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{"sheet":"INPUT","index":0,"n_rows":23,"n_cols":17,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
[null,"Calucation of channeling half-angles"]
[null,"enter parameters","in yellow cells only"]
[]
[]
[]
[null,"Beam",null,null,null,null,null,null,"Target",null,null,null,"axis factor fa=",{"$f":"+'channeling cal'!G13","v":1.7320508075688772}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"plane factor fp="]
[null,"atomic number of projectile","Z₁",35,{"$f":"+'channeling cal'!D5","v":"Br"},null,null,null,"atomic # of target","Z₂",13,{"$f":"+'channeling cal'!D6","v":"Al"},null,null,null,null,{"$f":"+'channeling cal'!G49","v":0.57735026918962584}]
[null,"Energy of projectile","E",0.04,"MeV",null,null,null,"atomic weight of target","M2",{"$f":"+'channeling cal'!C7","v":26.981539999999999},"amu"]
[null,null,null,null,null,null,null,null,"conventional cell size","cc",null,"Ang",{"$f":"+'channeling cal'!C9","v":4.0500000000000007}]
[null,null,null,null,null,null,null,null,"lattice  ",null,{"$f":"+'channeling cal'!C10","v":"fcc"}]
[null,null,null,null,null,null,null,null,null,null,"uvw or hkl"]
[null,null,null,null,null,null,null,null,"Miller indeces",null,111]
[null,null,null,null,null,null,null,null,"Room Temp","T",293,"K"]
[null,null,null,null,null,null,null,null,"density","rho",{"$f":"INDEX(tables!$K$8:$Q$99,K8,4)","v":2.7},"g/cm3"]
[]
[]
[null,"axial Ψ1/2",{"$f":"+'channeling cal'!C36","v":3.431230763777088},"deg"]
[null,"planar Ψ1/2",{"$f":"+'channeling cal'!C62","v":4.2991292290740066},"deg",null,null,"overlayer","Zo",14,{"$f":"+'channeling cal'!Q22","v":"Si"}]
[null,null,null,null,null,null,null,"Mo",{"$f":"+'channeling cal'!P23","v":28.0855},"amu"]
[null,"axial χ-min",{"$f":"+'channeling cal'!$P$40","v":0.18318060178721671},"w/overlayer",null,null,"density","rho-o",{"$f":"+'channeling cal'!P25","v":2.33},"g/cm3"]
[null,"axial χ-min",{"$f":"+'channeling cal'!P8","v":0.18318060178721671},"w/o overlayer",null,null,"thickness of overlayer","t",1,"A"]
[null,"planar χ-min",{"$f":"+'channeling cal'!P49","v":0.17042399603803085},"w/o overlayer"]

{"sheet":"channeling cal","index":1,"n_rows":62,"n_cols":22,"rows_kept":62,"cut":false,"hidden":false,"merged":[]}
[]
["axial channeling",null,"1/2 angles",null,null,null,null,null,null,null,null,null,null,"Chi-mins"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"AXIAL"]
["e^2",null,{"$f":"0.0000144","v":1.4399999999999999E-5},"MeV-A"]
["atomic number of projectile","Z₁",{"$f":"+INPUT!D8","v":35},{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!C5,1)","v":"Br"},null,null,null,null,null,null,null,null,null,"Chi-min","Lindhard",{"$f":"C54*C14*3.14159*(2*C23^2+C18^2)","v":8.2346873563574216E-2},null,"Lindhard"]
["atomic # of target","Z₂",{"$f":"+INPUT!K8","v":13},{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!C6,1)","v":"Al"},null,null,null,null,null,null,null,null,null,null,null,null,null,"A15.7"]
["atomic weight of target","M2",{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!C6,3)","v":26.981539999999999},"amu",null,null,null,null,null,null,null,null,null,"Xh",null,{"$f":"126*$C$23/($C$36*$C$14)","v":0.55273289746079046},null,"Barrett"]
["Energy of projectile","E",{"$f":"+INPUT!D9","v":0.04},"MeV",null,null,null,null,null,null,null,null,null,"Chi-min","Barrett",{"$f":"18.8*$C$54*$C$14*$C$23^2*SQRT(1+1/$P$7^2)","v":0.18318060178721671},null,"A15.8"]
["conventional cell size","cc",{"$f":"INDEX(tables!$K$8:$Q$99,$C$6,7)*10","v":4.0500000000000007},"Ang","p647 Black IBA Handbook"]
["lattice  ",null,{"$f":"INDEX(tables!$K$8:$Q$99,$C$6,5)","v":"fcc"}]
[null,null,"uvw or hkl","u","v","w",null,null,null,null,null,null,null,"Chi-min","Barrett",{"$f":"18.8*C54*C14*C23^2","v":8.8614355987004845E-2},null,"A15.9",null,null,null,"same as last at high E?"]
["Miller indeces",null,{"$f":"+INPUT!K13","v":111},{"$f":"INT(C12/100)","v":1},{"$f":"INT((C12-100*D12)/10)","v":1},{"$f":"+INT(C12-100*D12-10*E12)","v":1}]
["axis lattice factor","fa",null,null,null,null,1.7320508075688772,null,null,null,null,null,null,"Xh",null,{"$f":"63*$C$23/($C$36*$C$14)","v":0.27636644873039523},null,"Mayer"]
["lattice spacing","d",{"$f":"+C9*G13","v":7.0148057706539539},"Ang",null,null,null,null,null,null,null,null,null,"CHi-min","Meyer",{"$f":"17*$C$54*$C$14*$C$23^2*SQRT(1+1/$P$7^2)","v":0.16564203353099385},null,"p.654"]
[]
["Following the EQUATIONSL FOR CHANNELING in the IBA Handbook, p645"]
[null,null,"0.4685*C6^-(1/3)",null,null,"0.4685/(C5^(1/2)+C6^(1/2))^(2/3)",null,null,"This TF screening gives best results",null,null,null,null,"w/overlayer"]
["thomas fermi screening length","a",{"$f":"0.4685*C6^-(1/3)","v":0.19924853847758092},"Ang",null,{"$f":"0.4685/(C5^(1/2)+C6^(1/2))^(2/3)","v":0.10428824575328724},null,null,{"$f":"(9*3.14^2/128)^0.333*0.53/(C5^0.666+C6^0.666)^0.5","v":0.11657823957132486},null,null,null,null,"overlayer"]
["Debye Temp","theat-D",{"$f":"INDEX(tables!$K$8:$Q$99,$C$6,6)","v":390},"K","p647 Black IBA Handbook",null,null,null,null,null,null,null,null," ","Z₁",{"$f":"+C5","v":35},{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!P19,1)","v":"Br"}]
["Room Temp","T",{"$f":"+INPUT!K14","v":293},"K",null,null,null,null,null,null,null,null,null,null,"Z₂",{"$f":"+C6","v":13},{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!P20,1)","v":"Al"}]
["x\"=Theta-D/T","x\"",{"$f":"C19/C20","v":1.3310580204778157},null,null,null,null,null,null,null,null,null,null,null,"a",{"$f":"+I18","v":0.11657823957132486},"A"]
["debye fn","phi-D",{"$f":"+'debye calc'!C28","v":0.73377827265457818},null,null,null,null,null,null,null,null,null,null,null,"Zo",{"$f":"+INPUT!I19","v":14},{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!P22,1)","v":"Si"},"overlayer"]
["rms thermal amplitude","u1",{"$f":"+'debye calc'!B32","v":0.10558697459361684},"Ang","fig. A15.1",null,null,null,null,null,null,null,null,null,"Mo",{"$f":"INDEX(tables!$K$8:$Q$99,'channeling cal'!P22,3)","v":28.0855},"amu"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"E",{"$f":"+C8","v":0.04},"MeV"]
["characteristic axial channeling angle","Ψ₁",{"$f":"0.307*SQRT(C5*C6/C8/C14)","v":12.362498526879071},"deg",null,null,null,null,null,null,null,null,null,null,"rho-o",{"$f":"INDEX(tables!$K$8:$Q$99,$P$22,4)","v":2.33},"g/cm3"]
[null,null,{"$f":"C25/57.3","v":0.2157504105912578},"rad",null,null,null,null,null,null,null,null,null,null,"Nav",6.0229999999999998E+23,"at/mole"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"N ",{"$f":"+P26*P25/P23","v":4.9967385305584727E+22},"atoms/cm3"]
["ratio of a to d","a/d",{"$f":"I18/C14","v":1.6618883456335082E-2},null,null,null,null,null,null,null,null,null,null,null,"N",{"$f":"P27*0.00000001^3","v":4.9967385305584734E-2},"atoms/A3"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"a-o",{"$f":"(9*3.14^2/128)^0.333*0.53/(P19^0.666+P22^0.666)^0.5","v":0.11558592128608777},"A"]
["parameter to use in Frs","x'",{"$f":"1.2*C23/I18","v":1.0868612356667127},null,null,null,null,null,null,null,null,null,null,null,"d",{"$f":"+C14","v":7.0148057706539539},"A"]
["adimentional axial channeling Fn","Frs",{"$f":"+FRS!C39","v":0.79525559876645757},null,"fig.A15.2",null,"best fits"]
[null,null,null,null,null,null,"usedhere","previous",null,null,null,null,null,null,"t",{"$f":"+INPUT!I22","v":1},"A","thickness of overlayer"]
["channeling 1/2 angle for Ψ₁<a/d","Ψ1/2",{"$f":"G33*C31*C25","v":8.5532711663711183},"deg",null,"prefactor",0.87,0.8,null,null,null,null,null,null,"m",{"$f":"3.14159*P29^2*P28*P32","v":2.0972297416233525E-3}]
["channeling 1/2 angle for Ψ₁>a/d","Ψ1/2",{"$f":"G34*SQRT(I18*C25/C14)","v":3.431230763777088},"deg",null,"prefactor",7.57,7.57]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"y",{"$f":"P29*P24/(2*P19*P22*C4)","v":0.32762449344129191}]
["channeling 1/2 angle to use","Ψ1/2",{"$f":"IF(C26<C28,C33,C34)","v":3.431230763777088},"deg",null,null,null,null,null,null,null,null,null,null,"Ψ1/2",{"$f":"+C37","v":5.9881863242183038E-2},"rad"]
[null,null,{"$f":"+C36/57.3","v":5.9881863242183038E-2},"rad",null,null,null,null,null,null,null,null,null,null,"theta-c",{"$f":"+P35*P36","v":1.9618765111040937E-2},"rad","Mayer"]
[null,null,{"$f":"(3*I18^2*C5*C6*144/C8/C14^3)^0.25","v":3.7295445266576399},"deg","kempshall uses third a"]
["planar channeling"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(thc,m)=",{"$f":"IF(P33<20,IF(P37<4,MAX('P(th,m)'!B68,P8),1),1)","v":0.18318060178721671}]
["atomic number of projectile","Z₁",{"$f":"+C5","v":35}]
["atomic # of target","Z₂",13]
["atomic weight of target","M2",26.981539999999999]
["Energy of projectile","E",0.04,"MeV"]
["conventional cell size","cc",4.0500000000000007,"Ang"]
["lattice  ",null,"fcc"]
["lattice type",null,null,"h ","k","l",null,null,null,null,null,null,null,"PLANAR",null,"Chi-mins",{"$f":"2*C18/C50","v":0.17042399603803085}]
["Miller indeces",null,111,{"$f":"INT(C48/100)","v":1},{"$f":"INT((C48-100*D48)/10)","v":1},{"$f":"+INT(C48-100*D48-10*E48)","v":1}]
["plane lattice factor","f' or fp",null,null,null,null,0.57735026918962584,"lookup",null,null,null,null,null,"Chi-min",null,{"$f":"2*C18/C50","v":0.17042399603803085},null,"lindhard"]
["avg atomic spacing between planes","dp",{"$f":"+C45*G49","v":2.3382685902179849},"Ang"]
["density","rho",{"$f":"+INPUT!K15","v":2.7},"g/cm3"]
["Avagodros number","Nav",6.0229999999999998E+23,"at/mole"]
["target atoms/cm3","N ",{"$f":"+C52*C51/C43","v":6.0271207647895559E+22},"atoms/cm3"]
[null,null,{"$f":"C53*0.00000001^3","v":6.0271207647895564E-2},"atoms/A3"]
["characteristic planer channeling angle","Ψa",{"$f":"0.545*SQRT(C41*C42*C54*I18*C50/C44)","v":7.4504601474684282},"deg"]
[]
["Fps parameters"]
[null,"x'",{"$f":"1.6*C23/I18","v":1.4491483142222839}]
[null,"y'",{"$f":"C50/I18","v":20.057504718000018}]
["adimentional planar channeling function","Fps",{"$f":"+FPS!B101","v":0.88773644001753815},null,"figA15.3",null,null,null,null,"best fits"]
[null,null,null,null,null,null,null,null,null,"used here","previous"]
["Planar channeling 1/2 angle","Ψ1/2",{"$f":"J62*C60*C55","v":4.2991292290740066},"deg",null,null,0.71000000000000019,null,"prefactor",0.65,0.72]

{"sheet":"debye calc","index":2,"n_rows":32,"n_cols":4,"rows_kept":32,"cut":false,"hidden":false,"merged":[]}
["Calculation of u1 - 1D vibrational amplitude"]
[]
["Parameterization of Debye Function"]
[null,"a",1]
[null,"b",4.3]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Debye fn. PhiD=exp(-x\"/4.3)"]
[]
["Theta-D",{"$f":"+'channeling cal'!C19","v":390},"K","p647 Black IBA Handbook"]
["T",{"$f":"+'channeling cal'!C20","v":293},"K","room temp"]
["x\"=Theta-D/T"]
["x\"",{"$f":"B23/B24","v":1.3310580204778157}]
[null,"x\""]
["debye fn",{"$f":"+B26","v":1.3310580204778157},{"$f":"$C$4*EXP(-B28/$C$5)","v":0.73377827265457818}]
[]
["M2",{"$f":"+'channeling cal'!C7","v":26.981539999999999}]
[]
["u1",{"$f":"12.1*((C28/B26+1/4)*(B30*B23)^-1)^0.5","v":0.10558697459361684},"A","eq A15.2"]

{"sheet":"FPS","index":3,"n_rows":101,"n_cols":2,"rows_kept":101,"cut":false,"hidden":false,"merged":[]}
["Parameterization of Fps"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["so the y intercept FPSo = 1.27(1-exp(-(y'^.76/3.0))"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["FPS=FPSo(exp(-(x'^p)/a)"]
["a=4.3*(1-exp(-(y'^1.1)/12))"]
["p=0.4*exp(-y'/12)+0.85"]
[]
["y'=",{"$f":"+'channeling cal'!C59","v":20.057504718000018}]
["FPSo=",{"$f":"1.27*(1-EXP(-(B60^0.76)/3))","v":1.2210237270121425}]
["a fit",4.3]
["p fit",0.85]
[]
["x'"]
[null,"FPS"]
[0,{"$f":"+$B$44*EXP(-(A67^$B$46)/$B$45)","v":{"$error":"#NUM!"}}]
[0.1,{"$f":"+$B$44*EXP(-(A68^$B$46)/$B$45)","v":{"$error":"#DIV/0!"}}]
[0.2,{"$f":"+$B$44*EXP(-(A69^$B$46)/$B$45)","v":{"$error":"#DIV/0!"}}]
[0.3,{"$error":"#DIV/0!"}]
[0.4,{"$error":"#DIV/0!"}]
[0.5,{"$error":"#DIV/0!"}]
[0.6,{"$error":"#DIV/0!"}]
[0.7,{"$error":"#DIV/0!"}]
[0.8,{"$error":"#DIV/0!"}]
[0.9,{"$error":"#DIV/0!"}]
[1,{"$error":"#DIV/0!"}]
[1.1000000000000001,{"$error":"#DIV/0!"}]
[1.2,{"$error":"#DIV/0!"}]
[1.3,{"$error":"#DIV/0!"}]
[1.4,{"$error":"#DIV/0!"}]
[1.5,{"$error":"#DIV/0!"}]
[1.6,{"$error":"#DIV/0!"}]
[1.7,{"$error":"#DIV/0!"}]
[1.8,{"$error":"#DIV/0!"}]
[1.9,{"$error":"#DIV/0!"}]
[2,{"$error":"#DIV/0!"}]
[2.1,{"$error":"#DIV/0!"}]
[2.2000000000000002,{"$f":"+$B$44*EXP(-(A89^$B$46)/$B$45)","v":{"$error":"#DIV/0!"}}]
[2.2999999999999998,{"$error":"#DIV/0!"}]
[2.4,{"$error":"#DIV/0!"}]
[2.5,{"$error":"#DIV/0!"}]
[2.6,{"$error":"#DIV/0!"}]
[2.7,{"$error":"#DIV/0!"}]
[2.8,{"$error":"#DIV/0!"}]
[2.9,{"$error":"#DIV/0!"}]
[3,{"$error":"#DIV/0!"}]
[]
[]
["x'","Fps"]
[{"$f":"+'channeling cal'!C58","v":1.4491483142222839},{"$f":"+$B$61*EXP(-(A101^$B$63)/$B$62)","v":0.88773644001753815}]

{"sheet":"FRS","index":4,"n_rows":39,"n_cols":3,"rows_kept":39,"cut":false,"hidden":false,"merged":[]}
["Parameterization of FRS(x')"]
[]
[null,"a",1.9]
[null,"b",1.2]
[null,"c",0.53]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"x'","Frs"]
[null,{"$f":"+'channeling cal'!C30","v":1.0868612356667127},{"$f":"$C$3*EXP(-(B39^$C$5)/$C$4)","v":0.79525559876645757}]

{"sheet":"P(th,m)","index":5,"n_rows":68,"n_cols":14,"rows_kept":68,"cut":false,"hidden":false,"merged":[]}
["Parameterization of P(th,m)"]
[]
["P=fexp(-(thc^pa)/a)+(1-f)exp(-thc^pb/b)"]
[]
["so the y intercept P=1"]
[]
["m",5,null,null,null,null,null,null,null,null,null,null,"power law fits"]
["f",0.92,"f",null,null,null,null,null,null,null,null,null,0.318,0.39100000000000001]
["a",35,"a ",null,null,null,null,null,null,null,null,null,1.63,0.82399999999999995]
["pa",2.2000000000000002,"pa",null,null,null,null,null,null,null,null,null,0.97399999999999998,0.28799999999999998]
["b",50,"b",null,null,null,null,null,null,null,null,null,0.67100000000000004,1.242]
["pb",5,"pb",null,null,null,null,null,null,null,null,null,1.6459999999999999,0.372]
[null,null,"f-fit"]
[null,null,"a -fit",null,null,null,null,null,null,null,null,null,1.17,0.41]
["m",{"$f":"+'channeling cal'!P33","v":2.0972297416233525E-3},"pa-fit",null,null,null,null,null,null,null,null,null,0.16,1.8]
["f-fit",{"$f":"+$M8*B$15^$N8","v":2.8522704928106168E-2},"b-fit",null,null,null,null,null,null,null,null,null,0.44,0.64]
["a -fit",{"$f":"+$M$14*B15^$N$14+$M$15*B15^$N$15","v":9.3340896097236142E-2},"pb-fit",null,null,null,null,null,null,null,null,null,4.8000000000000001E-2,2.3199999999999998]
["pa-fit",{"$f":"+$M10*B$15^$N10","v":0.16488950231409702},"para",null,null,null,null,null,null,null,null,null,0.44,0.64]
["b-fit",{"$f":"+$M$16*B15^$N$16+$M$17*B15^$N$17","v":8.497821827487961E-3},null,null,null,null,null,null,null,null,null,null,4.8000000000000001E-2,2.3199999999999998]
["pb-fit",{"$f":"+$M12*B$15^$N12","v":0.16599008443395058}]
[]
[]
["thc"]
[null,"P"]
[0,{"$f":"+B$17*EXP(-($A25^B$18)/B$16)+(1-B$17)*EXP(-($A25^B$20)/B$19)","v":1}]
[0.1,{"$f":"+B$16*EXP(-($A26^B$18)/B$17)+(1-B$16)*EXP(-($A26^B$20)/B$19)","v":1.8719395359458742E-5}]
[0.2,{"$f":"+B$16*EXP(-($A27^B$18)/B$17)+(1-B$16)*EXP(-($A27^B$20)/B$19)","v":7.7073618826657617E-6}]
[0.3,4.3670237367540537E-6]
[0.4,2.8500800558864291E-6]
[0.5,2.018028618645779E-6]
[0.6,1.5075229324684151E-6]
[0.7,1.1699313140462487E-6]
[0.8,9.343203777815104E-7]
[0.9,7.6303849890907413E-7]
[1,6.344721428001091E-7]
[1.1000000000000001,5.3544336017448672E-7]
[1.2,4.5752279312709227E-7]
[1.3,3.951034618389902E-7]
[1.4,3.4433233721923592E-7]
[1.5,3.0248773705870283E-7]
[1.6,2.6760117905881127E-7]
[1.7,2.3821946031052829E-7]
[1.8,2.1325033598396382E-7]
[1.9,1.9185972859637283E-7]
[2,1.7340164116986105E-7]
[2.1,1.5736936719866281E-7]
[2.2000000000000002,1.4336089028919709E-7]
[2.2999999999999998,1.3105393392330437E-7]
[2.4,1.2018769640567042E-7]
[2.5,1.1054929513130225E-7]
[2.6,1.0196357918614695E-7]
[2.7,9.4285384910019088E-8]
[2.8,8.7393586057358466E-8]
[2.9,8.1186477876567841E-8]
[3,7.5578163533161328E-8]
[3.1,7.0495701359094733E-8]
[3.2,6.5876835048064327E-8]
[3.3,6.1668174428408859E-8]
[3.4,5.7823727360426056E-8]
[3.5,5.4303707359927894E-8]
[3.6,5.1073559302466479E-8]
[3.7,4.8103158784821443E-8]
[3.8,4.5366150653502243E-8]
[3.9,4.2839399733147953E-8]
[4,4.0502532529369458E-8]
[]
["thc","P(thc,m)"]
[{"$f":"+'channeling cal'!P37","v":1.9618765111040937E-2},{"$f":"+B$16*EXP(-($A68^B$18)/B$17)+(1-B$16)*EXP(-($A68^B$20)/B$19)","v":1.051749142654448E-4}]

{"sheet":"stereographs","index":6,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"tables","index":7,"n_rows":99,"n_cols":17,"rows_kept":99,"cut":false,"hidden":false,"merged":[]}
[]
["symbol","Z2","M2","g/cm3","Structure","Debye Temp","Lattice constant",null,null,null,null,null,"amu","g/cm3"]
[{"$f":"INDEX($K$8:$N$99,B3,1)","v":"C"},6,{"$f":"INDEX($K$8:$N$99,B3,3)","v":12.010999999999999},{"$f":"INDEX($K$8:$N$99,B3,4)","v":3.51},"diamond",2000,0.35670000000000002,null,null,null,"target","target","target","target"]
[{"$f":"INDEX($K$8:$N$99,B4,1)","v":"Al"},13,{"$f":"INDEX($K$8:$N$99,B4,3)","v":26.981539999999999},{"$f":"INDEX($K$8:$N$99,B4,4)","v":2.7},"fcc",390,0.40500000000000003,null,null,null,"___________________________________________________________________________________"]
["Si",14,28.0855,2.33,"diamond",543,0.54310000000000003,null,null,null,"element","Z","mass ","density","structure","Debye T","Lattice constant"]
["V",23,50.941499999999998,5.8,"bcc",360,0.3024,null,null,null,"___________________________________________________________________________________"]
["Cr",24,51.996000000000002,7.19,"bcc",485,0.28839999999999999]
["Fe",26,55.847000000000001,7.86,"bcc",420,0.28670000000000001,null,null,null,"H",1,1.0079,8.9899999999999994E-2]
["Ni",28,58.7,8.9,"fcc",425,0.35239999999999999,null,null,null,"He",2,4.0026000000000002,0.1787]
["Cu",29,63.545999999999999,8.9600000000000009,"fcc",315,0.36149999999999999,null,null,null,"Li",3,6.9409999999999998,0.53]
["Ge",32,72.59,5.32,"diamond",290,0.56569999999999998,null,null,null,"Be",4,9.0121599999999997,1.85]
["Nb",41,92.906400000000005,8.5500000000000007,"bcc",275,0.33,null,null,null,"B",5,10.81,2.34]
["Mo",42,95.94,10.199999999999999,"bcc",380,0.31469999999999998,null,null,null,"C",6,12.010999999999999,3.51,"diamond",2000,0.35670000000000002]
["Rh",45,102.9055,12.4,"fcc",340,0.38030000000000003,null,null,null,"N",7,14.0067,1.2509999999999999]
["Pd",46,106.4,12,"fcc",275,0.38900000000000001,null,null,null,"O",8,15.9994,1.429]
["Ag",47,107.86799999999999,10.5,"fcc",215,0.40860000000000002,null,null,null,"F",9,18.998403,1.696]
["Ta",73,180.9479,16.600000000000001,"bcc",245,0.3306,null,null,null,"Ne",10,20.178999999999998,0.90100000000000002]
["W",74,183.85,19.3,"bcc",310,0.3165,null,null,null,"Na",11,22.98977,0.97]
["Pt",78,195.09,21.4,"fcc",225,0.39229999999999998,null,null,null,"Mg",12,24.305,1.74]
["Au",79,196.9665,19.3,"fcc",170,0.4078,null,null,null,"Al",13,26.981539999999999,2.7,"fcc",390,0.40500000000000003]
["Pb",82,207.2,11.4,"fcc",88,0.49509999999999998,null,null,null,"Si",14,28.0855,2.33,"diamond",543,0.54310000000000003]
[null,null,null,null,null,null,null,null,null,null,"P",15,30.973759999999999,1.82]
[null,null,null,null,null,null,null,null,null,null,"S",16,32.06,2.0699999999999998]
[null,null,null,null,null,null,null,null,null,null,"Cl",17,35.453000000000003,3.17]
[null,null,null,null,null,null,null,null,null,null,"Ar",18,39.948,1.784]
[null,null,null,null,null,null,null,null,null,null,"K",19,39.098300000000002,0.86]
[null,null,null,null,null,null,null,null,null,null,"Ca",20,40.08,1.55]
[null,null,null,null,null,null,null,null,null,null,"Sc",21,44.9559,3]
[null,null,null,null,null,null,null,null,null,null,"Ti",22,47.9,4.5]
[null,null,null,null,null,null,null,null,null,null,"V",23,50.941499999999998,5.8,"bcc",360,0.3024]
[null,null,null,null,null,null,null,null,null,null,"Cr",24,51.996000000000002,7.19,"bcc",485,0.28839999999999999]
[null,null,null,null,null,null,null,null,null,null,"Mn",25,54.938000000000002,7.43]
[null,null,null,null,null,null,null,null,null,null,"Fe",26,55.847000000000001,7.86,"bcc",420,0.28670000000000001]
[null,null,null,null,null,null,null,null,null,null,"Co",27,58.933199999999999,8.9]
[null,null,null,null,null,null,null,null,null,null,"Ni",28,58.7,8.9,"fcc",425,0.35239999999999999]
[null,null,null,null,null,null,null,null,null,null,"Cu",29,63.545999999999999,8.9600000000000009,"fcc",315,0.36149999999999999]
[null,null,null,null,null,null,null,null,null,null,"Zn",30,65.38,7.14]
[null,null,null,null,null,null,null,null,null,null,"Ga",31,69.72,5.91]
[null,null,null,null,null,null,null,null,null,null,"Ge",32,72.59,5.32,"diamond",290,0.56569999999999998]
[null,null,null,null,null,null,null,null,null,null,"As",33,74.921599999999998,5.72]
[null,null,null,null,null,null,null,null,null,null,"Se",34,78.959999999999994,4.8]
[null,null,null,null,null,null,null,null,null,null,"Br",35,79.903999999999996,3.12]
[null,null,null,null,null,null,null,null,null,null,"Kr",36,83.8,3.74]
[null,null,null,null,null,null,null,null,null,null,"Rb",37,85.467799999999997,1.53]
[null,null,null,null,null,null,null,null,null,null,"Sr",38,87.62,2.6]
[null,null,null,null,null,null,null,null,null,null,"Y",39,88.905900000000003,4.5]
[null,null,null,null,null,null,null,null,null,null,"Zr",40,91.22,6.49]
[null,null,null,null,null,null,null,null,null,null,"Nb",41,92.906400000000005,8.5500000000000007,"bcc",275,0.33]
[null,null,null,null,null,null,null,null,null,null,"Mo",42,95.94,10.199999999999999,"bcc",380,0.31469999999999998]
[null,null,null,null,null,null,null,null,null,null,"Tc",43,98,11.5]
[null,null,null,null,null,null,null,null,null,null,"Ru",44,101.07,12.2]
[null,null,null,null,null,null,null,null,null,null,"Rh",45,102.9055,12.4,"fcc",340,0.38030000000000003]
[null,null,null,null,null,null,null,null,null,null,"Pd",46,106.4,12,"fcc",275,0.38900000000000001]
[null,null,null,null,null,null,null,null,null,null,"Ag",47,107.86799999999999,10.5,"fcc",215,0.40860000000000002]
[null,null,null,null,null,null,null,null,null,null,"Cd",48,112.41,8.65]
[null,null,null,null,null,null,null,null,null,null,"In",49,114.82,7.31]
[null,null,null,null,null,null,null,null,null,null,"Sn",50,118.69,7.3]
[null,null,null,null,null,null,null,null,null,null,"Sb",51,121.75,6.68]
[null,null,null,null,null,null,null,null,null,null,"Te",52,127.6,6.24]
[null,null,null,null,null,null,null,null,null,null,"I",53,126.9045,4.92]
[null,null,null,null,null,null,null,null,null,null,"Xe",54,131.30000000000001,5.89]
[null,null,null,null,null,null,null,null,null,null,"Cs",55,132.90539999999999,1.87]
[null,null,null,null,null,null,null,null,null,null,"Ba",56,137.33000000000001,3.5]
[null,null,null,null,null,null,null,null,null,null,"La",57,138.90549999999999,6.7]
[null,null,null,null,null,null,null,null,null,null,"Ce",58,140.12,6.78]
[null,null,null,null,null,null,null,null,null,null,"Pr",59,140.90770000000001,6.77]
[null,null,null,null,null,null,null,null,null,null,"Nd",60,144.24,7]
[null,null,null,null,null,null,null,null,null,null,"Pm",61,145,6.4749999999999996]
[null,null,null,null,null,null,null,null,null,null,"Sm",62,150.4,7.54]
[null,null,null,null,null,null,null,null,null,null,"Eu",63,151.96,5.26]
[null,null,null,null,null,null,null,null,null,null,"Gd",64,157.25,7.89]
[null,null,null,null,null,null,null,null,null,null,"Tb",65,158.9254,8.27]
[null,null,null,null,null,null,null,null,null,null,"Dy",66,162.5,8.5399999999999991]
[null,null,null,null,null,null,null,null,null,null,"Ho",67,164.93039999999999,8.8000000000000007]
[null,null,null,null,null,null,null,null,null,null,"Er",68,167.26,9.0500000000000007]
[null,null,null,null,null,null,null,null,null,null,"Tm",69,168.9342,9.33]
[null,null,null,null,null,null,null,null,null,null,"Yb",70,173.04,6.98]
[null,null,null,null,null,null,null,null,null,null,"Lu",71,174.96700000000001,9.84]
[null,null,null,null,null,null,null,null,null,null,"Hf",72,178.49,13.1]
[null,null,null,null,null,null,null,null,null,null,"Ta",73,180.9479,16.600000000000001,"bcc",245,0.3306]
[null,null,null,null,null,null,null,null,null,null,"W",74,183.85,19.3,"bcc",310,0.3165]
[null,null,null,null,null,null,null,null,null,null,"Re",75,186.20699999999999,21]
[null,null,null,null,null,null,null,null,null,null,"Os",76,190.2,22.4]
[null,null,null,null,null,null,null,null,null,null,"Ir",77,192.22,22.5]
[null,null,null,null,null,null,null,null,null,null,"Pt",78,195.09,21.4,"fcc",225,0.39229999999999998]
[null,null,null,null,null,null,null,null,null,null,"Au",79,196.9665,19.3,"fcc",170,0.4078]
[null,null,null,null,null,null,null,null,null,null,"Hg",80,200.59,13.53]
[null,null,null,null,null,null,null,null,null,null,"Tl",81,204.37,11.85]
[null,null,null,null,null,null,null,null,null,null,"Pb",82,207.2,11.4,"fcc",88,0.49509999999999998]
[null,null,null,null,null,null,null,null,null,null,"Bi",83,208.9804,9.8000000000000007]
[null,null,null,null,null,null,null,null,null,null,"Po",84,209,9.4]
[null,null,null,null,null,null,null,null,null,null,"At",85,210]
[null,null,null,null,null,null,null,null,null,null,"Rn",86,222,9.91]
[null,null,null,null,null,null,null,null,null,null,"Fr",87,223]
[null,null,null,null,null,null,null,null,null,null,"Ra",88,226.02539999999999,5]
[null,null,null,null,null,null,null,null,null,null,"Ac",89,227.02780000000001,10.07]
[null,null,null,null,null,null,null,null,null,null,"Th",90,232.03809999999999,11.7]
[null,null,null,null,null,null,null,null,null,null,"Pa",91,231.0359,15.4]
[null,null,null,null,null,null,null,null,null,null,"U",92,238.029,18.899999999999999]

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["bcc"]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"atoms in","axis factor","plane factor"]
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[null,null,null,null,null,null,null,null,1,0,0,0,0,null,null,"sum odd?"]
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{"sheet":"fcc atoms","index":9,"n_rows":191,"n_cols":16,"rows_kept":191,"cut":false,"hidden":false,"merged":[]}
["fcc"]
[]
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{"sheet":"diamond atoms","index":10,"n_rows":191,"n_cols":15,"rows_kept":191,"cut":false,"hidden":false,"merged":[]}
["diamond"]
[]
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[]
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[null,null,null,null,null,null,null,null,154,5,2,0,1,5.3851648071345037,9.284766908852593E-2]
[null,null,null,null,null,null,null,null,155,5,2,1,1,5.4772255750516612,9.1287092917527679E-2]
[null,null,null,null,null,null,null,null,156,5,2,2,1,5.7445626465380286,8.7038827977848926E-2]
[null,null,null,null,null,null,null,null,157,5,2,3,1,6.164414002968976,8.1110710565381272E-2]
[null,null,null,null,null,null,null,null,158,5,2,4,1,6.7082039324993694,7.4535599249992993E-2]
[null,null,null,null,null,null,null,null,159,5,2,5,1,7.3484692283495345,6.804138174397717E-2]
[null,null,null,null,null,null,null,null,160,5,3,0,1,5.8309518948453007,8.574929257125441E-2]
[null,null,null,null,null,null,null,null,161,5,3,1,2,2.9580398915498081,8.4515425472851652E-2]
[null,null,null,null,null,null,null,null,162,5,3,2,1,6.164414002968976,8.1110710565381272E-2]
[null,null,null,null,null,null,null,null,163,5,3,3,2,3.2787192621510002,7.6249285166302333E-2]
[null,null,null,null,null,null,null,null,164,5,3,4,1,7.0710678118654755,7.0710678118654752E-2]
[null,null,null,null,null,null,null,null,165,5,3,5,2,3.8405728739343039,6.5094455490411943E-2]
[null,null,null,null,null,null,null,null,166,5,4,0,1,6.4031242374328485,7.8086880944303036E-2]
[null,null,null,null,null,null,null,null,167,5,4,1,2,3.2403703492039302,7.7151674981045956E-2]
[null,null,null,null,null,null,null,null,168,5,4,2,1,6.7082039324993694,7.4535599249992993E-2]
[null,null,null,null,null,null,null,null,169,5,4,3,1,7.0710678118654755,7.0710678118654752E-2]
[null,null,null,null,null,null,null,null,170,5,4,4,1,7.5498344352707498,6.6226617853252193E-2]
[null,null,null,null,null,null,null,null,171,5,4,5,2,4.0620192023179804,6.1545745489666362E-2]
[null,null,null,null,null,null,null,null,172,5,5,1,2,3.5707142142714252,7.0014004201400484E-2]
[null,null,null,null,null,null,null,null,173,5,5,2,1,7.3484692283495345,6.804138174397717E-2]
[null,null,null,null,null,null,null,null,174,5,5,3,2,3.8405728739343039,6.5094455490411943E-2]
[null,null,null,null,null,null,null,null,175,5,5,4,2,4.0620192023179804,6.1545745489666362E-2]

{"sheet":"b","index":11,"n_rows":70,"n_cols":6,"rows_kept":70,"cut":false,"hidden":false,"merged":[]}
[null,"minimum impact parameter and calculation of recoil energy transferred to target atom along row"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Z1",14]
[null,"Z2",14]
[null,"e2",{"$f":"1.19995^2","v":1.4398800025000003},"MeV fm",{"$f":"+C23*0.00001","v":1.4398800025000003E-5},"MeV A"]
[null,"dR",5.43,"A"]
[null,"a",0.13800000000000001,"A"]
[null,"E",1,"MeV  "]
[]
[null,"alpha",{"$f":"+C21*C22*E23*C24/C25^2/C26","v":0.80468152124590431}]
[]
[null,"r-crit",{"$f":"2/3*C25*SQRT(C28)*(1-SQRT(C28)/19+C28/700)","v":7.8726235654453552E-2},null,"A"]
[null,"E"]
[null,"Si-Si","r-crit doyle"]
[null,{"$f":"+C26","v":1},{"$f":"+C30","v":7.8726235654453552E-2}]
[null,1.0000000000000001E-5,2636.4938966174709]
[null,{"$f":"10*B34","v":1E-4},64.15857479385906]
[null,{"$f":"10*B35","v":1E-3},1.7134345940896554]
[null,0.01,0.53051125581579051]
[null,0.1,0.22501206730575435]
[null,1,7.8726235654453552E-2]
[null,10,2.5710920968116686E-2]
[]
[]
[null,"B-Si"]
[null,null,"r-crit doyle"]
[null,1,4.8127233996640095E-2]
[null,1.0000000000000001E-5,377.15920824843931]
[null,1E-4,8.1072415886757678]
[null,1E-3,0.83420236265001524]
[null,0.01,0.38767393455211274]
[null,0.1,0.14436742546025053]
[null,1,4.8127233996640095E-2]
[null,10,1.5475978811794728E-2]
[]
[]
[null,"For M1=M2"]
[null,null,null,"recoil-lab=",{"$f":"90-E58","v":87.946068834009225},"deg"]
[]
[null,null,null,"th-lab=",{"$f":"E60/C30*180/3.14159","v":2.0539311659907749},"deg"]
[]
[null,null,null,"kappa=",{"$f":"+E62/2/E64","v":2.8221648049000007E-3}]
[]
[null,null,null,"k=",{"$f":"+C21*C22*E23","v":2.8221648049000007E-3}]
[]
[null,null,null,"To'=",{"$f":"+C26/2","v":0.5}]
[]
[]
[null,null,null,{"$f":"+C30","v":7.8726235654453552E-2},"A"]
[]
[null,null,null,"approx"]
[null,"E-recoil=",{"$f":"+C26*(E60/D67)^2","v":1.2850670000568369E-3},{"$f":"9*C21*C22*E23/4/C24","v":1.1694053058977903E-3},"MeV"]