|
|
 |
|||||||||||||||||
|
|||||||||||||||||
 |
|||||||||||||||||
| JOURNAL HOME | HELP | FEEDBACK/COMMNET | SUBSCRIBE | ARCHIVE | SEARCH | TABLE OF CONTENTS |
Articles |
1 Institute of Mineralogy and Petrography, pr. Ak.Koptyuga, 3, Novosibirsk, 630090, Russia
2 Institute for Silicate Chemistry, ul. Odoevskogo, 24, korp.2, St. Petersburg, 199155, Russia
* E-mail: svg{at}uiggm.nsc.ru
This paper was presented at the EMPG VIII meeting in Bergamo, Italy (April 2000)
 |
Abstract |
|---|
 Top Abstract 1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
The natrolite structure has some advantages upon other zeolites to understand the amorphization mechanism, because samples of this mineral surrounded by a non-penetrating medium show no crystal phase transitions with increasing pressure. Lattice energy minimization calculated with variable unit-cell dimensions shows the crystal structure to become unstable at about 5.5 GPa, thereby apparently explaining the amorphization process at 4–7 GPa. This instability is connected with shear acoustic modes coupled with soft internal framework vibrations.
Key-words: Raman spectra, IR spectrum, natrolite, lattice dynamics, vibrational modes, phonon dispersion curves.
|
1. Introduction |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
The structure of natrolite Na4[Al4Si6O20] 4H2O, which is the simplest one among zeolites (Gottardi & Galli, 1985), can be used as an example of calculation of a full set of vibrational modes and their subsequent comparison with the observed vibrational modes, especially Raman-and IR- active frequencies obtained from a single crystal. The results of such calculations involve the determination of symmetry and relative displacements of all atoms in the modes, including the external modes of water molecules in the channels, as well as the evaluation of the elastic moduli and the bulk modulus.
The problem of pressure-induced amorphization of crystals, including the influence of preceding or accompanying solid-phase transformations, is widely studied at present (Gillet et al., 1996; Hemley & Ashcroft, 1998; Ovsyuk & Goryainov, 1999). Since static deformations of crystals connected with variation of thermodynamical parameters can also be considered as frozen vibrations, our calculations can verifiy the instability range of the natrolite structure at high pressure, thereby providing a possibility to elucidate amorphization mechanisms. Note that the natrolite structure has some advantage over other zeolite structures to understand the amorphization mechanisms; such an advantage occurs because only natrolite shows no pressure-dependent crystal phase transitions, if compressed in a non-penetrating medium (Kholdeev et al., 1987; Belitsky et al., 1992).
|
2. Experimental and calculation techniques |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
|
|
|
|
3. Results and discussion |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
Factor group analysis and lattice-dynamical calculations of natrolite vibrations were carried out for the primitive cell of Fdd2 space group symmetry, Z = 2, containing 46 atoms: Na4[Al4Si6O20] 4H2O. According to theory, there should be a total of 99 optically active modes 24A1 + 25A2 + 25B1 + 25B2 concerning motion of framework and intrachannel cations, to be compared with a total of 78 peaks observed in Raman and IR spectra (28A1 + 15A2 + 12B2 + 23B2), and a few additional modes discussed below (Tables 1 and 2, Fig. 1). All the Raman bands below 1100 cm–1 are quite narrow with a bandwidth of about 5–7 cm–1. Of the predicted total of 74 IR-active modes (not concerning water vibrations), 36 peaks only were observed in the IR spectra, and of the predicted 36 optically-active (Raman and IR) modes 9A1 + 9A2 + 9B1 + 9B2 implying water molecules, only 16 main modes 7A1 + 3A2 + 3B1 + 3B2 were reliably observed. In addition, 16 O-H vibrational peaks (4A1 + 4A2 + 4B1 + 4B2) could be detected. Several external modes of H2O seem to be overlapped by strong framework bands (Tables 1–3). Using light-scattering geometry (Fig. 1, Table 1) the appropriate symmetry and TO-LO labelling could be assigned to the different modes. Some purely transverse optical (TO) modes are marked in Table 1, whereas the other modes belong to mixed longitudinal-transverse optical LO-TO type. Additional peaks (including A1 modes at 520, 976 and 1072 cm–1) appear to be due to the effect of longitudinal-transverse interaction on phonon frequency; such a phenomenon is similar to the dependence of Si-O vibration frequency upon the wave vector direction, which has been observed in quartz (Wilkinson, 1973).
|
|
|
Intensities of (aa), (bb) and (cc) polarization spectra in Fig. 1 essentially differ, thereby proving the existence of strong anisotropy in bond polarizability. In our calculations of the intensity of Raman peaks, we assumed longitudinal polarizability of T-O bonds; the calculated intensities are in satisfactory agreement with the experimental values. Such results suggest that the Sil-O-Si2 bonds making an angle of about 20° with the a-axis are essentially covalent and give a strong contribution to the intensity of the Raman bands, whereas the Sil-O-Al bonds elongated along the b-axis are essentially ionic and result in a smaller intensity of the bands. The polarization of the Si2-O-Al bonds gives equal contributions in all (aa), (bb) and (cc) polarization spectra.
3.2 Vibrations of water molecules in natrolite
The Raman frequencies of D2O-natrolite were calculated (see Table 3) using the M-2 model with the same valence force constants as for H2O-natrolite and also using the M-3 model, which uses essentially different valence force constants (Table 4). These data prove that molecular geometry and hydrogen bonds differ in H2O- and D2O-natrolites.
|
The Raman spectrum of water in natural natrolite in Fig. 1 exhibits two main O-H bands at V1 = 3331 cm–1 and V3 = 3542 cm–1 and several additional bands of smaller intensity, which can be combined in two doublets at v’1 = 3187, v’3 = 3385 and v"1 = 3226, v"3 = 3473 cm–1. These two doublets can be ascribed to vibration of H2O molecules located in two additional sites in the crystal, W’ and W", with approximate relative occupancy of about 5 % with respect to that of the main W site, which is almost completely occupied. This assumption is supported by the chemical composition of natural natrolite, which shows an excess of water of at least 1.5 % (or 0.03 H2O per ideal 2 H2O formula unit).
The frequencies of internal vibrations with different symmetry practically coincide, thereby suggesting the absence of strong water-water interaction. The small bandwidth (25–35 cm–1) of internal H2O vibrations (vibrons) is in favour of proton ordering in all positions of water in natrolite. Note that there are different contributions in the broadening of bands. For instance, the increase of the vibron bandwidth at phase transition from ice VIII to ice VII at high pressure has been tentatively assigned to its decay into bending modes (Besson et al., 1997).
The external vibrations of water molecules in natrolite are given in Table 3. Reliably observed bands of this kind occur at 706 and 187 cm–1 or at 143 cm–1 in the Raman or IR spectrum, respectively, and are essentially shifted on deuteration. In the Raman spectrum these bands have low intensity, and are slightly broader than the other bands. The Raman bands at 502 and 673 cm–1 proper to D2O-natrolite are well distinguished. The latter one cannot belong to a D2O libration mode, and should rather be ascribed to a framework mode with intensity enhanced due to interaction with heavy water. Several external H2O vibration bands were not distinguished, very probably because they are overlapped by strong framework bands. Moreover, there are several additional framework modes which strongly interact with external water modes, and this situation leads to large frequency shifts on deuteration, for instance, the H2O-natrolite framework mode at 414 cm–1 shifts in D2O-natrolite to 396 cm–1. The observation of external vibrations of water for zeolites allows to elucidate essential features of hydrogen bonds and watercation interaction. Although such a feature is especially characteristic for zeolites, a similar situation concerning such modes occurs in natrolite and gypsum (Berenblut et al., 1971). At low temperatures, apparent bands of external vibrations of water molecules in proton-ordered ices were recorded (Sherman & Wilkinson, 1980). In liquid water at ambient conditions, a translational modes were observed in Raman spectra at 50 and 170 cm–1 (Moskovits & Michaelian, 1978), which are essentially lower than corresponding vibrations in natrolite (Table 3). In liquid water there is a translational mode at 290 cm–1, which can be interpreted as the W-W motion, leading to high frequency due to the small effective mass (coefficient 1/2). Such motions are impossible in natrolite, where each water molecule is isolated and there is no water-water interaction. Note that the libration modes of H2O in dioptase were observed at 613 and 732 cm–1 (Goryainov, 1996); such values are close to the corresponding modes in natrolite (Table 3).
In comparison with the Raman spectra reported by Pechar et al. (1981), we observed about 40 additional bands involving framework and extra framework cations in different scattering geometry, which can be related to 27 modes. Since the intensity of many bands reported by these authors is essentially different from our results, a first possible explanation could be that the crystals used come from different localities and are physically different; however, their compositions are close to that of the ideal formula. Therefore, we have good reasons for assuming that there are mistakes in the table of Raman intensities given by Pechar et al. (1981). The frequencies of many corresponding bands also significantly differ, as for instance our (bb) peak at 492 cm–1 versus 480–482 cm–1, or our 3331 cm–1 versus 3293 cm–1 of Pechar et al. (1981). The good accuracy of our wavelength measurements obtained from neon-line lamp calibration is confirmed by the frequency coincidence of the corresponding bands in different geometry of Raman scattering, as well as by the vicinity of Raman and IR frequencies of several bands, including the O-H stretching bands.
3.3 Parameters of the valence force field models
As it was stated before, our calculations of vibrational spectra were performed using a number of VFF (M-1, M-2, M-3) and lAP models. In the VFF M-1 and IAP models the water molecule H2O was represented as effective atom. The details of the parameter fitting in different models are discussed below, while the results of the M-1 model are given in Fig. 2 to 4. The forms of two modes, most intensive in Raman spectra, calculated in the M-1 model are represented in Fig. 2 and 3.
|
The parameters in VFF models (M-1, M-2, M-3) were adjusted on the basis of best fit of the calculated frequencies to the corresponding experimental values, and as a result the set of force constants was obtained and reported in Table 4. For instance, the force constant K(Si-O) varies from 4.8 to 5.15 mdyn/Å for different Si-O bonds. These values of K(Si-O) fitted in the model are not connected with Si-O bond length, which changes very little in natrolite, but they express the effective influence of surrounding atoms. Other force constants are given a unique value for each kind of bonds (Al-O) and angles.
For the M-1 model the diagonal force constants are K(Al-O) = 3.2 mdyn/Å, K(O-Si-O) = 0.89 mdyn·Å, K(O-Al-O) = 0.55 mdyn·Å, K(T-O-T) = 0.28 mdyn·Å, where T = Al, Sil, Si2. Cationframework interactions are expressed in terms of force constants K(Na-O) = 0.2 mdyn/Å at distances up to 3 Å. Always in this M-1 model, the interaction of water with the coordination polyhedra involves the force constants K(W-Na) = 0.1 mdyn/Å and K(W-O) = 0.15 mdyn/Å, where W is the oxygen atom of the water molecule.
Three VFF models also involve a long-distance intertetrahedral interaction expressed in the decreasing sequence of force O-O constants, given in Table 4. This stepwise approximation is based on the calculated dependence of O-O force constant on distance (Mirgorodsky et al., 1999). Such long-distance O-O interaction plays an essential role in reproducing the experimental bulk modulus value of quartz (Lazarev & Mirgorodsky, 1991). Note that in the case of natrolite the crystal stiffness increase with respect to quartz is essentially due to Na-O interaction, and as a result the intertetrahedral O-O interaction plays a minor role.
In the M-2 model with H2O as water molecule (while in the M-1 model H2O was considered as effective atom), we found that several force constants in the optimized set of parameters are notably different from those in the M-1 model. For instance: K(T-O-T) = 0.056 mdyn·Å, K(Na-O) = 0.17 mdyn/Å, K(W-Na) = 0.05 mdyn/Å, K(W-O) = 0.045 mdyn/Å, K(O-H1) = 0.11 mdyn/Å, K(OH2) = 0.087 mdyn/Å, K(W-H1) = 6.05 mdyn/Å, K(W-H2) = 6.75 mdyn/Å, K(H1-W-H2) = 0.58 mdyn·Å.
In Table 3, together with the corresponding experimental values, the calculated vibrational frequencies of D2O-natrolite are reported, where the same force constants as in the M-2 model have been used. In addition, those obtained from the M-3 model are also reported: here, the internal force constants for the water molecule are higher: K(W-D1) = 6.67 mdyn/Å, K(W-D2) = 7.0 mdyn/Å, K(D1-W-D2) = 0.582 mdyn·Å.
3.4 Calculation of elactic moduli. Measured and calculated bulk modulus
The value of the bulk modulus K0 = 52.7 GPa calculated in the M-2 model is close to the corresponding experimental value K0 = 47 ± 6 GPa, which was obtained from treatment of our X-ray diffraction data in DAC (Kholdeev et al., 1987) (Fig. 5). Note that the bulk modulus in quartz is 37.1 GPa, and that in coesite is 96 GPa (Kuskov & Fabrichnaya, 1987). Elastic moduli of natrolite at zero pressure calculated in the M-2 model are equal (in GPa) to: C11 = 82.2, C22 = 78.5, C33 = 146.6, C44 = 34, C55 = 38.2, C66 = 31.9, C12 = 30.3, C13 = 39.5, C23 = 34.9.
|
According to some authors (Pasquarello & Car, 1998; Sykes & Kubicki, 1996), silicate glasses exhibit two sharp peaks at 495 and 606 cm–1 in the Raman spectrum, which correspond to breathing vibrations of four- and three-membered rings. Frameworks of zeolites contain different four-membered rings: therefore, using zeolite structures a correlation between the frequency of strong breathing modes and the geometry of four-membered rings can be obtained. For these reasons, the present assignment of the observed vibrational modes of natrolite is the first step to establish this correlation in terms of composition and form of four-membered rings, a point which would be precious to elucidate the internal structure of glasses. For instance, the strongest Raman band at 534 cm–1 in natrolite corresponds to the breathing mode in the so-called <<double-covered>> four-membered ring with internal circle -Al-O3-Si2-O4-Al-O3-Si2-O4- (see Fig. 3), which is covered from above and below by two SilO4 tetrahedra; instead, a similar peak ascribable to such a breathing mode in double-covered four-membered rings has not been observed in Raman spectra of glasses (Pasquarello & Car, 1998). For such non-crystalline materials, the main peak at 495 cm–1 corresponds to simple (<<non-covered>>) four-membered rings, and such result agrees with calculations (Sykes & Kubicki, 1996). This peak is very close to the strongest peak at about 500 cm–1 in analcime (Goryainov et al., 1996), a peak which rather belongs to the breathing mode in simple four-membered rings.
The Raman spectrum of natrolite exhibits a second intensive band at 443 cm–1, which corresponds to a localized O2 oxygen bridge mode (Fig. 2). This mode may be also interpreted as a collapse mode of the helical eight-membered ring forming the channel along [001] or as a non-symmetric breathing mode of the closed eight-membered rings forming the channels along [110]. The origin of the strong 430-cm–1 peak D1’ in glasses is discussed in Pasquarello & Car (1998), or also in Sykes & Kubicki (1996). Our reasonably grounded assignment of strong bands at 434 and 443 cm–1 in natrolite (Table 2), which are close to the D1’ peak, as it is obtained from lattice dynamics, should elucidate the nature of the glass peak: we suggest that it is a breathing mode of eight-membered ring, presumably involving the motion of the four O atoms inside the ring.
3.6 Interatomic potential model calculation of pressure-induced instability of natrolite
Lattice energy minimization using interatomic potentials was also performed in the IAP model for a set of variable unit-cell parameters, in order to predict thermodynamical behaviour of natrolite with respect to pressure. To describe the long-range interaction, the electrostatic or coulombic term is used
 |
 |
For Na-W, W-O interatomic interaction the Born-Karman potential with constants Eij = d2U/drij2, Fij = (1/rij)dU/drij is used in Table 5 (Smirnov et al., 1995).
|
|
4. Concluding remarks |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
|
Acknowledgements |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
Received 15 June 2000
Modified version received 15 January 2001
Accepted 2 February 2001
|
References |
|---|
|
TopAbstract1. Introduction2. Experimental and calculation...3. Results and discussion4. Concluding remarksAcknowledgementsReferences |
|---|
Bartsch, M., Bornhauser, P., Calzaferri, G., Imhof, R. (1994): H8Si8Si8O12: A model for the vibrational structure of zeolite-A. J. Phys. Chem., 98, 2817–2831.[CrossRef][ISI]
Belitsky, I.A., Fursenko, B.A., Gabuda, S.P., Kholdeev, O.V., Seryotkin, Yu.V. (1992): Structural transformation in natrolite and edingtonite. Phys. Chem. Minerals, 18, 497–505.[CrossRef]
Berenblut, B.J., Dawson, P., Wilkinson, G.R. (1971): The Raman spectrum of gypsum. Spectrochim. Acta, 27A, 1849–1863.[CrossRef]
Besson, J.M, Kobayashi, M., Nakai, T., Endo, S., Pruzan, Ph. (1997): Pressure dependence of Raman linewidths in ices VII and VIII. Phys. Rev. B, 55, 11191–11201.[CrossRef]
Chaplin, T., Price, G.D., Ross, N.L. (1998): Computer simulation of the infrared and Raman activity of pyrope garnet, and assignment of calculated modes to specific atomic motions. Am. Mineral., 83, 841–847.[Abstract][ISI][GeoRef]
Gillet, P., Malézieux, J.-M., Itié, J.-P. (1996): Phase changes and amorphization of zeolites at high pressures: The case of scolecite and mesolite. Am. Mineral., 81, 651–657.[Abstract][ISI][GeoRef]
Goryainov, S.V. (1996): Dehydration-induced changes in the vibrational states of dioptase Cu6Si6O18 6H2O. J. Structural Chem., 37, 58–64.[CrossRef]
Goryainov, S.V. & Belitsky, I.A. (1995): Raman spec-troscopy of water tracer diffusion in zeolite single crystals. Phys. Chem. Minerals, 22, 443–452.
Goryainov, S.V., Fursenko, B.A., Belitsky, I.A. (1996): Phase transitions in analcime and wairakite at lowhigh temperatures and high pressure. Phys. Chem. Minerals, 23, 297–298.
Gottardi, G. & Galli, E. (1985): Natural zeolites. Springer-Verlag, Berlin Heidelberg New York.
Hemley, R.J. & Ashcroft, N.W. (1998): The revealing role of pressure in the condensed matter sciences. Phys. Today, 51, 26–32.
Iishi, K., Salje, E., Wemeke, C. (1979): Phonon spectra and rigid-ion model calculations on andalusite. Phys. Chem. Minerals, 4, 173–188.[CrossRef]
Kholdeev, O.V., Belitsky, I.A., Fursenko, B.A., Goryainov, S.V. (1987): Structural phase transformations in natrolite at high pressures. Doklady Akademii Nauk, 297, (4), 946–950 (in Russian). Translated in: Doklady Earth Sciences, 1987, 297.
Kuskov, O.L. & Fabrichnaya, O.B. (1987): The SiO2 polymorphs: the equations of state and thermodynamic properties of phase transformations. Phys. Chem. Minerals, 14, 58–66.[CrossRef]
Lazarev, A.N. & Mirgorodsky, A.P. (1991): Molecular force constants in dynamical model of 
-quartz. A calculation of phonon spectrum, elastic and piezoelectric properties. Phys. Chem. Minerals, 18, 231–243.
McKeown, D.A., Bell, M.I., Etz, E.S. (1999): Raman spectra and vibrational analysis of the trioctahedral mica phogopite. Am. Mineral., 84, 970–976.[Abstract][ISI][GeoRef]
Mirgorodsky, A.P., Smirnov, M.B., Abdelmounim, E., Merle, T., Quintard, P.E. (1995): Molecular approach to the modelling of elasticity and piezoelectricity of SiC polytypes. Phys. Rev. B, 52, 3993–4000.[CrossRef]
Mirgorodsky, A.P., Smirnov, M.B., Quintard, P.E. (1999): Phonon spectra evolution and soft-mode instabilities of zirconia during the c-t-m transformation. J. Phys. Chem. Solids, 60, 985–992.[CrossRef]
Moskovits, M. & Michaelian, K.H. (1978): A reinvestigation of the Raman spectrum of water. J. Chem. Phys., 69, 2306–2311.[CrossRef]
Ovsyuk, N.N. & Goryainov, S.V. (1999): High-pressure twisting of tetrahedra and amorphization in -quartz. Phys. Rev. B, 60, 14481–14484.[CrossRef]
Pasquarello, A. & Car, R. (1998): Identification of Raman defect lines as signatures of ring structures in vitreous silica. Phys. Rev. Lett., 23, 5145–5147.
Patel, A., Price, G.D., Mendelssohn, M.J. (1991): A computer simulation approach to modelling the structure, thermodynamics and oxygen isotope equilibria of silicates. Phys. Chem. Minerals, 17, 690–699.
Pechar, F., Gregora, I., Rykl, D. (1981): Laser Raman polarisation spectra of natural zeolite -natrolite. Coll. Czechoslovak. Chem. Commun., 46, 3043–3048.
Pilati, T., Demartin, F., Gramaccioli, C.M. (1996): Atomic displacement parameters for garnets: A lattice-dynamical evaluation. Acta Cryst., B52, 239–250.[ISI]
Pilati, T., Demartin, F., Gramaccioli, C.M. (1997a): Transferability of empirical force fields in silicates: Lattice-dynamical evaluation of atomic displacement parameters and thermodynamic properties for the Al2SiO4 polymorphs. Acta Cryst., B53, 82–94.[ISI]
Pilati, T., Demartin, F., Gramaccioli, C.M. (1997b): Lattice-dynamical evaluation of thermodynamic properties and atomic displacement parameters for beryl using a transferable force field. Am. Mineral., 82, 1054–1062.[Abstract][ISI][GeoRef]
Salje, E. & Werneke, C. (1982): The phase equilibrium between sillimanite and andalusite as determined from lattice vibrations. Contrib. Mineral. Petrol., 79, 56–67.[CrossRef][ISI][GeoRef]
Sherman, W.F. & Wilkinson, G.R. (1980): Raman and infrared studies of crystals at variable pressure and temperature. In: "Advances in Infrared and Raman Spectroscopy", Heyden, London, Vol. 6, p. 287–290.
Smirnov, M.B., Mirgorodsky, A.P., Quintard, P. (1995): CRYME: a program for simulating structural, vibrational, elastic, piezoelectric and dielectric properties of materials within a phenomenological model of their potential function. J. Mol. Struc., 348, 159–162.[CrossRef]
Sykes, D. & Kubicki, J.D. (1996): Four-membered rings in silica and aluminosilicate glasses. Am. Mineral., 81, 265–272.[Abstract][ISI][GeoRef]
Wilkinson, G.R. (1973): Raman spectra of ionic, covalent and metallic crystals. In: "The Raman effect. Applications", (Anderson A, ed.), Vol. 2, Chapter 5. Dekker, New York.
Winkler, B. & Buehrer, W. (1990): Lattice dynamics of andalusite: prediction and experiment. Phys. Chem. Minerals, 17, 453–463.
Winkler, B., Dove, M. T., Leslie, M. (1991): Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Am. Mineral., 76, 313–331.[Abstract][ISI][GeoRef]
This article has been cited by other articles:
|
|
 |
|
  B.A. Kolesov and C.A. Geiger Behavior of H2O molecules in the channels of natrolite and scolecite: A Raman and IR spectroscopic investigation of hydrous microporous silicates American Mineralogist, July 1, 2006; 91(7): 1039 - 1048. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 S. V. GORYAINOV Amorphization of natrolite and edingtonite at high pressure European Journal of Mineralogy, April 1, 2005; 17(2): 201 - 206. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
N. N. OVSYUK and S. V. GORYAINOV Role of internal pressure in a ferroelastic phase transition European Journal of Mineralogy, April 1, 2005; 17(2): 215 - 222. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
G. D. Gatta, G. D. Gatta, T. B. Ballaran, P. ComodI, and P. F. Zanazzi Isothermal equation of state and compressional behavior of tetragonal edingtonite American Mineralogist, April 1, 2004; 89(4): 633 - 639. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
R. Arletti, R. Arletti, O. Ferro, S. Quartieri, A. Sani, G. Tabacchi, and G. Vezzalini Structural deformation mechanisms of zeolites under pressure American Mineralogist, October 1, 2003; 88(10): 1416 - 1422. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
O. Ferro, S. Quartieri, G. Vezzalini, E. Fois, A. Gamba, and G. Tabacchi High-pressure behavior of bikitaite: An integrated theoretical and experimental approach American Mineralogist, October 1, 2002; 87(10): 1415 - 1425. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| JOURNAL HOME | HELP | FEEDBACK/COMMNET | SUBSCRIBE | ARCHIVE | SEARCH | TABLE OF CONTENTS |
), calculated using the valence force field M-1 model.