Determination of the Spectral Intensity

Determination of the Spectral Intensity ... 1975) It is sufficient to measure the Isv'(Ehk~) modified by the quantum efiiciency of the detector in the...

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Determination of the Spectral Intensity

of the Incident Beam In the Energy Disperslve X ray Dlffractlon by Ryosei UNO and Jun ISHIGAKI College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajosui, Setagaya-ku, Tokyo 156, Japan

In the determination of structure factors by means of the energy dispersive X-ray diffraction, the spectral intensity of the incident beam was the most difficult quantity for

us to measure. The most accurate method of the measurement is that the spectral intensity is estimated from the integrated intensities of a well-defined Bragg reflexion

at more than 10 energies by the use of calculated structure factors of the refiexion at relevant energies. The spectral intensity directly measured by the SSD at very low tube

current can be used to determine the structure factors with moderate accuracy, when anomalous X-ray sources do not appear on the anticathode at the reduced tube current.

Introduction In the energy dispersive X-ray diffraction of a thick powder sample, the relative integrated intensity of a Bragg reflexion, I. (hkl) , in the symmetric reflection case, is

given by (Cole, 1970) I , .(Ehkl)m(hkl) I F. (hkl) 1 2 1 + cos226hkl

p*(Ehkl)Ehkl 2sin3ehkl where 6 hht is the Bragg angle of the reflexion hkl, E; hl the X-ray energy at the Bragg peak, pr(Ehkt) the relative absorption coefiicient at Ehhz, I "(Ehkb) the incident beam in-

tensity at Ehhl' m(hkl) the multiplicity factor and F.(hkl) the relative structure factor.

In order to obtain F.(hkl) from I.(hkl), Enht, Pr(Ehkt), Iu'r(Ehkl) and 6hkl should be

known, among which lu"(Ehhl) was the most difficult quantity for us to measure. (Uno, 1975) It is sufficient to measure the Isv'(Ehk ) modified by the quantum efiiciency of the detector in the energy dispersive X-ray diffraction, because the measured I.(nk ) is also modified by the same quantum efflciency. In this paper the spectral intensity means that modified by the quantum efficiency of the detector.

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Proceedings of the Institute of Natural Sciences (1980)

In the measurement of I .(Ehk ) by the use of the solid state detector (SSD), two kinds of measurements were tried. In the first one, the spectral intensity was estimated

from the integrated intensity of a well-defined reflexion measured at several energies.

In order to obtain I .(E, kl) from eq. (1), F.(hkl) and pr at E, t should be known in-

dependently. In this method I.(hkl) had to be measured at more than 10 Bragg angles,

so that one of merits of the energy dispersive method is lost. The merit is that the

structure factors can be obtained from measurements at 2 or 3 Bragg angles. In the second one, the spectral intensity was directly measured by the SSD. In this case, the intensity of the incident beam should be reduced to about 2000 cps or less. This could be realized by the use of a pin-hole slit, of a proper absorber or by the reduction of the tube current.

The most accurate method to obtain the spectral intensity of the incident beam is the first one. If the X-ray energy is high enough, so that the anomalous dispersion of

the sample can be neglected, it is recommended to measure the integrated intensity of

a well-defined Bragg reflexion of the sample, because I*.(E)/p.(E) can be estimated from I.(hkl. E) with assuming that the F.(hkl. E) is constant against energy, and the

F.(hkl)'s of the other reflexions can be obtained from lr(hkl) and lw'(E)/pr(E). In this case F.(hkl)'s are free from errors in p.(E).

The direct measurement of I,*.(E) by the use of the SSD may be available for the

measurement of the relative structure factors with moderate accuracy, when the tube current is reduced to several pA and strong anomalous sources of X-ray are not appeared on the anticathode.

Experimental The schematic diagram of our system is shown in Fig. 1. The goniometer was an

r

Goniometer

Cryostat '

lb Q . S pedmen ..

2e SSD Pre ' SiCLi) A Arnp Sotter

l

l

t I suppl:y Fig' I The schematic diagram I of t_ub the system mea.t X_-ral _ surementofin our the energy Printer

dispersive X-ray diffrac-

su p ply

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Determination of the Spectral Intensity of the Incident Beam in the Energy Dispersive X-ray Diffraction

ordinary one of horizontally scanning type, modified that the X-ray tube was scanned in

place of the counter. The detector was the Si (Li) SSD, the full width at half maximum

(FWHM) of which was about 300 eV in the range from 13 to 25 keV. The detector was followed by an amplifler and a multichannel analyser with 1000 channels. H .T. Trans. (-H J.)

X-ray tube

Shunt

Resistcr

D.C.

= 80V

mA ' ,

C.V.T.

AC. I OOV

Fig. 2 The diagram of our system to reduce the X-ray tube current.

The dimension of powder sample of GaSb was less than 3 pm, which was cllected by means 0L sedimentation in xylene. The diagram of our system to reduce the tube current to several pA is shown in Fig. 2. The resistor of 27 kl2 was connected in paral-

lel with the X-ray tube, in order to guarantee proper operation of a vacuum tube by which the tube voltage was regulated.

Results (1) The spectral intensity of the incident beam estimated from the integrated intensity of a well-defined reflexion.

The 220 reflexion of a GaSb powder sample was chosen as the well-defined reflexion.

Its integrated intensity was measured at 13 Bragg angles in the energy range from 13 to 25 keV. In order to measure the relative absorption coefflcient at the Bragg peaks, a thin slice of a polycrystalline GaSb was prepared, the thickness of which was about 60

;tm. The integrated intensities of Bragg peaks were Ineasured when the slice was set in the path of the incident beam (1.abs), and when it was taken off (Ir) ' The relative absorption coefficient was obtained from the ratio of lr and I. b* by p.(E) = In [Ir(E) /1. bs (E) J .

The result rs shown m Fig. 3. The p.(E) can be approximated to be proportional to

E-2.64, as shown m Frg 4

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Proceedings of the Institute of Natural Sciences (1980)

Relative Abeorpton Coefftcient

¥

of OaSb

4

Re!ative Absorption Coefficient

of Gasb

¥ Ei2 4

O・G

ao

//

0・4

JJr El

¥<:2

l**

¥

20

ot , !

0・2

' L Ele

0

lo g Fr

R o

o

0,0

X ¥0 _

¥¥ 1'o 1'2 1'4 o

1 )

to9 E

0.2

1 5 25 E 20

l'l

keV

Fig. 4 The logarithm of the relative absorp-

Fig 3 The relative absorption coeflicient of

tion coeflicient of GaSb against the log-

GaSb against the X-ray energy.

arithm of the X-ray energy.

The integrated intensity of the 220

Spectrum of Incident Beam

reflexion of GaSb powder sample at 13

X I 0 3 A

8,0

From lrf220)

/' x; &x¥;¥ oA o

By SSD

. ; 500cps :¥

1500cps

2000cps

7.0

1'3

o

Bragg angles are shown in Table l. The

+ A

structure factors at relevant energies are calculated by F..1 (220) = 4[ ( f G. (220) + f G. (E)

Xl

+ if "Ga (E) ) exp ( - BGa (sine / 1) 2202) lwr

+ (fsb (220) + f sb (E) + i f "sb (E) )

e,o

x

X exp ( - J Sb (sin e / I ) 2202) J .

¥

The correction terms for the anomalous

¥

)< l 5.0

dispersion are calculated following the

method of Cromer (1965) . The temperature factors of the same sample have been

o 4,0

already obtained by the usual angle dis-

15 25 keV

persive method, as BG*=1.91A2 and Bsb

Incident beam from a tungsten tube by

from I.(220, E), p.(E) and F..1(220, E).

two methods. The one was estimated

The result are shown in Fig. 5, and

20 E

Fig. 5 The observed spectral intensity of the

from the integrated intensity of the 220

refiexion of GaSb and the others were directly measured by the SSD at very

=1.05A2. Then I .(E) was estimated

smoothly interpolated by a solid line.

In the eq. (1), it is assumed that

low tube current.

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Determination of the Spectral Intensity of the Incident Beam in the Energy Dispersive X-Jay Diffraction

The spectral intensity of the incident beam from a tungsten tube and the integrated

Tab le 1

intensity of the 220 reflexion of GaSb at 13 Bragg angles.

E

I . (220)

(keV)

(deg)

F (220)

I

. (E)

ur

Time (sec)

13.

80

12.

06

12482. 8

233. 20

8. 205 X 10-3

3. 881

2 x 104

12.

78

13.

OO

13365. 7

234. 72

6. 621

3. 246

2 x 104

11.

86

14.

OO

19209. 7

235. 43

7. 193

2. 692

2 x 104

11. 06

15. OO

26543. 9

235. 73

7. 611

2. 239

2 x 104

10. 34

16. 03

17294. 1

235. 82

7. 650

1. 864

1 x 104

9.

74

17.

OO

22224. 8

235. 77

7. 817

1. 583

1 x 104

9.

20

17. 99

27573. 6

235. 63

7. 833

l. 360

1 x 104

8.

71

19. OO

33482. 8

235. 42

7. 811

1. 183

1 x 104

8.

27

20. OO

31069. 9

235. 16

7. 586

1. 045

8 x 103

7.

51

22. O1

23460. 3

234. 52

6. 955

O. 8366

5 x 103

7.

18

23. 02

26667. 2

234. 13

6. 442

O. 7448

5 x 103

6.

88

24.

02

26907. 2

233. 67

6. 429

O. 6481

5 x 103

6.

61

24.

99

27862. 2

233. 14

4. 504

O. 5391

5 x 103

2e0=90

Relative change of polarization factor

30

Pow d er

W tube T= O keV i = ,5mA 20

60 . 120

p - pa

pa (Ql.)

10

20

E{kev]

40

1 0'

20

150'

30

Fig. 6 The effect of the polarization of the incident continuous X-ray on the polarization factor obtained by J.S. Olsen et al (Acta Cryst. A 34 (1978)84).

the incident beam is not polarized. This assumption is not correct near the high energy

limit of the continuous X-rays. Results of the measurement by Olsen et al (1978) on the influence of the polarization of the continuous X-rays on the polarization factor in

the case of tungusten tube, are shown in Fig. 6. The influence is less than 1

and

constant against the energy, when the X-ray energy is less than about two thirds of the

high energy limit and the Bragg angle is less than 20 degrees. Since our measurement satisfied these conditions, our lw'(E) had negligible contribution of the polarization of

the incident beam.

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Proceedings of the Institute 0L Natural Sciences (1980)

(2) The spectral intensity of the incident beam measured directly by the SSD.

In this case, the intensity of the incident beam have to be reduced to about 2000

counts/sec or less. This was realized by three methods. The flrst one is the use of a pin-hole slit, the diameter of the hole of which was about 0.03mm. The result is shown in Fig. 7, along with the specral intensity obtained at low tube current without the pin-

hole slit. The result is very much modified by the absorption at the edge of the slit.

Counts 2000

Incident Beam Spectrum of

fncident Beam spectrum cf WTube

x//

Cu-Tube at 40kV 3.0 Q e m,sasuredwfthby SSD Cu absorbcr Q x est'mated from

: ¥x e'-5

/x x / /¥X¥xa ¥x

ll

x¥ :r(220) of eaP 2.0 x ¥x¥x e)¥

1000

o pjnhole slit 0'03 mm OF51 mA ¥x¥ x Low Tube Current

O114 mA

200 400 Channet 600 800 1000 No. Fig. 7 The apparent spectral intensity of the incident

beam from a tungsten tube measured by the SSD with a pin-hole slit and at low tube current.

! wr 6¥

1.0 ¥¥xo¥ 15 20 E25keV 30

O

Fig. 8 The observed spectral intensity of the incident beam from a copper tube. The one was estimated from the integrated intensity of the 220 reflexion

The second one is the use of absorbers.

As the attenuation of the absorbers i_s

of GaP and the other was directly obtained by the SSD with a Cu absorber.

strongly dependent on the X-ray energy, the accuracy is low at the energy range where the attenuation is high. The preliminary result on copper tube is shown in Fig. 8, along with the spectral intensity of the incident beam obtained from the integrated intensity of the 220 reflexion of a GaP powder sample.

The absorbers were made of Cu

films. The attenuation factor at energy less than 18 keV was so high that the estimated spectral intensity at that energy range contained much error compared with that at

higher energy. In the third one the intensity of the incident beam was reduced by the reduction of

the tube current. When the tube voltage was fixed at 40 keV and the tube current

was made about I ;4A higher than that at cold emission, the t.otal intensity indicated by a ratemeter connected just after the amplifier, was about 2000 cps. The results are

shown in Fig. 5, along with the data shown by the solid line which was obtained from the integrated intensity of the 220 reflexion. The data are normalized at 15 keV. When

the tube current was increased, the higher energy region of the spectrum increased and

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Determination of the Spectral Intensity of the Incident Beam in the Energy Dispersive X-ray Diffraction

the whole spectrum became closer to the

Spectrum of Incident Beam

sloid line. It is probable that this effect

o

o Shaping Time ofAmp 10 pS

XI0 2

arise from two origins. The one might be

8,0

IX- X

/X

in the detector system and the other in the

/

X-ray tube itself. In or.der to check the

o

pile-up effect of the amplifier, the shaping

7,0

+

2 PS

¥

( 2000 c JD,s )

¥

X

time of the pulse was changed from 10 ps to 2 ; s, when the intensity of the incident

.



lw r

beam was about 2000 cps. Anomalous

6 ,o

points near 16 keV in the case of 10 ps

¥

were lowered in the case of 2 kes, as shown in Fig. 9. Since the energy of those points

5,0

is about twice of that of the La line of tungusten, those points in the case of 10 ps show the effect of piling up of pulses.

The pin-hole photographs of the X-ray source at different tube currents are shown

in Fig. 10. At tube current of 2 mA, the

shape of the source was regular, having dimension of about O. I X 10mm2.

20 E keV 15 25

Fig. 9 The spectral intensity of the incident beam directly obtained by the SSD with different shaping times of pulse, 2 ps and 10 /es.

At the lowest current of 27 pA, about I pA higher

than the cold-emission-current containing the leakage, anomalous spots were found, as

shown in Fig. 10, above the regular source. The spots became relatively weaker as the tube current was increased. The total time of operation of this tube was about

1500 hours at about 40 kV and 10 mA. The pin-hole photographs of the X-ray source of an old, Iong tirne operated, tungsten tube are shown in Fig. 11. By the use of this tube, a considerable dependence of the apparent spectral intensity of the incident beam

on the total intensity was first found. Only anomalous spots were observed at low tube current.

If a part of the incident beam comes from the anomalous spots, the effctive takeoff-angle of the X-ray is different from that from the normal source. From the geometry

of taking photographs, the anomalous spots lies nearer to the tube window, so that its

take-off-angle is larger than that from the normal source. The low energy part of the

X-ray from the anomalous spots is less absorbed than that from the normal source, because the X-ray path from the anomalous spots in the anticathode is shorter. When the intensity of X-ray from the anomalous spots was relatively reduced at higher tube current, the high energy part of the specral intensity increased relatively.

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Proceedings of the lnstitute of Natural Sciences(1980)

 08μA    DOmm                 405μA    3min                   Cold Emission26μA

Fig.10 The p玉n−hole photographs of the Xray source on the anticathoδe of a new  tungsten tube at di仔erent tube currents at40kV.

150μA    lhr                 640μA    3min F量9.

                  Cold Emission130μA ll The pin・hole photographs of the X−ray source on tungsten tube at different tube currents at40kV.

18一

he anticathode of an old



Table 2 The structure factors of several reHexions o{GaSb

9

R

obtained from the spectral lntensity of the incident beam estimated

薯.

from the integrated intensity of the220reHexion.

……

hki

Bragg A. sinθ/λ   (A−1)

1

111

0.1421

200 220 311 222 400 331 420 422 333 440 531

0,1641

13.94   13.80   12.78   11.86   11.06   10.34 (deg)

9,74

9.20     8.71     8,27     7.51     7.18

6.61

王95.1    191.9    196.8

(73,8)

83.4

 84.8     79.8     81.0

      (272.5)

234.3

236.0

237,2

234.2

235.1

235.3

236.5

236,2 233.4 (240.1)

0.2721

157.4  157.2

156.5

156.6

157.1

154.7

155.4

(160.6)

156.1

154,5

0.2842

 61.9  

63.9

58.3

53.6

56.8

0.3281

192.1  189.6

187.4

190.8

191.4

0.3576

140.5   138.1

139.6

138,1

139.4

56.1 186.8

59.1 185.7

 54.0

55.8

196.4

80.0 234.4

195.5



(75.6)

ω

232.8

165.6

164,4     166.6

0.4263

112,5

100.4   111.5

0.4641

145.5

145.1

Φ





o 『



59.7 口

(176。6)



126.9

口 望.

33.9

0.3669 0.4019

96.1

o



o

0.2320

0,4853

6.88



o ゲ Φ

92.9

昌 9.

α







1

Table 3 The structure factors of several reHexions of GaSb

obtained from the spectral intensity of the incident beam directly

ω

9 ヨ

measured by the SSD at very low tube current.

5’

hkl

Bragg A, sinθ/λ   (A−1)

13.94    13.80    12.78    11.86    11.06    10.34 (deg)

9,74

9.20     8,71     8.27     7.51     7.18

6.88

6.61

チ Φ



111



197.4    192,9    197.2

0.1421

200 220

0.1641

0,2320

      (275,9)

236、0

236,7

237.0

233.7

234.8

311

0.2721

157,8   157.5

156、3

156.4

157.2

155.5

157.2

222 400

0,2842

 61.9  

0,3281

191。9   189.4

188.0

192.9

194、9

190.4

331

0.3576

141曾0   138.7

141.4

140.8

141.7

124.3

420 422 333 440

0。3669

531

0.4853

(74.5)

63,9

58、1

53.5

56.9

56.7

60,1 186.0

235.7 (163.5)

 55.1 (165.4)

83.9

 85、0     79.6     80.8

238.0

239.1    238.2    244.3

159.4

156,4

56.7

58.9

196.4

79,9 239,4

195.2  75.5 (224.7)

の 『

磯 鴇

o

勺 Φ 厩

< Φ

32。0

図 貞 卑

0.4019

168.3

167.2   167.7   166.0



0.4263

114,9

102.5    112.1



0,4641

146。3

145.0

92.8

88,3

題 『 帥

o

o



Proceedings of the Institute of Natural Sciences (1980)

Structure FactOrS of GaSb Structure Factors of GQSb

!ncident Beam speetrulll by the SSD

lncident Bearft Spectrum from the b(220)

220 TI ) [240/oRO

2230 oo e 220 O rle o eLO o o_O

230 f200 zlo

210

at 2000 cps t2JJS)

)

111

111

200

o oo -x oo 400 ISO x x X

190 fl60 170

x XX

ISO

fleo 3 1 1 ll50 /; ( rx

15o 90

70

70 2 OO

¥

----__

X x XXx XX 222

50 E

keV 10

C tculatcd

Observld

O

200

60

XX)
OO eO O oX ,

eo

BO oo o

15

X

311

x x X- --X

222

'( X X ¥

C

XxxxX XX XX

90 o catculated o e x o observed ¥ ) x

O OO e)O x X 400

i5 20 25

keV

Fig. 12 The structure factors of several reflexions of GaSb obtained from the spectral intensity of the incident beam estimated from the in-

Fig. 13 The structure factors of several reflexions GaSb obtained from the spectral intensity of the incident

tegrated intensity of the 220 refiex-

SSD at very low tube current, are shown against the X-ray energy.

beam directly measured by the

ion, are shown against the X-ray energy.

Discussion

As a measure of the accuracy of the spectral intensity of the mcident beam the structure factors of several refiexions obtained from the spectral intensity estimated from

the integrated intensity of the 220 Iine, are shown in Table 2 and plotted against the

X-ray energy in Fig. 12. The solid lines show the calculated structure factors. The accuracy of a structure factor is sufficient if the obtained structure factors stand parallel

to the relevant solid line. The F(220) is the fitted structure factor. In the case of the

F(311) the accuracy is about 2 ・ If the theoretical values of the correction terms for

the anomalous dispersion and the temperature factors are reasonable, this accuracy is free from the effect of the surface roughness, the porosity effect and so on, except that

of the prefered orientation, because the X-ray path is different at different energies.

The F(111) and the F(400) are lower than the calculated ones and the accuracy is about

3

. It is about 10

in the case of weak lines such as 222.

The structure factors obtained from the spectrum directly measured by the SSD, are

- 20 -

Determination of the Spectral Intensity of the Incident Beam in the Energy Dispersive X-ray Diffraction

given inlTable 3 and plotted in Fig. 13, when the intensity was 2000 cps and the shap-

ing time constant was 2 ps. The accuracy is less than that in the case of Fig. 12, but

it is enough for the measurement with moderate accuracy of about 5% for strong lines.

Acknowledgement The authors are indebted to our students, Mr. Y. Morita, Mr. I. Kanai and Mr. N. Shibata for their help in our measurements. Ref erences

Cole, H. (1970). J. Appl. Cryst. 3, 405-406.

Cromer. D.T. (1965). Acta Cryst. 18, 17-23. Olsen. J. S., Buras, B.. Jensen, T.. Alstrup, O., Gerward. L. and Selsmark B (1978) Acta Cryst. A34, 84-87. Uno. R. and Ishigaki, J. (1975), J. Appl. Cryst. 8 578-581.

,

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