Proton Glass Dielectric Susceptibility 
Compared with Monte Carlo and Bound 
Charge Semiconductor Model Predictions
Authors: V.H. Schmidt, Z. Trybula, D. He, J.E. 
Drumheller, C. Stigers, Z. Li, and F.L. Howell
This is an Accepted Manuscript of an article published in Ferroelectrics in June 1990, available 
online: http://www.tandfonline.com/10.1080/00150199008214569.
Schmidt, V. H., Z. Trybula, D. He, J. E. Drumheller, C. Stigers, Z. Li, and F. L. Howell. “Proton 
Glass Dielectric Susceptibility Compared with Monte Carlo and Bound Charge Semiconductor 
Model Predictions.” Ferroelectrics 106, no. 1 (June 1, 1990): 119–124. 
doi: 10.1080/00150199008214569.
Made available through Montana State University’s ScholarWorks 
scholarworks.montana.edu 
Ferroelecrrics, 1990, Vol. 106, pp. 119-124 
Reprints available directly from the publisher 
Photocopying permitted by license only 
0 1990 Gordon and Breach Science Publishers S.A. 
Printed in the United States of America 
PROTON GLASS DIELECTRIC SUSCEPTIBILITY COMPARED WITH 
MONTE CARL0 AND BOUND CHARGE SEMICONDUCTOR MODEL 
PREDICTIONS 
V.H. SCHMIDT, Z. TRYBUCA, D. HE, J.E. DRUMHELLER, C. 
STIGERS, Z. LI, and F.L. HOWELL* 
Physics Dept., Montana State Univ., Bozeman, MT 
59717 
*Physics Dept., U. North Dakota, Grand Forks, ND 
58202 
Abstract Our latest results for dielectric 
permittivity and loss and protonic conductivity in 
RADP, RADA and DRADA proton glasses are presented. 
Improvements in our "bound charge semiconductor" 
model for dielectric behavior are discussed. Monte 
Carlo studies of the phase diagram and polarization 
decay are described. Bias order parameter c. 
temperature plots from the simulation and from ND, 
deuteron NMR lineshapes are compared. 
We describe here our proton glass dielectric measurements, 
and their interpretation by Monte Carlo simulations based on 
a short-range-interaction model and by an analytic model €or 
diffusion of effective charge carriers. 
We made dielectric measurements on 50% ammoniated 
rubidium dihydrogen phosphate (RADP) between 93 and 348 K. 
The losses in this temperature range are caused by protonic 
conductivity, which is plotted in Fig. 1. The conductivity 
is similar to that of other crystals in this family. 
The inverse permittivity plotted in Fig. 2 gives a 
straight Curie-Weiss plot for E, near 5. The Curie-Weiss 
constant is 2800 K, close to the Slater' theory value of 
a*~P,~/4ke, = 2700 K. 
Dielectric results are presented also for 20% ammoniated 
rubidium dihydrogen arsenate (RADA), in Figs. 3 and 4. These 
show typical proton glass behavior, similar to our results in 
35% ammoniated RADA.' However, the 4% ammoniated crystal 
shows unusual behavior. In Fig. 5 the ferroelectric 
transition at 80 K is followed by typical proton glass 
dispersion below 30 K, as seen also in Fig. 6 and in the loss 
curves of Fig. 7. We believe that local regions with high Rb' 
concentrations are ferroelectric, while NH,'-rich regions show 
proton glass behavior. 
[ 11911955 
b '  I I I 
0 
IO'/T 
FIGURE 1 Conductivity 
along's of 50150 RADP. 
C=2800i 600 K 
I 'roo , I 1 
o o o o o  
5 0  r$J O=I  k H z  
&p 0=30 hHz 
a 
OO I00 200 300 
.. 
T ( K )  
FIGURE 2 Curie-Weiss 
behavior of 50150 RADP. 
10 20 30 YO 
T(K) T (to 
FIGURE 3 Permittivity FIGURE 4 Loss along 
a of 80120 RADA. - along 5 of 80120 RADA. 
I60 
I20 
E: 
80 
L(0 
0 
I I I I I I 
0 
0 0 
OQ3 000  
FIGURE 5 Permittivity along 5 of 96/04 RADA, showing 
both ferroelectric transition and dielectric dispersion. 
PROTON GLASS DIELECTRIC SUSCEPTIBILITY . . .  [ 121]/957 
0 
I I I I I I 
T ( K I  
0 2 0  Y O  6 0  
FIGURE 6 Permittivity 
6 
q 
E; 
2 
0 
20 40 
T IK) 
FIGURE 7 Loss along 
a of 9 6 / 0 4  RADA. along a of 9 6 / 0 4  RADA. - 
T(K1 
FIGURE 8 Permittivity 
along a of 72/28 DRADA. 
T(k) 
FIGURE 9 Loss along 
- a of 72/28 DRADA. 
[122]/958 V. H. SCHMIDT et al. 
We made the first dielectric measurements on 
deuterated rubidium/ammonium dihydrogen arsenate (DRADA) , 
on a 28% ammoniated crystal. The results shown in Figs. 8 
and 9 resemble those found by Courtens3 in DRADP, because 
both DRADA and DRADP show considerable frequency dispersion 
in this region, while undeuterated RADA and RADP do not. 
our Ilbound charge semiconductor" model4 I 
polarization change results from drift of HP04 and H3P04 
carriers in an effective field which is the sum of the 
applied and configurational fields. The relaxation time 
spread results from mobility being a function of time t 
after step cutoff of an applied dc field. The polarization 
decay from initial value Pi along the c axis obeys 
We are analyzing this dielectric behavior in terms of 
in which 
where n is fractional carrier density, To is Curie-Weiss 
temperature, €4 is rms diffusion step energy change, To is 
attempt time, and 7 is t for small t and approaches a fixed 
value for large t. This expression includes the dc 
susceptibility proposed by Sherrington and Kirkpatrick, in 
which the bias order parameter q is evaluated using the 
expression derived by Pirc, Tadib, and Blinc. 
temperature which were too broad. In the present model, 
the power of the logarithm in Eq. (1) is 4 instead of 2, 
and in its argument t is replaced by 7 which becomes 
constant at large t. Both changes narrow the range of 
mobility as t increases, and should fit experiment better. 
10,ll The Monte Carlo simulations are based on a model 
employing short-range interactions and random bias. We can 
simulate polarization decay from a state with initial 
ferroelectric order (Fig. 10) or antiferroelectric order. 
To find the Edwards-Anderson order parameter we record a 
proton configuration,let the system evolve, and find the 
correlation of the new configuration with the previous one. 
7 
An earlier version of our model8'' gave loss peaks E. 
m~ 
2 2-; 
z ? : I  
P ": 
- = N O  BIAS 
--- = B I A S  
= Seed D 
: :  
.4 
FIGURE 11 Monte Carlo determination of phase diagram 
for a proton glass model, showing phase boundaries with and 
without a random bias field. 
0.V 
$3 ' R I A ~ S  ORDER'PAR.  
g -  
I I I 
100 200 
T(K1 
FIGURE 12 Monte Carlo determination of bias order 
parameter for a proton glass model, compared with values 
found (Ref. 1 2 )  by deuteron NMR artd theory for 5 6 / 4 4  DKADP. 
[124]/960 V. H. SCHMIDT et al. 
We find the bias order parameter similarly, but warm and then 
cool the system so it loses memory of the particular poten- 
tial minimum it may have been trapped in. 
To find the phase diagram, we assume the system is in 
the ferroelectric or antiferroelectric state if it retains 90% 
of such initial order after a long running time. We found the 
phase diagram both with and without random bias, as shown in 
Fig. 11. The bias widens the proton glass concentration 
range, as expected, because in the NaCN/KCN system which has 
no frustration, random bias alone produces a phase diagram 
similar to that of proton glass systems. 
We found the bias order parameter - vs. temperature from 
our Monte Carlo simulation and compared it to that found from 
deuteron NMR of ammonium deuterons in DRADP proton glass,” as 
shown in Fig. 12. The agreement is quite good. 
In summary, we have shown new dielectric results, particu- 
larly for arsenate proton glasses. Our Monte Carlo and bound 
charge carrier models which are based on the crystal structure 
and interactions explain these results well. 
This work was supported by NSF Grant DMR-8714487. 
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