as interstitial atoms 
Each knock-on event produces a pair of defects: a vacancy and an interstitial (a Frenkel pair). 
The above sequence of events occurs extremely quickly: in about 10
-11
 s. In the following 
10
-9
 s, things settle down, with some recombination of vacancies and interstitials occurring, but 
the extent of this (energetically desirable) recombination is limited because the vacancies and 
interstitials diffuse away from each other. 
The initial mean free path between collisions is of the order of 1 cm for fast neutrons but 
decreases as energy is dissipated in successive collisions; the result is that displacement 
cascades are concentrated in volumes 1 to 10 nm in diameter. 
 
A displacement cascade is illustrated 
schematically in this image. There is 
a high density of vacancies in the 
core, with the surrounding material 
rich in interstitials. 
 
 
FH43 Course F: Materials under Extreme Conditions FH43 
 
 
 
This atomistic simulation of copper 
illustrates the effect of an incident 
neutron of very high energy (e.g. 
from a fusion reactor). The 
displacement cascade is spread out 
and can be interpreted as a 
branching series of subcascades. 
 
 
 grey: vacant lattice sites 
 black: displaced atoms 
 
 
 
3.3 Damage rates 
The displacement energy, Ed, is the minimum energy that must be transferred to a lattice atom 
in order for it to be displaced from its lattice site (typically about 25 eV). If the energy 
transferred by a knock-on atom to the struck lattice atom is less than the displacement energy, 
the lattice atom will not be dislodged from its lattice site. It will instead vibrate around an 
equilibrium position and the energy will be dissipated as heat. 
We begin with an example calculation to estimate how many atoms are involved in a 
displacement cascade. On collision, the maximum energy transferable from a neutron of energy 
En to a nucleus of atomic mass number A is ζEn, and the average energy transferred is ζEn/2, 
where: 
 
2
4
1
A
ζ
A


 
For a neutron hitting an 
56
Fe nucleus, ζ = 0.069. Taking the neutron to have an energy of 
1 MeV, the average energy transferred to an iron atom (the expected energy of the PKA, Ep) 
would be Ep = 3.45  10
4 
eV. 
The average number of atoms displaced per PKA is Ep/2Ed, where Ed is the energy required to 
displace an atom from its lattice site. For -Fe, Ed ≈ 40 eV, so that the number of displaced 
atoms is 431. 
The accumulated damage in irradiated material can be characterised as the average number of 
displacements per atom (dpa). The rate of damage of course depends on the incident neutron 
FH44 Course F: Materials under Extreme Conditions FH44 
 
 
flux, and also on the relevant collision cross-sections (which describe the probability of 
different nuclear reactions occurring). Typical damage rates (measured as displacements per 
atom per second, dpa s
-1
) range from 10
-9
 dpa s
-1
 in thermal reactors to 10
-5
 dpa s
-1
 in the first 
wall of proposed fusion reactors. 
Over the lifetime of a component in a nuclear fission reactor, each atom could be displaced as 
many as 100 times. Clearly such extreme conditions can have profound effects on the 
microstructure of the alloys involved. These effects include dissolution of precipitates, changes 
in their morphology, and appearance of non-equilibrium phases. Here, we will focus on the 
effects on the main crystal lattice. 
 
3.4 Principal types of damage 
We have seen that each PKA generates excess populations of vacancies and interstitials in the 
displacement cascade. In principle, the vacancies and interstitials might recombine directly to 
restore the equilibrium structure, but they are too widely separated. Interstitial atoms have 
higher excess energies than vacancies and they are also more mobile. They quickly disappear 
at dislocations and grain boundaries acting as sinks. Dislocations act as sinks for interstitials 
through the process of negative climb (FH22), without any need for vacancy migration. As a 
result displacement cascades are left with an excess of vacancies. 
The effects on the structure of the irradiated solid depend on temperature, with dislocation 
loops forming at lower temperatures, and voids forming at higher temperatures. 
3.4.1 Dislocation loops 
Dislocation loops can form at lower temperatures (T < 0.2 Tm, where Tm is the absolute melting 
temperature of the irradiated alloy). In a face-centred cubic metal (for example the austeniticstainless steel cladding of fuel rods), interstitial atoms can condense as monolayer discs 
between the close-packed {111} planes of the crystal, forming an interstitial loop. Vacancies 
likewise can condense as discs between {111} planes, forming a vacancy loop, and the lattice 
above and below the vacancy disc closes in. Both types of dislocation loop disrupt the 
ABCABC stacking sequence of the close-packed planes, resulting in a stacking fault. 
 
 
Interstitial loop Vacancy loop 
FH45 Course F: Materials under Extreme Conditions FH45 
 
 
In these dislocation loops, the Burgers vector is normal to the planes and of magnitude equal to 
the interplanar spacing (± a/3<111>). The dislocation is sessile (unable to glide). 
The formation of vacancy-type and interstitial-type loops under irradiation gives an increase in 
dislocation density, analogous to that obtained on cold-working. However, as irradiation 
continues, a steady-state dislocation density is reached when the rate of damage equals the rate 
at which defects are annealed out (due to local heating of the material). The steady-state 
dislocation density depends on damage rate and temperature. 
Typical dislocation densities in austenitic stainless steels: 
 Annealed: 1012 m-2 
 Cold-worked: 1015 to 1016 m-2 
 Irradiated: (6 ± 3)  1014 m-2 (at steady state) 
This figure shows dislocation density 
as a function of irradiation dose in 
annealed and cold-worked austenitic 
stainless steels, irradiated at 500°C. 
The irradiation drives the dislocation 
density to the same steady-state value, 
independent of the starting value. A 
cold-worked material can actually 
show a decrease in dislocation density 
on irradiation. 
3.4.2 Voids 
Irradiation at higher temperatures (T > 0.2 Tm), leads to cavities or voids. Once voids are 
nucleated they grow easily; the interstitials formed in displacement cascades are absorbed 
mainly at dislocations and the vacancies mainly join the voids. Void nucleation and growth 
under irradiation have the feature, not often encountered in metallurgical precipitation, that the 
precipitating species (vacancies) are under continual production; without this, voids already 
produced would largely disappear on annealing. 
The formation of voids leads to swelling, which is the most studied type of radiation damage. 
In austenitic stainless steels, the steady-state swelling rate is ~1% per dpa. The maximum 
reported swelling under neutron irradiation is 88% (i.e. almost doubling the volume). 
FH46 Course F: Materials under Extreme Conditions FH46 
 
 
 
These images show void swelling at different 
temperatures in an austenitic stainless steel at 
~1.41027 neutrons/m2, equivalent to ~70 dpa. 
In each case, the total volume of the voids is 
approximately the same. However, at low 
temperatures, many small voids are seen, 
whereas at high temperatures, fewer larger 
voids are seen. This arises due to a balance of 
nucleation and growth (as seen in course C). 
 
From the first observations of void formation in 1967, it was recognised that this is a 
particularly important form of radiation damage, leading to swelling and distortion of irradiated 
components. It can cause hardening of irradiated alloys and associated embrittlement and loss 
of ductility. The development of voids on grain boundaries shortens creep life. 
This image shows swelling (~10% linear, 33% 
by volume) of a stainless steel cladding tube 
irradiated at 1.5×10
27
 neutrons/m
2
, equivalent 
to ~75 dpa, at 510°C. Note that all relative 
proportions are preserved during swelling. 
 
 
3.4.3 Structural changes on irradiation 
We have seen that in typical structural alloys, there are major microstructural effects of 
irradiation, but the crystal lattice itself is rather stable, continual repair processes counteracting 
damage rates. In contrast, some minerals containing radioactive U or Th, are amorphised by the 
internal bombardment resulting from  decay processes. These metamict glassy minerals can 
show faceted forms inherited from their crystalline precursors, and may crystallise on heating. 
Whether damage or repair processes dominate is largely dependent on damage rate and 
temperature. 
FH47 Course F: Materials under Extreme Conditions FH47 
 
 
4. Life under extreme conditions 
4.1 Extremophiles 
Extremophiles are organisms that have adapted to be able to survive (and in fact thrive) in 
physically or chemically extreme conditions that would be detrimental to most life on Earth. 
Many extremophiles are simple single-cell organisms, but others are much more complex. For 
example, in course E, you learnt about several extremophiles: 
 plants that can survive extremely dry conditions (by forming glasses rather than mineral 
crystals – EH49) 
 fish that can survive very cold conditions because their blood plasma contains 
antifreeze proteins (EH50) 
 frogs that can survive cold conditions because ice nucleating agents promote the 
formation of ice outside their cells rather than inside (EH50-51). 
There are many classes of extremophiles including: 
 Acidophiles are adapted to life at pH 3 or below 
 Alkaliphiles are adapted to life at pH 9 or above 
 Thermophiles thrive at temperatures between 45°C and 122°C 
 Psychrophiles survive at temperatures of -15°C or lower for long periods 
 Halophiles require high concentrations of salt (> 0.2 M) for growth 
 Piezophiles are adapted to life at high pressures (such as underground or deep in the 
ocean) 
 Xerophiles can grow in extremely dry conditions 
 Radioresistant extremophiles are resistant to high levels of ionising radiation (UV or 
nuclear radiation) 
Many extremophiles fall under more than one category and are termed polyextremophiles. For 
example, there are worms and shrimps that live in or near deep ocean thermal vents (where 
there are high temperatures, high pressures and extreme pH), and many types of bacteria thrive 
in geothermal areas and hot springs (where there are high temperatures and very low pH). 
 
 
FH48 Course F: Materials under Extreme Conditions FH48 
 
 
4.2 Tardigrades 
Perhaps the most impressive example of a polyextremophile is the Tardigrade (from the Italian 
“Tardigrada”, meaning “slow stepper”), otherwise known as the waterbear (from their original 
German name “kleiner Wasserbär”). 
Tardigrades can reversibly suspend their metabolism, dehydrate and go into a state of 
crytobiosis which makes them able to survive: 
 Temperatures from just above absolute zero, to well above the boiling point of water 
 Pressures as low as the vacuum of outer space (hey are the first known animal to 
survive in outer space) and six times higher than those found in the deepest ocean 
trenches 
 Ionising radiation at doses hundreds of times higher than the lethal does for a human 
 Going without food or water for more than 10 years 
 Drying out to the point where they contain less than 3% water 
Tardigrades have 8 legs and are typically about 0.5 mm long. There are over 1000 different 
species, and they are found all over the world, from the Himalayas to the deep sea, and from 
the polar regions to the equator). 
 
(from Wikipedia commons) 
 
(From www.nps.gov) 
 
 
FH49 Course F: Materials under Extreme Conditions FH49 
 
 
4.3 Applications of extremophiles 
4.3.1 Hydrogen peroxide removal: Thermus brockianus 
Hydrogen peroxide is used in industrial