Energetics, equation of state, and elasticity of NAL phase: Potential host for alkali and aluminum in the lower mantle

Authors


Abstract

[1] The new aluminous (NAL) phase and aluminous phase with calcium ferrite (CF) structure constitutes more than 25 volume % of the deeply subducted crust at lower mantle depths. Using first principle simulations, we calculate the energetics, equation of state, and elasticity of NAL phase with a widely varying composition including CaMg2Al6O12, NaNa2Al3Si3O12 and KNa2Al3Si3O12. Our calculations indicate the relative stability of NAL and CF phases is a sensitive function of pressure, temperature, and composition, with increasing pressure tending to favor the CF phase, and increasing temperature, Mg-content and alkali-content tending to favor the NAL phase. The sound wave velocities of the NAL phase is significantly lower than CF phases and other major lower mantle phases. In deeply subducted MORB and CC, the faster sound velocity of silica (SiO2) and its high-pressure polymorphic phase is likely to be compensated with the slower sound wave velocities of NAL phase.

1. Introduction

[2] Subducted crust has a distinct major and trace element chemistry in comparison to peridotites. While the bulk silicate Earth contains 4.5 wt% alumina [McDonough and Sun, 1995], oceanic (MORB) and continental crust (CC) are significantly enriched with ∼15–16 wt% alumina [Irifune and Ringwood, 1993; Kesson et al., 1994], while subducted terrigenous sediments may have alumina content of 20 wt% [Irifune et al., 1994]. This high alumina content stabilizes aluminous phases in deeply subducted crust that are not present in mantle peridotite. At lower mantle depths, the volume fraction of the CF and NAL phases in MORB is ∼10–25 vol% [Ricolleau et al., 2010] (Figure 1). NAL may also be stabilized in deeply subducted Archean continental crust (CC) of tonalite-trondjhemite-granodiorite (TTG) composition [Kawai et al., 2009; Komabayashi et al., 2009]. Moreover, the NAL and CF phases are known to host the alkali elements (Na and K) that are enriched in subducted crust as compared with average mantle [Miyajima et al., 2001].

Figure 1.

(a) Schematic diagram illustrating mantle heterogeneity consisting of fragments of subducted oceanic crusts. The recycled oceanic crust, through subduction, is the primary source of heterogeneity in the mantle [Brandenburg and van Keken, 2007; Nakagawa et al., 2010]. It is likely that the subducted crusts might have accumulated at the CMB over geological times [Kawai et al., 2009; Komabayashi et al., 2009]. (b) A tetrahedral plot showing the various end-member composition of the aluminous phase. In this study we have considered, NAL phases with KNa2Al3Si3O12 (light blue star); NaNa2Al3Si3012 (grey star) and CaMg2Al6O12 (green star) stoichiometry; crystal structure of (c) NAL phase and (d) CF phase. The energetics along NaAlSiO4-KAlSiO4 join (e) at 0 GPa, (f) at 30 GPa, and (g) at 120 GPa; the blue filled rhomb represents the NAL phase with KNa2Al3SiO12stoichiometry; the end members, open circles- CF phase; open rhombs NAL phase. The energetics along CaAl2O4-MgAl2O4 join is shown in (h) at 0 GPa, (i) at 30 GPa, and (j) at 120 GPa; the green filled rhomb represents CaMg2Al6O12stoichiometry with hexagonal symmetry; the end members, open circles- CF phase; open rhombs NAL phase. The relative magnitude of –TSconfig term for complete disorder configuration of K and Na atom in KNa2Al3Si3O12 and Ca and Mg in CaMg2Al6O12 is also shown at T = 2000 K.

[3] Despite their importance in understanding the buoyancy of subducted crust and its possible accumulation at the base of the mantle [Ricolleau et al., 2010], and its seismic detectability, little is known of the physical properties of the aluminous phases compared with those stable in peridotite. The seismic wave velocities of the NAL and CF phases are unknown at lower mantle conditions, and the density is known in only a few bulk compositions. Moreover, the factors governing the relative stability of CF and NAL phases are poorly understood. Which of these phases is stable, and over what range of pressure, temperature, and bulk composition, may be important because they are likely to have distinct physical properties. One of the challenges in understanding these phases is that they exhibit a wide range of compositions incorporating alkali and alkaline earth elements as well as Al and Si.

[4] In this article, we explore the relative stability of NAL and CF phases and compare their physical properties, including density and seismic wave velocities in order to evaluate their role in subducted crustal buoyancy and the detectability of deeply subducted crust. We compute the enthalpy, equation of state, and full elastic constant tensor across a wide range of plausible mantle compositions along the Na3Al3Si3O12-K3Al3Si3O12 and Ca3Al6O12-Mg3Al6O12 joins. Computations of equation of state and elasticity focus on the NAL phase, which we compare with our previous calculations of these quantities in the CF phase [Mookherjee, 2011].

2. Method

[5] The NAL phase has a hexagonal space group P63/m [Miura et al., 2000] and a structural formula of AIXB2VIIIC6VIO12. The AIXsite is a nine-fold coordinated tunnel with a hexagonal cross-section and is typically occupied by a large monovalent (e.g., Na+, K+) or divalent cation (e.g., Ca2+). The cation in the AIX site is likely to be disordered owing to its Wyckoff symmetry being 2a and only one atom occupies either of the two equivalent sites, i.e., half occupancy. The BVIIIsite has a di-trigonal cross section and is typically occupied by a smaller cation (e.g., Mg2+, Fe2+). The CVIsite is octahedral site and is typically occupied by a framework-forming cation (e.g., Al3+, Si4+). The octahedral units form edge-sharing double chains in the hexagonal aluminous phase (Figure 1). The structural formula of the CF phase may be written in a 12 oxygen basis to permit direct comparison with that of the NAL phase: B3VIIIC6VIO12 with an orthorhombic space group (Pbnm) and four formula units (Z = 4 on a 4 O primitive basis) in the unit cell [Decker and Kasper, 1957]. The BVIII sites are often occupied by Na1+, Mg2+ or Ca2+ cations whereas the CVIsites are typically a framework-forming cation (e.g., Al3+, Si4+) similar to the NAL phases (Figure 1).

[6] Static, density functional theory calculations (VASP) were performed with the local density approximation (LDA) and ultrasoft pseudopotentials as described in Mookherjee and Steinle-Neumann [2009a, 2009b] and Mookherjee [2011]. Calculations for NAL phase are performed in a 21 atom primitive unit cell, and for the CF phases a 28 atom primitive unit cell. We consider the following compositions for both phases: Ca3Al6O12, Mg3Al6O12, Na3(Al3Si3)O12, K3(Al3Si3)O12 and for the more flexible NAL phase only the intermediate compositions: CaMg2Al6O12, KNa2(Al3Si3)O12 and NaNa2(Al3Si3)O12. We use an energy cutoff Ecut = 600 eV and k-point mesh of 2 × 2 × 2. A series of convergence tests demonstrated that these computational parameters yield total energies that are converged to within 10 meV/atom. We analyze bulk compression behavior using the third order-Birch Murnaghan equation-of-state [Birch, 1978]. Full elastic constant tensor were determined by straining the lattice by 1%, the details of the methods are described in [Karki et al., 2001]. Four distinct strain tensors inline image are applied to calculate the five elastic constants C11, C12, C13, C33, and C44 of hexagonal symmetry. Finite strain fits to the elasticity data were made using the finite strain formulations as in our previous studies [Karki et al., 2001; Mookherjee et al., 2011]. We computed the single crystal azimuthal anisotropy for P- and S-waves using the formulation for maximum polarization anisotropy [Mainprice, 1990].

3. Results

[7] Our calculations reveal that with increasing pressure, the enthalpy of the CF phase lowers with respect to the NAL phase for all compositions. This trend explains the disappearance of NAL from the MORB compositions at pressures ∼40 GPa [Ricolleau et al., 2010]. On the alkali (K-Na) join NAL remains more stable than CF even at core-mantle boundary pressure. This emphasizes that the large ions are readily accommodated in the NAL structure, which unlike the CF structure, features a nine-fold coordinated site. There is excellent agreement between our predicted energetics and the experimental phase diagram along the Ca3Al6O12-Mg3Al6O12 join [Akaogi et al., 1999] including the stability of NAL at the Mg3Al6O12-end, the CF phase at the Ca3Al6O12-end, and the field of pure NAL at CaMg2Al6O12composition at all pressures up to CMB, with the 1:2 Ca:Mg ratio accommodated by the 1:2 ratio of nine- to eight-fold coordinated sites in the NAL structure (Figure 1).

[8] The equation of state of the NAL phase is well represented by a third order Birch-Murnaghan formulation (Figure 2 and Table 1). The theoretical results are in good agreement with the experimentally observed and theoretically determined compressibilities for NAL phase [Vanpeteghem et al., 2003; Guignot and Andrault, 2004; Kawai and Tsuchiya, 2012].

Figure 2.

(a) Equation of state (pressure-volume plot) for NAL phases and CF phases with NaAlSiO4 [Mookherjee, 2011] and CaMg2Al6O12 stoichiometry. The CaMg2Al6O12 stoichiometry is derived from [(1/3) CaAl2O4 + (2/3) MgAl2O4]. (b) Lattice parameter-a; and (c) cvs. unit-cell volume; experimental data are from GA: [Guignot and Andrault, 2004]; V: [Vanpeteghem et al., 2003] and S: [Shinmei et al., 2005]; calculations, NAL refers to NaNa2Al3Si3O12; KNAL refers to KNa2Al3Si3O12 and CaMg refers to CaMg2Al6O12; Calculated elastic constants: (d–f) longitudinal elastic constants C11; C33, off-diagonal elastic constantsC12 and C13 and shear elastic constants C44; (g–i) Bulk (K) and shear (G) moduli for the NAL phases considered in this study. Lines are finite strain fits with the parameters listed in (Table 2).

Table 1. Equation of State Parameter for NAL and CF Phasesa
ChemistryV0K0K′References
  • a

    Unit of volume (V0) and bulk modulus (K0) are Å3 and GPa respectively.

  • b

    Stoichiometry expressed in 12 oxygen basis; in brackets, we report the V0 for 4 oxygen atom basis.

NAL Phase
(Na)(Na)2Al3Si3O12178.3 (59.4)1854.0LDA [this study]
(K)(Na)2Al3Si3O12183.7 (61.2)1774.9 
(K)(K)2Al3Si3O12210.7 (70.2)1474.8 
(Mg)(Mg)2Al6O12179.1 (59.7)2114.0 
(Ca)(Mg)2Al6O12181.8 (60.6)2124.2 
(Ca)(Ca)2Al6O12196.8 (65.6)1994.2 
 
CF Phase
(Na)3Al3Si3O12b235.4 (58.9)1954.0 
(K)3Al3Si3O12b284.0 (71.0)1304.0 
(Mg)3(Al3Al3)O12b235.9 (59.0)2133.8 
(Ca)3(Al3Al3)O12b258.5 (64.6)1964.3 
 
Experiments
Na, Mg rich188.0 (62.7)1844.0Guignot and Andrault [2004]
Ca, Na rich185.3 (61.8)1776.5 
Ca, Na rich184.2 (61.4)2264.0 
K rich186.4 (62.1)1835.8 
K rich185.8 (61.9)2174.0 
Na, Mg rich184.6 (61.5)2143.0Vanpeteghem et al. [2003]
 
Ab Inito
NaAlSiO4176.1 (58.7)1974.5Kawai and Tsuchiya [2012]

[9] The elastic constants of the NAL phase increase monotonically with pressure up to lower mantle pressure for all phases and compositions, demonstrating mechanical stability (Figure 2). The C33 elastic modulus is always stiffer than C11 at all pressures and in all compositions. The maximum stiffness along c-axes is related to the sharing of edges by the stiff octahedral units along the channel direction (Figure 1). In the direction perpendicular to the channel, these polyhedra share corners and the compression is accommodated by adjusting the Si(Al)-O-Si(Al) hinge angles and di-trigonal shape of the channels. The shear elastic modulusC44is the softest compared to the principal and off-diagonal elastic modulus (Figure 2).

[10] The elasticity of the aluminous phases are sensitive to the chemistry and the crystal structure, i.e., NAL vs. CF phase (Figure 3 and Table 2). The S-wave velocity of the NAL phase is substantially less than that of the CF phase in alkali- (Na-K) and alkaline-earth (Ca-Mg) compositions. In both phases, alkaline-earth compositions are faster than alkali compositions when compared at the same density, consistent with the greater compressibility of alkali cations as compared with alkaline-earth cations [Hazen and Finger, 1979]. The elastic anisotropy also depends on chemistry and crystal structure (Figure 3). At the upper part of the lower mantle the anisotropy of the CF phase [Mookherjee, 2011] is larger than the NAL phase (Figure 3). At higher pressure, AP and AS1 anisotropy significantly reduces, whereas AS2 increases.

Figure 3.

Velocity density systematics: (a) compressional and (b) shear wave velocities, the solid black lines represents the linear relation for constant mean atomic weights; the thick grey line represents PREM [Dziewonski and Anderson, 1981]. The velocities of major mantle phases - MgSiO3 perovskite, MgO, CaSiO3 perovskite, SiO2 and Al2O3 are from [Karki et al., 2001]. Two aluminous phases (NaAlSiO4 and MgAl2O4) with CF structure are from [Mookherjee, 2011]; the grey; blue and green filled circles represents NAL phase with NaNa2Al3Si3O12, KNa2Al3Si3O12 and CaMg2Al6O12stoichiometry from this study; (c) dependence of P-wave; (d) S1- and S2- wave velocities with direction at V ∼ 155 Å3 for NAL phases; (e) variation of AP; (f) AS1 and AS2 anisotropy with pressure.

Table 2. Elastic Constants (Cij), and Bulk (K) and Shear (G) Moduli for NAL Phasea
VPC11C12C13C33C44KVoigtKReussGVoigtGReuss
  • a

    Pressure (P) and elastic moduli (Cij, K and G) are in GPa and volume (V) is in Å3.

  • b

    Pressure derivatives, ∂M/∂P, where M refers to Cij; K and G.

KNa2Al3Si3O12
195−9202417146711313811610799
185−12967794515132182170131126
17510390125121576151232226153149
16525483180157657175290286176172
15546593253206759201364362200195
14575726342270883232455455228228
1351178764613561041269571571257249
12517610736164711244316723723294282
 
Finite Strain Fit
18403078298522134194186138136
  8.0b4.32.76.41.93.94.11.71.6
 
NaNa2Al3Si3O12
195−14118−387454107115559071
185−621348111463125159130108100
1754333108109541147207198140135
16517420153142613171258252163158
15534518215185703197323319186181
14558632289244815229404401213213
13590760384322950269503501241233
1251349255044281122319633631277265
 
Finite Strain Fit
178027077114520138194183137133
  8.9b4.62.06.22.13.84.11.71.6
 
CaMg2Al6O12
185−438247212479115200200136131
180242650614294126224224147143
1759466545163110137249249158154
16525554631216162164313313179176
15547668735275208193384384209205
14578787862362284229477477235232
1351199231017470379274591591264259
 
Finite Strain Fit
182041013588494122216216145141
  6.5b3.32.76.01.83.83.81.61.6

4. Geophysical Implications

[11] Our results indicate that the relative stability of the NAL and CF phases is a sensitive function of pressure, temperature, and composition. While pressure tends to favor stability of the CF phase, enrichment in Mg or alkalis tends to favor the NAL phase. We anticipate the range of stability of the NAL phase in the lower mantle will be a sensitive function of composition, particularly of the whole-rock Mg and alkali concentrations. Previous experimental results on one particular basalt composition, which shows the NAL phase stable to about 40 GPa [Ricolleau et al., 2010], may not be representative of all geophysically relevant basalts, and variations in alkali or Mg content, due for example to processing of subducted oceanic crust on its way down through the arc, or differing conditions of oceanic crust formation in the early earth may lead to differing extents of NAL stability. Stability of NAL in continental crustal compositions likely also depends on the bulk composition, e.g. present day mean CC vs. TTG compositions that may have been more important in the past [Komabayashi et al., 2009].

[12] The relative stability of NAL and CF phases is important because as shown by our results, they have distinctive physical properties. The NAL phase is seismically slower than the CF phase. Thus any attempt to draw conclusions about the seismic signature of deeply subducted crust, or possible large-scale ponding of ancient crust at the base of the mantle, must account for the relative stability of these two phases. Stability of the NAL phase in the deep lower mantle may be particularly important for understanding the origin of large-scale low velocity provinces [Garnero and McNamara, 2008]. Our results indicate that previous attempts to model the seismic signature of subducted crust need to be modified to account for the possibly stability of NAL. In the study of [Ricard et al., 2005], excess alumina in subducted crust was modeled as pure Al2O3 (and high pressure polymorphs) phase. This is incorrect since based on phase relations it is known that crustal compositions stabilize CF and NAL phases, and CF and NAL are much slower than pure Al2O3 compounds (Figure 3). Recent studies on seismic profiles of MORB have incorporated CF phases [Xu et al., 2008] as a proxy for the entire suite of possible aluminous phase in subducted crust. This requires further revisions since our study indicates that (a) chemistry (large incompatible cations) dictates the relative stability of NAL and CF phase; and (b) NAL has very low seismic velocity compared with CF.

Acknowledgment

[13] The Editor thanks the anonymous reviewers. Authors acknowledge constructive criticism by two anonymous reviewers.