Part IB
AP1
DIFFUSION: HEAT FLOW ANALOGUE
1. Introduction
The diffusion of heat and of mass can be treated in a similar fashion by solving the
diffusion equation with appropriate boundary conditions. For one dimensional heat flow
the diffusion equation becomes
T   T 


t x  x 
where is the thermal diffusivity and T(x,t) is the temperature at time t at a distance x from a
suitable origin. The object of this experiment is to determine the thermal diffusivity  of each
of the three strips (X,Y and Z), given that the appropriate solution for the diffusion equation for
the temperature T(x,t) at a distance x from a heat source after a time is given by:


T x,t   A  B erf x / 2 t 
x
where A and B are constants and erf (x) is defined as
2

√ 
e-u2 du
0
2. Experimental Procedure
steel
weight
insulating
b oard
NB These
become hot!
temp erature
-sensitive
b and s
hot
p late
black line (aligned with
edge of heating element)
metal
strip
Experimental arrangement for study of diffusional heat flow
a) Ensure heater controller is set to position 2 and has been on for at least 30 minutes.
b) While strip is cold, measure the distances of each of the temperature indicating bands from
the black line on the strip indicating the end of the heating element.
c) Set timer to zero.
d) Using the insulating gloves or the tongs to raise a corner of the insulating sheet, place metal
strip X between the hot-plate and the weighted insulating sheet so that the black line on the
strip is aligned with the edge of the heating element.
e) Immediately start the timer.
f) Observe the liquid crystal temperature-indicating bands and record the times as the
temperatures are reached and the colours change:
either from yellow to orange (for a temperature of 50 ˚C)
or
from red to black (for the remaining temperatures).
g) Estimate the temperature of the heating element using a thermocouple, keeping the metal
strip in position.
h) Using the insulating gloves or the tongs if required, remove the metal strip from the hotplate and place on the metal sheet provided (not on the bench).
Part IB
AP1/2
i) Carry out the analysis outlined in §3.
j) Repeat the operation for both strips Y and Z.
3. Analysis of Data
i) Plot a graph of distance versus √ time for each of the five temperatures on the liquid crystal
temperature-indicating bands. Both axes on the graph should begin at zero.
ii) By using suitable boundary conditions, derive expressions in terms of temperature for the
constants A and B in the equation provided. Note that erf (0) = 0 and erf () = l.
iii) Using the values of the constants obtained, determine the thermal diffusivity of the material
from each of the gradients of the lines plotted. Values of the error function are given in the
Data Book. Would you expect, and do you see, a systematic variation in ?
4. Discussion
The metallographic mounts (X, Y and Z) are of polished sections of the strips prior to rolling.
Examine the sections and discuss whether the relative values of thermal diffusivity can be
explained in terms of the observed microstructures.
Explain briefly whether or not values of
i)
diffusion coefficient and
ii) electrical conductivity
for the three materials would be expected to follow a similar pattern to the values of thermal
diffusivity.
For strip X describe and account for the colours observed in the section which had been heated.
HDB/IB/00
Part IB
AP2
SOLIDIFICATION AND FABRICATION
1. Introduction
This practical has two purposes - the direct observation of solidification phenomena
and an introduction to some of the casting techniques in industrial use.
When a liquid metal or alloy is poured into a mould and allowed to solidify undisturbed,
the grain structure of the resulting ingot usually consists of zones containing chill,
columnar or equiaxed grains. The relative proportion of these zones varies with the
cooling rate and the composition of the alloy. The first experiment is a study of how
these zones develop, using a transparent model-system. The phenomenon observed
is precipitation from a supersaturated solution, rather than a conventional solidification
process, but many of the features of the grain structure are similar in the two situations.
The microstructure of cast metal is profoundly affected by the morphology of the
liquid/solid interface. In many cases, this is dendritic. The shape and size of individual
dendrites, and the extent of the mushy zone composed of dendrites and surrounding
liquid, is dependent on the atomic structure of the interface, solute redistribution and
heat flow. The second experiment involves the study of various interfacial structures,
again using transparent model-systems. Two materials will be studied. In one of these
the entropy of fusion is relatively low, as in most metallic systems, giving rise to an
interface which is rough on an atomic scale and hence to dendrites that are rounded.
In the other, the entropy of fusion is higher, as in many non-metallic systems, leading to
atomically smooth interfaces, a tendency for certain crystallographic planes to be
preferentially exposed and hence the formation of dendrites with facets.
In the last part of the practical, there will be an opportunity to look at castings produced
using a variety of techniques. Details of the microstructure, surface finish and defects
such as porosity and macrosegregation may be correlated with the solidification
conditions during casting. The techniques to be described include sand casting,
gravity die casting, pressure die casting, squeeze casting, investment casting and
centrifugal casting. One objective is to identify the constraints imposed by each
technique in terms of shape complexity, size, wall thickness, soundness, surface finish
and cost.
2. Observation of Grain Structure Development
(a) SAFETY GLASSES MUST BE WORN WHEN USING LIQUID NITROGEN.
(b) DO NOT TOUCH ANY OBJECT THAT HAS BEEN COOLED IN LIQUID NITROGEN
Three brass moulds with transparent sides are cooled by pouring liquid nitrogen into
the dish in which the mould stands, but not into the mould itself. When frost has
formed on the mould, clear the outside of the perspex window facing you by spraying
with alcohol from a wash bottle, but do not get alcohol into the mould. Illuminate the
mould from behind in order to see the structures being formed.
Part IB
AP2/2
Make up a saturated solution of ammonium chloride in a beaker by stirring in the
crystals at 60˚C on a hot-plate. Continue until dissolution stops. Pour some of this
solution into a cooled mould. Observe that many fine crystals are formed during initial
contact with the mould wall (“big bang” nucleation) and that these become redistributed
throughout the liquid. This often occurs during the casting of metals. Those in the bulk
of the liquid may quickly remelt, depending on the pouring superheat. This is desirable
since they may grow and block the feed of liquid metal needed to compensate for the
freezing contraction. In the present experiment, such remelting is difficult because of
the lower thermal conductivity of non-metallic systems. Depending on whether the
solution was fully saturated, you may observe that many of the “big bang” crystallites
survive and grow to form equiaxed grains. In any event, those which remained
adjacent to the mould walls after pouring stay unmelted and form the chill zone.
The remelting of the “big bang” crystallites is promoted by a high pouring superheat.
This can be simulated by heating the saturated solution from 60˚C to 90˚C before
pouring into the mould. You should then see the liquid clear quickly after pouring, as
most of the precipitates are taken back into solution. The development of the
columnar zone should then be clearly visible. In some cases, this will extend across
the complete section of the casting. In practice, it might be arrested by the
development of an equiaxed zone as a result of solid fragments surviving ahead of the
advancing columnar grains. A common source of solid fragments to form the equiaxed
zone is the free surface, where crystallisation is stimulated by heat loss. These surface
crystals sediment down into the interior. You can promote this process by blowing
gently on the free surface. Another mechanism by which equiaxed crystals form in
castings is grain multiplication, for example by the detachment of dendrite arms at
the advancing front as a result of mechanical and/or thermal disturbances. This cannot
be readily promoted in the present experiment, since the growing crystals do not have
the branched dendritic morphology which favours this. You may be able to promote
grain multiplication by (gently!) tapping the windows.
3. Observation of Dendritic Structures
3.1 Dendritic Growth
The interface remains planar during crystal growth from a pure melt with a positive
temperature gradient in the direction of growth. Although a positive thermal gradient is
usually present, the melt is never entirely pure. An impurity which partitions into the
liquid leads to an accumulation of solute in the liquid adjacent to the growing crystal,
thereby depressing its freezing point. There is then a larger driving force for
solidification of liquid ahead of the interface than at the interface, even though the
former is hotter. Such liquid is said to be “constitutionally” undercooled, to highlight the
fact that it is its composition, rather than its temperature, which is responsible for its
having a strong tendency to freeze. In this unstable situation, protrusions on the
growth front grow rapidly into the supercooled liquid, giving familiar dendritic (from
Greek for “tree”) structure.
Part IB
AP2/3
Constitutional undercooling can usually only be avoided at very slow growth rates. The
details of the growth morphology tend to vary with the strength of the constitutional
undercooling. If the effect is weak, then cellular structures are formed, composed of
arrays of parallel prisms. As the strength of the undercooling increases, these cells
start to develop side branches and also to exhibit a stronger tendency to grow along
well-defined crystallographic directions (the so-called “easy growth” directions). For
cubic metals, these are the <100> directions. The precise reasons why this occurs are
still not entirely clear, but the effect is thought to be due to anisotropy of the atomic
addition kinetics at the interface. (Non-metals, most of which have atomically flat
interfaces, tend to exhibit this growth anisotropy over the complete range of growth
conditions.) The reorientation to the nearest easy growth direction is often taken as
marking the transition from a cell to a dendrite. Further changes occur as
constitutional undercooling increases, with side arms forming and a highly branched
morphology developing. A change in growth rate tends to have two separate effects.
It may alter the degree of constitutional undercooling, and hence the dendrite
morphology, it also affects the scale of the structure, with faster cooling giving rise to
finer dendrite spacings.
3.2 Experimental Procedure
view with
microscope
camphene or
salol liquid
glass
slides
sealed with glue
around edge
heater
cooler
Experimental arrangement for study of dendritic growth
The set-up is shown in the figure. Specimens will have been left for some time
beforehand on each apparatus, with heaters and coolers switched on, to reach thermal
equilibrium. The liquid/solid interface should be approximately planar and be located
somewhere around the centre of the glass slide in the viewing field of the microscope.
Growth can be stimulated by perturbing the thermal field. The easiest method of doing
this is to slide the specimen towards the cooler. (The specimen is simply resting on
both the heater and the cooler.) This should cause the growth front to advance. The
growth rate can be controlled by changing the distance the specimen is moved. A
degree of fine control can be exercised by blowing gently on the specimen.
Part IB
AP2/4
Two types of specimen are provided. One is camphene (melts at 51˚C) and the other
is salol (melts at 42˚C). In both cases, impurity content is such that constitutional
undercooling is readily stimulated. Camphene forms dendrites in a similar manner to
metals. This is because it has a similarly low entropy of fusion since the molecules can
move from the liquid to the crystal in a number of alternative orientations. This is
analogous to a (monomolecular) metal, the atoms of which do not need to rotate as
they enter the crystal structure.
A number of the features outlined above can be studied with this specimen. The
breakdown of a planar front to cells, followed by reorientation to the easy growth
directions and the development a branched dendritic structure can be observed. It is
also possible to study the competitive growth between neighbouring grains which is
responsible for the development of the columnar zone. It will be seen that the
dendrites of a grain in which one of the easy growth directions is approximately parallel
to the heat flow direction will grow faster than those of a less favourably oriented
neighbour, which will gradually be excluded from further growth.
The other specimen, salol, provides an analogue for the growth of faceted dendrites. It
has a relatively high entropy of fusion, typical of materials with strong directional bonds
and with molecular structures in which reorientation, as well as translation, are
necessary as transfer takes place from liquid to solid. (Faceted dendrites can also
arise with metallic phases, provided the entropy of fusion is high for some reason, e.g.
Al dendrites in a tin-rich Sn-Al alloy. The entropy of fusion is high because the Al is so
dilute in the melt, an unusual situation for a primary metallic phase.) The structures
observed with the salol are often a little less obviously dendritic than the camphene,
since the facets tend to dominate the appearance. Nevertheless, a plane front tends to
break down to a dendritic structure in a similar manner as the camphene. The
transition is more sluggish and reorientation is not observed, since growth only occurs
in an easy direction. Both of these effects are consequences of the relatively high
undercoolings needed for any interfacial advance.
References
1. W.Kurz and D.J.Fisher, "Fundamentals of Solidification", Trans Tech., (1986)
[Ng100]
2. www.msm.cam.ac.uk/phase-trans/dendrites.html
3. www.msm.cam.ac.uk/phase-trans/phase.field.models/movies2.html
4. www.msm.cam.ac.uk/phase-trans/phase.field.models/movies.html
The last two references are computer generated or real movies of solidification, showing all of the
features studied in this practical. You should feel free to download references 2-4 on to your own
computers for future reference.
HDB/IB/00
Part IB
AP3
THE HARDENABILITY OF STEEL
1. Introduction
Most heat treatments for steels begin by heating the specimen into the austenite phase
field. The resulting austenite is then cooled continuously to room temperature. This is
achieved by plunging the specimen into a bath of water or oil, or by removing it from
the furnace to cool in air (“normalising”). If very slow cooling is required then the
sample is left in the furnace which is switched off. The actual cooling rates may vary in
different regions of the sample. These variations may be large since steels are
relatively poor conductors of heat (thermal diffusivity of steel is about 10 -5 m2 s-1, of
copper about ~10-4 m2 s-1).
The properties of steels are sensitive to microstructure. It is useful to know how the
microstructure develops in different parts of a specimen during heat treatment. For a
given steel composition, a Continuous Cooling Transformation (CCT) diagram can be
constructed from experimental data, allowing the microstructural development to be
followed as a function of the cooling conditions. Fig.1 shows a CCT diagram for a
eutectoid
(Fe-0.8 wt %C) steel. Curves are plotted for the onset and completion of reactions to
form pearlite, bainite and martensite. The former two have the “C” shape because the
driving force is small at high temperatures whereas diffusion becomes sluggish at low
temperatures. Martensitic transformation is represented by a line parallel to the time
axis, since no diffusion is involved and because of the very high rate of growth, the
fraction transformed depends only on the temperature.
900
Austenitising Temperature
800
Eutectoid
Temperature
Temperature (ÞC)
700
600
Pearlite
500
400
Bainite
300
Martens ite
200
100
Water Quench
MARTENSITE
10
-1
Normalise
Oil Quench
FINE
MARTENSITE/ BAINITE/
PEARLITE
FINE PEARLITE
0
10
1
10
10 2
103
Furnace Cool
COARSE
PEARLITE
4
10
Time (s)
Figure 1. Typical CCT diagram for a eutectoid steel.
CCT diagrams are usually plotted with a linear temperature axis and a logarithmic time
axis. A constant cooling rate therefore plots as having a continuously increasing
gradient. In analysing real experimental results the true thermal history can be plotted
even when the cooling rate is not constant.
The dotted cooling line represents critical cooling conditions. Cooling faster than this
avoids all transformations other than martensite. Since this will normally produce a
specimen having the highest hardness, the critical cooling rate is a measure of the
hardenability of the steel. The hardness generally decreases with decreasing cooling
rate, even for microstructures without martensite.
A steel with a high hardenability is one which has a low critical cooling rate, so that
even slow cooling will lead to a martensitic structure. This has the advantage that hard
material can be generated without the risk of “quench cracking” due to high thermal
gradients associated with rapid cooling. On the other hand, it means that hard (and
brittle) material may inadvertently be produced in finished artefacts, notably as a result
of welding operations.
2. The Jominy End Quench Test
The hardenability is measured by quenching one end of a hot bar (Fig.2). The bar is
heated to the austenitising temperature, placed on a support and directionally cooled
with a water jet. When cold, the specimen is sectioned and hardness measurements
are made at intervals along its length. A wide variety of cooling rates and
corresponding hardness data are revealed in a single and spectacular test.
Part IB
AP3/2
The hardenability may be represented by the critical cooling rate, or the critical distance
along the bar at which the hardness (martensite content) starts to drop. It is useful to
examine the microstructure and correlate it with the hardness as a function of position
along the Jominy bar.
Figure 2.
Jominy end-quench specimen and corresponding hardness plot
3. Factors affecting Hardenability
The alloying elements in steel have a big influence on hardenability. This is particularly
so for diffusional transformations such as ferrite and pearlite, where the solutes not
only influence the thermodynamic stability of the austenite but can slow the reactions
by diffusion since their solubility in ferrite will be different from that in austenite.
Displacive transformations such as bainite and martensite are less affected. Elements
(Mn, Ni, C) which retard the transformation of austenite and hence shift the ‘C’ curves
to longer times and vice versa (Co, Al).
Hardenability is also affected by the austenite grain size. A finer grain size gives a
larger number density of heterogeneous nucleation sites and hence reduces
hardenability.
4. Tempering and Secondary Hardening
Martensite in steel can be hard but brittle because of its excessive carbon content.
Tempering involves a heat treatment which allows the carbon to precipitate as carbides
(e.g. cementite). This, and the annealing of defects, causes the martensite to become
softer but tougher. If the tempering temperature is sufficiently high (500 C) then
substitutional elements such as Mo and Cr become mobile. Fine carbides such as
Mo2C then precipitate at the expense of cementite and lead to secondary hardening.
5. Experimental Procedure
The compositions of the steels studied are given in Table 1. Two sets of specimens
with these compositions have already been quenched. One of these sets was
tempered after quenching (Table II). There are therefore, six sections available for
hardness tests along the length of the bars.
Part IB
AP3/3
Specimen
Composition (wt %)
Code
C
Mn
Mo
Ni
Cr
S1
0.31
-
-
-
-
S2
0.33
1.5
0.25
-
-
S3
0.31
-
0.5
3.3
0.8
Table I. Compositions of the three steels used for Jominy end quench testing.
Treatment
Times and Temperatures
Code
Austenitising
Quenching
Ageing
O
1 hour @ 900˚C
End Quenched
-
X
1 hour @ 900˚C
End Quenched
30 mins. @ 650˚C
Table II. Heat treatments applied to the three steels used for Jominy end quench testing.
5.2
Operations
5.2.1 The Jominy End Quench Test
Do this test on any specimen, with the assistance of a demonstrator.
5.2.2 Vickers Hardness Measurement
Measure hardness along the length of two Jominy specimens from the same alloy, one
in the quenched (O) and the other in the quenched and tempered (X) condition .
Results should be shared with other groups to compile hardness profiles for each of the
specimens S1, S2 and S3.
5.2.3 Hardenability Assessment
For S1(O), S2(O) and S3(O), establish the critical distance along the bar at which the
hardness starts to fall below that of the fully martensitic structure. For low hardenability
steels martensite is produced in a thin layer near the quenched surface. Rank the
specimens in order of hardenability.
For S1(O), S2(O) and S3(O), estimate the critical cooling rates using a simple analysis
of the heat flow during quenching (see practical AP1). Assume that the specimen is
initially at 900˚C and that the quench instantaneously brings one end to a temperature
of 50˚C. The error function solution then allows the complete thermal history of the bar
to be predicted. (thermal diffusivity  10-5 m2 s-1.) The transformation diagram for
each steel is provided in Fig.4. For the distance from the quenched end of the bar
found experimentally to be the limit of martensite formation, plot on the transformation
diagram the predicted (error function) thermal history and see whether this does indeed
just miss the nose of the diffusional transformation curve. Calculate the (constant)
cooling rate which would also give a curve passing through this point. Comment on
any discrepancies.
Part IB
AP3/4
5.2.4 Metallographic Examination
Examine the microstructures of the mounted specimen S2(O) at several positions
along the length of the bar. Many of the important features of steel microstructures are
impossible to see using optical microscopy. You will not, for example, be able to see
the carbides that form on tempering martensite. Transmission or scanning electron
microscopy has to be used. Examples of such micrographs have been provided.
Correlate these observations with the measured hardness profiles. Repeat for
specimen S2(X). Explain your observations.
Figure 4. Transformation diagrams for 3 steels having
similar compositions to specimens S1-S3
References
1. R.W.K Honeycombe and H.K.D.H. Bhadeshia, “Steels”, 2nd edition,
Edward Arnold (1995)
[De88]
2. D.A. Porter & K.E. Easterling, “Phase Transformations in Metals & Alloys”,
Chapters 5 and 6, Van Nostrand Rheinhold, (1981)
[Ln30]
3. R.E. Reed-Hill, “Physical Metallurgical Principles”, Chapter 18,
Van Nostrand Rheinhold, (1973)
[A108]
HDB/IB/00
Part IB
AP4
EXAMPLES CLASS
Start with Qu.1 or Qu.2, as directed. The class takes up the first 40 minutes of the practical period.
1. A zinc die casting is to be produced with a maximum section thickness of 8 mm. The casting
must be ejected from the die 4 seconds after the liquid charge has been injected. The die
remains at 100˚C throughout and the liquid is injected without superheat. Estimate the
minimum heat transfer coefficient required at the die/casting interface if the casting is to be
fully solid when ejected. Comment on the practical feasibility of achieving the required value.
[For Zn, fusion temperature, Tf  420˚C, latent heat of fusion, H f  5 108 J m–3 ,
thermal conductivity, K  40 W m–1 K –1 ]
2. The carburization of steels is an important example of a surface-hardening process. Since the
surface concentration of carbon is held constant as the carbon diffuses into the steel, the error
function solution to the diffusion equation is applicable. In this question we solve this equation
using the MATTER software. Open the MATTER module on Atomic Diffusion in metals and
Alloys - Interstitial Diffusion, and turn to p.14. Assume that the initial concentration of carbon
in the steel is 0.2 wt.%, and that the surface concentration is 0.8 wt.%. Set these values (under
‘Options’), and a temperature of close to 1100˚C. Select the plotting interval ‘small
(smoother)’. Plot.
(a)
(b)
(c)
(d)
What is the diffusion coefficient of carbon?
After 1000 s of carburization what depth of material has a carbon content  0.6 wt.%?
After 1000 s of carburization what depth of material has a carbon content  0.4 wt.%?
A sample given this carburizing treatment is air-cooled to room temperature. Indicate,
using sketches, how the microstructures near the surface of the sample and in the bulk
would differ.
[This examples class is followed, within the normal practical period, by an assessed practical lasting
one hour. The assessed practical is based on AP1, AP2, AP3, and this examples class; it includes a
small amount of practical work and some usage of the MATTER software.
HDB/IB/00