ON THE EXACT CALCULATION OF ELASTIC CONSTANTS OF CRYSTALS FROM ULTRASONIC VELOCITIES ALONG ARBITRARY DIRECTIONS-APPLICATION TO SODIUM CHLORATE

Abstract

A  technique  For  evaluating  the  exact  elastic  constants  of  anisotropic  crystals  from  ultrasonic  velocities along  arbitrary directions  is  developed.  This  involves  a  numerical  iteration  of  the  full  cubic  Christoffei  equation  to correct the  approximate  analytic  expressions for the velocities  in  terms  of  the  e1astic  constants.  The  method  is  tested  on  cubic  sodium  chlorate.  From  the  three  ultrasonic  pulse  echo  velocities along  an  arbitrary direction  the  ci  are  evaluated.  The  results  agree  wjth  the  values  obtained  from  simple  [I00]  and  [111]  directions,  viz.,  c,,==4.95,  C12=1.45 and C14=1.14 (X10^10 N/m^2)