Evans balance

An Evans balance, also known as a Johnson Matthey Magnetic Susceptibility Balance, is a scientific instrument used to measure the magnetic susceptibility of solids and liquids. Magnetic susceptibility quantifies the extent to which a material becomes magnetized in an applied magnetic field, and can be measured using various devices that modify the shape of the magnetic field and method of force measurement.

The Evans balance operates by measuring the force exerted on a magnet within the magnetic field rather than directly on the sample.

Mechanism
The Evans balance operates by measuring the change in current necessary to maintain equilibrium of suspended permanent magnets after their magnetic fields interact with a sample. The balance consists of magnets positioned on one end of a beam whose position shifts upon interaction with the sample. This displacement is detected by photodiodes located opposite the equilibrium point of the beam. These diodes transmit signals to an amplifier that adjusts the current in a coil to counteract the interaction force. A digital voltmeter measures the current flowing through a precision resistor in series with the coil, and displays the measurement on a digital readout.

The original Evans balance, devised by Dennis F. Evans in 1973, was based on a torsional balance developed earlier by Alexander Rankine in 1937. Evans utilized Ticonal bars with cadmium-plated mild steel yokes as magnets, and a suspension strip made from a Johnson Matthey gold alloy, hence the alternate name "Johnson Matthey balance". These components were bonded together using epoxy resin on a phosphor bronze spacer. The sample tubes were crafted from NMR tubes and current was supplied via CdS photoresistors. Modifications to the original design were later made with assistance from Johnson Matthey, involving the placement of two pairs of magnets within an H-frame. The sample was inserted between one pair of magnets, while a small coil was positioned between the second pair. This entire assembly pivoted horizontally around a torsion strip. When a sample tube was introduced between the magnets, the torsional force was counterbalanced by the current passing through the coil, providing a reading on the display instead of using a Helipot potentiometer.

Comparison to alternative magnetic balances
In contrast to other magnetic balances, the Evans balance does not necessitate a precision weighing device. It offers faster measurements compared to Gouy or Faraday balances, albeit with reduced accuracy and sensitivity. The Evans balance is capable of measuring within a range of 0.001 x 10−7 to 1.99 x 10−7 CGS volume susceptibility units. The original model demonstrated an accuracy within 1% of literature values for diamagnetic solutions and within 2% for paramagnetic solids.

The system facilitates measurements across solid, liquid, and gaseous forms of a wide spectrum of paramagnetic and diamagnetic materials, typically requiring approximately 250 mg of sample for each measurement.

Calibration
The Evans balance determines susceptibility indirectly by referencing a calibration standard with a known susceptibility. A commonly used calibration compound is mercury cobalt thiocyanate, HgCo(NCS)4, which has a susceptibility of 16.44×10−6 (±0.5%) CGS at 20°C. Another frequently used standard is [Ni(en)$3$]S$2$O$3$, with a susceptibility of 1.104 x 10−5 erg G−2 cm−3. Calibration involves taking three readings: one with an empty tube R0, one with the tube filled with the calibrant, and one with the tube filled with the sample Rs. Some balances feature an auto-tare function, which eliminates the need for the R0 measurement.

The accuracy of the measurement is influenced by the homogeneity of the sample packing. The first two readings provide a calibration constant (C). The mass susceptibility (χg) in grams is calculated using the formula:
 * $$\chi_g= \frac{C L (R_s-R_0)}{10^9 m}$$

where L is the length of the sample, C is the calibration constant (usually 1 if the device has been calibrated), and m is the mass in grams. The reading for the empty tube accounts for the diamagnetic properties of the glass. There is an additional V term (volume susceptibility of air) and an A term (cross-sectional area of the sample) in the most general form of the equation, but these terms can be ignored for solid samples.

To calculate the volume magnetic susceptibility (χ) for liquid samples, the equation includes the V term in the numerator and divides by the density (d) of the solution instead of the mass (m).