- Email: [email protected]
Evidence for a diffuse transition in lead chloride
cP~
Solid State Communications, Vol.31, pp.29—33. Pergamon Press Ltd. 1979. Printed in Great Britain.
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE * F.E.A.Melo, K.W.Carrett, J.Mendes Fliho and J.E.Moreira Departamento de F~sica, Universidade Federal do Cear~ Caixa Postal 1262, 60000 Fortaleza, Cear~, Brasil (Received 15 April 1978 by R.C.C.Leite)
The Raman spectra and the electrical conductivity of lead chloride single crystals at various temperatures, up to the melting point, have been investigated. From the results of both techniques we have found evidence of the beginnings of a diffuse transition to a state of high conductivity at temperatures close to the melting point of PbC1 2.
I. INTRODUCTION
number of impurities present in the crystal, and c1~(B/T)exp{I—U—(E/3)~fkT} in the intrinsic region where the vacancies increase exponentially as the temperature is increased. migrational energyfor of a ion Atheand B are constants a chloride given crystal, U is vacancy to a normal position of the lattice
Lead chloride has been previously studied by several techniques including Raman 2’3’~’. In this paper we study the spectroscopy’ and electrical conductivity measurements relation between the Raman spectra and the electrical conductivity of PbC1 2 at various temperatures, up to the melting point. PbCI2 is an ionic crystal with ortho— 5 with four molecules inD3~ the (F) unit rombic structure, belonging to the cell. space From group the factor group analysis of the primitive cell it is predicted that 18 modes are Reman—active and are distributed as follows: 6 Ag(xx,yy,zz); 6 B 1 (xy); 3 B2 (xz); 3 B3g(YZ). g g Reman spectra of PbCl2 at room temperatire have been studied by Ozin’. Although a correct assignment of the Raman bands at room temperature is difficult because of the broad linewidths and accidental coincidence of the 1 to shifts, a comparison of the Reman spectra of divide the its Reman modes into two classes: PbC12 and isomorphous PbBr2 led Ozin one, involving motion of the lead atoms, at frequencies below 100 cm’ which are invariant
and E is the formation energy of a vacancy. An attempt has been made to classify ionic crystals into three groups in accordance with review paper1 discusses evidenceAfor this their sublattice melting the behaviour. recent classification and lists some salts that fall into these classes, with their general properties. Class I salts undergo one first— order phase transition (melting) where both anionic and cationic sublattices disorder simultaneously. Class II salts have two first—order phase transitions, becoming solid electrolytes at the lower temperature transition where one sublattice disorders. At the higher temperature transition the remaining Class III salts disordering ions disorder on also the undergo melting two of the crystal. transitions but the solid electrolyte one is not first—order but is spread over a fairly large temperature range. PbCI 2 is classified as a “normal” class I crystal and indeed its entropy of fusion is usually quoted as the standard against which class II and class III salts are compared. However, we report here conductivity and Raman measurements which indicate that PbCl2 is not a true class I salt but undergoes the beginnings of a diffuse transition just below its melting point.
on passing from PbC12 to PbBr2 and the other, involving motion of the anions, corresponding to frequencies greater than 100 cm~ and shifting by a factor given by the square root of the halide mass ratio, From the point of view of the electrical conductivity, lead chloride is considered a typical anionic, conductor with transference numbers t4~O, t_”l and te~Ofor all temperatures up to the melting point at 501°C. The ionic motion is explained by the Schottky De the Vries and Van mechanism2’3’6. through mobility of Santen2 anion showed that the conductivity of PbCl vacancies 2 could be represented by cT~(A/T)exp(—U/kT) in the extrinsic region where the number oLvacancies is virtually constant and is a result of the *
2. EXPERIMENTAL this work were chloride grown from the zone—refined The lead single crystals used in melt by the Bridginan method and oriented by X—ray Laue back—reflection. Raman scattering experiments were carried out using a Spectra Physics argon ion laser, a Spex double mono— chromator equipped with a RCA S—20 photo— multiplier and d.c. recording. Resolution was kept constant throughout the measurements and was better than 2 cm’. Low temperature Reman spectra were taken with the crystal mounted in an Air Products cryotip where the temperature
Partially supported by Conseiho Nacional de Desenvolvimento Cient~fico e Tecnologico (CNPq) and Financiamento de Estudos e Pesqui— sas (PINEP) — Brasil 29
30
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
Vol. 31, No. 1
could be controlled from about 15 K up to room temperature. Reman data at temperatures varying from room temperature to the melting point of PbC1 2 were taken using a “hot—finger” provided
perfo ed C12 ;;tal; in a of direction at right angles to the cleavage planes (c—direction). The sample holder used was similar to that described by Shahi and Chandra’ and graphite paint (acquadag) was used to improve the electrical contact between the palladium electrodes and the sample. Measurements were made with the crystal in an atmosphere of pure dry nitrogen gas. The crystal was annealed in its sample holder at 495°Cfor two hours and three runs were performed on each crystal. In each case, measurements were taken with increasing temperature. The temperature range from room temperature to 497°C, four degrees below the melting point, was studied. Great care was taken to confirm that the crystal was not oxidizing or degrading in any way. This was apparent in the agreement bets.een different runs on the same crystal and on visual inspection of the crystal after the experiment. The electrical conductivity of the crystals was measured using a modified General Radio 716—C Schering bridge at a frequency of I kHz. For one sample the conductivity was measured at frequencies of 100 Hz, 1 kHz, 10 kHz and 100 kHz to ascertain the variation of conductivity with frequency. It was found that above 100°Cvariation of frequency had no discernable effect on the electrical conductivity.
~ 300°C U)
—
/ I
—
c 250°C .~
—
—
1000 C
c
—
— —
—
J 200
16K
150
100 50 —1 Raman Shift cm
Fig. 1 — Reman spectra of PbCl2 for the configuration X(yy)Z (Ag symmetry) for different temperatures. For clarity the curves are shifted vertically. Gain is the same for the spectra at high temperatures.~The 16 K spectrum, with a different gain, is shown for comparison.
3. RESULTS Typical Reman spectra, at Ag(yy), Ag(xx) and B~g(xy) symmetries, taken at various temperatures, are shown in Figs. 1, 2 and 3. Detailed spectra in all polarizations and assignment for the 18 Raman modes will be published elsewhere. Features that are common to the spectra of Figs. 1, 2 and 3 and to the spectra of the other four possible polarizations are as follows. (1) At very low temperature (16 K) all lines are narrow. As the temperature increases some lines broaden more rapidly than others. For example, in the Ag(yy) spectrum of even very while linesnarrow with Fig. at 1 the 62high cm’ temperatures mode keeps relatively frequencies greater than 100 cm’ are so broad that it is difficult to distinguish them from the background. The 62 cm’ Ag(yy) mode is 1 typical of a group of six PbCl2 Reman lines, which are frequency relativelyless intense all with than and aboutshow 90 only cm a moderate broadening even at temperatures near the melting point. The 43 cm1 and 88 cm’Blg modes seen in Pig. 3 also belong to this group. Broadening of Raman modes with frequency shifts greater than 90 cm1 is more pronounced as can be seen in Fig. 1 and 2 for the 148 cm1, 162 cm1 and 181 em~ Ag bands and in Fig. 3 for the 160 cm1, 183 cm1 and 194 cmB 12 modes. The lead chloride Reman modes can He
classified into one of these two patterns of behaviour but one has to allow some degree of uncertainty in the characterization of the weaker lines. (2) When the temperature reaches about 2600 C the intensity of all Reman peaks decreases rapidly while the background increases. (3) A graph of the logarithm of the linewidth against the inverse of the absolute temperature for those Raman lines that broaden more rapidly with temperature is approximately a straight line. Around 2600 C there is a change in the slope of this straight line. This is1 Ag(xx) Reman mode. (4) When4the exemplified in Fig. for temperature the 162 cm approaches the melting point of PbCl 2 the Raman spectra in all geometries can be described as a remaining distinct mode, at low frequency, extending out to around 200 mC’. background above a practically structureless Electrical conductivity results of a typical crystal are presented in Figs. 5 and 6. The change in the conductivity from the extrinsic to the intrinsic region is clearly demonstrated in the Arhennius plot of Fig. 5 at around 35Q0 C. Values of U and E/3 deduced from the inclination of the curves show good agreement with De Vries and Van Santen’ (see Table I) for the c—direction. However, it is also apparent that there
Vol. 31, No. 1
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
Big Ag Y(XX)Z
/1
t\
400’C
_________
j
Fig. 3
~‘~——‘~
I
/~
_.._-‘
I%JV
~.
‘...~
~
30 C •...i~jçj
~
‘
—
a,.,
lt
15%.)
lOu
—
Reman spectra of PbCl
2 for the configuration Y(xy)Z (B1 symmetry) for different temperatures. g For clarity shifted Gain is the the samecurves for thearespectra atvertically. high
I
I
//
2.00
____
~
/
—
Y(XY)Z 450°C
4’
/ /
31
..)U
-~
Roman shift cm Fig. 2 — Raman spectra of PbCl2 for the configuration Y(~cx)Z (Ag symmetry) for different temperatures. For clarity the curves are shifted vertically. Gain is the same for the spectra at high temperatures. The 16 K spectrum, with a different gain, is shown for comparison. is another change of slope at about 460°C where the conductivity increases much more rapidly. This is readily seen in the more detailed plot shown in Fig. 6. 4. DISCUSSION The approximately linear dependence of the logarithm of the linewidth with the inverse temperature can be the indication of an exponential relation of r with some sort of activation energy. One could be tempted to correlate the changes in slope seen inf Pigs. 4 and 5 for the linewidths of the Reman lines and for the conductivity. Such relation has
temperatures. The 16 K spectrum, with a different gain, is shown for comparison. 9 who been proposed by Peyrard and Nisset measured the temperature dependauce of the phonon linewidth in f3—AgI. In the case of PbCl 2 however the straight of Fig. 4 givesthetooslope smallfor a value for the line energy as compared to the energies of formation or migration of vacancies (Table I). Also, the graph for the linewidth occurs at a lower temperature than the one in the graph for the conductivity. It can be speculated that’ the Raman results reflect an increase of the disorder mechanisms of the lead chloride crystal which leads eventually to the rapid formation of vacancies in the intrinsic region. 1 that thesupport lines with Moreover, our results give to the assumption greater frequency of Ozin than 100 cm1 can be assigned to vibrations of the chloride sublattice. Since the chloride are repsonsible for the conduction in PbCl 2 and assuming that a substantical part of the broadening of the Reman bands at high temperature is due to the increasing disorder in the chloride sublattice, the separation of the modes into two groups, one for each sublattice, is qualitatively justified. We haveidentifled the more rapid increase in the conductivity at 460°Cas the beginning of a diffuse transition in which the chloride sublattice becomes more disordered than would be expected from the normal thermal growth of vacancies. However, the material does not
32
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
300
mr
100 I
500 I I
Vol. 31, No. 1
300 200 bc ‘ I F
100
~~
~
3.8
1~2
3.6O\~~
32
10-
-
1-5
2-0 ~
~ 2.5
(r~.cm)
Fig. 4 — Logarithm of the linewidth of the 162 cm’(Ag symmetry) Reman mode against the inverse of the absolute temperature. become a true solid electrolyte, up to the temperature measured as the melting point of the crystal is too close to the onset of the transition. Generally, for type III crystals the conductivity change is about a factor of io~spread over a hundred degrees or more and the conductivity is a continuous function7. For lead chloride we have found an increase of the order of a factor of 10 for a temperature range of about 35 degrees, which is of the same relative order. Recent work on n-AgI’°” have shown that the Reman spectra for this material in the solid electrolyte phase have very broad and structureless features. For temperatures above the transition the spectrum decreasTs
.
5 Ir~~ W -
I
1.2
1.6
2.0 1fl3/T ‘U
Fig. 5
—
Electrical
I
2.4
28
V~1 I’
conductivity
of PbCI 2
from the laser line out to around 200 cm with no other feature than a weak shoulder near 100 cm . In fact, these spectra for cL—AgI are qualitatively similar to the spectra of PbC12 at temperatures near its melting point, as those seen in Figs. 1, 2 and ~, if one discounts for the peaks at low frequencies. No detailed explanation for this kind of spectrum has been yet presented although many speculative reasoning have been advanced based on scattering from fluctuations due to ionic motion, attempt frequency for hopping or disorder removal of the k~’O selection rule. Our Reman results are consistent with the conductivity evidences that PbCl2 is neither a normal ionic conductor (class I) nor a solid electrolyte of class II. High temperature spectra, as seen in Figs. 1 2 and 3~show both normal crystalline and disorder features,
in
the c—direction, against the inverse temperature. All results are on the same crystal
4. CONCLUSION We have shown that lead chloride is not a true type I normal ionic salt but undergoes the beginnings of a diffuse transition at about 30 degrees below its melting point. The conductivity has been measured up to a few degrees below the melting point but did not show solid electrolyte behaviour. Reman spectra of PbCl2 single crystals indicate a high degree of disorder but not a complete melting of the chloride sublattice. Lead chloride can thus be considered to be a type III ionic salt in which the higher temperature transition (melting) intervenes before true
Vol. 31, No. 1
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
500
460 I
I
TC
420 I
•
33
TABLEI Values of the migrational energy (U) and the formation energy (E/3) of a chloride ion vacancy in PbCl 9, calculated from Fig. 5, compared with 2. tfie results of De Vries and Van Santen Be Vries
Present
Van Santea
0~
,.~ -l’s. (.CITI ‘~
U
•
(eV)
E/3 (eV)
0.30 ±0.20 0.52
± 0.04
0.30 ±0.01 0.50
± 0.05
-
• I
1.3 Fig. 6
—
solid electrolyte behaviour is observed. Ana~zledg~mant — The authors are indebted to J.F.Juliao who grew and oriented the single crystals used in this work.
1-35 1~4 1.45 10~’T,K~
Electrical conductivity of PbC1
2 against the inverse temperature. A magnI~cation of the high temperature results of Fig. 5.
REFERENCES 1. OZIN,G.A., Can.J.Chem. 48, 2931 (1970) 2. DE VRIES,K.J. ~ VAN SANTEN,J.H. Physica 29, 482 (1963) 3. SlM~OVICU,G.,J.Phys.Chem.Solids 24, 213 (1963) 4. JULIAO,J.F., Rev. Bras.Pisica3, 17 (1973) 299. John Wiley & Sons, New York (1963) 5. WICKOFF,R.W.C., Crystal Structures, Vol.11, p. 6. MOTT,N.F. & GURNEY,R.W., Electronic Processes in Ionic Crystals, p.54 Clarendon Press, Oxford (1957) 7. O’KEEPE,M., Comm.Sol.State Phys. 7, 163 (1977) 8. SUA1II,K. & SRANDRA,S., Phys.Status Solidi (a) 28, 653 (1975) 9. PEYRARD M. & MISSET,J.P., Solid State Countun. 17, 1487 (1975) 10. DELANEY,M.J. & USRIODA,S., Phys.Rev. B 16, 1410 (1977) 11. BURNS,G.., DACOL F.R. & SBAFER,M.W., Phys.Rev. B 16, 1416 (1977)
Solid State Communications, Vol.31, pp.29—33. Pergamon Press Ltd. 1979. Printed in Great Britain.
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE * F.E.A.Melo, K.W.Carrett, J.Mendes Fliho and J.E.Moreira Departamento de F~sica, Universidade Federal do Cear~ Caixa Postal 1262, 60000 Fortaleza, Cear~, Brasil (Received 15 April 1978 by R.C.C.Leite)
The Raman spectra and the electrical conductivity of lead chloride single crystals at various temperatures, up to the melting point, have been investigated. From the results of both techniques we have found evidence of the beginnings of a diffuse transition to a state of high conductivity at temperatures close to the melting point of PbC1 2.
I. INTRODUCTION
number of impurities present in the crystal, and c1~(B/T)exp{I—U—(E/3)~fkT} in the intrinsic region where the vacancies increase exponentially as the temperature is increased. migrational energyfor of a ion Atheand B are constants a chloride given crystal, U is vacancy to a normal position of the lattice
Lead chloride has been previously studied by several techniques including Raman 2’3’~’. In this paper we study the spectroscopy’ and electrical conductivity measurements relation between the Raman spectra and the electrical conductivity of PbC1 2 at various temperatures, up to the melting point. PbCI2 is an ionic crystal with ortho— 5 with four molecules inD3~ the (F) unit rombic structure, belonging to the cell. space From group the factor group analysis of the primitive cell it is predicted that 18 modes are Reman—active and are distributed as follows: 6 Ag(xx,yy,zz); 6 B 1 (xy); 3 B2 (xz); 3 B3g(YZ). g g Reman spectra of PbCl2 at room temperatire have been studied by Ozin’. Although a correct assignment of the Raman bands at room temperature is difficult because of the broad linewidths and accidental coincidence of the 1 to shifts, a comparison of the Reman spectra of divide the its Reman modes into two classes: PbC12 and isomorphous PbBr2 led Ozin one, involving motion of the lead atoms, at frequencies below 100 cm’ which are invariant
and E is the formation energy of a vacancy. An attempt has been made to classify ionic crystals into three groups in accordance with review paper1 discusses evidenceAfor this their sublattice melting the behaviour. recent classification and lists some salts that fall into these classes, with their general properties. Class I salts undergo one first— order phase transition (melting) where both anionic and cationic sublattices disorder simultaneously. Class II salts have two first—order phase transitions, becoming solid electrolytes at the lower temperature transition where one sublattice disorders. At the higher temperature transition the remaining Class III salts disordering ions disorder on also the undergo melting two of the crystal. transitions but the solid electrolyte one is not first—order but is spread over a fairly large temperature range. PbCI 2 is classified as a “normal” class I crystal and indeed its entropy of fusion is usually quoted as the standard against which class II and class III salts are compared. However, we report here conductivity and Raman measurements which indicate that PbCl2 is not a true class I salt but undergoes the beginnings of a diffuse transition just below its melting point.
on passing from PbC12 to PbBr2 and the other, involving motion of the anions, corresponding to frequencies greater than 100 cm~ and shifting by a factor given by the square root of the halide mass ratio, From the point of view of the electrical conductivity, lead chloride is considered a typical anionic, conductor with transference numbers t4~O, t_”l and te~Ofor all temperatures up to the melting point at 501°C. The ionic motion is explained by the Schottky De the Vries and Van mechanism2’3’6. through mobility of Santen2 anion showed that the conductivity of PbCl vacancies 2 could be represented by cT~(A/T)exp(—U/kT) in the extrinsic region where the number oLvacancies is virtually constant and is a result of the *
2. EXPERIMENTAL this work were chloride grown from the zone—refined The lead single crystals used in melt by the Bridginan method and oriented by X—ray Laue back—reflection. Raman scattering experiments were carried out using a Spectra Physics argon ion laser, a Spex double mono— chromator equipped with a RCA S—20 photo— multiplier and d.c. recording. Resolution was kept constant throughout the measurements and was better than 2 cm’. Low temperature Reman spectra were taken with the crystal mounted in an Air Products cryotip where the temperature
Partially supported by Conseiho Nacional de Desenvolvimento Cient~fico e Tecnologico (CNPq) and Financiamento de Estudos e Pesqui— sas (PINEP) — Brasil 29
30
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
Vol. 31, No. 1
could be controlled from about 15 K up to room temperature. Reman data at temperatures varying from room temperature to the melting point of PbC1 2 were taken using a “hot—finger” provided
perfo ed C12 ;;tal; in a of direction at right angles to the cleavage planes (c—direction). The sample holder used was similar to that described by Shahi and Chandra’ and graphite paint (acquadag) was used to improve the electrical contact between the palladium electrodes and the sample. Measurements were made with the crystal in an atmosphere of pure dry nitrogen gas. The crystal was annealed in its sample holder at 495°Cfor two hours and three runs were performed on each crystal. In each case, measurements were taken with increasing temperature. The temperature range from room temperature to 497°C, four degrees below the melting point, was studied. Great care was taken to confirm that the crystal was not oxidizing or degrading in any way. This was apparent in the agreement bets.een different runs on the same crystal and on visual inspection of the crystal after the experiment. The electrical conductivity of the crystals was measured using a modified General Radio 716—C Schering bridge at a frequency of I kHz. For one sample the conductivity was measured at frequencies of 100 Hz, 1 kHz, 10 kHz and 100 kHz to ascertain the variation of conductivity with frequency. It was found that above 100°Cvariation of frequency had no discernable effect on the electrical conductivity.
~ 300°C U)
—
/ I
—
c 250°C .~
—
—
1000 C
c
—
— —
—
J 200
16K
150
100 50 —1 Raman Shift cm
Fig. 1 — Reman spectra of PbCl2 for the configuration X(yy)Z (Ag symmetry) for different temperatures. For clarity the curves are shifted vertically. Gain is the same for the spectra at high temperatures.~The 16 K spectrum, with a different gain, is shown for comparison.
3. RESULTS Typical Reman spectra, at Ag(yy), Ag(xx) and B~g(xy) symmetries, taken at various temperatures, are shown in Figs. 1, 2 and 3. Detailed spectra in all polarizations and assignment for the 18 Raman modes will be published elsewhere. Features that are common to the spectra of Figs. 1, 2 and 3 and to the spectra of the other four possible polarizations are as follows. (1) At very low temperature (16 K) all lines are narrow. As the temperature increases some lines broaden more rapidly than others. For example, in the Ag(yy) spectrum of even very while linesnarrow with Fig. at 1 the 62high cm’ temperatures mode keeps relatively frequencies greater than 100 cm’ are so broad that it is difficult to distinguish them from the background. The 62 cm’ Ag(yy) mode is 1 typical of a group of six PbCl2 Reman lines, which are frequency relativelyless intense all with than and aboutshow 90 only cm a moderate broadening even at temperatures near the melting point. The 43 cm1 and 88 cm’Blg modes seen in Pig. 3 also belong to this group. Broadening of Raman modes with frequency shifts greater than 90 cm1 is more pronounced as can be seen in Fig. 1 and 2 for the 148 cm1, 162 cm1 and 181 em~ Ag bands and in Fig. 3 for the 160 cm1, 183 cm1 and 194 cmB 12 modes. The lead chloride Reman modes can He
classified into one of these two patterns of behaviour but one has to allow some degree of uncertainty in the characterization of the weaker lines. (2) When the temperature reaches about 2600 C the intensity of all Reman peaks decreases rapidly while the background increases. (3) A graph of the logarithm of the linewidth against the inverse of the absolute temperature for those Raman lines that broaden more rapidly with temperature is approximately a straight line. Around 2600 C there is a change in the slope of this straight line. This is1 Ag(xx) Reman mode. (4) When4the exemplified in Fig. for temperature the 162 cm approaches the melting point of PbCl 2 the Raman spectra in all geometries can be described as a remaining distinct mode, at low frequency, extending out to around 200 mC’. background above a practically structureless Electrical conductivity results of a typical crystal are presented in Figs. 5 and 6. The change in the conductivity from the extrinsic to the intrinsic region is clearly demonstrated in the Arhennius plot of Fig. 5 at around 35Q0 C. Values of U and E/3 deduced from the inclination of the curves show good agreement with De Vries and Van Santen’ (see Table I) for the c—direction. However, it is also apparent that there
Vol. 31, No. 1
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
Big Ag Y(XX)Z
/1
t\
400’C
_________
j
Fig. 3
~‘~——‘~
I
/~
_.._-‘
I%JV
~.
‘...~
~
30 C •...i~jçj
~
‘
—
a,.,
lt
15%.)
lOu
—
Reman spectra of PbCl
2 for the configuration Y(xy)Z (B1 symmetry) for different temperatures. g For clarity shifted Gain is the the samecurves for thearespectra atvertically. high
I
I
//
2.00
____
~
/
—
Y(XY)Z 450°C
4’
/ /
31
..)U
-~
Roman shift cm Fig. 2 — Raman spectra of PbCl2 for the configuration Y(~cx)Z (Ag symmetry) for different temperatures. For clarity the curves are shifted vertically. Gain is the same for the spectra at high temperatures. The 16 K spectrum, with a different gain, is shown for comparison. is another change of slope at about 460°C where the conductivity increases much more rapidly. This is readily seen in the more detailed plot shown in Fig. 6. 4. DISCUSSION The approximately linear dependence of the logarithm of the linewidth with the inverse temperature can be the indication of an exponential relation of r with some sort of activation energy. One could be tempted to correlate the changes in slope seen inf Pigs. 4 and 5 for the linewidths of the Reman lines and for the conductivity. Such relation has
temperatures. The 16 K spectrum, with a different gain, is shown for comparison. 9 who been proposed by Peyrard and Nisset measured the temperature dependauce of the phonon linewidth in f3—AgI. In the case of PbCl 2 however the straight of Fig. 4 givesthetooslope smallfor a value for the line energy as compared to the energies of formation or migration of vacancies (Table I). Also, the graph for the linewidth occurs at a lower temperature than the one in the graph for the conductivity. It can be speculated that’ the Raman results reflect an increase of the disorder mechanisms of the lead chloride crystal which leads eventually to the rapid formation of vacancies in the intrinsic region. 1 that thesupport lines with Moreover, our results give to the assumption greater frequency of Ozin than 100 cm1 can be assigned to vibrations of the chloride sublattice. Since the chloride are repsonsible for the conduction in PbCl 2 and assuming that a substantical part of the broadening of the Reman bands at high temperature is due to the increasing disorder in the chloride sublattice, the separation of the modes into two groups, one for each sublattice, is qualitatively justified. We haveidentifled the more rapid increase in the conductivity at 460°Cas the beginning of a diffuse transition in which the chloride sublattice becomes more disordered than would be expected from the normal thermal growth of vacancies. However, the material does not
32
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
300
mr
100 I
500 I I
Vol. 31, No. 1
300 200 bc ‘ I F
100
~~
~
3.8
1~2
3.6O\~~
32
10-
-
1-5
2-0 ~
~ 2.5
(r~.cm)
Fig. 4 — Logarithm of the linewidth of the 162 cm’(Ag symmetry) Reman mode against the inverse of the absolute temperature. become a true solid electrolyte, up to the temperature measured as the melting point of the crystal is too close to the onset of the transition. Generally, for type III crystals the conductivity change is about a factor of io~spread over a hundred degrees or more and the conductivity is a continuous function7. For lead chloride we have found an increase of the order of a factor of 10 for a temperature range of about 35 degrees, which is of the same relative order. Recent work on n-AgI’°” have shown that the Reman spectra for this material in the solid electrolyte phase have very broad and structureless features. For temperatures above the transition the spectrum decreasTs
.
5 Ir~~ W -
I
1.2
1.6
2.0 1fl3/T ‘U
Fig. 5
—
Electrical
I
2.4
28
V~1 I’
conductivity
of PbCI 2
from the laser line out to around 200 cm with no other feature than a weak shoulder near 100 cm . In fact, these spectra for cL—AgI are qualitatively similar to the spectra of PbC12 at temperatures near its melting point, as those seen in Figs. 1, 2 and ~, if one discounts for the peaks at low frequencies. No detailed explanation for this kind of spectrum has been yet presented although many speculative reasoning have been advanced based on scattering from fluctuations due to ionic motion, attempt frequency for hopping or disorder removal of the k~’O selection rule. Our Reman results are consistent with the conductivity evidences that PbCl2 is neither a normal ionic conductor (class I) nor a solid electrolyte of class II. High temperature spectra, as seen in Figs. 1 2 and 3~show both normal crystalline and disorder features,
in
the c—direction, against the inverse temperature. All results are on the same crystal
4. CONCLUSION We have shown that lead chloride is not a true type I normal ionic salt but undergoes the beginnings of a diffuse transition at about 30 degrees below its melting point. The conductivity has been measured up to a few degrees below the melting point but did not show solid electrolyte behaviour. Reman spectra of PbCl2 single crystals indicate a high degree of disorder but not a complete melting of the chloride sublattice. Lead chloride can thus be considered to be a type III ionic salt in which the higher temperature transition (melting) intervenes before true
Vol. 31, No. 1
EVIDENCE FOR A DIFFUSE TRANSITION IN LEAD CHLORIDE
500
460 I
I
TC
420 I
•
33
TABLEI Values of the migrational energy (U) and the formation energy (E/3) of a chloride ion vacancy in PbCl 9, calculated from Fig. 5, compared with 2. tfie results of De Vries and Van Santen Be Vries
Present
Van Santea
0~
,.~ -l’s. (.CITI ‘~
U
•
(eV)
E/3 (eV)
0.30 ±0.20 0.52
± 0.04
0.30 ±0.01 0.50
± 0.05
-
• I
1.3 Fig. 6
—
solid electrolyte behaviour is observed. Ana~zledg~mant — The authors are indebted to J.F.Juliao who grew and oriented the single crystals used in this work.
1-35 1~4 1.45 10~’T,K~
Electrical conductivity of PbC1
2 against the inverse temperature. A magnI~cation of the high temperature results of Fig. 5.
REFERENCES 1. OZIN,G.A., Can.J.Chem. 48, 2931 (1970) 2. DE VRIES,K.J. ~ VAN SANTEN,J.H. Physica 29, 482 (1963) 3. SlM~OVICU,G.,J.Phys.Chem.Solids 24, 213 (1963) 4. JULIAO,J.F., Rev. Bras.Pisica3, 17 (1973) 299. John Wiley & Sons, New York (1963) 5. WICKOFF,R.W.C., Crystal Structures, Vol.11, p. 6. MOTT,N.F. & GURNEY,R.W., Electronic Processes in Ionic Crystals, p.54 Clarendon Press, Oxford (1957) 7. O’KEEPE,M., Comm.Sol.State Phys. 7, 163 (1977) 8. SUA1II,K. & SRANDRA,S., Phys.Status Solidi (a) 28, 653 (1975) 9. PEYRARD M. & MISSET,J.P., Solid State Countun. 17, 1487 (1975) 10. DELANEY,M.J. & USRIODA,S., Phys.Rev. B 16, 1410 (1977) 11. BURNS,G.., DACOL F.R. & SBAFER,M.W., Phys.Rev. B 16, 1416 (1977)