- Email: [email protected]
Kinetic studies of the crystallisation of coesite using synchrotron radiation
s __
_l!!B
Nuclear Instruments and Methods in Physics Research B 97 (1995) 89-91
NUMB
Beam Interactions with Materials&Atoms
ELSEVIER
Kinetic studies of the crystallisation of coesite using synchrotron radiation P. Zinn a,* , J. Lauterjung b Institutjiir
a, E. Hinze b
a GeoForschungsZentrum Potsdam, Telegrafenberg ASO, D-14473 Potsdam, Germany Geowissenschaften and Lithosptirenforschung, Universitiit Giessen, Senckenbergstrabe 3, D-35390 Giessen, Germany
Abstract For energy-dispersive X-ray powder diffraction under high pressure and high temperature a multi-anvil-X-ray apparatus (MAX 80) has been installed at HASYLAB. This instrument allows to measure diffraction data at very short intervals and thus study time dependent phenomena. As an example we have investigated the kinetics of the a-quartz-coesite phase transformation. The kinetics was determined by in situ experiments between temperatures of 870 and 1170 K and in a pressure range of 30-50 kbar. The structural changes were directly imaged using synchrotron radiation. The experimental results yield the rate constant K, for the growth of coesite from quartz as a starting material under dry conditions. For the transition three K, values from 6.0 X lo4 to 2.2 X lo4 s-’ for different p/t-ranges were determined.
1. Introduction It is well known that silica (SiO,) has different crystalline phases for different pressure and temperature ranges. With the exception of stishovite all phases are built up of three-dimensional frameworks of SiO, tetrahedra each of it is linked with one other SiO, tetrahedron. Therefore the SiO, polymorphs have a rather low density. SiO, transforms to a crystal structure of lower symmetry under high pressure. The high pressure form of SiO, known as coesite, [2], crystallises in the space group C2/c. The cY-quartz-coesite transition is well known and has been established by several authors reviewed by Liu and Bassett [3]. This transformation is connected with a volume decrease of 10% inducing fractures around inclusions of polycrystalline quartz in some host minerals like garnet as first mentioned by Chesnokov and Popov [4]. The identification of coesite in metamorphic rocks led to a new “ultra-high pressure” metamorphic facies [s]. The ultra high pressures indicated by the coesite are far higher than previously documented and significantly expand the knowledge of the maximum depths from which tectonic exhumation of metamorphic material can occur. The kinetic behaviour and the stability of the coesite phase is needed not only for determining the p/t-time paths of metamorphic material but also e.g. for the analysis of defects in Czochralski-grown silicon crystals [6]. In this
* Corresponding author, fax f49 0331-288-1474, 0331-288-1468, e-mail: [email protected].
tel. +49
paper we wish to demonstrate a method to measure the time dependence of the phase transitions as a function of pressure and temperature.
2. Experimental The diffractometer is a high pressure device [7], combined with an energy-dispersive solid state detector. The high pressure vessel is a cubic anvil apparatus which compresses a cube with an edge length of 8 mm by six tungsten carbide anvils [l]. The cube is made of a mixture of boron and epoxy resin for high X-ray transparency with the sample in the centre. The anvils glide in guide blocks which are fitted to a hydraulic ram. The synchrotron beam impinges on the sample between the anvils along the face diagonal, and the diffracted beam can be detected under angles up to 30”. With this apparatus a pressure of 80 kbar and a maximum temperature of 2000 K can be achieved. Pressure is determined by the shift of diffraction lines of an internal standard with well known Pm-data (e.g. NaCl). The sample can be heated by an internal graphite furnace, controlled by a thermocouple. The experimental setup for energy-dispersive X-ray diffraction experiments has been previously described [8]. The sample in a high pressure-high temperature environment is illuminated by a white X-ray beam. The scattered beam is analysed by a solid state detector under a fixed scattering angle. The resulting spectrum is stored in a multi-channel analyser. For the evaluation of the diffraction diagrams a sophisticated software is available [9].
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. AI1 rights reserved SSDI 0168-583X(94)00348-3
II. CERAMICS
90
P. Zinn et al. / Nucl. Instr. and Meth. in Phys. Res. B 97 (I 995) 89-91 ibO0
counts (arb. units)
IO
20
0
30 1)
JO
Energie (KcV)
Fig. 1. Sequence of diffraction
diagrams versus time during the phase transition.
Because of the high intensity of synchrotron radiation diffraction diagrams can be recorded within a few seconds, typically 20-200 s. This offers the possibility to carry out time resolved studies during a phase transition. The method is simple: in preliminary experiments the phase boundary is determined. For the kinetic experiment the conditions (P, T) are chosen below the phase boundary; then the temperature is raised quickly beyond the boundary. The diffraction diagrams are collected in a fast sequence for fixed time intervals until the transition is completed. In Fig. 1 series of diffraction diagrams are shown, taken at 35
kbar and 1073 K demonstrating the a-quartz-coesite sition.
tran-
3. Results The kinetics of an interface-controlled solid state phase transition can be described by the Avrami equation [lo], even at high pressure conditions [ll]: X(t) = 1 - exp( -Zct”),
(1)
with: X(t) = degree of transformation, k = rate function (function of pressure, temperature, grain size etc.), t = time, IZ= exponent, determined by the mechanism of nucleation. In our experiments the degree of transformation X(t) has been estimated from the observed Bragg intensities of the coesite phase due to Znragg= Vsample. Eq. (1) leads to: x(t) = ZBra&)/ZO, with I,, = Bragg intensity after the transformation is completed [lo]. The parameters k and n can be calculated by fitting a plot versus In t (Fig. 2). We have measured a total of three k values for the a-quartz-
T !
Table 1 Observed and calculated temperature conditions 800
time
lZO0
(set)
Fig. 2. X(t) as a function of time t, where X is the normalized intensity of the coesite-phase diffraction line indicated in Fig. 1. The data (circles) are fitted by the Avrami equation (solid lines).
X,-values
for different
pressure
Nr.
P [kbar]
T [Kl
k x lo4 [s- ‘1
1 2 3
35 36 45
1170 1143 1093
6.00 5.40 2.20
and
P, Zinn ef af. /Nucl. Instr. and Me&. in Phys. Rtts. B 97 (fwts) 89-91
coesite transition at different temperatures and pressures (Table 1). The “fuh pattern” method gives a complete diffraction diagram at every time interval. Therefore it not only leads to the rate constant k,, but aIso contains fuI1 information on the crystal structure [12]. Main characteristic of the transition is a change from space group P3,21 for a-quartz to C2/c which results from the building of four-rings chains consisting of I~iU~J4--t~trahedr~s in the case of coesite.
4. Discussion and conclusions The experiments described in this paper have demonstrated that energy-dispersive X-ray di~raction combined with high intensity synchrotron radiation is a most powerful instrument for geological research. We were able to calculate important thermodynamicaly data describing the rate of a phase transition with good accuracy. The pressure temperature dependence of the rate constant K, could be determined. When using the “full pattern” method we were also able to observe the structural change of the phases during the transition and to give evidence for specific mechanism during the transformation. On the formation of coesite from starting o-quartz, a similar strained quartz is recognised as an intermediate stage from the broadness of the di~ract~on lines of the o-quartz phase,
91
Acknowledgement This work was supported by the German Federal Minister of Research and Technology under contract number no. 05 447 K&M9.
References [I] E. Hinze, J. Kremmler and J. Lautejung, HASYLAB Jahresbericht (1991). [2] L. Goes, Science 118 (1953) 113. [3] G-gun Liu and W.A. Bassett, Elements, Oxides, and Sili-
cates - High-Pressures Phases with Implications for the Earth’s Interior (Oxfort University Press, New York, 1986). fitt B.V. Chesnokov and VA Popovsftokt. Al&. Nauk SSSR, 162 (1965) 176. [5] C. Chopin, Contrib Mineral Petrol 86 (1984) 107. [6] A. Bourret,E. Hinze, H.D. Hochheimer,Phys. Chem. Minerals 13 (1986) 206. {7] 0. S&momma et al., in: Solid State Physics under pressure, S. Minomura~ cd., ffieidel, Dordrecht, 1985) p, 351. [s] J. Lauterjung and G. Will, Physica B 139/l& (19%) 343. [9] .I. Lautejung, G. Will and E. Hinze, Nucl. Ins@. and Meth. A 239 (1985) 281. [lo] J.W. Cahn, Acta Metallurgica 4 (1956) 449. Ill] E. Hinze, J. Lauterjung and G. Will, Nucl. Instr. and Meth. 208 (1983) 569. [I21 J. Lauterjung, fnauguraf Dissertation, Bonn, 1985.
_l!!B
Nuclear Instruments and Methods in Physics Research B 97 (1995) 89-91
NUMB
Beam Interactions with Materials&Atoms
ELSEVIER
Kinetic studies of the crystallisation of coesite using synchrotron radiation P. Zinn a,* , J. Lauterjung b Institutjiir
a, E. Hinze b
a GeoForschungsZentrum Potsdam, Telegrafenberg ASO, D-14473 Potsdam, Germany Geowissenschaften and Lithosptirenforschung, Universitiit Giessen, Senckenbergstrabe 3, D-35390 Giessen, Germany
Abstract For energy-dispersive X-ray powder diffraction under high pressure and high temperature a multi-anvil-X-ray apparatus (MAX 80) has been installed at HASYLAB. This instrument allows to measure diffraction data at very short intervals and thus study time dependent phenomena. As an example we have investigated the kinetics of the a-quartz-coesite phase transformation. The kinetics was determined by in situ experiments between temperatures of 870 and 1170 K and in a pressure range of 30-50 kbar. The structural changes were directly imaged using synchrotron radiation. The experimental results yield the rate constant K, for the growth of coesite from quartz as a starting material under dry conditions. For the transition three K, values from 6.0 X lo4 to 2.2 X lo4 s-’ for different p/t-ranges were determined.
1. Introduction It is well known that silica (SiO,) has different crystalline phases for different pressure and temperature ranges. With the exception of stishovite all phases are built up of three-dimensional frameworks of SiO, tetrahedra each of it is linked with one other SiO, tetrahedron. Therefore the SiO, polymorphs have a rather low density. SiO, transforms to a crystal structure of lower symmetry under high pressure. The high pressure form of SiO, known as coesite, [2], crystallises in the space group C2/c. The cY-quartz-coesite transition is well known and has been established by several authors reviewed by Liu and Bassett [3]. This transformation is connected with a volume decrease of 10% inducing fractures around inclusions of polycrystalline quartz in some host minerals like garnet as first mentioned by Chesnokov and Popov [4]. The identification of coesite in metamorphic rocks led to a new “ultra-high pressure” metamorphic facies [s]. The ultra high pressures indicated by the coesite are far higher than previously documented and significantly expand the knowledge of the maximum depths from which tectonic exhumation of metamorphic material can occur. The kinetic behaviour and the stability of the coesite phase is needed not only for determining the p/t-time paths of metamorphic material but also e.g. for the analysis of defects in Czochralski-grown silicon crystals [6]. In this
* Corresponding author, fax f49 0331-288-1474, 0331-288-1468, e-mail: [email protected].
tel. +49
paper we wish to demonstrate a method to measure the time dependence of the phase transitions as a function of pressure and temperature.
2. Experimental The diffractometer is a high pressure device [7], combined with an energy-dispersive solid state detector. The high pressure vessel is a cubic anvil apparatus which compresses a cube with an edge length of 8 mm by six tungsten carbide anvils [l]. The cube is made of a mixture of boron and epoxy resin for high X-ray transparency with the sample in the centre. The anvils glide in guide blocks which are fitted to a hydraulic ram. The synchrotron beam impinges on the sample between the anvils along the face diagonal, and the diffracted beam can be detected under angles up to 30”. With this apparatus a pressure of 80 kbar and a maximum temperature of 2000 K can be achieved. Pressure is determined by the shift of diffraction lines of an internal standard with well known Pm-data (e.g. NaCl). The sample can be heated by an internal graphite furnace, controlled by a thermocouple. The experimental setup for energy-dispersive X-ray diffraction experiments has been previously described [8]. The sample in a high pressure-high temperature environment is illuminated by a white X-ray beam. The scattered beam is analysed by a solid state detector under a fixed scattering angle. The resulting spectrum is stored in a multi-channel analyser. For the evaluation of the diffraction diagrams a sophisticated software is available [9].
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. AI1 rights reserved SSDI 0168-583X(94)00348-3
II. CERAMICS
90
P. Zinn et al. / Nucl. Instr. and Meth. in Phys. Res. B 97 (I 995) 89-91 ibO0
counts (arb. units)
IO
20
0
30 1)
JO
Energie (KcV)
Fig. 1. Sequence of diffraction
diagrams versus time during the phase transition.
Because of the high intensity of synchrotron radiation diffraction diagrams can be recorded within a few seconds, typically 20-200 s. This offers the possibility to carry out time resolved studies during a phase transition. The method is simple: in preliminary experiments the phase boundary is determined. For the kinetic experiment the conditions (P, T) are chosen below the phase boundary; then the temperature is raised quickly beyond the boundary. The diffraction diagrams are collected in a fast sequence for fixed time intervals until the transition is completed. In Fig. 1 series of diffraction diagrams are shown, taken at 35
kbar and 1073 K demonstrating the a-quartz-coesite sition.
tran-
3. Results The kinetics of an interface-controlled solid state phase transition can be described by the Avrami equation [lo], even at high pressure conditions [ll]: X(t) = 1 - exp( -Zct”),
(1)
with: X(t) = degree of transformation, k = rate function (function of pressure, temperature, grain size etc.), t = time, IZ= exponent, determined by the mechanism of nucleation. In our experiments the degree of transformation X(t) has been estimated from the observed Bragg intensities of the coesite phase due to Znragg= Vsample. Eq. (1) leads to: x(t) = ZBra&)/ZO, with I,, = Bragg intensity after the transformation is completed [lo]. The parameters k and n can be calculated by fitting a plot versus In t (Fig. 2). We have measured a total of three k values for the a-quartz-
T !
Table 1 Observed and calculated temperature conditions 800
time
lZO0
(set)
Fig. 2. X(t) as a function of time t, where X is the normalized intensity of the coesite-phase diffraction line indicated in Fig. 1. The data (circles) are fitted by the Avrami equation (solid lines).
X,-values
for different
pressure
Nr.
P [kbar]
T [Kl
k x lo4 [s- ‘1
1 2 3
35 36 45
1170 1143 1093
6.00 5.40 2.20
and
P, Zinn ef af. /Nucl. Instr. and Me&. in Phys. Rtts. B 97 (fwts) 89-91
coesite transition at different temperatures and pressures (Table 1). The “fuh pattern” method gives a complete diffraction diagram at every time interval. Therefore it not only leads to the rate constant k,, but aIso contains fuI1 information on the crystal structure [12]. Main characteristic of the transition is a change from space group P3,21 for a-quartz to C2/c which results from the building of four-rings chains consisting of I~iU~J4--t~trahedr~s in the case of coesite.
4. Discussion and conclusions The experiments described in this paper have demonstrated that energy-dispersive X-ray di~raction combined with high intensity synchrotron radiation is a most powerful instrument for geological research. We were able to calculate important thermodynamicaly data describing the rate of a phase transition with good accuracy. The pressure temperature dependence of the rate constant K, could be determined. When using the “full pattern” method we were also able to observe the structural change of the phases during the transition and to give evidence for specific mechanism during the transformation. On the formation of coesite from starting o-quartz, a similar strained quartz is recognised as an intermediate stage from the broadness of the di~ract~on lines of the o-quartz phase,
91
Acknowledgement This work was supported by the German Federal Minister of Research and Technology under contract number no. 05 447 K&M9.
References [I] E. Hinze, J. Kremmler and J. Lautejung, HASYLAB Jahresbericht (1991). [2] L. Goes, Science 118 (1953) 113. [3] G-gun Liu and W.A. Bassett, Elements, Oxides, and Sili-
cates - High-Pressures Phases with Implications for the Earth’s Interior (Oxfort University Press, New York, 1986). fitt B.V. Chesnokov and VA Popovsftokt. Al&. Nauk SSSR, 162 (1965) 176. [5] C. Chopin, Contrib Mineral Petrol 86 (1984) 107. [6] A. Bourret,E. Hinze, H.D. Hochheimer,Phys. Chem. Minerals 13 (1986) 206. {7] 0. S&momma et al., in: Solid State Physics under pressure, S. Minomura~ cd., ffieidel, Dordrecht, 1985) p, 351. [s] J. Lauterjung and G. Will, Physica B 139/l& (19%) 343. [9] .I. Lautejung, G. Will and E. Hinze, Nucl. Ins@. and Meth. A 239 (1985) 281. [lo] J.W. Cahn, Acta Metallurgica 4 (1956) 449. Ill] E. Hinze, J. Lauterjung and G. Will, Nucl. Instr. and Meth. 208 (1983) 569. [I21 J. Lauterjung, fnauguraf Dissertation, Bonn, 1985.