# Analyzing Ceramic Powders

Particle size analysis has traditionally been accomplished through the Brunauer, Emmett and Teller (BET) technique, in which liquid nitrogen is used to measure the total surface area of the particles. However, the BET technique is time-consuming, requiring up to 60 minutes to complete, and the cryogenic temperatures required to handle the liquid nitrogen make the technique expensive to perform.

An automated instrument called the envelope surface area analyzer (ESA) has been developed to reduce the time and costs associated with particle size analysis. Based on theoretical and experimental work from several sources, including Carman,[1] Kraus, Gerard, Ross, John W., Girifalco, L. A.,[2] and Emmett, P.H.,[3] the instrument determines the envelope surface area of powders from their gas permeability. The equipment is designed for quality control and development-it is fast, easy to use and reproducible for determining the exterior surface area and the average particle size of a sample. The average particle size is the diameter of spheres of equivalent exterior surface area. For spherical sample particles, the ESA results compare well with the real particle diameter. Specific surface area obtained with ESA on particles with no internal voids compares well with that obtained through BET.

## Theoretical Background

Carman first suggested the use of liquid permeability and the Kozeny equation (see Equation 1) for measurement of the surface area of powders in 1937.[1] Experimental work through the 40s and 50s proved that the concept gave reproducible values for both specific surface area and average particle size in comparison to the nitrogen adsorption method.In the 50s, gas permeability was developed as an alternative to liquid permeability. Because the gas permeability method left the sample physically unaltered as a result of the test, that method became preferred. However, it was quickly found that the use of gases at low pressures required a modification of the Kozeny equation to account for molecular or slip flow. This additional term is equivalent to the Knudsen flow equation. Equation 2 gives this combined equation.

For samples of very small capillary size, such as a packed powder bed, the molecular or slip flow cannot be ignored even at the atmospheric pressure. Using Equation 2, the specific surface area of a sample can be calculated. From the specific surface area, a value for the average particle size can be calculated. Equation 3 shows how the specific surface area can be used to calculate a mean diameter by assuming spherical particle shape. Using these equations, the average particle size of a sample can be determined from the gas permeability.

## Method of Operation

The ESA is based on gas permeability technology. Figure 1 shows an example of some of the screens in the control software. The test monitors the gas flow through the sample as a function of the differential pressure across the sample. The pressure is accurately controlled and increased in small steps. The differential pressure and flow at each step is allowed to stabilize before the data for that point is taken to ensure a steady state reading. To ensure a sufficient average, the test is designed to take data at several differential pressures.The method is completely automated, requiring only the initial input of the sample parameters such as sample mass and absolute density. The test from initial weighing to the removal of the sample chamber can be accomplished in less than 15 minutes-much faster than the 60 minutes needed for a BET analysis. Additionally, the ESA method, unlike the BET method, does not require any special gases or cryogenic liquids. The data is analyzed using analysis software. The results are provided automatically at the end of each test and can be reviewed at any future point. A wide range of sample surface areas, from 0.1 to 10 m2/g, can be tested.

## Results

Three types of samples were tested with the ESA. The first two samples, A and B, were magnesium stearate powders; the next two, C and D, were glass bubbles; and the others were alumina powders. The three types of samples were also tested using BET for comparison of BET data with those of ESA. The BET results for the magnesium stearate samples used nitrogen adsorption, while the glass bubbles used krypton.A comparison of the two methods is presented in Table 1. This table shows that a very good comparison exists between the BET and ESA results.

Figure 2 shows typical results for samples C and D.

The average particle size is related to the envelope surface area rather than the total surface area. Therefore, the envelope surface area measured in ESA is more appropriate for estimating the average particle size of the powders (see Table 3).