Printing:A Positron Lifetime Spectrometer

M. Salahuddin | H. Jaeger | Department of Physics, Miami University, Oxford, OH, USA

Abstract

Data analysis

Results

Conclusion

Reference

A spectrometer for measuring positron lifetimes in solids is

described. It consists of a pair of BaF2 scintillators coupled to

photomultiplier tubes and a fast-slow coincidence system

composed of standard NIM modules. The instrumental resolution

curve as determined with a 60Co source is well-described by a

Gaussian with a FWHM of approx. 300𝑝𝑠. We apply this apparatus

setup to the positron lifetime experiment of metal and polymer

samples. We used this apparatus to determine the lifetime of

positrons in commercial grade Al and PTFE (Teflon) at room

temperature with a 22Na positron source enclosed in Kapton foil.

Both samples show a lifetime component in the 350– 450𝑝𝑠 range.

While the PTFE sample has a long component near 2𝑛𝑠, the Al

sample has a short (approximately 200𝑝𝑠 ) as well a long

component (> 2𝑛𝑠).

Experimental setup

Positronium formation

𝐷 𝑡 =

𝑖=1

𝑘+1

𝐴𝑖𝑒−(𝑡−𝑡0)𝜏𝑖

𝐷 𝑡 = 𝐴1𝑒−(𝑡−𝑡0)𝜏1 𝜏1 = 𝜏𝐵 = Bulk lifetime

𝐷 𝑡 =

𝑖=1

𝑘+1𝐴𝑖2𝑒𝑥𝑝 −

𝑡 − 𝑡0 −𝜎2

4𝜏𝑖𝜏𝑖

1 − 𝑒𝑟𝑓𝜎

2𝜏𝑖−𝑡 − 𝑡0𝜎

+ 𝐵𝐺

𝜒𝑟𝑒𝑑2 =1

𝜈 𝑂(𝑡) − 𝐷(𝑡) 2

𝜎2𝜈 = 𝑁 − 𝑛 − 1

𝐹𝑊𝐻𝑀 = 2𝜎 ln 2

= 𝐴𝑒−𝑡−𝑡0𝜎

2

+ 𝐵𝐺Gaussian with background

Parameters values for 60Co

Fundamental equations:

𝑒− + 𝑒+ → 𝛾 + 𝛾

FWHM (𝑝𝑠) 318 ± 2

𝑡0 (𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑢𝑛𝑖𝑡𝑠) 1074.32 ± 0.03

Background 10.9 ± 4

Time Calibration 18.65𝑝𝑠/𝑐ℎ

Reduced 𝜒𝑟𝑒𝑑2 1.00

𝜏 (𝑝𝑠) 188.34 ± 0.9

𝐴 (𝑐𝑜𝑢𝑛𝑡𝑠) 45976.40 ± 220Matter-anti-matter reaction

𝛾 → 𝑒− + 𝑒+ Pair production

𝑝 → 𝑛 + 𝑒+ + 𝜈𝑒 𝛽+ decay

𝑛 → 𝑝 + 𝑒− + 𝜈𝑒 𝛽− decay 𝑝 + 𝑒− → 𝑛 + 𝜈𝑒 Electron Capture decay

Application

The positron lifetime technique is the most sensitive and also the only

defect-specific one. It is nicely applicable to atomic and molecular free

volumes and holes in polymers, solids.

−𝑑𝑛(𝑡)

𝑑𝑥=

𝑖

𝐴𝑖𝜏𝑖𝑒−𝑡𝜏𝑖

• Intensities, 𝐴𝑖 – proportional with vacancy concentration

• Lifetimes 𝜏𝑖 – characteristic value for each vacancy type

typically 100-300ps (bulk solid, vacancies) 1-2ns (large

voids, positronium)

Typical lifetime spectrum

𝑡0 (𝑐ℎ𝑎𝑛𝑛𝑒𝑙 𝑢𝑛𝑖𝑡𝑠) 1075.53

Background (𝐵𝐺)(𝑐𝑜𝑢𝑛𝑡𝑠)

9.06

𝐴 (𝑐𝑜𝑢𝑛𝑡𝑠) 10103.2

FWHM (𝑝𝑠) 284.65

Time Calibration 18.63𝑝𝑠/𝑐ℎ

Parameters values for 207Bi

Decay scheme of 22Na

𝐿+ = 𝐷+𝜏

𝐷+ ∝ 𝑇−1/2

Metals: 𝐿+ = 100𝑛𝑚Semiconductor: 𝐿+ = 200𝑛𝑚

Diffusion trapping model

FWHM (𝑝𝑠) 283.8 ± 2

𝜏1 (𝑝𝑠) 170.97 ± 11

𝐴1 (𝑐𝑜𝑢𝑛𝑡𝑠) 16848.28 ± 983.2

𝜏2 (𝑝𝑠) 347.02 ± 15

𝐴2 (𝑐𝑜𝑢𝑛𝑡𝑠) 7942.84 ± 1308

𝜏3 (𝑝𝑠) 2133.71 ± 410

𝐴3(𝑐𝑜𝑢𝑛𝑡𝑠) 43.05 ± 13

𝐼1 (%) 50.28 ± 6

𝐼2 (%) 48.11 ± 9

𝐼3 (%) 1.60 ± 0.6

Parameters values for Al

The figure on the left side shows the decay

scheme of 60Co and 207Bi respectively

Lederer, C. M., Hollander, J. M., and Perlman, I.,

Table of isotopes(1967).

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3388 (2006)

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Condens. Matter, 8(12), 2081(1996).

4. Monge, M. A., and Del Rio, J., Position annihilation in Kapton source-supporting foils. J. Phys. Condens. Matter,

6(13), 2643(1994)

• We use a positron lifetime spectrometer that is efficient for defect detection in metals and

their alloys.

• The performance of the setup has been tested by 207Bi radioactive isotope.

• We measure the lifetime of commercial grade Al which has longer lifetime than the bulk

lifetime 165𝑝𝑠[3 − 5]. However, after annealing process the lifetime gets closer to bulk

lifetime.

• We measure the lifetime of Teflon shows comparatively longer component of lifetime due to

positronium formation, hence the graph for Teflon is shallower than Al.