/************************************************************************************* * Program: XRDCALC1.2 * * Purpose: Calculate ferrite and austenite lattice parameters and phase fractions * * from peak positions. Program also attempts to calculate size and strain from * * the broadness of the peaks (this feature experimental and should be used with * * extra caution. * * Author: Dr Marimuthu Murugananth and Mr Mathew J Peet * * Version: 1.2 * * Date: 14-December-09 * * Location: http://mathewpeet.org/thesis/programs/ * * License: GPL, Gnu Public License, you are free to modify and use this program * * if you distribute the program you must also distribute the code, along with any * * changes you make. Do not modify this header. * * * ************************************************************************************/ #include #include #include #define PI 3.141592654 int no_fer_peaks,fer_h[20],fer_k[20],fer_l[20],fer_hkl2[20]; int no_aus_peaks,aus_h[20],aus_k[20],aus_l[20], aus_hkl2[20]; float wavelength; float aus_peak_theta_rad[20],fer_peak_theta_rad[20]; float aus_breadth[20],fer_breadth[20]; FILE *fres, *fentry; float gradient, intercept; float aus_a[20],fer_a[20],LPF_aus[20],LPF_fer[20]; int i,system_choice,option_alloy; char iptchoice; int MF_aus[20],MF_fer[20]; float value; float aus_peak_2theta[20],fer_peak_2theta[20],aus_peak_theta[20],fer_peak_theta[20]; float sine_by_lambda_fer[20],sine_by_lambda_aus[20],fer_d[20],aus_d[20]; float F_aus[20],F_fer[20],F_aus2[20],F_fer2[20]; float asc; /*float atom_scatter();*/ float e2m_aus[20],e2m_fer[20],aus_Iint[20],fer_Iint[20]; float inten_err_aus[20],R_fer[20],R_aus[20],inten_err_fer[20],IbyR_aus[20],IbyR_fer[20]; float ave_aus,ave_fer,Afer,Aaus,Aus_frac,Fer_frac,inten_err_aus_total; float inten_err_fer_total,pre_total_error,total_error; char name[50],filename[61],inputfname[58]; int main(void) { title(); printf("Type the Identification name of the material : \t"); scanf("%s",name); sprintf(filename,"%s_XRD_result",name); sprintf(inputfname,".%s_inputs",name); printf("\n%s\n",inputfname); getchar(); if((fentry=fopen(inputfname,"r"))!=NULL) { printf("\n\nYour input file \"%s\" for the identification name \"%s\" exists\n Do you want to use that (Y/N)? \t",inputfname,name); scanf("%c",&iptchoice); printf("%c",iptchoice); iptchoice = toupper(iptchoice); printf("%c",iptchoice); if(iptchoice=='Y') { get_values_from_file(); } else { printf("\n\nExiting XRDCALC..."); exit(0); } } else { get_values_from_stdio(); print_to_entry_file(); } printf ("here"); getchar(); if((fres=fopen(filename,"w"))!=NULL) { calculate_stuff(); calculate_d_spacings(); calculate_lattice_param(); calculte_lorentz_polarization_factor(); regression(LPF_aus,aus_a,no_aus_peaks); print_lp(); regression(LPF_fer,fer_a,no_fer_peaks); print_lp(); calculate_multiplicity_factor(); calculate_structure_factor(); calculate_temperature_factor(); calculate_R_factor(); result_to_stdio(); average_lattice_param(); print_to_file(); } else { printf("%s already exists\n\nPlease rename it and then run this program\n\n", filename); printf("\n\nExiting XRDCALC..."); exit(0); } } float atom_scatter(lambda,opt,sin_by_lambda) int opt; float sin_by_lambda,lambda; { float ffe,fni,fcr,f,f_err,ratio_lambda; ffe=298.541*pow(sin_by_lambda,7)-1416.84*pow(sin_by_lambda,6)+2708.46*pow(sin_by_lambda,5)-2647.53*pow(sin_by_lambda,4)+1369.02*pow(sin_by_lambda,3)-323.115*pow(sin_by_lambda,2)-8.21796*sin_by_lambda+26.0038; fni=164.627*pow(sin_by_lambda,7)-881.92*pow(sin_by_lambda,6)+1866.91*pow(sin_by_lambda,5)-1994.09*pow(sin_by_lambda,4)+1115.99*pow(sin_by_lambda,3)-281.002*pow(sin_by_lambda,2)-11.5068*sin_by_lambda+28.0041; fcr=255.541*pow(sin_by_lambda,7)-1208.95*pow(sin_by_lambda,6)+2301.11*pow(sin_by_lambda,5)-2237.69*pow(sin_by_lambda,4)+1149.36*pow(sin_by_lambda,3)-266.194*pow(sin_by_lambda,2)-11.4846*sin_by_lambda+23.9948; switch(opt) { case 1: f=ffe;break; case 2: f=(ffe+fni)/2;printf("\n[ %f ]Selected Fe and Ni \tffe=%f fni=%f f = %f",sin_by_lambda,ffe,fni,f);break; case 3: f=(ffe+fcr)/2;break; case 4: f=(ffe+fcr+fni)/3;break; } ratio_lambda=lambda/1.74346; if (ratio_lambda <= 1) { f_err=-33745.3*pow(ratio_lambda,10) + 158121*pow(ratio_lambda,9) - 314972*pow(ratio_lambda,8) + 347441*pow(ratio_lambda,7) - 231665*pow(ratio_lambda,6) + 95617.5*pow(ratio_lambda,5) - 24013.6*pow(ratio_lambda,4) + 3450.3*pow(ratio_lambda,3) - 248.253*pow(ratio_lambda,2) + 7.56109*ratio_lambda + 0.0341823; printf("\nError Associated [ratio_lambda = %f ]\t ratio <= 1:\t%f\n",ratio_lambda ,f_err); } else if (ratio_lambda > 1 && ratio_lambda <= 1.13) { f_err=327.877*pow(ratio_lambda,7)-3700.62*pow(ratio_lambda,6)+17745.5*pow(ratio_lambda,5)-46856.2*pow(ratio_lambda,4)+73564.1*pow(ratio_lambda,3)-68668*pow(ratio_lambda,2)+35288.7*ratio_lambda-7705.91 ; printf("\nError Associated [Ratio_lambda = %f ]\t:\t%f\n",ratio_lambda ,f_err); } else /*if(ratio_lambda > 1.13) */ { f_err=2.31485*pow(ratio_lambda,6)-19.2679*pow(ratio_lambda,5)+61.2172*pow(ratio_lambda,4)-87.0473*pow(ratio_lambda,3)+38.6116*pow(ratio_lambda,2)+28.3705*ratio_lambda-27.3772; printf("\nError Associated [ratio_lambda = %f ]\t:\t%f\n",ratio_lambda,f_err); } return(f+f_err); } int title() { printf("----------------------------------------------------------------------\n"); printf("\n"); printf("\t CALCULATION OF PHASE FRACTIONS USING XRD DATA\n\n"); printf("----------------------------------------------------------------------\n\n\n\n"); printf("\n\n\n\t\t\t By\n\t\t\tMurugananth M\n\t\tPhase Transformation Group\n\t\t University of Cambridge\n\n\n\n"); } /*CALCULATE CRYSTALLITE SIZE AND STRAIN */ int size_strain() { int i,j; float fer_four_sin_theta[20],fer_breadth_2theta_radians[20],fer_beta_cos_theta[20]; float aus_four_sin_theta[20],aus_breadth_2theta_radians[20],aus_beta_cos_theta[20]; float slope, constant; for(i=1;i<=no_fer_peaks;i++) { fer_four_sin_theta[i]=4*sin(fer_peak_theta_rad[i]); fer_breadth_2theta_radians[i]=fer_breadth[i]*(PI/180); fer_beta_cos_theta[i]=fer_breadth_2theta_radians[i]*cos(fer_peak_theta_rad[i]); printf("theta_rad = %f breadth= %f breadth_rad= %f ",fer_peak_theta_rad[i],fer_breadth[i],fer_breadth_2theta_radians[i]); printf("4sin(theta) = %f",fer_four_sin_theta[i]); printf("beta_cos(theta) = %f\n",fer_beta_cos_theta[i]); } printf("Searching peaks \n", i, j); for(i=1;i<=no_fer_peaks;i++) for(j=1;j<=no_fer_peaks;j++) { if((2*fer_h[i])==fer_h[j] && (2*fer_l[i])==fer_l[j] && (2*fer_k[i])==fer_k[j] || (3*fer_h[i])==fer_h[j] && (3*fer_l[i])==fer_l[j] && (3*fer_k[i])==fer_k[j]) { printf("\nPeak %d (%d %d %d) and peak %d (%d %d %d) of ferrite are of the same direction\n", i,fer_h[i],fer_l[i],fer_k[i],j,fer_h[j],fer_l[j],fer_k[j]); constant = (fer_beta_cos_theta[j]-fer_beta_cos_theta[i])/(fer_four_sin_theta[j]-fer_four_sin_theta[i]); printf("\nGradient = strain = %f",slope); fprintf(fres,"\nGradient = strain = %f",slope); slope = fer_beta_cos_theta[i] - slope*fer_four_sin_theta[i]; printf("\nIntercept = %f",constant); printf("\nSize = %f nanometers\n",wavelength*0.1*0.9/constant); fprintf(fres,"\nSize = %f nanometers\n",wavelength*0.1*0.9/constant); } else printf("."); } printf("\nRegression on ferrite peaks"); fprintf(fres,"\nRegression on ferrite peaks"); regression(fer_four_sin_theta,fer_beta_cos_theta,no_fer_peaks); print_regression(); for(i=1;i<=no_aus_peaks;i++) { aus_four_sin_theta[i]=4*sin(aus_peak_theta_rad[i]); aus_breadth_2theta_radians[i]=aus_breadth[i]*(PI/180); aus_beta_cos_theta[i]=aus_breadth_2theta_radians[i]*cos(aus_peak_theta_rad[i]); printf("theta_rad = %f breadth= %f breadth_rad= %f ",aus_peak_theta_rad[i],aus_breadth[i],aus_breadth_2theta_radians[i]); printf("4sin(theta) = %f",aus_four_sin_theta[i]); printf("beta_cos(theta) = %f\n",aus_beta_cos_theta[i]); } printf("Searching peaks \n", i, j); for(i=1;i<=no_aus_peaks;i++) for(j=1;j<=no_aus_peaks;j++) { if((2*aus_h[i])==aus_h[j] && (2*aus_l[i])==aus_l[j] && (2*aus_k[i])==aus_k[j] || (3*aus_h[i])==aus_h[j] && (3*aus_l[i])==aus_l[j] && (3*aus_k[i])==aus_k[j]) { printf("\nPeak %d (%d %d %d) and peak %d (%d %d %d) of austenite are of the same direction\n", i,aus_h[i],aus_l[i],aus_k[i],j,aus_h[j],aus_l[j],aus_k[j]); slope = (aus_beta_cos_theta[j]-aus_beta_cos_theta[i])/(aus_four_sin_theta[j]-aus_four_sin_theta[i]); printf("\nGradient = strain = %f",slope); fprintf(fres,"\nGradient = strain = %f",slope); constant = aus_beta_cos_theta[i] - slope*aus_four_sin_theta[i]; printf("\nIntercept = %f",constant); printf("\nSize = %f nanometers\n",wavelength*0.1*0.9/constant); fprintf(fres,"\nSize = %f nanometers\n",wavelength*0.1*0.9/constant); } else printf("."); } printf("\nRegression on austenite peaks"); fprintf(fres,"\nRegression on austenite peaks"); regression(aus_four_sin_theta,aus_beta_cos_theta,no_aus_peaks); print_regression(); } int regression(float x[20], float y[20], int N) { int i; float Ex, Ey, Ex2, Ey2, Exy; float corr; float sxx,syy,sxy; Ex = 0.0; Ey = 0.0; Ex2 = 0.0; Ey2 = 0.0; Exy = 0.0; for(i=1;i<=N;i++) { Ex=Ex+x[i]; Ey=Ey+y[i]; Exy=Exy+x[i]*y[i]; Ey2=Ey2+y[i]*y[i]; Ex2=Ex2+x[i]*x[i]; /* printf("\ni = %d",i);*/ /*for testing */ } sxx = Ex2 - Ex * Ex / N; syy = Ey2 - Ey * Ey / N; sxy = Exy - Ex * Ey / N; gradient = sxy / sxx; intercept = Ey/N-gradient*Ex/N; corr = sxy / sqrt(sxx * syy); printf("\nsxx= %lf, syy = %lf, sxy = %lf, gradient = %lf, intercept = %lf, corr= %lf \n",sxx,syy,sxy,gradient,intercept,corr); fprintf(fres,"\nsxx= %lf, syy = %lf, sxy = %lf, gradient = %lf, intercept = %lf, corr= %lf \n",sxx,syy,sxy,gradient,intercept,corr); } int print_regression(void) { printf("\n-----------REGRESSION-----------\n"); printf("\nGradient = strain = %f",gradient); printf("\nSize = %f nanometers",wavelength*0.1*0.9/intercept); fprintf(fres,"\nGradient = strain = %f",gradient); fprintf(fres,"\nSize = %f nanometers\n",wavelength*0.1*0.9/intercept); } int print_lp(void) { printf("\nLattice Parameter = %f",intercept); fprintf(fres,"\nLattice Parameter = %f ",intercept); } int get_values_from_file(void) { printf("\nReading from file %s\n", name); fscanf(fentry,"%s",name); fscanf(fentry,"%f",&wavelength); fscanf(fentry,"%d",&no_aus_peaks); fscanf(fentry,"%d",&no_fer_peaks); for(i=1;i<=no_aus_peaks;i++) fscanf(fentry,"%d %d %d %f %f %f",&aus_h[i],&aus_k[i],&aus_l[i],&aus_peak_2theta[i],&aus_Iint[i],&aus_breadth[i]); for(i=1;i<=no_fer_peaks;i++) fscanf(fentry,"%d %d %d %f %f %f",&fer_h[i],&fer_k[i],&fer_l[i],&fer_peak_2theta[i],&fer_Iint[i],&fer_breadth[i]); fscanf(fentry,"%d",&system_choice); fscanf(fentry,"%d",&option_alloy); fclose(fentry); } int get_values_from_stdio() { printf("Input entries will be logged to \t : %s\n\n", inputfname); printf("Enter the wavelength of the X-radiation used in Angroms:\t"); scanf("%f",&wavelength); printf("\n\nHow many austenite peaks have you got\t:\t"); scanf("%d",&no_aus_peaks); printf("How many ferrite peaks have you got\t:\t"); scanf("%d",&no_fer_peaks); for(i=1;i<=no_aus_peaks;i++) { printf("\nEnter {hkl} for AUSTENITE peak %d (h k l seperated by spaces):\t", i); scanf("%d %d %d",&aus_h[i],&aus_k[i],&aus_l[i]); printf("Enter the TWO THETA value:\t",i); scanf("%f",&aus_peak_2theta[i]); printf("Enter Integrated Intensity:\t",i,aus_peak_2theta[i]); scanf("%f",&aus_Iint[i]); printf("Enter Breadth:\t",i); scanf("%f",&aus_breadth[i]); printf("\nPeak %d of austenite, is {%d %d %d}, 2theta %f, Integrated intensity %f, breadth %f, do you accept (Y/N)?", i,aus_h[i],aus_k[i],aus_l[i],aus_peak_2theta[i],aus_Iint[i],aus_breadth[i]); getchar(); scanf("%c",&iptchoice); iptchoice = toupper(iptchoice); if(iptchoice!='Y') i=i-1; } for(i=1;i<=no_fer_peaks;i++) { printf("\nEnter {hkl} for FERRITE peak %d (h k l seperated by spaces):\t", i); scanf("%d %d %d",&fer_h[i],&fer_k[i],&fer_l[i]); printf("Enter the TWO THETA value for peak %d of FERRITE:\t",i); scanf("%f",&fer_peak_2theta[i]); printf("Integrated Intensity for peak %d with 2-Theta %f of FERRITE:\t",i,fer_peak_2theta[i]); scanf("%f",&fer_Iint[i]); printf("Enter Breadth of peak %d of FERRITE:\t",i); scanf("%f",&fer_breadth[i]); printf("\nPeak %d of ferrite, is {%d %d %d}, 2theta %f, Integrated intensity %f, breadth %f, do you accept (Y/N)?", i,fer_h[i],fer_k[i],fer_l[i],fer_peak_2theta[i],fer_Iint[i],fer_breadth[i]); getchar(); scanf("%c",&system_choice);/*corrected from iptchoice?*/ iptchoice = toupper(iptchoice); if(iptchoice!='Y') i=i-1; } printf("\n\n\nWhich system_choice are you using\n"); printf("\n\t1.\tCUBIC\n\t2.\tHEXAGONAL and RHOMBHOHEDRAL\n\t3.\tTETRAGONAL\n\t4.\tORTHORHOMBIC\n\t5.\tMONOCLINIC\n\t6.\tTRICLINIC\n\n"); printf("Enter option:\t"); /*scanf("%d",&system_choice);*/ /* if(iptchoice!=1)scanf("%d",&system_choice);*/ /* choice commented out because the other options are not yet available */ if(system_choice!=1) { system_choice=1; printf("\nSorry forcing system choice to 1\n"); } printf("\n\n-------------- STRUCTURE FACTOR --------------------\n\n"); printf("\n\nThe major alloying elements in your steel are\t:\n\t1.\tFe only\n\t2.\tFe and Ni\n\t3.\tFe and Cr\n\t4.\tFe, Ni and Cr\n\n\tChoose option:\t"); /*scanf("%d",&option_alloy); */ printf("\nSorry forcing alloy option to 1 (feature not implimented)\n"); } int print_to_entry_file() { fentry=fopen(inputfname,"w"); fprintf(fentry, "%s\n%f\n%d\n%d\n", name,wavelength,no_aus_peaks,no_fer_peaks); for(i=1;i<=no_aus_peaks;i++) { fprintf(fentry,"%d %d %d \t %f %f %f\n",aus_h[i],aus_k[i],aus_l[i],aus_peak_2theta[i],aus_Iint[i],aus_breadth[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fentry,"%d %d %d \t%f %f %f\n",fer_h[i],fer_k[i],fer_l[i],fer_peak_2theta[i],fer_Iint[i],aus_breadth[i]); } fprintf(fentry,"%d\n",system_choice); fprintf(fentry,"%d\n",option_alloy); fclose(fentry); } int print_to_file() { fprintf(fres,"\n----------------------------------------------------------------------\n"); fprintf(fres,"\n"); fprintf(fres,"\t\tCALCULATION OF PHASE FRACTIONS USING XRD DATA\n"); fprintf(fres,"\n"); fprintf(fres,"----------------------------------------------------------------------\n"); fprintf(fres, "Material Identification : \t %s", name); fprintf(fres, "\n\nWAVELENGTH USED : %f", wavelength); fprintf(fres,"\n\n--------------THETA VALUES--------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres,"2theta for AUSTENITE : %f\t sin(theta)_by_lambda : %f \n", aus_peak_2theta[i],sine_by_lambda_aus[i]); fprintf(fres,"Integrated Intensity %d AUSTENITE: %f\n\n",i, aus_Iint[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres,"2theta for FERRITE : %f\t sin(theta)_by_lambda : %f \n", fer_peak_2theta[i],sine_by_lambda_fer[i]); fprintf(fres,"Integrated Intensity %d FERRITE: %f\n\n",i, fer_Iint[i]); } fprintf(fres,"\n\n-------------- D-SPACING --------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres,"d-spacing for AUSTENITE : %f \n",aus_d[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres,"d-spacing for FERRITE : %f \n",fer_d[i]); } fprintf(fres,"\n\n--------------LATTICE PARAMETER RESULTS--------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres, "\nAUSTENITE [ 2-Theta=%f ]: \t %f",aus_peak_2theta[i],aus_a[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres,"\nFERRITE [ 2-Theta=%f ] : \t %f",fer_peak_2theta[i], fer_a[i]); } fprintf(fres,"\n\n-------------- LORENTZ POLARIZATION FACTOR --------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres, "AUSTENITE 2-Theta : %f\t LPF [ %d ] : %f \n", aus_peak_2theta[i], i, LPF_aus[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres, "FERRITE 2-Theta : %f\t LPF [ %d ] : %f \n", fer_peak_2theta[i], i, LPF_fer[i]); } fprintf(fres,"\n\n-------------- MULTIPLICITY FACTOR --------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres, "Multipilicity factor [ 2-Theta = %f, {%d%d%d} ] : %d\n",aus_peak_2theta[i],aus_h[i], aus_k[i], aus_l[i], MF_aus[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres, "Multipilicity factor [ 2-Theta = %f, {%d%d%d} ] : %d\n",fer_peak_2theta[i],fer_h[i], fer_k[i], fer_l[i], MF_fer[i]); } fprintf(fres,"\n\n-------------- STRUCTURE FACTOR --------------------\n\n"); if (option_alloy==1) fprintf(fres, "Selected system Fe only\n\n"); else if (option_alloy==2) fprintf(fres, "Selected system Fe & Ni only\n\n"); else if (option_alloy==3) fprintf(fres, "Selected system Fe & Cr only\n\n"); else if (option_alloy==4) fprintf(fres, "Selected system Fe, Cr & Ni only\n\n"); for(i=1;i<=no_fer_peaks;i++) { fprintf(fres, "Fer [ sin(theta)_by_lambda=%f ]\tAtomic Scattering factor=%f \t F2=%f\n", sine_by_lambda_fer[i],asc, F_fer2[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres, "Aus [ sin(theta)_by_lambda=%f ]\tAtomic Scattering factor=%f \t F2=%f\n", sine_by_lambda_aus[i],asc, F_aus2[i]); } fprintf(fres,"\n\n-------------- TEMPERATURE FACTOR --------------------\n\n"); for(i=1;i<=no_aus_peaks;i++) { fprintf(fres,"Austenite e^-2m [ sin(theta)_by_lambda=%f ]: %f\n", sine_by_lambda_aus[i],e2m_aus[i]); } for(i=1;i<=no_fer_peaks;i++) { fprintf(fres,"Ferrite e^-2m [ sin(theta)_by_lambda=%f ]: %f\n", sine_by_lambda_fer[i],e2m_fer[i]); } fprintf(fres,"\n\n-------------- R FACTOR --------------------\n\n"); for(i=1;i<=no_fer_peaks;i++) { fprintf(fres,"Ferrite R : %f\n",R_fer[i]); } for(i=1;i<=no_aus_peaks;i++) { fprintf(fres,"Austenite R : %f\n",R_aus[i]); } fprintf(fres,"\n\n-------------- RESULT --------------------\n\n"); fprintf(fres,"Fraction of Austenite : %f Ferrite : %f \n",Aus_frac, Fer_frac); fprintf(fres,"\n\nPercentage of austenite :\t%.3f %%\tError : %.4f%%", Aus_frac*100,total_error*100); fprintf(fres,"\nPercentage of ferrite :\t%.3f %%\tError : %.4f %%\n\n", Fer_frac*100, total_error*100); size_strain(); fprintf(fres, "------------------------- END --------------------------------------"); fclose(fres); } int calculate_stuff() { inten_err_aus_total=0.0; inten_err_fer_total=0.0; /*these variables need to be initialised*/ for(i=1;i<=no_aus_peaks;i++) { aus_hkl2[i]=aus_h[i]*aus_h[i]+aus_k[i]*aus_k[i]+aus_l[i]*aus_l[i]; aus_peak_theta[i]=aus_peak_2theta[i]/2; aus_peak_theta_rad[i]=(PI/180)*aus_peak_theta[i]; sine_by_lambda_aus[i]=sin(aus_peak_theta_rad[i])/wavelength; inten_err_aus[i]=1/sqrt(aus_Iint[i]); inten_err_aus_total=inten_err_aus_total+inten_err_aus[i]; } for(i=1;i<=no_fer_peaks;i++) { fer_hkl2[i]=fer_h[i]*fer_h[i]+fer_k[i]*fer_k[i]+fer_l[i]*fer_l[i]; fer_peak_theta[i]=fer_peak_2theta[i]/2; fer_peak_theta_rad[i]=(PI/180)*fer_peak_theta[i]; sine_by_lambda_fer[i]=sin(fer_peak_theta_rad[i])/wavelength; inten_err_fer[i]=1/sqrt(fer_Iint[i]); inten_err_fer_total=inten_err_fer_total+inten_err_fer[i]; } } int calculate_d_spacings() { /*printf("\n-----------D SPACING------------\n");*/ for(i=1;i<=no_aus_peaks;i++) { aus_d[i]=wavelength/(2*sin(aus_peak_theta_rad[i])); } for(i=1;i<=no_fer_peaks;i++) { fer_d[i]=wavelength/(2*sin(fer_peak_theta_rad[i])); } } int calculate_lattice_param() { /* printf("\n------LATTICE PARAMETER---------\n");*/ for(i=1;i<=no_aus_peaks;i++) { aus_a[i]=sqrt(aus_d[i]*aus_d[i]*aus_hkl2[i]); /* printf("\nAUSTENITE [ 2-Theta=%f ]: \t %f",aus_peak_2theta[i],aus_a[i]);*/ } printf("\n\n"); for(i=1;i<=no_fer_peaks;i++) { fer_a[i]=sqrt(fer_d[i]*fer_d[i]*fer_hkl2[i]); /* printf("\nFERRITE [ 2-Theta=%f ] : \t %f",fer_peak_2theta[i], fer_a[i]);*/ } } int calculte_lorentz_polarization_factor() { /* printf("\n------LORENTZ POLARIZATION FACTOR--------\n");*/ for(i=1;i<=no_aus_peaks;i++) { LPF_aus[i]=(1+cos(2*aus_peak_theta_rad[i])*cos(2*aus_peak_theta_rad[i]))/(sin(aus_peak_theta_rad[i])*sin(aus_peak_theta_rad[i])*cos(aus_peak_theta_rad[i])); } for(i=1;i<=no_fer_peaks;i++) { LPF_fer[i]=(1+cos(2*fer_peak_theta_rad[i])*cos(2*fer_peak_theta_rad[i]))/(sin(fer_peak_theta_rad[i])*sin(fer_peak_theta_rad[i])*cos(fer_peak_theta_rad[i])); } } int calculate_multiplicity_factor() { switch(system_choice) { case 1: /*printf("\n\nSelected system : CUBIC\n\n"); fprintf(fres, "\n\nSelected system : CUBIC\n\n");*/ for(i=1;i<=no_aus_peaks;i++) { printf("\nAustenite: {%d%d%d}",aus_h[i],aus_k[i],aus_l[i]); if(aus_h[i]!=aus_k[i] && aus_k[i] != aus_l[i]) MF_aus[i]=48; if(aus_h[i]==aus_k[i] && aus_k[i] != aus_l[i]) MF_aus[i]=24; if(aus_h[i]==0 && aus_k[i] != aus_l[i]) MF_aus[i]=24; if(aus_h[i]==0 && aus_k[i] == aus_l[i]) MF_aus[i]=12; if(aus_h[i]==aus_k[i] && aus_k[i] == aus_l[i]) MF_aus[i]=8; if(aus_h[i]==0 && aus_k[i] ==0) MF_aus[i]=6; /* printf("\nMultipilicity factor [ 2-Theta = %f ]:\t%d\t sin_lambda:\t%f",aus_peak_2theta[i],MF_aus[i],sine_by_lambda_aus[i]); */ } printf("\n\n\n"); for(i=1;i<=no_fer_peaks;i++) { /* printf("\nFerrite: {%d%d%d}",fer_h[i],fer_k[i],fer_l[i]);*/ if(fer_h[i]!=fer_k[i] && fer_k[i] != fer_l[i]) MF_fer[i]=48; if(fer_h[i]==fer_k[i] && fer_k[i] != fer_l[i]) MF_fer[i]=24; if(fer_h[i]==0 && fer_k[i] != fer_l[i]) MF_fer[i]=24; if(fer_h[i]==0 && fer_k[i] == fer_l[i]) MF_fer[i]=12; if(fer_h[i]==fer_k[i] && fer_k[i] == fer_l[i]) MF_fer[i]=8; if(fer_h[i]==0 && fer_k[i] ==0) MF_fer[i]=6; /* printf("\nMultipilicity factor [ 2-Theta = %f ]:\t%d\t sin_lambda:\t%f",fer_peak_2theta[i],MF_fer[i],sine_by_lambda_fer[i]);*/ } break; case 2: printf("\n\nSelected system : HEXAGONAL and RHOMBHOHEDRAL\n\n"); break; case 3: printf("\n\nSelected system : TETRAGONAL\n\n"); break; case 4: printf("\n\nSelected system : ORTHORHOMBIC\n\n"); break; case 5: printf("\n\nSelected system : MONOCLINIC\n\n"); break; case 6: printf("\n\nSelected system : TRICLINIC\n\n"); break; } } int calculate_structure_factor() { /* printf("\n------STRUCTURE FACTOR---------\n");*/ for(i=1;i<=no_fer_peaks;i++) { if((fer_h[i]+fer_k[i]+fer_l[i])%2 == 0) { asc=atom_scatter(wavelength,option_alloy,sine_by_lambda_fer[i]); F_fer[i]=2*asc; F_fer2[i]=F_fer[i]*F_fer[i]; /* printf("\nFer [ sin_by_lambda %f ] asc=%f \t F2=%f",sine_by_lambda_fer[i],asc, F_fer2[i]);*/ } else F_fer[i]=0; } for(i=1;i<=no_aus_peaks;i++) { if((aus_h[i]+aus_k[i])%2==0 && (aus_h[i]+aus_l[i])%2==0 && (aus_k[i]+aus_l[i])%2==0) { asc=atom_scatter(wavelength,option_alloy,sine_by_lambda_aus[i]); F_aus[i]=4*asc; F_aus2[i]=F_aus[i]*F_aus[i]; /*printf("\nAus [ sin_by_lambda %f ] asc=%f \t F2=%f", sine_by_lambda_aus[i],asc, F_aus2[i]);*/ } else F_aus[i]=0; } } int calculate_temperature_factor() { /* printf("\n--------------TEMPERATURE FACTOR---------------------------------\n");*/ double debeye = 470; // Debeye temperature of the material in Kelvin from Kittel C, Introduction to solid state physics 7th Ed (Wiliey) 1995. double T_K = 23+273; // Temperature in Kelvin double A = 55; //Atomic weight double m = 0; // 'factor' double sine_by_lambda =0; for(i=1;i<=no_aus_peaks;i++) { /* debeye temperature factor? */ /*I assume this is for room temperature */ e2m_aus[i]=0.150728*pow(sine_by_lambda_aus[i],3)-0.630945*pow(sine_by_lambda_aus[i],2)-0.0277821*sine_by_lambda_aus[i] + 1.00055; printf ("old e2m_aus[%d], %lf \n ",i,e2m_aus[i]); /* see elements of X-ray diffraction 3rd edition, Cullity and stock p156 */ /* my solution is not exact and works with linear regression on the data from cullity good for when debeye/T < 2 its ok for steel in range 200 kelvin and above */ sine_by_lambda = sine_by_lambda_aus[i]; // equation is same for below for ferrite m = (11500 * T_K / (A*debeye*debeye)) * (exp(-0.25102875*(debeye/T_K)) + debeye/(T_K*4)) * (sine_by_lambda*sine_by_lambda); // m is factor :) e2m_aus[i] = exp(-m); printf ("new e2m_aus[%d], %lf \n ",i,e2m_aus[i]); } for(i=1;i<=no_fer_peaks;i++) { e2m_fer[i]=0.150728*pow(sine_by_lambda_fer[i],3)-0.630945*pow(sine_by_lambda_fer[i],2)-0.0277821*sine_by_lambda_fer[i] + 1.00055; printf ("old e2m_fer[%d], %lf \n ",i,e2m_fer[i]); sine_by_lambda = sine_by_lambda_fer[i]; // equation is same below -- read comments above m = (11500 * T_K / (A*debeye*debeye)) * (exp(-0.25102875*(debeye/T_K)) + debeye/(T_K*4)) * (sine_by_lambda*sine_by_lambda); e2m_fer[i] = exp(-m); printf ("new e2m_fer[%d], %lf \n ",i,e2m_fer[i]); } } int calculate_R_factor() { /* printf("\n---------------R FACTOR-----------------\n");*/ for(i=1;i<=no_fer_peaks;i++) { R_fer[i]=(F_fer2[i]*MF_fer[i]*LPF_fer[i]*e2m_fer[i])/pow(fer_a[i],6); IbyR_fer[i]=fer_Iint[i]/R_fer[i]; Afer=IbyR_fer[i]+Afer; } for(i=1;i<=no_aus_peaks;i++) { R_aus[i]=(F_aus2[i]*MF_aus[i]*LPF_aus[i]*e2m_aus[i])/pow(aus_a[i],6); IbyR_aus[i]=aus_Iint[i]/R_aus[i]; Aaus=IbyR_aus[i]+Aaus; } ave_fer=Afer/no_fer_peaks; ave_aus=Aaus/no_aus_peaks; Aus_frac=1/(1+(ave_fer/ave_aus)); Fer_frac=1-Aus_frac; pre_total_error=inten_err_aus_total*inten_err_fer_total; total_error=pre_total_error/(1+pre_total_error); } int result_to_stdio() { printf("\n\n-------------- RESULT --------------------\n\n"); printf("preT:%f Aus:%f fer:%f",pre_total_error, inten_err_aus_total,inten_err_fer_total); printf("\n\nPercentage of austenite :\t%.3f %%\t Error : %.4f %%", Aus_frac*100,total_error*100); printf("\nPercentage of ferrite :\t%.3f %%\t Error : %.4f %%\n\n", Fer_frac*100, total_error*100); printf("Look into the filename %s for your results\n\n\t\t\t Thank you for using xrdcalc- Ananth\n", filename); } int average_lattice_param() { float austenite_lp=0.0; float ferrite_lp=0.0; float aus_err[20]; //float aus_err_sum=0.0; float fer_err[20]; //float fer_err_sum=0.0; printf("Regression of austenite peaks, Cohen method, error sources according to A.Wilson\n\n"); printf("Apparant LP\t\tError\n"); for(i=1;i<=no_aus_peaks;i++) { //form below is for errors in camera debeye-sherrer only // aus_err[i]=0.5*(((cos(aus_a[i])*cos(aus_a[i]))/(sin(aus_a[i])*sin(aus_a[i])))+((cos(aus_a[i])*cos(aus_a[i]))/aus_a[i])); // // Major errors in Counter Diffractometry would be expected to be from // specimen flatness, and displacement, both have the form cos(th)cot(th) aus_err[i]=(cos(aus_peak_theta_rad[i])*cos(aus_peak_theta_rad[i]))/sin(aus_peak_theta_rad[i]); //this is the form for d spacings //should use values for angles not d spacing (form is correct) //aus_peak_theta_rad[i] printf("%f\t\t%f\n",aus_a[i],aus_err[i]); } // austenite_lp=(aus_a[1]+aus_a[2]+aus_a[3]+aus_a[4]); // austenite_lp=(aus_a[1]+aus_a[2]+aus_a[3]+aus_a[4]); // maybe not the best way? Check Cullity. regression(aus_err,aus_a,no_aus_peaks); printf("\n-----------REGRESSION-----------\n"); printf("\nGradient = %f",gradient); printf("\nIntercept = %f\n",intercept); austenite_lp = intercept + gradient*(cos(90*PI/180)*cos(90*PI/180))/sin(90*PI/180); // should be same as intecerpt! printf("Regression of ferrite peaks, Cohen method, error sources according to A.Wilson\n\n"); printf("Apparant LP\t\tError\n"); for(i=1;i<=no_fer_peaks;i++) { //form below is for errors in camera debeye-sherrer only // fer_err[i]=0.5* (((cos(fer_a[i])*cos(fer_a[i]))/( sin(fer_a[i])*sin(fer_a[i])))+((cos(fer_a[i])*cos(fer_a[i]))/fer_a[i])); // // Major errors in Counter Diffractometry would be expected to be from // specimen flatness, and displacement, both have the form cos(th)cot(th) fer_err[i]=(cos(fer_peak_theta_rad[i])*cos(fer_peak_theta_rad[i]))/sin(fer_peak_theta_rad[i]); printf("%f\t\t%f\n",fer_a[i],fer_err[i]); } regression(fer_err,fer_a,no_fer_peaks); printf("\n-----------REGRESSION-----------\n"); printf("\nGradient = %f",gradient); printf("\nIntercept = %f\n",intercept); ferrite_lp = intercept; // ferrite_lp=(fer_a[1]+fer_a[2]+fer_a[3]+fer_a[4]); // ferrite_lp=(fer_a[1]/fer_err[1]+fer_a[2]/fer_err[2]+fer_a[3]/fer_err[3]+fer_a[4]/fer_err[4])*fer_err_sum; printf("Lattice Parameter determined extrapolating (Cohen Method - Cullity p368)\n"); printf("\n\n\taustenite_lp=\t %lf", austenite_lp); printf("\n\tferrite_lp=\t %lf\n\n", ferrite_lp); }