| c_ID[I][J] | one element of array
@@ -1198,7 +1198,7 @@ data and scalar/vector/array data.
input, that could be an element of a vector or array. Likewise a
vector input could be a column of an array.
-
+
| Command | Input | Output | |
| thermo_style custom | global scalars | screen, log file | |
| dump custom | per-atom vectors | dump file | |
@@ -1448,36 +1448,36 @@ frictional walls, as well as triangulated surfaces.
4.18 Elastic constants
Elastic constants characterize the stiffness of a material. The formal
-definition is provided by the linear relation that holds between
-the stress and strain tensors in the limit of infinitesimal deformation.
-In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
+definition is provided by the linear relation that holds between the
+stress and strain tensors in the limit of infinitesimal deformation.
+In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
the repeated indices imply summation. s_ij are the elements of the
-symmetric stress tensor. e_kl are the elements of the symmetric
-strain tensor. C_ijkl are the elements of the fourth rank tensor
-of elastic constants. In three dimensions, this tensor has 3^4=81
-elements. Using Voigt notation, the tensor can be written
-as a 6x6 matrix, where C_ij is now the derivative of s_i
-w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
-that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
+symmetric stress tensor. e_kl are the elements of the symmetric strain
+tensor. C_ijkl are the elements of the fourth rank tensor of elastic
+constants. In three dimensions, this tensor has 3^4=81 elements. Using
+Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
+is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
+derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
+most 6*5/2 = 21 distinct elements.
At zero temperature, it is easy to estimate these derivatives by
-deforming the cell in one of the six directions using
-the command displace_box
-and measuring the change in the stress tensor. A general-purpose
-script that does this is given in the examples/elastic directory
-described in this section.
+deforming the cell in one of the six directions using the command
+displace_box and measuring the change in the
+stress tensor. A general-purpose script that does this is given in the
+examples/elastic directory described in this
+section.
-Calculating elastic constants at finite temperature is more challenging,
-because it is necessary to run a simulation that perfoms time averages
-of differential properties. One way to do this is to measure the change in
-average stress tensor in an NVT simulations when the cell volume undergoes a
-finite deformation. In order to balance
-the systematic and statistical errors in this method, the magnitude of the
-deformation must be chosen judiciously, and care must be taken to fully
-equilibrate the deformed cell before sampling the stress tensor. Another
-approach is to sample the triclinic cell fluctuations that occur in an
-NPT simulation. This method can also be slow to converge and requires
-careful post-processing (Shinoda)
+ Calculating elastic constants at finite temperature is more
+challenging, because it is necessary to run a simulation that perfoms
+time averages of differential properties. One way to do this is to
+measure the change in average stress tensor in an NVT simulations when
+the cell volume undergoes a finite deformation. In order to balance
+the systematic and statistical errors in this method, the magnitude of
+the deformation must be chosen judiciously, and care must be taken to
+fully equilibrate the deformed cell before sampling the stress
+tensor. Another approach is to sample the triclinic cell fluctuations
+that occur in an NPT simulation. This method can also be slow to
+converge and requires careful post-processing (Shinoda)
diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt
index ec5fc1fa34..efe7620dca 100644
--- a/doc/Section_howto.txt
+++ b/doc/Section_howto.txt
@@ -1437,36 +1437,36 @@ frictional walls, as well as triangulated surfaces.
4.18 Elastic constants :link(4_18),h4
Elastic constants characterize the stiffness of a material. The formal
-definition is provided by the linear relation that holds between
-the stress and strain tensors in the limit of infinitesimal deformation.
-In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
+definition is provided by the linear relation that holds between the
+stress and strain tensors in the limit of infinitesimal deformation.
+In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
the repeated indices imply summation. s_ij are the elements of the
-symmetric stress tensor. e_kl are the elements of the symmetric
-strain tensor. C_ijkl are the elements of the fourth rank tensor
-of elastic constants. In three dimensions, this tensor has 3^4=81
-elements. Using Voigt notation, the tensor can be written
-as a 6x6 matrix, where C_ij is now the derivative of s_i
-w.r.t. e_j. Because s_i is itself a derivative w.r.t. e_i, it follows
-that C_ij is also symmetric, with at most 6*5/2 = 21 distinct elements.
+symmetric stress tensor. e_kl are the elements of the symmetric strain
+tensor. C_ijkl are the elements of the fourth rank tensor of elastic
+constants. In three dimensions, this tensor has 3^4=81 elements. Using
+Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
+is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
+derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
+most 6*5/2 = 21 distinct elements.
At zero temperature, it is easy to estimate these derivatives by
-deforming the cell in one of the six directions using
-the command "displace_box"_displace_box.html
-and measuring the change in the stress tensor. A general-purpose
-script that does this is given in the examples/elastic directory
-described in "this section"_Section_example.html.
+deforming the cell in one of the six directions using the command
+"displace_box"_displace_box.html and measuring the change in the
+stress tensor. A general-purpose script that does this is given in the
+examples/elastic directory described in "this
+section"_Section_example.html.
-Calculating elastic constants at finite temperature is more challenging,
-because it is necessary to run a simulation that perfoms time averages
-of differential properties. One way to do this is to measure the change in
-average stress tensor in an NVT simulations when the cell volume undergoes a
-finite deformation. In order to balance
-the systematic and statistical errors in this method, the magnitude of the
-deformation must be chosen judiciously, and care must be taken to fully
-equilibrate the deformed cell before sampling the stress tensor. Another
-approach is to sample the triclinic cell fluctuations that occur in an
-NPT simulation. This method can also be slow to converge and requires
-careful post-processing "(Shinoda)"_#Shinoda
+Calculating elastic constants at finite temperature is more
+challenging, because it is necessary to run a simulation that perfoms
+time averages of differential properties. One way to do this is to
+measure the change in average stress tensor in an NVT simulations when
+the cell volume undergoes a finite deformation. In order to balance
+the systematic and statistical errors in this method, the magnitude of
+the deformation must be chosen judiciously, and care must be taken to
+fully equilibrate the deformed cell before sampling the stress
+tensor. Another approach is to sample the triclinic cell fluctuations
+that occur in an NPT simulation. This method can also be slow to
+converge and requires careful post-processing "(Shinoda)"_#Shinoda
:line
:line
|