Why Frenkel defect does not impact the density of the solid?

Question

The following text is from Chemistry Part I - Textbook for Class XII (NCERT), chapter "The Solid State", page 23, topic "1.9 Imperfections in Solids", sub topic "1.9.1 Types of Point Defects - (iii) Frenkel Defect":

This defect is shown by ionic solids. The smaller ion (usually cation) is dislocated from its normal site to an interstitial site. It creates a vacancy defect at its original site and an interstitial defect at its new location.

Frenkel defect is also called dislocation defect. It does not change the density of the solid.

^{(Emphasis mine)}

Earlier I've learnt that a vacancy defect results in decrease in the density of the substance, and an interstitial defect increases the density of the substance. I could understand, due to the presence of vacancy or interstitial defects, the density varies locally or in other words density of the substance is not uniform throughout.

According to the quoted text, Frenkel defect creates a vacancy defect at one location and an interstitial defect at a different location (not at the same location), so I think the density will again have local variations and so the density changes. But it is given Frenkel defect doesn't alter the density. What is the reason for this fact? Why does the same logic fail here?

The Wikipedia article on "Frenkel defect" gives the following statement:

Frenkel defect does not have any impact on the density of the solid as it involves only the migration of the ions within the crystal, thus preserving both the volume as well as mass.^{[citation needed]}

^{Source : Frenkel Defect - Effect on density}

If density is plainly defined as the ratio of mass and volume it doesn't seem to change, but in reality I think there will be variations within the crystal having this defect. But why is this fact not specified in many sources?

Answer 1

The sources may not explicitly say this, but I suspect that they consider mass density to be a macroscopic property, to be measured from at least milligrams and cubic millimetres.

If the volume considered is small enough, then yes, one would see local variations of the density. However, if you make the volume even smaller, you would see huge variations in the density as additional nuclei are included. (Similar statements will be true for Frenkel defect concentrations.) On this level, the definition of mass density simply breaks down and is no longer very useful.

Answer 2

Yes, there will be local variations in density as the density would decrease where there is a vacancy defect (as volume is the same and mass becomes less) and it would increase at the point where there is an interstitial defect (as volume is the same and mass becomes more). But since there is no loss of ions in the compound, the overall density of the compound remains the same (as the ions just move to an interstitial site).