Teach the Earth > Mineralogy > Mineral Physics > Deformation Mechanisms

# High Pressure Deformation Experiments

by Pamela C. Burnley, University of Nevada Las Vegas

# Introduction to High Pressure Rock Deformation Techniques

Pressure has a profound impact on the deformation behavior of rocks. At the conditions present at Earth's surface, with the exception of ice, rocks deform by brittle fracture. Yet at relatively shallow depth (just a few tens of km) brittle fracture is suppressed and in most circumstances rocks deform by ductile flow. The goal of high pressure deformation studies is usually to learn something about how rocks deform inside the earth. Many studies seek to quantify the relationship between stress and strain over some range of pressure, temperature and strain rates. Others are conducted to produce samples for microstructural analysis.

## Experimental Stress States

In order to properly wrap you head around deformation studies you first have to understand stress and strain. If you are unsure of these concepts now is a good time to review them. There is a module in this series on Tensors, Stress, Strain and Elasticity, which contains a basic overview. High pressure deformation apparatus can be thought of as falling into two basic categories depending on the nature of the stress field that they produce; so-called "uniaxial" designs and triaxial designs. A "uniaxial" deformation experiment has cylindrical (also known as axisymmetric) symmetry, therefore σ12≠ σ3. Where as, in triaxial experiments, there is no symmetry to the stress field and σ1≠σ2≠ σ3. The reason for all the prevarication around "uniaxial" is that technically, the term is reserved for σ12=0≠ σ3 . But since there is no handy term for "axisymmetric high pressure stress state", we just call it "uniaxial"; from here on out we will dispense with the quotes. We refer to σ12 as the confining pressure and the difference between σ1and σ3 as the differential stress. Some authors use σ1 for the maximum compressive stress and some use σ3(as I will). Geologists often designate compressive stress as positive, but engineers consider compressive stress as negative.

# Techniques

## The Gas Apparatus

Paterson gas apparatus - The axial actuator which is used to compress or extend the sample can be seen at the bottom. Cooling coils around the upper portion of the apparatus remove waste heat. Click for larger image.
Photo taken in D. Kohlstedt's lab at the University of Minnesota
Drawing of Paterson gas apparatus. Click for large image.
Mackwell and Paterson, 2002
The gold standard for quantitative high pressure deformation studies is the gas apparatus. The apparatus can either compress or extend the sample. Some gas apparatus, for example, the Paterson gas apparatus (Paterson, 1970), can also deform the sample in torsion. Torsion allows much higher strains to be reached. Because the amount of strain in the sample varies radically from the center to the edge in torsion experiments, torsion samples are constructed in the shape of a thin ring with jacket materials filling the center. What gives the gas apparatus its edge is that the gas confining medium (usually Ar) provides a perfect uniaxial stress field. Because the gas supports no shear tractions along the sides of the sample or pistons, an external load cell can accurately measure the load supported by the sample. Unfortunately, the gas apparatus can only achieve a confining pressure of 500 MPa (0.5 kbar). This pressure is equivalent to the pressure at 15 km depth in the earth. The limited pressure range is a severe limitation for students of the deep earth.

Torsion actuator. Click for larger image.
Photo taken in D. Kohlstedt's lab at the University of Minnesota
Gas apparatus viewed from the top - the sample assembly is placed into the bore of the vessel, which is visible at the center of the photo. Click for larger image.
Photo taken in D. Kohlstedt's lab at the University of Minnesota
Control panel for Paterson apparatus. Click for larger image.
Paterson gas apparatus in D. Kohlstedt's lab at the University of Minnesota, image courtesy of University of Minnesota

Sample loaded into it's steel jacket. Click for larger image.
Photo taken in D. Kohlstedt's lab at the University of Minnesota
Pistons and torsion sample (top) and steel jacket (bottom). Click for larger image.
Photo taken in D. Kohlstedt's lab at the University of Minnesota
Torsion experiment (in jacket) after deformation. Click for larger image.
image courtesy of University of Minnesota
Diagram of a torsion sample. Click for larger image.

## The Griggs Modified Piston Cylinder Apparatus

Griggs Apparatus. Click for larger image.
Photo taken in P. Burnley's lab at the University of Nevada, Las Vegas

Since its invention in the 1960s by David Griggs of UCLA, the Griggs apparatus has been the most widely used high pressure deformation apparatus. The Griggs apparatus is based on a piston cylinder apparatus. It uses a hydraulic ram to pressurize a sample assembly contained in a cylindrical vessel. The hydraulic ram has a hole though the center which allows a second piston (the differential piston or σ3 piston) to be driven into the vessel by a gear train attached to the top of the apparatus. Between the gear train and the σ3 piston there is a load cell that measures the force required to move the σ3 piston.

Griggs Apparatus sample assembly. Click for larger image .
Drawing provided by P. Burnley
The sample assembly (which shares some common elements with the multi-anvil cell assembly) consists of a set of nested cylinders with the sample located at the center. Commonly the outermost cylinder is composed of NaCl which is relatively soft and transmits the confining pressure to the interior portion of the sample assembly. Inside the confining medium sits a thin graphite cylinder and an alumina support sleeve. The graphite cylinder is used for resistive heating much as it is in a multi-anvil sample assembly. Inside the graphite furnace there is another sleeve of a soft confining medium – typically NaCl. There is a type of sample assembly design called a molten salt cell (Borch and Green, 1989; Gleason and Tullis, 1995) in which the inner confining media consists of a ternary eutectic salt that melts at moderate temperature and provides a truly hydrostatic environment immediately adjacent to the sample during deformation. In this style assembly a thick-walled Ni sleeve is used to confine the molten salt and keep it from attacking the furnace. In all assemblies, the sample sits in the very center of the assembly perched on a piston (typically alumina) which in turn sits on a WC anvil. Another piston rests on top of the sample. The σ3 piston which is driven by the loading column, pushes on the upper piston which transmits the load to the sample. Either one or two thermocouples, encased in mullite ceramic insulation, touch the sample (usually entering from the side) and provide temperature measurement.

The strength of the Griggs apparatus is that it provides a relatively well defined uniaxial stress field, the strain rate can be varied from 10-3 to 10-8/second and samples are relatively large (~0.5 inches long). The greatest weakness of the apparatus is that the highest pressure most Griggs apparatus can achieve is only 2 GPa. An end-load Griggs apparatus has achieved up to 4 GPa confining pressure, but above that pressure the strength of the σ3 piston (which is unconfined above the sample assembly) is exceeded, which places a fundamental limit on the maximum pressure that the Griggs apparatus can achieve. Historically, much of the experimental work done in the Griggs machine did not use a molten salt assembly so that there were significant friction effects included in strength measurements which compromised the usefulness of quantitative rheology measurements made in the apparatus.

Griggs Apparatus baseplate. Click for larger image.
Photo taken in P. Burnley's lab at the University of Nevada, Las Vegas
Griggs Apparatus bomb. Click for larger image.
Photo taken in P. Burnley's lab at the University of Nevada, Las Vegas
Griggs Apparatus confining pressure and σ3pistons. Click for larger image.
Photo taken in P. Burnley's lab at the University of Nevada, Las Vegas

## Multi-Anvil Apparatus

Lacking a better method for deforming samples above 4 GPa, several experimentalists have attempted to use anisotropic compression in the multi-anvil apparatus to deform samples. The simplest way to do this is to put hard parts above and below the sample in the sample assembly which causes the sample to deform during pressurization. Since cold compression is of relatively little use in geophysics this strategy has not been widely adopted. In order to produce controlled deformation in the multi-anvil apparatus fundamental design changes were required in order to allow for the sample cell to be compressed in a non-uniform fashion. The resulting machines are called the D-DIA and the D-Tcup.

For a more detailed discussion of Multi-anvil apparatus see the Multi-anvil apparatus module

## D-DIA Apparatus

The D-DIA apparatus is a multi anvil apparatus. The D-DIA apparatus was invented to permit controlled deformation. The apparatus is based on a modified version of the DIA apparatus (Osugi et al 1964; Shimomura et al 1985) that uses 6 hard anvils (primarily WC) to compress a cube-shaped sample assembly. The anvils are driven inwards by two wedged guide blocks that are forced together by a large hydraulic press. In the DIA apparatus the anvils advance at the same rate, but in the D-DIA small hydraulic rams incorporated in the guide blocks allow the top and bottom anvils to be advanced independently (Durham et al 2002, Wang et al 2003).

D-DIA module. The guide block is shown in olive green. The wedges and upper and lower ram in blue and the anvils in green. Click for larger image.
(Wang et al., 2003)
D-DIA module at X17B2. The press is open. The top anvil can be seen protruding from the upper guide block. The back sides of the wedged are covered with Teflon sheet (white) to lubricate them as the slide against the guide blocks. The x-ray detector can be seen in the background. Click for larger image.
Image courtesy of P. Burnley
Looking down on the sample assembly in the D-DIA. The back sides of the wedged are covered with Teflon sheet (white) to lubricate them as the slide against the guide blocks. The path of the x-rays between the anvils and through the sample assembly is shown in yellow. Notice that the diffracted x-rays must pass through the anvil tips. For this reason the anvils on this side are made of transparent materials, either cubic boron nitride or sintered diamond. Click for larger image.
Image courtesy of P. Burnley
D-DIA module with the side anvils pulled back after an experiment. The bottom anvil is in the center and the sample assembly is sitting on top of it. As the assembly is pressurized the soft confining material extrudes between the anvils providing the pressure seal. The fins of extruded sample assembly are visible at the top and the bottom – the fins along the sides have already crumbled. Click for larger image.
Image courtesy of P. Burnley

### D-DIA Sample Assembly

D-DIA sample assembly. Click for larger image.
Image by P. Burnley
The sample assembly consists of a cubic volume of a soft material that serves as the confining medium, most commonly boron epoxy or mullite are used. A cylindrical graphite furnace with or without a supporting alumina sleeve is positioned at the center of the assembly such that the axis of the cylinder is parallel to the differential compression direction. The sample sits at the center of the furnace, as with the Griggs machine it is surrounded on the sides by a soft material (usually BN, NaCl, 90% or NaCl 10% BN) and above and below the sample are hard alumina pistons. Depending on the chemistry of the sample, a sample jacket may not be required. If a jacketing material is used it must to be x-ray transparent. A number of experimentalist use 25mm thick Ni metal foil to make a jacket. In order to measure the sample size as the deformation experiment proceeds, metal foils (either Ni or Pt) are placed on either end of the sample. A W3%Re-W25%Re thermocouple can be introduced from the side or the top to measure the sample temperature. Because of the relatively large size of the thermocouple compared to the assembly and the fact that the alumina insulation acts as a heat sink, some investigators prefer not to use thermocouples. However, this move has proved controversial.

D-DIA sample assembly. This assembly is made from a mullite sphere surrounded by pyrophyllite (dark grey) seats. A cylindrical graphite (gray) surrounded by an alumina protective sleeve (white) fit inside the sphere. Inside the furnace the sample is surrounded by BN confining media (seen in upper right). First row, from left to right: Alumina thermocouple outer sleeve and platinum contact, graphite and aluminum oxide rings and crushable alumina piston, crushable ring and piston assembled, cube assembled (looking down), cube assembled (on its side), empty cube, furnace and alumina support sleeve assembled, BN confining media, sample capsule. Second row, from left to right: Alumina thermocouple insulators with 45 degrees Miter cuts, thermocouple assembled, alumina furnace support, graphite furnace, pyrophyllite seat, mullite sphere, nickel foil for capsule, sample and inner piston with nickel foil markers, rolled nickel foil for capsule. Click for larger image.
Image courtesy of S.M. Thomas
Top entry thermocouple for D-DIA assembly. Click for larger image.
Image courtesy of P. Burnley
D-DIA sample assembly with top entry thermocouple. Click for larger image.
Image courtesy of P. Burnley

### In-Situ Stress and Strain Measurement in the D-DIA

Diffraction geometry for D-DIA. Click for larger image.
Burnley and Zhang, 2008
The D-DIA has been in use since 2001 and the technique is still under development. Both the beauty and the challenge of this technique is that the stress must be measured by x-ray diffraction. Using diffraction from the sample during deformation provides a direct measure of the stress state in the sample and therefore completely avoids all the issues with friction discussed above. The challenge is that the diffraction data is very complicated – reflecting the true complexity of the stress state in the sample during plastic deformation.
D-DIA. Click for larger image.
Photo taken at beamline x17B2, NSLS, Brookhaven National Laboratory
At this writing, the experimental community has yet to settle upon a single strategy for determining how the stress supported by the sample is related to the variety of stress states measured from the sample during the experiment. Strategies include measuring the stress state of an elastically deforming piston, averaging the stress states measured from the sample and using elastic plastic self consistent modelling to estimate the flow strength from the measured stress states. In comparison, strain measurements are quite straightforward and made using a radiograph of the sample and measuring the distance between metal foils that have been placed on either end.

D-DIA radiograph. Click for larger image.
Image by P. Burnley

## D-Tcup (6/8)

The d-tcup is similar in many ways to the D-DIA except that the sample assembly is based on an octahedra. The 8 cubes that compress the sample assembly are oriented in the press such that the compression direction is along the body diagonal of the cube.

## Rotational Drickamer Apparatus

Rotational Drickamer Appratus. Click for larger image.
RDA in S. Karato's lab at the Department of Geology and Geophysics, Yale University. Image courtesy of Yale University
The rotational Drickamer cell (RDA) relies on a completely different design for deformation that is more closely related to rotary shear experiments used for frictional studies. The RDA is an opposed anvil device in which the two anvils rotate in opposite directions relative to each other. The sample is compressed and then sheared between the rotating anvils. The advantage of this apparatus is that large strains can be achieved. In the uniaxial geometry achievable strains are limited by the deformation of the furnace and other assembly elements. Thus, RDA experiments can mimic strains in the earth, which can be very large. Quantitative measurements of the stress state in the RDA are challenging because the stress state varies radially across the sample assembly.

RDA anvils and gasket. Click for larger image.
Karato and Weidner, 2008
RDA schematic drawing. Click for larger image.
Durham, et al. 2002
RDA sample assembly. Click for larger image.
Karato, et al., 2008

## Deformation in the Diamond Anvil Cell

DAC. Click for larger image.
Cross section of polycrystalline yield strength experiment in the diamond cell, with schematic illustration of the non-hydrostatic stresses across the sample. Meade and Jeanloz, 1988
If one places a sample in the DAC without a gasket the sample will experience tremendous pressure gradients and deform. A number studies have sought to take advantage of this to study deformation of the sample. The stress state varies dramatically both from the center to the edge but also from the face of one anvil to the other. Such a complicated stress state does not lend itself to interpretation and the microstructures produced during deformation may not be relevant for the Earth. However, for deformation studies at pressure above ~20-30 GPa the DAC is the only option.

# Guest Lecturer

"Beyond Elasticity: Stress, Strain, Time" Prof. Donald J. Weidner

Part 1 (55 minutes) ( 66.7MB Sep12 12)

Part 2 (35 minutes) ( 58.5MB Sep12 12)

Flow and Fracture of Rocks. Eds. H.C. Heard, I.Y. Borg, N.L. Carter, C.B. Raleigh. The Griggs Volume. American Geophysical Union. Washington. 1972

Mineral and Rock Deformation: Laboratory Studies. Eds. B.E. Hobbs, H.C. Heard. The Paterson Volume. American Geophysical Union. Washington. 1986

Plastic Deformation of Minerals and Rocks. Eds.S. Karato, H. Wenk. Reviews in Mineralogy and Geochemistry, vol 51. The Mineralogical Society of America. Washington, 2002

The Brittle-Ductile Transition in Rocks. Eds. A.G. Duba, W.B. Durham, J.W. Handin, H.F. The Heard Volume. Washington. Wang. American Geophysical Union. 1990

# References Cited

Borch, R. S., Green, H. W. (1989) Deformation of Peridotite at high Pressure In a New Molten Salt Cell: Comparison of Traditional and Homologous Temperature Treatments. Physics of the Earth and Planetary Interiors 55, 3-4, 269-276.

Durham, W.B., Weidner, D.J., Karato, S., Wang, Y. (2002) New Developments in Deformation Experiments at High Pressure. Reviews in Mineralogy and Geochemistry 51, 21 - 49.

Gleason, G. C., Tullis, J. (1993) Improving Flow Laws and Piezometers for Quartz and Feldspar Aggregates. Geophysical Research Letters 20, 19, 2111-2114.

Gleason, G. C., Tullis, J. (1995) A flow law for dislocation creep of quartz aggregates determined with the molten salt cell. Tectonophysics 247, 1 - 23.

Green, H. W., Borch, R. S. (1989) A new molten salt cell for precision stress measurement at high pressure. European Journal of Mineralogy 1, 213 - 219.

Mackwell, S.J., Paterson, M.S. (2002) New developments in deformation studies: High-strain deformation. Reviews in Mineralogy and Geochemistry 51, 1 - 19.

Meade, C., Jeanloz, R. (1988) Yield Strength of MgO to 40 GPa. Journal of Geophysical Research, 93, B4, 3261 - 3269.

Osugi, J., Shimizu, K., Inoue, K., Yasunami, K., (1964) A compact cubic anvil high pressure apparatus. The Review of Physical Chemistry of Japan, 34, 1, 1 - 6.

Paterson, M.S. (1970) A high-pressure, high-temperature apparatus for rock deformation. International Journal of Rock Mechanics and Mining Sciences 7, 5, 525 - 526.

Shimomura, O., Yamaoka, S., Yagi, T., Wakatsuki, M., Tsuji, K., Fukunaga, O., Kawamura, H., Aoki, K., and Akimoto, S., (1985) Multi-anvil type high pressure apparatus for synchrotron radiation: Solid state physics under pressure. Recent Advance with Anvil Devices, 351 - 356.

Yamazaki, D., Karato, S. (2001) High-pressure rotational deformation apparatus to 15 GPa. Review of Scientific Instruments 72, 11, 4207 - 4211.

Wang, Y., Durham, W. B., Getting, I. C., and Weidner, D. J. (2003) The deformation-DIA: A new apparatus for high temperature triaxial deformation to pressures up to 15 GPa. Review of Scientific Instruments 74, 6, 3002 - 3011

Shun-ichiro Karato's Lab at Yale

David L. Kohlstedt's lab at UMN

An interview with Mervyn Paterson

Tracy Rushmer's lab at MQ

Pamela Burnley's lab at UNLV

# Acknowledgements

These materials are being developed with the support of COMPRES, the Consortium for Materials Properties Research in Earth Sciences, under NSF Cooperative Agreement EAR 10-43050 and is partially supported by UNLV's High Pressure Science and Engineering Center, a DOE NNSA Center of Excellence supported under DOE NNSA Cooperative Agreement No. DE FC52-06NA26274.