Phase diagram and phase transitions in ferroelectric $\mathbf{tris}$-sarcosine calcium chloride and its brominated isomorphs

Tris-sarcosine calcium chloride [(TSCC), (${\mathrm{CH}}_3{\mathrm{NHCH}}_2\mathrm{COOH}){}_3{\mathrm{CaCl}}_2$] is a uniaxial ferroelectric (FE) with a displacive second-order phase transition near $T_c=130$ K. A continuous range of solid solutions can be made by substituting Br for Cl, which lowers $T_c$ to 0 K at ∼72% Br. Such a quantum critical point differs from that in pseudocubic FEs, such as O-18 SrTiO${}_3$ or doped KTaO${}_3$. For many years, this system was thought to have only two phases, paraelectric and FE, at ambient pressure. However, we find from dielectric and resonant ultrasound spectroscopy that there are four phase transitions in TSCC and in TSCC:Br (for 0 < Br < 40%): Order-disorder of the sarcosine methyl group at 185 K; displacive FE transition at 130 K (in pure TSCC); a second FE transition [previously hypothesized to be antiferroelectric (AFE) but probably not] at 64 K; and a new anomaly at ∼45 K which might be due to a phase transition or to Debye-like freezing of orientational disorder of some part of the sarcosine molecule. The probable sequence of structures is (upon cooling): Pnma with $Z=4(D_{2h}^{16})$ ambient 500 K > $T$ > 185 K, disordered; Pnma with $Z=4(D_{2h}^{16})185\hspace{0.5em}\mathrm{K}>T>130\hspace{0.5em}\mathrm{K}$ (ordered); $\mathit{Pn}{2}_{1}a$ with $Z=4(C_{2v}^9)130\hspace{0.5em}\mathrm{K}>T>64\hspace{0.5em}\mathrm{K}$ (FE); $P{2}_{1}a$ $(C_{2h}^5)$ with $Z$ $=$4, 64 K > $T$ > 45 K (not AFE); $T$ < 45 K, unknown structure. A sixth hexagonal structure at high temperatures (>500 K) is hypothesized to be $D_{6h}^3$(P6${}_3$/mcm) with $Z$ $=$2, but the samples decompose first at 503 K (230 °C).

Figure 1

Structure of sarcosine molecules. The carbons and hydrogens are not shown. In the crystal phase, the COOH ion has its H (zwitter ion) come off, attaching as an N-H–Cl hydrogen bond) to the other side of the N ion shown and leaving three polar COO ions around each Ca${}^{++}$ ion.

Figure 2

Structure of TSCC, after Sawada et al.[25]

Figure 3

Temperature versus Br concentration phase diagram for TSCC and its brominated isomorphs. The newer data for brominated samples have slightly lower Curie temperatures than the older data, probably due to a difference between the starting Br concentration and the amount in the grown crystals. The curve is shown connecting to a value of 64 K at 40% Br, but this is probably misleading, as discussed in the text. (b) Dielectric 20%-Br sample for cooling (peak near 103 K) and heating (peak near 64 K). This is not due to thermal hysteresis.

Figure 4

Diagram of growth habitat used for orienting and cutting samples.

Figure 5

Inverse dielectric constants $1/{\varepsilon }_b$ versus temperature, showing a ratio of 2.00:1 above and below $T_c$ for the 40% brominated sample. The numerical results for 10% and 20% Br are given in the text. Unbrominated results are given in earlier literature.

Figure 6

Real part of dielectric constant at 10 kHz for different Br concentrations; curves at 0.01, 0.1, and 1.0 V applied ac test voltages. All data were in thermal equilibrium and steady state except for the pure TSCC sample, which was intentionally heated very quickly; in this case, especially at 1.0 V, the pyroelectric effect revealed low-temperature phase transition(s) near 64 K.

Figure 7

Unsaturated polarization $p$($E$) at 330 kV/m along the polar axis of pure TSCC. The lossless curve above $T_c=130$ K returns below 64 K.

Figure 8

Resonant ultrasonic response versus frequency at different temperatures for TSCC. The stack of spectra reveals anomalies in elastic coefficients $C_{\mathit{ij}}(T)$ in the 100-kHz regime and is very sensitive to nonpolar phase transitions. Data near temperatures at which anomalies occur in vibrational frequency or damping are indicated by arrows.

Figure 9

Resonant ultrasonic frequency for one mode near 420 kHz and its loss versus temperature for TSCC.

Figure 10

DMA results for Young's modulus. Each set of runs produced approximately 20 000 data points. Excel was used to average every hundred points, and it is these averages that are plotted.

Figure 11

Temperature versus pressure phase diagram for pure TSCC (after Refs. [18], [20], and [21]), showing hypothetical interaction of the order-disorder phase near 185 K with the FE phase. The dashed line assumes that the 185-K phase boundary at atmospheric pressure is pressure independent. Speculation is not made at higher pressures in the AFE phase, and the nature of the vertices is quite unknown.