From a47a87c216e28d962800827a2e031eefcc9a33d1 Mon Sep 17 00:00:00 2001 From: sjplimp Date: Mon, 29 Jan 2007 23:28:45 +0000 Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@252 f3b2605a-c512-4ea7-a41b-209d697bcdaa --- doc/Section_commands.html | 4 +- doc/Section_commands.txt | 1 + doc/pair_coeff.html | 1 + doc/pair_coeff.txt | 1 + doc/pair_style.html | 2 + doc/pair_style.txt | 2 + doc/pair_style_dpd.html | 6 ++ doc/pair_style_dpd.txt | 5 + doc/pair_style_eam.html | 10 +- doc/pair_style_eam.txt | 10 +- doc/pair_style_meam.html | 207 ++++++++++++++++++++++++++++++++++++++ doc/pair_style_meam.txt | 200 ++++++++++++++++++++++++++++++++++++ 12 files changed, 437 insertions(+), 12 deletions(-) create mode 100644 doc/pair_style_meam.html create mode 100644 doc/pair_style_meam.txt diff --git a/doc/Section_commands.html b/doc/Section_commands.html index c3a0356f3d..ba27ef7aaa 100644 --- a/doc/Section_commands.html +++ b/doc/Section_commands.html @@ -326,8 +326,8 @@ description: lj/charmm/coul/charmmlj/charmm/coul/charmm/implicitlj/charmm/coul/longlj/class2 lj/class2/coul/cutlj/class2/coul/longlj/cutlj/cut/coul/cut lj/cut/coul/debyelj/cut/coul/longlj/cut/coul/long/tip4plj/expand -lj/smoothmorsesoftsw -tabletersoffyukawa +lj/smoothmeammorsesoft +swtabletersoffyukawa

Bond styles. See the bond_style command for an diff --git a/doc/Section_commands.txt b/doc/Section_commands.txt index c5041bd9c8..f2eb2a32bb 100644 --- a/doc/Section_commands.txt +++ b/doc/Section_commands.txt @@ -433,6 +433,7 @@ description: "lj/cut/coul/long/tip4p"_pair_style_lj.html, "lj/expand"_pair_style_lj_expand.html, "lj/smooth"_pair_style_lj_smooth.html, +"meam"_pair_style_meam.html, "morse"_pair_style_morse.html, "soft"_pair_style_soft.html, "sw"_pair_style_sw.html, diff --git a/doc/pair_coeff.html b/doc/pair_coeff.html index 6ea3ed4cda..0c121c3221 100644 --- a/doc/pair_coeff.html +++ b/doc/pair_coeff.html @@ -110,6 +110,7 @@ the pair_style command, and coefficients specified by the associated

  • pair_style lj/cut/coul/long/tip4p - LJ with long-range Coulomb for TIP4P water
  • pair_style lj/expand - Lennard-Jones for variable size particles
  • pair_style lj/smooth - smoothed Lennard-Jones potential +
  • pair_style meam - modified embedded atom method (MEAM)
  • pair_style morse - Morse potential
  • pair_style soft - Soft (cosine) potential
  • pair_style sw - Stillinger-Weber 3-body potential diff --git a/doc/pair_coeff.txt b/doc/pair_coeff.txt index 4fb3ddfe98..97618acbbf 100644 --- a/doc/pair_coeff.txt +++ b/doc/pair_coeff.txt @@ -107,6 +107,7 @@ the pair_style command, and coefficients specified by the associated "pair_style lj/cut/coul/long/tip4p"_pair_style_lj.html - LJ with long-range Coulomb for TIP4P water "pair_style lj/expand"_pair_style_lj_expand.html - Lennard-Jones for variable size particles "pair_style lj/smooth"_pair_style_lj_smooth.html - smoothed Lennard-Jones potential +"pair_style meam"_pair_style_meam.html - modified embedded atom method (MEAM) "pair_style morse"_pair_style_morse.html - Morse potential "pair_style soft"_pair_style_soft.html - Soft (cosine) potential "pair_style sw"_pair_style_sw.html - Stillinger-Weber 3-body potential diff --git a/doc/pair_style.html b/doc/pair_style.html index 0999112c2c..a0465ad058 100644 --- a/doc/pair_style.html +++ b/doc/pair_style.html @@ -29,6 +29,7 @@
  • lj/cut or lj/cut/coul/cut or lj/cut/coul/debye or lj/cut/coul/long or lj/cut/coul/long/tip4p
  • lj/expand
  • lj/smooth +
  • meam
  • morse
  • soft
  • sw @@ -126,6 +127,7 @@ the pair_style command, and coefficients specified by the associated
  • pair_style lj/cut/coul/long/tip4p - LJ with long-range Coulomb for TIP4P water
  • pair_style lj/expand - Lennard-Jones for variable size particles
  • pair_style lj/smooth - smoothed Lennard-Jones potential +
  • pair_style meam - modified embedded atom method (MEAM)
  • pair_style morse - Morse potential
  • pair_style soft - Soft (cosine) potential
  • pair_style sw - Stillinger-Weber 3-body potential diff --git a/doc/pair_style.txt b/doc/pair_style.txt index e311b404a8..02eabb7238 100644 --- a/doc/pair_style.txt +++ b/doc/pair_style.txt @@ -26,6 +26,7 @@ style = one of the following :ulb,l {lj/cut} or {lj/cut/coul/cut} or {lj/cut/coul/debye} or {lj/cut/coul/long} or {lj/cut/coul/long/tip4p} {lj/expand} {lj/smooth} +{meam} {morse} {soft} {sw} @@ -123,6 +124,7 @@ the pair_style command, and coefficients specified by the associated "pair_style lj/cut/coul/long/tip4p"_pair_style_lj.html - LJ with long-range Coulomb for TIP4P water "pair_style lj/expand"_pair_style_lj_expand.html - Lennard-Jones for variable size particles "pair_style lj/smooth"_pair_style_lj_smooth.html - smoothed Lennard-Jones potential +"pair_style meam"_pair_style_meam.html - modified embedded atom method (MEAM) "pair_style morse"_pair_style_morse.html - Morse potential "pair_style soft"_pair_style_soft.html - Soft (cosine) potential "pair_style sw"_pair_style_sw.html - Stillinger-Weber 3-body potential diff --git a/doc/pair_style_dpd.html b/doc/pair_style_dpd.html index 3814a8cad6..851a8a0bd3 100644 --- a/doc/pair_style_dpd.html +++ b/doc/pair_style_dpd.html @@ -72,4 +72,10 @@ pairs must be specified explicitly.

    Default: none

    +
    + + + +

    (Groot) Groot and Warren, J Chem Phys, 107, 4423-35 (1997). +

    diff --git a/doc/pair_style_dpd.txt b/doc/pair_style_dpd.txt index 5cbb8cb980..a2fdb47ddc 100644 --- a/doc/pair_style_dpd.txt +++ b/doc/pair_style_dpd.txt @@ -68,3 +68,8 @@ pairs must be specified explicitly. "pair_coeff"_pair_coeff.html [Default:] none + +:line + +:link(Groot) +[(Groot)] Groot and Warren, J Chem Phys, 107, 4423-35 (1997). diff --git a/doc/pair_style_eam.html b/doc/pair_style_eam.html index 00452fcd0b..ca2c94d78d 100644 --- a/doc/pair_style_eam.html +++ b/doc/pair_style_eam.html @@ -51,11 +51,11 @@ within the cutoff distance.

    The cutoff distance and the tabulated values of the functionals F, rho, and phi are listed in one or more files which are specified by the pair_coeff command. These are ASCII text files -in a DYNAMO-style format which is described in the documentation for -the pair_coeff command. DYNAMO is a serial MD code -Several DYNAMO potential files for different metals are included in -the "potentials" directory of the LAMMPS distribution. All of these -are paremeterized in terms of LAMMPS metal units. +in a DYNAMO-style format which is described below. DYNAMO is a serial +MD code. Several DYNAMO potential files for different metals are +included in the "potentials" directory of the LAMMPS distribution. +All of these are parameterized in terms of LAMMPS metal +units.

    IMPORTANT NOTE: The eam style reads single-element EAM potentials in the DYNAMO funcfl format. Either single element or alloy systems diff --git a/doc/pair_style_eam.txt b/doc/pair_style_eam.txt index 7cf6f7a10e..10a742d2e2 100644 --- a/doc/pair_style_eam.txt +++ b/doc/pair_style_eam.txt @@ -46,11 +46,11 @@ within the cutoff distance. The cutoff distance and the tabulated values of the functionals F, rho, and phi are listed in one or more files which are specified by the "pair_coeff"_pair_coeff.html command. These are ASCII text files -in a DYNAMO-style format which is described in the documentation for -the "pair_coeff"_pair_coeff.html command. DYNAMO is a serial MD code -Several DYNAMO potential files for different metals are included in -the "potentials" directory of the LAMMPS distribution. All of these -are paremeterized in terms of LAMMPS "metal units"_units.html. +in a DYNAMO-style format which is described below. DYNAMO is a serial +MD code. Several DYNAMO potential files for different metals are +included in the "potentials" directory of the LAMMPS distribution. +All of these are parameterized in terms of LAMMPS "metal +units"_units.html. IMPORTANT NOTE: The {eam} style reads single-element EAM potentials in the DYNAMO {funcfl} format. Either single element or alloy systems diff --git a/doc/pair_style_meam.html b/doc/pair_style_meam.html new file mode 100644 index 0000000000..95eec0a590 --- /dev/null +++ b/doc/pair_style_meam.html @@ -0,0 +1,207 @@ + +

    LAMMPS WWW Site - LAMMPS Documentation - LAMMPS Commands +
    + + + + + + +
    + +

    pair_style meam command +

    +

    Syntax: +

    +
    pair_style mean 
    +
    +

    Examples: +

    +
    pair_style meam
    +pair_coeff * * ../potentials/library.meam Si ../potentials/si.meam Si
    +pair_coeff * * ../potentials/library.meam Ni Al NULL Ni Al Ni Ni 
    +
    +

    Description: +

    +

    Style meam computes pairwise interactions for a variety of materials +using modified embedded-atom method (MEAM) potentials +(Baskes). Conceptually, it is an extension to the original +EAM potentials which adds angular forces. It is +thus suitable for modeling metals and alloys with fcc, bcc, hcp and +diamond cubic structures, as well as covalently bonded materials like +silicon and carbon. +

    +

    In the MEAM formulation, the total energy E of a system of atoms is +given by: +

    +
    +
    +

    where F is the embedding energy which is a function of the atomic +electron density rho, and phi is a pair potential interaction. The +pair interaction is summed over all neighbors J of atom I within the +cutoff distance. As with EAM, the multi-body nature of the MEAM +potential is a result of the embedding energy term. Details of the +computation of the embedding and pair energies, as implemented in +LAMMPS, are given in (Gullet) and references therein. +

    +

    The various parameters in the MEAM formulas are listed in two files +which are specified by the pair_coeff command. +These are ASCII text files in a format consistent with other MD codes +that implement MEAM potentials, such as the serial DYNAMO code and +Warp. Several MEAM potential files with parameters for different +materials are included in the "potentials" directory of the LAMMPS +distribution with a ",meam" suffix. All of these are parameterized in +terms of LAMMPS metal units. +

    +

    Note that unlike for other potentials, cutoffs for MEAM potentials are +not set in the pair_style or pair_coeff command; they are specified in +the MEAM potential files themselves. +

    +

    Only a single pair_coeff command is used with the meam style which +specifies two MEAM files and the element(s) to extract information +for. The MEAM elements are mapped to LAMMPS atom types by specifying +N additional arguments after the 2nd filename in the pair_coeff +command, where N is the number of LAMMPS atom types: +

    + +

    As an example, the potentials/library.meam file has generic MEAM +settings for a variety of elements. The potentials/sic.meam file has +specific parameter settings for a Si and C alloy system. If your +LAMMPS simulation has 4 atoms types and you want the 1st 3 to be Si, +and the 4th to be C, you would use the following pair_coeff command: +

    +
    pair_coeff * * library.meam Si C sic.meam Si Si Si C 
    +
    +

    The 1st 2 arguments must be * * so as to span all LAMMPS atom types. +The two filenames are for the library and parameter file respectively. +The Si and C arguments (between the file names) are the two elements +for which info will be extracted from the library file. The first +three trailing Si arguments map LAMMPS atom types 1,2,3 to the MEAM Si +element. The final C argument maps LAMMPS atom type 4 to the MEAM C +element. +

    +

    If the 2nd filename is specified as NULL, no parameter file is read, +which simply means the generic parameters in the library file are +used. Use of the NULL specification for the parameter file is +discouraged for systems with more than a single element type +(e.g. alloys), since the parameter file is expected to set element +interaction terms that are not captured by the information in the +library file. +

    +

    If a mapping value is specified as NULL, the mapping is not performed. +This can be used when a meam potential is used as part of the +hybrid pair style. The NULL values are placeholders for atom types +that will be used with other potentials. +

    +

    The MEAM library file provided with LAMMPS has the name +potentials/library.meam. It is the "meamf" file used by other MD +codes. Aside from blank and comment lines (start with #) which can +appear anywhere, it is formatted as a series of entries, each of which +has 19 parameters and can span multiple lines: +

    +

    elt, lat, z, ielement, atwt, alpha, b0, b1, b2, b3, alat, esub, asub, +t0, t1, t2, t3, rozero, ibar +

    +

    The "elt" and "lat" parameters are text strings, such as elt = Si or +Cu and lat = dia or fcc. Because the library file is used by Fortran +MD codes, these strings may be enclosed in single quotes, but this is +not required. The other numeric parameters match values in the +formulas above. The value of the "elt" string is what is used in the +pair_coeff command to identify which settings from the library file +you wish to read in. There can be multiple entries in the library +file with the same "elt" value; LAMMPS reads the 1st matching entry it +finds and ignores the rest. +

    +

    If used, the MEAM parameter file contains settings that override or +complement the library file settings. Examples of such parameter +files are in the potentials directory with a ".meam" suffix. Their +format is the same as is read by other Fortran MD codes. Aside from +blank and comment lines (start with #) which can appear anywhere, each +line has one of the following forms. Each line can also have a +trailing comment (starting with #) which is ignored. +

    +
    keyword = value
    +keyword(I) = value
    +keyword(I,J) = value
    +keyword(I,J,K) = value 
    +
    +

    The recognized keywords are as follows: +

    +

    Ec, alpha, rho0, delta, lattce, attrac, repuls, nn2, Cmin, Cmax, rc, delr, +augt1, gsmooth_factor, re +

    +

    where +

    +
    rc          = cutoff radius for cutoff function; default = 4.0
    +delr        = length of smoothing distance for cutoff function; default = 0.1
    +rho0(I)     = relative density for element I (overwrites value
    +              read from meamf file)
    +Ec(I,J)     = cohesive energy of reference structure for I-J mixture
    +delta(I,J)  = heat of formation for I-J alloy; if Ec_IJ is input as
    +              zero, then WARP sets Ec_IJ = (Ec_II + Ec_JJ)/2 - delta_IJ
    +alpha(I,J)  = alpha parameter for pair potential between I and J (can
    +              be computed from bulk modulus of reference structure
    +re(I,J)     = equilibrium distance between I and J in the reference
    +              structure
    +Cmax(I,J,K) = Cmax screening parameter when I-J pair is screened 
    +              by K (I<=J); default = 2.8
    +Cmin(I,J,K) = Cmin screening parameter when I-J pair is screened 
    +              by K (I<=J); default = 2.0
    +lattce(I,J) = lattice structure of I-J reference structure:
    +                dia = diamond (interlaced fcc for alloy)
    +                fcc = face centered cubic
    +                bcc = body centered cubic
    +                dim = dimer 
    +                B1  = rock salt (NaCl structure)
    +gsmooth_factor  = factor determining the length of the G-function smoothing
    +                  region; only significant for ibar=0 or ibar=4.
    +                      99.0 = short smoothing region, sharp step
    +                      0.5  = long smoothing region, smooth step
    +                      default = 99.0
    +augt1           = integer flag for whether to augment t1 parameter by
    +                  3/5*t3 to account for old vs. new meam formulations;
    +                    0 = don't augment t1
    +                    1 = augment t1
    +                    default = 1 
    +
    +

    Each keyword represents a quantity which is either a scalar, vector, +2d array, or 3d array and must be specified with the correct +corresponding array syntax. The indices I,J,K each run from 1 to N +where N is the number of MEAM elements being used. +

    +

    Thus these lines +

    +
    rho0(2) = 2.25
    +alpha(1,2) = 4.37 
    +
    +

    mean set rho0 for the 2nd element to the value 2.25 and set alpha for +the alloy interaction between elements 1 and 2 to 4.37. +

    +
    + +

    Restrictions: none +

    +

    Related commands: +

    +

    pair_coeff, pair_style eam +

    +

    Default: none +

    +
    + + + +

    (Baskes) Baskes, Phys Rev B, 46, 2727-2742 (1992). +

    + + +

    (Gullet) Gullet, Wagner, Slepoy, SANDIA Report 2003-8782 (2003). +This report may be accessed on-line via this link. +

    + + + diff --git a/doc/pair_style_meam.txt b/doc/pair_style_meam.txt new file mode 100644 index 0000000000..2da4baa798 --- /dev/null +++ b/doc/pair_style_meam.txt @@ -0,0 +1,200 @@ +"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c + +:link(lws,http://lammps.sandia.gov) +:link(ld,Manual.html) +:link(lc,Section_commands.html#comm) + +:line + +pair_style meam command :h3 + +[Syntax:] + +pair_style mean :pre + +[Examples:] + +pair_style meam +pair_coeff * * ../potentials/library.meam Si ../potentials/si.meam Si +pair_coeff * * ../potentials/library.meam Ni Al NULL Ni Al Ni Ni :pre + +[Description:] + +Style {meam} computes pairwise interactions for a variety of materials +using modified embedded-atom method (MEAM) potentials +"(Baskes)"_#Baskes. Conceptually, it is an extension to the original +"EAM potentials"_pair_style_eam.html which adds angular forces. It is +thus suitable for modeling metals and alloys with fcc, bcc, hcp and +diamond cubic structures, as well as covalently bonded materials like +silicon and carbon. + +In the MEAM formulation, the total energy E of a system of atoms is +given by: + +:c,image(Eqs/pair_meam.jpg) + +where F is the embedding energy which is a function of the atomic +electron density rho, and phi is a pair potential interaction. The +pair interaction is summed over all neighbors J of atom I within the +cutoff distance. As with EAM, the multi-body nature of the MEAM +potential is a result of the embedding energy term. Details of the +computation of the embedding and pair energies, as implemented in +LAMMPS, are given in "(Gullet)"_#Gullet and references therein. + +The various parameters in the MEAM formulas are listed in two files +which are specified by the "pair_coeff"_pair_coeff.html command. +These are ASCII text files in a format consistent with other MD codes +that implement MEAM potentials, such as the serial DYNAMO code and +Warp. Several MEAM potential files with parameters for different +materials are included in the "potentials" directory of the LAMMPS +distribution with a ",meam" suffix. All of these are parameterized in +terms of LAMMPS "metal units"_units.html. + +Note that unlike for other potentials, cutoffs for MEAM potentials are +not set in the pair_style or pair_coeff command; they are specified in +the MEAM potential files themselves. + +Only a single pair_coeff command is used with the {meam} style which +specifies two MEAM files and the element(s) to extract information +for. The MEAM elements are mapped to LAMMPS atom types by specifying +N additional arguments after the 2nd filename in the pair_coeff +command, where N is the number of LAMMPS atom types: + +MEAM library file +Elem1, Elem2, ... +MEAM parameter file +N element names = mapping of MEAM elements to atom types :ul + +As an example, the potentials/library.meam file has generic MEAM +settings for a variety of elements. The potentials/sic.meam file has +specific parameter settings for a Si and C alloy system. If your +LAMMPS simulation has 4 atoms types and you want the 1st 3 to be Si, +and the 4th to be C, you would use the following pair_coeff command: + +pair_coeff * * library.meam Si C sic.meam Si Si Si C :pre + +The 1st 2 arguments must be * * so as to span all LAMMPS atom types. +The two filenames are for the library and parameter file respectively. +The Si and C arguments (between the file names) are the two elements +for which info will be extracted from the library file. The first +three trailing Si arguments map LAMMPS atom types 1,2,3 to the MEAM Si +element. The final C argument maps LAMMPS atom type 4 to the MEAM C +element. + +If the 2nd filename is specified as NULL, no parameter file is read, +which simply means the generic parameters in the library file are +used. Use of the NULL specification for the parameter file is +discouraged for systems with more than a single element type +(e.g. alloys), since the parameter file is expected to set element +interaction terms that are not captured by the information in the +library file. + +If a mapping value is specified as NULL, the mapping is not performed. +This can be used when a {meam} potential is used as part of the +{hybrid} pair style. The NULL values are placeholders for atom types +that will be used with other potentials. + +The MEAM library file provided with LAMMPS has the name +potentials/library.meam. It is the "meamf" file used by other MD +codes. Aside from blank and comment lines (start with #) which can +appear anywhere, it is formatted as a series of entries, each of which +has 19 parameters and can span multiple lines: + +elt, lat, z, ielement, atwt, alpha, b0, b1, b2, b3, alat, esub, asub, +t0, t1, t2, t3, rozero, ibar + +The "elt" and "lat" parameters are text strings, such as elt = Si or +Cu and lat = dia or fcc. Because the library file is used by Fortran +MD codes, these strings may be enclosed in single quotes, but this is +not required. The other numeric parameters match values in the +formulas above. The value of the "elt" string is what is used in the +pair_coeff command to identify which settings from the library file +you wish to read in. There can be multiple entries in the library +file with the same "elt" value; LAMMPS reads the 1st matching entry it +finds and ignores the rest. + +If used, the MEAM parameter file contains settings that override or +complement the library file settings. Examples of such parameter +files are in the potentials directory with a ".meam" suffix. Their +format is the same as is read by other Fortran MD codes. Aside from +blank and comment lines (start with #) which can appear anywhere, each +line has one of the following forms. Each line can also have a +trailing comment (starting with #) which is ignored. + +keyword = value +keyword(I) = value +keyword(I,J) = value +keyword(I,J,K) = value :pre + +The recognized keywords are as follows: + +Ec, alpha, rho0, delta, lattce, attrac, repuls, nn2, Cmin, Cmax, rc, delr, +augt1, gsmooth_factor, re + +where + +rc = cutoff radius for cutoff function; default = 4.0 +delr = length of smoothing distance for cutoff function; default = 0.1 +rho0(I) = relative density for element I (overwrites value + read from meamf file) +Ec(I,J) = cohesive energy of reference structure for I-J mixture +delta(I,J) = heat of formation for I-J alloy; if Ec_IJ is input as + zero, then WARP sets Ec_IJ = (Ec_II + Ec_JJ)/2 - delta_IJ +alpha(I,J) = alpha parameter for pair potential between I and J (can + be computed from bulk modulus of reference structure +re(I,J) = equilibrium distance between I and J in the reference + structure +Cmax(I,J,K) = Cmax screening parameter when I-J pair is screened + by K (I<=J); default = 2.8 +Cmin(I,J,K) = Cmin screening parameter when I-J pair is screened + by K (I<=J); default = 2.0 +lattce(I,J) = lattice structure of I-J reference structure: + dia = diamond (interlaced fcc for alloy) + fcc = face centered cubic + bcc = body centered cubic + dim = dimer + B1 = rock salt (NaCl structure) +gsmooth_factor = factor determining the length of the G-function smoothing + region; only significant for ibar=0 or ibar=4. + 99.0 = short smoothing region, sharp step + 0.5 = long smoothing region, smooth step + default = 99.0 +augt1 = integer flag for whether to augment t1 parameter by + 3/5*t3 to account for old vs. new meam formulations; + 0 = don't augment t1 + 1 = augment t1 + default = 1 :pre + +Each keyword represents a quantity which is either a scalar, vector, +2d array, or 3d array and must be specified with the correct +corresponding array syntax. The indices I,J,K each run from 1 to N +where N is the number of MEAM elements being used. + +Thus these lines + +rho0(2) = 2.25 +alpha(1,2) = 4.37 :pre + +mean set rho0 for the 2nd element to the value 2.25 and set alpha for +the alloy interaction between elements 1 and 2 to 4.37. + +:line + +[Restrictions:] none + +[Related commands:] + +"pair_coeff"_pair_coeff.html, "pair_style eam"_pair_style_eam.html + +[Default:] none + +:line + +:link(Baskes) +[(Baskes)] Baskes, Phys Rev B, 46, 2727-2742 (1992). + +:link(Gullet) +[(Gullet)] Gullet, Wagner, Slepoy, SANDIA Report 2003-8782 (2003). +This report may be accessed on-line via "this link"_sandreport. + +:link(sandreport,http://www.prod.sandia.gov/cgi-bin/techlib/access-control.pl/2003/038782.pdf) \ No newline at end of file