[904] | 1 | <!-- ******************************************************** --> |
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| 2 | <!-- --> |
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| 3 | <!-- [History] --> |
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| 4 | <!-- Converted to DocBook: Katsuya Amako, Aug-2006 --> |
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| 5 | <!-- Changed by: Katsuya Amako, 14-Jul-1998 --> |
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| 6 | <!-- Proof read by: Joe Chuma, 29-Jun-1999 --> |
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| 7 | <!-- --> |
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| 8 | <!-- ******************************************************** --> |
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| 9 | |
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| 10 | |
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| 11 | <!-- ******************* Section (Level#1) ****************** --> |
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| 12 | <sect1 id="sect.Mate"> |
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| 13 | <title> |
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| 14 | Material |
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| 15 | </title> |
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| 16 | |
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| 17 | |
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| 18 | <!-- ******************* Section (Level#2) ****************** --> |
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| 19 | <sect2 id="sect.Mate.GenCons"> |
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| 20 | <title> |
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| 21 | General considerations |
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| 22 | </title> |
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| 23 | |
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| 24 | <para> |
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| 25 | In nature, materials (chemical compounds, mixtures) are made of |
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| 26 | elements, and elements are made of isotopes. Geant4 has three main |
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| 27 | classes designed to reflect this organization. Each of these |
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| 28 | classes has a table, which is a static data member, used to keep |
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| 29 | track of the instances of the respective classes created. |
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| 30 | |
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| 31 | <variablelist><title></title> |
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| 32 | <varlistentry> |
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| 33 | <term> |
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| 34 | <emphasis>G4Isotope</emphasis> |
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| 35 | </term> |
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| 36 | <listitem><para> |
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| 37 | This class describes the properties of atoms: atomic number, |
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| 38 | number of nucleons, mass per mole, etc. |
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| 39 | </para></listitem> |
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| 40 | </varlistentry> |
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| 41 | <varlistentry> |
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| 42 | <term> |
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| 43 | <emphasis>G4Element</emphasis> |
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| 44 | </term> |
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| 45 | <listitem><para> |
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| 46 | This class describes the properties of elements: effective |
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| 47 | atomic number, effective number of nucleons, effective mass per |
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| 48 | mole, number of isotopes, shell energy, and quantities like cross |
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| 49 | section per atom, etc. |
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| 50 | </para></listitem> |
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| 51 | </varlistentry> |
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| 52 | <varlistentry> |
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| 53 | <term> |
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| 54 | <emphasis>G4Material</emphasis> |
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| 55 | </term> |
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| 56 | <listitem><para> |
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| 57 | This class describes the macroscopic properties of matter: |
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| 58 | density, state, temperature, pressure, and macroscopic quantities |
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| 59 | like radiation length, mean free path, dE/dx, etc. |
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| 60 | </para></listitem> |
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| 61 | </varlistentry> |
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| 62 | </variablelist> |
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| 63 | </para> |
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| 64 | |
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| 65 | <para> |
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| 66 | Only the <emphasis>G4Material</emphasis> class is visible to the rest of the |
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| 67 | toolkit and used by the tracking, the geometry and the physics. It |
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| 68 | contains all the information relevant to its constituent elements |
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| 69 | and isotopes, while at the same time hiding their implementation |
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| 70 | details. |
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| 71 | </para> |
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| 72 | |
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| 73 | </sect2> |
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| 74 | |
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| 75 | |
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| 76 | <!-- ******************* Section (Level#2) ****************** --> |
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| 77 | <sect2 id="sect.Mate.Intro"> |
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| 78 | <title> |
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| 79 | Introduction to the Classes |
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| 80 | </title> |
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| 81 | |
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| 82 | |
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| 83 | <!-- ******************* Section (Level#3) ****************** --> |
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| 84 | <sect3 id="sect.Mate.Intro.Iso"> |
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| 85 | <title> |
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| 86 | G4Isotope |
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| 87 | </title> |
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| 88 | |
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| 89 | <para> |
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| 90 | A <emphasis>G4Isotope</emphasis> object has a name, atomic number, number of |
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| 91 | nucleons, mass per mole, and an index in the table. The constructor |
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| 92 | automatically stores "this" isotope in the isotopes table, which |
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| 93 | will assign it an index number. |
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| 94 | </para> |
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| 95 | |
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| 96 | </sect3> |
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| 97 | |
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| 98 | <!-- ******************* Section (Level#3) ****************** --> |
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| 99 | <sect3 id="sect.Mate.Intro.Ele"> |
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| 100 | <title> |
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| 101 | G4Element |
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| 102 | </title> |
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| 103 | |
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| 104 | <para> |
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| 105 | A <emphasis>G4Element</emphasis> object has a name, symbol, effective atomic |
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| 106 | number, effective number of nucleons, effective mass of a mole, an |
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| 107 | index in the elements table, the number of isotopes, a vector of |
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| 108 | pointers to such isotopes, and a vector of relative abundances |
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| 109 | referring to such isotopes (where relative abundance means the |
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| 110 | number of atoms per volume). In addition, the class has methods to |
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| 111 | add, one by one, the isotopes which are to form the element. |
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| 112 | </para> |
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| 113 | |
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| 114 | <para> |
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| 115 | A <emphasis>G4Element</emphasis> object can be constructed by directly |
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| 116 | providing the effective atomic number, effective number of |
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| 117 | nucleons, and effective mass of a mole, if the user explicitly |
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| 118 | wants to do so. Alternatively, a <emphasis>G4Element</emphasis> object can be |
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| 119 | constructed by declaring the number of isotopes of which it will be |
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| 120 | composed. The constructor will "new" a vector of pointers to |
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| 121 | <emphasis>G4Isotopes</emphasis> and a vector of doubles to store their relative |
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| 122 | abundances. Finally, the method to add an isotope must be invoked |
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| 123 | for each of the desired (pre-existing) isotope objects, providing |
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| 124 | their addresses and relative abundances. At the last isotope entry, |
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| 125 | the system will automatically compute the effective atomic number, |
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| 126 | effective number of nucleons and effective mass of a mole, and will |
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| 127 | store "this" element in the elements table. |
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| 128 | </para> |
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| 129 | |
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| 130 | <para> |
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| 131 | A few quantities, with physical meaning or not, which are |
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| 132 | constant in a given element, are computed and stored here as |
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| 133 | "derived data members". |
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| 134 | </para> |
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| 135 | |
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| 136 | <para> |
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| 137 | Using the internal Geant4 database, a <emphasis>G4Element</emphasis> can be accessed |
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| 138 | by atomic number or by atomic symbol ("Al", "Fe", "Pb"...). In that |
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| 139 | case <emphasis>G4Element</emphasis> will be found from the list of existing elements or |
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| 140 | will be constructed using data from the Geant4 database, which is |
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| 141 | derived from the |
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| 142 | <ulink url="http://physics.nist.gov/PhysRefData/Compositions/index.html">NIST database |
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| 143 | of elements and isotope compositions</ulink>. |
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| 144 | Thus, the natural isotope composition can be built by default. |
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| 145 | The same element |
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| 146 | can be created as using the NIST database with the |
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| 147 | natural composition of isotopes |
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| 148 | and from scratch in user code with user defined isotope composition. |
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| 149 | </para> |
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| 150 | |
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| 151 | </sect3> |
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| 152 | |
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| 153 | <!-- ******************* Section (Level#3) ****************** --> |
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| 154 | <sect3 id="sect.Mate.Intro.Mate"> |
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| 155 | <title> |
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| 156 | G4Material |
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| 157 | </title> |
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| 158 | |
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| 159 | <para> |
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| 160 | A <emphasis>G4Material</emphasis> object has a name, density, physical state, |
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| 161 | temperature and pressure (by default the standard conditions), the |
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| 162 | number of elements and a vector of pointers to such elements, a |
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| 163 | vector of the fraction of mass for each element, a vector of the |
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| 164 | atoms (or molecules) numbers of each element, and an index in the |
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| 165 | materials table. In addition, the class has methods to add, one by |
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| 166 | one, the elements which will comprise the material. |
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| 167 | </para> |
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| 168 | |
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| 169 | <para> |
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| 170 | A <emphasis>G4Material</emphasis> object can be constructed by directly |
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| 171 | providing the resulting effective numbers, if the user explicitly |
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| 172 | wants to do so (an underlying element will be created with these |
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| 173 | numbers). Alternatively, a <emphasis>G4Material</emphasis> object can be |
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| 174 | constructed by declaring the number of elements of which it will be |
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| 175 | composed. The constructor will "new" a vector of pointers to |
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| 176 | <emphasis>G4Element</emphasis> and a vector of doubles to store their fraction of |
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| 177 | mass. Finally, the method to add an element must be invoked for |
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| 178 | each of the desired (pre-existing) element objects, providing their |
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| 179 | addresses and mass fractions. At the last element entry, the system |
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| 180 | will automatically compute the vector of the number of atoms of |
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| 181 | each element per volume, the total number of electrons per volume, |
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| 182 | and will store "this" material in the materials table. In the same |
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| 183 | way, a material can be constructed as a mixture of other materials |
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| 184 | and elements. |
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| 185 | </para> |
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| 186 | |
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| 187 | <para> |
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| 188 | It should be noted that if the user provides the number of atoms |
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| 189 | (or molecules) for each element comprising the chemical compound, |
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| 190 | the system automatically computes the mass fraction. A few |
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| 191 | quantities, with physical meaning or not, which are constant in a |
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| 192 | given material, are computed and stored here as "derived data |
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| 193 | members". |
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| 194 | </para> |
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| 195 | |
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| 196 | <para> |
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| 197 | Some materials are included in the internal Geant4 database, |
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| 198 | which were derived from the |
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| 199 | <ulink url="http://physics.nist.gov/PhysRefData/Star/Text/method.html">NIST database |
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| 200 | of material properties</ulink>. |
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| 201 | Additionally a number of materials friquently used in HEP is |
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| 202 | included in the database. Materials are interrogated or constructed |
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| 203 | by their <emphasis>names</emphasis> (<xref linkend="sect.G4MatrDb" />). |
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| 204 | There are UI commands for the material category, which provide |
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| 205 | an interactive access to the database. If material is created |
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| 206 | using the NIST database by it will |
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| 207 | consist by default of elements with the natural composition of isotopes. |
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| 208 | </para> |
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| 209 | |
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| 210 | </sect3> |
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| 211 | |
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| 212 | <!-- ******************* Section (Level#3) ****************** --> |
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| 213 | <sect3 id="sect.Mate.Intro.Fin"> |
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| 214 | <title> |
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| 215 | Final Considerations |
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| 216 | </title> |
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| 217 | |
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| 218 | <para> |
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| 219 | The classes will automatically decide |
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| 220 | if the total of the mass fractions is correct, and perform the |
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| 221 | necessary checks. The main reason why a fixed index is kept as a |
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| 222 | data member is that many cross section and energy tables will be |
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| 223 | built in the physics processes "by rows of materials (or elements, |
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| 224 | or even isotopes)". The tracking gives the physics process the |
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| 225 | address of a material object (the material of the current volume). |
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| 226 | If the material has an index according to which the cross section |
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| 227 | table has been built, then direct access is available when a number |
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| 228 | in such a table must be accessed. We get directly to the correct |
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| 229 | row, and the energy of the particle will tell us the column. |
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| 230 | Without such an index, every access to the cross section or energy |
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| 231 | tables would imply a search to get to the correct material's row. |
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| 232 | More details will be given in the section on processes. |
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| 233 | </para> |
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| 234 | |
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| 235 | <para> |
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| 236 | Isotopes, elements and materials must be instantiated dynamically |
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| 237 | in the user application; they are automatically registered in |
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| 238 | internal stores and the system takes care to free the memory |
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| 239 | allocated at the end of the job. |
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| 240 | </para> |
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| 241 | |
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| 242 | </sect3> |
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| 243 | </sect2> |
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| 244 | |
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| 245 | |
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| 246 | <!-- ******************* Section (Level#2) ****************** --> |
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| 247 | <sect2 id="sect.Mate.Recep"> |
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| 248 | <title> |
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| 249 | Recipes for Building Elements and Materials |
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| 250 | </title> |
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| 251 | |
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| 252 | <para> |
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| 253 | <xref linkend="programlist_Mate_1" /> illustrates the different ways to define |
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| 254 | materials. |
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| 255 | </para> |
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| 256 | |
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| 257 | <example id="programlist_Mate_1"> |
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| 258 | <title> |
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| 259 | A program which illustrates the different ways to define materials. |
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| 260 | </title> |
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| 261 | |
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| 262 | <programlisting> |
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| 263 | #include "G4Isotope.hh" |
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| 264 | #include "G4Element.hh" |
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| 265 | #include "G4Material.hh" |
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| 266 | #include "G4UnitsTable.hh" |
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| 267 | |
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| 268 | int main() { |
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| 269 | G4String name, symbol; // a=mass of a mole; |
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| 270 | G4double a, z, density; // z=mean number of protons; |
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| 271 | G4int iz, n; // iz=nb of protons in an isotope; |
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| 272 | // n=nb of nucleons in an isotope; |
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| 273 | G4int ncomponents, natoms; |
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| 274 | G4double abundance, fractionmass; |
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| 275 | G4double temperature, pressure; |
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| 276 | |
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| 277 | G4UnitDefinition::BuildUnitsTable(); |
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| 278 | |
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| 279 | // define Elements |
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| 280 | a = 1.01*g/mole; |
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| 281 | G4Element* elH = new G4Element(name="Hydrogen",symbol="H" , z= 1., a); |
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| 282 | |
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| 283 | a = 12.01*g/mole; |
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| 284 | G4Element* elC = new G4Element(name="Carbon" ,symbol="C" , z= 6., a); |
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| 285 | |
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| 286 | a = 14.01*g/mole; |
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| 287 | G4Element* elN = new G4Element(name="Nitrogen",symbol="N" , z= 7., a); |
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| 288 | |
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| 289 | a = 16.00*g/mole; |
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| 290 | G4Element* elO = new G4Element(name="Oxygen" ,symbol="O" , z= 8., a); |
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| 291 | |
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| 292 | a = 28.09*g/mole; |
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| 293 | G4Element* elSi = new G4Element(name="Silicon", symbol="Si", z=14., a); |
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| 294 | |
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| 295 | a = 55.85*g/mole; |
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| 296 | G4Element* elFe = new G4Element(name="Iron" ,symbol="Fe", z=26., a); |
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| 297 | |
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| 298 | a = 183.84*g/mole; |
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| 299 | G4Element* elW = new G4Element(name="Tungsten" ,symbol="W", z=74., a); |
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| 300 | |
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| 301 | a = 207.20*g/mole; |
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| 302 | G4Element* elPb = new G4Element(name="Lead" ,symbol="Pb", z=82., a); |
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| 303 | |
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| 304 | // define an Element from isotopes, by relative abundance |
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| 305 | G4Isotope* U5 = new G4Isotope(name="U235", iz=92, n=235, a=235.01*g/mole); |
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| 306 | G4Isotope* U8 = new G4Isotope(name="U238", iz=92, n=238, a=238.03*g/mole); |
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| 307 | |
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| 308 | G4Element* elU = new G4Element(name="enriched Uranium", symbol="U", ncomponents=2); |
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| 309 | elU->AddIsotope(U5, abundance= 90.*perCent); |
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| 310 | elU->AddIsotope(U8, abundance= 10.*perCent); |
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| 311 | |
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| 312 | cout << *(G4Isotope::GetIsotopeTable()) << endl; |
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| 313 | cout << *(G4Element::GetElementTable()) << endl; |
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| 314 | </programlisting> |
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| 315 | </example> |
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| 316 | <informalexample> |
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| 317 | <programlisting> |
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| 318 | // define simple materials |
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| 319 | density = 2.700*g/cm3; |
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| 320 | a = 26.98*g/mole; |
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| 321 | G4Material* Al = new G4Material(name="Aluminum", z=13., a, density); |
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| 322 | |
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| 323 | density = 1.390*g/cm3; |
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| 324 | a = 39.95*g/mole; |
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| 325 | vG4Material* lAr = new G4Material(name="liquidArgon", z=18., a, density); |
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| 326 | |
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| 327 | density = 8.960*g/cm3; |
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| 328 | a = 63.55*g/mole; |
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| 329 | G4Material* Cu = new G4Material(name="Copper" , z=29., a, density); |
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| 330 | |
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| 331 | // define a material from elements. case 1: chemical molecule |
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| 332 | density = 1.000*g/cm3; |
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| 333 | G4Material* H2O = new G4Material(name="Water", density, ncomponents=2); |
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| 334 | H2O->AddElement(elH, natoms=2); |
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| 335 | H2O->AddElement(elO, natoms=1); |
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| 336 | |
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| 337 | density = 1.032*g/cm3; |
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| 338 | G4Material* Sci = new G4Material(name="Scintillator", density, ncomponents=2); |
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| 339 | Sci->AddElement(elC, natoms=9); |
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| 340 | Sci->AddElement(elH, natoms=10); |
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| 341 | |
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| 342 | density = 2.200*g/cm3; |
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| 343 | G4Material* SiO2 = new G4Material(name="quartz", density, ncomponents=2); |
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| 344 | SiO2->AddElement(elSi, natoms=1); |
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| 345 | SiO2->AddElement(elO , natoms=2); |
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| 346 | |
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| 347 | density = 8.280*g/cm3; |
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| 348 | G4Material* PbWO4= new G4Material(name="PbWO4", density, ncomponents=3); |
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| 349 | PbWO4->AddElement(elO , natoms=4); |
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| 350 | PbWO4->AddElement(elW , natoms=1); |
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| 351 | PbWO4->AddElement(elPb, natoms=1); |
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| 352 | |
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| 353 | // define a material from elements. case 2: mixture by fractional mass |
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| 354 | density = 1.290*mg/cm3; |
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| 355 | G4Material* Air = new G4Material(name="Air " , density, ncomponents=2); |
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| 356 | Air->AddElement(elN, fractionmass=0.7); |
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| 357 | Air->AddElement(elO, fractionmass=0.3); |
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| 358 | |
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| 359 | // define a material from elements and/or others materials (mixture of mixtures) |
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| 360 | density = 0.200*g/cm3; |
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| 361 | G4Material* Aerog = new G4Material(name="Aerogel", density, ncomponents=3); |
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| 362 | Aerog->AddMaterial(SiO2, fractionmass=62.5*perCent); |
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| 363 | Aerog->AddMaterial(H2O , fractionmass=37.4*perCent); |
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| 364 | Aerog->AddElement (elC , fractionmass= 0.1*perCent); |
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| 365 | </programlisting> |
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| 366 | </informalexample> |
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| 367 | <informalexample> |
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| 368 | <programlisting> |
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| 369 | // examples of gas in non STP conditions |
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| 370 | density = 27.*mg/cm3; |
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| 371 | pressure = 50.*atmosphere; |
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| 372 | temperature = 325.*kelvin; |
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| 373 | G4Material* CO2 = new G4Material(name="Carbonic gas", density, ncomponents=2, |
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| 374 | kStateGas,temperature,pressure); |
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| 375 | CO2->AddElement(elC, natoms=1); |
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| 376 | CO2->AddElement(elO, natoms=2); |
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| 377 | |
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| 378 | density = 0.3*mg/cm3; |
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| 379 | pressure = 2.*atmosphere; |
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| 380 | temperature = 500.*kelvin; |
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| 381 | G4Material* steam = new G4Material(name="Water steam ", density, ncomponents=1, |
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| 382 | kStateGas,temperature,pressure); |
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| 383 | steam->AddMaterial(H2O, fractionmass=1.); |
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| 384 | |
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| 385 | // What about vacuum ? Vacuum is an ordinary gas with very low density |
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| 386 | density = universe_mean_density; //from PhysicalConstants.h |
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| 387 | pressure = 1.e-19*pascal; |
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| 388 | temperature = 0.1*kelvin; |
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| 389 | new G4Material(name="Galactic", z=1., a=1.01*g/mole, density, |
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| 390 | kStateGas,temperature,pressure); |
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| 391 | |
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| 392 | density = 1.e-5*g/cm3; |
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| 393 | pressure = 2.e-2*bar; |
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| 394 | temperature = STP_Temperature; //from PhysicalConstants.h |
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| 395 | G4Material* beam = new G4Material(name="Beam ", density, ncomponents=1, |
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| 396 | kStateGas,temperature,pressure); |
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| 397 | beam->AddMaterial(Air, fractionmass=1.); |
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| 398 | |
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| 399 | // print the table of materials |
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| 400 | G4cout << *(G4Material::GetMaterialTable()) << endl; |
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| 401 | |
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| 402 | return EXIT_SUCCESS; |
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| 403 | } |
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| 404 | </programlisting> |
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| 405 | </informalexample> |
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| 406 | <para> |
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| 407 | As can be seen in the later examples, a material has a state: |
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| 408 | solid (the default), liquid, or gas. The constructor checks the |
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| 409 | density and automatically sets the state to gas below a given |
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| 410 | threshold (10 mg/cm3). |
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| 411 | </para> |
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| 412 | |
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| 413 | <para> |
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| 414 | In the case of a gas, one may specify the temperature and |
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| 415 | pressure. The defaults are STP conditions defined in |
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| 416 | <literal>PhysicalConstants.hh</literal>. |
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| 417 | </para> |
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| 418 | |
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| 419 | <para> |
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| 420 | An element must have the number of nucleons >= number of |
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| 421 | protons >= 1. |
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| 422 | </para> |
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| 423 | |
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| 424 | <para> |
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| 425 | A material must have non-zero values of density, temperature and |
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| 426 | pressure. |
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| 427 | </para> |
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| 428 | |
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| 429 | <para> |
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| 430 | Materials can also be defined using the internal Geant4 |
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| 431 | database. <xref linkend="programlist_Mate_2" /> illustrates |
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| 432 | how to do this for the same materials used in |
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| 433 | <xref linkend="programlist_Mate_1" />. |
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| 434 | There are also UI commands which allow the database to be accessed. |
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| 435 | <emphasis>The list of currently avalable material names</emphasis> |
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| 436 | (<xref linkend="sect.G4MatrDb" />) is extended permanetly. |
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| 437 | </para> |
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| 438 | |
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| 439 | <example id="programlist_Mate_2"> |
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| 440 | <title> |
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| 441 | A program which shows how to define materials from the internal database. |
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| 442 | </title> |
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| 443 | |
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| 444 | <programlisting> |
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| 445 | #include "globals.hh" |
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| 446 | #include "G4Material.hh" |
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| 447 | #include "G4NistManager.hh" |
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| 448 | |
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| 449 | int main() { |
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| 450 | G4NistManager* man = G4NistManager::Instance(); |
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| 451 | man->SetVerbose(1); |
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| 452 | |
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| 453 | // define elements |
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| 454 | G4Element* C = man->FindOrBuildElement("C"); |
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| 455 | G4Element* Pb = man->FindOrBuildMaterial("Pb"); |
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| 456 | |
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| 457 | // define pure NIST materials |
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| 458 | G4Material* Al = man->FindOrBuildMaterial("G4_Al"); |
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| 459 | G4Material* Cu = man->FindOrBuildMaterial("G4_Cu"); |
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| 460 | |
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| 461 | // define NIST materials |
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| 462 | G4Material* H2O = man->FindOrBuildMaterial("G4_WATER"); |
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| 463 | G4Material* Sci = man->FindOrBuildMaterial("G4_PLASTIC_SC_VINYLTOLUENE"); |
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| 464 | G4Material* SiO2 = man->FindOrBuildMaterial("G4_SILICON_DIOXIDE"); |
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| 465 | G4Material* Air = man->FindOrBuildMaterial("G4_AIR"); |
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| 466 | |
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| 467 | // HEP materials |
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| 468 | G4Material* PbWO4 = man->FindOrBuildMaterial("G4_PbWO4"); |
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| 469 | G4Material* lAr = man->FindOrBuildMaterial("G4_lAr"); |
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| 470 | G4Material* vac = man->FindOrBuildMaterial("G4_Galactic"); |
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| 471 | |
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| 472 | // define gas material at non STP conditions (T = 120K, P=0.5atm) |
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| 473 | G4Material* coldAr = man->ConstructNewGasdMaterial("ColdAr","G4_Ar",120.*kelvin,0.5*atmosphere); |
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| 474 | |
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| 475 | // print the table of materials |
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| 476 | G4cout << *(G4Material::GetMaterialTable()) << endl; |
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| 477 | |
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| 478 | return EXIT_SUCCESS; |
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| 479 | } |
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| 480 | </programlisting> |
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| 481 | </example> |
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| 482 | |
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| 483 | </sect2> |
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| 484 | |
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| 485 | |
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| 486 | <!-- ******************* Section (Level#2) ****************** --> |
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| 487 | <sect2 id="sect.Mate.Tables"> |
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| 488 | <title> |
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| 489 | The Tables |
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| 490 | </title> |
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| 491 | |
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| 492 | <!-- ******************* Section (Level#3) ****************** --> |
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| 493 | <sect3 id="sect.Mate.Tables.PrintCons"> |
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| 494 | <title> |
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| 495 | Print a constituent |
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| 496 | </title> |
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| 497 | |
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| 498 | <para> |
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| 499 | The following shows how to print a constituent: |
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| 500 | |
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| 501 | <informalexample> |
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| 502 | <programlisting> |
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| 503 | G4cout << elU << endl; |
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| 504 | G4cout << Air << endl; |
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| 505 | </programlisting> |
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| 506 | </informalexample> |
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| 507 | </para> |
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| 508 | |
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| 509 | </sect3> |
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| 510 | |
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| 511 | <!-- ******************* Section (Level#3) ****************** --> |
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| 512 | <sect3 id="sect.Mate.Tables.PrintTab"> |
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| 513 | <title> |
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| 514 | Print the table of materials |
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| 515 | </title> |
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| 516 | |
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| 517 | <para> |
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| 518 | The following shows how to print the table of materials: |
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| 519 | |
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| 520 | <informalexample> |
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| 521 | <programlisting> |
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| 522 | G4cout << *(G4Material::GetMaterialTable()) << endl; |
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| 523 | </programlisting> |
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| 524 | </informalexample> |
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| 525 | </para> |
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| 526 | |
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| 527 | |
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| 528 | </sect3> |
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| 529 | </sect2> |
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| 530 | </sect1> |
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