(JP2019077720) 1. The crystal structure of the hydroxyapatite at least a portion of calcium ions in the hydroxyapatite is substituted by silver ions from the particle derivative and the anti-microbial, anti-microbial particles of hydroxyapatite and hydroxyapatite derivatives XRD crystal phase is quantified by 90% or more and a purity, the particle size of the hydroxyapatite derivative microbial 10nm-1,000nm is within the range, of the particles of the hydroxyapatite derivative microbial a-axis length of 9. 424Å or more and, hydroxyapatite derivative particles of the particle group. 2. And one of a predetermined microorganism / μl 5.0x104, wherein a concentration of at least 2.47mmol/L in terms of silver ions in the antimicrobial hydroxyapatite particles and derivatives, coexist to prepare a dispersion liquid, the dispersion medium is used to obtain, after 37°C in a 90% ratio is 1 or more McFaiiand and sterilization, wherein the predetermined microorganism, which is Escherichia coli, particles of the particle group according to claim 1 hydroxyapatite derivatives. 3. Wherein the antimicrobial particles of the hydroxyapatite derivative, characterized in that the sintering and hydroxyapatite derivative particles, particles of the particle group according to claim 1 or 2 hydroxyapatite derivatives. 4. The anti-microbial a-axis length of the hydroxyapatite derivative particles of less than or equal to 9. 442Å, the particles of the hydroxyapatite derivative recited in any one of claims 1-3 group.