10Ge 131Chapter TwoMaterial Behavior; Fundamental Principles of High Pressure Physics“Rocks”, “Ices” and “Gases”The cosmically most abundant elements can be divided into three groups:“Gases”: those that do not condense (i.e. form solids or liquids) underconditions plausibly reached when planets formed;“Ices”: those that form volatile compounds and condense but only at lowtemperatures (beyond the asteroid belt);“Rocks” : those that condense at high temperatures and provide the buildingblocks for the terrestrial planets.It is important to understand that these are labels of convenience; nothing isever so simple that you could so easily subdivide materials. The quotationmarks are there to remind you that what we call an ice is sometimes in thegas or liquid phase, etc. But the subdivision proves nonetheless of greatusefulness because of the large differences in behavior and abundancesamong these groups.The gases are hydrogen, helium and (to a much lesser extent) the noblegases. [Note: Noble gases on Earth are tiny quantities carried to Earthadsorbed on solid particles; thus neon is of low abundance on Earth despitehaving much higher cosmic abundance than silicon.] The gases are thusoverwhelmingly what the universe is made of, and what the Sun is made ofand (as we shall see ) what Jupiter is made of. The hydrogen molecule H2 isthe low pressure thermodynamic state of H and it interacts with otherhydrogen molecules and with helium by a van der Waals interaction,meaning that it is a very weak force except when the molecules are pushedvery close together. That’s why condensing hydrogen requires very lowtemperatures. It’s also why it’s easy to squeeze hydrogen (as a liquid or solidor, of course, as a gas) until you approach densities where the distancebetween molecules is about the size of a molecule.The ices are mostly hydrides of the next set of light elements: O, C and N(i.e. water, methane and ammonia respectively). But they also include other11combinations among themselves (e.g. N2, CO, CO2, HCN....) As wediscussed last time, hydrides do not necessarily dominate (they don’t seemto in the interstellar medium) but they are thermodynamically favored whenthe partial pressure of hydrogen is high and will thus form if temperature orpressure permits reactions to occur. Water is the least volatile of this setbecause of hydrogen bonding between water molecules (which you canthink of loosely as a weak form of ionic bonding arising from the very non-uniform charge distribution around the water molecule). Ammonia also hassome hydrogen bonding. Methane and molecular nitrogen rely on van derWaals bonding in the liquid and solid state. CO has a small dipole momentbut also interacts mostly by Van der Waals.“Rocks” include both metallic materials (iron and iron-nickel alloys) as wellas what we might usually call rock (oxides and silicates) . Here one hasstrong ionic and covalent bonding. Metallic bonding can be thought of as aspecial case of ionic bonding (with the electrons providing a spatiallydistributed charge rather than the discrete charges of an ionic material suchas NaCl). These materials are much more tightly bound, hence involatile andstiffer. The main constituents are Fe, MgSiO3, Mg2SiO4, “FeO” (quotationmarks refer to several different oxidation states), but of course Fe cansubstitute for Mg to a limited extent and form solid solutions, e.g.,(Mg,Fe)2SiO4.To summarize then, we have:Type ofbondingExamples SolidDensities atlow PBulkmodulus ofsolidLocationsfoundVan derWaalsHydrogen,helium,methane, N2e.g hydrogenis ~0.07 g/cce.g. hydrogenis a fewkilobarsGiant planets(also CH4 &N2 on icysatellites)HydrogenbondingWater,ammonia AroundunityTen kilobar(roughly)Giantplanets, icysatellitesIonic andcovalent(includingmetallic)“Rocks”,metallic ironRocks arearound 3g/cc;iron is near 8g/ccTypically oforder onemegabarTerrestrialplanets, coresof giantplanets(?),icy satellites.12The type of bonding refers to the low pressure behavior; everythingbecomes a metal at high pressure. (In Jupiter, the only material that fails tometallize is helium).The bulk modulus is an important material property:Adiabatic bulk modulus Ks≡p      sIsothermal bulk modulus KT≡p      Tp = pressureT = temperature= mass densityS = entropyso bulk modulus has units of pressure. [Reminder: One bar is 106 dynes/cm2or 105 Pascals; and it is roughly the pressure at Earth’s surface. ]So What are the Pressures inside Planets?Clearly the bulk modulus is a measure of the strength of interaction amongthe molecules in the material... soft (weakly bound, volatile) materialscompress easily while tightly bound materials are stiff. It is also a guide as tohow much density change might arise in a planet due to internal pressure.From the definition of K, ∆ρ/ρ ~ p/K (i.e., the fractional change in densitybetween surface and deep interior is roughly the pressure in the deep interiordivided by the bulk modulus). If the actual pressure is comparable to thebulk modulus then you might expect the density inside the planet to beconsiderably larger than at the surface. We can estimate the pressure byassuming that the density is roughly constant; obviously this is only a veryrough guide but it gives a “warning” (i.e., tells you whether your assumptionwas a good one) and actually not too bad an approximation. In the following,ρ with an overbar is the mean density, M(r) is the mass inside radius r, etc.13Hydrostatic equilibrium ⇒ dpdr= − (r)g(r)g(r) =GM(r)r2≈43G rp(r) ≈43rR∫G2xdx∴p(r) ≈23G2(R2− r2)pcenter≈ (1.4 kilobars).1g/cc     2.R1000km    2For the Moon this predicts about the true central pressure (not surprisingly).For Earth, it predicts around 2 Megabars (true value about 3.6). For Jupiter,it predicts around 10Mbar (actual is 40 or more). This crude formulaunderpredicts the central pressure of differentiated bodies (which is to say,all planets), especially when the core has a density much larger than themean density.How do We Figure out the Behavior of Materials at High Pressure?If we want to figure out what goes on in a planet then we need to know howthe materials listed above behave at planetary pressures. One approach isexperiment. This is extremely important, and we will talk about someexperimental constraints in due course. The experimental techniques are oftwo kinds: shock waves or static compression