a r X i v :c o n d -m a t /0109045v 1 [c o n d -m a t .m t r l -s c i ] 4 S e p 2001
Phys.Rev.B (submitted,2001)
Fully relativistic calculation of magnetic properties of Fe,Co and Ni adclusters on
Ag(100)
https://www.doczj.com/doc/ee9570168.html,zarovits 1,L.Szunyogh 1,2and P.Weinberger 1
1
Center for Computational Materials Science,Technical University Vienna,
A-1060Gumpendorferstr.1.a.,Wien,Austria
2
Department of Theoretical Physics,Budapest University of Technology,
Budafoki ′u t 8,H-1521,Budapest,Hungary
We present ?rst principles calculations of the magnetic moments and magnetic anisotropy energies
of small Fe,Co and Ni clusters on top of a Ag(100)surface as well as the exchange-coupling en-ergy between two single adatoms of Fe or Co on Ag(100).The calculations are performed fully relativistically using the embedding technique within the Korringa–Kohn–Rostoker method.The magnetic anisotropy and the exchange–coupling energies are calculated by means of the force the-orem.In the case of adatoms and dimers of iron and cobalt we obtain enhanced spin moments and,especially,unusually large orbital moments,while for nickel our calculations predict a complete absence of magnetism.For larger clusters,the magnitudes of the local moments of the atoms in the center of the cluster are very close to those calculated for the corresponding monolayers.Similar to the orbital moments,the contributions of the individual atoms to the magnetic anisotropy energy strongly depend on the position,hence,on the local environment of a particular atom within a given cluster.We ?nd strong ferromagnetic coupling between two neighboring Fe or Co atoms and a rapid,oscillatory decay of the exchange-coupling energy with increasing distance between these two adatoms.
PACS numbers:71.24.+q,71.70.Gm,75.30.Gw,75.30.Hx
I.INTRODUCTION
Magnetic nanostructures such as impurities,clusters and wires on top or in the uppermost layers of surfaces are of special interest for nano-scale technologies,in par-ticular,regarding their possible application as magnetic nano-devices and high-density magnetic recording me-dia.A quantitatively correct description of the mag-netic properties of such structures,namely,the magni-tude and the orientation of spin and orbital moments,magnetic anisotropy energies and the magnetic interac-tions,is,therefore,an important issue to be addressed.Concomitantly,the understanding of the changes of phys-ical properties from nanostructures to thin ?lms or even bulk systems has always been a fascinating theoretical challenge.
Because of the lack of translational symmetry tight-binding (TB)methods have been an e?cient tool to study larger clusters.By using a tight–binding Hub-bard Hamiltonian in the unrestricted Hartree–Fock ap-proximation,Pastor and co–workers revealed the size and structural dependence of magnetic properties of free Cr n ,Fe n and Ni n (n ≤15)clusters 1,and also the exchange in-teraction and local environments e?ects in Fe n clusters 2.By including a spin–orbit coupling term into the Hamil-tonian,they also investigated various e?ects on the mag-netic anisotropy energy (MAE)of small unsupported Fe clusters 3and,recently,of Co n clusters on Pd(111)4.Fi-nite temperature magnetism of small clusters,remark-ably di?erent from that of bulk systems,has also been studied in terms of a similar approach by taking into account both electronic and structural excitations 5.A great advantage of the TB methods seems to be that
they easily can be combined with molecular dynamics calculations enabling thus investigations of relaxation ef-fects which proved to be important in determining the magnetic moments 6–8and the MAE 9of transition metal clusters.
The embedding technique based on the Korringa–Kohn–Rostoker (KKR)Green’s function method in the local spin-density approximation (LSDA)has been ap-plied to the magnetism of transition metal adatoms and clusters deposited on surfaces 10,11.The main feature of this approach is that the interaction between adatoms and host surface atoms can be analyzed within ?rst principles electronic structure calculations 12,13,in sev-eral cases exhibiting novel phenomena in nanomagnetism such as the existence of metamagnetic states 14,15or inter-mixing e?ects between adatoms and the host surface 16.An accurate calculation of the total energy in terms of full potential or full charge density schemes made possi-ble the investigations of the energetics of adatoms 17–19.As compared to TB methods an obvious drawback of the embedded KKR technique is that,with respect to com-putational limitations,the number of the atoms in the cluster is restricted to about less than 100.Furthermore,the inclusion of structural relaxations is exceedingly dif-?cult.In order to circumvent these problems,a quasi-ab initio molecular–dynamics method has been employed by parameterizing interatomic potentials to the ?rst princi-ples KKR Green’s function electronic structures 20.On the level of a fully relativistic spin-polarized electron the-ory,recently,strongly enhanced orbital magnetism and MAE of adatoms and small clusters on Ag and Au(100)surfaces have been reported 21,22.
From the mid-nineties on we carried out systematic investigations of the magnetism,in particular of the
MAE,of transition metal multilayer systems by using the fully relativistic spin-polarized screened Korringa–Kohn–Rostoker(SKKR)method23–25.Speci?cally,within the single-site approximation,we explored the oscillatory be-havior of the MAE of an Fe impurity buried in a Au(100) host26.The purpose of the present work is to extend these studies by including self–consistent e?ects(elec-tronic relaxations)of the host atoms in order to perform realistic investigations for magnetic clusters on metallic surfaces.For this very reason we make use of a real–space embedding technique in order to calculate the electronic structure of the cluster,and also to be able to treat the Poisson equation with appropriate boundary condition. Theoretical and computational details are given in Sec-tions II and III,respectively.In Section IV our results of the magnetic moments and the MAE of small planar Fe, Co and Ni clusters on Ag(100),as well as of the magnetic correlation between Fe or Co adatoms are presented.Fi-nally,in Section V we summarize and draw conclusions.
II.THEORETICAL APPROACH
Within multiple scattering theory the scattering path operator(SPO)matrix,τ(E)={τ
n(E)δnm}={t n
QQ′
(E)δnm}and G(E)={G
pq h (k ,E)},within the framework of the
SKKR method23,where p and q denote layers and the
k are vectors in the surface Brillouin zone(SBZ).The
real–space SPO is then given by
τ
?SBZ
SBZ
e?i(T i?T j)k τ
were treated within the atomic sphere approximation (ASA).For the calculation of the t–matrices and for the multipole expansion of the charge densities,necessary to evaluate the Madelung potentials,a cut–o?of?max=2 was used.In order to perform the energy integrations,16 points on a semicircular contour in the complex energy plane were sampled according to an asymmetric Gaussian quadrature.Both,for the self–consistent calculation of the Ag(100)surface and for the evaluation of Eq.(2)we used45k –points in the irreducible wedge of the SBZ. For some restricted cases we checked the convergence of the results by increasing the number of k –points to210. In the present study we made no attempts to include lattice relaxation e?ects,therefore,the host and the clus-ter sites refer to positions of an ideal fcc parent lattice29 with the experimental Ag lattice constant(4.12?A).Three layers of self–consistently treated empty sites were used to represent the vacuum region23;the magnetic adatoms occupy sites in the?rst vacuum layer.As shown in Fig.1, we considered dimers and linear trimers oriented along the x axis,square–like tetramers,centered pentamers(as in Ref.22),as well as a cluster arranged on positions of a 3×3square denoted in the following simply as3×3clus-ter.In Fig.1,for each particular cluster the equivalent atoms with respect to an orientation of the magnetization along the x or y axis are labelled by the same number. Note that for a magnetization aligned in the z direction, the atoms labelled by2and3in the pentamer and the 3×3cluster become equivalent.Up to a total of67sites, the clusters consisted of adatoms,several substrate Ag atoms and empty sites from neighboring shells.A sta-bility test of the local electronic and magnetic properties for a single Fe adatom with respect to the number of self–consistently treated neighboring shells is shown in Fig.2.Although the calculated orbital moment of the Fe adatom shows a somewhat slower convergence than the valence charge and the spin moment,it is remark-able that considering only a?rst shell of neighbors this already yields values which di?er by less than1%from the fully converged ones.
IV.RESULTS AND DISCUSSION
A.Spin and orbital moments Calculations for di?erent orientations of the magneti-zation revealed that the spin moments are fairly insensi-tive to the direction of the magnetization,while for the orbital moments remarkably large anisotropy e?ects ap-ply,a phenomenon that will be discussed in the next Sec-tion.For a magnetization along the z axis,the calculated values of the spin and orbital moments for an adatom and selected clusters of Fe,Co and Ni on Ag(100)are listed in Table I.In there the position indices in a particu-lar cluster refer to the corresponding numbers in Fig.1 and the number of nearest neighbors of magnetic atoms (coordination number,n c)is also given.
As compared to the corresponding monolayer values (3.15μB for Fe and2.03μB for Co),the spin moment of a single adatom of Fe(3.39μB)and Co(2.10μB)is slightly increased.In the case of Fe clusters,the spin moments decrease monotonously with increasing n c.A slight de-viation from that behavior can be seen for the3×3clus-ter,where the atoms with n c=2and3exhibit the same spin moment.For the central atom of the pentamer and, in particular,of the3×3cluster,the monolayer value is practically achieved.The above results compare fairly well to those of Cabria et al.22and re?ect a very short ranged magnetic correlation between the Fe atoms. The general tendency of decreasing spin moments with increasing n c is obvious also for the Co clusters up to the pentamer case.For the3×3cluster,however,just the opposite trend applies.Establishing a correlation between S z and n c for Co seems to be more ambiguous than for Fe,because the changes of the spin moment are much smaller in this case.Nevertheless,it is tempting to say that in the formation of the magnetic moment of Co, further o?neighbors play a more signi?cant role than in the case of Fe.
In the case of an adatom and dimer of Ni we found no stable magnetic state.Quite contradictory,Cabria et al.22reported a spin moment of about0.5μB for a Ni adatom on Ag(100).As the computational method of these authors is very similar to ours,it is at present puzzling what causes this discrepancy between the two calculations.Our result is,however,in line with the experiments of Beckmann and Bergmann who found no magnetic moment for Ni adatoms on Au surface30,which as a substrate is rather similar to Ag.It should be noted, however,that in Ref.30the actual surface orientation is not speci?ed.
For clusters of Ni one can observe an opposite ten-dency as for Fe and Co:the spin moment enhances with increasing number of neighbors.This clearly can be seen from Table I.Having in mind the calculated monolayer value(0.71μB),our small cluster calculations indicate a fairly slow evolution of the spin moment of Ni with in-creasing cluster size,implying that the magnetism of Ni is subject to correlation e?ects on a much longer scale than in Fe or Co.
Apparently,the orbital moments show a di?erent,in fact,more complex behavior as the spin moments.For single adatoms of Fe and Co we found orbital moments enhanced by a factor of～6and～4.5,respectively, as compared to the monolayer values(0.14μB for Fe and0.27μB for Co).This is a direct consequence of the reduced crystal?eld splitting,being relatively large in monolayers,and,in particular,in corresponding bulk systems31.In spite of a qualitative agreement,our L z values for the adatoms are considerably larger than those calculated by Cabria et al.22(0.55μB for Fe and0.76μB for Co).It should be noted,however,that by including orbital polarization e?ects(Hund’s second rule)in terms of Brooks’parameterization32,33,Nonas et al.21found orbital moments for Fe and Co adatoms on Ag(100)close to the atomic limit(2.20μB for Fe and2.57μB for Co). For dimers of Fe and Co,the value of L z drops to about40%in magnitude as compared to a single adatom. The evolution of the orbital moment seems,however,to
decrease explicitly only for the central atom of larger clusters.In a previous paper34we showed that the (local)symmetry can be correlated with the magnetic anisotropy,i.e.,with the quenching e?ect of the crystal ?eld experienced by an atom.A single adatom and the central atom of the linear trimers,pentamers and the 3×3clusters exhibit well–de?ned rotational symmetry, namely,C1,C2,C4and C4,respectively.The corre-sponding values of L z,namely,0.88μB,0.25μB,0.15μB,and0.12μB for Fe,and1.19μB,0.49μB,0.25μB and0.23μB for Co,nicely re?ect the increasing rota-tional symmetry of the respective atoms.Although the outer magnetic atoms exhibit systematically larger or-bital moments than the central ones,even a qualitative correlation with the local environment(n c)can hardly be stated.The orbital moment for the trimer of Ni is already close to the monolayer value(0.19μB)but shows rather big?uctuations with respect to the size of the cluster and also to the positions of the individual atoms.
B.Anisotropies of orbital moments and magnetic
anisotropy energies
By using the self–consistent potentials for a given ori-entation of the magnetization(along z),we calculated magnetic anisotropy energies by means of the magnetic force theorem35,36as di?erences of band–energies,
?E x?z=E b;x?E b;z and?E y?z=E b;y?E b;z.(7) For a particular orientationα,the band–energy is ob-tained as a sum of contributions from all atoms in the cluster,
E b;α= i∈C E i b;α(α=x,y,z),(8)
E i b;α= ?F?B d?(???F)n iα(?),(9)
where?F is the Fermi energy of the substrate,?B is the bottom of the valence band and n iα(?)is the density of states for atom i.Clearly,the above formalism allows us to de?ne the MAE as a sum of atom–like contributions, which facilitates to trace its spatial distribution in the cluster.
The anisotropies of the orbital moments and the con-tributions of the individual magnetic atoms to the MAE are displayed in Tables II,III and IV for Fe,Co and Ni clusters,respectively.In addition,the total MAE per magnetic atoms of the clusters including the neighbor-hood is also given.Although the dominating contribu-tions to the MAE arise from the magnetic species,the environment,in particular,the Ag atoms and the empty sites within the?rst shell add a remarkable amount to the MAE.However,due to the weak polarization of the Ag atoms,we obtained a fast convergence of the total MAE with respect to the size of the cluster(environment).
As can be inferred from the corresponding positive val-ues of the MAE in Tables II and III,single adatoms of Fe and Co exhibit a magnetization oriented perpendic-ular to the surface.This again is in perfect agreement with the experiments of Beckmann and Bergmann30.As compared with the monolayer case(0.47meV),the MAE of an Fe adatom(5.61meV)is enhanced by a factor of twelve.Contrary to our results,Cabria et al.22predicted in–plane magnetism(?E x?z=-0.98meV)for an Fe adatom on Ag(100),and perpendicular magnetism for Co,albeit with a much larger anisotropy energy(>7 meV)than ours(4.36meV).It should be stressed at this point,that our calculations are consistent with a qualitative rule,valid for transition metals with a more than half–?lled d–band and based on simple,perturba-tive phenomenological or tight–binding reasoning31:the direction,along which the orbital moment is the largest, is energetically favored.
As can be seen from Table II,perpendicular mag-netism is characteristic for all Fe clusters considered.For the dimer and the trimer we observe a small in–plane anisotropy with preference of the x axis,i.e.,in the di-rection of the Fe-Fe bonds.In agreement with the reduc-tion of the orbital moment,as discussed in the previous section,the contribution of the central atom to the MAE for the trimer,the pentamer and the3×3cluster rapidly decreases,being even less than the monolayer value in the case of the3×3cluster.The outer atoms in the pen-tamer and in the3×3cluster can add considerably more to the MAE than the central atom.As a consequence, the average MAE strongly?uctuates with increasing size of the magnetic cluster and shows a very slow tendency to converge to the MAE of an Fe monolayer on Ag(100). Such a complicated behavior of the MAE with respect to the cluster size has also been found by Guirado–L′o pez9 for free–standing fcc transition metal clusters.
In comparison to an adatom,for a Co dimer?E x?z drops to a large negative value(-3.49meV/per Co),while ?E y?z remains slightly positive(0.76meV/per Co),im-plying that a Co dimer favors the x(in–plane)direction of the magnetization and also experiences a strong in–plane anisotropy.The strong tendency of Co clusters to in–plane magnetization pertains to larger clusters and is characteristic also for a Co monolayer(?E x?z=-1.31 meV).The atom–like resolution of the MAE indicates, that this tendency is driven by nearest–neighbor Co-Co interactions.An explanation of this e?ect in terms of perturbation theory and symmetry resolved densities of states can be found in Refs.37–39.As an unexpected consequence,the contribution to the MAE of the cen-tral atom in the cluster can be larger than that of some outer atoms.Quite obviously,the MAE of the central atom of the trimer,the pentamer and the3×3cluster, -9.06meV,-2.46meV,and-1.86meV,respectively,fall monotonously o?to the monolayer value,whereas the av-erage MAE possesses a much more complicated evolution also in this case.
With exception of the tetramer,for which we found a MAE close to zero,all Ni clusters prefer an in–plane magnetization.The in–plane anisotropy,seen from Ta-
ble IV for the trimer,but also from the atom–like contri-butions for the larger clusters,is,however,smaller than in the case of Co.Again the complicated nature of the magnetism of Ni shows up,in particular,for the3×3 cluster:while the contribution of the central atom to the MAE almost vanishes,those of the outer atoms oscillate in magnitude.Considering the MAE of a Ni monolayer on Ag(100)(-2.23meV),no straightforward connection with the magnetic anisotropy properties of small clusters can be traced.
C.Magnetic interaction between adatoms Interactions between magnetic nanoclusters are of great importance for technological applications.Clearly enough the most important questions are(i)what is the magnetic structure of the individual entities,(ii)of what nature(strength,range,etc.)is the coupling between them,and(iii)what in?uences the magnetic orientation of these entities relative to each other.In this section we present a preliminary study in this?eld by investigating the interaction of two Fe or Co adatoms on Ag(100). We?rst performed self–consistent calculations for two adatoms by varying the distance d between them from a to5a along the x direction,where a is the2D lattice con-stant and keeping the orientation of the magnetizations parallel to each other(along the z axis).The calculated spin and orbital moments of the(coupled)adatoms are shown in Fig.3.Note that the distance a refers to the bondlength in dimers.As can be seen from Fig.3,both for Fe and Co the values of S z and L z rapidly converge to the respective single adatom value.
Next we calculated the exchange-coupling energy,?E X,between the two adatoms by taking the energy dif-ference between a parallel(↑↑)and an antiparallel(↑↓) orientation of the two adatoms,
?E X=E b(↑↑)?E b(↑↓).(10) using,however,the self–consistent potentials for the par-allel con?guration.We are aware of the fact that,due to the lack of self–consistency in the antiparallel case,for near adatoms this approach might be quite poor.We be-lieve,however,that this approximation provides a good estimate of the sign and the magnitude of the interaction. The calculated?E X is shown in Fig.4for Fe and Co as a function of the distance d between the two adatoms. Apparently,for d=a in both cases a strong,ferromag-netic nearest–neighbor exchange-coupling between these two atoms applies,with an interaction energy somewhat larger for Fe than for Co.As the two adatoms are adja-cent in this case,this strong coupling can be attributed to a direct exchange mechanism.Increasing the separa-tion between the two adatoms,?E X rapidly decreases. For d=2a it changes sign,i.e.,the coupling becomes antiferromagnetic.Since for an antiparallel alignment of the spin moments of the two adatoms,lying close to each other,the electronic structure and the magnetic moments might be expected to di?er to some extent as compared to a parallel con?guration,the corresponding values of S z and L z in Table3can be questioned.Therefore,for this particular case we performed self–consistent calcula-tions also for the antiparallel alignment.Assuringly,for both Fe and Co,we obtained the same value of S z and L z within1%relative accuracy as in the case of a parallel alignment.For larger distances we observe ferromagnetic coupling,which virtually vanishes for d≥5a,implying a very weak,short ranged exchange interaction between the adatoms of Fe and Co induced by the Ag host.
V.SUMMARY AND CONCLUSIONS
By using a real–space embedding technique based on the Korringa–Kohn–Rostoker Green’s function method, we have performed fully relativistic,self-consistent cal-culations for adatoms and small clusters of Fe,Co and Ni on Ag(100).Due to the decreased coordination of the magnetic atoms,we obtained slightly enhanced spin mo-ments for adatoms and small clusters of Fe and Co and found that the spin moments are already close to the monolayer values for a cluster of9atoms.In agreement with experiments30the adatoms and dimers of Ni turned out to be nonmagnetic,while the spin moments in larger Ni clusters indicated a complex formation of magnetism. In connection with strongly enhanced orbital moments, for Fe and Co adatoms we revealed an unusually strong tendency to perpendicular magnetism.The perpendic-ular magnetism persisted also for Fe clusters of increas-ing size,whereby the atom–like contributions showed an oscillating behavior depending mainly on the local rota-tional symmetry.The preferred orientation for clusters of Co and Ni obtained was in–plane.In addition,we inves-tigated the magnetic coupling between two adatoms of Fe or Co,for which we established a’good local–moment’behavior.In terms of calculated exchange-coupling en-ergies,the dimers show a strong ferromagnetic coupling, which immediately drops two orders of magnitude with increasing distance between the two adatoms,indicating a weak,indirect coupling between them.
The main outcome of the present paper is that by per-forming?rst principles calculations,not only the qual-itative trends of small cluster magnetism of transition metals,but even quantitative results can be obtained which in turn can directly be compared with experiments. By using a parallelized version of our computer code the number of atoms treated in the cluster can be easily in-creased to some hundreds.This is encouraging to extend the present calculations to larger nanostructures(mag-netic wires,dots,corrals etc.)currently being in the very focus of technological applications.
ACKNOWLEDGMENTS
This paper resulted from a collaboration partially funded by the RTN network“Computational Magneto-electronics”(Contract No.RTN1-1999-00145).Finan-cial support was also provided by the Center for Com-
putational Materials Science(Contract No.GZ45.451), the Austrian Science Foundation(Contract No.W004), and the Hungarian National Scienti?c Research Founda-tion(OTKA T030240and OTKA T029813).We thank Prof.P.H.Dederichs for valuable discussions.
TABLE II.Calculated orbital moment anisotropies(?L), in units ofμB,and contributions of the Fe atoms to the MAE,?E,in units of meV,for small clusters of Fe on Ag(100). For each cluster,the total MAE per Fe atom of the cluster including the neighborhood is also given in parentheses. Cluster position n c?L x?z?E x?z?L y?z?E y?z adatom0-0.37 5.07-0.37 5.07
(5.61)(5.61) dimer11-0.12 2.14-0.11 1.66
(2.30)(1.83) trimer12-0.12 1.93-0.080.93
21-0.16 2.83-0.15 2.39
(2.72)(2.13) tetramer12-0.020.50-0.020.50
(0.54)(0.54) pentamer14-0.030.49-0.030.49
21-0.030.92-0.080.85
31-0.080.85-0.030.92
(0.90)(0.90) 3×3cluster140.000.230.000.23
23-0.020.43-0.010.84
33-0.010.84-0.020.43
42-0.13 1.86-0.13 1.86
(1.20)(1.20)
TABLE III.As in Table II for Co clusters.
Cluster position n c?L x?z?E x?z?L y?z?E y?z adatom0-0.26 4.20-0.26 4.20
(4.36)(4.36) dimer110.15-3.50-0.010.67
(-3.49)(0.76) trimer120.40-9.06-0.02-0.11
210.34-6.290.05-0.04
(-7.44)(-0.01) tetramer120.15-2.290.15-2.29
(-2.37)(-2.37) pentamer140.12-2.460.12-2.46
210.21-4.16-0.01-0.03
31-0.01-0.030.21-4.16
(-2.22)(-2.22) 3×3cluster140.13-1.860.13-1.86
230.10-1.560.18-2.96
330.18-2.960.10-1.56
420.16-2.600.16-2.60
(-2.45)(-2.45)
TABLE IV.As in Table II for Ni clusters.
Cluster position n c?L x?z?E x?z?L y?z?E y?z trimer120.19-6.120.18-1.38
210.11-3.720.08-1.00
(-4.63)(-1.13) tetramer12-0.050.07-0.050.07
(0.10)(0.10) pentamer140.15-2.260.15-2.26
210.01-1.640.05-0.69
310.05-0.690.01-1.64
(-1.41)(-1.41) 3×3cluster14-0.06-0.02-0.06-0.02
230.02-0.750.06-2.00
330.06-2.000.02-0.75
420.05-1.210.05-1.21
(-1.17)(-1.17)
FIG.1.Sketch of the planar clusters considered.For an
orientation of the magnetization along the x or y axis,the equivalent atoms in a cluster are labelled by the same
number.
Shells
0.870
0.875
0.880L z (μΒ
)
3.3803.385
3.390S
z (μΒ
)
7.3657.3707.375N v a l
FIG.2.Calculated number of valence electrons (N val ),
spin moment
(S z )and
orbital moment
(L z )
of a single
Fe adatom on a Ag(100)
surface as a
function of the
number of
the self-consistently treated atomic shells
around the Fe
atom.
d (a)
0.0
1.0L z (μΒ
)
2.0
3.0
S
z (
μΒ
)FIG.3.
Calculated spin
and orbital moments of two adatoms of Fe or Co on Ag(100)as a function of their dis-tance d measured in units of the 2D lattice constant a .
d (a)
-300
-200-1000
?E X (m e V )
-300-200-1000
?E X (m e V )
FIG.4.Calculated exchange coupling energy,?E X ,be-tween two adatoms of Fe or Co on Ag(100)as a function of the distance d measured in units of the 2D lattice constant a .The insets show the range 2a ≤d ≤5a on a blown up scale.
Mass Balance Calculation 1. Measured Items: ●Crude Ore ●Waste ?Wet End Waste ?Dry End Waste ?Unpacked Filler ?Leaking ●Products ?Filter Aid ?Filler ?Naturals 2. Methods: ●Crude Ore Ask load truck operators to count the number of loads during his shift. Multiply this number and the average dry weight of each load that we measured in the past. Comments: there are a lot of uncertainties going on. Operators could forget putting down the number or to make the number of loads higher, namely better, he could lift less material in each load. The measured average dry weight of each load varies from shift to shift and depends on what combination of crude ores is being used to make product. Improvement: we need to make the operators accountable for these numbers. Award and punishment system can be implemented. (Short-term). There is no metrics of mass flow in the system. To eliminate human errors and have a better monitoring system, a weight belt is necessary and doable at this point. The data can be retrieved and treated due to the presence of PLC that is used on the spot. Similarly, we are tracking diesel usage every day by looking at the data history. (Long-term) ●Waste ?Wet end waste, dry end waste, unpacked filler These components are tracked every day on production report. Basically, they use the number of loads or bags multiplied by the average dry weight per unit. Similar problems could occur at any time. But because the variance is a small amount, we just need to make the production leader accountable for these numbers. ?Leaking It is happening all the time. Pretty hard to measure and quantify, we may be able to calculate it if we have good measurement on crude ore.
UFI CALCULATION STANDARDS and DEFINITIONS The figures requested for an UFI approved event, as mentioned in article 3 of the UFI Internal Rules, will be counted and audited according to the following definitions and rules. A. Calculation Standard for the Surface Area of an Exhibition For an Organizer, the figure to be certified and provided is the "total net exhibition space", defined as follows: total floor space - indoors and outdoors - occupied by exhibitors. This is also called “contracted space”, and may include both paid and unpaid space. It also includes space allocated to special shows having a direct relation to the theme of the exhibition. For an Exhibition Centre operator, the figure to be provided is the "total gross exhibition space". This is the total space provided by the venue operator for use by the organizers or, the total space used by the fair, including circulation. Catering areas, offices, storage, etc. are excluded. When exhibition space figures are communicated, they must always be specified as “total net” or “total gross”. B. Calculation Standard for the Number of Exhibitors B.1. Exhibitors (“direct” exhibitors) Only the exhibitors (“direct” exhibitors) will be counted. Considered as such are both the main exhibitors and the co-exhibitors. The main exhibitors are those bodies contracting directly with the organizer. The co-exhibitors are those organizations/companies present on a main exhibitor's stand, with their own staff and their own products and/or services. They must be clearly identified via several means, e.g. mentioned on the application form of the main exhibitor or declared by an official co-ordinating body, or in the exhibition catalogue forms. In the case of a collective participation, the space must be rented and paid for by the exhibitor organising the collective participation. The area is shared by several participants who are considered to be co-exhibitors if they occupy their own area, appear under their own name and present their own products/services by their own staff. If each of these conditions is not fulfilled, they are considered as “represented companies” (“indirect” exhibitors), and may not be counted in the exhibitor tally. In any communication with reference to the UFI standard, or to the UFI approval of an event, only the figures related to direct exhibitors may be used. B.2. Represented companies (“indirect” exhibitors) Represented companies are those organizations/companies not present with their own staff, and whose products or services are present on a main exhibitor's or co-exhibitor's stand. These represented companies are excluded from the calculation of the total number of exhibitors. B.3 To avoid any confusion, it must be clearly mentioned which category of exhibitors were counted.
RTA Form 395K September 2006 Roads and Traffic Authority, NSW SEAL OR RESEAL DESIGN CALCULATION SHEET (FOR CONVENTIONAL, EMULSION, POLYMER BINDER and GEOTEXTILE TREATMENTS) T y p e o f T r e a t m e n t Seal (S) or Reseal (RS) Single / Single (S/S) Single / Double (S/D) Double / Double (D/D) Geotextile Reinforced Seal (GRS)High Strength Seal (HSS) Strain Alleviating Membrane (SAM) or Strain Alleviating Membrane Interlayer (SAMI)Primersealed (PS), Sealed (S) Existing Aggregate Size (nominal) Primed (P) Asphalt (AC), Slurry Surfacing (SS) Cement Concrete (CC)Timber Bridge Deck (TD) Unit Shoulder Lane 1 Lane 2 Lane 3 Lane 4 Surface Texture mm Ball Penetration Depth of Prime or Primerseal (required for seals only)mm E x i s t i n g S u r f a c e C o n d i t i o n s Age of Surface Years Aggregate Design Unit 1st layer 2nd layer Nominal Size -mm Crushed (C), Partly Crushed (PC) or Rounded (R)--Compatible with existing seal (size checked)-yes/no Average Least Dimension ALD ALD mm ALD 1 = ALD 2 = Basic Aggregate Spread Rate (Table 1A/1B)F m 2/m 3 Factors for Spread Rate (Table 2)I -Design Aggregate Spread Rate = F x I H m 2/m 3 Geotextile Type - eg Polyester or Polypropylene M a t e r i a l s f o r S e a l o r R e s e a l Binder Type/Class Road Number/Name:Location: J o b D e t a i l s Length Width Area Number of Lanes Roadloc: to Date: Job/Order Number: Office: Segment Number: km to km from towards m m m 2 mm File
Different Methods of Depreciation Calculation Depreciation Calculation Methods Various depreciation calculation methods are mentioned below: i. Base Method ii. Declining Balance Method iii. Maximum Amount Method iv. Multi Level Method v. Period Control Method i. Base Method Base Method- SPRO> IMG> Financial Accounting (New)> Asset Accounting>Depreciation> Valuation Methods> Depreciation Key> Calculation Methods>Define Base Methods Base method primarily specifies: ?The Type of depreciation (Ordinary/ Special Depreciation) ?Depreciation Method used (Straight Line/ Written Down value Method) ?Treatment of the depreciation at the end of Planned useful life of asset or when the Net Book value of asset is zero (Explained in detail later in other related transactions ). Straight Line Method (SLM) ?This is the simple method of depreciation. ?It charges equal amount of depreciation each year over useful life of asset. ?It first add up all the costs incurred to bring the asset in use and then it divides that by the useful life of asset in years to calculate the depreciation expense. ? E.g.: Say a Computer costs Rs. 30,000 and Rs. 11,000 (as additional set-up/installation/maintenance expenses) = Rs 41,000 and it is anticipated that its scrap value will be Rs. 1,000 at the end of its useful life, of say, 5 yrs. Total Cost = Cost of Computer + Installation Exp. + Other Direct Costs Depreciable Amount over No. of years = Total Cost - Salvage Value (At end of useful life) 30,000 +11,000 =41,000 (Total cost) 41,000 – 1,000 = 40,000 as the Depreciable Amount Depreciable Amount = Rs. 40,000, Spread out over 5 years = Rs. 40,000/5(Yrs) = Rs. 8000/- depreciation per annum. Written Down Value Method (WDV) ?This method involves applying the depreciation rate on the Net Book Value (NBV) of asset. In this method, depreciation of the asset is done at a constant rate. ?In this method depreciation charges reduces each successive period.
关于Maxwell参数化扫描时添加calculations报错的说明当需要考查某一物理量改变时，对其他量的影响，这时需要用到参数化扫描的功能。以同步发电机为例，常常需要考察不同励磁电流下，空载电压的大小，以便绘制空载特性曲线。这时，可以将励磁电流作为变量，然后扫描之,具体操作为：右键Optimetrics，选择add parametric，通过add定义励磁电流变化范围。在calculations里面，点击左下角setup calculations,report type选择transient,parameter选择moving1,category选择winding，quantity 选择A相induced voltage,function选择none。这时，点击add calculation，done，就会发现出现红叉叉，系统提示“calculation must be a dimension reducing ranged function,when using solution'setup1:transient'”。之所以出现这个错误，原因就在于定义的A相induced voltage是一个函数，是随时间变化的量，而软件要求A相induced voltage也就是calculation expression 必须是“single, real number”，因此在上述操作的基础上，还需点击右上角的Range function，category选择math，function选择rms，点击ok。这时，再add calculation，done，就正确了。以上操作的目的是，通过扫描励磁电流和A相电压有效值的关系，实现了绘制同步发电机空载特性曲线的功能。 现在，该知道错在哪里，以及如何避免出错了吧？ 其实，setup calculations功能完全多此一举，即使这个地方不设置，求解完成后，后处理一样可以得到表达式与扫描量的关系，不会的同学可自己试着发掘一下 Maxwellhelp文件为Maxwell2D/3D的瞬态求解设置铁芯损耗一、铁损定义（coreloss definition）铁损的计算属性定义（CalculatingPropertiesforCoreLoss(BPCurve)要提取损耗特征的外特性（BP曲线），先在View/EditMaterial对话框中设置损耗类型（CoreLoss Type）是硅钢片（ElectricalSteel）还是铁氧体（PowerFerrite）。以设置硅钢片为例。1、点击Tools>EditConfiguredLibraries>Materials. 或者，在左侧project的窗口中，往下拉会有一个文件夹名为definitions，点开加号，有个materials文件夹，右击，选择EditAllLibraries.，“EditLibraries”对话框就会出现。2、点击AddMaterial，“View/EditMaterial”对话框会出现。3、在“CoreLossType”行，有个“Value”的框，单击，会弹出下拉菜单，可以拉下选择是硅钢片（ElectricalSteel）还是铁氧体（PowerFerrite）。其他的参数出现在“CoreLossType”行的下面，例如硅钢片的Kh,Kc,Ke,andKdc，功率铁氧体的Cm,X,Y,andKdc。如果是硅钢片，对话框底部的“CalculatePropertiesfor”下拉菜单也是可以使用的，通过它可以从外部引入制造厂商提供的铁损曲线等数据（Kh,Kc,Ke,andKdc）确定损耗系数（CoreLossCoefficient）。4、如果你选择的是硅钢片，按如下操作：①从对话框底部的“CalculatePropertiesfor”下拉菜单中选择损耗系数的确定方法（永磁铁permanentmagnet、单一频率的铁损corelossatonefrequency、多频率的铁损corelossversusfrequency）,然后会蹦出BP曲线对话框。单一频率的损耗：点击图表上面的“Importfromfile.”可以直接导入BP曲线数据文件，但要“*。Tab”格式文件。如果纵横轴错了，可以点击“SwapX-YData”按钮，调换B轴和P轴的数据，但是B轴和P轴的方向不变。或者直接在左侧的表格中填入对应的B值和P值，行不够了可以点击“AddRowAbove”按钮，和“addrowbelow”分别从上面和下面添加行，“appendrows”是一口气加好几行，或者删除行“deleterows”。表下面的“frequency”表示当前的BP曲线是在什么频率下的性能。“Thickness”表示硅钢片的厚度，“conductivity”是电导率。点击“OK”确定。多频率的损耗：打开对话框后左下方有个“Edit”窗口，是添加要设定BP曲线的频率的。分别加上几个频率，如1Hz和2Hz。每填写一个赫兹点一下“Add”按钮，就会把频率添加到上面的
应用指南 版本号：发布日期：作者：00 2007-10-31 Markus Hermwille 关键词：IGBT驱动器，计算，栅极电荷，功率，栅极电流IGBT 驱动器的计算 引言 (1) 栅极电荷曲线 (1) 测量栅极电荷 (3) 确定栅极电荷 (3) 驱动器输出功率 (5) 栅极电流 (5) 栅极峰值电流 (6) 选择合适的IGBT驱动器 (6) DriverSel – 简便的IGBT驱动器计算方法 (6) 符号和术语 (7) 参考文献 (8) 本应用指南提供了关于确定用于开关IGBT的驱动器输出 性能的信息。所提供的信息仅包括提示并不包含完整的设 计规则。信息并不全面，设计是否合适取决于用户自己。 引言 除功率模块自身外，电力电子系统的一个关键器件是IGBT驱动器，它在功率晶体管和控制器之间形成了一个极为重要的接口。基于这个原因，驱动器的选择和驱动器输出功率的正确计算与转换器方案的可靠性紧密相连。驱动力的不足或驱动器选择错误可能会导致模块和驱动器故障。 栅极电荷曲线 IGBT模块的开关行为（导通和关断）取决于它的结构、内部电容（电荷）以及内部和外部阻抗。当需要计算IGBT驱动器电路的输出功率时，关键的参数是栅极电荷。栅极电荷由等效输入电容C GC和C GE决定。 IGBT 电容
应用指南 寄生寄生电容电容电容和和 低信号电容 C ies , C oes , C res = f(V CE ) 电容 意义 C GE 栅极-发射极电容 C CE 集电极-发射极电容 C GC 栅极-集电极电容 （密勒电容） 低信号电容 意义 C ies = C GE + C GC 输入电容 C res = C GC 反向传输电容 C oes = C GC + C CE 输出电容 V GE = 0V f = 1MHz 下表给出了IGBT 导通期间简化的栅极电荷波形 V GE = f(t) 、 I G =f(t)、V CE =f(t)和 I C =f(t) 。导通过程可分为三个阶段，分别为栅极-发射极电容充电阶段、栅极-集电极电容充电阶段和栅极-发射极电容充电直到IGBT 完全饱和阶段。 对于开关特性和驱动器的计算，输入电容可能只具有一定程度的影响。确定驱动器输出功率更实际的方法是采用IGBT 数据表中给出的栅极电荷特性。该特性给出了栅极-发射级电压V GE 和栅极电荷Q G 之间的关系。在IGBT 模块的额定电流下，栅极电荷线性增长。栅极电荷也依赖于直流环节电压，尽管程度较轻。在更高的运行电压下，由于密勒电容的巨大影响，栅极电荷增大。在大多数应用中，该影响可忽略不计。 简化的栅极电荷波形 栅极电荷特征
FAULT CALCULATION Sompol C Power System Fault Analysis All protection Engineers should have and understanding to :- Calculate power system currents and voltages during fault condition Check the breaking capacity of switchgear is not exceeded Determine the quantities which can be used by relays to distinguish between healthy (i.e. loaded ) and fault conditions Appreciate the effect of the method of earthing on the detection of earth faults Selected the best relay characteristics for fault detection Ensure that load and short circuit ratings of plant are not exceeded Select relay settings for fault detection and discrimination Understand principles of relay operation Conduct post fault analysis
Introduction of Thermodynamic Calculation Software 1. Thermo-Calc 1.1 Introduction Thermo-Calc has over the past 30 years gained a world-wide reputation as the best and most powerful software package for thermodynamic calculations. Thermo-Calc series of software have been developed originally at the Department of Materials Science and Engineering of KTH (Royal Institute of Technology), Stockholm, Sweden, and since 1997 further by the company Thermo-Calc Software (TCS). They are the results of more than 35 years and 150 man-years R&D and many national/international collaborations through various R&D projects. The main products include: Thermo-Calc(including classic version TCC and windows version TCW), focusing on thermodynamics based upon a powerful Gibbs Energy Minimizer DICTRA (for Diffusion-Controlled phase TRAnsformation), focusing on kinetics TC-PRISMA, focusing on nucleation, growth/dissolution and coarsening MICRESS(the MICRostructure Evolution Simulation Software), focusing on the calculation of microstructure formation based on the multiphase-field concept Software Development Kits(including TQ-Interface, TC-API and TC-Toolbox for MA TLAB), focusing on secondary development by different users 1.2 Database ?Steels and Fe-alloys ?Nickel-based superalloys ?Magnesium-based alloys ?Solder alloys ?Noble metal alloys ?Slag, molten salts, oxides and ionic solutions ?Aqueous solutions ?Nuclear materials ?Minerals ?Databases from Thermotech Ltd 1.3 Capability Thermo-Calc is widely used for a variety of calculations including calculating: ?Stable and meta-stable heterogeneous phase equilibria ?Amounts of phases and their compositions ?Thermochemical data such as enthalpies, heat capacity and activities ?Transformation temperatures, such as liquidus and solidus ?Driving force for phase transformations ?Phase diagrams (binary, ternary and multi-component) ?Solidification applying the Scheil-Gulliver model ?Thermodynamic properties of chemical reactions
Ocean Engineering28(2001)915–932 Technical note Empirical calculation of roll damping for ships and barges Subrata Chakrabarti* Offshore Structure Analysis,Inc.,13613Capista Drive,Plain?eld,IL60544,USA Received28January2000;accepted15March2000 Abstract For a large?oating structure in waves,the damping is computed by the linear diffraction/radiation theory.For most degrees of freedom,this radiation damping is adequate for an accurate prediction of the rigid body motions of the structure at the wave frequencies. This is not particularly true for the roll motion of a long?oating structure.For ships,barges and similar long offshore structures,the roll damping is highly nonlinear.In these cases the radiation damping is generally quite small compared to the total damping in the system.More-over,the dynamic ampli?cation in roll may be large for such structures since the roll natural period generally falls within the frequency range of a typical wave energy spectrum experi-enced by them.Therefore,it is of utmost importance that a good estimate of the roll damping is made for such structures.The actual prediction of roll damping is a dif?cult analytical task. The nonlinear components of roll damping are determined from model and full scale experi-ments.This paper examines the roll damping components and their empirical contributions. These empirical expressions should help the designer of such?oating structures.The numerical values of roll damping components of typical ships and barges in waves and current(or for-ward speed)are presented.?2001Elsevier Science Ltd.All rights reserved. Keywords:Damping;Roll;Ships;Formulas;Barges;Experiments 1.Introduction The purpose of this paper is to examine the damping characteristics of a variety of ship shapes and offshore structures undergoing roll motion in the presence of waves.Unlike other degrees of freedom motion,roll damping is *Tel.:+1-815-436-4863;fax:+1-815-436-4921. E-mail address:chakrab@https://www.doczj.com/doc/ee9570168.html,(S.Chakrabarti). 0029-8018/01/$-see front matter?2001Elsevier Science Ltd.All rights reserved. PII:S0029-8018(00)00036-6