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This can be explained on the basis of nature of bonding present in ionic solids. In them, electrostatic force of attraction acts between the positively charged ion, cation and negatively charged ion, anion.Since, electrostatic force has a very high magnitude, it keeps the ionic solids hard. However it is to be noted that unlike covalent bonds which have a direction of e density/charge hence are directional, ionic solids have no specific  direction requirement for bond formation i.e. are non-directional. Hence, the solids are brittle in nature.

To summarize, the primary cause of hard and brittle nature of ionic solids lies in their bond type which is electrostatic and non-directional.

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