晶面夹角公式.doc

晶面夹角公式：设晶面（h1k1l1）和晶面（h2k2l2）的面间距分别为d］、d2,则二晶面的夹角w以下列公式计算（V为单胞体积）立方晶系：cos+k2+12)€2+k2+12丿11222hh+kk+ll正方晶系：cos,hh+kkll+a2c2六方晶系：cos,hh+kk+-(hk+hk丿+32ll1212212214c212l21114c213a2'h2+k2+hk+竺l222224c22丿正交晶系：cos,hhkkll12+12+a2b2c2菱方晶系：a4ddcossin2<(hh+kk+11丿+121212(cos2<-cos<)(kl+kl+1h+1h+hk+hk丿］122112211221」单斜晶系：ddcos,„1a-sin2‘hhkksin2‘11(lh+1h)cos++———a2b2c2ac三斜晶系：ddcos,„12V2立方晶系：正方晶系：Shh+Skk+Sll+S11122212331223(kl+kl)+S(lh+lh)+S(hk+hk)」1221131221121221cos,„+k2+1211hh+kk+ll—1)(◎)h2+k2+12222hh+kkll—h^2^2+a2c2h2+k212)1a+亠Ia2c2丿立方晶系：cos,„hh+kk+-€hk+hk)+沁111212212214c212l21114c213a2'h2+k2+hk+竺1222224c22丿正交晶系：cos,„hhkk1112+12+a2b2c2菱方晶系：a4ddcos,„V2单斜晶系：ddcos,„1a-sin2‘三斜晶系：cos,„sin2<(hh+kk+11)+121212hhkksin2^-2+a2b2dd12SV2112<-cos<)(k1+k1+1h+1h+hk+hk)]122112211221」11(1h+1h)cos+-+-2-——c2achh+Skk+S11+S(k1+k1)+S(1h+1h)+S(hk+hk)」1222123312231221131221121221晶面间距公式：立方晶系：1d2hklh2€k2€l2a2正方晶系六方晶系1h2€k2l2—+或者d=d2a2c2a2正交晶系：单斜晶系：三斜晶系：a)22+k2+12)sin2„+2(hk+kl+hl)(cos2„一cos„)a2G-3cos2„+2cos3„)€k2€121h2k2l2—++-d2a2b2c22+k2+12)sin2„+2(hk+kl+hl)(cos2„一cos„)a2G-3cos2„+2cos3„)—二丄(Sh2+Sk2+S12+2Shk+2Skl+2Slh)d2V2112233122313V二abc'1-cos2„—cos2卩一cos2y+2cos„cos卩cosyS=b2c211S=a2c2sin2p22S=a2b2sin2y33S12S23S13=abc2(cos„cosp-cosy)=a2bc(cospcosy一cos„)=ab2c(cosycos„-cosp)。