write a summary of each of the techniques for measuring vacancyconcentrations, noted therein. (1) Measurements of the quenched-in residual electricalresistivity of aluminium rapidly cooled from temperatures be-low about 800 K with initial quenching rates of 2 × 106 K s−1give the enthalpy of formation of monovacancies H F1V =(0.65 ± 0.01) eV.(2) Comparison of the quenching data with high-temperature differential-dilatometry data gives the monova-cancy formation entropy SF1V = (0.76 ± 0.4)kB (kB =Boltzmann’s constant) and the low-temperature resistivity perunit concentration of vacancies ρ1V = (1.9 ± 0.1) μm.(3) The binding enthalpy of divacancies in Al is H B2V =(0.17 5 ± 0.02 5) eV. This is in agreement with earlier ex-perimental determinations by Doyama and Koehler 48) and byLevy et al. 49, 50) but in marked contrast to the claim of Carlinget al., 23) based on computations with the generalized gradi-ent approximation, that in Al H B2V is zero or even negativeand therefore the contribution of divacancies to the thermal-equilibrium concentration of vacant sites is negligibly small.(4) The monovacancy formation enthalpies obtained bypositron annihilation show a relatively large scatter but arecompatible with the result stated in conclusion (1).(5) At high temperatures, the capture radius of monova-cancies in Al for positrons is r0 = 1.2a0 . The data sup-port the view that at high temperatures the positron captureis diffusion-limited and that the positron diffusivity is limitedby phonon scattering.(6) Combination of conclusion (1) with self-diffusivitydata gives the monovacancy migration enthalpy H M1V =(0.61 ± 0.02) eV.(7) Specific-heat measurements by Shukla, Plint andDimars 67, 68) are compatible with conclusions (1), (2) and (3).(8) In the case of aluminium, ab-initio computationsbased on the local-density approximation give better resultsfor H F1V than computations based on the generalized gradientapproximation but, as the counterexample of copper 65) shows,this is not a generic result.AcknowledgementsThe authors would like to thank Professor M. F ̈ahnle fornumerous thorough discussions on ab-initio calculations ondefects in metals and Professor H. D. Carstanjen and Profes-sor W. Frank for their critical reading of the paper. One of theauthors (A. S.) gratefully acknowledges the hospitality of theStructure/Property Relations Group at Los Alamos NationalLaboratory, Los Alamos, N. M., where part of the presentwork was done.
write a summary of each of the techniques for measuring vacancyconcentrations, noted therein. (1) Measurements of the quenched-in residual electricalresistivity of aluminium rapidly cooled from temperatures be-low about 800 K with initial quenching rates of 2 × 106 K s−1give the enthalpy of formation of monovacancies H F1V =(0.65 ± 0.01) eV.(2) Comparison of the quenching data with high-temperature differential-dilatometry data gives the monova-cancy formation entropy SF1V = (0.76 ± 0.4)kB (kB =Boltzmann’s constant) and the low-temperature resistivity perunit concentration of vacancies ρ1V = (1.9 ± 0.1) μm.(3) The binding enthalpy of divacancies in Al is H B2V =(0.17 5 ± 0.02 5) eV. This is in agreement with earlier ex-perimental determinations by Doyama and Koehler 48) and byLevy et al. 49, 50) but in marked contrast to the claim of Carlinget al., 23) based on computations with the generalized gradi-ent approximation, that in Al H B2V is zero or even negativeand therefore the contribution of divacancies to the thermal-equilibrium concentration of vacant sites is negligibly small.(4) The monovacancy formation enthalpies obtained bypositron annihilation show a relatively large scatter but arecompatible with the result stated in conclusion (1).(5) At high temperatures, the capture radius of monova-cancies in Al for positrons is r0 = 1.2a0 . The data sup-port the view that at high temperatures the positron captureis diffusion-limited and that the positron diffusivity is limitedby phonon scattering.(6) Combination of conclusion (1) with self-diffusivitydata gives the monovacancy migration enthalpy H M1V =(0.61 ± 0.02) eV.(7) Specific-heat measurements by Shukla, Plint andDimars 67, 68) are compatible with conclusions (1), (2) and (3).(8) In the case of aluminium, ab-initio computationsbased on the local-density approximation give better resultsfor H F1V than computations based on the generalized gradientapproximation but, as the counterexample of copper 65) shows,this is not a generic result.AcknowledgementsThe authors would like to thank Professor M. F ̈ahnle fornumerous thorough discussions on ab-initio calculations ondefects in metals and Professor H. D. Carstanjen and Profes-sor W. Frank for their critical reading of the paper. One of theauthors (A. S.) gratefully acknowledges the hospitality of theStructure/Property Relations Group at Los Alamos NationalLaboratory, Los Alamos, N. M., where part of the presentwork was done.
Principles of Instrumental Analysis
7th Edition
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Chapter9: Atomic Absorption And Atomic Fluorescence Spectrometry
Section: Chapter Questions
Problem 9.23QAP
Related questions
Question
write a summary of each of the techniques for measuring vacancy
concentrations, noted therein.
(1) Measurements of the quenched-in residual electrical
resistivity of aluminium rapidly cooled from temperatures be-
low about 800 K with initial quenching rates of 2 × 106 K s−1
give the enthalpy of formation of monovacancies H F
1V =
(0.65 ± 0.01) eV.
(2) Comparison of the quenching data with high-
temperature differential-dilatometry data gives the monova-
cancy formation entropy SF
1V = (0.76 ± 0.4)kB (kB =
Boltzmann’s constant) and the low-temperature resistivity per
unit concentration of vacancies ρ1V = (1.9 ± 0.1) μm.
(3) The binding enthalpy of divacancies in Al is H B
2V =
(0.17 5 ± 0.02 5) eV. This is in agreement with earlier ex-
perimental determinations by Doyama and Koehler 48) and by
Levy et al. 49, 50) but in marked contrast to the claim of Carling
et al., 23) based on computations with the generalized gradi-
ent approximation, that in Al H B
2V is zero or even negative
and therefore the contribution of divacancies to the thermal-
equilibrium concentration of vacant sites is negligibly small.
(4) The monovacancy formation enthalpies obtained by
positron annihilation show a relatively large scatter but are
compatible with the result stated in conclusion (1).
(5) At high temperatures, the capture radius of monova-
cancies in Al for positrons is r0 = 1.2a0 . The data sup-
port the view that at high temperatures the positron capture
is diffusion-limited and that the positron diffusivity is limited
by phonon scattering.
(6) Combination of conclusion (1) with self-diffusivity
data gives the monovacancy migration enthalpy H M
1V =
(0.61 ± 0.02) eV.
(7) Specific-heat measurements by Shukla, Plint and
Dimars 67, 68) are compatible with conclusions (1), (2) and (3).
(8) In the case of aluminium, ab-initio computations
based on the local-density approximation give better results
for H F
1V than computations based on the generalized gradient
approximation but, as the counterexample of copper 65) shows,
this is not a generic result.
Acknowledgements
The authors would like to thank Professor M. F ̈ahnle for
numerous thorough discussions on ab-initio calculations on
defects in metals and Professor H. D. Carstanjen and Profes-
sor W. Frank for their critical reading of the paper. One of the
authors (A. S.) gratefully acknowledges the hospitality of the
Structure/Property Relations Group at Los Alamos National
Laboratory, Los Alamos, N. M., where part of the present
work was done.
resistivity of aluminium rapidly cooled from temperatures be-
low about 800 K with initial quenching rates of 2 × 106 K s−1
give the enthalpy of formation of monovacancies H F
1V =
(0.65 ± 0.01) eV.
(2) Comparison of the quenching data with high-
temperature differential-dilatometry data gives the monova-
cancy formation entropy SF
1V = (0.76 ± 0.4)kB (kB =
Boltzmann’s constant) and the low-temperature resistivity per
unit concentration of vacancies ρ1V = (1.9 ± 0.1) μm.
(3) The binding enthalpy of divacancies in Al is H B
2V =
(0.17 5 ± 0.02 5) eV. This is in agreement with earlier ex-
perimental determinations by Doyama and Koehler 48) and by
Levy et al. 49, 50) but in marked contrast to the claim of Carling
et al., 23) based on computations with the generalized gradi-
ent approximation, that in Al H B
2V is zero or even negative
and therefore the contribution of divacancies to the thermal-
equilibrium concentration of vacant sites is negligibly small.
(4) The monovacancy formation enthalpies obtained by
positron annihilation show a relatively large scatter but are
compatible with the result stated in conclusion (1).
(5) At high temperatures, the capture radius of monova-
cancies in Al for positrons is r0 = 1.2a0 . The data sup-
port the view that at high temperatures the positron capture
is diffusion-limited and that the positron diffusivity is limited
by phonon scattering.
(6) Combination of conclusion (1) with self-diffusivity
data gives the monovacancy migration enthalpy H M
1V =
(0.61 ± 0.02) eV.
(7) Specific-heat measurements by Shukla, Plint and
Dimars 67, 68) are compatible with conclusions (1), (2) and (3).
(8) In the case of aluminium, ab-initio computations
based on the local-density approximation give better results
for H F
1V than computations based on the generalized gradient
approximation but, as the counterexample of copper 65) shows,
this is not a generic result.
Acknowledgements
The authors would like to thank Professor M. F ̈ahnle for
numerous thorough discussions on ab-initio calculations on
defects in metals and Professor H. D. Carstanjen and Profes-
sor W. Frank for their critical reading of the paper. One of the
authors (A. S.) gratefully acknowledges the hospitality of the
Structure/Property Relations Group at Los Alamos National
Laboratory, Los Alamos, N. M., where part of the present
work was done.
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