Method and apparatus for measuring physical properties of matter

A method for determining volumetric strain in a sample of compressible material immersed in a fluid medium as the sample is exposed to varying hydrostatic stress, comprising:

• (a) causing the fluid medium to have a first density, ρ1;
• (b) causing the fluid medium to have an nth density, ρn;
• (c) exposing the sample to an acceleration in a first direction while immersed in the fluid medium having the first density;
• (d) determining a first voltage related to a first applied force in a second direction opposite the first direction, where the first applied force is sufficient to maintain the sample in static equilibrium while the acceleration is applied and the object is immersed in the fluid medium having the first density;
• (e) exposing the sample to the acceleration in the first direction while immersed in the fluid medium having the nth density;
• (f) determining an nth voltage related to an nth applied force in the second direction which is sufficient to maintain the sample in static equilibrium while exposed to the acceleration and immersed in the fluid medium having the nth density;
• (g) completely immersing a calibration standard of known density in the fluid medium having the first density;
• (h) exposing the calibration standard to the acceleration in the first direction while immersed in the fluid medium having the first density;
• (i) determining a first calibration voltage related to a first calibration force in the second direction, where the first calibration force is sufficient to maintain the calibration standard in static equilibrium while the acceleration is applied and the calibration standard is immersed in the fluid medium having the first density;
• (j) completely immersing the calibration standard in the fluid medium having the nth density;
• (k) exposing the calibration standard to the acceleration in the first direction while immersed in the fluid medium having the nth density;
• and
• (l) determining an nth calibration voltage related to an nth calibration force in the second direction which is sufficient to maintain the calibration standard in static equilibrium while exposed to the acceleration and immersed in the fluid medium having the nth density;
• (m) calculating a calibration ratio according to:
• C 1 C n = v cn ⁡ ( ρ c - ρ 1 ) v c1 ⁡ ( ρ c - ρ n ) ,
• where C 1 C n
• is the calibration ratio, ρc is the known density of the calibration standard, vc1 is the first calibration voltage related to the first calibration force, and vcn is the nth calibration voltage related to the nth calibration force;
• and
• (n) determining the volumetric strain in the sample according to:
• Δ ⁢ ⁢ V V 1 = ( v 1 - C n C 1 ⁢ v n ) M ⁡ ( ρ 1 - ρ n ) - 1 ,
• where Δ ⁢ ⁢ V V 1
• is the volumetric strain, v1 is the voltage related to the first applied force, vn is the voltage related to the nth applied force, and M is given by
• M=−V1×g,
• where V1 is the initial volume of the sample and g is the acceleration in the first direction.

A method for operating an apparatus to determine bulk modulus of a sample, the apparatus including a beam balance enclosed within a pressure chamber, the beam balance including a sample pan coupled to a first end of the beam balance and a counter-force application device disposed at an opposing second end of the beam balance, the apparatus further including a calibration standard of known density, a temperature sensor, and a pressure sensor, the method comprising:

• (a) sealing the sample within the pressure chamber;
• (b) purging the pressure chamber of air;
• (c) pressurizing the chamber to a first pressure using a fluid medium;
• (d) determining a first force applied by the counter-force application device required to balance the beam balance with the sample on the sample pan with the pressure chamber pressurized to the first pressure;
• (e) measuring a first temperature within the pressure chamber using the temperature sensor with the pressure chamber pressurized to the first pressure;
• (f) measuring the pressure within the pressure chamber using the pressure sensor with the pressure chamber pressurized to the first pressure;
• (g) calculating a first density of the fluid medium based upon a predetermined relationship between density, pressure, and temperature of the fluid medium;
• (h) pressurizing the chamber to an nth pressure, which is different from the first pressure;
• (i) determining an nth force applied by the counter-force application device required to balance the beam balance with the sample on the sample pan with the pressure chamber pressurized to the nth pressure;
• (j) measuring an nth temperature within the pressure chamber using the temperature sensor with the pressure chamber pressurized to the nth pressure;
• (k) measuring the pressure within the pressure chamber using the pressure sensor with the pressure chamber pressurized to the nth pressure;
• (l) calculating an nth density of the fluid medium based upon the predetermined relationship between density, pressure, and temperature of the fluid medium;
• and
• (m) calculating the bulk modulus of the sample based at least in part on the first and nth densities of the fluid medium and the first and nth forces applied by the counter-force application device.

An apparatus for determining bulk modulus of a sample having a sample mass and a sample volume while the sample is immersed in a fluid medium having variable density, and the sample is exposed to an acceleration in a first direction and a net buoyancy force in a second direction opposite the first direction, where the net buoyancy force is a sum of buoyancy forces in the first and second directions exerted on the sample by the fluid medium, the apparatus comprising:

• a chamber for containing the fluid medium and the sample immersed in the fluid medium;
• means for selectively varying the density of the fluid medium in the chamber over a range of densities;
• means for producing at least one electrical signal related to the density of the fluid medium in the chamber as he density of the fluid medium is varied;
• a beam balance disposed within the chamber and having opposing first and second ends, the beam balance further comprising:
• a sample pan disposed adjacent the first end of the beam balance, the sample pan having a sample pan volume and a sample pan mass, and creating a sample pan moment adjacent the first end of the beam balance;
• a first counter-weight disposed adjacent the second end of the beam balance, the first counter-weight having a first counter-weight volume which is substantially equivalent to the sample pan volume, a first counter-weight mass which is substantially equivalent to the sample pan mass, and creating a first counter-weight moment adjacent the second end of the beam balance which is substantially equivalent to the sample pan moment;
• a coil assembly disposed adjacent the second end of the beam balance, the coil assembly having a coil assembly volume and a coil assembly mass, and creating a coil assembly moment adjacent the second end of the beam balance, the coil assembly electrically coupled to a controller;
• a second counter-weight disposed adjacent the first end of the beam balance, the second counter-weight having a second counter-weight volume which is substantially equivalent to the coil assembly volume, a second counter-weight mass which is substantially equivalent to the coil assembly mass, and creating a second counter-weight moment adjacent the first end of the beam balance which is substantially equivalent to the coil assembly moment;
• a magnet assembly disposed adjacent to and magnetically interacting with the coil assembly;
• the controller for providing a coil current to the coil assembly, thereby generating a magnetic field which interacts with the magnet assembly, the interaction between the magnetic field of the coil assembly and the magnet assembly causing a force to be applied to the second end of the beam to keep the beam balanced as the density of the fluid medium in the chamber is varied over the range of densities, where the force applied to the second end of the beam is substantially equivalent to the difference between the net buoyancy force and the product of the sample mass times the acceleration while the sample is immersed in the fluid medium as the density of the gaseous medium is varied over the range of densities;
• and
• a computing device for receiving the at least one electrical signal related to the density of the fluid medium and at least one electrical signal related to the coil current, and for calculating the bulk modulus of the sample based at least in part upon the at least one electrical signal related to the density of the gaseous medium and the at least one electrical signal related to the coil current.