Phonon Softening and High-Pressure Low-Symmetry Phases of Cesium Iodide Page: 1,069
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Phonon Softening and High-Pressure Low-Symmetry Phases of Cesium Iodide
Marco Buongiorno Nardelli and Stefano Baroni
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Beirut 2/4, 1-34014 Trieste, Italy
Scuola Normale Superiore (SNS), Piazza dei Cavalieri 7, 1-56100 Pisa, Italy
(Received 15 April 1992)
The relative stability of various high-pressure phases of CsI is studied from first principles and ana-
lyzed using the Landau theory of phase transitions. We demonstrate that the cubic-to-orthorhombic
transition recently observed to occur slightly below 20 GPa is driven by the softening of an acoustic pho-
non at the M point of the Brillouin zone. The coupling between this mode and anisotropic strain makes
the transition slightly first order (with a volume variation of the order of 0.1%), and stabilizes the experi-
mentally observed orthorhombic phase with respect to other competing symmetry-allowed structures.
PACS numbers: 62.50.+p
The high-pressure properties of CsI are the subject of
current experimental interest both in conjunction with
band-overlap metallization and also because this cubic
salt undergoes a rather unexpected transition to a low-
symmetry phase at an applied pressure of a few tens of
GPa [1-3]. Until recently, the commonly accepted pic-
ture was that a cubic-to-tetragonal martensitic transition
would occur at a pressure of about 40 GPa. A further
transition from the tetragonal to an orthorhombic phase
at 56 GPa has been reported in Ref. , but this finding
has not been confirmed by subsequent experimental [1,31
nor theoretical [4-7] work. In particular, though the
cubic-to-tetragonal transition has been theoretically pre-
dicted by both semiempirical  and first-principles [5,6]
calculations, no evidence of the further orthorhombic dis-
tortion has been found by either methods .
Recent experiments [8,9] suggest that Cs undergoes a
continuous transition from the cubic (B2) to an hcp
structure, passing through an orthorhombic phase, CL,,
which is, however, different from the previously proposed
structure , Djh. In this paper we study the relative
stability of various phases of CsI at high pressure (cubic,
tetragonal, and the newly proposed orthorhombic struc-
ture). We identify the amplitude of a sixfold-degenerate
phonon mode (M5) as the relevant order parameter of
the transition in the Landau sense. The frequency of this
phonon is found to vanish at a pressure of -23 GPa,
which is well below the transition from the cubic to the
tetragonal phase. Neglecting the coupling between the
soft mode and anisotropic macroscopic strain, we find
that the transition would be second order from the cubic
to a tetrahedral (T5) phase; the coupling with macro-
scopic strain stabilizes the orthorhombic structure, mak-
ing the transition first order, with a very small volume
change ( 0.1%) and a transition pressure ( 21 GPa)
slightly below the softening pressure of the M5 phonon.
We also find that the orthorhombic structure is always
favored with respect to the tetragonal structure, up to
pressures of 60 GPa.
The cubic-to-tetragonal transition reported in Refs.
[1-3] was originally thought to be second order. Group-
theoretical considerations show that this transition must
be first order , and a discontinuity in the order pa-
rameter, c/a, at the transition was actually found in both
semiempirical  and first-principles [5,6] calculations.
Even so, this transition is driven by a dramatic softening
of the shear constant, cs = (cl -cl2), which in fact
vanishes at a volume slightly below the transition [4-61.
The shear constant is also proportional to the square of
the sound velocity along the (110) direction for vibrations
polarized along (110). This observation suggests that the
softening of the shear constant could be associated with
the softening of a transverse phonon along the (110)
direction. In fact, the gliding of one of the (110)
planes-which was indicated in Ref.  as characterizing
the low-symmetry phase of Csl- represents a lattice dis-
tortion which is very similar to that due to a doubly de-
generate acoustic phonon mode at the M point of the
Brillouin zone (BZ), M5.
In order to clarify the nature of the transition, we have
performed extensive density-functional-theory (DFT) cal-
culations of the static and vibrational properties of CsI at
high pressure, using the local-density approximation
(LDA), norm-conserving pseudopotentials, and large
plane-wave basis sets. The computational details are
similar to those described in Ref. , with the only
difference that we have now used a somewhat larger
kinetic-energy cutoff (25 Ry): The resulting values of the
equilibrium lattice constant and bulk modulus are 4.44 A
and 15 GPa, respectively. The vibrational properties
have been calculated using the density-functional pertur-
bation theory described in Ref. [111. In Table I some
phonon frequencies calculated at the equilibrium volume
are compared with experimental data. The agreement is
quite satisfactory, giving confidence in the predictive
power of our calculations.
In Fig. 1 we display the ionic displacements along the
normal coordinates of the M5 acoustic phonon , to-
gether with the dependence of the corresponding frequen-
cy upon molar volume. The displacement pattern is simi-
lar to but different from that proposed in Ref.  (the
magnitude of the cationic and anionic displacements are
VOLUME 69, NUMBER 7
PHYSICAL REVIEW LETTERS
17 AUGUST 1992
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Buongiorno Nardelli, Marco; Baroni, Stefano & Giannozzi, Paolo. Phonon Softening and High-Pressure Low-Symmetry Phases of Cesium Iodide, article, August 17, 1992; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc270786/m1/1/: accessed April 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.