Evans balance

See also: Faraday balance

An Evans balance, also referred to as a Johnson-Matthey Magnetic Susceptibility Balance, is a device to measure the magnetic susceptibility of solids and liquids. Magnetic susceptibility is related to the force experienced by a substance inside a magnetic field. Different types of devices can be used to measure this magnetic susceptibility, modifying the shape of the magnetic field inside and the method by which the force is measured.

The Evans balance measures the force on the magnet instead of the sample in the magnetic field.

Mechanism

The Evan’s balance measures the change in current required to keep a set of suspended permanent magnets in balance after their magnetic fields interact with the sample. The magnets are located on one end of the balance beam and change the position of the beam by interacting with the sample. This change is registered by a pair of photodiodes set on the opposite side of the balance beam’s equilibrium position. These diodes send signals to an amplifier that supplies current to a coil that will exactly cancel the interaction force. A digital voltmeter, connected across a precision resistor, in series with the coil, measures the current directly and is displayed on the digital readout.

Dennis F. Evans described the original Evans balance in 1973, based on a torsional balance developed by Alexander Rankine in 1937. Evans used Ticonal bars with cadmium-plated mild steel yokes as the magnets and a Johnson Matthey gold alloy (hence the other name of the balance) for the suspension strip, glued together with epoxy resin onto a phosphor brown spacer. The tubes were made from NMR tubes and the current came from CdS photocells. This original was modified with help from the Johnson Matthey company. Two pairs of magnets were glued between the arms of an H-frame. The sample was placed into the gap between one pair of magnets and a small coil in the gap between the second pair of magnets. This entire construction pivoted horizontally around a torsion strip. When a sample tube was placed between the first pair of magnets, the torsional force was restored by the current passed through the coil between the second pair of magnets, giving a reading on a display instead of a Helipot potentiometer.

Comparison to alternative magnetic balances

An Evans balance does not require a precision weighing device, a key advantage over alternative magnetic balances. Moreover, an Evans balance consumes less time than a Gouy balance or Faraday balance but offers less accuracy and less sensitivity. An Evans balance has a range from 0.001 x 10⁻⁷ to 1.99 x 10⁻⁷ CGS volume susceptibility units. The original Evans balance had an accuracy of within 1% of the literature values for diamagnetic solutions and within 2% of the literature values for paramagnetic solids.

The system allows for measurements of solid, liquid, and gaseous forms of a wide range of paramagnetic and diamagnetic materials. For each measurement, around 250 mg of sample is required.

Calibration

The Evans balance measures susceptibility indirectly by referring to a calibration standard of known susceptibility. The most convenient compound for this purpose is mercury cobalt thiocyanate, HgCo(NCS)₄, which has a susceptibility of 16.44×10⁻⁶ (±0.5%) CGS at 20°C. Another common calibration standard is [Ni(en)₃]S₂O₃ which has a susceptibility of 1.104 x 10⁻⁵ erg G⁻² cm⁻³. Three readings of the meter are needed: of an empty tube, R₀; of the tube filled with calibrant; and of the tube filled with the sample, R_s. Some balances have an auto-tare feature that eliminates the need for the R₀ measurement. Accuracy depends somewhat on the homogeneous packing of the sample. The first two provide a calibration constant, C. The mass susceptibility in grams is calculated as

$\chi _{g}={\frac {CL(R_{s}-R_{0})}{10^{9}m}}$

where L is the length of the sample, C is the calibration constant (usually 1 if it has been calibrated), and m is its mass in grams. The reading for the empty tube is needed because the tube glass is diamagnetic. There is a V term multiplied by an A term in the most general form of the equation. These two terms (V∗A) are collectively added to the numerator in the above equation. The V term is the volume susceptibility of air (0.029 x 10⁻⁶ erg G⁻² cm⁻³) and A is the cross-sectional area of the sample. These two terms can be ignored for solid samples, yielding the original equation written above.

To calculate the volume magnetic susceptibility (χ) instead of the weight susceptibility (χ_g), such as in a liquid sample, the equation would have the extra V term added to the numerator and instead of being divided by m, the equation would be divided by d for the density of the solution.