Ab initio investigation of high-pressure phase relation and elasticity in the NaAlSi2O6 system

Authors


Abstract

[1] Subducted crusts contain aluminous phases with incompatible elements such as sodium. In order to understand the fate of subducted crusts and how they recycle within the Earth, it is important to investigate high-pressure stability and elastic properties of host phases. Here we have studied NaAlSi2O6 jadeite, a NaAlSiO4 calcium ferrite (CF)-type phase, and SiO2 stishovite by means of a first principles computation method. Jadeite was found to dissociate into an assemblage of the CF-type phase and stishovite at about 18 GPa, associated with remarkable increases of compressional wave (18.7%), shear wave (26.4%), bulk sound (13.3%) velocities, and density (15.1%). Proximity of this transition condition to the 660 km discontinuity in the mantle transition zone suggests that seismically observed splitting of the reflection could be related to this phase transition, implying subduction of crustal materials down to the mantle transition zone.

1. Introduction

[2] Incompatible elements are known to concentrate in the crust rather than in the mantle [Taylor and McLennan, 1985]. Meanwhile, many geochemical studies have suggested the recycling of subducted crusts [e.g., Hofmann, 1997]. It is important to know how the crust is sinking down into the deep Earth. Among those elements, alkaline metals such as sodium have an important role in the deep Earth's interior since they usually decrease the melting temperature of silicates. Also, subducted crusts may be stagnant in the mantle transition zone [Kawai et al., 2009]. High-pressure phase equilibrium and elastic properties of jadeite, one of the typical sodium-bearing silicate minerals in the crust, are fundamental to understanding the fate of the subducted crust.

[3] Previous experimental studies on host phases of alkaline elements show that NaAlSi3O8 albite dissociates into quartz and jadeite at 2–3GPa and 1300 K [Birch and LeComte, 1960] and then dominant NaAlSi2O6 jadeite further dissociates into an assemblage of stishovite and a calcium ferrite (CF)-type NaAlSiO4 phase:

equation image

at about 23 GPa and 1300–1500 K [Liu, 1978; Yagi et al., 1994]. Later, Akaogi et al. [2002] investigated the thermodynamic properties of NaAlSiO4 nepheline and calcium ferrite, NaAlSi2O6 jadeite, and NaAlO2 phases and confirmed the dissociation of jadeite at consistent P-T conditions. In contrast to the phase stability, elasticity of these phases and its pressure dependence has not yet been studied, although it is interesting to clarify if this transition can produce a seismologically detectable signature. Hence, we have studied first the high-pressure stability of NaAlSi2O6 jadeite, and then the high-pressure elasticity of this system by means of ab initio density functional computation methods.

2. Methods

[4] Our first principles calculations are based on density functional theory [Hohenberg and Kohn, 1964; Kohn and Sham, 1965], the local density approximation (LDA) [Ceperley and Alder, 1980; Perdew and Zunger, 1981] for elasticity and generalized gradient approximation (GGA) [Perdew et al., 1996] for stability. The plane wave energy cutoff was set to 50 Ry. The Brillouin zone was sampled on 2 × 2 × 4 for jadeite and the CF-type phase and 4 × 4 × 6 k-point mesh for stishovite (or CaCl2) using the Monkhorst-Pack method [Monkhorst and Pack, 1976]. Pseudopotentials were generated using the Vanderbilt's [1990] method for Na and O and Troullier and Martins' [1991] methods for Al and Si. The electric configurations psudized are 2s22p63s1 for Na, 3s23p1 for Al, 3s23p23d0 for Si, and 2s22p4 for O. Most of these have been well tested in our previous studies [Tsuchiya et al., 2004a; Tsuchiya et al., 2005]. The effects of using the larger cutoff and k -points on the calculated properties were found insignificant. The full elastic constant tensors of the monoclinic structure with thirteen independent components for jadeite and the orthorhombic structures with nine independent components for the CF-type phase and stishovite were calculated using stress-strain relations [Karki et al., 2001; Tsuchiya et al., 2004b]. The magnitude of all applied strains was 0.01. We confirmed that the linear relation was ensured enough for this strain range. All structural parameters were fully relaxed to a static (0 K) configuration using damped variable cell shape molecular dynamics [Wentzcovitch, 1991] using the PWSCF code until residual forces became less than 5.0 × 10−5 Ry/a.u.

3. Results and Discussion

[5] Jadeite and the CF-type phase have crystal structures with the space group C2/c and Pbnm, respectively (Figure 1a). Jadeite is composed of parallel sheets of octahedrally coordinated aluminum and eight coordinated sodium polyhedra connected by silicate SiO4 tetrahedral chains running parallel to the c-axis [Prewitt and Burnham, 1966]. Yamada et al. [1983] reported that the CF-phase has a framework composed of M1O6 and M2O6 octahedra forming edge-shared double chains running parallel to the c-axis with sodium ions located in eightfold coordination sites in tunnels formed by the octahedral chains. We have tested all possible Al/Si distributions in the M1 and M2 sites in a single unit cell, and found the most stable structure with the Al and Si configuration alternately changing along the a-axis (Figure 1a), which seems energetically favorable in terms of the well-known aluminum avoidance rule.

Figure 1.

(a) Crystal structures of NaAlSi2O6 jadeite and a NaAlSiO4 CF-type phase. Yellow, light blue, dark blue and red spheres are Na, Al, Si, and O atoms, respectively. (b) Volumes calculated within LDA (bold lines). Triangles indicate experimental results for jadeite (red) [Zhao et al., 1997] and stishovite (green) [Ross et al., 1990; Hemley et al., 1994]. Experimental volumes for the CF-type phase are computed using a third order Birch-Murnaghan equation of state with parameters proposed by Akaogi et al. [2002] (blue dotted line). (c) The enthalpy difference of the CF-type phase and stishovite mixture relative to the jadeite calculated based on the GGA.

[6] Calculated pressure-volume relations for jadeite, the CF-type phase, and stishovite are shown in Figure 1b. Equation of state parameters of zero-pressure bulk moduli and its pressure derivatives of jadeite, the CF-type phase, and stishovite are determined by least-squares fitting this data to the third-order Birch-Murnaghan equation (Table 1). We can obtain good agreement with experimental data for jadeite and stishovite [Zhao et al., 1997; Akaogi et al., 2002; Ross et al., 1990; Hemley et al., 1994]. On the other hand, agreement for the CF-type phase is relatively worse but its compression curve has been poorly constrained experimentally so far as reported by Akaogi et al. [2002].

Table 1. Equation of State Parameters for Jadeite, the CF-Type Phase and Stishovite-Calculated Within LDA at the Static Temperaturea
 V0 (cm3/mol)K0 (GPa)K′0
Jadeite (calc)59.3133.23.7
Jadeite (exp)60.4b125c5c
CF-type (calc)35.3196.54.5
CF-type (exp)36.3d240e4e
Stishovite (calc)14.0310.84.7
Stishovite (exp)14.0f291f4.29f

[7] Since previous experimental studies [e.g., Liu, 1978] have reported a dissociation of jadeite to the CF-type phase and stishovite (equation (1)), we investigate the high-pressure thermodynamic stability limit of jadeite by examining the enthalpy balance between jadeite and the CF-type phase + stishovite mixture (Figure 1c). Yamada et al. [1983] have reported the Al-Si disorder in the M sites of the CF-type phase. We first examined the effects of the Al-Si disordering of the CF-type phase for all the cation ordering and found that the CF-type phase structure shown in Figure 1a has the lowest enthalpy. Therefore, in this study we consider this structure to be the CF-type phase. The enthalpy of jadeite becomes higher at 18 GPa than the sum of the enthalpies of the CF-type phase and stishovite, indicating jadeite's dissociation. This behavior matches quite well with experimental results, considering that the reaction boundary has a small positive Clapeyron slope of 3.1 ± 1.0 MPa/K [Akaogi et al., 2002]. Taking a temperature of 1500 K into account, the dissociation boundary becomes 22.5 ± 1.5 GPa corresponding to the depth of 638 ± 30 km which is very close to 660 km.

[8] Elastic constants of jadeite, the CF-type phase and stishovite are shown in Figure 2 as a function of pressure from 0 to 50 GPa. Zero pressure values are also listed in Table 2, and those of jadeite are in excellent agreement with values reported experimentally by Brillouin spectroscopy [Kandelin and Weidner, 1988]. On the other hand, stishovite, which has a tetragonal unit cell with six independent elastic constants, becomes elastically unstable between 40 and 50 GPa due to the breaking of the tetragonal shear stability (C11−C12)/2 > 0 as given by Karki et al. [1997]. Due to this, stishovite undergoes a ferroelastic phase transition to the CaCl2-type phase which is orthorhombic and has nine independent elastic constants.

Figure 2.

Elastic constants as a function of pressure. (a–c) Longitudinal, off-diagonal, and shear elastic constants for monoclinic jadeite, respectively. Circles and squares indicate experimental results at 0 GPa by Kandelin and Weidner [1988]. (d–f) The same groups for the orthorhombic CF-type phase.

Table 2. Elastic Constants (cij), Aggregate Bulk (B) and Shear (G) Moduli of Jadeite and the CF-Type Phase at 0 GPa
 Jadeite (calc)Jadeite (exp)aCF-Type
C11 (GPa)262.7274364.55
C22255.75253353.65
C33285.1282508.9
C4490.8588124.2
C5559.4565151.25
C6693.694125.75
C1289.39485.8
C1362.8571105.55
C2378.958292.4
C1515.854-
C2516.714-
C3516.6528-
C4610.913-
B141.0144.8196.6
G85.485.8141.5
VP (km/s)8.648.829.79
Vs5.0150.85.93
Vϕ6.436.596.99

[9] Taking the Voigt-Reuss-Hill averages of calculated elastic constants, we have obtained the isotropic bulk and shear moduli, and elastic velocities VP, Vϕ, and VS of jadeite, the CF-type phase, and stishovite as a function of pressure (Figures 3a and 3b). The values of jadeite at zero pressure are also consistent with those measured by Kandelin and Weidner [1988]. Using these results, we have next taken the Voigt-Reuss-Hill average of an assemblage of the CF-type phase and stishovite to obtain the aggregate velocities (Figure 3c). The assemblage is 15.1% denser than jadeite because stishovite and the CF-type are both denser than jadeite by +18.3% and +13.8%, respectively. In addition, we computed the azimuthal anisotropy of compressional (AP) and shear (AS) waves [Tsuchiya et al., 2004b] of jadeite and the CF-type phase at 20 GPa. AP = 16.8% and AS = 29.3% were obtained for jadeite and AP = 13.3% and AS = 15.4% for the CF-type phase. AS of jadeite is found particularly larger than that of the CF-type phase.

Figure 3.

(a) Aggregate bulk and shear moduli of jadeite, the CF-type phase and stishovite in the pressure range from 0 to 50 GPa. Open circles indicate experimental results of jadeite at 0 GPa by Kandelin and Weidner [1988]. (b) Longitudinal, bulk and shear wave velocities and densities of jadeite, the CF-type phase, and stishovite. (c) Velocities and densities of jadeite and an assemblage of the CF-type phase and stishovite.

[10] The crust contains alkaline-bearing minerals and jadeite is one of the representative minerals, when the crust descends into the deep Earth. The present calculations and previous experiments indicate that the breakout of jadeite at 18 GPa produces remarkable velocity jumps of the compressional wave (+18.7%), shear wave (+26.4%), and bulk sound (+13.3%) velocities (Figure 3c). While the continental crust has a large volumetric proportion of alkaline-bearing minerals [Irifune et al., 1994; Wu et al., 2009], the oceanic crust has a relatively small proportion [e.g., Irifune and Ringwood, 1993; Hirose et al., 2005]. Even though the volumetric proportion of jadeite would be small in the mantle, these velocity increases may have substantial effects because they are much more significant than those associated with the phase transitions of wadsleyite to ringwoodite, the dominant minerals expected in the transition zone, of at most 2.5% [Kiefer et al., 1997; Kiefer et al., 2001]. The velocity/impedance contrast that jadeite, with even 10 volumetric%, may produce is comparable to the contrast that wadsleyite, with 70 volumetric%, may produce, which is the typical proportion in the pyrolite composition. Deuss and Woodhouse [2001] seismologically observed splitting of the mid-transition zone discontinuity, which is localized beneath the circum Pacific. The depth of jadeite dissociation seems to match this observation. While in a global context, the 660 km discontinuity is due to the phase transition from ringwoodite to an assemblage of perovskite and ferropericlase which are expected to exist widely below the mantle transition zone. Splitting of the 660 km discontinuity is possibly related to the dissociation of jadeite to the CF-type phase plus stishovite assemblage which would be carried entangled in subducted crusts. Also, this might imply the existence of stagnant crusts in the mantle transition zone [Kawai et al., 2009]. Continental crusts also contain potassium feldspar. Its high-pressure phase with a hollandite structure was recently reported to also show a characteristic elastic behavior under pressure about 33 GPa [Mookherjee and Steinle-Neumann, 2009], which was anticipated to be related to the 920 km seismic scattering [Kawakatsu and Niu, 1994].

Acknowledgments

[11] We thank Shigenori Maruyama for valuable discussions. We also thank Haruhiko Dekura and Yoshinori Tange for their technical instruction. KK is supported by JSPS Fellowships for Young Scientists and JSPS Excellent Young Researcher Overseas Visit Program. This work was completed under the supports in part of the Grant-in-Aid for Scientific Research from JSPS (grant 21740379) to TT and of Ehime Univ. Global Centers of Excellence program “Deep Earth Mineralogy” to TT and KK.

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