AN AB-INITIO STUDY OF X-RAY EMISSION IN ScPd3 AND YPd3

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AN AB-INITIO STUDY OF X-RAY EMISSION IN ScPd3 AND YPd3

M. Khan, C. Koenig

To cite this version:

M. Khan, C. Koenig. AN AB-INITIO STUDY OF X-RAY EMISSION IN ScPd3 AND YPd3. Jour-

nal de Physique Colloques, 1987, 48 (C9), pp.C9-1067-C9-1070. �10.1051/jphyscol:19879194�. �jpa-

00227311�

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AN AB-INITIO STUDY OF X-RAY EMISSION IN ScPd, AND YPd,

M.A. KHAN and C. KOENIG

Laboratoire de Magnetisme et de Structure Electronique des Solides (CNRS UA-306). Universite Louis Pasteur, 4, Rue Blaise Pascal, F-67070 Strasbourg Cedex, France

R6sumd - Nous avons calcul6 de fason autocohdrente la structure dlectronique de ScPd3 et YPd par la m6thode des orbitales "Yuffin-tin:' lingarisdes (LMTO).

Les 6nergies propres et les vecteurs propres fournis par ce calcul servent 3 3 calculer les intensitds des spectres d16mission de rayons X, en tenant compte proprement des probabilitss de transition et des densit& d16tats partielles.

Abstract

-

The electronic structuresof ScPd and YPd are calculated self- consistently by the method of ine ear-Muf f

in- in-0rbi3als

3 ^(LMTO)

.

The eigen- values and eigenvectors thus obtained are used to calculate the intensity of the X-ray emission spectra where the transition probabilities and the partial densities of states are properly taken into account.

I - INTRODUCTION

The study of ScPd and particularly YPd3 is an interesting initial step to under- stand the

physics?

properties of intermetallic compounds with heavier rare earth ele- ments which have been extensively studied because of the heavy fermions / I / . The pho- toemission (XPS) and the Bremsstrahlung Isochromat Spectroscopy (BIS) measurements have been performed on YPd3 /2/ and a good agreement with the calculated density of states of the occupied and empty states has been obtained /2,3/. The optical absorption of YPd has been measured /4,5/ and in the high energy range the structuresdue to interbani transitions have been confirmed. In s ~ i t e of the great interest in the spectroscopic measurements the soft X-ray emission and absorption spectra of ScPd and YPd are not yet available. Here we present the theoretical curves of X-ray emis- 3 sion in ScPd3 and YPd 5or different core levels like ls(K), 3 2p (L2,3) and 3d(M _{) .} In the next section we give a brief description of the energy band calculation 4tf?en 3 the formalism to calculate the emission spectra. Finally we shall present and discuss our results.

I1 - ENERGY BANDS

For the self-consistent calculation of the band structure (BS) we have used the LMTO method 161. The details of the calculation of BS of ScPd and YPd with Is', 'p' and

3 3

Id' (i.e. 1 < 2) conduction electrons have been already published by one of us /3/.

For the present case we have included the 'f' states (i.e. 1 = 3) in the conduction band. Thus, instead of a 36 x 36 matrixwhave a 64 x 64 matrix to resolve for each k-point. The ~rystal~structure of ,ScPd and YPd is of AuCu3 type. The lattice para- meters are : 3.9595 A and 4.0727 A /3? for

ik~d

and YP6 respectively.

The details of band structure do not vary apprec~ably 3. wit! the inclusion of the 'f' states as compared to those obtained without them. We present in figs 1 and 2 the total density of states (TDOS) and total number states (TNOS) for ScPd3 and YPd3 respectively. The presence of 'f' electrons in the occupied states is negligible. In any case on any atomic site the number of 'f' electrons below the Fermi level never exceeds 0.35Z.The high density regions in YPd, are com~arable to those observed in XPS and BIS /2/.

or-the

present study we havi limited~ourselves to 165 k-points in the irreducible Brillouin Zone.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879194

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JOURNAL DE PHYSIQUE

Figs. 1 and 2 : Total (T) Density (D) and Number (N) Of States (0s) per Ily and per Spin for a unit cell in ScPd3 (Fig.1) and YPd (Fig.2).

3 I11 - X-RAY EMISSION

From the band structures calculation now we know the initial states

I

^jk>with j being the band index. The final states are the core levels InRJ> (n and

R

are the principal and orbital quantum numbers and J is the total moment) where some holes have been created. The respective energy levels of the initial and final states are Ej

(E)

and XnRJ. For photon energy w = Ei (k)- EnRJ

(H

= 2m=e2/2 = 1) the intensity of emission is / 7 / : InRJ(w) a w3?

nRJ (1)

FnRJ(w) is the so called oscillator strength and is written as /8/ :

3 R + 1 2

R

FnaJ(w) =

-

^2L+ I ( ~ R J I ~ I R +

1 1 1

nec1(~) + I ( ~ ! - J I ~ I L - ~ ) I ~ n,-,(~) (2) with E = w+ EnRJ

nR(E) is the 'R' projected density of states os the conduction band and (nR.JlrlRt) are the radial integrals : (nRJlrlRt) = ~ ~ r3+nRJ PR, (E,r) d r

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S is the atomic sphere radius and d (E,r) and +nRJ represent the radial parts of the conduction and the core states. R

IV

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RESULT AND DISCUSSION

In fig.3 we present some emission spectra as obtained with help of the expression 1 (curves A). These ab initio curves A have many fine structures which are not usually observed experimentally. Thus, to facilitate the comparison with any future measurements, these one particle curves have been convoluted to include the lifetime broadening due to the core hole. In the absence of any experimental data we have used arbi- trarily the life times T

'

⁼0.2 and 0.5 eV. The convolution is a Lorenzian broadening 181. These two life-time broadening effects are indicated as curves B and C on each emission spectrum.

In fig.3 the K, L and ?I emission spectra are presented in first, second and third columns. ~hz'girst t$65rows show the emission on Scflst) and Pd(2nd row) in ScPd3 while the last two represent the corresponding spectra on Y(3rd row) and Pd

(4th row) in YPd3. All the emission spectra are with reference to the Fermi level EF.

We shall not comment on each individual spectrum here, since the prominent features and structures that should be observed experimentally are evident in fig.3. However, it should be noted that the Pd emission spectra in YPd3 and ScPd

,

even though they have the same general features, yet they differ in t h e ~ r detailea structures. Parti- cularly, the PdK and PdY show that the 'p' partial densities of states on Pd sites in YPd and ScPd are no$'?dentical. Looking at the shapes ofthe Y and Sc ernissionspec- tra in YPd3 and 3cpd3 if is not easy t0distineuish between them unless one cheks the 3

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experimental data. Due to the well established fact that the simple one particle ap- proach gives satisfactory results for X-ray emission / 8 , 9 / provided the so-called

"final state rule" / l o / is properly taken into account, we are certain that in this work we have presented all the observable details of the X-ray emission in ScPdg and YPd3.

DEAG/ cmr

ScL 2 9 3

Fig.3

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Soft X-ray emission in ScPdg (First two rows) and YPd3 (Last two rows)

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JOURNAL

DE

PHYSIQUE

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