Geos 306, Fall 2009, Lecture 12, Mineralogy of the Earth and its Core

Geos 306, Fall 2009, Lecture 12
Mineralogy of the Earth and its Core

We are now going to change directions a little. We have been studying the scientific background required to understand minerals. Things like what are chemical bonds, and how do they form, and what do the resulting arrangement of atoms in a mineral look like. Now we will apply this scientific background to the individual phases that make up the bulk of the earth.

The earth has gross radial structure with boundaries that are defined by seismic discontinuities. Why do we define the structure of the earth this way?

The Preliminary Reference Earth Model (PREM) of compressional velocity (Vp), shear velocity (Vs), and density (ρ) as a function of depth in the Earth.
(After Oziewonski and Anderson, 1981)

The location of the seismic discontinuities leads to defining the earth in terms of 3 very different parts: (1) the core, (2) the mantle, (3) the crust. The core is further divided into two parts, the inner and outer cores, and the mantle has 3 parts, the lower mantle, the transition zone and the upper mantle. The crust is an extremely thin layer, and its volume is quite small compared to the rest of the earth.
The reasons for these discontinuities are not yet completely understood in detail, however this is an area of active geological research, and we are learning quite a bit each year. The current consensus is that the seismic boundaries define regions of different mineralogical phases. There are two main aspects to this consensus:

The phases are different because of a chemical composition boundary, and
The phases are different because the pressure-temperature conditions lead to bonding changes, which, in turn, produce different crystal structures.

The pressure surrounding a given point in the earth increases with the depth of that point. The radius of a given atom changes with pressure, with some atoms appearing to be more "soft" than others, i.e. the change in radius with depth is greater for some elements than it is for others. Consequently, the radius ratio values in a given crystal change with depth in the earth. This invariably leads to coordination number changes. Coordination arrangements that are not dense enough at a given depth (or pressure) then promote the cation to migrate to regions of lower pressures in the earth. This leads to a chemical stratification within the earth.
An example that we are all familar with is the crust/atmosphere boundary, displaying both chemical and structural changes.
The relationship between a region of the earth and its major phase mineralogy is currently believed to be:

Region (depths)	Mineralogy
Inner core (6371-5150 km)	HCP iron
Outer core (5150- 2891 km)	Liquid iron
Lower mantle (2891-670 km)	Magnesio-wüstite, magnesium silicate perovskite, stishovite
Transition zone (670-410 km)	Structures with both SiO₄ and SiO₆ groups, e.g., majorite garnet
Upper mantle (410-40 km)	Olivine, pyroxene, garnet, spinel
Crust (average depth 40 km)	Feldspar, quartz

We determine the depth of the boundaries from analysis of seismic waves.
We get the pressure at the boundaries from a mathematical relationship between depth and pressure.
We then model the likelihood of different phases (made from O, Fe, Si and Mg) undergoing the transformation. For instance, the transformation of olivine is likely the cause of the 410 km discontinuity. We subject a sample of olivine to the pressure found at 410 km, then heat it up till it transforms to a new phase. The temperature of the earth at 410 km is then assumed to be the temperature at which the olivine transformed.
In such a way, the pressure/temperature profile of the earth is constructed. This profile is called the geotherm.
Since the earth is made of Mg, Fe, Si and O, then the mineralogy of the earth can be studied by examining the phases into which these elements combine along the conditions of the geotherm.

The estimate of the pressure in the earth as a function of its depth is quite accurate. The estimate of the temperature profile of the earth is poor. Error may be higher than 500 K when estimating the core temperatures. Sadly, we do not really even know the size of the errors.

Pressure

For our purposes, 1 atmosphere is the pressure of air at the surface of the earth. This pressure is also commonly called a "bar".
1 kilobar = 1 kbar = 1000 bars = 1000 atmospheres of pressure.
1 GPa = 1 gigapascal = 10 kbar. This is the conventional unit of pressure when discussing the deep earth.
From the surface to the transition zone - lower mantle boundary (670 km depth) we can estimate the pressure by the simple rule of thumb that 30 km depth change is close to 1 GPa pressure change.

The core

The core consists of 2 distinct regions, the inner core, which is solid, and the outer core, which is liquid. We know this by examining the velocity profiles. Shear waves do not propagate in the outer core. (Why not?)
Let us examine the phase diagram of iron. In general, the phase diagram for materials with a given chemistry is a plot in temperature/pressure space of the conditions at which the structure transforms.
The phase diagram of iron is well known to 20 GPa and 2000 K. (Why not higher?) We observe that there are several phases of Fe in this region.
At room conditions Fe adopts BCC packing, and is called the a phase. With increasing temperature it transforms to FCC (g phase) and then back to BCC (d phase) and finally to a liquid.
With increasing pressure, Fe adopts a HCP structure (e phase).
In general, how are these phase boundaries determined? X-ray at high P and T (example1), (example2), (example3), plus Raman spectroscopy (example with silica) to look for structural changes.
Let's examine the slopes of the boundaries in the phase diagram. The liquid-solid boundary has a positive slope. That means that if the pressure around the iron is increased, then more heat is needed to cause the transformation. This suggests that the transformation is vibrationally driven. The phase undergoes a change when the amplitude of the vibrating atoms exceeds a threshold. The effect of pressure on the transition boundary is to require greater temperature in order to get the atoms to vibrate with amplitudes above the threshold. They vibrate right out of their potential energy wells and rearrange into a new structure.
In contrast, notice that the slope of the a /g transition is negative. As pressure is increased, we see that less heat (i.e. vibrational energy) is needed to drive the transformation. What does this mean? Pressure is straining the structure and moving the atoms literally closer to the point at which the transformation would take place. Consequently, the amplitude that the atom has to vibrate is smaller before it vibrates out of its potential energy well. So not as much heat is required to do this, and thus the temperature can decrease.
Examine the phase diagram of iron that goes from 0 to 360 GPa. Determine where the geotherm passes through the phase diagram. Note the following:

Depth (km)	P (GPa)	T (K)
2571(D``/m)	117	3018
2741	127	3564
2891 (c/D``)	135	3750
3571	206	4265
3971	243	4500
4371	277	4693
4771	306	4846
5150 (ic/oc)	329	4961
5571	349	5041
5971	360	5087
6371 (Center)	364	5151

The phase diagram does not match the geotherm data at the inner/outer core boundary. Why not?
Nature of the solid inner core. Right now, we think that HCP e phase is correct. The structure type affects the physical properties. If the structure were cubic, then none of its properties would have directional dependencies. If hexagonal, then the value of a given property is the same if measured in any direction parallel to a monolayer, but it differs in the direction perpendicular to the planes, (i.e. a=b¹ c).

This leads to a model that the inner core of the earth is one large hcp single-crystal (pdf1, pdf2). The direction of magnetic flux is parallel to the c-axis. Furthermore, a closest-packed structure can slip easily in directions parallel to the monolayers. This may account for the change in the direction of the earth's magnetic poles.

Steel

One of the reasons that the P&T conditions measured for Fe do not seem to match the observed core conditions is that the core is not pure Fe, but contains Co, Ni and maybe other elements such as O, Si, H. This is largely an educated guess (see pdf), but we can learn a lot by studying the effect of impurities in the Fe structure. A good example of this is the phase diagram of steel.
The greatest interest in iron is its industrial use as the major component of steel. Steel is a mixture of Fe and C. It is complicated by the a -g phase transition at 900 ° C.
Only the a phase is ferromagnetic.
The g phase is non-magnetic, called austenite. It contains up to 7 C atoms/100 Fe atoms (approx Fe₁₄C). Any more than this and carbon does not mix into the Fe structure, and instead it nucleates and forms inclusions of graphite. Carbon, mixed into the g -Fe structure, extends the field of g -Fe down to 700 ° C. At temperatures below 700 ° C the structure breaks down into ferrite (a phase, no C) plus cementite (Fe₃C).
Cementite is soft and breaks easily. It is also called pig iron. When it is heated it goes to graphite plus g -Fe.

Reading:
Wenk and Bulakh, Chapter 35