Department of Geology

Laboratory for Mineral Deposits Research



copyright by Philip A. Candela, 1997.



Matter and radiation exist. Energy, color, entropy, momentum, wavelength, mass (inertia), temperature, Young's modulus, poisson's ratio, viscosity etc. are attributes of matter and/or radiation, and do not have an existence independent of matter or radiation. matter can be converted into radiation, and vice versa; however, matter cannot be converted into energy (however, energy contributes to the inertia (mass) of a body{m= E/c2}; also, nuclear potential energy, which contributes to the mass of a nucleus, may be converted to the kinetic energy of other particles, as in nuclear fission).


We are concerned primarily with three states of matter on the earth: gaseous, liquid and solid. Simply put, a solid has its own shape (whether it's a molded brick, an anhedral lump of quartz, or a garnet crystal); a liquid takes the shape, but not necessarily the volume, of its container; and a gas takes both the shape and volume of its container.


The following paragraphs draw heavily on the EXCELLENT text by Ranalli: "Rheology of the Earth", Chapman hall, 2nd Ed., 1995.

"Fluid" is a rheological term meaning "something that can flow"; that is, a fluid will deform (strain) continuously (exhibit steady state flow) upon the application of a constant and finite shear stress. If the rate of shear (strain rate) is proportional to the applied shear stress ( e.g. for water running downhill in a river), then the fluid is newtonian. Both gases and liquids are fluids. For a fluid of high viscosity (visc of water at 200C = 0.001 Pa s), a large stress is needed to produce a given strain rate. A material is a fluid, independent of the presence or absence of long range order, if it flows under constant stress. A solid has a finite yield stress (and therefore has its own "shape"); a crystalline solid diffracts x-rays (but an amorphous solid does not; a glass is a special type of amorphous solid that has formed by supercooling a molten material). Solids behave elastically (up to a point). In an elastic solid, stress is proportional to strain (not strain rate as in viscous flow), and the constant of proportionality is Young's modulus. At low T and P, rocks often show a behavior where deformation is nearly instantaneous upon loading, recovery is total and nearly instantaneous upon removal of the load, and the strain is proportional to the stress. This occurs below a threshold strain (the elastic limit), above which the stress - strain relation is non-linear; with further increase of (differential) stress up to the yield stress, the material fails; the region of nonlinear behavior is small. Failure may be brittle, with loss of continuity along a surface, or it may occur by irrecoverable continuous deformation (without any apparent loss of continuity), which is called plastic flow or deformation (this is different from the flow of a Newtonian fluid, because of the existence of a yield stress). Generally, the deviatoric stress matrix must have non-zero elements for deformation to occur. Note that hot creep fractures are ductile fractures.


Brittle shear fracture of a material under triaxial compression is the most common type of failure in the Earth's upper lithosphere (Ranalli). Failure occurs in one or two planes forming an angle of usually less than 45 degrees with sigma one. According to the Mohr criterion for failure, fracturing occurs across the plane or planes for which the shear stress first reaches (c + µS), the Coulomb-Navier (C-N) Failure Criterion. c is the "cohesive strength" (the shear stress at failure in the case where the confining (normal) stress, S, is zero), and µ is the "internal friction" (which decreases slightly as the normal stress (S) increases - a limitation of the C-N relation). As P & T increase, failure is less likely to occur in well defined planes, and more likely to occur in broad zones until finally, failure becomes truly ductile, with no recognizable macroscopic loss of cohesion of the material as it strains beyond the elastic limit.


Griffith Crack Theory yields a similar criterion for failure. In Griffith Theory, bodies contain high-aspect ratio ellipsoidal cracks which generate stress concentrations at their tips. In this case, the "internal friction" represents the friction across the microcracks, which are in a closed configuration when under compression. What of pore fluid pressure? IF a fluid is present, the pore pressure acts against the "solid" normal stress, effectively reducing the friction along the surfaces of the Griffith cracks. Therefore, a pore fluid increases the probability of fracturing and shearing.


AT TEMPS GREATER THAN ABOUT THE HALF MELTING POINT (in Kelvins) SILICATE POLYXLS HAVE VANISHING YIELD STRESS FOR LONG TIMESCALE DEFORMATION....THIS IS NOT THE B/D TRANSITION, (which simply SEPARATES ELASTIC/brittle from ELASTIC/plastic). This separates the LITHOSPHERE FROM VISCOUS MATERIAL (no yield stress) BELOW. These materials can be approximated as Maxwell bodies - at long time scales of deformation ( greater than t = viscosity/shear rigidity) the time necessary for creep deformation at a constant strain rate is equal to the elastic deformation for the given load. Solids can behave as fluids when the time scale of deformation is long relative to the ratio of the viscosity to Young's modulus; this ratio is called the Maxwell Relaxation time. For the mantle, t = 10^10 sec = 10^21 Pa s/10^11 Pa. IN THE CASE OF THE B/D TRANSITION, THERE *IS* STILL A YIELD STRESS IN BOTH THE brittle AND THE ductile regime. THE B/D TRANSITION region IS SIMPLY A MATTER OF WHAT THE MODE OF FAILURE IS.


Figure 5.5 on page 96 from Ranalli shows how the B/D transition depends upon the existence of yield stresses for both brittle and plastic failure - note that the transition exists because of the variation in the two yield stresses as a function of T and P. Generally, elastic strength increases significantly with pressure, while plastic strength does not, so at higher P, plastic failure occurs first (i.e. ductile behavior). Temperature does not affect brittle behavior as much, but the plastic strength decreases greatly as T increases, so again, plastic failure occurs first as high T. Therefore, B-->D with both increasing T and increasing P . Because viscosity decreases with increasing temperature, solids are more likely to behave like a fluid if they are deformed at elevated temperature. {For example, the Earth's mantle can convect, e.g. flow, even though it is solid (olivine, pyroxene, garnet etc. for the upper mantle), and many rock deformation modes involve the ductile behavior of rock. The transition from brittle to ductile behavior occurs somewhere in the temperature range of 250-450oC for quartz-rich mixtures (these temperatures may obtain at depths of 10-20 km in the crust).


In geology, the solids we deal with are minerals (geochemical compounds), or rocks (aggregates of minerals), or glasses or other amorphous/poorly to partly crystalline solids (e.g., deweylite).


Liquids include: water; molten rock (e.g. "silicate melt"); molten sulfide (even liquid bismuth or mercury on occasion); petroleum; and, brine.


Gases include: the Earth's atmosphere; soil and phreatic atmospheres; "natural" (organic) gas; steam (geothermal steam); and, high temperature gases in metamorphic or igneous environments.


Note that gases are generally considered to be miscible in all proportions. Many liquids are not completely miscible (i.e. mixtures of water with non-polar liquids such as petroleum). Many authors make the mistake of saying that water is the "universal solvent" because of the strong interactions between water molecules and ions. This gives students the mistaken impression that solubility is dependent somehow upon solvation reactions. Nothing could be further from the truth: the mutual, complete solubility of all gases should be seen as prima facie evidence that this notion is false. Water and other polar liquids are good solvents for ionic substances, and other polar compounds, and are poor solvents for relatively non-polar substances. "Universal" really overstates the case! Non-polar substances have low solubilities in water because, upon dissolving in water, the molecules would separate the highly polar water molecules, and, in so doing, increase the electrical potential energy among the water dipoles; this would increase the internal energy of the solution, and would thereby raise the chemical potential of both the solvent and the solute. When ionic or polar materials come between the water molecules, their own charge results in a lowering of the potential energy of the molecular system.


Seawater is a liquid solution comprising mostly H2O plus "dissolved solids". Further, seawater is an electrolyte - it conducts electricity; we therefore postulate the existence of ions: (the most abundant cations, in order of deceasing molar concentration, are Na+, Mg2+,Ca2+,K+, Sr2+, and the most abundant anions, (again, in order of deceasing molar concentration), are Cl-, (SO4)2-, HCO3-, Br-, (BO3)3-, F-.


Solid solutions are more complex; solids may be miscible, but the end-member solids must have similar structures. Good examples include the feldspar solid solutions which make up a large part of the Earth's crust: plagioclase feldspar (a solution of the two components: NaAlSi3O8 - CaAl2Si2O8), and alkali feldspar (sometimes called potassium feldspar) which is a solution of KAlSi3O8-NaAlSi3O8.



This work would not be possible without the support of the National Science Foundation, the Department of Geology, and the University of Maryland.


©2003-2018 Laboratory for Mineral Deposits Research