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Tutorials/TOF Calibration/Calibration of a TOF powder diffractometer.htm
r1745 r2390 25 25 <o:Author>Von Dreele</o:Author> 26 26 <o:LastAuthor>Von Dreele</o:LastAuthor> 27 <o:Revision> 5</o:Revision>28 <o:TotalTime>67 3</o:TotalTime>27 <o:Revision>7</o:Revision> 28 <o:TotalTime>676</o:TotalTime> 29 29 <o:Created>2015-02-12T20:52:00Z</o:Created> 30 <o:LastSaved>201 5-03-20T13:39:00Z</o:LastSaved>30 <o:LastSaved>2016-07-28T18:55:00Z</o:LastSaved> 31 31 <o:Pages>1</o:Pages> 32 <o:Words>218 2</o:Words>33 <o:Characters>124 42</o:Characters>32 <o:Words>2181</o:Words> 33 <o:Characters>12437</o:Characters> 34 34 <o:Company>Argonne National Laboratory</o:Company> 35 35 <o:Lines>103</o:Lines> 36 36 <o:Paragraphs>29</o:Paragraphs> 37 <o:CharactersWithSpaces>145 95</o:CharactersWithSpaces>38 <o:Version>1 5.00</o:Version>37 <o:CharactersWithSpaces>14589</o:CharactersWithSpaces> 38 <o:Version>16.00</o:Version> 39 39 </o:DocumentProperties> 40 40 <o:OfficeDocumentSettings> … … 48 48 <!--[if gte mso 9]><xml> 49 49 <w:WordDocument> 50 <w:Zoom>116</w:Zoom>51 50 <w:SpellingState>Clean</w:SpellingState> 52 51 <w:GrammarState>Clean</w:GrammarState> … … 1038 1037 mso-hansi-font-family:"Courier New"; 1039 1038 mso-bidi-font-family:"Courier New";} 1039 p.msonormal0, li.msonormal0, div.msonormal0 1040 {mso-style-name:msonormal; 1041 mso-style-noshow:yes; 1042 mso-style-priority:99; 1043 mso-style-unhide:no; 1044 mso-margin-top-alt:auto; 1045 margin-right:0in; 1046 mso-margin-bottom-alt:auto; 1047 margin-left:0in; 1048 mso-pagination:widow-orphan; 1049 font-size:12.0pt; 1050 font-family:"Times New Roman",serif; 1051 mso-fareast-font-family:"Times New Roman"; 1052 mso-fareast-theme-font:minor-fareast;} 1040 1053 span.DocumentMapChar 1041 1054 {mso-style-name:"Document Map Char"; … … 1071 1084 {mso-style-name:""; 1072 1085 mso-spl-e:yes;} 1073 span.GramE1074 {mso-style-name:"";1075 mso-gram-e:yes;}1076 1086 .MsoChpDefault 1077 1087 {mso-style-type:export-only; … … 1138 1148 <p class=MsoNormal>In this tutorial, data collected on the SNS instrument 1139 1149 POWGEN, are used. The calibration process will use the fitted positions of all 1140 visible peaks in a pattern of NIST SRM 660b La<sup>1 0</sup>B<sub>6</sub>1150 visible peaks in a pattern of NIST SRM 660b La<sup>11</sup>B<sub>6</sub> 1141 1151 (a=4.15689Å) obtained in a multiple single peak fit. The positions will be 1142 1152 compared to those expected from the known lattice parameters to establish the … … 1177 1187 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1178 1188 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; 1179 mso-bidi-theme-font:minor-latin'> /exercises/TOF Calibration</span></b> and then1189 mso-bidi-theme-font:minor-latin'>TOF Calibration/data</span></b> and then 1180 1190 select the file <b style='mso-bidi-font-weight:normal'><span style='font-family: 1181 1191 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: … … 1190 1200 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 1191 1201 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof: 1192 yes'>Yes</span></b><span style='mso-no-proof:yes'>. The file selection dialog 1193 willreappear; select the </span><b style='mso-bidi-font-weight:normal'><span1202 yes'>Yes</span></b><span style='mso-no-proof:yes'>. The file selection dialog will 1203 reappear; select the </span><b style='mso-bidi-font-weight:normal'><span 1194 1204 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1195 1205 mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>PGHR_60-2015A.prm</span></b><span 1196 1206 style='mso-no-proof:yes'> file. It contains the POWGEN instrument parameters 1197 1207 provided along with the data; this file is in the old GSAS iparm file format 1198 and does not include all the instrument parameters used by GSAS-II. This is what1199 w e will be improving in this tutorial.<o:p></o:p></span></p>1208 and does not include all the instrument parameters used by GSAS-II. This is 1209 what we will be improving in this tutorial.<o:p></o:p></span></p> 1200 1210 1201 1211 <p class=MsoNormal><span style='mso-no-proof:yes'><o:p> </o:p></span></p> … … 1461 1471 mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape 1462 1472 id="_x0000_i1025" type="#_x0000_t75" style='width:2in;height:18.75pt'> 1463 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 12.png"1473 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image027.png" 1464 1474 o:title="" chromakey="white"/> 1465 1475 </v:shape><![endif]--><![if !vml]><img width=192 height=25 1466 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 13.png"1476 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image028.png" 1467 1477 v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> 1468 1478 … … 1500 1510 mso-hansi-theme-font:minor-latin'>difC</span></b></span><b style='mso-bidi-font-weight: 1501 1511 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1502 minor-latin;mso-hansi-theme-font:minor-latin'> <span class=GramE>Refine</span></span></b>? 1503 <span class=GramE>box</span> and do <b style='mso-bidi-font-weight:normal'><span 1504 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1505 mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>; the plot 1506 will show the result of the calibration</p> 1512 minor-latin;mso-hansi-theme-font:minor-latin'> Refine</span></b>? box and do <b 1513 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 1514 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>; 1515 the plot will show the result of the calibration</p> 1507 1516 1508 1517 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape … … 1522 1531 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: 1523 1532 minor-latin'>Index Peak List</span></b>. Select that data item from the tree. 1524 The bad point is at the bottom of the table; uncheck the < span class=SpellE><b1525 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 1526 m so-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>use</span></b></span>1527 b ox for it. Go back to <b style='mso-bidi-font-weight:normal'><span1528 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1529 mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> and repeat <b 1530 style=' mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;1531 mso- ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>;1532 the plotwill look a lot better.</p>1533 The bad point is at the bottom of the table; uncheck the <b style='mso-bidi-font-weight: 1534 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1535 minor-latin;mso-hansi-theme-font:minor-latin'>use</span></b> box for it. Go 1536 back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 1537 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument 1538 Parameters</span></b> and repeat <b style='mso-bidi-font-weight:normal'><span 1539 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1540 mso-hansi-theme-font:minor-latin'>Operations/Calibrate</span></b>; the plot 1541 will look a lot better.</p> 1533 1542 1534 1543 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape … … 1635 1644 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1636 1645 mso-hansi-theme-font:minor-latin'>No. <span class=SpellE>coeff</span>.</span></b> 1637 <span class=GramE>to</span> <b style='mso-bidi-font-weight:normal'><span 1638 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 1639 mso-hansi-theme-font:minor-latin'>10</span></b>. This will select 10 fixed 1640 position points across the pattern between the limits located in constant <span 1641 class=GramE>log(</span>TOF) steps; this puts more points at the short TOF end 1646 to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 1647 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>. 1648 This will select 10 fixed position points across the pattern between the limits 1649 located in constant log(TOF) steps; this puts more points at the short TOF end 1642 1650 of the pattern where the background is changing most rapidly. Return to <b 1643 1651 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; … … 1741 1749 <p class=MsoNormal>You should realize that alpha largely affects the sharpness 1742 1750 of the leading TOF edge of each peak; larger values mean sharper front edges. 1743 Beta terms affect the trailing TOF edge in the same way. Sig terms affect the Gaussian1744 shape component of the peak profiles; larger values result in broader peaks. 1745 The coefficients describe the alpha, beta and sig values as follows:</p>1751 Beta terms affect the trailing TOF edge in the same way. Sig terms affect the 1752 Gaussian shape component of the peak profiles; larger values result in broader 1753 peaks. The coefficients describe the alpha, beta and sig values as follows:</p> 1746 1754 1747 1755 <p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style: … … 1761 1769 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1762 1770 type="#_x0000_t75" style='width:48pt;height:19.5pt'> 1763 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image02 7.png"1771 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image029.png" 1764 1772 o:title="" chromakey="white"/> 1765 1773 </v:shape><![endif]--><![if !vml]><img width=64 height=26 1766 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 28.png"1774 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image030.png" 1767 1775 v:shapes="_x0000_i1025"><![endif]></span><![endif]><span 1768 1776 style='mso-spacerun:yes'> </span><!--[if gte msEquation 12]><m:oMath><i … … 1806 1814 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1807 1815 type="#_x0000_t75" style='width:123pt;height:24pt'> 1808 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 29.png"1816 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image031.png" 1809 1817 o:title="" chromakey="white"/> 1810 1818 </v:shape><![endif]--><![if !vml]><img width=164 height=32 1811 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 0.png"1819 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image032.png" 1812 1820 v:shapes="_x0000_i1025"><![endif]></span><![endif]><span 1813 1821 style='mso-spacerun:yes'> </span><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span … … 1816 1824 normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: 1817 1825 normal'><span style='font-family:"Cambria Math",serif'><m:r><span 1818 style='mso-spacerun:yes'> 1819 style='mso-spacerun:yes'> </span></m:r><m:r>σ</m:r></span></i></m:e><m:sup><i1826 style='mso-spacerun:yes'> </span><span style='mso-spacerun:yes'> </span><span 1827 style='mso-spacerun:yes'> </span></m:r><m:r>σ</m:r></span></i></m:e><m:sup><i 1820 1828 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i 1821 1829 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span … … 1870 1878 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1871 1879 type="#_x0000_t75" style='width:183pt;height:25.5pt'> 1872 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 1.png"1880 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image033.png" 1873 1881 o:title="" chromakey="white"/> 1874 1882 </v:shape><![endif]--><![if !vml]><img width=244 height=34 1875 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 2.png"1883 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image034.png" 1876 1884 v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> 1877 1885 … … 1890 1898 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1891 1899 type="#_x0000_t75" style='width:12pt;height:14.25pt'> 1892 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 3.png"1900 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image035.png" 1893 1901 o:title="" chromakey="white"/> 1894 1902 </v:shape><![endif]--><![if !vml]><img width=16 height=19 1895 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 4.png"1903 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image036.png" 1896 1904 v:shapes="_x0000_i1025"><![endif]></span><![endif]>), beta-1 (<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span 1897 1905 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1905 1913 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1906 1914 type="#_x0000_t75" style='width:12pt;height:14.25pt'> 1907 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 5.png"1915 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image037.png" 1908 1916 o:title="" chromakey="white"/> 1909 1917 </v:shape><![endif]--><![if !vml]><img width=16 height=19 1910 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 6.png"1918 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image038.png" 1911 1919 v:shapes="_x0000_i1025"><![endif]></span><![endif]>), beta-q (<!--[if gte msEquation 12]><m:oMath><m:sSub><m:sSubPr><span 1912 1920 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1920 1928 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1921 1929 type="#_x0000_t75" style='width:12pt;height:15.75pt'> 1922 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image03 7.png"1930 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image039.png" 1923 1931 o:title="" chromakey="white"/> 1924 1932 </v:shape><![endif]--><![if !vml]><img width=16 height=21 1925 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 38.png"1933 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image040.png" 1926 1934 v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-0 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span 1927 1935 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1936 1944 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1937 1945 type="#_x0000_t75" style='width:13.5pt;height:14.25pt'> 1938 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 39.png"1946 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image041.png" 1939 1947 o:title="" chromakey="white"/> 1940 1948 </v:shape><![endif]--><![if !vml]><img width=18 height=19 1941 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image04 0.png"1949 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image042.png" 1942 1950 v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-1 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span 1943 1951 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1952 1960 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1953 1961 type="#_x0000_t75" style='width:13.5pt;height:14.25pt'> 1954 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image04 1.png"1962 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image043.png" 1955 1963 o:title="" chromakey="white"/> 1956 1964 </v:shape><![endif]--><![if !vml]><img width=18 height=19 1957 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image04 2.png"1965 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image044.png" 1958 1966 v:shapes="_x0000_i1025"><![endif]></span><![endif]>), sig-2 (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span 1959 1967 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1968 1976 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1969 1977 type="#_x0000_t75" style='width:13.5pt;height:14.25pt'> 1970 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image04 3.png"1978 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image045.png" 1971 1979 o:title="" chromakey="white"/> 1972 1980 </v:shape><![endif]--><![if !vml]><img width=18 height=19 1973 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image04 4.png"1981 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image046.png" 1974 1982 v:shapes="_x0000_i1025"><![endif]></span><![endif]>) and sig-q (<!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span 1975 1983 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; … … 1984 1992 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1985 1993 type="#_x0000_t75" style='width:13.5pt;height:15.75pt'> 1986 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 45.png"1994 <v:imagedata src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image058.png" 1987 1995 o:title="" chromakey="white"/> 1988 1996 </v:shape><![endif]--><![if !vml]><img width=18 height=21 1989 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image0 46.png"1997 src="Calibration%20of%20a%20TOF%20powder%20diffractometer_files/image059.png" 1990 1998 v:shapes="_x0000_i1025"><![endif]></span><![endif]>). Some of the values given 1991 1999 above are probably not appropriate; looking at the difference curve it appears … … 2013 2021 mso-hansi-theme-font:minor-latin'>sig-0</span></b> and <b style='mso-bidi-font-weight: 2014 2022 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 2015 minor-latin;mso-hansi-theme-font:minor-latin'>sig-q</span></b> to the refinement,2016 my residual improved slightly to <span class=SpellE>Rwp</span>=6.9%. A zoom 2017 view of some peaks around TOF~20000µs</p>2023 minor-latin;mso-hansi-theme-font:minor-latin'>sig-q</span></b> to the 2024 refinement, my residual improved slightly to <span class=SpellE>Rwp</span>=6.9%. 2025 A zoom view of some peaks around TOF~20000µs</p> 2018 2026 2019 2027 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape … … 2147 2155 and uncheck all the profile coefficient <b style='mso-bidi-font-weight:normal'><span 2148 2156 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 2149 mso-hansi-theme-font:minor-latin'>Refine?</span></b> <span class=GramE>boxes</span>;2150 then check those you varied at the beginning of the tutorial (<span 2151 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family: 2152 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: 2153 minor-latin'>difC</span></b></span>, <span class=SpellE><b style='mso-bidi-font-weight: 2154 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 2155 m inor-latin;mso-hansi-theme-font:minor-latin'>difA</span></b></span> & <b2157 mso-hansi-theme-font:minor-latin'>Refine?</span></b> boxes; then check those 2158 you varied at the beginning of the tutorial (<span class=SpellE><b 2159 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 2160 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>difC</span></b></span>, 2161 <span class=SpellE><b style='mso-bidi-font-weight:normal'><span 2162 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; 2163 mso-hansi-theme-font:minor-latin'>difA</span></b></span> & <b 2156 2164 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; 2157 2165 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Zero</span></b>).
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