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GSA DATA REPOSITORY 2012018 Chilean flat-slab subduction controlled by overriding plate thickness Vlad C. Manea1, Marta Pérez-Gussinyé2 & Marina Manea1

1Computational Geodynamics Laboratory, Centro de Geociencias, Campus Juriquilla, Queretaro, Universidad Nacional Autónoma de México, México

2Department of Earth Sciences, Royal Holloway, University of London, Egham Hill, Egham, TW20 0EX, UK.

1. Supplementary Methods

1.1 Central Chile Geodynamic Modelling Constraints We have tailored our modelling constraints to simulate the Chilean flat-slab at ~31°S where the geometry of the slab (Davila et al., 2004) and temporal and spatial evolution of volcanism (Kay et al., 1999; Davila et al., 2010) are relatively well-known. The Nazca and South American (SAM) plate velocities are absolute values in the Indo-Atlantic hotspot reference frame (Schellart et al., 2007) for the last 30 Myr, projected on a profile perpendicular to the trench at ~31°S. We prefer the Indo-Atlantic reference frame because it represents the closer resemblance of the true absolute velocities (Schellart et al., 2007). Both the Nazca and SAM velocities are time dependent (Fig. DR1A). The trench migration velocity has been corrected for the rate of accretion/erosion and shortening of the overriding SAM plate for the last 25 Myr (see ref. 5) (Fig. DR1B). Then, we linearly extrapolate the rate of accretion/erosion from 25 to 30 Ma. Note that because the trench experienced erosion (Kley and Monaldi, 1998), the distance between the craton and the trench diminishes with time.

We also constrain the Nazca plate age variation at the trench for the last 30 Myr (Sdrolias and Muller, 2006) (Fig. DR1C). The starting model is placed in time at 30 Ma and has an initial steep geometry (45° dip angle). Although there was also volcanism further east for this period of time (Davila et al, 2004; Davila et al., 2010), this initial slab geometry is consistent with space-time patterns of early Miocene arc volcanism in central Chile (Ramos et al., 2002) (Fig. DR2).

The overriding continental plate has an over thickened part that corresponds to a

cratonic keel. This may be an important component in subduction dynamics, when the overriding plate is continental, as cratons are considerably thicker than younger continental lithosphere, therefore imposing a constrain in the shape of the mantle wedge when they are located in the vicinity of an active subduction system. In particular, Pérez-Gussinyé et al. (2008) and Humphreys (2009) have suggested that flat slabs in South and North America, respectively, may have been caused by trenchward motion of the thick cratonic keels forming these continents. In the Chilean flat subduction zone of South America, a thick, > 200 km, cratonic keel has been imaged by magnetotelluric experiments which corresponds to the Rio de la Plata craton, extending as far west as ~64º W.

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1.2 Potential Influence of the Juan Fernandez Ridge on Flat Subduction Although it has been proposed that it was the north to south subduction of the Juan Fernandez ridge which caused the slab flattening in Chile, many aspects of the temporal relationship between the Juan Fernandez subduction and the development of different flat-slab segments within the Andes remain under debate. A recent seismic experiment (CHARGE) (Beck et al., 2001) revealed the trace of the Juan Fernandez ridge on top of the flat-slab segment. However, modelling experiments show that this is what one would expect if the ridge were not completely eroded as it subducts and does not directly imply a causal relationship between the ridge subduction and the flat-slab (Gerya et al., 2009). Moreover, subduction of the Juan Fernandez ridge did not continuously produce flat slabs as it subducted, making it necessary to speculate about periods of decreased magmatism along the ridge (Humphreys, 2009). Also, Kay et al. (1999) propose that the Juan Fernandez ridge must have been unrealistically wide, that is ~100 km wider than it is today, in order to flatten the >500 km wide Chilean flat-slab. Furthermore, the inward migration of volcanism did not occur first in the north and then in the south, as one would expect from a ridge that progressively subducts at more southerly latitudes, as proposed for the Juan Fernandez, rather the migration of arc volcanism occurs more or less simultaneously across the entire flat-slab region. Thus here we model a 5° wide lithospheric section along latitude 31°S and compare our results to observations on the time and spatial evolution of volcanism and deformation along the same latitude (Kay and Abbruzzi, 1996).

1.3 Numerical Method and Model Setup

Using the incompressible version of the finite element package CitcomS (Tan et al., 2006; Zhong et al., 2000), the computations are performed within a thin spherical domain (r,ϕ,θ), where r is radius, ϕ is longitude and θ is latitude. The inner radius corresponds to a depth of 2000 km, the outer radius is the surface of the Earth. The span in longitude is 70°, from –110° to -40°, and only 5° in latitude, from -28° to -33°. We kept constant all boundary and initial conditions along the strike (θ direction). This domain is evenly divided into 512 elements in the radial, 1280 elements in longitude, and 128 elements in latitude, corresponding to a 4 x 5 x 4 km resolution. The boundary conditions are as follows: the top and bottom boundaries are isothermal, and the lateral boundaries are reflective; the top boundary has an imposed velocity boundary condition (Fig. DR1A); the bottom is free slip, and the sides are reflecting.

The initial thermal structure is described by a thermal boundary layer (age

controlled) at the top and isothermal mantle with an initial slab with 45°dip angle (see Fig. DR2A). Parameters held constant are summarized in Supplementary Table 1. We model mantle convection, which is governed by the coupling between fluid flow and energy transport, while neglecting inertial terms. The calculations are performed within a very thin 3-D cut through a sphere on a non-deforming grid, by solving the conservation equations of mass, momentum and energy:

The equations are written in non-dimensional form as:

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(ui ),i = 0 (1)

−P,i +η(ui, j + uj ,i ), j + δρgδ ir = 0 (2)

T,t + uiT ,i = kT ,ii +H (3)

where ui is the velocity, P is the dynamic pressure, η is the viscosity, T is the temperature, ρ is the density, g is the gravitational acceleration, δij is the Kroneker delta tensor, k is the thermal diffusivity, and H is the heat production rate. X,y represents the derivative of X with respect to y, i, j and k are spatial indices, and t is time. Our models also incorporate phase changes at 410 km and 670 km discontinuities.

Density anomaly due to temperature and phase transitions is:

δρ = −α ρ

_

(T − Ta

_

) + δρphΓ (4)

where _

ρ is the radial profile of density, α is the coefficient of thermal expansion, _

aT is the radial profile of adiabatic temperature, phδρ is the density jump across the phase change, and Γ is the phase function, defined as following:

Γ =12

1+ tanhπ

ρgwph

_

(5)

π = ρ

_

g(1− r − dph ) − γ ph T − Tph( ) (6)

where π is the reduced pressure, dph and Tph are the ambient depth and temperature of phase change at 410 km or 670 km depth, γph is the Clapeyron slope of the phase change, and wph is the width of the phase transition.

The oceanic plate has a variable thickness and accounts for age variations. The over-thickened continental plate (craton) has a variable thickness from 100 km to 300 km and viscosities from 50x1021 to 100x1021 Pa s. The viscosity contrast between the oceanic and continental plates and the upper mantle is 102. The maximum viscosity contrast between the upper mantle and the mantle wedge is also 102, giving a viscosity variation of 104 across the whole computational domain. We use as reference wedge viscosity a value of 0.10x1021 Pa s. In Section 2.1 we show that lower wedge viscosities also reproduce the same results.

To calculate the amount of melt in the mantle wedge, we use the parameterisation

of hydrous melting of mantle peridotite developed by Katz et al. (2003): F=f(P,T,XH2O,Mcpx)

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where F is the weight fraction of melt, P is the pressure (GPa), T is the temperature (°C), XH2O is the weight fraction of water dissolved in the melt and Mcpx is the modal cpx of the residual peridotite. The calculations are performed within a mantle region delimited by the shape of the low viscosity wedge where the enthalpy is conserved for each grid point. The water content used is 0.1 bulk wt% and considered constant for the entire low viscosity wedge; modal cpx is set to 17%. The temperature field for a specific time period is used as an input parameter for melting calculation. 2. Modelling Results

Figure DR3 shows numerical experiments where we systematically varied the craton thickness and its initial position from the trench, while we kept the mantle wedge viscosity at 0.10x1021 Pa s. In a real situation we expect the viscosity within the narrowing wedge to become large as the wedge closes and the temperature decreases. We use in our models a constant low viscosity within the wedge that actually favours steep rather than flat slab geometries. The experiments marked with grey background represent the best fit models to the Chilean flat subduction zone according to two criteria: the slab geometry as given by the slab earthquake data (Humphreys, 2009) (R2 >=0.90), and the present distance of trench to craton, considering the craton to be at 64°W according to magnetotelluric studies (Booker et al., 2004; Favetto et al., 2008). The coefficient of determination R2 relates to the agreement between predicted slab geometry (models) and observed slab geometry (Alvarado et al., 2009). An R2 of 1.0 would indicate that the modelled slab surface (from tracers) perfectly fits the observed slab geometry. The variables that are compared are the depth to of slab surface given by the tracers and the real slab depth measured for the same distance from the trench as the tracers.

There are several interpretations on the position of the limit of the Rio de la Plata

craton (Favetto et al., 2008). While some studies have used either surface geology or aeromagnetics to describe the limit of the craton on the surface, magnetotelluric surveys show the limits of the craton in the subsurface at ~64° W, which is what is of interest from a modelling point of view. As this is the position of the craton in the subsurface, to calculate the R2 factor we have allowed an uncertainty of 100 km in the craton position at the surface.

The craton thickness and its distance from the trench greatly influence the

development of the slab geometry: in general, the thicker and closer to the trench the craton is, the shallower the slab (Fig. DR3). However, when the craton is thick and initially close to the trench (250 km thick and 600 km from the trench or 300 km thick and ≤700 km distance from the trench) the front of the high-viscous craton and the shallowing slab collide at depth, so that the craton can not advance resulting in that the slab buckles backward, which is dissimilar to the observations in Chile (Fig. DR3). On the other hand, when the craton is initially at distances of ≥1100 km from the trench, normal subduction occurs and no flat slab is generated. Furthermore, when no craton is present, as in the reference model, our calculations show that the continent’s large trenchward velocity at flat subduction zones decreases the slab’s angle of entrance from ~45° to ~30°, but is not enough to explain slab flattening at ~100 km depth, as observed

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in Chile (Supplementary movie SM1). In Figure DR4, we show comparatively modelling results after 30 Myr of evolution for one of the best fitting models (200 km thick craton) and for the reference model without craton. Note how the negative pressure (up to -200 MPa) located above the flat-slab sector maintains the slab in horizontal position, and consequently the maximum shear-stress in the flat slab model (Fig. DR4F) extends much further inland than in the reference model (Fig. DR4C). At 0 Ma the location of the Precodillera (P) and Sierras Pampeanas (SP) is shown.

2.1 Influence of Mantle Wedge Viscosity Wedge viscosity is an important factor in determining the suction force. It is well

known that wedge viscosity influences slab geometry, where large viscosities increase the suction between upper an lower plates thereby favouring flat subduction (Turcotte and Schubert, 2002; Manea and Gurnis, 2007). In order to show that our results are independent of wedge viscosity in Figure DR5 we present modelling results with a range of wedge viscosities (0.02x1021 Pa s to 0.60x1021 Pa) that are larger and smaller than the 0.10x1021 Pa s used to generate the models in all figures in the main manuscript. Figure DR5 shows that when the upper plate includes a craton (with the initial craton-trench distances and craton thicknesses corresponding to the three best-fitting models presented in Figure 2), flat-slab results regardless of the wedge viscosity. This implies that, the increase in suction produced by the narrowing wedge as the craton approaches the trench, offsets the decrease in suction associated to small wedge viscosities (smaller than 0.10x1021 Pa s).

However, for models without a craton in the upper plate a significant change in

slab geometry is observed around a mantle wedge viscosity value of 0.10x1021 Pa s (Figure DR5). For smaller viscosities the slab dips into the mantle at steeper and similar angles as for 0.10x1021 Pa s, whereas for higher values the slab starts shallowing progressively as the suction forces increase. Hence the average mantle wedge viscosity at which the slab successfully decouples from the overriding plate is considered to be 0.10x1021 Pa s, which is the one used to run the experiments in the main article.

In Figure DR6 we have compared the trench geometries for models without craton

to the seismicity in a region immediately southwards of the flat-slab region (Alvarado et al, 2009), where the slab dips at a normal angle. The figure shows that viscosities larger than > 0.10x1021 Pa s, are too high to model the wedge, as they do not fit the geometry of the normally dipping subduction area (see R2 values). However, mantle wedge viscosities of 0.10x1021 Pa s or less, do show a good fit and similar slab geometries. Also, when a craton is included in the upper plate a viscosity of 0.10x1021 Pa s, best fits the seismicity in the flat slab region. This viscosity is also in good agreement with results by Billen and Gurnis (2001) who show that a low viscosity wedge has a significant influence on the force balance in a subduction zone, and a mantle wedge viscosity with at least a factor of 10 smaller than surrounding mantle simultaneously best fits the observable signal in the topography, gravity and geoid. In addition, a low mantle wedge viscosity of 0.10x1021 Pa s is consistent with estimates from seismic dissipation and deformation experiments (Kohlstedt et al., 1995). Therefore we conclude that a mantle wedge viscosity of

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0.10x1021 Pa s is a good choice for investigating the role of overthickened continental lithosphere on the slab dynamics in central Chile.

2.2 Trench Motion and Slab Geometry As the craton approaches the trench two different factors control the slab

geometry. The first one is the increase of suction force as the wedge closes. The second is the dynamic push that the flow in the mantle, confined within the closing wedge, exerts on the slab, pushing it backwards and effectively steepening it. When the slab retreats this second effect is strongly diminished, because the rate of wedge closure is small due to retreating movement of the trench. However, this effect becomes important when the trench does not retreat. For example, Figure DR7 shows an experiment where the velocities of South America and Nazca in the last 30 Myr are equal to previous examples, but the trench eastward velocity is equal to the South American westward velocity, resulting in that the trench is fixed in space as time evolves. Such an increase in trenchward velocity could occur if the trench erosion rate increases. The example also includes a craton in the upper plate and a low viscosity wedge of 0.10x1021 Pa s, and shows that if the trench does not retreat flat subduction does not occur. This is because the increase in suction due to craton trenchward motion and wedge closure, does not counter-balance the dynamic push on the slab by the mantle in the narrowing wedge, and the slab effectively steepens. This dynamic push will even be larger in the case the trench advances. So we stress here that for flat-slab subduction to occur not only a craton approaching the trench is necessary, but this needs to occur in conjunction with trench retreat, as has occurred in the Chilean flat-slab area for the last 25 Myr.

Note that an important factor in to our modeling is that we use oceanic and

continental velocities, as well as trench velocities that are well constrained by independent plate models for the last 30 Myr of evolution. These boundary conditions are more realistic than those used previously to investigate flat subduction where oceanic and continental velocities were constant in time and the trench and continent always moved at the same velocity (e.g. van Hunen et al., 2004; Manea and Gurnis, 2007). As explained above, we find however, that the relative velocity of the trench with respect to the advancing continents is key to understand slab dip variations along the Andean margin.

2.3 Stress Distribution and Flat-Slab Subduction

The principal stresses and the angle that defines the principal direction (θ) derived from normal (σϕϕ,σrr) and shear stresses (τϕr) have the following form:

σ1,2 =

σϕϕ + σ rr

2±

σϕϕ − σ rr

2

2

+ τϕr2

(7a)

tan2θ =

2τϕr

σϕϕ − σ rr

(7b)

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The maximum shear stress (τmax) is:

τmax =

σ1 − σ 2

2

(8)

The distribution and orientation of principal stress axes, for one of our best-fitting

model, is presented in Figure DR8. Note how the descending slab is in extension while the upper plate is in compression, in agreement with stress tensor orientations analysed in the Chilean flat slab subduction zone (Alvarado et al., 2009).

The distribution of maximum shear stress for the reference model and the best-fitting

model, which incorporates a 200 km thick craton, is showed in Figure DR8. Note the distinctive pattern of maximum shear stress distribution in the overriding plate in these models: the maximum shear stress in the 200 km thick craton model propagates much farther inland compared the reference model. This stress difference becomes obvious when the subducting Nazca slab starts shallowing, consistent with broadening of deformation from the Principal cordillera to the Pre-cordillera.

The landward migration of the maximum shear stress in the upper plate starts

from 20-15 Ma in our best-fit model (Fig. DR9A), which is consistent with broadening of deformation from the Principal cordillera to the Pre-cordillera during this period (Schellart et al., 2007). From 15 Ma the slab continues to flatten and the maximum shear stress region broadens further landward and by ~5 Ma extends as far inland as 65° W, which fits well with the location of the Sierras Pampeanas, where thick-skinned deformation occurred from ~5-2 Ma (Ramos et al., 2002).

3. Importance of 3D flow in Modeling Flat Subduction Since our modelling setup incorporates reflecting sides, we simulate a subduction

zone that is infinite in trench-parallel extent, and therefore do not allow for any flow around lateral slab edges. Schellart et al. (2010) have recently shown that even in case the slab is very wide, the kinematics and dynamics of subduction, as well as flow in the mantle, and thereby subduction forces in the mantle wedge region, are probably affected by the presence of lateral slab edges thousands of km away. How our experiments would change with lateral flow of the mantle in the wedge needs to be investigated with models which are not infinite along strike is out of the scope of this work.

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2. Supplementary Figures and Captions

Supplementary Figure DR1. Modelling constraints specific for central Chile. A: Convergence rates for the Nazca and South America plates in the Indo-Atlantic hotspot reference frame for the last 30 Ma (Sdrolias and Muller, 2006). B: Miocene-Present shortening model with a total of shortening of 300 km (Kley and Monaldi, 1998). C: The age variation of the subducting Nazca plate at the trench in Central Chile, at the latitude of 28°-33°S (Sdrolias and Muller, 2006).

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Supplementary Figure DR2. Initial model configuration. A: temperature distribution. The initial slab dips at 45° and penetrates the 410 km discontinuity. Dashed box depicts the model domain where we show our modelling results. Inset: purple particle show the top of the slab and the initial temperature distribution. B: viscosity distribution. The model incorporates a low viscosity wedge and channel (viscosity drop of one order of magnitude in respect with the upper mantle). The thickness of the craton varies from 150 km to 300 km (hcr). Also its initial distance from the trench (dini

cr) varies from 600 km to 1200 km.

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Supplementary Figure DR3. Modelling results after 30 Myr of evolution as a function of craton depth and initial distance from the trench. The left-corner model is the reference model without craton. The models on grey background are those that best-fit the present flat-slab geometry (R2 >= 0.90) as given by slab earthquake data (Alvarado et al., 2009), and craton’s present distance from the trench (64°±1° W), which is at ~64° W according to magnetotelluric studies (Booker et al., 2004; Favetto et al., 2008).

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Supplementary Figure DR4. The temperature, pressure and maximum shear stress distribution after 30 Myr of evolution is shown for our reference model without a craton (A, B, C) and one of the best fit models: 200 km thick craton at 600 km initial distance from the trench (D, E, F). The thick black line is the slab surface. In A and D black vectors illustrate the flow pattern and yellow circles the seismicity in the flat slab (D) and nearby steep slab regions of Chile (Alvarado et al, 2009) (A). Dashed black line located at 200 km depth represents the final shape of the craton after 30 Myr of evolution. Black upside-down arrows mark the final position of craton, C, and trench, T, after 30 Myr of evolution. In B, E: only the negative pressure is shown. Negative pressure (up to -200 MPa) located above the flat-slab sector maintains the slab in the horizontal position. The maximum shear-stress in the flat slab model, F, extends much further inland than in the reference model, C. At 0 Ma the location of the Precodillera (P) and Sierras Pampeanas (SP) is shown.

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Supplementary Figure DR5. Modelling results after 30 Myr of evolution as a function of craton depth, initial distance from the trench and mantle wedge viscosity. When the models incorporate a craton, flat-slabs are obtained for a wide range of mantle wedge viscosities. Bottom models represent the reference models without craton as a function of different mantle wedge viscosities. Note how the slab becomes shallower for mantle wedge viscosities >0.10x1021 Pa s. On the other hand, for wedge viscosities ≤0.10x1021 Pa s the subducting slab successfully decouples from the overriding plate, and the slab plunges into the mantle at steeper angles. Dashed box in the lower left model depicts the model domain where we show modelling results as present-day slab geometries in Figure DR6.

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Supplementary Figure DR6. Slab geometries after 30 Myr of evolution, as a function of craton depth, initial distance from the trench and mantle wedge viscosity, compared with earthquake distribution (Alvarado et al., 2009). Note the good fit with the recorded seismicity for both sets of models, with and without craton, but only for mantle wedge viscosities ≤0.10x1021 Pa s.

Supplementary Figure DR7. Modelling results (ηLVW=0.10x1021 Pa s) when a craton is moving towards the trench but there is no rollback and the trench is stationary. Note that no flat-slab is generated. This explains the absence of flat-slab in the Central Andes in the area of the Bolivian orocline where a craton may also be close to the trench but trench rollforward is occurring since 25 Ma.

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Supplementary Figure DR8. Distribution and orientation of principal stress axes. Blue axes represent tension and red axes show compression. Note that the descending slab is in extension while the upper plate is in compression, in agreement with stress tensor orientations analysed in the Chilean flat slab subduction zone (Alvarado et al., 2009).

Supplementary Figure DR9. Time-space variation of maximum shear stress distribution since early Miocene. A, experiment with a 200 km thick craton located initially at 600 km from the trench. Black line represents the slab surface. Thick black dashed line located at 200 km depth represents the shape of the craton. T and black arrow mark the position of the trench. Note how maximum shear stress in the overriding plate moves inland while slab shallows. The pattern is consistent with broadening of deformation from the Principal cordillera to the Pre-cordillera (P). SP – Sierras Pampeanas. B, experiment without craton (reference model). The maximum shear stress in the overriding plate remains located closer to the trench compared with the craton model.

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3. Supplementary Movie Legends Supplementary movie DR1 (MOVIE_DR1.mov). Movie showing the slab temperature and geometry evolution when no craton on the overlaying plate is considered. Purple particles represent the slab surface. After 30 Myr of evolution, the final slab geometry does not resemble the present day flat-slab shape characteristic for central Chile at ~31°S. Colour indicates temperature. Supplementary movie DR2 (MOVIE_DR2.mov). Movie showing the slab temperature and geometry evolution when a 200 km thick craton is considered. The initial distance of the 200 km thick craton from the trench is 600 km. After 30 Myr of evolution, the final slab geometry closely resemble the present day flat-slab shape characteristic for central Chile at ~31°S. Colour indicates temperature. Supplementary Table DR1. Model Parameters Held Constant Parameter Symbol Value Dimension reference density ρ0 3300 kg m-3 reference temperature T0 1350 °C reference viscosity η0 1x1021 Pa s thermal expansion coefficient α 2x10-5 K-1 gravitational acceleration g 10 m s-2 thermal diffusivity k 1x10-6 m2 s-1 heat capacity cp 1200 J kg-1 K-1 Clapeyron slope 410 phase transition

γ410 3.0 MPaK-1

Clapeyron slope 670 phase transition

γ670 -2.5 MPaK-1

density jump across the 410 km phase transition

δρ410 270 kg m-3

density jump across the 670 km phase transition

δρ670 340 kg m-3

width of the 410 km phase transition

δw410 37x103 m

width of the 670 km phase transition

δw670 37x103 m

ambient temperature of the 410 km phase change

T410 0.78x1350 °C

ambient temperature of the 670 km phase change

T670 0.87x1350 °C

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