|
|
| Line 1: |
Line 1: |
| The '''threshold displacement energy''' <math>T_d</math> is the minimum [[kinetic energy]]
| | They are typically a free website that are pre-designed for enabling businesses of every size in marking the presence on the internet and allows them in showcasing the product services and range through images, contents and various other elements. Good luck on continue learning how to make a wordpress website. PSD files are incompatible to browsers and are suppose to be converted into wordpress compatible files so that it opens up in browser. After confirming the account, login with your username and password at Ad - Mob. By using this method one can see whether the theme has the potential to become popular or not and is their any scope of improvement in the theme. <br><br>These folders as well as files have to copied and the saved. If you cherished this article and you would like to get additional info pertaining to [http://off2.net/wordpressbackup49850 wordpress dropbox backup] kindly stop by the website. You may either choose to link only to the top-level category pages or the ones that contain information about your products and services. There are number of web services that offer Word press development across the world. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. W3C compliant HTML and a good open source powered by Word - Press CMS site is regarded as the prime minister. <br><br>Saying that, despite the launch of Wordpress Express many months ago, there has still been no sign of a Wordpress video tutorial on offer UNTIL NOW. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. Use this section to change many formatting elements. In crux the developer must have a detailed knowledge not only about the marketing tool but also about the ways in which it can be applied profitably. After that the developer adds the unordered list for navigations. <br><br>Numerous bloggers are utilizing Word - Press and with good reason. Find more information about Design To Wordpress here. Next you'll go by way of to your simple Word - Press site. There are many advantages of hiring Wordpress developers for Wordpress project development:. The popularity of Word - Press has increased the demand for Word - Press themes and these themes sells like hot cake on the internet. <br><br>Under Settings —> Reading, determine if posts or a static page will be your home page, and if your home page is a static page, what page will contain blog posts. In fact portfolio Word - Press themes is a smooth and attractive but considerably flawed Word - Press theme in creating simpler to the photographers or designers to develop a specific internet site showcasing their most current perform since it appear modern-day and has fantastic typography and large photographs which would develop an attractive wanting portfolio internet site. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. Word - Press is the most popular personal publishing platform which was launched in 2003. Your topic is going to be the basis of your site's name. |
| that an atom in a [[solid]] needs to be permanently | |
| displaced from its lattice site to a
| |
| [[crystallographic defect|defect]] position.
| |
| It is also known as "displacement threshold energy" or just "displacement energy".
| |
| In a [[crystal]], a separate threshold displacement
| |
| energy exists for each [[Crystallography|crystallographic]]
| |
| direction. Then one should distinguish between the
| |
| minimum <math>T_{d,min}</math> and average <math>T_{d,ave}</math> over all
| |
| lattice directions threshold displacement energies.
| |
| In [[amorphous]] solids it may be possible to define an effective
| |
| displacement energy to describe some other average quantity of interest.
| |
| Threshold displacement energies in typical solids are
| |
| of the order of 10 - 50 [[Electronvolt|eV]].
| |
| <ref name="And79">H. H. Andersen, The Depth Resolution of Sputter Profiling,
| |
| Appl. Phys. 18, 131 (1979)</ref>
| |
| <ref name="Nastasi">M. Nastasi, J. Mayer, and J. Hirvonen, Ion-Solid Interactions - Fundamentals and Applications, Cambridge University Press, Cambridge, Great Britain, 1996</ref>
| |
| <ref name="Luc75">P. Lucasson, The production of Frenkel defects in metals,
| |
| in Fundamental Aspects of Radiation Damage in Metals, edited by
| |
| M. T. Robinson and F. N. Young Jr., pages 42--65, Springfield, 1975, ORNL</ref>
| |
| <ref name="Ave98">R. S. Averback and T. Diaz de la Rubia, Displacement damage in irradiated metals and semiconductors, in Solid State Physics, edited by H. Ehrenfest and F. Spaepen, volume 51, pages 281--402, Academic Press, New York, 1998.</ref><ref name="Smith">R. Smith (ed.), Atomic & ion collisions in solids and at surfaces: theory, simulation and applications, Cambridge University Press, Cambridge, UK, 1997</ref>
| |
| | |
| == Theory and simulation ==
| |
| | |
| The threshold displacement energy is a materials property relevant during high-energy [[particle radiation]] of materials.
| |
| The maximum energy <math>T_{max}</math> that an irradiating particle can transfer in a
| |
| [[binary collision approximation|binary collision]]
| |
| to an atom in a material is given by (including [[Special relativity|relativistic]] effects) | |
| | |
| <math>
| |
| T_{max} = {2 M E (E+2 m c^2) \over (m+M)^2 c^2+2 M E}
| |
| </math>
| |
| | |
| where E is the kinetic energy and m the mass of the incoming irradiating particle and M the mass of the material atom. c is the velocity of light.
| |
| If the kinetic energy E is much smaller than the mass <math>m c^2</math> of the irradiating particle, the equation reduces to
| |
| | |
| <math>
| |
| T_{max} = E {4 M m \over (m+M)^2 }
| |
| </math>
| |
| | |
| In order for a permanent defect to be produced from initially perfect [[crystal]] lattice, the kinetic energy that it receives <math>T_{max}</math> must be larger than the formation energy of a [[Frenkel pair]].
| |
| However, while the Frenkel pair formation energies in crystals are typically around 5–10 eV, the average threshold displacement energies are much higher, 20–50 eV.<ref name="And79" /> The reason for this apparent discrepancy is that the defect formation is a complex multi-body collision process (a small [[collision cascade]]) where the atom that receives a recoil energy can also bounce back, or kick another atom back to its lattice site. Hence, even the minimum threshold displacement energy is usually clearly higher than the Frenkel pair formation energy.
| |
| | |
| Each crystal direction has in principle its own threshold displacement energy, so for a full description one should know the full threshold displacement surface
| |
| <math>
| |
| T_d(\theta,\phi) = T_d([hkl])
| |
| </math>
| |
| for all non-equivalent [[Miller index|crystallographic directions]] [hkl]. Then
| |
| <math>
| |
| T_{d,min} = \min(T_d(\theta,\phi))
| |
| </math>
| |
| and
| |
| <math>
| |
| T_{d,ave} = {\rm ave}(T_d(\theta,\phi))
| |
| </math>
| |
| where the minimum and average is with respect to all angles in three dimensions.
| |
| | |
| An additional complication is that the threshold displacement energy for a given direction is not necessarily a step function, but there can be an intermediate
| |
| energy region where a defect may or may not be formed depending on the random atom displacements.
| |
| The one can define a lower threshold where a defect may be formed <math>T^l_d</math>,
| |
| and an upper one where it is certainly formed <math>T^u_d</math> | |
| .<ref name="Mal02">L. Malerba and J. M. Perlado,
| |
| Basic mechanisms of atomic displacement production in cubic silicon carbide: A molecular dynamics study, Phys. Rev. B 65, 045202 (2002)</ref>
| |
| The difference between these two may be surprisingly large, and whether or not this effect is taken into account may have a large effect on the average threshold displacement energy.
| |
| .<ref name="Nor05c">K. Nordlund, J. Wallenius, and L. Malerba, Molecular dynamics simulations of threshold energies in Fe, Nucl. Instr. Meth. Phys. Res. B 246, 322 (2005)</ref> | |
| | |
| It is not possible to write down a single analytical equation that would relate e.g. elastic material properties or defect formation energies to the threshold displacement energy. Hence theoretical study of the threshold displacement energy is conventionally carried out using either classical
| |
| <ref name="Mal02" />
| |
| <ref name="Nor05c" />
| |
| <ref name="Gib60">J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard,
| |
| Dynamics of Radiation Damage, Phys. Rev 120, 1229 (1960)</ref>
| |
| <ref name="Erg64">C. Erginsoy, G. H. Vineyard, and A. Englert, Dynamics of Radiation Damage in a Body-Centered Cubic Lattice, Phys. Rev. 133, A595 (1964)</ref><ref name="Cat94">M.-J. Caturla, T. Diaz de la Rubia, and G. H. Gilmer, Point defect production, geometry and stability in Silicon: a molecular dynamics simulation study, Mat. Res. Soc. Symp. Proc. 316, 141 (1994)</ref>
| |
| <ref name="Par01">B. Park, W. J. Weber, and L. R. Corrales, Molecular-dynamics simulation study of threshold displacements and defect formation in zircon, Phys. Rev. B 64, 174108 (2001)</ref>
| |
| or quantum mechanical | |
| <ref name="Uhl97">S. Uhlmann, T. Frauenheim, K. Boyd, D.Marton, and J. Rabalais, Radiat. Eff. Defects Solids 141, 185 (1997).</ref>
| |
| <ref name="Win98">W. Windl, T. J. Lenosky, J. D. Kress, and A. F. Voter, Nucl. Instr. and Meth. B 141, 61 (1998).</ref>
| |
| <ref name="Maz01">M. Mazzarolo, L. Colombo, G. Lulli, and E. Albertazzi, Phys.
| |
| Rev. B 63, 195207 (2001).</ref>
| |
| <ref name="Hol08">E. Holmström, A. Kuronen, and K. Nordlund, Threshold defect production in silicon determined by density functional theory molecular dynamics simulations, Phys. Rev. B (Rapid Comm.) 78, 045202 (2008).</ref>
| |
| [[molecular dynamics]] computer simulations. Although an analytical description of the
| |
| displacement is not possible, the "sudden approximation" gives fairly good approximations
| |
| of the threshold displacement energies at least in covalent materials and low-index crystal
| |
| directions <ref name="Win98" />
| |
| | |
| An example molecular dynamics simulation of a threshold displacement event is available in [http://www.youtube.com/watch?v=ZWu5Qf8y6iQ]. The animation shows how a defect ([[Frenkel defect|Frenkel pair]], i.e. an [[interstitial defect|interstitial]] and [[vacancy defect|vacancy]]) is formed in silicon when a lattice atom is given a recoil energy of 20 eV in the 100 direction. The data for the animation was obtained from [[density functional theory]] [[molecular dynamics]] computer simulations.<ref name="Hol08" />
| |
| | |
| Such simulations have given significant qualitative insights into the threshold displacement energy, but the quantitative results should be viewed with caution.
| |
| The classical [[molecular dynamics|interatomic potential]]s are usually fit only to equilibrium properties, and hence their predictive capability may be limited. Even in the most studied materials such as Si and Fe, there are variations of more than a factor of two in the predicted threshold displacement energies.<ref name="Nor05c" /><ref name="Hol08" /> The quantum mechanical simulations based on [[density functional theory]] (DFT) are likely to be much more accurate, but very few comparative studies of different DFT methods on this issue have yet been carried out to assess their quantitative reliability.
| |
| | |
| == Experimental studies ==
| |
| | |
| The threshold displacement energies have been studied
| |
| extensively with [[particle radiation|electron irradiation]]
| |
| experiments. Electrons with kinetic energies of the order of hundreds of [[keV]]s or a few [[MeV]]s can to a very good approximation be considered to collide with a single lattice atom at a time.
| |
| Since the initial energy for electrons coming from a particle accelerator is accurately known, one can thus
| |
| at least in principle determine the lower minimum threshold displacement
| |
| <math>T^l_{d,min}</math>
| |
| energy by irradiating a crystal with electrons of increasing energy until defect formation is observed. Using the equations given above one can then translate the electron energy E into the threshold energy T. If the irradiation is carried out on a single crystal in a known [[Miller index|crystallographic directions]] one can determine also direction-specific thresholds
| |
| <math>T_d^l(\theta,\phi)</math>.<ref name="And79" /><ref name="And79" /><ref name="Luc75" /><ref name="Ave98" /><ref name="Lof58">J. Loferski and P. Rappaport, Phys. Rev. 111, 432 (1958).</ref><ref name="Ban99">F.~Banhart, Rep. Prog. Phys. 62 (1999) 1181</ref> | |
| | |
| There are several complications in interpreting the experimental results, however. To name a few, in thick samples the electron beam will spread, and hence the measurement on single crystals
| |
| does not probe only a single well-defined crystal direction. Impurities may cause the threshold
| |
| to appear lower than they would be in pure materials. | |
| | |
| == Temperature dependence ==
| |
| | |
| Particular care has to be taken when interpreting threshold displacement energies
| |
| at temperatures where [[point defect|defects]] are mobile and can recombine. At such temperatures,
| |
| one should consider
| |
| two distinct processes: the creation of the defect by the high-energy
| |
| ion (stage A), and subsequent thermal recombination effects (stage B).
| |
| | |
| The initial stage A. of defect creation, until all excess kinetic | |
| energy has dissipated in the lattice and it is back to its
| |
| initial temperature T<sub>0</sub>, takes < 5 ps. This is the fundamental
| |
| ("primary damage") threshold displacement energy, and also the one
| |
| usually simulated by [[molecular dynamics]] computer simulations.
| |
| After this
| |
| (stage B), however, close [[Frenkel pair]]s may be recombined
| |
| by thermal processes. Since low-energy recoils just above the
| |
| threshold only produce close Frenkel pairs, recombination
| |
| is quite likely. | |
| | |
| Hence on experimental time scales and temperatures above the first
| |
| (stage I) recombination temperature, what one sees is the combined
| |
| effect of stage A and B. Hence the net effect often is that the
| |
| threshold energy appears to increase with increasing temperature,
| |
| since the Frenkel pairs produced by the lowest-energy recoils
| |
| above threshold all recombine, and only defects produced by higher-energy
| |
| recoils remain. Since thermal recombination is time-dependent,
| |
| any stage B kind of recombination also implies that the
| |
| results may have a dependence on the ion irradiation flux.
| |
| | |
| In a wide range of materials, defect recombination occurs already below
| |
| room temperature. E.g. in metals the initial ("stage I") close Frenkel
| |
| pair recombination and interstitial migration starts to happen already
| |
| around 10-20 K.<ref name="Ehr91">P. Ehrhart,
| |
| Properties and interactions of atomic defects in metals and alloys,
| |
| volume 25 of Landolt-B"ornstein, New Series III, chapter 2,
| |
| page 88, Springer, Berlin, 1991</ref>
| |
| Similarly, in Si major recombination of damage happens already
| |
| around 100 K during ion irradiation and 4 K during electron irradiation
| |
| <ref name="Par00">P. Partyka, Y. Zhong, K. Nordlund, R. S. Averback, I. K. Robinson, and
| |
| P. Ehrhart,
| |
| Grazing incidence diffuse x-ray scattering investigation of the
| |
| properties of irradiation-induced point defects in silicon,
| |
| Phys. Rev. B 64, 235207 (2002)</ref>
| |
| | |
| Even the stage A threshold displacement energy can be expected
| |
| to have a temperature dependence, due to effects such as thermal
| |
| expansion, temperature dependence of the elastic constants and increased
| |
| probability of recombination before the lattice has cooled down back to the
| |
| ambient temperature T<sub>0</sub>.
| |
| These effects, are, however, likely to be much weaker than the
| |
| stage B thermal recombination effects.
| |
| | |
| == Relation to higher-energy damage production ==
| |
| | |
| The threshold displacement energy is often used to estimate the total
| |
| amount of [[Crystallographic defect|defects]] produced by higher energy irradiation using the Kinchin-Pease or NRT
| |
| equations<ref name="NRT">M. J. Norgett, M. T. Robinson, and I. M. Torrens,
| |
| A proposed method of calculating displacement dose rates,
| |
| Nucl. Engr. and Design 33, 50 (1975)</ref><ref name="ASTMFe">ASTM Standard E693-94,
| |
| Standard practice for characterising neutron exposure in iron and low
| |
| alloy steels in terms of displacements per atom (dpa), 1994</ref>
| |
| which says that the number of Frenkel pairs produced <math>N_{FP}</math>
| |
| for a [[stopping power (particle radiation)|nuclear deposited energy]] of <math>F_{Dn}</math> is
| |
| | |
| <math>
| |
| N_{FP} = 0.8 {F_{Dn} \over 2 T_{d,ave}}
| |
| </math>
| |
| | |
| for any nuclear deposited energy above <math> 2 T_{d,ave}/0.8</math>.
| |
| | |
| However, this equation should be used with great caution for several
| |
| reasons. For instance, it does not account for any thermally activated
| |
| recombination of damage, nor the well known fact that in metals
| |
| the damage production is for high energies only something like
| |
| 20% of the Kinchin-Pease prediction.<ref name="Ave98" />
| |
| | |
| The threshold displacement energy is also often used in
| |
| [[binary collision approximation]]
| |
| computer codes such as [[Stopping and Range of Ions in Matter|SRIM]]<ref>http://www.srim.org</ref> to estimate
| |
| damage. However, the same caveats as for the Kinchin-Pease equation
| |
| also apply for these codes (unless they are extended with a damage
| |
| recombination model).
| |
| | |
| Moreover, neither the Kinchin-Pease equation nor SRIM take in any way
| |
| account of [[Ion implantation|ion channeling]], which may in crystalline or
| |
| polycrystalline materials reduce the nuclear deposited
| |
| energy and thus the damage production dramatically for some
| |
| ion-target combinations. For instance, keV ion implantation
| |
| into the Si 110 crystal direction leads to massive channeling
| |
| and thus reductions in stopping power.<ref name="Sil00">
| |
| J. Sillanpää, K. Nordlund, and J. Keinonen, Electronic stopping of
| |
| Silicon from a 3D Charge Distribution, Phys. Rev. B 62, 3109 (2000)</ref>
| |
| Similarly, light ion like He irradiation of a BCC metal like Fe
| |
| leads to massive channeling even in a randomly selected
| |
| crystal direction.<ref name="Nor09">K. Nordlund, MDRANGE range
| |
| calculations of He in Fe (2009), public presentation
| |
| at the EFDA MATREMEV meeting, Alicante 19.11.2009</ref>
| |
| | |
| == See also ==
| |
| | |
| * [[Threshold energy]]
| |
| * [[Stopping power (particle radiation)]]
| |
| * [[Crystallographic defect]]
| |
| | |
| == References ==
| |
| | |
| <references/>
| |
| | |
| [[Category:Condensed matter physics]]
| |
| [[Category:Radiation effects]]
| |