4Misc_Start4Platform@ xHH@Rg(HHdh xHH@Rg(HHdh x HH@Rg(HHdh ^Graph*uWDashSettings#  ! Y 6Normal@ Lucida Console<HHHH$$4 4 4 4 4 4 hometldC:Users:Eli:OneDrive - Johns Hopkins:Documents:Postdoc Research:Igor:Li2CuO2:C:Users:Eli:OneDrive - Johns Hopkins:Documents:Postdoc Research:Igor:Li2CuO2i-C:\Users\Eli\OneDrive - Johns Hopkins\Documents\Li2CuO2Research\Igor\e - H0DC:\Users\Eli\Oneive - HHoIgor_1lddC:Users:Eli:OneDrive - Johns Hopkins:Documents:Postdoc Research:Igor:C:Users:Eli:OneDrive - Johns Hopkins:Documents:Postdoc Research:Igori-C:\Users\Eli\OneDrive - Johns Hopkins\Documents\Igoroc Research\ive - H0DC:\Users\Eli\Oneive - HHoRecentWindowsGraph1:HC_samp_JperKmole_0T_select vs T_sample_0T_select;...Graph1_1:HC_samp_JperKmole_0T_select vs T_sample_0T_select;...Igor Reference.ihf 4Misc_EndTXOPState_Start PeakFunctions2-64eetWidgetFont4XOPState_EndV_chisqYLT@V_numNaNsV_numINFsV_npntse@V_nterms@V_nheldV_startRowx@V_endRowȁ@V_startColV_endColV_startLayerV_endLayerV_startChunkV_endChunkV_value?V_FlagS_nameUiiG0%)make/D/O/N=300 test setscale/I x, 0, 1, test display test SetAxis/A setscale/I x, 0, 5, test test = 1 + x^2 + (0.1)*x^3 SetAxis/A SetAxis left 0,* test = x^2 + 1/x Make/D/N=2/O W_coef W_coef[0] = {2,0} FuncFit/H="01" fit W_coef test[pcsr(A),pcsr(B)] /D Fit converged properly Curve fit with data subrange: test[47,299] fit_test= fit(W_coef,x) W_coef={1.0194,0} V_chisq= 50.7455;V_npnts= 253;V_numNaNs= 0;V_numINFs= 0; V_startRow= 47;V_endRow= 299; W_sigma={0.00231,0} Coefficient values one standard deviation a =1.0194 0.00231 b =0 0 test = x^2 + 5/x test = x^2 + 0.1/x test = x^2 + 0.1/x test = x^3 + 0.1/x test = x^3 + 1/x test = x^3 + 1/sqrt(x) test = x^2 + 5/x SetAxis/A test = x^2 + 5/x test = x^2 + 10/x Make/D/N=2/O W_coef W_coef[0] = {2,0} FuncFit/H="01" fit W_coef test[pcsr(A),pcsr(B)] /D Fit converged properly Curve fit with data subrange: test[47,299] fit_test= fit(W_coef,x) W_coef={1.1942,0} V_chisq= 5074.55;V_npnts= 253;V_numNaNs= 0;V_numINFs= 0; V_startRow= 47;V_endRow= 299; W_sigma={0.0231,0} Coefficient values one standard deviation a =1.1942 0.0231 b =0 0 Edit/K=0 root:test Findvalue /V=598 test Findvalue /V=598 test; print V_value -1 Findvalue /V=598.0002796389302 test; print V_value 1 Make/D/N=2/O W_coef W_coef[0] = {2,0} Display HC_samp_JperKmole_0T_select vs T_sample_0T_select SetAxis/A Label left "\\Z30 Cp (J/K mol)" ModifyGraph msize=2,mrkThick=2 AppendToGraph fit_HC_s_JpKmol_0T_s_Tmin_156 ModifyGraph mode(fit_HC_s_JpKmol_0T_s_Tmin_156)=0 AppendToGraph fit_HC_s_JpKmol_0T_s_DE_T_70 RemoveFromGraph fit_HC_s_JpKmol_0T_s_DE_T_70 RemoveFromGraph fit_HC_s_JpKmol_0T_s_Tmin_156 AppendToGraph fit_HC_s_JpKmol_0T_s_DE_T_70 ModifyGraph mode(fit_HC_s_JpKmol_0T_s_DE_T_70)=0 AppendToGraph DebEinExt_0T_sel_T_70K_Sfree ReplaceWave /X trace=DebEinExt_0T_sel_T_70K_Sfree, T_sample_0T_select ModifyGraph lsize=2,lstyle(DebEinExt_0T_sel_T_70K_Sfree)=3 AppendToGraph HC_s_JpKm_0T_s_subDE_T_70 vs T_sample_0T_select ModifyGraph mode(HC_s_JpKm_0T_s_subDE_T_70)=3,marker(HC_s_JpKm_0T_s_subDE_T_70)=19,rgb(HC_s_JpKm_0T_s_subDE_T_70)=(0,65535,0) ModifyGraph msize(HC_s_JpKm_0T_s_subDE_T_70)=2,mrkThick(HC_s_JpKm_0T_s_subDE_T_70)=2 ModifyGraph zero(left)=4 Legend/C/N=text0/J/F=0/A=MC "\\s(HC_samp_JperKmole_0T_select) Measured data";DelayUpdate AppendText "\\s(fit_HC_s_JpKmol_0T_s_DE_T_70) Fit to \"debyePlusEinstein\" in range T = [70 K, 300 K]";DelayUpdate AppendText "\\s(DebEinExt_0T_sel_T_70K_Sfree) Extrapolation of the fit to low T\r\n\\s(HC_s_JpKm_0T_s_subDE_T_70) Measured data - fit\r" SetAxis left *,100 Legend/C/N=text0/J "\\s(HC_samp_JperKmole_0T_select) Measured data\r\\s(fit_HC_s_JpKmol_0T_s_DE_T_70) Fit to \"debyePlusEinstein\" in range T = [70 K, 300 K]";DelayUpdate AppendText/N=text0 "\\s(DebEinExt_0T_sel_T_70K_Sfree) Extrapolation of the fit to low T\r\n\\s(HC_s_JpKm_0T_s_subDE_T_70) Measured data - fit" Legend/C/N=text0/J/B=1 SetDrawEnv arrow= 1 SetAxis bottom 0,* ModifyGraph hideTrace(fit_HC_s_JpKmol_0T_s_DE_T_70)=1,hideTrace(HC_s_JpKm_0T_s_subDE_T_70)=1 ModifyGraph hideTrace(DebEinExt_0T_sel_T_70K_Sfree)=1 Make/D/N=4/O W_coef W_coef[0] = {600,4.7,100,0.3} FuncFit debyePlusEinstein W_coef HC_samp_JperKmole_0T_select[pcsr(A),pcsr(B)] /X=T_sample_0T_select /D Fit converged properly Curve fit with data subrange: HC_samp_JperKmole_0T_select[399,567] fit_HC_samp_JperKmole_0T_select= debyePlusEinstein(W_coef,x) W_coef={793.51,4.221,-193.6,0.64548} V_chisq= 2.37011;V_npnts= 169;V_numNaNs= 0;V_numINFs= 0; V_startRow= 399;V_endRow= 567; W_sigma={2.62,0.014,4.25,0.018} Coefficient values one standard deviation thetaD =793.51 2.62 sD =4.221 0.014 thetaE =-193.6 4.25 sE =0.64548 0.018 ModifyGraph rgb(fit_HC_samp_JperKmole_0T_select)=(65535,65535,0) Make/D/N=4/O W_coef W_coef[0] = {600,4.7,100,0.3} Make/O/T/N=4 T_Constraints T_Constraints[0] = {"K0 > 0","K1 > 0","K2 > 0","K3 > 0"} FuncFit debyePlusEinstein W_coef HC_samp_JperKmole_0T_select[pcsr(A),pcsr(B)] /X=T_sample_0T_select /D /C=T_Constraints Fit converged properly --Curve fit with constraints-- No constraints active or violated Curve fit with data subrange: HC_samp_JperKmole_0T_select[399,567] fit_HC_samp_JperKmole_0T_select= debyePlusEinstein(W_coef,x) W_coef={749.94,4.4415,1.1924e-007,0.34235} V_chisq= 9.42411;V_npnts= 169;V_numNaNs= 0;V_numINFs= 0; V_startRow= 399;V_endRow= 567; W_sigma={1.35,0.00397,7.7e-05,0.00355} Coefficient values one standard deviation thetaD =749.94 1.35 sD =4.4415 0.00397 thetaE =1.1924e-007 7.7e-005 sE =0.34235 0.00355 makeDebyePlusEinstein(749.94,749.94,1.1924e-007,0.34235,T_sample_0T_select,"DebEinRestrictExt_T_70K_Sfree") AppendToGraph DebEinRestrictExt_T_70K_Sfree vs T_sample_0T_select SetAxis/A makeDebyePlusEinstein(749.94,4.4415,1.1924e-007,0.34235,T_sample_0T_select,"DebEinRestrictExt_T_70K_Sfree") ModifyGraph mode(DebEinRestrictExt_T_70K_Sfree)=0,lstyle(DebEinRestrictExt_T_70K_Sfree)=3,rgb(DebEinRestrictExt_T_70K_Sfree)=(65535,65535,0) ModifyGraph hideTrace(fit_HC_s_JpKmol_0T_s_DE_T_70)=0 duplicate HC_s_JpKm_0T_s_subDE_T_70, HC_s_JpKm_0T_s_subDER_T_70 HC_s_JpKm_0T_s_subDER_T_70 -=DebEinRestrictExt_T_70K_Sfree ModifyGraph hideTrace(HC_s_JpKm_0T_s_subDE_T_70)=0 AppendToGraph HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select duplicate/O HC_samp_JperKmole_0T_select, HC_s_JpKm_0T_s_subDER_T_70 HC_s_JpKm_0T_s_subDER_T_70 -=DebEinRestrictExt_T_70K_Sfree SetAxis/A ModifyGraph hideTrace(DebEinRestrictExt_T_70K_Sfree)=1,hideTrace(HC_s_JpKm_0T_s_subDER_T_70)=1 ModifyGraph hideTrace(fit_HC_samp_JperKmole_0T_select)=1 Make/D/N=4/O W_coef W_coef[0] = {700,4.7,100,0.3} Make/O/T/N=4 T_Constraints T_Constraints[0] = {"K0 > 0","K1 > 0","K2 > 0","K3 > 0"} FuncFit debyePlusEinsteint W_coef HC_samp_JperKmole_0T_select[pcsr(A),pcsr(B)] /X=T_sample_0T_select /D /C=T_Constraints Fit converged properly --Curve fit with constraints-- No constraints active or violated Curve fit with data subrange: HC_samp_JperKmole_0T_select[396,569] fit_HC_samp_JperKmole_0T_select= debyePlusEinsteint(W_coef,x) W_coef={792.55,4.2212,193.16,0.64188} V_chisq= 2.54128;V_npnts= 174;V_numNaNs= 0;V_numINFs= 0; V_startRow= 396;V_endRow= 569; W_sigma={2.42,0.0126,3.75,0.0162} Coefficient values one standard deviation thetaD =792.55 2.42 sD =4.2212 0.0126 thetaE =193.16 3.75 sE =0.64188 0.0162 ModifyGraph hideTrace(DebEinExt_0T_sel_T_70K_Sfree)=0 RemoveFromGraph DebEinExt_0T_sel_T_70K_Sfree AppendToGraph DebEinExt_0T_sel_T_70K_Sfree vs T_sample_0T_select ModifyGraph lstyle(DebEinExt_0T_sel_T_70K_Sfree)=3,lsize(DebEinExt_0T_sel_T_70K_Sfree)=2 Legend/C/N=text0/J "\\s(HC_samp_JperKmole_0T_select) Measured data\r\\s(fit_HC_s_JpKmol_0T_s_DE_T_70) Fit to \"debyePlusEinstein\" in range T = [70 K, 300 K]";DelayUpdate AppendText/N=text0 "\\s(DebEinExt_0T_sel_T_70K_Sfree) Fit extrapolated to low T";DelayUpdate AppendText/N=text0 "\n\\s(HC_s_JpKm_0T_s_subDE_T_70) Measured data - extrapolated fit (point by point)\r" RemoveFromGraph HC_samp_JperKmole_0T_select,fit_HC_s_JpKmol_0T_s_DE_T_70,DebEinExt_0T_sel_T_70K_Sfree,fit_HC_samp_JperKmole_0T_select,DebEinRestrictExt_T_70K_Sfree,HC_s_JpKm_0T_s_subDER_T_70 Legend/C/N=text0/J "" ModifyGraph fSize=20;DelayUpdate Label left " ";DelayUpdate Label bottom " " SetDrawEnv arrow= 1,linethick= 2.00 SetDrawEnv arrow= 1,linethick= 2.00 DrawText 0.546840958605665,0.887240356083086,"Regions of oversubtraction" Graph1_1 inserted into Graph1 as Graph1#Graph1_1 SetAxis bottom 0,300 SetDrawEnv arrow= 1,linethick= 2.00 SetDrawEnv arrow= 1,linethick= 2.00 RemoveFromGraph DebEinExt_0T_sel_T_70K_Sfree RemoveFromGraph fit_HC_s_JpKmol_0T_s_DE_T_70 RemoveFromGraph HC_s_JpKm_0T_s_subDE_T_70 Make/D/N=4/O W_coef W_coef[0] = {700,4.3,100,0.3} Make/O/T/N=4 T_Constraints T_Constraints[0] = {"K0 > 0","K1 > 0","K2 > 0","K3 > 0"} FuncFit debyePlusEinsteinRestrict W_coef HC_samp_JperKmole_0T_select[pcsr(A),pcsr(B)] /X=T_sample_0T_select /D /C=T_Constraints Fit converged properly --Curve fit with constraints-- No constraints active or violated Curve fit with data subrange: HC_samp_JperKmole_0T_select[396,569] fit_HC_samp_JperKmole_0T_select= debyePlusEinsteinRestrict(W_coef,x) W_coef={792.55,4.2212,193.15,0.64187} V_chisq= 2.54128;V_npnts= 174;V_numNaNs= 0;V_numINFs= 0; V_startRow= 396;V_endRow= 569; W_sigma={2.42,0.0126,3.75,0.0162} Coefficient values one standard deviation thetaD =792.55 2.42 sD =4.2212 0.0126 thetaE =193.15 3.75 sE =0.64187 0.0162 makeDebyePlusEinstein(W_coef[0],W_coef[1],W_coef[2],W_coef[3],T_sample_0T_select,"DebEinRestrictExt_T_70K_Sfree") AppendToGraph fit_HC_s_JperKmole_0T_DER_T_70; AppendToGraph DebEinRestrictExt_T_70K vs T_sample_0T_select ModifyGraph mode(fit_HC_s_JperKmole_0T_DER_T_70#1)=0,rgb(fit_HC_s_JperKmole_0T_DER_T_70#1)=(65535,0,0),mode(DebEinRestrictExt_T_70K#1)=0,lstyle(DebEinRestrictExt_T_70K#1)=3 duplicate/O HC_samp_JperKmole_0T_select,HC_s_JpKm_0T_s_subDER_T_70 HC_s_JpKm_0T_s_subDER_T_70-=DebEinRestrictExt_T_70K AppendToGraph HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select ModifyGraph mode(HC_s_JpKm_0T_s_subDER_T_70#1)=3,marker(HC_s_JpKm_0T_s_subDER_T_70#1)=19,rgb(HC_s_JpKm_0T_s_subDER_T_70#1)=(0,65535,0) ModifyGraph msize(HC_s_JpKm_0T_s_subDER_T_70#1)=2,mrkThick(HC_s_JpKm_0T_s_subDER_T_70#1)=2 ReplaceWave trace=HC_s_JpKm_0T_s_subDE_T_70, HC_s_JpKm_0T_s_subDER_T_70 Legend/C/N=text0/J "\\s(HC_samp_JperKmole_0T_select) Measured data";DelayUpdate AppendText/N=text0 "\\s(fit_HC_s_JperKmole_0T_DER_T_70#1) Fit to \"debyePlusEinsteinRestrict\" in range T = [70 K, 300 K]";DelayUpdate AppendText/N=text0 "\\s(DebEinRestrictExt_T_70K#1) Fit extrapolated to low T\r\\s(HC_s_JpKm_0T_s_subDER_T_70#1) Measured data - extrapolated fit (point by point)" SetDrawEnv xcoord= bottom;DelayUpdate DrawLine 70,0.672992700729927,70,0.808759124087591 SetDrawEnv arrow= 1 SetDrawEnv linethick= 2.00 SetDrawEnv xcoord= bottom,arrow= 1,linethick= 2.00;DelayUpdate DrawLine 70,0.614598540145985,70,0.78978102189781 DrawLine 70,0.632116788321167,70,0.807299270072992 DrawLine 70,0.708029197080292,70,0.816058394160583 DrawLine 70,0.706569343065693,70,0.808759124087591 DrawText 0.232558139534884,0.651094890510949,"T\\Bmin\\M for fit" DrawText 0.224418604651163,0.635036496350365,"T\\Bmin\\M for fit" !L;`2WLW_coef????dT\aĈ@ry@s$h@1?ڪ` VLW_sigma????aQZ@+h ?i; 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Ҭc"'@JS+'@%'@V\[>)@:)@teLG)@f}^+@F c+@(l+@m^-@->-@m͗-@/@U,G/@s/@Lˉ 1@7Wa: 1@x`1@G2@QL2@]kcS2@tC3@dI3@^D3@4@*{4@F4@ZK 6@ 6@Cƌ6@faVJT7@;~[7@`Pg7@>-8@'|!8@LkDz8@mՖ9@>Z9@oC:@/d;;@$FI;@|MJ;@b|o<@ut<@M]Ơ<@[#=@=@Z=@E5n/A?@vN?@?W?@X٪M@@YX@@$vY@@]@@dw A@^ A@CA@7eA@/)@A@0adB@H5RmB@slB@=] C@Šk[)C@X'C@tкC@qhC@#cC@점njD@LTvrD@8[wD@9~VE@nk0q'E@Ez+ $E@$M"E@hLE@#WE@1?3hF@:!yF@<` F@:G@lnGf$G@ˠl#G@`ʸG@*G@tޥ'}G@aH@nm?pH@ZrH@"e I@}HI@nY߯"I@zI@6O9I@P KI@˟=J@= J@U+J@K@p .K@Ÿm4K@!L@t4L@̼0L@ M@.8:1M@ M@N@n].N@ф-N@IxO@XNTO@wz] O@>\"O@UP@G~];O@2@qP@w sP@oP@XLm-P@69P@ROIsP@ޑHQ@$,0"JQ@XאMQ@Q@ѐ۵Q@$.Q@ ZkR@R@hRvz&R@rR@ GtR@3{tR@ z4R@^ R@ @'R@SY)S@$E(S@72Ȏe*S@*S@U1]|S@I %S@X;VS@t~sS@B9S@ɜ.T@b'T@7,-T@=٨vT@ʰpT@|LiuT@/T@RʸT@>ظT@Ó" T@]dT@T@mzBU@f.w5U@?6U@ufzU@)~jrU@HҊsU@m<]U@6"`U@4U@tYBU@R/U@<0U@CGm5V@ۃ[V@໻&V@.klcV@ʟ\V@AcV@xa&V@ϥ9V@1V@HV@ozV@6кV@P$LE:T_sample_0T_select:????0x?V?Tw?,Ml@$o@I%q@fĻg@yCuΪj@Xl@Gz.U@9w^Z@@ ]@)E@ùJ@^u.ցM@l?= @0h? @GA @wa/ @ձ5 @6 @l.( @T- @LJ. @@v@#@$&@@ 9̑@`Ò@ @0@Ev@XA@ @^}@,<[@Rl@\_14x@>nd{@Wf^U|@t@@CI1x@۞ y@ڽq@QKs+u@,-v@8Qm@ +&q@n`r@/'h@tVzm@Bm@OH!d@_h@QQPi@yIAi@EXQj@gj@` i@ߨm@0aqhn@x m@d̸s@Qs@ q@4>x@dNx@~ȋ: @S5> @> @/ @2L @[ʞ| @!5'"@^V$&"@rK"@i!"@ "@q%t"@75"@|:hj"@(%"@tr"@07"@-NB"@q"@"@a"@B"@]ky#@]5#@뱈@ #@*x #@gL #@(z=#@'kv#@O#@7o%#@Y=q&#@&T'#@V'#@cQy'#@T)#@:4#@Lx!%4#@vW,46#@>/ZA#@_A#@j"}B#@I2E#@: kF#@?T1G#@z ,N#@SN#@ jN#@P}:[#@U[#@uZA[#@I'a#@̚b#@f#@cf]|#@<|#@mRX#@@-#@SD/#@X#@W#@tM5#@h3n#@.w#@i#@FL#@ (ab#@&v#@ Ԭ}K#@㙆#@Vb#@Nw$@DQO$@GĔH$@)$@jWV4$@EƟ4$@c"4$@yN$@3R臭N$@̱N$@FN$@-N$@9N$@f|$@~l$@=;k$@Ie9Z%@18Z%@%"\%@B !%@{3jJ%@uU%@tB`&@g`&@ZHsb&@,baL&@C3&@,&@Y+d'@@d'@!Yf'@'@ƽ'@0~'@5Eag(@m ˟g(@;q9^h(@ۥ (@v;(@!H(@,k)@HN&nl)@l)@+nb~)@()@_sa)@g{p*@q*@X xq*@f~*@8L4H*@Cp*@GtFv+@:7mv+@}Fv+@O*+@؟N+@C8fٓ+@y,@bA z,@ߠz,@K*n,@v,@m,@ $~-@~NA~-@aq~-@-@RC .@}x #.@= $}.@j ӂ.@#1A ߂.@뭁/@J8/@A/@[%X/@gj+/@JY/@B"mO0@o^0@ms0@S9)E0@6E0@lw}E0@!80@F&H0@T*g0@qW"0@N`:0@+j0 0@P1@P 1@S. 1@VSJ1@G J1@)J1@ɓk&1@OV W1@Dk1@mQf1@G,1@m1@+} 2@~{ 2@i 2@ikD0N2@ "RN2@,`O2@m2@^22@1е/2@7N2@I2@u2@p3@ x3@QhY3@P0{Q3@CKR3@B 8R3@xJx3@Za3@K3@!3@\~l3@:zަ3@1c4@L4@m4@sSrNT4@QdT4@#T4@b T4@hVU4@8*7U4@= $}N7@v5yR7@/R( _S7@NaJ:@_FT:@bE U:@ơ~F=@ariR=@T=@i #@@Wx(@@z΅*@@/jA@ȑA@)ǺA@\8"C@mU'C@E>)C@D@Xo ӥD@׽ D@}z F@||Bv$F@I%r'F@֪G@htG@{юG@uq I@I +'I@H<'I@_J@6J@)t^J@([ZL@%L@F!'L@ )"*M@B"LQM@l [M@\-O@FA"O@ht#O@)rJP@(PP@W9mPP@$ Q@0c 8Q@\wbQ@-vQ@a9Q@ zQ@kR@|a2R@cJR@AH0HS@fʉMS@UMS@s|8T@e) T@ K_@0B_@$@M-C_@/iQ_@`@Y`@kC8^`@->x``@y``@A`н`@vT5AԿ`@~R8`@*oG8-a@=Ua@˜.a@&6׆|a@~a@yX5~a@b('a@ma@"a@.=;b@ c=b@mn=b@$\b@:zަb@Y8Ŝb@>?b@$]3b@ޫV&b@)3b@ Nb@=!7b@eac@ c@e6$c@K=d@`-@d@S:X@d@CVd@&d@7T7d@#e@d]Kȃe@[%Xe@£##f@nض(%f@=%f@ۅ:f@af@@YUf>@Q1.C?@?@A^{0('@@%j@@|@@Pm.@@O3A@nxvA@A@)A@A@B@ E.B@Ke*MB@p1+_ C@`LC@D]gNC@o%C@pjsD@HWD@_D@-[D@IE@N`E@ކF{E@ ,E@h %F@uPfF@4 F@PF@D^)G@#O@OsO@d 1O@h>>O@dA{pP@'Tj!P@=e ;P@\EZTP@hqmP@ SYP@0^mP@RcP@ ׹lP@z P@nAQ@C{Q@N55CT@sCTT@SӪ-eT@uT@o T@_T@$pT@^T@-ҿT@Ap׳T@Zڍ݅T@,.6T@5'QU@F2U@з%U@6 4U@+XCU@RU@PYpaU@pp%)pU@'ɪ~U@ָU@iU@8 HU@+ g㮷U@xU@A|U@7U@\U@ϸ'VU@ "B V@܍V@9/$V@jd]@1V@Rd5>V@pO)KV@7I WV@qdV@lpV@-ߣj}V@ӿV@ 28V@n&V@%V@HSV@V@V@Curve fit with data subrange: HC_samp_JperKmole_0T_select[396,569] fit_HC_samp_JperKmole_0T_select= debyePlusEinstein(W_coef,x) W_coef={798.63,4.1903,201.63,0.68271} V_chisq= 460.411;V_npnts= 174;V_numNaNs= 0;V_numINFs= 0; V_startRow= 396;V_endRow= 569; W_sigma={0.944,0.00365,0.995,0.00532} Coefficient values ± one standard deviation thetaD =798.63 ± 0.944 sD =4.1903 ± 0.00365 thetaE =201.63 ± 0.995 sE =0.68271 ± 0.00532 PՎ.LxI:DebEinExt_0T_sel_T_70K:????əJ?2RNP?%R?3c%?:G%?%?>ٜv-?E0HM-?p-?tR3?"J3?T+U3?G9?Bo#9?|-9?^3#t@?R'\x@?{,}@?uD?߱nD?A+D?f]I?ɱZlI?FynI?F%@N?A3N?@N?*R?6_9u4R?tR?z3 7V? 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($7dE¿/*?¸_,?r?ﲡzB?O)??e5ܦ?G?ԅ;?q]?V?.y\4Q?pw?_`W?|??Tw?l}?8Ț??JH?2t?m̪?bg ? ?؋&i?Ds?,?g%WB?_?{?[FS?%2??ShT?g$?'n? ?jX?&?p?(}*cg?PjwNv04ىÿIͿ ۜX%ɿPп+Ϳ?|sRԿ*Tc$:+r{ſ:íF*ɯ%r0пԿ-)\׿hwͿWc׿| DL fit_HC_s_JperKmole_0T_DER_T_70wCA????-vQ@ë-@7.@bM9 a/@& 0@0@1@iv1@B1@:ASQL_2@`92@ngK3@E-3@$*:4@*n|4@n),5@gT5@qR"6@ ",X6@g7@=4W7@?1_8@ {ʕ8@{a9@:h89@w"u:@J:@P\R;@) f;@j<@F S<@,&u&=@K%=@/>@S`>@Ƣ<:?@ݿ?@M"@@!|e@@'M @@h ?@@!7/A@arA@j'A@Fm?A@ZNIgO@ P@`#P@ms.=P@'wVP@3oP@ wP@<׃0P@=P@ƿBP@~J;P@T5Q@GcQ@ 1Q@"IQ@ߨIF`Q@^ipUwQ@J)6Q@l+Q@mQ@Q@Q@FډQ@%;R@X)R@;K>R@rcTR@IJ2iR@d#~R@s?OR@LځR@3~~JR@&J3R@*LR@(h;R@Xw S@lS@08 3S@NUFS@+uYS@1llS@ `:S@=S@F;`S@0oS@S@]S@0dS@#D S@J'*T@j!T@2T@DT@ iUT@geT@놀DvT@^J?T@!űT@<T@"H-T@/6T@Ͻ%T@EPT@gT@4+U@<>iU@%U@4U@^CU@ERU@`fdaU@IpU@~U@U@ 'U@^KU@{QU@u9U@!/U@zUU@EjAU@MU@Om V@9EV@xMd#V@bf0V@N=V@nyJV@JVV@`cV@޶}oV@\=|V@U V@KV@9rrƠV@ V@HV@a>kV@Z`@LV@Curve fit with data subrange: HC_samp_JperKmole_0T_select[396,569] fit_HC_samp_JperKmole_0T_select= debyePlusEinsteinRestrict(W_coef,x) W_coef={792.55,4.2212,193.15,0.64187} V_chisq= 2.54128;V_npnts= 174;V_numNaNs= 0;V_numINFs= 0; V_startRow= 396;V_endRow= 569; W_sigma={2.42,0.0126,3.75,0.0162} Coefficient values ± one standard deviation thetaD =792.55 ± 2.42 sD =4.2212 ± 0.0126 thetaE =193.15 ± 3.75 sE =0.64187 ± 0.0162 :[9+L>>'toIntegrate'W????7[?@{?iѓ|?Mlz?Bp?a8^NӮ?㏍,?nVK?L-;?DOv7?@h%Ә?v?'bi]?~!͚?'e?F.t? s?XGJ?(_?k"Aw?{vY?շgN?= V?@fo?W^?+Zڌ?h y?쇌?D*#?qk!?5Է_?J[T^?^?u3?}rj? ?ʄW)?r$r?DZ?tʙ@!-WG@}CY@90Ѣ@%gKP@(M@v@ի U@`@yc@!ͤO@pr @Bf o@"; @$UT$ @U^x @9k @^v @2r@ @ @` @I8 @:t@YD@Ggz@:~ @8@^2Xs@ Uo@V@K@߄J@g{@bhq ݩ@n1,@&Q@UH(@TN@ufq@o @=7<@X<@@]%>@ͫIϔ@r#@EOM(7@h. @OiGZ @ː7* @+ @dt @Z  @?>5 @]b @} @% @LpYO @H @^ @#QS< @U@#hS@k,*@7 E#@'du@C@ K@t*,i@4̃@Z@޸`@h+ @S&@ C]@ t#@WMYj@#_@>F @fhƹ@-h@Z@j@Nw@FT(@+Ϸ@Cʍ@cכA@e ?U낟W?nPz[?2?|#?-?(?r ?d7u?Ӫ2?o4j?b?] e?|0L?/ T%Wh?р(g?Fr?*v?I7l?b?'?3<*?:V5?a+M?$J?,Ӿw?5?`ZT?x5C?}T? ~?R}?x 3?ܖ !d?&h ?GT#N_?ʭ¯?Vd^?\0AZ?t*??`j0p?{?9s9?1H6?yV ?PU|?YdC?vuEa?Y mx?Q?y?RL?҇8?R?Onװ?Afa?%?jz?@-R| ?Qh_?%Ϭ1?hXz?m6Ra?̆?t4?]-s? o+?VP? 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NewPath/Z Igor_1 "::" DefaultFont "Arial" MoveWindow/C 535.5,568.25,1960.5,737 MoveWindow/P 723.75,89,1423.5,544.25 Graph1() Graph1_1() KillStrings/Z root:gWMSetNextTextFilesTextEncoding Window Graph1_1() : Graph PauseUpdate; Silent 1 // building window... Display /W=(650.25,44,1501.5,680) HC_samp_JperKmole_0T_select vs T_sample_0T_select AppendToGraph fit_HC_s_JperKmole_0T_DER_T_70 AppendToGraph DebEinRestrictExt_T_70K vs T_sample_0T_select AppendToGraph HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select AppendToGraph fit_HC_s_JperKmole_0T_DER_T_70 AppendToGraph DebEinRestrictExt_T_70K vs T_sample_0T_select AppendToGraph HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select ModifyGraph mode(HC_samp_JperKmole_0T_select)=3,mode(HC_s_JpKm_0T_s_subDER_T_70#1)=3 ModifyGraph marker(HC_samp_JperKmole_0T_select)=16,marker(fit_HC_s_JperKmole_0T_DER_T_70)=16 ModifyGraph marker(DebEinRestrictExt_T_70K)=19,marker(fit_HC_s_JperKmole_0T_DER_T_70#1)=16 ModifyGraph marker(DebEinRestrictExt_T_70K#1)=19,marker(HC_s_JpKm_0T_s_subDER_T_70#1)=19 ModifyGraph lSize(HC_samp_JperKmole_0T_select)=2,lSize(fit_HC_s_JperKmole_0T_DER_T_70)=2 ModifyGraph lSize(DebEinRestrictExt_T_70K)=2,lSize(fit_HC_s_JperKmole_0T_DER_T_70#1)=2 ModifyGraph lSize(DebEinRestrictExt_T_70K#1)=2 ModifyGraph lStyle(DebEinRestrictExt_T_70K)=3,lStyle(DebEinRestrictExt_T_70K#1)=3 ModifyGraph rgb(HC_samp_JperKmole_0T_select)=(0,0,0),rgb(fit_HC_s_JperKmole_0T_DER_T_70)=(65535,65535,0) ModifyGraph rgb(DebEinRestrictExt_T_70K)=(65535,65535,0),rgb(HC_s_JpKm_0T_s_subDER_T_70#1)=(0,65535,0) ModifyGraph msize(HC_samp_JperKmole_0T_select)=2,msize(HC_s_JpKm_0T_s_subDER_T_70#1)=2 ModifyGraph mrkThick(HC_samp_JperKmole_0T_select)=2,mrkThick(fit_HC_s_JperKmole_0T_DER_T_70)=1 ModifyGraph mrkThick(DebEinRestrictExt_T_70K)=1,mrkThick(fit_HC_s_JperKmole_0T_DER_T_70#1)=1 ModifyGraph mrkThick(DebEinRestrictExt_T_70K#1)=1,mrkThick(HC_s_JpKm_0T_s_subDER_T_70#1)=2 ModifyGraph hideTrace(fit_HC_s_JperKmole_0T_DER_T_70)=1,hideTrace(DebEinRestrictExt_T_70K)=1 ModifyGraph hideTrace(HC_s_JpKm_0T_s_subDER_T_70)=1 ModifyGraph zero(left)=4 ModifyGraph mirror=1 ModifyGraph nticks(left)=10,nticks(bottom)=8 ModifyGraph fSize=28 ModifyGraph lowTrip(left)=0.01 ModifyGraph lblMargin(left)=9,lblMargin(bottom)=3 ModifyGraph axOffset(left)=1.28571 ModifyGraph axThick=2 ModifyGraph lblLatPos(left)=-2,lblLatPos(bottom)=13 Label left "\\Z30 Cp (J/K mol)" Label bottom "\\f02T\\f00 (K)" SetAxis bottom 0,300 Cursor/P A HC_samp_JperKmole_0T_select 396;Cursor/P B HC_samp_JperKmole_0T_select 569 ShowInfo Legend/C/N=text0/J/F=0/B=1/A=MC/X=-9.19/Y=40.44 "\\s(HC_samp_JperKmole_0T_select) Measured data" AppendText "\\s(fit_HC_s_JperKmole_0T_DER_T_70#1) Fit to \"debyePlusEinsteinRestrict\" in range T = [70 K, 300 K]" AppendText "\\s(DebEinRestrictExt_T_70K#1) Fit extrapolated to low T\r\\s(HC_s_JpKm_0T_s_subDER_T_70#1) Measured data - extrapolated fit (point by point)" ShowTools/A SetDrawLayer UserFront SetDrawEnv linethick= 2,arrow= 1 DrawLine 0.603488372093023,0.7859375,0.288372093023256,0.98125 SetDrawEnv linethick= 2,arrow= 1 DrawLine 0.940697674418605,0.7828125,1.00116279069767,0.984375 SetDrawEnv xcoord= bottom,ycoord= prel,linethick= 2,arrow= 1 DrawLine 70,0.708029197080292,70,0.816058394160583 DrawText 0.196511627906977,0.694890510948905,"T\\Bmin\\M for fit" Display/W=(0.507,0.372,0.925,0.777)/HOST=# HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select ModifyGraph mode=3 ModifyGraph marker=19 ModifyGraph rgb=(0,65535,0) ModifyGraph msize=2 ModifyGraph mrkThick=2 ModifyGraph zero(left)=4 ModifyGraph mirror=1 ModifyGraph nticks(left)=10,nticks(bottom)=8 ModifyGraph fSize=20 ModifyGraph lowTrip(left)=0.01 ModifyGraph lblMargin(left)=9,lblMargin(bottom)=3 ModifyGraph axOffset(left)=1.28571 ModifyGraph axThick=2 ModifyGraph lblLatPos(left)=-2,lblLatPos(bottom)=13 Label left " " Label bottom " " SetAxis left -0.574316138404778,0.46716386593074 SetAxis bottom 63.1295843920808,305.019330743332 RenameWindow #,Graph1_1 SetActiveSubwindow ## EndMacro Window Graph1() : Graph PauseUpdate; Silent 1 // building window... Display /W=(40.5,46.25,891.75,682.25) HC_samp_JperKmole_0T_select vs T_sample_0T_select AppendToGraph fit_HC_s_JpKmol_0T_s_DE_T_70 AppendToGraph HC_s_JpKm_0T_s_subDE_T_70 vs T_sample_0T_select AppendToGraph fit_HC_s_JperKmole_0T_DER_T_70 AppendToGraph DebEinRestrictExt_T_70K vs T_sample_0T_select AppendToGraph HC_s_JpKm_0T_s_subDER_T_70 vs T_sample_0T_select AppendToGraph DebEinExt_0T_sel_T_70K vs T_sample_0T_select ModifyGraph mode(HC_samp_JperKmole_0T_select)=3,mode(HC_s_JpKm_0T_s_subDE_T_70)=3 ModifyGraph marker(HC_samp_JperKmole_0T_select)=16,marker(fit_HC_s_JpKmol_0T_s_DE_T_70)=19 ModifyGraph marker(HC_s_JpKm_0T_s_subDE_T_70)=19,marker(fit_HC_s_JperKmole_0T_DER_T_70)=16 ModifyGraph marker(DebEinRestrictExt_T_70K)=19 ModifyGraph lSize(HC_samp_JperKmole_0T_select)=2,lSize(fit_HC_s_JpKmol_0T_s_DE_T_70)=2 ModifyGraph lSize(fit_HC_s_JperKmole_0T_DER_T_70)=2,lSize(DebEinRestrictExt_T_70K)=2 ModifyGraph lSize(DebEinExt_0T_sel_T_70K)=2 ModifyGraph lStyle(DebEinRestrictExt_T_70K)=3,lStyle(DebEinExt_0T_sel_T_70K)=3 ModifyGraph rgb(HC_samp_JperKmole_0T_select)=(0,0,0),rgb(HC_s_JpKm_0T_s_subDE_T_70)=(0,65535,0) ModifyGraph rgb(fit_HC_s_JperKmole_0T_DER_T_70)=(65535,65535,0),rgb(DebEinRestrictExt_T_70K)=(65535,65535,0) ModifyGraph msize(HC_samp_JperKmole_0T_select)=2,msize(HC_s_JpKm_0T_s_subDE_T_70)=2 ModifyGraph mrkThick(HC_samp_JperKmole_0T_select)=2,mrkThick(fit_HC_s_JpKmol_0T_s_DE_T_70)=1 ModifyGraph mrkThick(HC_s_JpKm_0T_s_subDE_T_70)=2,mrkThick(fit_HC_s_JperKmole_0T_DER_T_70)=1 ModifyGraph mrkThick(DebEinRestrictExt_T_70K)=1 ModifyGraph hideTrace(fit_HC_s_JperKmole_0T_DER_T_70)=1,hideTrace(DebEinRestrictExt_T_70K)=1 ModifyGraph hideTrace(HC_s_JpKm_0T_s_subDER_T_70)=1 ModifyGraph zero(left)=4 ModifyGraph mirror=1 ModifyGraph nticks(left)=10,nticks(bottom)=8 ModifyGraph fSize=28 ModifyGraph lowTrip(left)=0.01 ModifyGraph lblMargin(left)=9,lblMargin(bottom)=3 ModifyGraph axOffset(left)=1.28571 ModifyGraph axThick=2 ModifyGraph lblLatPos(left)=-2,lblLatPos(bottom)=13 Label left "\\Z30 Cp (J/K mol)" Label bottom "\\f02T\\f00 (K)" SetAxis bottom 0,300 Cursor/P A HC_samp_JperKmole_0T_select 396;Cursor/P B HC_samp_JperKmole_0T_select 569 ShowInfo Legend/C/N=text0/J/F=0/B=1/A=MC/X=-13.72/Y=38.28 "\\s(HC_samp_JperKmole_0T_select) Measured data" AppendText "\\s(fit_HC_s_JpKmol_0T_s_DE_T_70) Fit to \"debyePlusEinstein\" in range T = [70 K, 300 K]\r\\s(DebEinExt_0T_sel_T_70K) Fit extrapolated to low T" AppendText "\n\\s(HC_s_JpKm_0T_s_subDE_T_70) Measured data - extrapolated fit (point by point)\r" ShowTools/A SetDrawLayer UserFront SetDrawEnv linethick= 2,arrow= 1 DrawLine 0.603488372093023,0.7859375,0.288372093023256,0.98125 SetDrawEnv linethick= 2,arrow= 1 DrawLine 0.940697674418605,0.7828125,1.00116279069767,0.984375 SetDrawEnv xcoord= bottom,ycoord= prel,linethick= 2,arrow= 1 DrawLine 70,0.706569343065693,70,0.808759124087591 DrawText 0.194186046511628,0.69051094890511,"T\\Bmin\\M for fit" Display/W=(0.507,0.372,0.925,0.777)/HOST=# HC_s_JpKm_0T_s_subDE_T_70 vs T_sample_0T_select ModifyGraph mode=3 ModifyGraph marker=19 ModifyGraph rgb=(0,65535,0) ModifyGraph msize=2 ModifyGraph mrkThick=2 ModifyGraph zero(left)=4 ModifyGraph mirror=1 ModifyGraph nticks(left)=10,nticks(bottom)=8 ModifyGraph fSize=20 ModifyGraph lowTrip(left)=0.01 ModifyGraph lblMargin(left)=9,lblMargin(bottom)=3 ModifyGraph axOffset(left)=1.28571 ModifyGraph axThick=2 ModifyGraph lblLatPos(left)=-2,lblLatPos(bottom)=13 Label left " " Label bottom " " SetAxis left -0.574316138404778,0.46716386593074 SetAxis bottom 63.1295843920808,305.019330743332 RenameWindow #,Graph1_1 SetActiveSubwindow ## EndMacro 9#pragma TextEncoding = "Windows-1252" #pragma rtGlobals=3 // Use modern global access method and strict wave access. #include Function debyeHelper(xd) variable xd if(xd ==0) return 0 else return ((xd^4)*Exp(xd))/(Exp(xd)-1)^2 endif end Function debyePlusEinstein(w,T) : FitFunc Wave w Variable T //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog. //CurveFitDialog/ Equation: //CurveFitDialog/ variable R = 8.31446 // in J/K*mole //CurveFitDialog/ variable numFitPoints = 10000 //CurveFitDialog/ make/D/O/N=(numFitPoints) toIntegrate //CurveFitDialog/ setscale/I x, (0),(thetaD/T), toIntegrate //CurveFitDialog/ toIntegrate = debyeHelper1(x) //CurveFitDialog/ f(T) = 9*R*sD*((T/thetaD)^3)*area(toIntegrate,0,thetaD/T) + 3*sE*R*((thetaE/T)^2)*((Exp(thetaE/T))/(Exp(thetaE/T) - 1)^2) //CurveFitDialog/ End of Equation //CurveFitDialog/ Independent Variables 1 //CurveFitDialog/ T //CurveFitDialog/ Coefficients 4 //CurveFitDialog/ w[0] = thetaD //CurveFitDialog/ w[1] = sD //CurveFitDialog/ w[2] = thetaE //CurveFitDialog/ w[3] = sE variable R = 8.31446 // in J/K*mole variable numFitPoints = 10000 make/D/O/N=(numFitPoints) toIntegrate setscale/I x, (0),(w[0]/T), toIntegrate toIntegrate = debyeHelper(x) return 9*R*w[1]*((T/w[0])^3)*area(toIntegrate,0,w[0]/T) + 3*w[3]*R*((w[2]/T)^2)*((Exp(w[2]/T))/(Exp(w[2]/T) - 1)^2) End Function debyePlusEinsteinRestrict(w,T) : FitFunc Wave w Variable T //CurveFitDialog/ These comments were created by the Curve Fitting dialog. Altering them will //CurveFitDialog/ make the function less convenient to work with in the Curve Fitting dialog. //CurveFitDialog/ Equation: //CurveFitDialog/ variable R = 8.31446 // in J/K*mole //CurveFitDialog/ variable numFitPoints = 10000 //CurveFitDialog/ make/D/O/N=(numFitPoints) toIntegrate //CurveFitDialog/ setscale/I x, (0),(thetaD/T), toIntegrate //CurveFitDialog/ toIntegrate = debyeHelper1(x) //CurveFitDialog/ f(T) = 9*R*sD*((T/thetaD)^3)*area(toIntegrate,0,thetaD/T) + 3*sE*R*((thetaE/T)^2)*((Exp(thetaE/T))/(Exp(thetaE/T) - 1)^2) //CurveFitDialog/ End of Equation //CurveFitDialog/ Independent Variables 1 //CurveFitDialog/ T //CurveFitDialog/ Coefficients 4 //CurveFitDialog/ w[0] = thetaD //CurveFitDialog/ w[1] = sD //CurveFitDialog/ w[2] = thetaE //CurveFitDialog/ w[3] = sE variable R = 8.31446 // in J/K*mole variable numFitPoints = 10000 make/D/O/N=(numFitPoints) toIntegrate setscale/I x, (0),(w[0]/T), toIntegrate toIntegrate = debyeHelper(x) wave HC_samp_JperKmole_0T_select variable i findvalue /V = (T) /T = 0.01 HC_samp_JperKmole_0T_select variable fitFuncValue = 9*R*w[1]*((T/w[0])^3)*area(toIntegrate,0,w[0]/T) + 3*w[3]*R*((w[2]/T)^2)*((Exp(w[2]/T))/(Exp(w[2]/T) - 1)^2) if(HC_samp_JperKmole_0T_select[i] < fitFuncValue) return 9*R*w[1]*((T/w[0])^3)*area(toIntegrate,0,w[0]/T) + 3*w[3]*R*((w[2]/T)^2)*((Exp(w[2]/T))/(Exp(w[2]/T) - 1)^2) endif End Function makeDebyePlusEinstein(thetaD,sD,thetaE,sE,temperatures,name) variable thetaD,sD,thetaE,sE wave temperatures string name wavestats/Q temperatures variable numFitPoints = 10000 variable R = 8.31446 // in J/K*mole make/D/O/N=(numFitPoints) toIntegrate setscale/I x, (0),(thetaD/v_min), toIntegrate toIntegrate = debyeHelper(x) make/D/O/N=(dimsize(temperatures,0)) $name wave debEinHeatCap = $name variable i,currTemp,deb,ein for(i=0;i<(dimsize(temperatures,0));i+=1) currTemp = temperatures[i] deb = 9*sD*R*((currTemp/thetaD)^3)*area(toIntegrate,0,thetaD/currTemp) ein = (3*sE*R*((thetaE/currTemp)^2)*exp(thetaE/currTemp))/(exp(thetaE/currTemp) - 1)^2 debEinHeatCap[i] = deb + ein endfor end