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Kinetics of crystallization processes in glass forming melts
Journal of Crystal Growth 48 (1979) 589—599 © North-Holland Publishing Company
KINETICS OF CRYSTALLIZATION PROCESSES IN GLASS FORMING MELTS I. GUTZOW Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria Received 18 July 1979
A survey is given of experimental results concerning the kinetics of nucleation and the mechanism of crystal growth in glass forming systems. The main aim of the review is, however, to correlate the kinetics of overall crystallization processes in glass forming melts with structural changes taking place in the initial melt during crystallization. Detailed investigations of the kinetics of overall crystallization summarized here for a number of phosphate and silicate melts, indicate that even in relatively simple glass forming melts crystallization is in fact connected with considerable molecular (e.g. anionic) reconstructions. It is shown that the kinetics of nucleation in glass forming melts can be described in terms of the more general, transient formulation of the classical theory of phase formation. Experimental evidence on the mode of crystal growth in glass forming melts is summarized, attention being concentrated on data obtained at low undercoolings. The conditions for the predominant manifestation of the basic mechanisms of crystal growth (normal, spiral and via surface nucleation) are considered, accounting for the structure of the initial melts and the state of the crystal/melt interface.
1. Introduction Glass forming systems represent a very convenient
main feature. Typical examples are glasses formed of organic high poylymers, silicate and phosphate systems, as well as chalcogenides (Se, As2S3), which can
model for investigating crystallization processes in undercooled melts. Such investigations may be also of technological interest, since a number of technically important materials, such as glass ceramics, partially crystalline semiconductors, etc., are obtained by direct or induced crystallization of glass forming melts. Considerable experimental evidence has been accumulated in recent years concerning the kinetics of crystallization in complex, multicomponent technical systems as well as in one-component, model glass forming melts. The available experimental data refer both to the time dependence of the two basic parameters of crystallization nucleation and growth and to the source of the overall crystallization process. From the fundamental point of view the results obtained for simple model glasses are of main interest, It is well known, however, that even the simplest one-component model glass forming melts have a complex structure, complicated associative, or polymeric molecular or anionic building units forming its
be described as inorganic polymers. It must also be pointed out that even in seemingly simple glass forming melts, processes of aggregation or association (e.g. due to hydrogen bonding) also lead to complicated structural elements. The complexity of the anionic or molecular structure has repeatedly been considered as a necessary condition for glass formation [1] and a number of authors (see e.g. refs. 2,3]) have treated polymerization, aggregation or association in the melt as an indispensable step in the process of vitrification of undercooled melts; it has also been shown [4] that polymeric structural units or additional association processes are a requisite in order to explain the temperature dependence of the thermodynamic functions of vitrifying systems. Condensed phosphates especially alkaline glasses are a classical example of glass forming systems where high temperature anionic polymerization equilibria are frozen-in [5—7]. The latest experiments have also proved the anionic polymer distribution in silicate glasses [9,10]. As the crystalline substances corresponding to simple glasses consist of structural
—
—
—
—
589
I. Gutzow / Kinetics of crystallization processes in melts
590
species of only one molecular or anionic type, it is to be expected that crystallization, even in the simplest glass forming systems, may be connected with considerable molecular or anionic reconstructions, as it was proved for the first time, years ago, in the case of sodium phosphste glasses [11 13]. The main aim of the present review is to correlate the kinetics of crystallization in glass forming melts with the structure of the corresponding systems. Thus the kinetics of the overall crystallization are compared with the molecular changes taking place in the ambient melt, and the mode of growth is juxtaposed with the structure of the melt/crystal interface for the corresponding substance. In considering the kinetics of crystallization processes, particular attention is paid to the non-steady-state effects [14,15] in the kinetics of nucleation which, as indicated in refs. [16,17], are of prime importance at phase transformations in glass forming systems. 2. Kinetics of nucleation and the course of overall crystallization By its very physical nature nucleation is a nonsteady-state process. This is due to the circumstance that the formation of a critical nucleus consisting of ~k molecules proceeds via a chain reaction, each step of which is determined by the incorporation (or separation) of an ambient phase molecule into the growing subcritical complex of the new phase. It is evident that in the absence of subcritical clusters capable of further growth (athermal nuclei) a certain time r must elapse before a steady-state distribution of clusters is established and the rate of nucleation 1(t) has reached its steady state value jo~This more general, transient formulation of the theory of nucleation has been given by Zeldovich [14] and Frenkel [15]; a survey of its basic premises may be found in ref. [16—18]. Following an approximate solution of the nonsteady-state nucleation problem given by Zeldovich himself [14], the momentary rate of nucleation 1(t) cam be expressed as
2
T
=
const. X (Tm/L~T)(13/71).
(2)
Here i~XT= Tm T denotes the undercooling, i.e. the thermodynamic driving force of the crystallization process in the melt, while its viscosity ~ is the redproce measure of the self-diffusion coefficient in the same system. The dimensionless factor 13 accounts for the incorporation hindrances across the nucleus/melt phase boundary; it is dependent on the complexity of the melt structure and on the mode of growth of the crystalline nucleus [16,18]. Usually the steady-state rate of nucleation is defined as (see also refs. [16,18]): 2), (3) = const. X (13/ri) exp(—K/Tz~T —
the constant K being determined mainly by the value of a, the specific surface energy at the crystal/melt interface. Once I~and rare known, the kinetics of the whole nucleation process can be evaluated. The numberN(t) of nuclei formed within the time interval 0, t per unit volume of the melt is given by N(t)
=
f
1(t) dt.
(4)
By accounting for eq. (1) or for the above-mentioned more accurate solutions, N(t) dependencies are obtained having a trend similar to that represented in fIg. la for the kinetics of induced nucleation in one or our basic model systems sodium metaphosphate NaPO 3 (Graham’s glass). This figure also shows the high values of the non-steady-state induction periods, as expected according to eq. (2) in glass forming substances in the vicinity of the temperature of vitrification Tg, where i~values up to l0~’— 1012 Poise are possible (for NaPO3 Tg = 275°C).Nonsteady-state effects of the same magnitude also determine the induction periods in the growth [16] of —
(1)
crystalline melts (fig. spherulites lb) and may in the considerably volume of influence glass forming the
r being the above-mentioned non-steady-state time lag. For considerations of a more or less quantitative
kinetics of the overall crystallization [21]. The overall crystallization kinetics of an under-
I’
‘=
I o exp~ r,It)
nature, as intended here, eq. (1) is of sufficient accuracy. A more precise solution can be found in ref. [19] as well as in the literature cited in ref. [16,18]. It can be shown [16] that in the case of an undercooled melt
~—
I. Gutzow /Kinetics of crystallization processes in melts
wherebx2/6.
_________________
I
~
(or Ifonathermal its surface) nuclei prior havetobeen the crystallization formed in the treatmelt ment, to the rclassical 0 is to expression be expected (5); however [24] andwith eq. (6) an expoleads
°
12,0
nent n reduced by unity, and the factor a depending
.
302°
as a ‘-~N
S _____________________
0
200
400
~
600
t (mm) 332° 326°
~
b
~
1:
313° ______________________________________ 0
200
400
600
800 t (mm)
Fig. 1. Non-steady-state kinetics of nucleation and growth in the induced crystallization of NaPO3 melts [16,201. (a) N(t) curves of nucleation of Na3(P309) spherolites on Ir crystallization cores at two temperatures (in °C); (b) growth of Na3(P3O9) spherolites formed around Pt cores: electron-microscopic data giving mean diameter ~ of spherolites depending on time t.
cooled melt is usually described in terms of the Kolmogorov—Avrami equation [22,23] 1). (5) co(t)In= this 1 exp(—at’ equation, cs(t) is the degree of crystallization at time t, n = 1, 2, 3, 4 is an integer depending on the dimensionality of growth of the crystallization centers, and a J~g’~~ is determined by the rates of steady-state nucleation J~and crystal growth g. In principle ca(t) is defined as a(t) = V(t)/V 0 from the volume V(t) crystallized at t and the initial volume V0 of the melt, and may be experimentally determined by the change of each parameter of the crystallizing system, depending on the crystal/melt ratio. It can be shown [21] that in a first approximation, transient nucleation would cause a simple shift of the ct(t) curve along the t-axis, so that 0, for 0 ~ t ~ bT, $t) = 5] for br ~ t <°°, (6) l~1 exp[—.a(t br)’ —
,
—
—
591
0g°~ on the number of active athermal crystallization centers N0. The kinetics of the overall crystallization process, taking place in a more or less finely dispersed initial phase (an assembly of molten droplets or samples of glass semolina, dust particles, etc.), should be described in terms of the mathematical formalism of topokinetic processes developed by Mampel [25] and Todes [26] (see also Young [27]). The ct(t) curves expected according to this treatment (which considers nucleation and growth from the surface of each particle) display an S-shaped trend
similar to those determined by eq. (5). No explicit general formula is possible, however, in the case of topokinetically determined crystallization; thus the analysis of the experimental results is given in the next section in terms of eqs. (5) and (6) even when crystallization of glass semolina is considered. It is taken in mind, however, that in such a case the integer n and the coefficient a become complicated functions of the mean radius R of the crystallizing particles, as it is discussed in ref. [271. 3. Experimental evidence on the overall crystallization kinetics A great variety of techniques (e.g. dilatometric measurements, quantitative X-ray analysis, DSC, etc.) have been used to determine the degree of crystallization. Here, however, only those methods are discussed which are of more or less methodical interest, providing moreover a direct possibility to follow the structural changes in crystallizing samples. Fig. 2 shows the course of crystallization in two model glasses determined by picnometric measurements. In such a case t~(t)can be determined as ~(t)
=
(p(t)
—
Po)/(Pm
—
P0)
(7)
Po, p(t), and Pm being the initial (glassy), the momen-
tary density line) (partly of crystalline), the samples, andrespectively. the final (fully In these crystaland
I. Gutzow / Kinetics of crystallization processesin melts
592
0
NaPO3, t [mirs] 160 240 720
80
U
2,5050 Z5000
Nci
2Si03
~~ 100
520
30’
______
2
~2. 54 50
~g2.54O° ztj 2.5350
,~
•
0
________________
‘T”~~’’~ .~
50 ~IIII
Q tLJ .~ zI.....
120
240
360
Na2 S103
, t
420
______________________
0
120
240
360
[mm]
420
(t-C~)[mm]
Fig. 2. Picnometric determination of the kinetics of overall crystallization in glass forming systems [29]. (a) Density versus time curves: (1) crystallization of NaPO3 at 330°C;(2) surface crystallization of sodium silicate glass at 520°C.(b) Crystallization of Na2SiO3 at different temperatures (°C)in coordinates n(t) versus (t — r0). Samples in both cases: glass semolina with d = 0.75— 1.00 mm.
further experiments described here (figs. 2 to 7) samples consisting of a great number of more or less finely ground glass semolina (with a mean diameter d indicated for each experiment) have been used [11, 13,28,29]. Under the described experimental conditions the individual crystallization process, taking place in each semolina particle, is averaged over the whole sample and very reproducible results are obtamed. Detailed microscopic observations indicate
gravimetry can be applied in determining cs(t) since crystalline LiPO3 is insoluble, while glassy LiPO3 is easily dissolved in water [30]. Li PU3 1.06°
-
of thecrystallization that particles (i.e.is this always is a typical initiatedMampel—Todes at the surface topokinetic process).
50~II-~-
0
The devitrification in rapidly quenched glass samples, as it is the case of the sodium silicate glass in fig. 2 (59 mole% Si02, 41 mole% Na20, quenched from 1300°C to room temperature), is preceded by a frozen-in high temperature values of p reaches the equilibrium process relaxation density of (atthet
385°
120
240
Cd
360
t[minl
(~o3)2
_____________________
500°
490°
-~
~
~ 50
/.80°
,
®.
—
0
21.0
480
720
I [miri] Fig. 3. Kinetics overalltemperatures crystallization metaphosphate melts atofdifferent (°C). in (a) LiPO3 according to gravimetric determinations [301;(b) Cd(PO3)2 picnometric measurements [28]. In both cases: glass semolina with d = 0.5—0.6 mm.
593
I. Gutzow /Kinetics of crystallization processes in melts
The crystallization product of Graham’s glass (NaPO3), i.e. the cyclic Na3(P309), differs so much from the anionic structure of the initial melt that a striking variety of methods can be applied in order to determine the degree of crystallization: analytical determinations [11] (here both the glass and the crystal are water soluble), quantitative IR [13] or Raman [31] spectroscopy, as well as filter-paper chromatography [13,32]. The crystallization of glass semolina NaPO3 sampies (figs. 2a and 4a) is initiated at the grain surface and follows the typical Avrami curves without induction periods; in coordinates log log[(l ~—a)’] versus log t satisfactory straight lines with n 2 (for ~ = 0.75—1.0 mm) are obtained. However, quite different results are reported by Westman and Krishna-Murthy
~ 50
310’
0
120
240
should be expected for a change from crystallization on preexisting athermal centers (on the active surface of glass smolina grains) to an overall crystallization process with thermal nucleation and a shift along the t-axis due to non-steady-state nucleation effects according to eq. (6). In accordance with the predictions of the Mampel—Todes treatment, a decrease in n is observed when the mean diameter of the crystallizing glass semolina samples is increased [11,29]. This effect can be seen also in fig. 5 where n decreases from n 3 for d = 0.5—0.6 mm (Cd(P03)2 melt) to n 2 for d = 0.75—1.0mm (NaPO3 melt). Thus the change in the crystallization kinetics shown in fig. 4 is not due to
‘“‘3.0
360 t [mm]
____________
~
~25 C)
500°
/0
,
I
/
/.90°
~ 1::
2~
Cd [PU3] 0
120
240
360
t[min]
Fig. 4. Kinetics of devitrification of NaPO3 melts at different temperatures (°C).(a) Glass semolina (d = 0.75—1.00 mm), IR measurements [131. (b) Glass beads with intact surWestman and Krishna-Murthy face quantitative filter-paper [32]. chromatography according to
2 I
2~
b
.1.,..
2,5
3,0
log t Fig. 5. Kinetics of devitrification 1] versus of metaphosphate log t. (a) Data from meltsfig. in 4a; (b) data from fig. 3b. coordinates log log[(1 — al’
I. Gutzow / Kinetics of crystallization processes in melts
594
differences in the grain diameter, but it is caused by
the Na different picnometric state determinations of the grain surface. (fig. 2a) The indicate also of of that no measurable (as inresults the case the crystallization 2SiO3) is involved ofvolume NaPO3. in relaxation the time lag observed in
MO Di
IRM IRI
4. Anionic reconstructions in phosphate and silicate glasses The structure and structural changes taking place in the crystallization of simple water soluble glass forming phosphate melts can be instructively visualized by filter-paper chromatography. Detailed descriptions of this method, of its possibilities and limitations may be found in refs. [5—7,13] and especially in ref. [8]. Samples of the original glass as well as of partially or fully crystallized material are dissolved in appropriate chromatographic solvents which can be chosen in such a way as to be complementary in their separation possibilities and applications [13]. Highly polymerized anions having a degree of polymerization x> 10, remain on the starting point of the chromatogram (H/po on fig. 6) whereas oligophosphate anions (x < 10) with linear or cyclic structure can be determined using reference or test substances, In alkaline phosphate melts (e.g. when glasses from the system NaPO3/Na4P2O7 are obtained from the perspective hydrogen phosphates) polycondensation processes of the types 2 Na2HPO4 + NaH2PO4 ~Na3P3O10 + 2 H20, 3 NaH2PO ~ Na3(P3O9) + 3
~
(8) (9)
determine the formation of linear (Na~P~O3~÷i) and cyclic (Na~P~O3~) anions. The mean degree of polymerization of linear anions in the resulting glasses can be expressed [5] as = 2/(Na/P 1) , (10) .~
TIM
II!iIIltpIII
H/~0 ~ —
I I II III IV V VI Fig. 6. Anionic composition change of NaPO3 glass semolina samples (d = 0.75—1.00 mm) during heat treatment at 320°C as revealed by filter-paper chromatography [13]. T, chromatogram with reference substances; I, initial glass; II, after 20 mm heat treatment; HI, after 80 mm; IV, after 140 mm; V, after 200 mm; VI, after 360 mm; Mo, monophosphate anion; Di, diphosphate; Tn, triphosphate; TRM, trimetaphosphate; TTM, tetnametaphosphate; H/po, high polymers.
Na3(P309)) in sodium phosphate glasses also depends on the Na/P ratio, decreasing from 8 to 10% for Na/P = 1 (in Graham’s glass, cf. fig. 4) to 1 to 2% for Na/P = 1.4 to 1.5. According to eq. (10) for sodium ,metaphosphate NaPO3 (Graham’s glass).~ should be expected. However, traces of residual water content reduce ~ in NaPO3 to approximately 300 [11]. The devitrification of sodium metaphosphate NaPO3 is in fact, as shown by analytical, chromatographic and IR determinations, a change from linear to cyclic anionic structure [11,13]. Upon heat treatment the amount of the cyclic Na3(P309)is gradually increased (figs. 4 and 6). The cyclic anions are formed from the long chains according to the scheme —~00
NO
o.’.~
~.o
ON.
~
NO 0 0
p 00
ON.~ 0
~
0
0 0 0
NO 0 ()
P
ON~
0 ON. ON,
00
‘,,~
N.~0
I’
0
P
0
—
~ON~
O
N,,O NO 0
ON. ~
P
ON.~
0
0 NP). NO
~
~
ON.~
ON p
P i
I’ -o ON, ON~
I
—
where Na/P is the molecular ratio of sodium to phosphorus for the given alkaline glass composition. Experimental data obtained by a number of authors [5—7] confirm theoretically calculated chain length distributions of linear anions [5,9,10], revealing moreover that the percentage of cyclic anions (mainly
00
o~
0
ON.
~
~O
O~\)._~
ON. ON.
0
o
NO)
o~ O~
o,
—
))
I, ON
(11)
I. Gutzow / Kinetics of crystallization processes in melts i.e. the chains of the (P
close again at the points of separation
309) rings [13]. A similar anionic decomposition takes place in the crystallization of another metaphosphate Mg(P03)2 where, however, the —
~
~
~
—
U,
~
I
I
595 I
I
I
I
I
5p
I
_____________
______________
________
____________
—
—
Mg2(P4012) is formed [33]. Glassy LiPO3 consists of chain polymers of rather 3” size anions (fig. 7); thus is in some medium (as compared withit NaPO3) and aspects of cyclica (P309) structural analogue of vitreous NaPO 3. However, the crystallization of LiPO3 is connected with just the opposite structural change: upon crystallization the mean degree of polymerization of already existing anionic chains is increased and cyclic polymers are transformed into linear chains [30], a water insoluble asbestos-like crystal being the result. Structural changes, similar to those observed in the crystallization of LiPO3, are also typical for most metaphosphates of bivalent metals (Cd(P03)2, Zn(P03)2, Ca(PO3)2, etc., seee refs. [34,35]. The anionic composition of pyrophosphates of bivalent metals also differs markedly from the respective crystals, where only one anionic structural element has been found. An example in this respect gives fig. 8, drawn according to results of filter-paper chromatography performed by Schulz and Hinz [36]. Considerable and very instructive structural tetrameric ring
‘4
~
—
~
0~ _______________ I
_______________
z
2 (I)
—
I
c~
~
_____
N — U,
_____ _~
z
_______________
________________
_________
______________
2
4~.I Z
6 L AS S
C RY
—
SI A L
Fig. 8. Anionic of pyrophosphates bivalent metals (as glassescomposition and as crystals) according to of filter-paper chromatographic data of Schulz and l-Iinz [36].
changes have been reported in the crystallization kinetics of glass forming melts from the system NaPO3/Na4P2O7 [11,13]. For glasses with Na/P< 1.3 (i.e. for compositions of the NaPO3 side of the respective eutectic, cf. [5]) the initially formed crystalline phase is again the cyclic Na3(P309) (fig. 9). The kinetics of crystallization follow the sigmoid Avrami course. However, the maximal percentage of Na3(P309) reached decreases with increasing the Na/P ratio as predicted by the phase diagram [37]. For Na phosphate glasses having Na/P> 1.3 (i.e.
—
MO~
for the Na5P3O10 side of the eutectic) the chain-
DI~
TPI TIM
w Nci/Prl,00
I
No/P ~1,12
~
100~:\=ø-L~-
__ Na/P =1.25
I.-.
~50
______
\No/P.1,L2
I
I
II
III
0
120
21.0
‘
360
t [mm] Fig. 7. Composition change of LiPO3 samples [30] (filterpaper chromatograms). 1, reference substances; I, initial glass; II, glassy part of 50% crystallized sample; III, completely crystallized sample.
Fig. 9. Kinetics of Na3(P3O9) formation in devitrifying sodium phosphate glass semolina samples (d = 0.75—1.00 mm) with different Na/P ratio at 330°C[37].
I. Gutzow / Kinetics of crystallization processes in melts
596
MOU iIIItIUIii,~
~IIIlIwIIHIIII~ ~~IIiim~ u~IIm,ll~. ~
~IlIIUII~III~tIIIIIftuIv’ •~II~llIIIIJ~Ii~~
T:~.~M~u ~
.• IIIIIh~.
l~-~——.—I—...u
TRM•II.~ TTM
~
Fig. 10. Filter-aper chromatograms of hexaphosphate glass (Na
8 P6 019, i.e. Na/P = 1.33) semolina samples (d = 0.75—1.00 mm) with different time of heat treatment at 330°C.T, reference substances; I, initial glass. Heat treatment: II, 20 mm; iii, 40 mm; IV, 60 min;V, 80 mm, VI, 140 mm, VII, 160 mm, VIII, 180 mm; IX, 200 mm; x, 360 mm. I—Ill, formation of linear Na3P301 o; IV—VIII, formation of cyclic Na3(P309); IX, X, complete crystallization [13].
polymeric Na3P3O10 (having Na/P = 1.65) is observed as the first crystalline phase [12,131. As a result of the Na3P3O10 crystallization the Na/P ratio in the residual melt decreases, while the average number chain length is increased (fig. 10). It is assumed that polycondensation reactions of the type + S 1x ~2(x+1)— 2(x+2)— + r~23x+1 Slx+lO3x+4 (12) ~3l’J4 take place in silicate melts of bivalent cations, si~O~~j’~ representing silicate anions where x is an integer ranging from to to The theoretical chain length distributions of silicate melts and glasses have °°.
Wt./.Sias
____________
_____________
‘~
_______
V________
—
:
~ , SiO~
—
zlO
Z
POty;~
<
been established years ago [9,10]. Their experimental verification became possible only after it has been shown that silicate anions can be extracted from the respective glasses in the form of their trimethylsilyl derivatives, which can be separated and determined by gas—liquid chromatography [38]. A special type of filter-paper chromatography of silicates has been alsoProcesses developedof[39]. anionic reconstruction, similar to those already discussed for phosphate glasses, are also typical in silicate melts. For example, glassy Pb 2SiO4 is constituted of different polysilicate anions. The corresponding high temperature crystalline modifica-
___
_____
dimen~ Units
0 ______________
GLASS
________________
—
120
240 1440 t [mm]
CRYSTAL-M1
Fig. 11. Composition of vitreous and crystalline Pb2SiO4 according to Gdtz, Hdbbel and Wicker [39].
Fig. 12. Changes in the anionic structure of devitrifying Pb2SiO4 samples (at 500°C) according to Gdtz, Mason and Castelliz [38].
I. Gutzow /Kinetics of crystallization processes in melts
597
tion consists, however, only of SiO~anions (as in the case of bivalent metal pyrophosphates, fig. 8) (fig.
of an idealized metallic melt or to the case of rigid inorganic network polymers (such as Si02, Ge02 or
11). During the crystallization of Pb2SiO4, anionic redistributions similar to those in alkaline phosphate glasses (cf. fig. 10) can be observed (fig. 12).
P205) which, from a thermodynamic point of view [4] may be also considered as “simple” liquids. A situation closer to reality may be expected when the crystallization of anionic polymers discussed in the foregoing section is confronted with a model describing the crystallization of chain-folding organic polymers with a high degree of polymerization (fig. 13d). However, these two simple models correspond only to two extreme cases of melt crystallization processes. In between these to limiting cases a great variety of reconstructive crystallization mechanisms is possible, which may be provisionally classified in the following way: (i) A low molecular crystal is formed (e.g. the case of NaPO3, Mg(P03)2) from the equilibrium polymeric distribution in the melt. Only a small amount of “crystalline” structural units is present in the initial melt (fig. 13b). (ii) The ambient melt, consisting of different mo-
5. Structural considerations and the mode of growth
It is obvious that the complicated structural chemistry of crystallization in the discussed and in similar systems must be taken into account when crystallization processes are compared with clasical theoretical models, describing mainly an undercooled melt as a loose random packing of equal spheres (fig. 13a). This model may apply directly only to the crystallization
000000 000000 000000 000000 000000
0~~0
!~.
~
lecular (or anionic) species with relatively low degree
~
b
~.I :
§P~....
d
•
melt/crystal
Fig. 13. Schematic representation of melt crystallization of substances with different structures. (a) Simple melt crystallizing without structural change (metals, inorganic network polymers). (b) Crystallizatmon with structural reconstruction (first type): formation of low-molecular crystal from polymer melt (“crystalline” cyclic structural units are shadowed). (c) Second type of structural reconstruction upon crystallization: formation of high polymeric crystal from low polymeric melt (cyclic structural units are shadowed again). (d) Crystallization of chain folding organic polymer.
in polymerization LiPO3 or in Cd(P03)2) crystallize to give a linear of (e.g.(fig. of linear high polymeric crystal 13c). and cyclic anions, as The schematic representation in fig. 13 includes all the above cases of melt crystallization: (a) crystallization of simple melts without reconstruction (including network polymers); (b), (c) reconstructive crystal. lization (eventually representative also for organic melts with hydrogen bounded associates); and (d) crystallization of high polymeric substances without noticeable molecular decomposition. as Existing experimental in two recent data reviews on the [40,41] of lead growth to thesummarized following conclusions, when themode mechanism of crystallization is compared with the four types of models presented in fig. 13. (a) Normal (or continuous) growth is the only possible mechanism for the simplest metallic or molecular substances with low entropy of melting (most of the metals, CBr4, cyclohexanol [40]) as well as for typical inorganic glass forming network polymers (sicl2, Ge02 [41]). (b) Spiral growth is typical for all organic glass forming substances with high entropy of melting (where possible hydrogen bonding can be expected —
598
I. Gutzow / Kinetics of crystallization processes in melts
e.g. thymol, salol, etc.) as well as for inorganic anionic polymeric glass formers, such as NaPO3, LiPO3 and Na2Si2O5, where a process of reconstructive crystallization hasbeen observed, By using elaborated experimental methods providing dislocation-free ideal crystals, the surface nucleation mechanism of growth of such substances with high entropy of melting is also possible, as verified by capillary technique in some cases (thymol, Na2S2O5 5H20, etc., see ref. [40]). Some metals (e.g. Ga) with possible melt association may also be included in this group. (c) The surface nucleation mechanism of growth is the predominant mode of crystallization for chain folding organic polymers. This follows from growth experiments at low undercoolings (see, e.g., the case of polyethylene [42]), from the temperature dependence of growth at high undercoolings [43,44] as well as from theoretical estimates [45—47],according to which surface nucleation is the most probable (or even the only possible) crystallization mechanism for chain folding polymers. Additional evidence in this respect is provided also by the experimentally verfied dependence of lamellar step heights in the bulk crystallization of organic polymers [45]. The mode of growth of a crystal depends on the state of the crystal/melt interface and the above mentioned experimental findings simply indicate that structural difference (or similarity) existing between the melt and the corresponding crystal also affects the predominant state of the interface. The thermodynamic measure of melt/crystal dissimilarity is the molecular entropy of melting ~m which, in the case of reconstructive crystallization, always has relatively high values, guarantying according to the existing concepts in the theory of crystal growth (cf. literature cited in refs. [40,41] the discontinuous (spiral or surface nucleation) mechanism of growth of substances crustallizing with molecular reconstructions. When considering the process of nucleation in undercooled melts, it is to be expected that for substances with reconstructive crystallization, very low 13 values (in eqs. (2) and (3)) should be obtained. This is in fact an experimental finding in the case of NaPO3 [20], where 13 = l0_6_lO_4 has been found. Such findings could possibly give a quantitative explanation of the kinetic stability of undercooled melts with more or less complicated structures, as
required by the already mentioned crystallographic criteria [1] for glass formation. In this connection it should be mentioned that according to the definition of 13, as given in refs. [16,17], values of this factor close to unity are to be expected for simple, easily crystallizable, molecular melts with diffuse melt/crystal interface and “liquid-like” growth kinetics (e.g. for CBr4, cyclohexanol, etc. [40]).
6. Discussion The main problem arising from the more or less detailed discussion of the “chemistry” of crystallization presented here, is to determine how the processes of molecular (or anionic) reconstruction are connected with the purely ‘physical” kinetics of the crystallization process. Two hypothese are obvious in this respect: (a) Crystallization begins only when processes of molecular (or anionic) rearrangement in the initial melt have led to some critical concentration of the crystallizing structural species. Crystallization begins only after chemical (or molecular) rearrangements have been completed. (b) The initial equilibrium (or frozen-in) distribution of molecular (or anionic) species in the ambient melt is violated by the crystallization process taking place in the system. Composition changes follow the kinetics of crystallization, as one of the components of the metastable equilibrium distribution in the melt precipitates onto the crystal. The present author has the feeling that the experimental evidence given in the preceding sections especially as far as phosphate systems are concerned strongly supports the second hypothesis. This is verified (i) by microscopic observations indicating that a perceptible change of the anionic composition may be detected only after measurable crystallization has occurred; (ii) it should be mentioned that the change of the molecular composition (e.g. the additional formation of NaPO3, fig. 4) follows under isothermal conditions the time dependences predicted by a mechanism of nucleation and growth (eqs. (5) and (6) or the topokinetic formalism of Mampel and Todes) i.e. by the crystallization process itself. The induction period observed in the formation of cyclic NaPO3 (fig. 4b) fully corresponds to that determined —
—
I. Gutzow / Kinetics of crystallization processes in melts
experiments (fig. 1, see also refs. [16,20]); (iii) no anionic changes can be observed during heat treatment even of non-equilibrium, glassy NaPO3 or LiPO3 condensates [48] before the from crystallization
—
—
proper crystallization process has started. (In the investigation [48] vacuum-quenched vitreous NaPO3 condensates without measurable content of cyclic Na3(P309) have been reported. It seems also that there are no changes in the anionic composition during the process of volume relaxation, as observed in the case of Na2SiO3 (fig. 2a and ref. [29]) or with glassy condensates [48].
References [11 G. Hägg, J. Chem. Phys. 3 (1935) 42. [2] P.P. Kobeko, Amorfnye veshtchestva (lzd. Akad. Nauk SSSR, Moscow, 1952) pp. 28—120. [3] V.V. Tarassov, Novye Voprosy Fiziki Stekia (Moscow, 1959) pp. 1—50. [4] I. Gutzow, in: The Physics of Non-crystalline Solids, Ed. G.H. Frischat (Trans. Tech. Publications, Aedermansdorf, Switzerland, 1977) p. 356. [51J.R. van Wazer, Phosphorus and its Compounds, Vol. 1 (Interscience, New York, 1958). [6] A.E.R. Westman and J. Crowther, J. Am. Ceram. Soc. 37 (1954) 420. [7] H. Grunze, Silikattechnik 7 (1956) 134. [8] H. Grunze and E. Thio, Sitz. Ber. Deut. Akad. Wiss. Berlin, Kl. Math. AIIg. Naturwiss., No.5 (1953). [9] P. Baltà and E. Balni, Introduction to the Physical Chemistry of the Vitreous State (Abacus, Tunbridge Wells, Kent, UK, 1976) pp. 69—107. [101 C.R. Mason, in: Glass ‘77, Proc. 11th Intern. Congress on Glass, Prague, 1977, Vol. 1, Ed. J. Gdtz (CVTS— Dum Techniky, Praha, 1977) p. 3. [11] I. Gutzow, Z. Anorg. AIlg. Chem. 302(1959) 259. [12] V. Gottardi and G. Bonetti, Vetro e Silicati 3 (1959) 31. [13] I. Gutzow, in: The Structure of Glass, Vol.6, Ed. E.A. Porai-Koshits (Consultants Bureau, New York, 1966) p. 154. [14] J.B. Zeldovich, ActaPhysicochim. URSS 18(1943)1. [15] J. Frenkel, Kinetic Theory of Liquids (Dover, New York, 1955) p. 398. [161 I. Gutzow and S. Toschev, in: Advances in Nucleation and Crystallization SW. Freiman (Am. Ceram. in Glasses, Soc., Eds. Columbus, L.L. Hench OH, 1971) and p. 10. [171 I. Gutzow, Comtemp. Phys. 20 (1979). [18] S. Toschev and I. Gutzow, Kristall Tech. 7 (1973) 43.
599
[19] D. Kashchiev, Surface Sci. 14 (1969) 209. 1201 I. Gutzow, E. Popov, M. Marinov and S. Toschev,Kristall Tech. 3(1968) 37, 337,485. [211 1. Gutzow and D. Kashchiev, in: Advances in Nucleation and Crystallization in Glasses, Eds. L.L. Hench and S.W. Freiman (Am. Ceram. Soc., Columbus, OH, 1971) p. 116. [22] AN. Kolmogorov, Bull. Acad. Sci. URSS (Sci. Math. Nat.), No. 3 (1937) 355. [23] M. Avrami, Chem. Phys. 7 (1939) 1103; 8 (1940) 212; 9(1941)177. [241D. Kashchiev, Surface Sci. 18 (1969) 389. [25] K. Mampel, Z. Physik. Chem. A187 (1940) 43, 235. [26] O.M. Todes, Zh. Fiz. Khim. 14(1940)1224. [27] D. Young, Dedomposition of Solids (Pergamon, Oxford, 1966) ch. 2. [28] I. Gutzow, Silikattechn. 20 (1969) 159. [29] I. Gutzow, D. Sawow, Z. Belitshanska and S. Gutzow, Annuaire Inst. Chim. Technol. Sofia 8(1961) 81. [30] 1. Avramov, R. Paskova, B. Samouneva and I. Gutzow, Phys. Chem. Glasses 20(1979) 91. [31] G.J. Exarhos and W.M. Risen, Jr., J. Am. Ceram. Soc. 57 (1974) 401. [32] A.E.R. Westman and M. Krishna-Murthy, in: Symposlum on Nucleation and Crystallization in Glasses and Melts, Eds. M.K. Reger, G. Smith and A. Insley (Am. Ceram. Soc., Columbus, OH, 1962) p. 91. [331Y. Abbe, K. Mon and A. Naruse, Yogyo-Kyokai-Shi 84(1976)111. [34J I. Schulz and W. Hinz, Silikattechnik 6 (1955) 235. [35] Y. Abbe, K. Mon and A. Naruse, in: Proc. 10th Intern. Congr. on Glass, Kyoto, 1974 (Ceram. Soc. Japan, Kyoto, 1974) p. 14. [36] I. Schulz and W. Hinz, Glastech. Ber. 29(1956) 319. [371I. Gutzow and M. Markova, unpublished results; see also ref. [11]. [381J. Gdtz, CR. Masson and L.M. Castelliz, in: Amorphous Materials, Eds. R.W. Douglas and B. Ellis (Wiley—Interscience, London, 1972) p. 317. [39] J. Götz, D. Hoebbel and W. Wieker, J. Non-Crystalline Solids 20(1976)413. [40] I. Gutzow, in: 1976 Crystal Growth and Materials, Eds. E. Kaldis and H.J. Scheel (North-Holland, Amsterdam, 1977) p. 380. [41] I. Gutzow, J. Crystal Growth 42 (1977) 15. [421 B. Wunderlich, J. Crystal Growth 42 (1977) 214. [43] L. Mandelkern, N.L. Jain and H. Kim, J. Polymer Sci. (A-2) 6(1968)165. [44] V.P. Privalko, Polymer 19 (1978) 1019. [45] F.P. Price, in: Nucleation,4O5—468. Ed. A.C. Zettlemoyer (Dek[46] D. ker,Hoffman, New York, SPE-Trans. 1969) pp.4, No. 6 (Oct. 1964) 1. [47] F. Gormick and J.D. Hoffman, Ind. Eng. Chem. 5841. [48] I. Gutzow, S. Kitova, M. Marinov and L. Tzakin, Glastech. Ber. 49(1976)144.
KINETICS OF CRYSTALLIZATION PROCESSES IN GLASS FORMING MELTS I. GUTZOW Institute of Physical Chemistry, Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria Received 18 July 1979
A survey is given of experimental results concerning the kinetics of nucleation and the mechanism of crystal growth in glass forming systems. The main aim of the review is, however, to correlate the kinetics of overall crystallization processes in glass forming melts with structural changes taking place in the initial melt during crystallization. Detailed investigations of the kinetics of overall crystallization summarized here for a number of phosphate and silicate melts, indicate that even in relatively simple glass forming melts crystallization is in fact connected with considerable molecular (e.g. anionic) reconstructions. It is shown that the kinetics of nucleation in glass forming melts can be described in terms of the more general, transient formulation of the classical theory of phase formation. Experimental evidence on the mode of crystal growth in glass forming melts is summarized, attention being concentrated on data obtained at low undercoolings. The conditions for the predominant manifestation of the basic mechanisms of crystal growth (normal, spiral and via surface nucleation) are considered, accounting for the structure of the initial melts and the state of the crystal/melt interface.
1. Introduction Glass forming systems represent a very convenient
main feature. Typical examples are glasses formed of organic high poylymers, silicate and phosphate systems, as well as chalcogenides (Se, As2S3), which can
model for investigating crystallization processes in undercooled melts. Such investigations may be also of technological interest, since a number of technically important materials, such as glass ceramics, partially crystalline semiconductors, etc., are obtained by direct or induced crystallization of glass forming melts. Considerable experimental evidence has been accumulated in recent years concerning the kinetics of crystallization in complex, multicomponent technical systems as well as in one-component, model glass forming melts. The available experimental data refer both to the time dependence of the two basic parameters of crystallization nucleation and growth and to the source of the overall crystallization process. From the fundamental point of view the results obtained for simple model glasses are of main interest, It is well known, however, that even the simplest one-component model glass forming melts have a complex structure, complicated associative, or polymeric molecular or anionic building units forming its
be described as inorganic polymers. It must also be pointed out that even in seemingly simple glass forming melts, processes of aggregation or association (e.g. due to hydrogen bonding) also lead to complicated structural elements. The complexity of the anionic or molecular structure has repeatedly been considered as a necessary condition for glass formation [1] and a number of authors (see e.g. refs. 2,3]) have treated polymerization, aggregation or association in the melt as an indispensable step in the process of vitrification of undercooled melts; it has also been shown [4] that polymeric structural units or additional association processes are a requisite in order to explain the temperature dependence of the thermodynamic functions of vitrifying systems. Condensed phosphates especially alkaline glasses are a classical example of glass forming systems where high temperature anionic polymerization equilibria are frozen-in [5—7]. The latest experiments have also proved the anionic polymer distribution in silicate glasses [9,10]. As the crystalline substances corresponding to simple glasses consist of structural
—
—
—
—
589
I. Gutzow / Kinetics of crystallization processes in melts
590
species of only one molecular or anionic type, it is to be expected that crystallization, even in the simplest glass forming systems, may be connected with considerable molecular or anionic reconstructions, as it was proved for the first time, years ago, in the case of sodium phosphste glasses [11 13]. The main aim of the present review is to correlate the kinetics of crystallization in glass forming melts with the structure of the corresponding systems. Thus the kinetics of the overall crystallization are compared with the molecular changes taking place in the ambient melt, and the mode of growth is juxtaposed with the structure of the melt/crystal interface for the corresponding substance. In considering the kinetics of crystallization processes, particular attention is paid to the non-steady-state effects [14,15] in the kinetics of nucleation which, as indicated in refs. [16,17], are of prime importance at phase transformations in glass forming systems. 2. Kinetics of nucleation and the course of overall crystallization By its very physical nature nucleation is a nonsteady-state process. This is due to the circumstance that the formation of a critical nucleus consisting of ~k molecules proceeds via a chain reaction, each step of which is determined by the incorporation (or separation) of an ambient phase molecule into the growing subcritical complex of the new phase. It is evident that in the absence of subcritical clusters capable of further growth (athermal nuclei) a certain time r must elapse before a steady-state distribution of clusters is established and the rate of nucleation 1(t) has reached its steady state value jo~This more general, transient formulation of the theory of nucleation has been given by Zeldovich [14] and Frenkel [15]; a survey of its basic premises may be found in ref. [16—18]. Following an approximate solution of the nonsteady-state nucleation problem given by Zeldovich himself [14], the momentary rate of nucleation 1(t) cam be expressed as
2
T
=
const. X (Tm/L~T)(13/71).
(2)
Here i~XT= Tm T denotes the undercooling, i.e. the thermodynamic driving force of the crystallization process in the melt, while its viscosity ~ is the redproce measure of the self-diffusion coefficient in the same system. The dimensionless factor 13 accounts for the incorporation hindrances across the nucleus/melt phase boundary; it is dependent on the complexity of the melt structure and on the mode of growth of the crystalline nucleus [16,18]. Usually the steady-state rate of nucleation is defined as (see also refs. [16,18]): 2), (3) = const. X (13/ri) exp(—K/Tz~T —
the constant K being determined mainly by the value of a, the specific surface energy at the crystal/melt interface. Once I~and rare known, the kinetics of the whole nucleation process can be evaluated. The numberN(t) of nuclei formed within the time interval 0, t per unit volume of the melt is given by N(t)
=
f
1(t) dt.
(4)
By accounting for eq. (1) or for the above-mentioned more accurate solutions, N(t) dependencies are obtained having a trend similar to that represented in fIg. la for the kinetics of induced nucleation in one or our basic model systems sodium metaphosphate NaPO 3 (Graham’s glass). This figure also shows the high values of the non-steady-state induction periods, as expected according to eq. (2) in glass forming substances in the vicinity of the temperature of vitrification Tg, where i~values up to l0~’— 1012 Poise are possible (for NaPO3 Tg = 275°C).Nonsteady-state effects of the same magnitude also determine the induction periods in the growth [16] of —
(1)
crystalline melts (fig. spherulites lb) and may in the considerably volume of influence glass forming the
r being the above-mentioned non-steady-state time lag. For considerations of a more or less quantitative
kinetics of the overall crystallization [21]. The overall crystallization kinetics of an under-
I’
‘=
I o exp~ r,It)
nature, as intended here, eq. (1) is of sufficient accuracy. A more precise solution can be found in ref. [19] as well as in the literature cited in ref. [16,18]. It can be shown [16] that in the case of an undercooled melt
~—
I. Gutzow /Kinetics of crystallization processes in melts
wherebx2/6.
_________________
I
~
(or Ifonathermal its surface) nuclei prior havetobeen the crystallization formed in the treatmelt ment, to the rclassical 0 is to expression be expected (5); however [24] andwith eq. (6) an expoleads
°
12,0
nent n reduced by unity, and the factor a depending
.
302°
as a ‘-~N
S _____________________
0
200
400
~
600
t (mm) 332° 326°
~
b
~
1:
313° ______________________________________ 0
200
400
600
800 t (mm)
Fig. 1. Non-steady-state kinetics of nucleation and growth in the induced crystallization of NaPO3 melts [16,201. (a) N(t) curves of nucleation of Na3(P309) spherolites on Ir crystallization cores at two temperatures (in °C); (b) growth of Na3(P3O9) spherolites formed around Pt cores: electron-microscopic data giving mean diameter ~ of spherolites depending on time t.
cooled melt is usually described in terms of the Kolmogorov—Avrami equation [22,23] 1). (5) co(t)In= this 1 exp(—at’ equation, cs(t) is the degree of crystallization at time t, n = 1, 2, 3, 4 is an integer depending on the dimensionality of growth of the crystallization centers, and a J~g’~~ is determined by the rates of steady-state nucleation J~and crystal growth g. In principle ca(t) is defined as a(t) = V(t)/V 0 from the volume V(t) crystallized at t and the initial volume V0 of the melt, and may be experimentally determined by the change of each parameter of the crystallizing system, depending on the crystal/melt ratio. It can be shown [21] that in a first approximation, transient nucleation would cause a simple shift of the ct(t) curve along the t-axis, so that 0, for 0 ~ t ~ bT, $t) = 5] for br ~ t <°°, (6) l~1 exp[—.a(t br)’ —
,
—
—
591
0g°~ on the number of active athermal crystallization centers N0. The kinetics of the overall crystallization process, taking place in a more or less finely dispersed initial phase (an assembly of molten droplets or samples of glass semolina, dust particles, etc.), should be described in terms of the mathematical formalism of topokinetic processes developed by Mampel [25] and Todes [26] (see also Young [27]). The ct(t) curves expected according to this treatment (which considers nucleation and growth from the surface of each particle) display an S-shaped trend
similar to those determined by eq. (5). No explicit general formula is possible, however, in the case of topokinetically determined crystallization; thus the analysis of the experimental results is given in the next section in terms of eqs. (5) and (6) even when crystallization of glass semolina is considered. It is taken in mind, however, that in such a case the integer n and the coefficient a become complicated functions of the mean radius R of the crystallizing particles, as it is discussed in ref. [271. 3. Experimental evidence on the overall crystallization kinetics A great variety of techniques (e.g. dilatometric measurements, quantitative X-ray analysis, DSC, etc.) have been used to determine the degree of crystallization. Here, however, only those methods are discussed which are of more or less methodical interest, providing moreover a direct possibility to follow the structural changes in crystallizing samples. Fig. 2 shows the course of crystallization in two model glasses determined by picnometric measurements. In such a case t~(t)can be determined as ~(t)
=
(p(t)
—
Po)/(Pm
—
P0)
(7)
Po, p(t), and Pm being the initial (glassy), the momen-
tary density line) (partly of crystalline), the samples, andrespectively. the final (fully In these crystaland
I. Gutzow / Kinetics of crystallization processesin melts
592
0
NaPO3, t [mirs] 160 240 720
80
U
2,5050 Z5000
Nci
2Si03
~~ 100
520
30’
______
2
~2. 54 50
~g2.54O° ztj 2.5350
,~
•
0
________________
‘T”~~’’~ .~
50 ~IIII
Q tLJ .~ zI.....
120
240
360
Na2 S103
, t
420
______________________
0
120
240
360
[mm]
420
(t-C~)[mm]
Fig. 2. Picnometric determination of the kinetics of overall crystallization in glass forming systems [29]. (a) Density versus time curves: (1) crystallization of NaPO3 at 330°C;(2) surface crystallization of sodium silicate glass at 520°C.(b) Crystallization of Na2SiO3 at different temperatures (°C)in coordinates n(t) versus (t — r0). Samples in both cases: glass semolina with d = 0.75— 1.00 mm.
further experiments described here (figs. 2 to 7) samples consisting of a great number of more or less finely ground glass semolina (with a mean diameter d indicated for each experiment) have been used [11, 13,28,29]. Under the described experimental conditions the individual crystallization process, taking place in each semolina particle, is averaged over the whole sample and very reproducible results are obtamed. Detailed microscopic observations indicate
gravimetry can be applied in determining cs(t) since crystalline LiPO3 is insoluble, while glassy LiPO3 is easily dissolved in water [30]. Li PU3 1.06°
-
of thecrystallization that particles (i.e.is this always is a typical initiatedMampel—Todes at the surface topokinetic process).
50~II-~-
0
The devitrification in rapidly quenched glass samples, as it is the case of the sodium silicate glass in fig. 2 (59 mole% Si02, 41 mole% Na20, quenched from 1300°C to room temperature), is preceded by a frozen-in high temperature values of p reaches the equilibrium process relaxation density of (atthet
385°
120
240
Cd
360
t[minl
(~o3)2
_____________________
500°
490°
-~
~
~ 50
/.80°
,
®.
—
0
21.0
480
720
I [miri] Fig. 3. Kinetics overalltemperatures crystallization metaphosphate melts atofdifferent (°C). in (a) LiPO3 according to gravimetric determinations [301;(b) Cd(PO3)2 picnometric measurements [28]. In both cases: glass semolina with d = 0.5—0.6 mm.
593
I. Gutzow /Kinetics of crystallization processes in melts
The crystallization product of Graham’s glass (NaPO3), i.e. the cyclic Na3(P309), differs so much from the anionic structure of the initial melt that a striking variety of methods can be applied in order to determine the degree of crystallization: analytical determinations [11] (here both the glass and the crystal are water soluble), quantitative IR [13] or Raman [31] spectroscopy, as well as filter-paper chromatography [13,32]. The crystallization of glass semolina NaPO3 sampies (figs. 2a and 4a) is initiated at the grain surface and follows the typical Avrami curves without induction periods; in coordinates log log[(l ~—a)’] versus log t satisfactory straight lines with n 2 (for ~ = 0.75—1.0 mm) are obtained. However, quite different results are reported by Westman and Krishna-Murthy
~ 50
310’
0
120
240
should be expected for a change from crystallization on preexisting athermal centers (on the active surface of glass smolina grains) to an overall crystallization process with thermal nucleation and a shift along the t-axis due to non-steady-state nucleation effects according to eq. (6). In accordance with the predictions of the Mampel—Todes treatment, a decrease in n is observed when the mean diameter of the crystallizing glass semolina samples is increased [11,29]. This effect can be seen also in fig. 5 where n decreases from n 3 for d = 0.5—0.6 mm (Cd(P03)2 melt) to n 2 for d = 0.75—1.0mm (NaPO3 melt). Thus the change in the crystallization kinetics shown in fig. 4 is not due to
‘“‘3.0
360 t [mm]
____________
~
~25 C)
500°
/0
,
I
/
/.90°
~ 1::
2~
Cd [PU3] 0
120
240
360
t[min]
Fig. 4. Kinetics of devitrification of NaPO3 melts at different temperatures (°C).(a) Glass semolina (d = 0.75—1.00 mm), IR measurements [131. (b) Glass beads with intact surWestman and Krishna-Murthy face quantitative filter-paper [32]. chromatography according to
2 I
2~
b
.1.,..
2,5
3,0
log t Fig. 5. Kinetics of devitrification 1] versus of metaphosphate log t. (a) Data from meltsfig. in 4a; (b) data from fig. 3b. coordinates log log[(1 — al’
I. Gutzow / Kinetics of crystallization processes in melts
594
differences in the grain diameter, but it is caused by
the Na different picnometric state determinations of the grain surface. (fig. 2a) The indicate also of of that no measurable (as inresults the case the crystallization 2SiO3) is involved ofvolume NaPO3. in relaxation the time lag observed in
MO Di
IRM IRI
4. Anionic reconstructions in phosphate and silicate glasses The structure and structural changes taking place in the crystallization of simple water soluble glass forming phosphate melts can be instructively visualized by filter-paper chromatography. Detailed descriptions of this method, of its possibilities and limitations may be found in refs. [5—7,13] and especially in ref. [8]. Samples of the original glass as well as of partially or fully crystallized material are dissolved in appropriate chromatographic solvents which can be chosen in such a way as to be complementary in their separation possibilities and applications [13]. Highly polymerized anions having a degree of polymerization x> 10, remain on the starting point of the chromatogram (H/po on fig. 6) whereas oligophosphate anions (x < 10) with linear or cyclic structure can be determined using reference or test substances, In alkaline phosphate melts (e.g. when glasses from the system NaPO3/Na4P2O7 are obtained from the perspective hydrogen phosphates) polycondensation processes of the types 2 Na2HPO4 + NaH2PO4 ~Na3P3O10 + 2 H20, 3 NaH2PO ~ Na3(P3O9) + 3
~
(8) (9)
determine the formation of linear (Na~P~O3~÷i) and cyclic (Na~P~O3~) anions. The mean degree of polymerization of linear anions in the resulting glasses can be expressed [5] as = 2/(Na/P 1) , (10) .~
TIM
II!iIIltpIII
H/~0 ~ —
I I II III IV V VI Fig. 6. Anionic composition change of NaPO3 glass semolina samples (d = 0.75—1.00 mm) during heat treatment at 320°C as revealed by filter-paper chromatography [13]. T, chromatogram with reference substances; I, initial glass; II, after 20 mm heat treatment; HI, after 80 mm; IV, after 140 mm; V, after 200 mm; VI, after 360 mm; Mo, monophosphate anion; Di, diphosphate; Tn, triphosphate; TRM, trimetaphosphate; TTM, tetnametaphosphate; H/po, high polymers.
Na3(P309)) in sodium phosphate glasses also depends on the Na/P ratio, decreasing from 8 to 10% for Na/P = 1 (in Graham’s glass, cf. fig. 4) to 1 to 2% for Na/P = 1.4 to 1.5. According to eq. (10) for sodium ,metaphosphate NaPO3 (Graham’s glass).~ should be expected. However, traces of residual water content reduce ~ in NaPO3 to approximately 300 [11]. The devitrification of sodium metaphosphate NaPO3 is in fact, as shown by analytical, chromatographic and IR determinations, a change from linear to cyclic anionic structure [11,13]. Upon heat treatment the amount of the cyclic Na3(P309)is gradually increased (figs. 4 and 6). The cyclic anions are formed from the long chains according to the scheme —~00
NO
o.’.~
~.o
ON.
~
NO 0 0
p 00
ON.~ 0
~
0
0 0 0
NO 0 ()
P
ON~
0 ON. ON,
00
‘,,~
N.~0
I’
0
P
0
—
~ON~
O
N,,O NO 0
ON. ~
P
ON.~
0
0 NP). NO
~
~
ON.~
ON p
P i
I’ -o ON, ON~
I
—
where Na/P is the molecular ratio of sodium to phosphorus for the given alkaline glass composition. Experimental data obtained by a number of authors [5—7] confirm theoretically calculated chain length distributions of linear anions [5,9,10], revealing moreover that the percentage of cyclic anions (mainly
00
o~
0
ON.
~
~O
O~\)._~
ON. ON.
0
o
NO)
o~ O~
o,
—
))
I, ON
(11)
I. Gutzow / Kinetics of crystallization processes in melts i.e. the chains of the (P
close again at the points of separation
309) rings [13]. A similar anionic decomposition takes place in the crystallization of another metaphosphate Mg(P03)2 where, however, the —
~
~
~
—
U,
~
I
I
595 I
I
I
I
I
5p
I
_____________
______________
________
____________
—
—
Mg2(P4012) is formed [33]. Glassy LiPO3 consists of chain polymers of rather 3” size anions (fig. 7); thus is in some medium (as compared withit NaPO3) and aspects of cyclica (P309) structural analogue of vitreous NaPO 3. However, the crystallization of LiPO3 is connected with just the opposite structural change: upon crystallization the mean degree of polymerization of already existing anionic chains is increased and cyclic polymers are transformed into linear chains [30], a water insoluble asbestos-like crystal being the result. Structural changes, similar to those observed in the crystallization of LiPO3, are also typical for most metaphosphates of bivalent metals (Cd(P03)2, Zn(P03)2, Ca(PO3)2, etc., seee refs. [34,35]. The anionic composition of pyrophosphates of bivalent metals also differs markedly from the respective crystals, where only one anionic structural element has been found. An example in this respect gives fig. 8, drawn according to results of filter-paper chromatography performed by Schulz and Hinz [36]. Considerable and very instructive structural tetrameric ring
‘4
~
—
~
0~ _______________ I
_______________
z
2 (I)
—
I
c~
~
_____
N — U,
_____ _~
z
_______________
________________
_________
______________
2
4~.I Z
6 L AS S
C RY
—
SI A L
Fig. 8. Anionic of pyrophosphates bivalent metals (as glassescomposition and as crystals) according to of filter-paper chromatographic data of Schulz and l-Iinz [36].
changes have been reported in the crystallization kinetics of glass forming melts from the system NaPO3/Na4P2O7 [11,13]. For glasses with Na/P< 1.3 (i.e. for compositions of the NaPO3 side of the respective eutectic, cf. [5]) the initially formed crystalline phase is again the cyclic Na3(P309) (fig. 9). The kinetics of crystallization follow the sigmoid Avrami course. However, the maximal percentage of Na3(P309) reached decreases with increasing the Na/P ratio as predicted by the phase diagram [37]. For Na phosphate glasses having Na/P> 1.3 (i.e.
—
MO~
for the Na5P3O10 side of the eutectic) the chain-
DI~
TPI TIM
w Nci/Prl,00
I
No/P ~1,12
~
100~:\=ø-L~-
__ Na/P =1.25
I.-.
~50
______
\No/P.1,L2
I
I
II
III
0
120
21.0
‘
360
t [mm] Fig. 7. Composition change of LiPO3 samples [30] (filterpaper chromatograms). 1, reference substances; I, initial glass; II, glassy part of 50% crystallized sample; III, completely crystallized sample.
Fig. 9. Kinetics of Na3(P3O9) formation in devitrifying sodium phosphate glass semolina samples (d = 0.75—1.00 mm) with different Na/P ratio at 330°C[37].
I. Gutzow / Kinetics of crystallization processes in melts
596
MOU iIIItIUIii,~
~IIIlIwIIHIIII~ ~~IIiim~ u~IIm,ll~. ~
~IlIIUII~III~tIIIIIftuIv’ •~II~llIIIIJ~Ii~~
T:~.~M~u ~
.• IIIIIh~.
l~-~——.—I—...u
TRM•II.~ TTM
~
Fig. 10. Filter-aper chromatograms of hexaphosphate glass (Na
8 P6 019, i.e. Na/P = 1.33) semolina samples (d = 0.75—1.00 mm) with different time of heat treatment at 330°C.T, reference substances; I, initial glass. Heat treatment: II, 20 mm; iii, 40 mm; IV, 60 min;V, 80 mm, VI, 140 mm, VII, 160 mm, VIII, 180 mm; IX, 200 mm; x, 360 mm. I—Ill, formation of linear Na3P301 o; IV—VIII, formation of cyclic Na3(P309); IX, X, complete crystallization [13].
polymeric Na3P3O10 (having Na/P = 1.65) is observed as the first crystalline phase [12,131. As a result of the Na3P3O10 crystallization the Na/P ratio in the residual melt decreases, while the average number chain length is increased (fig. 10). It is assumed that polycondensation reactions of the type + S 1x ~2(x+1)— 2(x+2)— + r~23x+1 Slx+lO3x+4 (12) ~3l’J4 take place in silicate melts of bivalent cations, si~O~~j’~ representing silicate anions where x is an integer ranging from to to The theoretical chain length distributions of silicate melts and glasses have °°.
Wt./.Sias
____________
_____________
‘~
_______
V________
—
:
~ , SiO~
—
zlO
Z
POty;~
<
been established years ago [9,10]. Their experimental verification became possible only after it has been shown that silicate anions can be extracted from the respective glasses in the form of their trimethylsilyl derivatives, which can be separated and determined by gas—liquid chromatography [38]. A special type of filter-paper chromatography of silicates has been alsoProcesses developedof[39]. anionic reconstruction, similar to those already discussed for phosphate glasses, are also typical in silicate melts. For example, glassy Pb 2SiO4 is constituted of different polysilicate anions. The corresponding high temperature crystalline modifica-
___
_____
dimen~ Units
0 ______________
GLASS
________________
—
120
240 1440 t [mm]
CRYSTAL-M1
Fig. 11. Composition of vitreous and crystalline Pb2SiO4 according to Gdtz, Hdbbel and Wicker [39].
Fig. 12. Changes in the anionic structure of devitrifying Pb2SiO4 samples (at 500°C) according to Gdtz, Mason and Castelliz [38].
I. Gutzow /Kinetics of crystallization processes in melts
597
tion consists, however, only of SiO~anions (as in the case of bivalent metal pyrophosphates, fig. 8) (fig.
of an idealized metallic melt or to the case of rigid inorganic network polymers (such as Si02, Ge02 or
11). During the crystallization of Pb2SiO4, anionic redistributions similar to those in alkaline phosphate glasses (cf. fig. 10) can be observed (fig. 12).
P205) which, from a thermodynamic point of view [4] may be also considered as “simple” liquids. A situation closer to reality may be expected when the crystallization of anionic polymers discussed in the foregoing section is confronted with a model describing the crystallization of chain-folding organic polymers with a high degree of polymerization (fig. 13d). However, these two simple models correspond only to two extreme cases of melt crystallization processes. In between these to limiting cases a great variety of reconstructive crystallization mechanisms is possible, which may be provisionally classified in the following way: (i) A low molecular crystal is formed (e.g. the case of NaPO3, Mg(P03)2) from the equilibrium polymeric distribution in the melt. Only a small amount of “crystalline” structural units is present in the initial melt (fig. 13b). (ii) The ambient melt, consisting of different mo-
5. Structural considerations and the mode of growth
It is obvious that the complicated structural chemistry of crystallization in the discussed and in similar systems must be taken into account when crystallization processes are compared with clasical theoretical models, describing mainly an undercooled melt as a loose random packing of equal spheres (fig. 13a). This model may apply directly only to the crystallization
000000 000000 000000 000000 000000
0~~0
!~.
~
lecular (or anionic) species with relatively low degree
~
b
~.I :
§P~....
d
•
melt/crystal
Fig. 13. Schematic representation of melt crystallization of substances with different structures. (a) Simple melt crystallizing without structural change (metals, inorganic network polymers). (b) Crystallizatmon with structural reconstruction (first type): formation of low-molecular crystal from polymer melt (“crystalline” cyclic structural units are shadowed). (c) Second type of structural reconstruction upon crystallization: formation of high polymeric crystal from low polymeric melt (cyclic structural units are shadowed again). (d) Crystallization of chain folding organic polymer.
in polymerization LiPO3 or in Cd(P03)2) crystallize to give a linear of (e.g.(fig. of linear high polymeric crystal 13c). and cyclic anions, as The schematic representation in fig. 13 includes all the above cases of melt crystallization: (a) crystallization of simple melts without reconstruction (including network polymers); (b), (c) reconstructive crystal. lization (eventually representative also for organic melts with hydrogen bounded associates); and (d) crystallization of high polymeric substances without noticeable molecular decomposition. as Existing experimental in two recent data reviews on the [40,41] of lead growth to thesummarized following conclusions, when themode mechanism of crystallization is compared with the four types of models presented in fig. 13. (a) Normal (or continuous) growth is the only possible mechanism for the simplest metallic or molecular substances with low entropy of melting (most of the metals, CBr4, cyclohexanol [40]) as well as for typical inorganic glass forming network polymers (sicl2, Ge02 [41]). (b) Spiral growth is typical for all organic glass forming substances with high entropy of melting (where possible hydrogen bonding can be expected —
598
I. Gutzow / Kinetics of crystallization processes in melts
e.g. thymol, salol, etc.) as well as for inorganic anionic polymeric glass formers, such as NaPO3, LiPO3 and Na2Si2O5, where a process of reconstructive crystallization hasbeen observed, By using elaborated experimental methods providing dislocation-free ideal crystals, the surface nucleation mechanism of growth of such substances with high entropy of melting is also possible, as verified by capillary technique in some cases (thymol, Na2S2O5 5H20, etc., see ref. [40]). Some metals (e.g. Ga) with possible melt association may also be included in this group. (c) The surface nucleation mechanism of growth is the predominant mode of crystallization for chain folding organic polymers. This follows from growth experiments at low undercoolings (see, e.g., the case of polyethylene [42]), from the temperature dependence of growth at high undercoolings [43,44] as well as from theoretical estimates [45—47],according to which surface nucleation is the most probable (or even the only possible) crystallization mechanism for chain folding polymers. Additional evidence in this respect is provided also by the experimentally verfied dependence of lamellar step heights in the bulk crystallization of organic polymers [45]. The mode of growth of a crystal depends on the state of the crystal/melt interface and the above mentioned experimental findings simply indicate that structural difference (or similarity) existing between the melt and the corresponding crystal also affects the predominant state of the interface. The thermodynamic measure of melt/crystal dissimilarity is the molecular entropy of melting ~m which, in the case of reconstructive crystallization, always has relatively high values, guarantying according to the existing concepts in the theory of crystal growth (cf. literature cited in refs. [40,41] the discontinuous (spiral or surface nucleation) mechanism of growth of substances crustallizing with molecular reconstructions. When considering the process of nucleation in undercooled melts, it is to be expected that for substances with reconstructive crystallization, very low 13 values (in eqs. (2) and (3)) should be obtained. This is in fact an experimental finding in the case of NaPO3 [20], where 13 = l0_6_lO_4 has been found. Such findings could possibly give a quantitative explanation of the kinetic stability of undercooled melts with more or less complicated structures, as
required by the already mentioned crystallographic criteria [1] for glass formation. In this connection it should be mentioned that according to the definition of 13, as given in refs. [16,17], values of this factor close to unity are to be expected for simple, easily crystallizable, molecular melts with diffuse melt/crystal interface and “liquid-like” growth kinetics (e.g. for CBr4, cyclohexanol, etc. [40]).
6. Discussion The main problem arising from the more or less detailed discussion of the “chemistry” of crystallization presented here, is to determine how the processes of molecular (or anionic) reconstruction are connected with the purely ‘physical” kinetics of the crystallization process. Two hypothese are obvious in this respect: (a) Crystallization begins only when processes of molecular (or anionic) rearrangement in the initial melt have led to some critical concentration of the crystallizing structural species. Crystallization begins only after chemical (or molecular) rearrangements have been completed. (b) The initial equilibrium (or frozen-in) distribution of molecular (or anionic) species in the ambient melt is violated by the crystallization process taking place in the system. Composition changes follow the kinetics of crystallization, as one of the components of the metastable equilibrium distribution in the melt precipitates onto the crystal. The present author has the feeling that the experimental evidence given in the preceding sections especially as far as phosphate systems are concerned strongly supports the second hypothesis. This is verified (i) by microscopic observations indicating that a perceptible change of the anionic composition may be detected only after measurable crystallization has occurred; (ii) it should be mentioned that the change of the molecular composition (e.g. the additional formation of NaPO3, fig. 4) follows under isothermal conditions the time dependences predicted by a mechanism of nucleation and growth (eqs. (5) and (6) or the topokinetic formalism of Mampel and Todes) i.e. by the crystallization process itself. The induction period observed in the formation of cyclic NaPO3 (fig. 4b) fully corresponds to that determined —
—
I. Gutzow / Kinetics of crystallization processes in melts
experiments (fig. 1, see also refs. [16,20]); (iii) no anionic changes can be observed during heat treatment even of non-equilibrium, glassy NaPO3 or LiPO3 condensates [48] before the from crystallization
—
—
proper crystallization process has started. (In the investigation [48] vacuum-quenched vitreous NaPO3 condensates without measurable content of cyclic Na3(P309) have been reported. It seems also that there are no changes in the anionic composition during the process of volume relaxation, as observed in the case of Na2SiO3 (fig. 2a and ref. [29]) or with glassy condensates [48].
References [11 G. Hägg, J. Chem. Phys. 3 (1935) 42. [2] P.P. Kobeko, Amorfnye veshtchestva (lzd. Akad. Nauk SSSR, Moscow, 1952) pp. 28—120. [3] V.V. Tarassov, Novye Voprosy Fiziki Stekia (Moscow, 1959) pp. 1—50. [4] I. Gutzow, in: The Physics of Non-crystalline Solids, Ed. G.H. Frischat (Trans. Tech. Publications, Aedermansdorf, Switzerland, 1977) p. 356. [51J.R. van Wazer, Phosphorus and its Compounds, Vol. 1 (Interscience, New York, 1958). [6] A.E.R. Westman and J. Crowther, J. Am. Ceram. Soc. 37 (1954) 420. [7] H. Grunze, Silikattechnik 7 (1956) 134. [8] H. Grunze and E. Thio, Sitz. Ber. Deut. Akad. Wiss. Berlin, Kl. Math. AIIg. Naturwiss., No.5 (1953). [9] P. Baltà and E. Balni, Introduction to the Physical Chemistry of the Vitreous State (Abacus, Tunbridge Wells, Kent, UK, 1976) pp. 69—107. [101 C.R. Mason, in: Glass ‘77, Proc. 11th Intern. Congress on Glass, Prague, 1977, Vol. 1, Ed. J. Gdtz (CVTS— Dum Techniky, Praha, 1977) p. 3. [11] I. Gutzow, Z. Anorg. AIlg. Chem. 302(1959) 259. [12] V. Gottardi and G. Bonetti, Vetro e Silicati 3 (1959) 31. [13] I. Gutzow, in: The Structure of Glass, Vol.6, Ed. E.A. Porai-Koshits (Consultants Bureau, New York, 1966) p. 154. [14] J.B. Zeldovich, ActaPhysicochim. URSS 18(1943)1. [15] J. Frenkel, Kinetic Theory of Liquids (Dover, New York, 1955) p. 398. [161 I. Gutzow and S. Toschev, in: Advances in Nucleation and Crystallization SW. Freiman (Am. Ceram. in Glasses, Soc., Eds. Columbus, L.L. Hench OH, 1971) and p. 10. [171 I. Gutzow, Comtemp. Phys. 20 (1979). [18] S. Toschev and I. Gutzow, Kristall Tech. 7 (1973) 43.
599
[19] D. Kashchiev, Surface Sci. 14 (1969) 209. 1201 I. Gutzow, E. Popov, M. Marinov and S. Toschev,Kristall Tech. 3(1968) 37, 337,485. [211 1. Gutzow and D. Kashchiev, in: Advances in Nucleation and Crystallization in Glasses, Eds. L.L. Hench and S.W. Freiman (Am. Ceram. Soc., Columbus, OH, 1971) p. 116. [22] AN. Kolmogorov, Bull. Acad. Sci. URSS (Sci. Math. Nat.), No. 3 (1937) 355. [23] M. Avrami, Chem. Phys. 7 (1939) 1103; 8 (1940) 212; 9(1941)177. [241D. Kashchiev, Surface Sci. 18 (1969) 389. [25] K. Mampel, Z. Physik. Chem. A187 (1940) 43, 235. [26] O.M. Todes, Zh. Fiz. Khim. 14(1940)1224. [27] D. Young, Dedomposition of Solids (Pergamon, Oxford, 1966) ch. 2. [28] I. Gutzow, Silikattechn. 20 (1969) 159. [29] I. Gutzow, D. Sawow, Z. Belitshanska and S. Gutzow, Annuaire Inst. Chim. Technol. Sofia 8(1961) 81. [30] 1. Avramov, R. Paskova, B. Samouneva and I. Gutzow, Phys. Chem. Glasses 20(1979) 91. [31] G.J. Exarhos and W.M. Risen, Jr., J. Am. Ceram. Soc. 57 (1974) 401. [32] A.E.R. Westman and M. Krishna-Murthy, in: Symposlum on Nucleation and Crystallization in Glasses and Melts, Eds. M.K. Reger, G. Smith and A. Insley (Am. Ceram. Soc., Columbus, OH, 1962) p. 91. [331Y. Abbe, K. Mon and A. Naruse, Yogyo-Kyokai-Shi 84(1976)111. [34J I. Schulz and W. Hinz, Silikattechnik 6 (1955) 235. [35] Y. Abbe, K. Mon and A. Naruse, in: Proc. 10th Intern. Congr. on Glass, Kyoto, 1974 (Ceram. Soc. Japan, Kyoto, 1974) p. 14. [36] I. Schulz and W. Hinz, Glastech. Ber. 29(1956) 319. [371I. Gutzow and M. Markova, unpublished results; see also ref. [11]. [381J. Gdtz, CR. Masson and L.M. Castelliz, in: Amorphous Materials, Eds. R.W. Douglas and B. Ellis (Wiley—Interscience, London, 1972) p. 317. [39] J. Götz, D. Hoebbel and W. Wieker, J. Non-Crystalline Solids 20(1976)413. [40] I. Gutzow, in: 1976 Crystal Growth and Materials, Eds. E. Kaldis and H.J. Scheel (North-Holland, Amsterdam, 1977) p. 380. [41] I. Gutzow, J. Crystal Growth 42 (1977) 15. [421 B. Wunderlich, J. Crystal Growth 42 (1977) 214. [43] L. Mandelkern, N.L. Jain and H. Kim, J. Polymer Sci. (A-2) 6(1968)165. [44] V.P. Privalko, Polymer 19 (1978) 1019. [45] F.P. Price, in: Nucleation,4O5—468. Ed. A.C. Zettlemoyer (Dek[46] D. ker,Hoffman, New York, SPE-Trans. 1969) pp.4, No. 6 (Oct. 1964) 1. [47] F. Gormick and J.D. Hoffman, Ind. Eng. Chem. 5841. [48] I. Gutzow, S. Kitova, M. Marinov and L. Tzakin, Glastech. Ber. 49(1976)144.