AlN,GaN, SiCのX線回折面(Mathematica)

　GaNは、ピエゾ分極によるQCSE（量子閉じ込めシュタルク）効果により、極性面からでは光取り出し効率が悪いため、最近は、無極性面や非極性面が着目されています。この場合、結晶性評価に用いるX線回折で、非対称面測定を行う場合、各面ごとに計算し直さなくてはいけません。禁制で強度が検出されないこともあり。毎回計算し直すのは面倒なので、数値計算ソフトを活用します。
【補足】

　練習目的：Mathematicaで数値計算
【計算結果】
（対称面 for 極性面） 
　GaN (002):17.2812, AlN (002):18.0126, 4H-SiC (004):17.8532
(非対称面 for 極性面)

　GaN (102):24.0464, AlN (102):24.9028, 4H-SiC (104):24.9045

　GaN (105):52.4951, AlN (105):55.5081, 4H-SiC (1010):54.9862

　GaN (204):54.5826, AlN (204):57.3689, 4H-SiC (208):57.3746

　GaN (114):49.9727, AlN (114):52.3895, 4H-SiC (118):52.297
(非対称面 for 極性面)

　GaN (102):43.1949, AlN (102):42.7466, 4H-SiC (108):43.2783

　GaN (105):20.5841, AlN (105):20.29, 4H-SiC (1010):20.6391

　GaN (204):43.1949, AlN (204):42.7466, 4H-SiC (208):43.2783

　GaN (114):39.1148, AlN (114):38.6755, 4H-SiC (118):39.1966

(* Constant *)

d=1.540562 (*Cu-Ka1*);

(*c-axis*)

cg=5.186 (*GaN*);

ca=4.982(*AlN*);

cs=10.05/2 (*SiC*);

(*a-axis*)

ag=3.189(*GaN*);

aa=3.112(*AlN*);

as=3.081(*SiC*);

(* Symmetric *)

Blag[c_]:=ArcSin [d/c]*180/Pi;

Print["GaN (002):", Blag[cg],", AlN (002):",Blag[ca],", 4H-SiC (004):",Blag[cs]];

(*Asymmetric*)

DA[h_,k_,l_,c_,a_]:=1/Sqrt[(4/3(h^2+k^2+h*k)/a^2+l^2/c^2)];

Print["GaN (102):", Blag[2*DA[1,0,2,cg,ag]],", AlN (102):",Blag[2*DA[1,0,2,ca,aa]],", 4H-SiC (104):",Blag[2*DA[1,0,2,cs,as]]];

Print["GaN (105):", Blag[2*DA[1,0,5,cg,ag]],", AlN (105):",Blag[2*DA[1,0,5,ca,aa]],", 4H-SiC (1010):",Blag[2*DA[1,0,5,cs,as]]];

Print["GaN (204):", Blag[2*DA[2,0,4,cg,ag]],", AlN (204):",Blag[2*DA[2,0,4,ca,aa]],", 4H-SiC (208):",Blag[2*DA[2,0,4,cs,as]]];

Print["GaN (114):", Blag[2*DA[1,1,4,cg,ag]],", AlN (114):",Blag[2*DA[1,1,4,ca,aa]],", 4H-SiC (118):",Blag[2*DA[1,1,4,cs,as]]];

(* skew-symmetric *)

X[h_,k_,l_,c_,a_]:=ArcCos[Sqrt[3a^2/(4c^2)]*l/Sqrt[h^2+k^2+h*k+3/4*a^2/c^2*l^2]]*180/Pi;

Print["GaN (102):",X[1,0,2,cg,ag], ", AlN (102):", X[1,0,2,ca,aa],", 4H-SiC (108):", X[1,0,2,cs,as]];

Print["GaN (105):",X[1,0,5,cg,ag], ", AlN (105):", X[1,0,5,ca,aa],", 4H-SiC (1010):", X[1,0,5,cs,as]];

Print["GaN (204):",X[2,0,4,cg,ag], ", AlN (204):", X[2,0,4,ca,aa],", 4H-SiC (208):", X[2,0,4,cs,as]];

Print["GaN (114):",X[1,1,4,cg,ag], ", AlN (114):", X[1,1,4,ca,aa],", 4H-SiC (118):", X[1,1,4,cs,as]];