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Phase coexistence and hysteresis
182
LETTERS
das relativ langsame vorgetluscht.
Anklingen
TO
THE
der Photoleitung
(8) Es besteht unserer Meinung nach kein Grund, Ueberlegungen iiber die Wechselwirkung von Strahlungsfeld und Exzitonenwellen fur ein Experiment anzustellen, das sich ohne Widerspruch durch die vie1 einfachere Annahme der Reabsorption von gestreutem Licht erkhiren lasst. (9) Eigene kiirzlich durchgeftihrte Untersuchungen mit zerteilten und wieder gekitteten Kristallen zeigen deutlich, dass die Abnahme der Photoleitung nach dem Zerbrechen mit einer Abnahme der Streulichtintensitat verbunden ist. (3) Dabei bleibt der Zusammenhang zwischen PhotoStrom und Lichtstrom am Ort der Leitfahigkeitsmessung in quantitativer Weise erhalten. Dies spricht eindeutig fur den Mechanismus der Lichtstreuung in den von uns untersuchten Kristallen. (10) Die hier erwahnten Messungen kijnnen sirmvoll erst diskutiert werden, wenn such optische Messungen in der von uns vorgeschlagenen Art durchgefiihrt worden sind. Es erscheint schwer verstandlich, dass die Diffusion von Exzitonen durch die optisch sichtbaren Storungen (Korngrenzen) der polykristallinen Schicht weniger gestbrt werden sol1 als die Ausbreitung des Lichtes. (11) Die Frage, warum DIEMERund HOOGENSTRAATENan einem Kristall eine Diskrepanz zwischen Photostrom und Lichtstrom gefunden haben, kann unseres Erachtens nur auf Grund weiterer sorgfaltiger Messungen geklart werden. DIEMER und HOOGENSTRAATEN fanden im tibrigen bei den meisten der von ihnen untersuchten Kristalle ebenfalls, dass der indirekt erzeugte Photostrom durch Reabsorption des gestreuten Lumineszenzlichtes erzeugt wird.(s) Institut fiir Elektronenmikroskopie am Fritz-Haber-Institut der Max-PlanckGessellschaft, Berlin-Dahlem
EDITORS
4. BALKANSKI M. und BROSER I., 2. Elektrochem., Ber. Bunsenges. physik. Chem. 61, 715-723 (1957). 5. DIEMER G. und HOOGENSTRAATEN W., Private Mitteilung.
Phase coexistence and hysteresis (Receiwed 15 September *
1958)
THE
strain that arises from the coexistence of two phases in the solid state has been used to provide explanations of the hysteresis that accompanies solid-state transitions. DINICHERT(~)assumed that strain displaced the ammonium chloride transition according to the Clausius-Clapeyron equation. However, THOMAS and STAVELEY@)showed that on the basis of the Turnbull theory of nucleation the transition rates would be extremely sensitive to temperature, and that the temperatures at which the rates become significant are displaced by the effects of strain and surface energy on the growing nuclei. Assuming an equilibrium theory of hysteresis, the strain terms can be regarded as perturbations on the bulk free energies of the two phases.(s) If XI is the value of the strain contribution to the free energy of the low-temperature phase and XII the contribution to that of the high-temperature phase, then for the I + II transition AXI = XII-XI will determine the displacement of the point of intersection of the free-energy curves. AX,1 is regarded as the maximum strain contribution that can be attained before mechanical breakdown occurs, after which the transition will proceed isothermally. Assuming AX,1 is small,
I. BROSER R. BROSER-WAFNINSKY
LITERATUR 1. BALKANSKIM., J. Phys. Chem. Solids 6, 401 (1958). 2. BROSER I. und BROSER-WARMINSKY R., J. Phys. Chem. Solids 6, 386 (1958). 3. BROSER I. und BROSER-WARMINSKYR., J. Phys. Chem. Solids 8, 177 (1959).
where AT1 is the displacement of the transition from the temperature at which the bulk phases would be in equilibrium. Similar reasoning for the II + I transition gives:
AX&-Ax,=
= A&.ATh,
where A& is the entropy change associated with the transition and ATh is the temperature range of the hysteresis. Hysteresis can also be obtained by varying the
LETTERS
TO
THE
EDITORS
183
Table 1. The transitions occurring in certain ammonium salts
(Data taken largely from ref. (2)) ____~_.___ Tt(‘K) N&Cl
(NH,)@,
242.6 2344 214.9 223.4
NH,DCl ND,HCI
244.6 ,247.g
NH,Br ND&
AT, (fzrn$Zle)
(cal/mtZzleg.)
0.15 0.03 0.08 0.35
1.3 l-3 1.3 4.0
120 110 70 570
0.11 0.07
::,“:
60 50
0.35 0.06 0.11 1.2 0.12 .!0.07
*Assuming that these transitions ammonium chloride.
have the same mechanism
pressure at constant temperature. If this process is carried out under similar initial conditions, we may assume that the maximum strain will not be significantly changed. Therefore A&&-Ax,,?
= A&. AVd,
where A.& is the range of the pressure hysteresis and AVt is the volume change accomp~ying the transition. The extent of the coexistence, and hence the hysteresis, will be governed by an equation of the Clausius-Clapeyron type : AT,, -=-* AP,
-__ (&mf%xi.
as that in the
Acknoeuledgement-Thanks are due to Dr. B. J. ALDJ3R for valuable comments and suggestions on this topic.
Department of Chemistry University of California Berkeley 4, California
E. BRIAN SMMITH
BBFBRBNCBB 1. DINICHBRTP., Helv. Phys. Actu 17, 389 (1944). 2. THOMAS D. G. and STAVELEYL. A. K., J. Chem. Sac. 2572 (1951). 3. UBBELOHDEA. R., Nature, Land. 169, 832 (1952).
AK A&
In the case of the gradual transitions which occur in ammonium salts, all the factors in the above equation have been measured with the exception of the range of pressure hysteresis. This is known to occur, but no quantitative results have been reported. Apart from any assumptions made, the calculations of the pressure hysteresis are limited by the accuracy of the measurements of ATI, and A&. However, they provide an estimate of the range of pressure hysteresis to be expected from a theory of this type. It seems improbable that these small pressure changes will affect the nucleation process considered by THOMASand STAVELEY.(~) Thus, experimental measurements of APh will help test the validity of the two approaches and provide valuable evidence on the mechanism of phase transitions in the solid state.
The a&ferromagnetic transformationsof the alloy AUMII (Received 29 September 1958) ACCORDING to
the results of magnetic and electrical measurements on a bulk specimen of AuMn reported from this Institute in 1955, the compound undergoes an antiferromagnetic transformation at about 23O”C.(1*s) From magnetic measurements on a powder specimen, MORRH and PRESTON@)later reported an antiferromagnetic transformation of this alloy at 92°C (but not one at 230°C). In a recent publication BACON and STREET@) give the results of measurements on one bulk specimen and one powder specimen of the same compound. These investigations confirm the results of GIANSOLnAT# and of MORRIS and EFxESTON.(~) For the powder specimen, BACON and STREETobtained the transformation at 92°C very distinctly. (The transformation at 230°C also appears on their curves for
LETTERS
das relativ langsame vorgetluscht.
Anklingen
TO
THE
der Photoleitung
(8) Es besteht unserer Meinung nach kein Grund, Ueberlegungen iiber die Wechselwirkung von Strahlungsfeld und Exzitonenwellen fur ein Experiment anzustellen, das sich ohne Widerspruch durch die vie1 einfachere Annahme der Reabsorption von gestreutem Licht erkhiren lasst. (9) Eigene kiirzlich durchgeftihrte Untersuchungen mit zerteilten und wieder gekitteten Kristallen zeigen deutlich, dass die Abnahme der Photoleitung nach dem Zerbrechen mit einer Abnahme der Streulichtintensitat verbunden ist. (3) Dabei bleibt der Zusammenhang zwischen PhotoStrom und Lichtstrom am Ort der Leitfahigkeitsmessung in quantitativer Weise erhalten. Dies spricht eindeutig fur den Mechanismus der Lichtstreuung in den von uns untersuchten Kristallen. (10) Die hier erwahnten Messungen kijnnen sirmvoll erst diskutiert werden, wenn such optische Messungen in der von uns vorgeschlagenen Art durchgefiihrt worden sind. Es erscheint schwer verstandlich, dass die Diffusion von Exzitonen durch die optisch sichtbaren Storungen (Korngrenzen) der polykristallinen Schicht weniger gestbrt werden sol1 als die Ausbreitung des Lichtes. (11) Die Frage, warum DIEMERund HOOGENSTRAATENan einem Kristall eine Diskrepanz zwischen Photostrom und Lichtstrom gefunden haben, kann unseres Erachtens nur auf Grund weiterer sorgfaltiger Messungen geklart werden. DIEMER und HOOGENSTRAATEN fanden im tibrigen bei den meisten der von ihnen untersuchten Kristalle ebenfalls, dass der indirekt erzeugte Photostrom durch Reabsorption des gestreuten Lumineszenzlichtes erzeugt wird.(s) Institut fiir Elektronenmikroskopie am Fritz-Haber-Institut der Max-PlanckGessellschaft, Berlin-Dahlem
EDITORS
4. BALKANSKI M. und BROSER I., 2. Elektrochem., Ber. Bunsenges. physik. Chem. 61, 715-723 (1957). 5. DIEMER G. und HOOGENSTRAATEN W., Private Mitteilung.
Phase coexistence and hysteresis (Receiwed 15 September *
1958)
THE
strain that arises from the coexistence of two phases in the solid state has been used to provide explanations of the hysteresis that accompanies solid-state transitions. DINICHERT(~)assumed that strain displaced the ammonium chloride transition according to the Clausius-Clapeyron equation. However, THOMAS and STAVELEY@)showed that on the basis of the Turnbull theory of nucleation the transition rates would be extremely sensitive to temperature, and that the temperatures at which the rates become significant are displaced by the effects of strain and surface energy on the growing nuclei. Assuming an equilibrium theory of hysteresis, the strain terms can be regarded as perturbations on the bulk free energies of the two phases.(s) If XI is the value of the strain contribution to the free energy of the low-temperature phase and XII the contribution to that of the high-temperature phase, then for the I + II transition AXI = XII-XI will determine the displacement of the point of intersection of the free-energy curves. AX,1 is regarded as the maximum strain contribution that can be attained before mechanical breakdown occurs, after which the transition will proceed isothermally. Assuming AX,1 is small,
I. BROSER R. BROSER-WAFNINSKY
LITERATUR 1. BALKANSKIM., J. Phys. Chem. Solids 6, 401 (1958). 2. BROSER I. und BROSER-WARMINSKY R., J. Phys. Chem. Solids 6, 386 (1958). 3. BROSER I. und BROSER-WARMINSKYR., J. Phys. Chem. Solids 8, 177 (1959).
where AT1 is the displacement of the transition from the temperature at which the bulk phases would be in equilibrium. Similar reasoning for the II + I transition gives:
AX&-Ax,=
= A&.ATh,
where A& is the entropy change associated with the transition and ATh is the temperature range of the hysteresis. Hysteresis can also be obtained by varying the
LETTERS
TO
THE
EDITORS
183
Table 1. The transitions occurring in certain ammonium salts
(Data taken largely from ref. (2)) ____~_.___ Tt(‘K) N&Cl
(NH,)@,
242.6 2344 214.9 223.4
NH,DCl ND,HCI
244.6 ,247.g
NH,Br ND&
AT, (fzrn$Zle)
(cal/mtZzleg.)
0.15 0.03 0.08 0.35
1.3 l-3 1.3 4.0
120 110 70 570
0.11 0.07
::,“:
60 50
0.35 0.06 0.11 1.2 0.12 .!0.07
*Assuming that these transitions ammonium chloride.
have the same mechanism
pressure at constant temperature. If this process is carried out under similar initial conditions, we may assume that the maximum strain will not be significantly changed. Therefore A&&-Ax,,?
= A&. AVd,
where A.& is the range of the pressure hysteresis and AVt is the volume change accomp~ying the transition. The extent of the coexistence, and hence the hysteresis, will be governed by an equation of the Clausius-Clapeyron type : AT,, -=-* AP,
-__ (&mf%xi.
as that in the
Acknoeuledgement-Thanks are due to Dr. B. J. ALDJ3R for valuable comments and suggestions on this topic.
Department of Chemistry University of California Berkeley 4, California
E. BRIAN SMMITH
BBFBRBNCBB 1. DINICHBRTP., Helv. Phys. Actu 17, 389 (1944). 2. THOMAS D. G. and STAVELEYL. A. K., J. Chem. Sac. 2572 (1951). 3. UBBELOHDEA. R., Nature, Land. 169, 832 (1952).
AK A&
In the case of the gradual transitions which occur in ammonium salts, all the factors in the above equation have been measured with the exception of the range of pressure hysteresis. This is known to occur, but no quantitative results have been reported. Apart from any assumptions made, the calculations of the pressure hysteresis are limited by the accuracy of the measurements of ATI, and A&. However, they provide an estimate of the range of pressure hysteresis to be expected from a theory of this type. It seems improbable that these small pressure changes will affect the nucleation process considered by THOMASand STAVELEY.(~) Thus, experimental measurements of APh will help test the validity of the two approaches and provide valuable evidence on the mechanism of phase transitions in the solid state.
The a&ferromagnetic transformationsof the alloy AUMII (Received 29 September 1958) ACCORDING to
the results of magnetic and electrical measurements on a bulk specimen of AuMn reported from this Institute in 1955, the compound undergoes an antiferromagnetic transformation at about 23O”C.(1*s) From magnetic measurements on a powder specimen, MORRH and PRESTON@)later reported an antiferromagnetic transformation of this alloy at 92°C (but not one at 230°C). In a recent publication BACON and STREET@) give the results of measurements on one bulk specimen and one powder specimen of the same compound. These investigations confirm the results of GIANSOLnAT# and of MORRIS and EFxESTON.(~) For the powder specimen, BACON and STREETobtained the transformation at 92°C very distinctly. (The transformation at 230°C also appears on their curves for