The true or real density is defined as the ratio of the mass to the volume occupied by that mass. According to the British Standards Institute (BSI) and the American Society for Testing and Materials (ASTM), this relates to the ratio of the mass and the volume (true volume) of a sample, excluding the volume of the opened pores, the closed pores, and the inter-particle voids. Therefore, the contribution to the volume made by pores or internal voids must be subtracted when measuring the true density. The true density of a solid is calculated as the true unit volume of the solid exclusive of its pore space which is divided into the weight of the sample. Regardless of whether pores and internal voids are present, the density of fine powders is often not the same as those of larger pieces of the same material because, in the process of preparing many powders, those atoms or molecules located near the surface are often forced out of their equilibrium positions within the solid structure. On large pieces of material, the percentage of atoms near the surface is negligibly small. As the particle size decreases, however, this percentage increases, with its resultant effect upon the density.

Powder is typically comprised of solid particles, interparticle voids, as well as open and closed pores of particles, as displayed  image. True density is among the main physical indicators for the evaluation of the quality of a powder type product. The true density is a basic parameter of the powder material. The open pores, the closed pores, and the inter-particle voids impact the final performance of the product. True density value corresponds to chemical composition and its purity, which determines the performance, quality, and application domain of the product.

 Internal structure of the powder material

If the powder has no porosity, the true density can be measured by displacement of any fluid in which the solid remains inert. The accuracy of the method is limited by the accuracy with which the fluid volume can be determined. Usually, however, the solid particles contain pores, cracks, or crevices, which will not easily be completely penetrated by a displaced liquid. In these instances, the true density can be measured by using a gas as the displaced fluid. Apparatus used to measure solid volumes are often referred to as pyknometers or pycnometers after the Greek 'pyknos', meaning thick or dense. Once the sample volume and mass have been determined, the density is readily calculated.

The true density is a key physical parameter of powder materials, it directly influences the performance, quality, and application of the powder material. There are many commercially available pycnometers for the determinations of the true density of powders, most of which operate on the principle of gas displacement, helium being the most frequently used gas because of its inertness and small size which enables it to penetrate even the smallest pores.

An automatic, manometric gas expansion pycnometer offers extreme simplicity of operation along with great speed and accuracy. A schematic diagram of such a pycnometer is shown as below. When the gas displacement method is used, the measurement system generally comprises a reference chamber, a sample chamber, valves, a pressure sensor, and a temperature control system. The sample chamber is utilized for the placement of the sample, while the reference chamber is utilized for gas expansion. Open pores of particles and inter-particle voids are filled with the gas in a gas pycnometer. The gas volume may be obtained via the calculation using the gas pressure before and after gas expansion at a fixed temperature and in sealed chambers with a known volume. The helium gas expansion pycnometer method is rapid, reliable, precise, and requires minimal analytical equipment and sample preparation, and also is non-destructive to samples.

sample. 

gas expansion pycnometer working schematic

Experimental determination of density is a function of measuring mass, and true volume. Mass is the weight of the sample and volume can be determined by various experimental methods. True volume is usually measured with a gas stereopycnometer (helium or nitrogen), excluding interparticular volume. It is preferable to use helium, as its small molecular diameter makes it possible to access pores of up to 3.5 Å.