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Mechanisms of hot pressing of magnesium oxide powders
CERAMURGIA
76
INTERNATIONAL,
Vol.
5. n. 2.
1979
Mechanisms of Hot Pressing of Magnesium Oxide Powders R. PAMPUCH Institute
of
Materials
Science,
Academy
Estimation of the rate controlling mechanisms of mass transport during the initial, intermediate and a portion of the final stage of hot pressing of powder compacts by an adequate application of the theory of creep of non-porous polycrystals at elevated temperature is first discussed and their significance for understanding of the relations between powder characteristics and their densification during hot pressing stressed. Review of recent developments of the creep theory indicates that if intraparticle (intracrystallite) i.e. dislocation mechanisms are acting to a negligible extent only, the steady-state strain rate 6, should be controlled entirely either by boundary reactions (emission/absorption of point defects at sources and sinks, e.g. at boundary linedefects) or by diffusion between sources and sinks (Nabarro-Herring and/or Coble creep). An analysis has been made in these terms of E observed with well characterised MgO powders, having a rather uniform crystallite size, during hot pressing at 771975K under loads of PA = 60-295 MPa. Two types of powders, obtained by thermal decomposition of Mg(OH), at different temperatures, have been studied, namely i. powders constituted by well-annealed fine crystallites (d = 28-56 nm) showing no lattice microstrains, and il. powders constituted by fine crystallites (25-45 nm) showing appreciable microstrains of the lattice and, consequently, a high density of the line defects. Experimental determination of the stress sensitivity, n, particle sensitivity, m, and true activation energy for creep, Q,, has shown that the data correspond very closely to i, D: P,,*/d in the first, and to i, = PA/d’ in the second case, respectively. The first situation is expected for strain rates controlled by boundary reactions while the second for the ones controlled by Coble creep, respectively. The different rate-controlling mechanisms enable to explain rationally the different densifications obtained under comparable conditions of hot pressing with the two types of MgO powders.
1 - INTRODUCTION
The wide interest in mechanisms and kinetics of mass transport in powder compacts during heating under applied stress, i.e. during hot pressing, resulted from theoretical predictions and practical experience which indicated that hot pressing seems to be the principal means to obtain ceramic polycrystals of full density. Despite the considerable theoretical information about the basic mechanisms for mass transport during hot pressing. the theory finds, however, little application in practice. This is mainly due to the relatively small number of studies made on well-characterized real powder compacts, suitable as model materials to check the predictions of the theory and to allow a demonstration of relations between the mechanism of hot, pressing and the characteristics of powder compacts. The knowledge of these relations is, namely, very important as there is ample evidence in technological practice that the controlled preparation of powders and powder compact is the most vital step of the fabrication cycle for sintered polycrystalline oxides.
of
Mining
and
Metallurgy,
Cracow,
Poland
The author has studied with his collaborators these relations in the case of magnesium oxide powders and powder compacts, and became aware that magnesium ovide obtained by thermal decomposition of hydroxide precursors might be a suitable model material. Although some of the results of these studies have been already published, an appraisal of their significance for an understanding of the relations between powder characteristics and the mechanism of mass transport during their hot pressing was thought timely, especially in view of recent developments in the theory of creep ‘-j.
2 - A SHORT PRESSING
SURVEY
OF
THE
THEORY
OF
HOT
The excellent review by Spriggs and Dutta * of the mechanisms of mass transport during hot pressing, covering the literature up to 1973, pointed out that the kinetics and mechanism of hot pressing are closely related to the mechanism of creep of non-porous polycrystals at elevated temperatures. The well-developed theory and practice of creep of such systems may thus serve as a guide for the estimation of the hot-pressing mechanisms, provided that the porous nature of the hot-pressed powder compacts and the small size of their constituent particles are being accounted for. The irreversible deformation of materials subjected to a constant applied stress, i.e. creep, is a thermallyactivated process and the secondary, or steady-state, strain rate 8, may be formalized for any conceivable mechanism under a given set of experimental conditions by an equation of the form: PR G”4
D
IIll
where A is a constant independent of applied stress and temperature, having dimensions of length, k is the Boltzmann constant, T is temperature, I is a length which may be equated to W’ or - b where n is the atomic volume and b is the Burgers vector, respectively, PA is the applied stress, equal to effective stress uerr acting on the particles in non-porous materials, G is the shear modulus, .d is the particle size. The temperature dependence of the strain rate is included in the diffusivity term, D = DO exp(-Q,/RTl, where Q, is the true activation energy for creep and R is the gas constant. The stress sensitivity n = (3lnhJCJlnP&. r and the particle sensitivity m = -_[31ni/31ndjp4. T have specific integral values for each particular mechariism of mass transport (Table II. Their experimental determination, together with the determination of CL, which has also a specific value for a given mechanism of transport by
MECHANISMS OF HOT PRESSING OF MAGNESIU’M OXIDE POWDERS
I.
Mechanisms controlled by point-defect between sources and sinks 1. Nabarro-Herring volume) 2. Coble
creep
creep
(diffusion
(diffusion
bondaries) 3. Diffusion around particle II.
IV.
lntraparticle
due
to
the
(lattice
1
D‘
I
Db
1
D’ or Db
1
2
Dh or D’
1
1
D’
0
3-5
D
Db - boundary diffusion
coefficient,
ledges
at
particle
mechanisms
Remarks: D’ -volume diffusion coefficient, coefficient in the liquid phase.
2
D’ - diffusion
Typical Name
Definition
- Predicted valuea for the stress (n) and particle (m) sensitivities and diffusion coefficients for different boundary (diffusional) creep mechanisms at elevated temperatures. Values for lattice disloca tion mechanisms are additionally included. (After Ref. 1.31. TABLE I
particle
1
phase
dislocation)
D
3 boundary
liquid
n
the
Boundary-reactions controlled diffusional mechanism (mechanism controlled by emission/ absorption of point defects)
III. Viscous flow boundaries
m diffusion
through
along
77
Determination
dimensions m
IO-‘- IO4
Crystallite
Coherently diffracting region of the lattice
X-ray diffraction line broadening
Aggregate
Compact, nonporous particle composed from crystallites
BET isotherms, electron microscopy
Agglomeration
Loose, porous particle composed from aggregates (or crystallites)
Optical and electron microscopy
virtue of the different diffusibilities entering in eqn. [I] for each mechanism, allows a meaningful estimation of the creep mechanism. In the study of hot pressing there are, however several points which must be taken into account. The steady-state strain rate & under any given conditions increases with increasing porosity which changes during nearly the entire hot-pressing time cycle. This arises mainly through the dependence of the effective stress and of the shear modulus upon porosity. At pore volume fractions V, Z 0.15, beIt and G depend strongly both on V, and the stress concentration factor which is also a function of the (changing) pore shape I. Hence, very complicated correction factors must be introduced in eqn. [I] to account for the porosity. After an initial decrease at small V,, the shear modulus remains, however, constant at V, 5 0.15-0.20 in most celt may be taken for this ceramic materials 6 while range of higher porosities as the applied stress PA divided by the relative density pr ‘. Consequently, for the initial, intermediate, and a portion of the final stage of hot pressing may be used the procedure proposed by McDonough and Spriggs 8, according to which the experimentally derived instantaneous strain rates ii = Acnerr at different porosities may be normalised to the true steady-state strain rate i, at V, = 0. Namely, when (%/3(1/p,)) = const = A% = &. In this way correct stress and particle sensitivities may be obtained from eqn. [I]. In order to calculate the activation energy for creep CL the fact must be taken into account that G z G,, where G, is the shear modulus for non-porous material. The particle size d in eqn. [l] should denote the dimension of the smallest particles of the powder
TABLE II - Constituent particles of powders and powder compacts. (After Ref. IO).
1o-5- IO4
compact the boundaries of which can act as effective source and sink for point defects, since the role of inner sources and sinks (as the lattice dislocations) should be negligible during the short time-cycle of hot-pressing 9. The definitions of the constituent particles of powders and powder compacts are given, according to .Feitknecht and Giovanolli ‘O, in Table II. If non-porous crystallite aggregates occur in the powder compact, d = aggregate size, since the coherent intercrystallite boundaries in such formations are inefficient sources and sinks for point defects. In other, more numerous cases, the crystallite size should be taken as the particle size d. As discussed later, the size of the crystallites, which is much smaller than that of grains in non-porous polycrystals, has important consequences for the specific nature of mechanisms of mass transport during hot pressing in comparison with creep of non-porous polycrystals. It is not necessary to recall in detail that for a meaningful estimation of n, m, and Q, the particle (crystallite) size should not change during the steady-state strain rate period and the particle size distribution should be as narrow as possible. The interpretation of 0, in the case of hot pressing of oxide powder compacts requires also some caution. It became evident that in general the different constituent species of the oxides may diffuse along different paths and it is necessary to use a complex diffusivity term, such as proposed by Gordon ‘I. It may be argued ” that D,‘ > D,’ and DchEcb< D,” 6,” where the index v denotes volume, b denotes boundary, while c and denote, respectively, cation and anion: U’ is the effective boundary width. It has been shown under this assumption that in general four controlling pro-
R. PAMPUCH
cesses
reduced
can and
be the
expected temperature
as the particle Size is is lowered D=‘+Dab sab+
energy for creep + D.’ + Deb6cb“. The true activation Q, = -BalnD/a(l/T) should thus have a straighforward meaning only if the experimental conditions do not cover transition regions between those controlled by a single diffusion constant. If several mechanisms of mass transport, e.g. intraparticle (dislocation) mechanisms, plus diffusional such as Nabarro-Herring and Coble mechanisms, operate independently, i.e. non-sequentially, creep, values of n and m as i. = cj=, i,. j and non-integral well as unpredictable values of Q. should be expected, having intermediate values between the ones for the simultaneously contributing mechanisms. The fact that such results have been obtained in most previous studies of hot pressing of oxide powder compacts has led to the conclusion that several if not all envisaged mechanisms of transport contribute independently to the strain during the entire hot-pressing process I’. This needs not be always so and the author feels that at least some of the values which did not coincide with the theoretical predictions may be attributed to integration over regions controlled by different single processes as well as to an inadequate characterisation of the powder and powder compacts. Let discuss this aspect in more detail. It is plausible to assume that if intraparticle (dislocation) and boundary (diffusional) mechanisms may take place, they should operate non-sequentially and nearly independently of each other. When well-annealed crystallite systems, which do not have a very high density of grown-in lattice dislocations, are subjected to stress and temperature under the usual conditions of hot pressing, the intraparticle (dislocation) mechanisms are not likely to be of importance in ceramic systems. The studies of creep of essentially non-porous oxide polycrystals indicate that these mechanisms to not occur below applied stresses of about 100 MPa ‘. This is not surprising since the dislocation movement in oxides is usually more difficult than in metals owing to their high elastic moduli and the geometrical complexity of moving lattice dislocations through a structure containing more than one species. In several cases there are not sufficient independent slip systems to allow coherent deformation of the system. Diffusional mechanism should be even more important in powder compacts which consist of crystallites, i.e. of particles having a very small size, where the movement of lattice dislocations is more difficult than in the larger grains of polycrystals and the threshold stress to move the lattice dislocations should be here higher than that cited before. Another factor is the usual presence of impurities which should, in general, increase, the diffusibilities and decrease the mobility of lattice dislocations in oxides. Additions of 0.10-8.08 w/o of FelOl have been shown, e.g., to inhibit dislocation creep of MgO polycrystals I3 while an increase of the lattice dislocation density in polycrystalline MgO has been observed only at isostatic Pressures above 400 MPa lb. Hence, a negligible contribution of intraparticle (lattice dislocation) mechanisms may be assumed during hot pressing of ceramic powder compacts, especially at the higher temperatures and at applied stresses usually used, except for isostatic hot pressing under high gas pressure. Now, with any diffusional mechanism two processes occur, namely, the emission/absorption of point defects at suitable sources/sinks and diffusion (through the volume or along the boundary) between sources and sinks. The two processes are clearly sequential and cannot occur independently of each other. For sequential processes I k, = C,=l (l/&J)
and when two latter expression
processes operate may be written
sequentially
the
If the strain rate due to each component process is different, the slower one should control the strain rate and, hence, determine entirely the values of n, m, and Q.. In the original Nabarro-Herring and Coble diffusional creep theory it was assumed that the source and sink operation was easy in which case all the applied stress is available to drive the diffusion fluxes responsible for diffusional creep. More recent studies “-” indicate, however, that even the particle boundaries are not perfect sources and sinks for point defects and some of the applied stress is necessary to drive the boundary reaction (emission and absorption of point defects). From numerous electron microscopic observations made on metals and ceramics “-” it is now known that the particle boundaries have distinct crystallographic features and contain line defects resembling dislocations. Emission and absorption of point defects should thus occur predominantly by climb of the boundary line defects having a component of the Burgers vector normal to the boundary. When the sequential processes of emission/absorption of point defects and their diffusion between sources and sinks are taken into account, one arrives at the expression for the steady-state strain rate: 1
BD
! PJ-l \
5, = d”kT if diffusion the volume
i.=
I 1 + (4BD”nlpbdMdkT)
between ‘, I9 or
sources
and
sinks
1
B’DbGb
[21
is
through
I
E31
P&
d”kT
1 1 + (4B’D%“n/pb:Md’kT)
if diffusion is along the boundary. B and B’ are numerical constants, b, is the component of the Burgers vector normal to the boundary, P is the density and M is the mobility of the boundary line defects, respectively. The remaining symbols have the same significance as before. When the factor in round brackets in [2] and C31 is small, i.e. the density p and/or the mobility M of the line defects are high, the expressions [2] and [31 respectively, to Nabarro-Herring and Coble reduce, creep equations the characteristic parameters of which are given in the 1” and 2”d row of Table I, respectively. Under the opposite set of conditions (low P and M) the expressions [2] and [3] reduce to pbtMP*
l-41
i, = d
Under the assumption that the boundary line defects behave parametrically in a similar way to lattice dislocations the following explicit.expression has been derived for the steady-state strain rate controlled by the (slower) boundary reactions ‘s “: E, =
47rPi(l -v)
(Z-l)
t?p:
A”b=PA’ D=
dGkT where pj is the probability line-defect a site capable a point defect, i.e. the
.
D
[151
dGkT
of finding on the boundary of accepting (or emitting) jog probability; Z is the
MECHANISMS OF HOT PRESSING OF #MAGNESIUM OXIDE POWDERS
coordination number of the ions in the material; v is the Poisson number; D is the coefficient of diffusion controlling the climb rate of the boundary line defects. Recent review on metals suggests that the majorjty of data where eqn. [5] is applicable correspond better to boundary than to volume diffusion coefficients*‘. It follows from eqn. [5] that for boundary-reaction controlled diffusional creep n = 2 and m = 1 (4”’ row in Table I). Owing to the l/d dependence as compared with the l/d” and 1/d’ dependence in case of the creep, respectively, the Nabarro-Herring and Coble importance of the boundary reactions as the ratecontrolling process of diffusional creep should increase with a decreasing particle size. This may be the reason for the common observation that with nonporous polycrystals there is a general trend for coarsegrained materials to exhibit B, 0~ PA/d’ and/or is = PA/d’ relations while with fine-grained materials, e.g. ultrafine grain one finds 24 something closer to ceramics, & = PAZ/d. The latter situation should also obtain on hot-pressing of powder compacts which consist of small-size crystallite% provided no appreciable growth of the crystallites occurs during hot pressing. If it is assumed that the boundary line defects behave parametrically analogous to lattice dislocations, the importance of the boundary-reaction controlled diffusional creep should be greater in ceramic than in metallic systems owing to the generally lower mobility of dislocations (and boundary line defects) in ceramic materials. The process of emission-absorption of point defects at the boundary line defects should give rise not only to non-conservative motion of the defects by climb normal to the boundary but also to glide of the defects along the boundary due to the component of the Burgers vector parallel to the boundary. This brings about a sliding of the particles past each other. On a purely geometrical basis, sliding cannot take in the absence of place in non-porous polycrystals any other process which allows accomodation of the sliding, e.g. by plastic flow or diffusional processes at triple points and at the irregularities along the
200- 7;,gp80 1 960m
NE 7-,1202 m
\ \
crystallite microstrains
_ \ \
size (nm) (hd,,kt/dhkl)
\\ :19;gG&o
E 2 80&J v) I $j 40-
’
20?2$0)
\
“t24;WJ80) ‘< ‘w
I 775
I
I 975
‘\ 148kl~(lOO1‘\ 1 I I 1175 temperature
I 1375
i
(K)
FIGURE 1 Average crystallite size, microstrains in crystallite% and equivalent BET-particle size in MgO BEJ surface area, powders obtained by thermal decomposition of MgCOH), at different temperatures.
79 boundary. If pores are present at the boundaries no extensive accomodation is necessary. Even if accomodation of the particle boundary sliding is required, this may occur by diffusion of atoms (ions) from part of the boundary under compression to another region under tension. An example of such a diffusion, which may play a role with small particles, is the diffusion around boundary ledges with m = 1 and n = 1 (3’d row in Table 1). The diffusional accomodation may occur either through the volume or along the boundary, i.e. in a similar way as in Nabarro-Herring and Coble creep, respectively, but in any case considered here the diffusion path is very short what is favourable for fast diffusional accomodation of the slower particleboundary sliding, accompanying the emission/absorption of point defects, and thus for control of the strain rate by the latter process. It may be thus expected that with the well-annealed fine-particle systems, such as the powder compacts, the situation is favourable for boundary-reaEtion controlled strain rate, especially during the intermediate and a portion of the final stage of hot pressing. This should, however, not apply to hot pressing of internally strained crystallite-systems having a high density of line defects p where [2] and [3] predict Nabarro-Herring or Coble creep controlled processes.
3 - MECHANISMS OF DEFORMATION OF MgO POWDER COMPACTS DURING HOT PRESSING AND THEIR RELATION TO THE POWDER CHARACTERISTICS The results described in this section have been obtained with magnesium oxide formed on thermal decomposition in air of a relatively pure Mg(OHII precursor. The major impurities of the precursor were: Fe below 500 p.p.m.w, and Si below 200 p.p.m.w. Electron microscopic observations have shown that the MgO powder consists of weakly interlinked MgOcrystallite chains” (see also Ref. 26) in which the crystallites have a relatively uniform size. The close agreement of the average size of crystallites, determined by X-rays, and of the equivalent BET particles, calculated from surface area measurements, over a wide range of thermal decomposition temperatures (Fig. I), suggests that the crystallites contact each other along the chain most probably over a very restricted area only and the probability of aggregate formation is low. Simultaneous resolving of the broadening of X-ray diffraction lines into the crystallite size effect and microstrain effect *, by using the method described by Librant and Pampuch “, showed that the crystallites are strained, i.e. contain most probably an enhanced density of grown-in lattice dislocations and boundary line defects. As indicated in Fig. 1 the largest microstrains are observed at the lower temperatures and decrease to zero at higher decomposition temperatures. All these features may be rationally explained by the inhomogeneous mechanism of thermal decomposition of Mg(OH)2 to MgO proposed by Ball and Taylor**. According to these authors the decomposition occurs via coherent MgO domains, formed by counterdiffusion of protons and magnesium ions in an immobile anionic lattice in the Mg(OH), matrix. Under assumption of this mechanism the first MgO crystallite% separated by phase boundaries, should form when the elastic strain energy stored in the system, and due to the different lattice parameters of Mg(OH)* and MgO,
* Microstrains deviation value of
of the dhLI.
are defined as Ad,,,,/d,,, where average interplanar spacing from
Adhti the
is
the
equilibrium
R. PAMPUCH
80
pA 100MPa
Ad/d =0
f- +
-----
------
-I_
- 60
-40
z 5 z
pA 195MPa
- 20 ‘3j E ._
1
,
,
I
5
10
20
30 Time (min)
FIGURE 2 - Crystallite size vs. time of hot-pressing at T, = 975 K of MgO powder compacts obtained by thermal decomposition of Mg(OH), at T, = 975 K. under the indicated applied stresses (after Ref. 31); microstrains are absent.
-30 ,;+_____-------+
2.
Tp=Ts 775 K 0 I’- 10 pA 100 MPa I
I
I
I
I
/
Time (min) size and microstrains vs. time of hot. FIGURE 3 - Crystallite pressing at T, = 775 K of Ma0 powder compacts obtained by thermal decomposition of MgtOH), at T, = 775 K, under the indicated applied stresses (after Ref. 31).
attains a value equal to the surface energy of the MgO crystallites “, Besides the weak interlinking of the adjacent MgO crystallites which most probably form by breaking out from the Mg(OH), matrix “‘, this should give rise to crystallites of a similar size since the elastic strain energy is a function of the dimensions of MgO domains. The first independent MgO crystallites have been found to form at about 625 K. Hence, heating to higher temperatures should result in a progressive annealing of the microstrains with increasing temperature. In the following text the behaviour during hot pressing of two different types of MgO powder compacts shall be considered, namely of compacts consisting of: i. - well-annealed MgO crystallites which show no microstrains, and ii. - MgO crystallites which show appreciable microstrains and hence should probably have a high density ;fefeyt;wn-in lattice dislocations and boundary line The former were obtained by heating Mg(OH)2 powder compacts, cold-pressed under 60 MPa, up to 975 K with a linear rate of temperature rise of 10 K/min and the latter by heating the Mg(OH12 compacts up to 775 K with the same rate of temperature rise. The compacts were subsequently isothermally hot pressed in an apparatus described in ‘I which allowed a continuous monitoring of changes of length of the compacts and thus the determination of L. In parallel experiments the compacts were taken out from the apparatus after succesive periods of time of hot pressing under the given conditions, and their apparent density as well as the crystallite characteristics in compacts were determined. This enabled calculation of the true steady-state strain rate by the already discussed McDonough-Spriggs relation ’ as well as characterization of the changes in crystallites during hot pressing. The’ characteristics of the crystallites for both types of compacts are given in Figs. 2 and 3. After an initial growth, presumably by coalescence due to surface diffusion which is indicated by the d’d,’ = Ct dependence, where C is a constant, t is time, and d, is the initial crystallite size, the average crystallite size attains in all cases a nearly constant value after 10 to 15 minutes of hot-pressing ?? *. This value is specific for each type of powder compact and temperature but is relatively independent of the applied stress at a given temperature. The period of constant crystallite size corresponds to the one of the steadystate strain rate which typically established after 10 to 15 minutes of hot pressing. In both types of MgO powder compacts, at a given hot-pressing temperature, the crystallites have thus a nearly constant size during the steady-state strain rate and most probably also a narrow size distribution since the growth by coalescence is not expected to increase the scatter of the crystallite sizes. In such cases a meaningful estimation of the mechanism of mass transport by using eqn. [I] is thus possible. Owing to the different characteristic of the crystallites as far as the microstrains are concerned, the two types of compacts are, however, expected to show a different behaviour on hot pressing and the results for each type shall be discussed separately. In Fig. 4 is shown a logarithmic plot of the true steady-state strain rate vs. applied stress for the compacts consisting of well-annealed crystallites, at hot-pressing temperatures 775, 875. and 975 K. From the slope of lines connecting the experimental data for each temperature a stress sensitivity n has been
* Except for the experiments and temperature of 975 K the in further analysis. ??
under results
applied stress of of which are not
100 MPa included
MECHANISMS
OF
HOT
PRESSING
OF
MAGNESIUM
OXIDE
81
POWDERS
Dm*/s
t
100
I
56P
I
\\\D' Dcomp\\ db '\
lo"*-
/
oTp775K Tp875 K oTp975K
\
lO-‘O-
n=1.96 b/564$
\
40r n=1.97+0.44 /
??
39v
A9 1' /
\
28
\
t
\ \
286 / n=1.99
DC\
1 0:3
Stress (MPa)
strain rate vs. applied stress for FIGURE 4 - True steady-state MgO powder compacts obtained by decomposition of Mg(OHI, at T, = 975 K and hot pressed at T, = 775, 875, and 975 K. The crystallite size during the period of steady-state strain rate is indicated at the experimental points. After Ref. 31. with correction of some missprints in the original publication.
/I
/ +/
/
/ /
,‘Tp875
I
\D1 creep \ \ \
'\
\
\ I
I
0.6
I
0.6
I
I
I
1
1.0 1.2 lOyT,OK"
FIGURE 6 - Magnesium and oxygen volume diffusion coefficients, surface diffusion coefficient, and Gordon’s complex coefficient for boundary-diffusion controlled creep (divided by the effective boundary width) in magnesium oxide. Further is shown the rate-controlling diffusion coefficient DC,..,, calculated from data for T, = 875 K and MgO powder compacts obtained at T, = 975 K.
obtained which nearly coincides with two at all the three temperatures covered experimentally. The slight spread of data observed is probably due to some variations of the crystallite size (indicated in Fig. 4) with changes of the applied stress. The value of n = 2 is specific for boundary-reactions controlled strain rate only (compare Table 11. It may be thus assumed that the behaviour of this type of MgO compacts obeys the eqn. [5]. In this case the experimental data plotted in logarithmic coordinates: &dT/Gb’ vs. the dimensionless term PA/G should lie along several parallel lines for the different hot-pressing temperatures covered experimentally, provided that A” in eqn. [5] is temperature and stress independent. This situation obtains with the MgO powder compacts discussed here (Fig. 51, which enables one to determine the true activation energy for creep from the sepa,ration of the lines in Fig. 5 since in this case, at a constant value of PA/G and for two temperatures TI and T2.
Tp 975 K;' 0'
I
\
\
K
/I
;,,,d,kT/G,b’ Rln (
&,,dlkT/G,b’
QC = (Tz -
i
2.lo-J
5.10-3
10-c
2.10-2
PAG / FIGURE 5 - Normalised true steady-state strain rate vs. normalised applied stress for MgO powder compacts obtained by decompoT, = 775. sition of Mg(0H)2 at T. = 975 K and hot-pressed et 875. and 975 K. The relative densities of compacts after hot pressing for 30 minutes under the conditions indicated varied between 0.28 end 0.80.
1
161
T,)/T, Tz
In order to construct Fig. 5 has been taken the value of G for non-porous MgO at the given temperature, according to Soga and Anderson 32. The neglecting of the influence of porosity upon G, however, should not give rise to an appreciable error since the ratio of the shear moduli appears in eqn. [6] and the changes of the shear modulus of porous MgO with temperature should be nearly the same as in porous material. The value of the true activation energy obtained from Fig. 5 and eqn. [6] is 194 kJ/mole. It lies between the known activation energies for volume diffusion
R. PAMPUCH
82 of magnesium and oxygen in MgO and the one for boundary diffusion of oxygen (Table III]. No value of the activation energy for magnesium boundary diffusion in MgO has been found in the literature but it follows from general considerations that it should be somewhat higher than that for oxygen boundary diffusion. Hodge. Lessing, and Gordon I3 quote a value of 279 kJ/mole as the upper limit of the activation energy for this case. According to the current views discussed in Section 2, the climb rate of the boundary line defects should be controlled at the low temperatures covered experimentally by boundary diffusion coefficient of magnesium for which the activation energy of 194 kJ/mole seems to be a reasonable one. Rate control by diffusion along the boundary is also indicated by the high value of the diffusion coefficient calculated from steady-state strain rates by using eqn. [53 for the experimentally covered hot-pressing temperatures (Fig. 6). In the calculations the jog probability in equilibrium, p, = IO-‘“, and the Poisson number v = 0,25 have been taken. As usually found in hot-pressing and creep experiments of oxides, it
TABLE III mechanisms
Diffusion coefficient
-
Activation energies for in magnesium oxide.
’
diffusion
n=l.OO+-0.39 *3./N / IO-*
I
I
I
jr*7 fl24
Illll
I
10’
I
I
I
IO2 Stress
( MPa)
FIGURE 7 - True steady-state strain rate vs. applied stress for MgO powder compacts obtained by thermal decomposition of MgfOH), at T, = 775 K and hot-pressed at the same temperature. The crystallite size during the period of steady-state strain rate is indicated at the experimental points.
self-diffusion
Activation energy (kJ/mole]
Source
267.4 261.4 146.5 370.0
33 34 35 36
D’,, Do D”o Ebo D’6” D”- surface
different
*y
-\
v
coefficient.
195 MPa’, \
Y ‘b
is 3 to 4 orders of magnitude greater than the (extrapolated to lower temperatures) volume diffusion coefficients in MgO and lies on the extension of data which correspond to Gordon’s complex diffusion coefficient for the boundary-diffusion controlled case and to surface diffusion in MgO. In the former case an effective boundary width of Eb = IO” m has been assumed and the values of CL and Do” for magnesium and oxygen have been taken from Ref. 13. The vales of n and Q, obtained in the case of hot pressing of well-annealed MgO crystallite systems thus give a consistent picture. Namely, the steady-state strain rate during hot pressing is most probably controlled by boundary-reactions, i.e. by emission and absorption of point defects at the line boundary line defects, the climb rate of which seems to be controlled by magnesium boundary diffusion. Different results have been found for hot pressing of the second type of MgO powder compacts, consisting of microstrained crystallites. The logarithmic plot of a, vs. the applied stress [Fig. 7) gives a slope which corresponds to n = 1 while a logarithmic plot of t, vs. the crystallite size d (for a different set of observations) [Fig. 81 gives a slope which corresponds to m = 3. Thus Coble creep, i.e. steady-state strain rate controlled by boundary diffusion between the sources and sinks and not by the boundary reactions, is indicated for this crystallite system. According to eqn. [3] this should obtain when the density and mobility of boundary line defects are high. Such a situation is very probable indeed with this crystallite system since the crystallites show here appreciable microstrains during the entire hot-pressing time-cycle and consequently should have a high density of both lattice dislocations and boundary line defects.
m=3.08
‘4 ,
3.04
y-n=
100 M$&
I
\
\
'k
‘\
h
I
I
I
25
30
I
35
40
Crystallite
size, d
(nm)
FIGURE 8 - The true steady-state strain rate vs. crystallite size for MgO powder compacts obtained by decomposition of MgfOH), at T, = 775 K and hot-pressed at the same temperature, under applied stresses of 100 and 195 MPa.
4 - CONCLUSIONS It has been tried in the present paper to show in respect to the hot-pressing behaviour of MgO powder compacts that when well-characterized powders and powder compacts are studied a rather consistent explanation of the mechanisms of mass transport is possible in terms of the theory. Some aspects of the relations between the hot-pressing behaviour and the powder and powder-compact characteristics are already evident. Under comparable applied stresses and at comparable temperatures, the control of the strain rate during hot pressing by the boundary reactions with well-annealed crystallite systems should result in lower densities after hot pressing as compared with the ones in the case of compacts consisting of microstrained crystallites where all the applied stress is available to drive the (boundary) diffusion fluxes responsible for the strain.
MECHANISMS OF HOT PRESSING OF MAGNESIUM
83
OXIDE POWDERS
..”
_
~_---
3. 4.
5. 6. 7. 8.
2
9.
E2
l?L
10.
‘0,
4
.
t I
m/
I
195 Applied stress,
100
275
( MPa)
FIGURE 9 - Apparent density vs. applied stress after 30 minutes of isothermal hot-pressing at T, = 775 K of MgO powder compacts obtained by decomposition of Mg(OH)Z at T, = 775 K [curve 1) and T, = 975 K (curve 2).
As an illustration may serve Fig. 9. which shows that the apparent densities obtained after hot-pressing at 775 K for 30 minutes of MgO powder compacts consisting of microstrained crystallites. (curve 1) are much higher * that those found at the same temperature and after the same time for MgO compacts consisting of well-annealed crystallites (curve 2). This applies especially for lower and intermediate applied stresses. Owing to the 6, 0~ P? dependence found in the case of well-annealed crystallites the apparent densities are expected to increase in this case strongly at higher applied stresses. Thus for an efficient application of hot pressing, at least for MgO obtained from the thermal decomposition of Mg(OHL, either highly microstrained crystallite systems at moderate applied stresses or very high applied stresses with well-annealed crystallite systems should be used. The excellent results obtained e.g. by isostatic hot pressing under high gas pressures confirm the latter trend.
11.
12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
25. 26. 27. 28. 29. 30. 31. 32.
REFERENCES 1. B. BURTON, Diffusional Creep Trans. Tech. Publ. Bay Village, 2. J.W. EDDINGTON, K.M. MELTON
33. of Polycrystalline Ohio (1977). and C,P. CUTLER,
Materials,
34. 35
in Progress 36 37
* Although the theoretical density has been not attained in this case, the hot-pressed compacts are here transparent [60 to 70% transmission of light at wave-lengths 700-1000 nm) owing to the very small pore size.
in Materials Science, B. Chalmers, J.W. Christian, T.B. Massalski. [Eds.). Pergamon Press, Oxford (1976) p. 61. A.G. EVANS and T.G. LANGDON, ibid., p. 171. R.M. SPRIGGS and S.K. DUTTA, in Sinterin,g and Related Phenomena. G.C. Kuczynski [Ed.). Plenum Press, New York (19731. p. 369. R.C. ROSSI. J. Amer. Ceram. Sot. 51 (1968) 433. R. PAMPUCH and J. PIEKARCZYK, Papers of the Ceram. Comm. Polish Acad. Sci. Cracow 24 (1976) 7 (in Polish). R.L. COBLE, J. Appl. Phys. 41 (1970) 4798. W.J. McDONOUGH and R.M. SPRIGGS. in Sintering end Related Phenomena, G.C. Kuczynski [Ed.), Plenum Press, New York (1973), p. 417. Ya. E. GEGUZIN and V.I. SOLONSKY. Fiz. Tverd. Tela 6 (1964). W. FEITKNECHT and R. GIOVANOLLI. in Compt. Rend. Journees d’Etudes. Les Solides Finement Divises. J.E. Ehretsman (Ed.), Dir. Docum. franc. Paris (1987). R.S. GORDON, in Mass Transport Phenomena in Ceramics, A.R. Cooper, A.H. Heuer (Eds.), Plenum Press, New York (1975), p. 445. R.S. GORDON, J. Amer. Ceram. Sot. 56 (1973) 147. J.D. HODGE. P.A. LESSING and R.S. GORDON, J. Amer. Ceram. Sot. 66 (1977) 1318. R.M. SPRIGGS and L. ATTERAAS. in Ceramic Microstructures. J.A. Pask, R.M. Fuhath [Eds.), J. Wiley and Sons, New York (1968). p. 701. G.R. TERWILLIGER. H.K. BOWDEN and R.S. GORDON, J. Amer. Ceram. Sot. 53 (1970) 241. T.A. AUTEN and V. RADCLIFFE, ibid., 59 [1976) 249. G.W. GREENWOOD, Scripta Metall. 3 (1970) 1971. Ya. E. GEGUZIN, Fiz. Metall. Metalloved. 36 (1973) 190. M.F. ASHBY. Surface Sci. 31 (1972) 498. W. BOLLMAN. Crystal Defects and Crystalline Interfaces, SPringer Verl. Wien (1973). A.H. HEUER. in Defects and Transport in Oxides, M.S. Seltzer, R.I. Jaffee (Eds.). Plenum Press, New York (1974). discussion. T.G. LANGDON. Mat. Sci. Engng. 7 (1971) 117. H. ‘GLEITER and B. CHALMERS, Progr. Mat. Sci. 16 (1973) 1. A.H. HEUER. R.M. CANNON and N.J. TIGHE, in Ultrafine Grain Ceramics J.J. Burke, N.L. Reid, V. Weiss (Eds.) Syracuse Univ. Press (1970), Chapt. 16. R. PAMPUCH and J. LIS. to be published in Ceramurgia Intern. V.A. PHILLImPS, H. OPPERHAUSER and J.L. KOLBE, J. Amer. Ceram. Sot. 61 (1978) 75. R. PAMPUCH and Z. LIBRANT. J. Amer. Ceram. Sot. 42 (1968) 288. M.C. BALL and H.F.W. TAYLOR, Mineral. Mag. 32 [1961) 754. R. PAMPUCH and Z. LIBRANT. Sci. Papers Acad. Minlng and Metallurgy, Cracow 11 (1969) 45 (in English). R.S. GORDON and W.D. KINGERY, J. Amer. Ceram. Sot. 50 (1967) 8. R. PAMPUCH. H. TOMASZEWSKI and K. HABERKO. Ceramurgia Intern. 1 (1975) 81. N. SOGA and O.L. ANDERSON, J. Amer. Ceram. Sot. 49 (19661 355. B.J. WUENSCH. W.C. STEELE and T. VASILOS, J. Chem. Phys. 58 (1972) 5258. Y. OISHI and W.D. KINGERY, J. Chem. Phys. 33 (19601 905. H. HASHIMOTO. M. HAM0 and S. SHIRAZAKI. J. Appl. Phys. 43 (1972) 4282. J.W. HENNEY and J.W.S. JONES, J. Mat. Sci. 3 (1988) 158. A.J. ARDELL. H. REISS and W.D. NIX, J. Appl. Phys. 36 (1965) 1727.
Received
February
14,
1979:
accepted
March
21.
1979.
76
INTERNATIONAL,
Vol.
5. n. 2.
1979
Mechanisms of Hot Pressing of Magnesium Oxide Powders R. PAMPUCH Institute
of
Materials
Science,
Academy
Estimation of the rate controlling mechanisms of mass transport during the initial, intermediate and a portion of the final stage of hot pressing of powder compacts by an adequate application of the theory of creep of non-porous polycrystals at elevated temperature is first discussed and their significance for understanding of the relations between powder characteristics and their densification during hot pressing stressed. Review of recent developments of the creep theory indicates that if intraparticle (intracrystallite) i.e. dislocation mechanisms are acting to a negligible extent only, the steady-state strain rate 6, should be controlled entirely either by boundary reactions (emission/absorption of point defects at sources and sinks, e.g. at boundary linedefects) or by diffusion between sources and sinks (Nabarro-Herring and/or Coble creep). An analysis has been made in these terms of E observed with well characterised MgO powders, having a rather uniform crystallite size, during hot pressing at 771975K under loads of PA = 60-295 MPa. Two types of powders, obtained by thermal decomposition of Mg(OH), at different temperatures, have been studied, namely i. powders constituted by well-annealed fine crystallites (d = 28-56 nm) showing no lattice microstrains, and il. powders constituted by fine crystallites (25-45 nm) showing appreciable microstrains of the lattice and, consequently, a high density of the line defects. Experimental determination of the stress sensitivity, n, particle sensitivity, m, and true activation energy for creep, Q,, has shown that the data correspond very closely to i, D: P,,*/d in the first, and to i, = PA/d’ in the second case, respectively. The first situation is expected for strain rates controlled by boundary reactions while the second for the ones controlled by Coble creep, respectively. The different rate-controlling mechanisms enable to explain rationally the different densifications obtained under comparable conditions of hot pressing with the two types of MgO powders.
1 - INTRODUCTION
The wide interest in mechanisms and kinetics of mass transport in powder compacts during heating under applied stress, i.e. during hot pressing, resulted from theoretical predictions and practical experience which indicated that hot pressing seems to be the principal means to obtain ceramic polycrystals of full density. Despite the considerable theoretical information about the basic mechanisms for mass transport during hot pressing. the theory finds, however, little application in practice. This is mainly due to the relatively small number of studies made on well-characterized real powder compacts, suitable as model materials to check the predictions of the theory and to allow a demonstration of relations between the mechanism of hot, pressing and the characteristics of powder compacts. The knowledge of these relations is, namely, very important as there is ample evidence in technological practice that the controlled preparation of powders and powder compact is the most vital step of the fabrication cycle for sintered polycrystalline oxides.
of
Mining
and
Metallurgy,
Cracow,
Poland
The author has studied with his collaborators these relations in the case of magnesium oxide powders and powder compacts, and became aware that magnesium ovide obtained by thermal decomposition of hydroxide precursors might be a suitable model material. Although some of the results of these studies have been already published, an appraisal of their significance for an understanding of the relations between powder characteristics and the mechanism of mass transport during their hot pressing was thought timely, especially in view of recent developments in the theory of creep ‘-j.
2 - A SHORT PRESSING
SURVEY
OF
THE
THEORY
OF
HOT
The excellent review by Spriggs and Dutta * of the mechanisms of mass transport during hot pressing, covering the literature up to 1973, pointed out that the kinetics and mechanism of hot pressing are closely related to the mechanism of creep of non-porous polycrystals at elevated temperatures. The well-developed theory and practice of creep of such systems may thus serve as a guide for the estimation of the hot-pressing mechanisms, provided that the porous nature of the hot-pressed powder compacts and the small size of their constituent particles are being accounted for. The irreversible deformation of materials subjected to a constant applied stress, i.e. creep, is a thermallyactivated process and the secondary, or steady-state, strain rate 8, may be formalized for any conceivable mechanism under a given set of experimental conditions by an equation of the form: PR G”4
D
IIll
where A is a constant independent of applied stress and temperature, having dimensions of length, k is the Boltzmann constant, T is temperature, I is a length which may be equated to W’ or - b where n is the atomic volume and b is the Burgers vector, respectively, PA is the applied stress, equal to effective stress uerr acting on the particles in non-porous materials, G is the shear modulus, .d is the particle size. The temperature dependence of the strain rate is included in the diffusivity term, D = DO exp(-Q,/RTl, where Q, is the true activation energy for creep and R is the gas constant. The stress sensitivity n = (3lnhJCJlnP&. r and the particle sensitivity m = -_[31ni/31ndjp4. T have specific integral values for each particular mechariism of mass transport (Table II. Their experimental determination, together with the determination of CL, which has also a specific value for a given mechanism of transport by
MECHANISMS OF HOT PRESSING OF MAGNESIU’M OXIDE POWDERS
I.
Mechanisms controlled by point-defect between sources and sinks 1. Nabarro-Herring volume) 2. Coble
creep
creep
(diffusion
(diffusion
bondaries) 3. Diffusion around particle II.
IV.
lntraparticle
due
to
the
(lattice
1
D‘
I
Db
1
D’ or Db
1
2
Dh or D’
1
1
D’
0
3-5
D
Db - boundary diffusion
coefficient,
ledges
at
particle
mechanisms
Remarks: D’ -volume diffusion coefficient, coefficient in the liquid phase.
2
D’ - diffusion
Typical Name
Definition
- Predicted valuea for the stress (n) and particle (m) sensitivities and diffusion coefficients for different boundary (diffusional) creep mechanisms at elevated temperatures. Values for lattice disloca tion mechanisms are additionally included. (After Ref. 1.31. TABLE I
particle
1
phase
dislocation)
D
3 boundary
liquid
n
the
Boundary-reactions controlled diffusional mechanism (mechanism controlled by emission/ absorption of point defects)
III. Viscous flow boundaries
m diffusion
through
along
77
Determination
dimensions m
IO-‘- IO4
Crystallite
Coherently diffracting region of the lattice
X-ray diffraction line broadening
Aggregate
Compact, nonporous particle composed from crystallites
BET isotherms, electron microscopy
Agglomeration
Loose, porous particle composed from aggregates (or crystallites)
Optical and electron microscopy
virtue of the different diffusibilities entering in eqn. [I] for each mechanism, allows a meaningful estimation of the creep mechanism. In the study of hot pressing there are, however several points which must be taken into account. The steady-state strain rate & under any given conditions increases with increasing porosity which changes during nearly the entire hot-pressing time cycle. This arises mainly through the dependence of the effective stress and of the shear modulus upon porosity. At pore volume fractions V, Z 0.15, beIt and G depend strongly both on V, and the stress concentration factor which is also a function of the (changing) pore shape I. Hence, very complicated correction factors must be introduced in eqn. [I] to account for the porosity. After an initial decrease at small V,, the shear modulus remains, however, constant at V, 5 0.15-0.20 in most celt may be taken for this ceramic materials 6 while range of higher porosities as the applied stress PA divided by the relative density pr ‘. Consequently, for the initial, intermediate, and a portion of the final stage of hot pressing may be used the procedure proposed by McDonough and Spriggs 8, according to which the experimentally derived instantaneous strain rates ii = Acnerr at different porosities may be normalised to the true steady-state strain rate i, at V, = 0. Namely, when (%/3(1/p,)) = const = A% = &. In this way correct stress and particle sensitivities may be obtained from eqn. [I]. In order to calculate the activation energy for creep CL the fact must be taken into account that G z G,, where G, is the shear modulus for non-porous material. The particle size d in eqn. [l] should denote the dimension of the smallest particles of the powder
TABLE II - Constituent particles of powders and powder compacts. (After Ref. IO).
1o-5- IO4
compact the boundaries of which can act as effective source and sink for point defects, since the role of inner sources and sinks (as the lattice dislocations) should be negligible during the short time-cycle of hot-pressing 9. The definitions of the constituent particles of powders and powder compacts are given, according to .Feitknecht and Giovanolli ‘O, in Table II. If non-porous crystallite aggregates occur in the powder compact, d = aggregate size, since the coherent intercrystallite boundaries in such formations are inefficient sources and sinks for point defects. In other, more numerous cases, the crystallite size should be taken as the particle size d. As discussed later, the size of the crystallites, which is much smaller than that of grains in non-porous polycrystals, has important consequences for the specific nature of mechanisms of mass transport during hot pressing in comparison with creep of non-porous polycrystals. It is not necessary to recall in detail that for a meaningful estimation of n, m, and Q, the particle (crystallite) size should not change during the steady-state strain rate period and the particle size distribution should be as narrow as possible. The interpretation of 0, in the case of hot pressing of oxide powder compacts requires also some caution. It became evident that in general the different constituent species of the oxides may diffuse along different paths and it is necessary to use a complex diffusivity term, such as proposed by Gordon ‘I. It may be argued ” that D,‘ > D,’ and DchEcb< D,” 6,” where the index v denotes volume, b denotes boundary, while c and denote, respectively, cation and anion: U’ is the effective boundary width. It has been shown under this assumption that in general four controlling pro-
R. PAMPUCH
cesses
reduced
can and
be the
expected temperature
as the particle Size is is lowered D=‘+Dab sab+
energy for creep + D.’ + Deb6cb“. The true activation Q, = -BalnD/a(l/T) should thus have a straighforward meaning only if the experimental conditions do not cover transition regions between those controlled by a single diffusion constant. If several mechanisms of mass transport, e.g. intraparticle (dislocation) mechanisms, plus diffusional such as Nabarro-Herring and Coble mechanisms, operate independently, i.e. non-sequentially, creep, values of n and m as i. = cj=, i,. j and non-integral well as unpredictable values of Q. should be expected, having intermediate values between the ones for the simultaneously contributing mechanisms. The fact that such results have been obtained in most previous studies of hot pressing of oxide powder compacts has led to the conclusion that several if not all envisaged mechanisms of transport contribute independently to the strain during the entire hot-pressing process I’. This needs not be always so and the author feels that at least some of the values which did not coincide with the theoretical predictions may be attributed to integration over regions controlled by different single processes as well as to an inadequate characterisation of the powder and powder compacts. Let discuss this aspect in more detail. It is plausible to assume that if intraparticle (dislocation) and boundary (diffusional) mechanisms may take place, they should operate non-sequentially and nearly independently of each other. When well-annealed crystallite systems, which do not have a very high density of grown-in lattice dislocations, are subjected to stress and temperature under the usual conditions of hot pressing, the intraparticle (dislocation) mechanisms are not likely to be of importance in ceramic systems. The studies of creep of essentially non-porous oxide polycrystals indicate that these mechanisms to not occur below applied stresses of about 100 MPa ‘. This is not surprising since the dislocation movement in oxides is usually more difficult than in metals owing to their high elastic moduli and the geometrical complexity of moving lattice dislocations through a structure containing more than one species. In several cases there are not sufficient independent slip systems to allow coherent deformation of the system. Diffusional mechanism should be even more important in powder compacts which consist of crystallites, i.e. of particles having a very small size, where the movement of lattice dislocations is more difficult than in the larger grains of polycrystals and the threshold stress to move the lattice dislocations should be here higher than that cited before. Another factor is the usual presence of impurities which should, in general, increase, the diffusibilities and decrease the mobility of lattice dislocations in oxides. Additions of 0.10-8.08 w/o of FelOl have been shown, e.g., to inhibit dislocation creep of MgO polycrystals I3 while an increase of the lattice dislocation density in polycrystalline MgO has been observed only at isostatic Pressures above 400 MPa lb. Hence, a negligible contribution of intraparticle (lattice dislocation) mechanisms may be assumed during hot pressing of ceramic powder compacts, especially at the higher temperatures and at applied stresses usually used, except for isostatic hot pressing under high gas pressure. Now, with any diffusional mechanism two processes occur, namely, the emission/absorption of point defects at suitable sources/sinks and diffusion (through the volume or along the boundary) between sources and sinks. The two processes are clearly sequential and cannot occur independently of each other. For sequential processes I k, = C,=l (l/&J)
and when two latter expression
processes operate may be written
sequentially
the
If the strain rate due to each component process is different, the slower one should control the strain rate and, hence, determine entirely the values of n, m, and Q.. In the original Nabarro-Herring and Coble diffusional creep theory it was assumed that the source and sink operation was easy in which case all the applied stress is available to drive the diffusion fluxes responsible for diffusional creep. More recent studies “-” indicate, however, that even the particle boundaries are not perfect sources and sinks for point defects and some of the applied stress is necessary to drive the boundary reaction (emission and absorption of point defects). From numerous electron microscopic observations made on metals and ceramics “-” it is now known that the particle boundaries have distinct crystallographic features and contain line defects resembling dislocations. Emission and absorption of point defects should thus occur predominantly by climb of the boundary line defects having a component of the Burgers vector normal to the boundary. When the sequential processes of emission/absorption of point defects and their diffusion between sources and sinks are taken into account, one arrives at the expression for the steady-state strain rate: 1
BD
! PJ-l \
5, = d”kT if diffusion the volume
i.=
I 1 + (4BD”nlpbdMdkT)
between ‘, I9 or
sources
and
sinks
1
B’DbGb
[21
is
through
I
E31
P&
d”kT
1 1 + (4B’D%“n/pb:Md’kT)
if diffusion is along the boundary. B and B’ are numerical constants, b, is the component of the Burgers vector normal to the boundary, P is the density and M is the mobility of the boundary line defects, respectively. The remaining symbols have the same significance as before. When the factor in round brackets in [2] and C31 is small, i.e. the density p and/or the mobility M of the line defects are high, the expressions [2] and [31 respectively, to Nabarro-Herring and Coble reduce, creep equations the characteristic parameters of which are given in the 1” and 2”d row of Table I, respectively. Under the opposite set of conditions (low P and M) the expressions [2] and [3] reduce to pbtMP*
l-41
i, = d
Under the assumption that the boundary line defects behave parametrically in a similar way to lattice dislocations the following explicit.expression has been derived for the steady-state strain rate controlled by the (slower) boundary reactions ‘s “: E, =
47rPi(l -v)
(Z-l)
t?p:
A”b=PA’ D=
dGkT where pj is the probability line-defect a site capable a point defect, i.e. the
.
D
[151
dGkT
of finding on the boundary of accepting (or emitting) jog probability; Z is the
MECHANISMS OF HOT PRESSING OF #MAGNESIUM OXIDE POWDERS
coordination number of the ions in the material; v is the Poisson number; D is the coefficient of diffusion controlling the climb rate of the boundary line defects. Recent review on metals suggests that the majorjty of data where eqn. [5] is applicable correspond better to boundary than to volume diffusion coefficients*‘. It follows from eqn. [5] that for boundary-reaction controlled diffusional creep n = 2 and m = 1 (4”’ row in Table I). Owing to the l/d dependence as compared with the l/d” and 1/d’ dependence in case of the creep, respectively, the Nabarro-Herring and Coble importance of the boundary reactions as the ratecontrolling process of diffusional creep should increase with a decreasing particle size. This may be the reason for the common observation that with nonporous polycrystals there is a general trend for coarsegrained materials to exhibit B, 0~ PA/d’ and/or is = PA/d’ relations while with fine-grained materials, e.g. ultrafine grain one finds 24 something closer to ceramics, & = PAZ/d. The latter situation should also obtain on hot-pressing of powder compacts which consist of small-size crystallite% provided no appreciable growth of the crystallites occurs during hot pressing. If it is assumed that the boundary line defects behave parametrically analogous to lattice dislocations, the importance of the boundary-reaction controlled diffusional creep should be greater in ceramic than in metallic systems owing to the generally lower mobility of dislocations (and boundary line defects) in ceramic materials. The process of emission-absorption of point defects at the boundary line defects should give rise not only to non-conservative motion of the defects by climb normal to the boundary but also to glide of the defects along the boundary due to the component of the Burgers vector parallel to the boundary. This brings about a sliding of the particles past each other. On a purely geometrical basis, sliding cannot take in the absence of place in non-porous polycrystals any other process which allows accomodation of the sliding, e.g. by plastic flow or diffusional processes at triple points and at the irregularities along the
200- 7;,gp80 1 960m
NE 7-,1202 m
\ \
crystallite microstrains
_ \ \
size (nm) (hd,,kt/dhkl)
\\ :19;gG&o
E 2 80&J v) I $j 40-
’
20?2$0)
\
“t24;WJ80) ‘< ‘w
I 775
I
I 975
‘\ 148kl~(lOO1‘\ 1 I I 1175 temperature
I 1375
i
(K)
FIGURE 1 Average crystallite size, microstrains in crystallite% and equivalent BET-particle size in MgO BEJ surface area, powders obtained by thermal decomposition of MgCOH), at different temperatures.
79 boundary. If pores are present at the boundaries no extensive accomodation is necessary. Even if accomodation of the particle boundary sliding is required, this may occur by diffusion of atoms (ions) from part of the boundary under compression to another region under tension. An example of such a diffusion, which may play a role with small particles, is the diffusion around boundary ledges with m = 1 and n = 1 (3’d row in Table 1). The diffusional accomodation may occur either through the volume or along the boundary, i.e. in a similar way as in Nabarro-Herring and Coble creep, respectively, but in any case considered here the diffusion path is very short what is favourable for fast diffusional accomodation of the slower particleboundary sliding, accompanying the emission/absorption of point defects, and thus for control of the strain rate by the latter process. It may be thus expected that with the well-annealed fine-particle systems, such as the powder compacts, the situation is favourable for boundary-reaEtion controlled strain rate, especially during the intermediate and a portion of the final stage of hot pressing. This should, however, not apply to hot pressing of internally strained crystallite-systems having a high density of line defects p where [2] and [3] predict Nabarro-Herring or Coble creep controlled processes.
3 - MECHANISMS OF DEFORMATION OF MgO POWDER COMPACTS DURING HOT PRESSING AND THEIR RELATION TO THE POWDER CHARACTERISTICS The results described in this section have been obtained with magnesium oxide formed on thermal decomposition in air of a relatively pure Mg(OHII precursor. The major impurities of the precursor were: Fe below 500 p.p.m.w, and Si below 200 p.p.m.w. Electron microscopic observations have shown that the MgO powder consists of weakly interlinked MgOcrystallite chains” (see also Ref. 26) in which the crystallites have a relatively uniform size. The close agreement of the average size of crystallites, determined by X-rays, and of the equivalent BET particles, calculated from surface area measurements, over a wide range of thermal decomposition temperatures (Fig. I), suggests that the crystallites contact each other along the chain most probably over a very restricted area only and the probability of aggregate formation is low. Simultaneous resolving of the broadening of X-ray diffraction lines into the crystallite size effect and microstrain effect *, by using the method described by Librant and Pampuch “, showed that the crystallites are strained, i.e. contain most probably an enhanced density of grown-in lattice dislocations and boundary line defects. As indicated in Fig. 1 the largest microstrains are observed at the lower temperatures and decrease to zero at higher decomposition temperatures. All these features may be rationally explained by the inhomogeneous mechanism of thermal decomposition of Mg(OH)2 to MgO proposed by Ball and Taylor**. According to these authors the decomposition occurs via coherent MgO domains, formed by counterdiffusion of protons and magnesium ions in an immobile anionic lattice in the Mg(OH), matrix. Under assumption of this mechanism the first MgO crystallite% separated by phase boundaries, should form when the elastic strain energy stored in the system, and due to the different lattice parameters of Mg(OH)* and MgO,
* Microstrains deviation value of
of the dhLI.
are defined as Ad,,,,/d,,, where average interplanar spacing from
Adhti the
is
the
equilibrium
R. PAMPUCH
80
pA 100MPa
Ad/d =0
f- +
-----
------
-I_
- 60
-40
z 5 z
pA 195MPa
- 20 ‘3j E ._
1
,
,
I
5
10
20
30 Time (min)
FIGURE 2 - Crystallite size vs. time of hot-pressing at T, = 975 K of MgO powder compacts obtained by thermal decomposition of Mg(OH), at T, = 975 K. under the indicated applied stresses (after Ref. 31); microstrains are absent.
-30 ,;+_____-------+
2.
Tp=Ts 775 K 0 I’- 10 pA 100 MPa I
I
I
I
I
/
Time (min) size and microstrains vs. time of hot. FIGURE 3 - Crystallite pressing at T, = 775 K of Ma0 powder compacts obtained by thermal decomposition of MgtOH), at T, = 775 K, under the indicated applied stresses (after Ref. 31).
attains a value equal to the surface energy of the MgO crystallites “, Besides the weak interlinking of the adjacent MgO crystallites which most probably form by breaking out from the Mg(OH), matrix “‘, this should give rise to crystallites of a similar size since the elastic strain energy is a function of the dimensions of MgO domains. The first independent MgO crystallites have been found to form at about 625 K. Hence, heating to higher temperatures should result in a progressive annealing of the microstrains with increasing temperature. In the following text the behaviour during hot pressing of two different types of MgO powder compacts shall be considered, namely of compacts consisting of: i. - well-annealed MgO crystallites which show no microstrains, and ii. - MgO crystallites which show appreciable microstrains and hence should probably have a high density ;fefeyt;wn-in lattice dislocations and boundary line The former were obtained by heating Mg(OH)2 powder compacts, cold-pressed under 60 MPa, up to 975 K with a linear rate of temperature rise of 10 K/min and the latter by heating the Mg(OH12 compacts up to 775 K with the same rate of temperature rise. The compacts were subsequently isothermally hot pressed in an apparatus described in ‘I which allowed a continuous monitoring of changes of length of the compacts and thus the determination of L. In parallel experiments the compacts were taken out from the apparatus after succesive periods of time of hot pressing under the given conditions, and their apparent density as well as the crystallite characteristics in compacts were determined. This enabled calculation of the true steady-state strain rate by the already discussed McDonough-Spriggs relation ’ as well as characterization of the changes in crystallites during hot pressing. The’ characteristics of the crystallites for both types of compacts are given in Figs. 2 and 3. After an initial growth, presumably by coalescence due to surface diffusion which is indicated by the d’d,’ = Ct dependence, where C is a constant, t is time, and d, is the initial crystallite size, the average crystallite size attains in all cases a nearly constant value after 10 to 15 minutes of hot-pressing ?? *. This value is specific for each type of powder compact and temperature but is relatively independent of the applied stress at a given temperature. The period of constant crystallite size corresponds to the one of the steadystate strain rate which typically established after 10 to 15 minutes of hot pressing. In both types of MgO powder compacts, at a given hot-pressing temperature, the crystallites have thus a nearly constant size during the steady-state strain rate and most probably also a narrow size distribution since the growth by coalescence is not expected to increase the scatter of the crystallite sizes. In such cases a meaningful estimation of the mechanism of mass transport by using eqn. [I] is thus possible. Owing to the different characteristic of the crystallites as far as the microstrains are concerned, the two types of compacts are, however, expected to show a different behaviour on hot pressing and the results for each type shall be discussed separately. In Fig. 4 is shown a logarithmic plot of the true steady-state strain rate vs. applied stress for the compacts consisting of well-annealed crystallites, at hot-pressing temperatures 775, 875. and 975 K. From the slope of lines connecting the experimental data for each temperature a stress sensitivity n has been
* Except for the experiments and temperature of 975 K the in further analysis. ??
under results
applied stress of of which are not
100 MPa included
MECHANISMS
OF
HOT
PRESSING
OF
MAGNESIUM
OXIDE
81
POWDERS
Dm*/s
t
100
I
56P
I
\\\D' Dcomp\\ db '\
lo"*-
/
oTp775K Tp875 K oTp975K
\
lO-‘O-
n=1.96 b/564$
\
40r n=1.97+0.44 /
??
39v
A9 1' /
\
28
\
t
\ \
286 / n=1.99
DC\
1 0:3
Stress (MPa)
strain rate vs. applied stress for FIGURE 4 - True steady-state MgO powder compacts obtained by decomposition of Mg(OHI, at T, = 975 K and hot pressed at T, = 775, 875, and 975 K. The crystallite size during the period of steady-state strain rate is indicated at the experimental points. After Ref. 31. with correction of some missprints in the original publication.
/I
/ +/
/
/ /
,‘Tp875
I
\D1 creep \ \ \
'\
\
\ I
I
0.6
I
0.6
I
I
I
1
1.0 1.2 lOyT,OK"
FIGURE 6 - Magnesium and oxygen volume diffusion coefficients, surface diffusion coefficient, and Gordon’s complex coefficient for boundary-diffusion controlled creep (divided by the effective boundary width) in magnesium oxide. Further is shown the rate-controlling diffusion coefficient DC,..,, calculated from data for T, = 875 K and MgO powder compacts obtained at T, = 975 K.
obtained which nearly coincides with two at all the three temperatures covered experimentally. The slight spread of data observed is probably due to some variations of the crystallite size (indicated in Fig. 4) with changes of the applied stress. The value of n = 2 is specific for boundary-reactions controlled strain rate only (compare Table 11. It may be thus assumed that the behaviour of this type of MgO compacts obeys the eqn. [5]. In this case the experimental data plotted in logarithmic coordinates: &dT/Gb’ vs. the dimensionless term PA/G should lie along several parallel lines for the different hot-pressing temperatures covered experimentally, provided that A” in eqn. [5] is temperature and stress independent. This situation obtains with the MgO powder compacts discussed here (Fig. 51, which enables one to determine the true activation energy for creep from the sepa,ration of the lines in Fig. 5 since in this case, at a constant value of PA/G and for two temperatures TI and T2.
Tp 975 K;' 0'
I
\
\
K
/I
;,,,d,kT/G,b’ Rln (
&,,dlkT/G,b’
QC = (Tz -
i
2.lo-J
5.10-3
10-c
2.10-2
PAG / FIGURE 5 - Normalised true steady-state strain rate vs. normalised applied stress for MgO powder compacts obtained by decompoT, = 775. sition of Mg(0H)2 at T. = 975 K and hot-pressed et 875. and 975 K. The relative densities of compacts after hot pressing for 30 minutes under the conditions indicated varied between 0.28 end 0.80.
1
161
T,)/T, Tz
In order to construct Fig. 5 has been taken the value of G for non-porous MgO at the given temperature, according to Soga and Anderson 32. The neglecting of the influence of porosity upon G, however, should not give rise to an appreciable error since the ratio of the shear moduli appears in eqn. [6] and the changes of the shear modulus of porous MgO with temperature should be nearly the same as in porous material. The value of the true activation energy obtained from Fig. 5 and eqn. [6] is 194 kJ/mole. It lies between the known activation energies for volume diffusion
R. PAMPUCH
82 of magnesium and oxygen in MgO and the one for boundary diffusion of oxygen (Table III]. No value of the activation energy for magnesium boundary diffusion in MgO has been found in the literature but it follows from general considerations that it should be somewhat higher than that for oxygen boundary diffusion. Hodge. Lessing, and Gordon I3 quote a value of 279 kJ/mole as the upper limit of the activation energy for this case. According to the current views discussed in Section 2, the climb rate of the boundary line defects should be controlled at the low temperatures covered experimentally by boundary diffusion coefficient of magnesium for which the activation energy of 194 kJ/mole seems to be a reasonable one. Rate control by diffusion along the boundary is also indicated by the high value of the diffusion coefficient calculated from steady-state strain rates by using eqn. [53 for the experimentally covered hot-pressing temperatures (Fig. 6). In the calculations the jog probability in equilibrium, p, = IO-‘“, and the Poisson number v = 0,25 have been taken. As usually found in hot-pressing and creep experiments of oxides, it
TABLE III mechanisms
Diffusion coefficient
-
Activation energies for in magnesium oxide.
’
diffusion
n=l.OO+-0.39 *3./N / IO-*
I
I
I
jr*7 fl24
Illll
I
10’
I
I
I
IO2 Stress
( MPa)
FIGURE 7 - True steady-state strain rate vs. applied stress for MgO powder compacts obtained by thermal decomposition of MgfOH), at T, = 775 K and hot-pressed at the same temperature. The crystallite size during the period of steady-state strain rate is indicated at the experimental points.
self-diffusion
Activation energy (kJ/mole]
Source
267.4 261.4 146.5 370.0
33 34 35 36
D’,, Do D”o Ebo D’6” D”- surface
different
*y
-\
v
coefficient.
195 MPa’, \
Y ‘b
is 3 to 4 orders of magnitude greater than the (extrapolated to lower temperatures) volume diffusion coefficients in MgO and lies on the extension of data which correspond to Gordon’s complex diffusion coefficient for the boundary-diffusion controlled case and to surface diffusion in MgO. In the former case an effective boundary width of Eb = IO” m has been assumed and the values of CL and Do” for magnesium and oxygen have been taken from Ref. 13. The vales of n and Q, obtained in the case of hot pressing of well-annealed MgO crystallite systems thus give a consistent picture. Namely, the steady-state strain rate during hot pressing is most probably controlled by boundary-reactions, i.e. by emission and absorption of point defects at the line boundary line defects, the climb rate of which seems to be controlled by magnesium boundary diffusion. Different results have been found for hot pressing of the second type of MgO powder compacts, consisting of microstrained crystallites. The logarithmic plot of a, vs. the applied stress [Fig. 7) gives a slope which corresponds to n = 1 while a logarithmic plot of t, vs. the crystallite size d (for a different set of observations) [Fig. 81 gives a slope which corresponds to m = 3. Thus Coble creep, i.e. steady-state strain rate controlled by boundary diffusion between the sources and sinks and not by the boundary reactions, is indicated for this crystallite system. According to eqn. [3] this should obtain when the density and mobility of boundary line defects are high. Such a situation is very probable indeed with this crystallite system since the crystallites show here appreciable microstrains during the entire hot-pressing time-cycle and consequently should have a high density of both lattice dislocations and boundary line defects.
m=3.08
‘4 ,
3.04
y-n=
100 M$&
I
\
\
'k
‘\
h
I
I
I
25
30
I
35
40
Crystallite
size, d
(nm)
FIGURE 8 - The true steady-state strain rate vs. crystallite size for MgO powder compacts obtained by decomposition of MgfOH), at T, = 775 K and hot-pressed at the same temperature, under applied stresses of 100 and 195 MPa.
4 - CONCLUSIONS It has been tried in the present paper to show in respect to the hot-pressing behaviour of MgO powder compacts that when well-characterized powders and powder compacts are studied a rather consistent explanation of the mechanisms of mass transport is possible in terms of the theory. Some aspects of the relations between the hot-pressing behaviour and the powder and powder-compact characteristics are already evident. Under comparable applied stresses and at comparable temperatures, the control of the strain rate during hot pressing by the boundary reactions with well-annealed crystallite systems should result in lower densities after hot pressing as compared with the ones in the case of compacts consisting of microstrained crystallites where all the applied stress is available to drive the (boundary) diffusion fluxes responsible for the strain.
MECHANISMS OF HOT PRESSING OF MAGNESIUM
83
OXIDE POWDERS
..”
_
~_---
3. 4.
5. 6. 7. 8.
2
9.
E2
l?L
10.
‘0,
4
.
t I
m/
I
195 Applied stress,
100
275
( MPa)
FIGURE 9 - Apparent density vs. applied stress after 30 minutes of isothermal hot-pressing at T, = 775 K of MgO powder compacts obtained by decomposition of Mg(OH)Z at T, = 775 K [curve 1) and T, = 975 K (curve 2).
As an illustration may serve Fig. 9. which shows that the apparent densities obtained after hot-pressing at 775 K for 30 minutes of MgO powder compacts consisting of microstrained crystallites. (curve 1) are much higher * that those found at the same temperature and after the same time for MgO compacts consisting of well-annealed crystallites (curve 2). This applies especially for lower and intermediate applied stresses. Owing to the 6, 0~ P? dependence found in the case of well-annealed crystallites the apparent densities are expected to increase in this case strongly at higher applied stresses. Thus for an efficient application of hot pressing, at least for MgO obtained from the thermal decomposition of Mg(OHL, either highly microstrained crystallite systems at moderate applied stresses or very high applied stresses with well-annealed crystallite systems should be used. The excellent results obtained e.g. by isostatic hot pressing under high gas pressures confirm the latter trend.
11.
12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
25. 26. 27. 28. 29. 30. 31. 32.
REFERENCES 1. B. BURTON, Diffusional Creep Trans. Tech. Publ. Bay Village, 2. J.W. EDDINGTON, K.M. MELTON
33. of Polycrystalline Ohio (1977). and C,P. CUTLER,
Materials,
34. 35
in Progress 36 37
* Although the theoretical density has been not attained in this case, the hot-pressed compacts are here transparent [60 to 70% transmission of light at wave-lengths 700-1000 nm) owing to the very small pore size.
in Materials Science, B. Chalmers, J.W. Christian, T.B. Massalski. [Eds.). Pergamon Press, Oxford (1976) p. 61. A.G. EVANS and T.G. LANGDON, ibid., p. 171. R.M. SPRIGGS and S.K. DUTTA, in Sinterin,g and Related Phenomena. G.C. Kuczynski [Ed.). Plenum Press, New York (19731. p. 369. R.C. ROSSI. J. Amer. Ceram. Sot. 51 (1968) 433. R. PAMPUCH and J. PIEKARCZYK, Papers of the Ceram. Comm. Polish Acad. Sci. Cracow 24 (1976) 7 (in Polish). R.L. COBLE, J. Appl. Phys. 41 (1970) 4798. W.J. McDONOUGH and R.M. SPRIGGS. in Sintering end Related Phenomena, G.C. Kuczynski [Ed.), Plenum Press, New York (1973), p. 417. Ya. E. GEGUZIN and V.I. SOLONSKY. Fiz. Tverd. Tela 6 (1964). W. FEITKNECHT and R. GIOVANOLLI. in Compt. Rend. Journees d’Etudes. Les Solides Finement Divises. J.E. Ehretsman (Ed.), Dir. Docum. franc. Paris (1987). R.S. GORDON, in Mass Transport Phenomena in Ceramics, A.R. Cooper, A.H. Heuer (Eds.), Plenum Press, New York (1975), p. 445. R.S. GORDON, J. Amer. Ceram. Sot. 56 (1973) 147. J.D. HODGE. P.A. LESSING and R.S. GORDON, J. Amer. Ceram. Sot. 66 (1977) 1318. R.M. SPRIGGS and L. ATTERAAS. in Ceramic Microstructures. J.A. Pask, R.M. Fuhath [Eds.), J. Wiley and Sons, New York (1968). p. 701. G.R. TERWILLIGER. H.K. BOWDEN and R.S. GORDON, J. Amer. Ceram. Sot. 53 (1970) 241. T.A. AUTEN and V. RADCLIFFE, ibid., 59 [1976) 249. G.W. GREENWOOD, Scripta Metall. 3 (1970) 1971. Ya. E. GEGUZIN, Fiz. Metall. Metalloved. 36 (1973) 190. M.F. ASHBY. Surface Sci. 31 (1972) 498. W. BOLLMAN. Crystal Defects and Crystalline Interfaces, SPringer Verl. Wien (1973). A.H. HEUER. in Defects and Transport in Oxides, M.S. Seltzer, R.I. Jaffee (Eds.). Plenum Press, New York (1974). discussion. T.G. LANGDON. Mat. Sci. Engng. 7 (1971) 117. H. ‘GLEITER and B. CHALMERS, Progr. Mat. Sci. 16 (1973) 1. A.H. HEUER. R.M. CANNON and N.J. TIGHE, in Ultrafine Grain Ceramics J.J. Burke, N.L. Reid, V. Weiss (Eds.) Syracuse Univ. Press (1970), Chapt. 16. R. PAMPUCH and J. LIS. to be published in Ceramurgia Intern. V.A. PHILLImPS, H. OPPERHAUSER and J.L. KOLBE, J. Amer. Ceram. Sot. 61 (1978) 75. R. PAMPUCH and Z. LIBRANT. J. Amer. Ceram. Sot. 42 (1968) 288. M.C. BALL and H.F.W. TAYLOR, Mineral. Mag. 32 [1961) 754. R. PAMPUCH and Z. LIBRANT. Sci. Papers Acad. Minlng and Metallurgy, Cracow 11 (1969) 45 (in English). R.S. GORDON and W.D. KINGERY, J. Amer. Ceram. Sot. 50 (1967) 8. R. PAMPUCH. H. TOMASZEWSKI and K. HABERKO. Ceramurgia Intern. 1 (1975) 81. N. SOGA and O.L. ANDERSON, J. Amer. Ceram. Sot. 49 (19661 355. B.J. WUENSCH. W.C. STEELE and T. VASILOS, J. Chem. Phys. 58 (1972) 5258. Y. OISHI and W.D. KINGERY, J. Chem. Phys. 33 (19601 905. H. HASHIMOTO. M. HAM0 and S. SHIRAZAKI. J. Appl. Phys. 43 (1972) 4282. J.W. HENNEY and J.W.S. JONES, J. Mat. Sci. 3 (1988) 158. A.J. ARDELL. H. REISS and W.D. NIX, J. Appl. Phys. 36 (1965) 1727.
Received
February
14,
1979:
accepted
March
21.
1979.