Physical properties of magmas (density ( ), viscosity ( ), thermal - - PowerPoint PPT Presentation

Physical properties of magmas (density (ρ), viscosity (η), thermal conductivity (κ): (control flow rates, cooling rates, eruption rates etc.)

• 1. Density ρ = M / V (g cm-3) Controls magma buoyancy, crystal settling rates, etc.

Density can be measured in lab, or calculated from first principles [ ρ = ΣxiMi/Σxivi ] where xi is mole fraction of component i, Mi formula wt of i and vi is partial molar vol. of i 900 1000 1100 1200 TºC ρ (g cm-3) 2.0 2.2 2.4 2.6 2.8

Basalt 1 Basalt 2 Andesite Rhyolite Liquidus T

Some lab measurements

From: Murase and McBirney (1973) GSA Bull, 84, 3563

ρ (g cm-3) 2.8 3.0 10 20 30 P (kbars)

Density of Kilauea basaltic magma as function of Pressure

Plag An80 From: Kushiro (1980) Phys Magm. Proc. Ch 3, p.93

Viscosity (η): measure of a fluid’s resistance to flow

ln η (1/T (deg-1)

Slope = E*/R

If η is constant over a range of σ, the fluid is said to exhibit Newtonian viscosity. Viscosity can be measured in field, in the lab, or calculated from first principles. The temperature dependence of viscosity is given by the Arrhenius Equation: ln η = A + E*/RT where E* is the activation energy for viscous flow, R is the gas constant, and T is the temperature in ºK. A plot

• f ln η vs. 1/T is a straight line.

Some typical values of viscosity of magmas are shown in the next slide. Viscosity has a control on magma flow rates, volcano morphology, rates of gas escape, rates of convection, rates of crystal settling or flotation, rates of diffusion and crystal growth. σ (shear stress) (Pa)

1 2 3 4

dv/dz = velocity gradient normal to applied shear stress = strain rate ė (s-1)

η = σ/ ė

η is called the coefficient of viscosity Units: Pa s

Fixed plate

v1 v2 v3 v4

1000 / T (°K) Log η (Pa·s)

0.6

Basalt O b s i d i a n + 6 % H

2

O

0.7 0.8 0.9 1.0 11 9 7 5 3 1

• 1

Obsidian (dry)

50 Pa·s at 1200°C 104 Pa·s at 880°C 1010 Pa·s at 830°C E* = 122 kcal E* = 42 kcal E* = 56 kcal

1156°C 977°C 838°C 727°C

Viscosity of Some Common Magmas

Notes: (1) rapid increase in viscosity of basaltic magma when crystals form (below ~1200ºC) and/or gas bubbles exsolve. As crystal/bubble content increases, basalts are no longer Newtonian. Flow is not initiated until a critical shear stress (yield stress: σ′) is

• exceeded. Effective viscosity: ηeff = η (1-1.35 φ)-2.5 where φ = crystal/bubble fraction.

(2) Dissolved water has a strong effect on viscosity of rhyolite. H2O depolymerizes the silica-rich liquid by breaking network-forming Si-O-Si bonds (bridging oxygens).

• a. Calculated viscosities of anhydrous silicate liquids at one atmosphere pressure,

calculated by the method of Bottinga and Weill (1972) [from Hess (1989) Origin of Igneous Rocks. Harvard University Press.] b. Variation in the viscosity of basalt as it crystallizes (after Murase and McBirney, 1973), Geol. Soc. Amer. Bull., 84, 3563-

• 3592. c. Variation in the viscosity of rhyolite at 1000ºC with increasing H2O content

(after Shaw, 1965, Amer. J. Sci., 263, 120-153). In a classic paper [Am J Sci, 272, 438 (1972)], Bottinga and Weill developed a method to calculate viscosity using the equation: ln ηmix = Σ xi ln ηi where xi is mole fraction of oxide i and ln ηi is the viscosity contribution of component i In another classic paper [Am J. Sci, 266, 225 (1968)] Shaw et al. measured the viscosity of basaltic magma in the still molten Makaopuhi lava lake, Hawaii.

Example of application of viscosity and density data

Stokes Law of settling/flotation: v = (2 r2 g ∆ρ) / 9 η Where v = the settling/flotation velocity r = crystal or bubble radius g = gravitational acceleration ∆ρ = density contrast between crystal or bubble and magma η = viscosity Ideally, Stokes law applies to spherical crystal and has to be modified to account for non-spherical crystals and crystal-crystal, bubble-bubble interactions.

Differential settling of chromite (black) and olivine crystals in the Stillwater Complex, Montana (maybe) Layering in the Skaergaard Intrusion, Greenland showing differential crystal settling (maybe).

1738 km 70 km

Depleted Mantle

Crust Core

550 km Plag Pl + Ol+Px

KREEP

layer Ilm- Ol-Px Ol Ol Px I n c r . F e

• Incr. Fe

Primitive Mantle

MOON at ~4.5 Ga

In a widely accepted model, olivine and pyroxene settled in lunar magma ocean to form the lunar mantle while plagioclase floated to form the lunar crust. Possible initial depth of lunar magma ocean (~550 km)

To determine cooling rates, we need to solve the Fourier equation dT/dt = k [d2T/dx2] where T is temp, t is time, x is distance Typical solution: T/T0 = ½ + ½ erf [x / 2(kt)½] where T0 is initial temp, x = distance

Thermal conductivity of magmas

√t

Thickness of crust in Alae lava lake,

• HI. Crust is stabilized at ~1065ºC

(~100ºC below eruption T). Note: linear relationship between crust thickness and square root of time (Peck et al., 1964)

(months)

Depth (ft)

1 2 4 3 6 5 10 20 30 40 50

T Tcountry rock

Temperature profile in lava flow at different times

T at t0

surface t1 t2

Thermal conductivity (K) is a measure of the rate at which heat is conducted through rocks and magmas. [Units: J cm-1 s-1 deg-1]. Typical values for rock range from 10-2 to 2.5 x 10-2 J cm-1 s-1 deg-1. In cooling rate calculations we use the thermal diffusivity (k): k = K / ρC (C is the specific heat). [Units of k: cm2 s-1].

Magmas: where are they generated and how?

Source regions: locations within earth where magmas are generated, i.e., regions

where the geothermal gradient intersects and exceeds the solidus at that depth.

Principal source regions: Upper mantle and lower to middle crust. Partial melting: Melting requires great amount of heat (heat of fusion) so melting is

always partial. At present, maximum melting in mantle is ~20%. Archean: up to 50%. Magmas are less dense than surrounding crystalline material—buoyant—therefore they will tend to rise (lava lamp). Must overcome strength of rock to form a conduit. Crust: Continental crust: highly variable in thickness and composition. Lower crust: gabbro (mafic rock) or metamorphic equivalent (amphibolite). Variable H2O content and variable geothermal gradient. Crustal melting source regions: located above subduction

• zones. Geothermal gradient is higher due to advected heat in the form of basaltic

magma intruded into the lower crust. H2O required for melting to take place. Most of this water is contained in amphiboles. Mantle: Composition: Peridotite (Ultramafic rock) composed of (in decreasing abundance) olivine, orthopyroxene, clinopyroxene and spinel (MgAl2O4). Spinel is stable up to ~25 kb. Spinel replaced by pyrope-rich garnet (Mg3Al2Si3O12) at higher pressures. Homogeneous on a small scale; heterogeneous on a larger scale. Only minor amounts

• f H2O (<<1%) usually contained in trace amounts of amphibole and/or biotite. Hottest

mantle--beneath spreading centers. Coolest--under continental interiors.

Partial melting of mantle peridotite

Melting begins when upwelling mantle intersects the peridotite

• solidus. With decreasing

pressure above the solidus, extent of melting

• increases. The amount of

melting is limited by the heat available since the heat of fusion is large. Extent of melting can vary from ~1% to ~20%. The T, P and % melting determine the composition

• f the basaltic magma

produced.

G r a p h i t e Diamond

solidus

Spinel lherzolite (Ol-opx-cpx-sp) Garnet lherzolite (Ol-opx-cpx-gar)

20% 1% 20% 10% 1%

10 20 30 40 50 60 P (kbars) 50 100 150 Depth (km) 1100 1200 1300 1400 1500 (TºC)

Plag lherzolite (ol-opx-cpx-pl)

adiabat