##  [Hall–Petch Relationship](/hall-petch-relationship) 

  ##  [Hall–Petch Relationship](https://health.quantumdictionary.io/hall-petch-relationship-0) 

  

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**Health & Life Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An empirical metallurgical relation stating that the yield strength (σy) of a polycrystalline metal or alloy increases as the average grain diameter (d) decreases, commonly expressed as σy = σ0 + k·d^(-1/2); the effect arises because grain boundaries impede dislocation motion and is observed over a range of conventional (micrometer-scale) grain sizes.