# Instrumentation: Which Measurement is Correct?

July 1, 2001
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When different measurement techniques produce different results for the same sample, which results should you trust?

When I was a graduate student in physics, a fellow student and I were working together on a homework set. We had spent the majority of the day on a particularly difficult problem that resulted in a lengthy equation expressed in terms of assorted variables. I turned to the back of the book to compare our result to that of the author’s and was astonished by the dissimilarity. I showed the “correct” solution to my friend, a far better and more confident student than I. After looking at it he asked, “Did we apply the appropriate theorems?” I affirmed that we had. Next, he asked, “Did we make any mathematical errors?” I was confident that we had not. “Then,” he proclaimed, “our solution is correct—we just are expressing it in different terms.”

I recall this incident whenever I encounter a debate over the “correctness” of the results obtained from measurements by two or more different analytical techniques. Provided that the equipment used was capable of producing high-quality data, the pertinent questions then should be, “was the sample properly prepared and properly measured,” and “were the analytical parameters applied correctly in reducing the data?” If the answers to both are “yes,” then both analytical results probably are equally correct; they are just expressed in different terms.

The precept of “different techniques yielding different correct results” applies to particle sizing, surface area, pore sizing and many other physical measurements. To illustrate this point, consider the seemingly uncomplicated task of determining the density of a solid sample. Density, in the simplest terms, is the mass of an object divided by its volume. However, it is much more complicated than that. The American Society for Testing and Materials (ASTM) offers over 40 definitions in its compendium of standard definitions.1 The British Standards Institute (BSI)2 has narrowed it down to 14 types of densities (see Table 1). By which definition of density are you measuring, and how do you know?

Determining mass is rather straightforward; determining volume presents the difficulty. “Volume,” as pertains to a solid, can’t be expressed universally in a single, neat definition. Various industries adopt definitions pertinent to their product, and the technique used to experimentally determine volume and, subsequently, the density, must be one that applies measurement rules consistent with the adopted definition.

Table 1.

## Defining Volumes and Densities

A common masonry brick serves as a good example of an object that contains all types of elemental volumes and that differs in volume, and therefore density, depending on the measurement technique. A brick is composed of solid material, but also contains surface irregularities and pores. Some pores communicate with the surface (open pores) and others are isolated within the bulk (closed or blind pores).

Surface irregularities are a type of void volume. For lack of a standard definition, this will be referred to as “external void volume” and will indicate the void in the valleys of the surface irregularities but will not include smaller pores that penetrate the interior. The meaning of the term is admittedly vague, but this volume can be determined under certain analytical conditions and provides an indication of surface roughness.

Materials in granular or powdered form contain another type of void: interparticle space. The total volume of interparticle voids depends on the size and shape of the individual particles and how well the particles are packed.

## Manual Laboratory Methods

Displacement. With hydrostatic weighing, the volume of a solid sample is determined by comparing the weight of the sample in air to the weight of the sample immersed in a liquid of known density. The volume of the sample is equal to the difference in the two weights divided by the density of the liquid.

If the sample is porous, whether or not the pores will be included with the volume must be decided. If they are, a sealing coating must be applied (see Bulk/Envelope Volume by Coating, below). If not, the liquid must displace the air in the pores. This is usually augmented by evacuation and boiling.3,4,5

The displacement medium is not limited to liquids; fine particles and gases can be used. The volume of the medium displaced by the sample is measured. If the sample material is porous, fine particles will not penetrate into the smaller pores that liquids or gases can enter. Mercury, being a non-wetting liquid to most solids, also will not penetrate pores under ambient pressure.6 Gases, helium in particular, will penetrate readily into very fine pores. Therefore, all three displacement mediums will likely produce a different volume (density) value because of the way pore volume is treated.

Bulk/Envelope Volume by Coating.7 Coating the sample allows determination of bulk volume or apparent volume of solids while preventing absorption of the suspension liquid.

Density Gradient Column.8 This is a column of liquid that varies in density with height. A sample is placed in the liquid and observed to determine at what vertical level in the column the sample is suspended. The density of the liquid at that level is the density of the sample. However, if the material is porous, one must understand how the liquid interacts with the surface irregularities and open pores of the sample.

Tap Density9 and Vibratory Packing Density. These are very similar methods for determining the bulk density of a collection of particles under specific conditions of packing. How well the material is packed will affect the interparticle void volume, a volume component that is included in the density calculation.

## Automated Analytical Instruments

Skeletal Volume and Density by Gas Pycnometry. A gas pycnometer operates by detecting the pressure change resulting from displacement of gas by a solid object. Expanding a quantity of gas at known pressure into an empty chamber and measuring the pressure establishes a baseline. Then, a sample is placed in the chamber, and the chamber is resealed. The same quantity of gas at the same pressure is again expanded into the sample chamber, and the pressure is measured. The difference in the two pressures combined with the known volume of the empty sample chamber allows the volume of the sample to be determined by way of the gas law. Sometimes, the difference in results obtained when using different gases is indicative of some sought-after characteristic of the sample.10

The accuracy and precision of the gas pycnometer in determining skeletal volume and density can be quite high, but the method relies greatly on the cleanliness of the sample material and purity of the analysis gas. The gas must be pure and dry air, and the sample pretreated to remove volatiles.

The accessibility to small open pores is quite high. The volume measured by this method will be less (density greater) than that determined by mercury porosimetry or other liquid displacement methods when small, open pores are in the sample.

Envelope Volume and Density by Displacement of a Dry Medium. This displacement technique applies to a solid object immersed in a bed of much smaller solid particles. It differs from liquid and gas displacement in the way the displaced medium conforms to the surface of the immersed object. Wetting liquids conform quite closely to the surface and invade pores. Solid particles invade pores, but pack around the sample, creating an envelope.

Repeatability and reproducibility are achieved by controlling compaction. The sample cell in which the dry medium is placed is a precision cylinder. A plunger compresses the powder as the cell vibrates. The force of compression is selectable and, therefore, repeatable from test to test. A preliminary compaction with only the displacement medium in the cell establishes a zero-volume baseline. The object is then placed in the cylinder with the dry medium and the compaction process is repeated. The difference in the distance the piston penetrates the cylinder during the test and during the baseline procedure is used to calculate the volume of the medium displaced by the solid object.

This relatively new technique by Micromeritics is finding applications where tap density and mercury displacement methods traditionally have been used.11,12

Bulk, Envelope, and Skeletal Volumes and Densities by Mercury Porosimetry. Mercury is a non-wetting liquid that must be forced to enter a pore by application of external pressure. The surface tension of mercury causes mercury to bridge the openings of pores, cracks and crevices until sufficient pressure is applied to force entry.13 For example, at atmospheric pressure, mercury will resist entering pores smaller than about 6 µm in diameter. When an object is surrounded by mercury, the mercury forms a closely fitting liquid envelope around the object. How closely the mercury conforms to the surface features of the object depends on the pressure applied. As pressure increases, mercury enters smaller and smaller voids in the sample. At a pressure of 60,000 psi (414 MPa), mercury has been forced to enter pores of diameters down to 0.003 micrometer. This fills essentially all pore volume in most materials.

Typically, the volume of mercury displaced at minimum pressure and that displaced at maximum pressure are used to determine bulk (or envelope) density and skeletal density, respectively. For powders, the total volume of the grains can be determined by subtracting the interparticle void volume from the bulk volume.

A mercury porosimeter is seldom used solely for the determination of envelope, bulk and skeletal volume determinations. These determinations more often are a byproduct of a data set that was obtained primarily for the determination of pore volume distribution by pore size.

## Choosing the Right Instrument

Volume and density are just two of the measurements often required in the development and quality control of ceramic materials, and there are a variety of ways to determine these characteristics, including the methods listed in this article. However, no single measurement technique is superior in all applications. The instrument or method selected for the density/volume determination must be suitable for the material to be measured and for the environment in which the material is to be used. It also must provide data consistent with industry definitions of the characteristic being measured.

The bottom line is that different measurement techniques and methods are likely to produce different results for the same sample, and all of them can be equally accurate. It all depends on exactly what is being measured. The best instrument for the application is the one that provides the best correlation between sample characteristics and material quality or performance.

## References

1. Compilation of ASTM Standard Definitions, 8th Edition, American Society for Testing and Materials, Philadelphia (1994).
2. British Standard BS 2955 Glossary of Terms Relating to Particle Technology, British Standards Institution, London, (1991).
3. C135 Test Method for True Specific Gravity of Refractory Materials by Water Immersion, American Society for Testing and Materials.
4. C20-00 Standard Test Methods for Apparent Porosity, Water Absorption, Apparent Specific Gravity, and Bulk Density of Burned Refractory Brick and Shapes by Boiling Water, American Society for Testing and Materials (2000).
5. C357-94 Standard Test Method for Bulk Density of Granular Refractory Materials, American Society for Testing and Materials (1998).
6. C493-98 Standard Test Method for Bulk Density and Porosity of Granular Refractory Materials by Mercury Displacement, American Society for Testing and Materials (1998).
7. C914-95 Standard Test Method for Bulk Density and Volume of Solid Refractories by Wax Immersion, American Society for Testing and Materials (1999).
8. D1505-98 Standard Test Method for Density of Plastics by the Density-Gradient Technique, American Society for Testing and Materials (1998).
9. B527-93 Standard Test Method for Determination of Tap Density of Metallic Powders and Compounds, American Society for Testing and Materials (1995).
10. He Huang; Keyu Wang; Bodily, D.M.; Hucka, V.J., “Density Measurements of Argonne Premium Coal Samples,” Energy & Fuels, 9(1), pp. 20-24 (1995).
11. El Saleh, Firas and Peter Kleinebudde, Mercury-Free Determination of Apparent Density and Porosity of Pellets by Powder Pycnometry, Pharmaceutical Technology Europe, Vol. 10 No. 11 November (1998).
12. P. Pei, M. C. Bhardwaj, J. Anderson, D. Minor and T. Thornton, Measuring Green Body Density, Ceramic Industry, Sept. 25 (2000).
13. Paul A. Webb, An Introduction to The Physical Characterization of Materials by Mercury Intrusion Porosimetry with Emphasis on Reduction and Presentation of Experimental Data, Micromeritics Instrument Corp., www.micromeritics.com.

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