Next Article in Journal
Prolactin and Growth Hormone Signaling and Interlink Focused on the Mammosomatotroph Paradigm: A Comprehensive Review of the Literature
Next Article in Special Issue
Thermodynamic Origin of Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in the GdF3-TbF3 System
Previous Article in Journal
The Effect of Fenugreek in Type 2 Diabetes and Prediabetes: A Systematic Review and Meta-Analysis of Randomized Controlled Trials
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
IJMS
Volume 24
Issue 18
10.3390/ijms241814000
ijms-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Two-Component Rare-Earth Fluoride Materials with Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in 50 RF3-R’F3 (R = La-Lu) Systems

by
Boris P. Sobolev
and
Elena A. Sulyanova
*
Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics”, Russian Academy of Sciences, Leninskiy Prospekt 59, 119333 Moscow, Russia
*
Author to whom correspondence should be addressed.
Int. J. Mol. Sci. 2023, 24(18), 14000; https://doi.org/10.3390/ijms241814000
Submission received: 29 June 2023 / Revised: 17 August 2023 / Accepted: 28 August 2023 / Published: 12 September 2023
(This article belongs to the Special Issue Recent Advances on Fluorine Chemistry)
Browse Figures
Versions Notes

Abstract

:
The formation of materials with negative thermal expansion (NTE) based on a phase transition-type mechanism (NTE-II) in 50 T–x (temperature–composition) RF3-R’F3 (R = La-Lu) systems out of 105 possible is predicted. The components of these systems are “mother” RF3 compounds (R = Pm, Sm, Eu, and Gd) with polymorphic transformations (PolTrs), which occur during heating between the main structural types of RF3: β-(β-YF3) → t-(mineral tysonite LaF3). The PolTr is characterized by a density anomaly: the formula volume (Vform) of the low-temperature modification (Vβ-) is higher than that of the high-temperature modification (Vt-) by a giant value (up to 4.7%). In RF3-R’F3 systems, isomorphic substitutions chemically modify RF3 by forming R1−xR’xF3 solid solutions (ss) based on both modifications. A two-phase composite (β-ss + t-ss) is a two-component NTE-II material with adjustable parameters. The prospects of using the material are estimated using the parameter of the average volume change (ΔV/Vav). The Vav at a fixed gross composition of a system is determined by the β-ss and t-ss decay (synthesis) curves and the temperature T. The regulation of ΔV/Vav is achieved by changing T within a “window ΔT”. The available ΔT values are determined using phase diagrams. A chemical classification (ChCl) translates the search for NTE-II materials from 15 RF3 into an array of 105 RF3-R’F3 systems. Phase diagrams are divided into 10 types of systems (TypeSs), in four of which NTE-II materials are formed. The tables of the systems that comprise these TypeSs are presented. The position of Ttrans of the PolTr on the T scale for a short quasi-system (QS) “from PmF3 to TbF3” determines the interval of the ΔTtrans offset achievable in the RF3-R’F3 systems: from −148 to 1186 ± 10 °C. NTE-II fluoride materials exceed known NTE-II materials by almost three times in this parameter. Equilibrium in RF3-R’F3 systems is established quickly. The number of qualitatively different two-component fluoride materials with the giant NTE-II can be increased by more than ten times compared to RF3 with NTE-II.

Graphical Abstract

1. Introduction

Trifluorides of rare-earth elements (REE), RF3, are polymorphic [1,2,3]. In [4], the discovery of an effect called a density anomaly in lanthanide (Ln) trifluorides, LnF3, was reported. The anomaly occurs during the PolTr This is because the density of the high-temperature modification is higher than that of the low-temperature modification. This usually happens in the opposite direction. Such an anomaly has been described [4] for LnF3 with Ln = Sm, Eu, and Gd. At that time, there was no interest in materials with NTE. The publication of [4] went unnoticed. In subsequent studies, there was no mention that any RF3 other than ScF3 [5,6,7] was an NTE material.
The polymorphism of PmF3 was not known because all its isotopes are short-lived, and the synthesis of Pm is possible only in atomic reactors. Recently, a method of structural and chemical modeling in a “CeF3-GdF3” QS was developed [8]. The composition 61(58Ce0.5Gd0.5)F3 with an atomic number (Z) of promethium, Z = 61, was proposed and named “pseudo-PmF3”. It has the structural and thermal (PolTr) properties of 61PmF3. “Pseudo-PmF3” polymorphism attached PmF3 to dimorphic LnF3 with Ln = Pm, Sm, Eu, and Gd, which are materials with NTE-II [9].
In this study, the concept [10] of the chemical modification of components of RF3-R’F3 (R = La-Lu) systems was used to predict 50 RF3-R’F3 systems (out of 105 possible) with two-phase composites having the giant NTE-II at the PolTr.
According to IUPAC, 17 REE were designated as R = Sc, Y, or La, and 14 Ln. When analyzing the periodicity in the properties of REE compounds, it is necessary to separate the d-element La from the 4f-elements Ln. If not necessary, the sum (La + Ln) is designated R.
The classification of materials with NTE presented in [10] cannot be considered complete. The authors of this article have written this statement. He identified materials with NTE-I (with NTE in a wide temperature (T) interval) and NTE-II (associated with the PolTr in a narrow “window ΔT”).
To verify the necessity and/or sufficiency of the empirical features of NTE-II materials [10], it is necessary to verify their compliance with the fundamental rules for constructing equilibrium phase diagrams of chemical systems. The materials formed in the NTE-II systems must comply with thermodynamic rules.
The origin of the features of NTE-II materials is discussed using an example of the phase diagram of this system. Their manifestation in the phase diagram is in line with the rules for constructing phase diagrams.
Such a comparison showed that the common features of NTE-II materials according to [10] (the “window ΔT” and two-phase region) neither separately nor together can determine NTE-II materials.
The necessary and sufficient signs of NTE-II materials are polymorphism and density anomaly. The anomaly is that the formula volume (Vform, the volume of one formula unit) of the low-temperature (β-) modification (Vlow) is higher than that of the high-temperature (t-) modification (Vhigh).
Chemical modification by isomorphism of known RF3 with NTE-II is possible only in a binary (and more complex) system. For trifluorides of R, such systems are RF3-R’F3. From 17 RF3, 136 systems are formed. From 15 fluorides (without fluorides of d-elements: ScF3 has a structure different from RF3 and YF3), 105 systems are formed. They are considered in this work.
Four dimorphic fluorides form the structural subgroup (SSGr) B: PmF3, SmF3, EuF3, and GdF3. They have the PolTr with the giant NTE-II (ΔV/V ~ 4.7% relative to the smaller value) [9].
Such an anomaly is rare for inorganic compounds. The structural mechanism of the giant NTE-II for the β- → t-PolTr (at heating) is unknown.
RF3-R’F3 systems are the most suitable for the creation of fluoride NTE-II materials. RF3 are ionic compounds with the simplest formula and high chemical stability. Their melting (Tfus) and PolTr (Ttrans) temperatures provide diffusion processes that quickly achieve equilibrium.
A long homologous series of LaF3 and 14 LnF3 (Ln = Ce-Lu) consists of extremely chemically similar (ChProx) compounds with a minimum difference in the Z of cations in the series (ΔZ = 1).
Over the whole length of the series, lanthanide compression of cations [11] leads to the formation of three types of structures: LaF3 (t-) [12,13], β-YF3 (β-) [14], and α-UO3 (α-) [15]. They are separated by two morphotropic transformations (MorphTrs).
High-temperature chemical interactions of the components in the RF3-R’F3 systems are described by the ChCl [16]. ChCl translates the search for NTE-II materials from 15 RF3 to a complete array of 105 RF3-R’F3 systems.
ChCl reflects periodic changes in the structure and properties of the RF3 homological series [16] and the systems formed by them. Unlike the “dimensionless” ChProx, the ChCl is based on the measurable parameter ΔZ = |NZ−MZ|.
The chemistry of the high-temperature interactions of components is visually reflected in the topological features (forms) of phase diagrams. The most common form of weak interaction in the RF3-R’F3 systems is isomorphism. Depending on ΔZ, it varies from perfect to limited.
Stronger forms of interactions are two types of morphotropic transformations. Their topological features are invariant phase reactions: peritectic (MorphTrs-1) and eutectic (MorphTrs-2). The maximum chemical differences between the components and ΔZ (from 8 to 14) are accompanied by the presence of both MorphTr-1 and MorphTr-2 in one system or a complete rupture of the isomorphic miscibility [1].
A chemical design of the RF3-R’F3 systems covers a complete array of 105 binary systems formed by REE fluorides (without ScF3 and YF3). It is based on studies of the chemistry of high-temperature interactions between components [1].
The structural and chemical modeling of “pseudo-61PmF3” detected the low-temperature “hidden” PolTr in it, gave the values of the lattice parameters, and detected the giant NTE-II [9].
The short “from PmF3 to TbF3” QS defines the limits of the “window ΔT” position on the T axis in the entire array of RF3-R’F3 systems as very wide.
All these studies, especially in recent years, have prepared the formulation of the chemical design of two-component NTE-II materials with REE trifluorides with adjustable properties.
The full range of regulated parameters of fluoride NTE-II materials in the RF3-R’F3 systems can be found from the analysis of the phase diagrams of the studied systems and the “from PmF3 to TbF3” QS [8]. The RF3-R’F3 phase diagrams presented in this paper were obtained experimentally. The ratio of the components in them varies from 0 to 100 mol. %.
The aim of this study is to predict, using the principle of isovalent isomorphism, RF3-R’F3 systems in which two-phase materials with NTE-II are formed.
Research objectives: (1) to identify the stages of the chemical design of RF3-R’F3 systems for the search for fluoride NTE-II materials; (2) based on the ChCl of RF3-R’F3 systems, give a forecast of 50 systems (out of 105) with two-phase composites having the giant NTE-II at the β-ss → t-ss PolTr (at heating); (3) using the concept of the “from LaF3 to LuF3” QS [8], determine the range of Ttrans of components in the area in which the position of the “window ΔT” on the T axis in the “from LaF3 to LuF3” QS is regulated; (4) evaluate the practical applicability of the (β-ss +t-ss) two-phase composite NTE-II materials from the kinetics of phase transformations in the subsolidus region of the studied RF3-R’F3 systems in which they are formed.

2. Results and Discussion

Four Stages of the Chemical Design of Rare-Earth Fluoride Materials with Adjustable NTE-II Parameters

This approach is called chemical design because it uses high-temperature chemical interactions in RF3-R’F3 systems.
The chemical design of materials with NTE-II includes four stages.
The first stage involves the choice of “mother” substances with the giant NTE-II. It is identical to the proposed paradigm [10].
The density anomaly at the PolTr is a necessary condition for NTE-II. By describing RF3 as a single-component material with NTE-II, we are actually doing this for the first time in the field of materials science.
In the literature, the coefficients of a volumetric (αV) or linear (αL) thermal expansion CTE are called NTE-II parameters. For the PolTr in single-component RF3 from the SSGr B, the CTE cannot be defined at ΔT = 0. Therefore, the CTE is not a parameter of NTE-II (see below and [10]).
The second stage involves the choice of isomorphism as a method of modifying the “mother” RF3. Isomorphism is the most common method for chemical modification of properties, including NTE-II.
The chemical design by chemical modification of simple RF3 compounds with the giant NTE-II by means of isovalent isomorphism leads to binary RF3-R’F3 systems as the simplest of the multicomponent systems.
Isovalent isomorphism is exceptionally effective in modifying the properties of REE trifluorides. Studies on the phase diagrams of 34 RF3-R’F3 systems of chemically similar fluorides [1] have shown a wide development of isomorphism and provided digital data for the second stage of the chemical design.
The third stage of the chemical design is new in NTE-II search concepts. It is based on studies of the high-temperature chemistry of the RF3-R’F3 systems. At this stage, the systems in which NTE-II materials are formed are predicted based on the chemical interactions of the components [1].
The possibility of using the chemical design is limited for most homologous series of REE compounds. The number of homologous series of REE compounds with the studied phase diagrams is usually small. It is often combined with an incomplete set of REE. There are no Pm compounds anywhere for the reason described above. The difference in the methods of studying compounds, sometimes separated by decades, reduces the comparability of data from different authors.
The long RF3 homological series of 15 trifluorides (LaF3 and 14 LnF3 with Ln = Ce-Lu) is unique in the completeness of the study of individual trifluorides and the systems formed by them. It is also unique in terms of the high rate of equilibrium in the formation of NTE-II materials (see above).
Fluoride rare-earth NTE-II materials are formed in systems with one or two RF3 components with the giant NTE-II [4,9].
Without ChCl, the analysis of such RF3-R’F3 systems is impossible. ChCl, which was recently created [16], is the basis of the third stage of the chemical design of systems with multicomponent NTE-II materials.
The third stage is discussed in the following section. For the first time four types of systems (out of 10) in which NTE-II materials are formed were identified in ChCl.
The fourth stage of the chemical design for the study of materials with NTE-II is used for the first time. Quantitative data forming NTE-II were obtained from the analysis of the position of NTE-II materials on a phase diagram, their phase composition, and equilibrium phase reactions in a binary system. They are the values of the ΔV/V volume change of a two-phase composite in the interval T, determined by the “window ΔT”.
The “window ΔT” and the ΔV/V = f(T) dependencies are calculated from the phase reaction curves. This stage is based on the thermodynamics of chemical systems, which has not been previously used for the analysis of NTE-II [10].
The proposed scheme for calculating the parameters of NTE-II materials can be applied to each of the studied RF3-R’F3 systems with NTE-II. To achieve this, the liquidus and solidus curves of solid solutions (ss) and the changes in their lattice parameters (Vform) with composition must be determined in these systems.
The special role of structural changes during the PolTr in the formation of NTE-II materials separates them from normal materials possessing NTE-I, in which the growth of ΔV/V occurs with the growth of T.
To date, there is no data on the structural mechanism of NTE-II in RF3. Its detection should be the fifth stage in the chemical design of fluoride NTE-II materials.

3. Materials and Methods

The chemical design of materials with NTE-II among 105 RF3-R’F3 systems is based on ChCl [16].

3.1. NTE-II and ChCl of the RF3-R’F3 Systems

ChCl built on the inversely proportional dependency of the degree of ChProx of RF3 on ΔZ (the difference in Z of cations) [16]. ChCl is represented as a coordinate semi-square, Figure 1.
The coordinate semi-square is a graphical representation of the number of combinations of 15 objects, two in each (C152). It is formed by the intersections of 15 columns of the long homologous series from LaF3 to LuF3 (without ScF3 and YF3) and 14 horizontal rows from CeF3 to LuF3. The upper right half of the square is discarded as a replicate.
There are 105 rectangles left. Each rectangle represents a separate RF3–R’F3 system. The studied systems are indicated by the REE symbols.
The first level of the ChCl divides 15 RF3 by structural features (a type of structure and the presence of the PolTr) into four structural subgroups (SSGrs A–D) (Table 1). We highlighted the SSGr B in bold, emphasizing the presence of the PolTr with NTE-II.
The second level of the ChCl comprises 10 TypeSs. The types are paired combinations of four SSGrs: 1 C-C’, 2 A-A’, 3 B-B’, 4 D-D’, 5 B-C, 6 C-D, 7 A-B, 8 A-C, 9 B-D, 10 A-D (arranged in ascending order of |ΔZmax| in Figure 1).
In the third level, four groups of systems (GrSs) are formed from TypeSs with a certain |ΔZmax| [1,16].
The GrSs and TypeSs include several systems. To compare the TypeSs and GrSs, two values of the ChProx in each are used: maximum |ΔZmax| and minimum |ΔZmin| (Table 2) [1,16]. Only |ΔZmax| is discussed here.
The third level of the GrSs is partially shown in Figure 1 in color: for GrS-1 in yellow and dark yellow, for GrS-2 in blue and dark blue, and for GrS-3 in green (the colors are the same as in the ChCl in [16]).
Six TypeSs remained colorless in Figure 1. These TypeSs are divided into two groups. Four TypeSs belong to the first group: TypeS-1 (C-C’), TypeS-2 (A-A’), TypeS-4 (D-D’) and TypeS-6 (C-D). The Zav of R from the SSG B cannot be realized in these SSGs. These systems do not contain materials with NTE-II.
The third stage of the chemical design allocates 50 RF3-R’F3 systems (Figure 1) with RF3 from the SSGr B (R = Pm, Sm, Eu, and Gd) as the sources of fluoride materials with adjustable NTE-II parameters. Only four TypeSs (TypeS-3, TypeS-5, TypeS-7, TypeS-9) (out of 10) contain RF3 with the β- → t- PTs (at heating) with NTE-II.
Table 2 lists the number of systems with NTE-II materials in each TypeS.

3.2. NTE-II Materials in TypeS-3 (B-B’) from RF3 of the SSGr B

The TypeS-3 (B-B’) from the components of the SSGr B includes six systems, as shown in Table 2 and Figure 1.
According to the ChProx these components are heterogeneous. Three systems, PmF3-SmF3, SmF3-EuF3, and EuF3-GdF3, were distinguished from the others in the TypeS-3 by the maximum ChProx |ΔZ| = 1 of the components. They are marked in dark yellow in Figure 1.
The TypeS-3 (B-B’) includes six systems. None have been studied. Of these, three systems (PmF3-SmF3, SmF3-EuF3, and EuF3-GdF3) are special “synthetic” systems. It is composed of RF3-R’F3 systems with ΔZ = 1.
The full QS was described in [8]. It contains 14 systems of 105 RF3-R’F3. Let us call these systems particular. The full QS is composed of LaF3-CeF3, CeF3-PrF3, PrF3-NdF3, NdF3-PmF3, PmF3-SmF3, SmF3-EuF3, EuF3-GdF3, GdF3-TbF3, TbF3-DyF3, DyF3-HoF3, HoF3-ErF3, ErF3-TmF3, TmF3-YbF3, and YbF3-LuF3 systems. “Particular” indicates that the condition |ΔZ| = 1 is “bound” to a system in this context. Only strictly defined systems that obey this condition can be adjacent to QS.
From full QS stands out the section of SSGr B. Let us call it short QS “from PmF3 to GdF3(TbF3)”. These systems are marked in dark yellow in Figure 1. This short QS is used to analyze the dependence of the position of RF3 (R = Pm-Tb) Ttrans.
Three particular systems of the short QS are shown in Figure 2. NTE-II during the PolTr in the SmF3-EuF3 system is indicated by an arrow. Similar PolTrs exist in two adjacent systems PmF3-SmF3 and EuF3-GdF3.
The PmF3-EuF3, SmF3-GdF3, and PmF3-GdF3 systems of the TypeS-3 have |ΔZ| > 1. They do not belong to the short QS, but are included in the list of systems from the TypeS-3 with NTE-II materials (Table 3). Continuous ss are formed between their components. The structural modifications of the components involved in the PolTrs cause NTE-II. These systems are marked in yellow in Figure 1.
In Figure 2, the MorphTr in the GdF3-TbF3 system is added to the two PolTrs considered. This is the true MorphTr (according to V.M. Goldschmidt [11]). This is the MorphTr of the first type (MorphTr-1) between the β-ss and t-ss. The appearance of the MorphTr-1 in the GdF3-TbF3 system is caused, as in RF3, by a change in the structure type. The change proceeds in accordance with the mechanism of the MorphTr, an invariant (T = const) peritectic phase reaction with the melt (Liq) [1]:
β-Gd0.49Tb0.51F3 ↔ Liq (melt) + t-Gd0.57Tb0.43F3

3.3. NTE-II Temperature Control in the Short “from PmF3 to TbF3” QS

The position of the ΔV/Vform jump of ΔT on the T axis plays a critical role for the practical use of NTE-II materials. Most applications require room temperature. In the short “from PmF3 to TbF3” QS ΔTtrans can be controlled by the RF3-R’F3 systems.
Dimorphic RF3 (R = Pm-Gd) have a uniquely large range of variation in Ttrans during the PolTrs. In RF3-R’F3 systems, there is a possibility of more “subtle” control of ΔTtrans by isomorphic substitutions.
The limit of Ttrans values for two-component materials with NTE-II is determined by the short QS of the full QS which contains RF3 of the SSGr B (R = Pm, Sm, Eu, and Gd). Curve a-b-c-d-e, Figure 2, in the short “from PmF3 (point a) to GdF3 (Gd0.57Tb0.43F3, point e)” QS presents the dependence of Ttrans on Z. Materials with this ΔTtrans and Z have NTE-II.
With the help of the chemical design of NTE-II materials in RF3-R’F3 systems, Ttrans can be changed from −148 °C in PmF3 [9] to 1186 ± 10 °C for the MorphTr-1 with t-Gd0.57Tb0.43F3 [1].
According to [10], the “window ΔT” of known NTE-II materials does not exceed 600 °C. Fluoride NTE-II materials surpass it by almost three times.
Fluoride NTE-II materials have a problem of accessibility when they need to be used at standard (room) T. The continuation of the curve a-b in Figure 2 to the room T region corresponds to the PmF3-SmF3 system with an inaccessible PmF3.
This problem is solved by the wide possibilities of carrying out structural and chemical modeling of the “lanthanide” for any average value of the atomic number Zav between 58Ce and 71Lu [9]. The necessary short QS is selected for modeling. The model composition with Zav can be calculated for the required Ttrans.
Structural and chemical modeling of “lanthanides” with an intermediate Zav moves the NTE-II “window ΔT” of the adjustable interval on the T scale (see above). This provides a solution to the availability problem (PmF3) and high cost of some REE, allowing the replacement of unavailable RF3.
The temperature range in which the chemical design can adjust Ttrans in RF3 follows from the short “from PmF3 to GdF3 (Gd0.57Tb0.43F3)” QS (the curve a–e, Figure 2). The isomorphism continuously changes the Ttrans of the R1-xR’xF3 PolTrs from (−148 °C) in PmF3 (and lower in the unexplored part of the NdF3-PmF3 system) up to 1186 ± 10 °C for MorphTr-1 with t-Gd0.57Tb0.43F3.
In the other three systems, |ΔZmax| increases to 2 and 3. This does not limit the formation of phases with NTE-II in the systems of the TypeS-3.

3.4. NTE-II Materials in the TypeS-5 (B-C), TypeS-7 (A-B), and TypeS-9 (B-D)

Let us arrange the TypeSs with the SSGs components in increasing order |ΔZmax| (Table 2): the TypeS-5 (B-C) |ΔZmax| = 6, TypeS-7 (A-B) |ΔZmax| = 7, and TypeS-9 (B-D) |ΔZmax| = 10.

3.4.1. NTE-II Materials in the TypeS-5 (B-C)

There are 12 systems in the TypeS-5 (Table 4). The phase diagrams of the GdF3-TbF3 and GdF3-DyF3 systems are shown in Figure 2 and Figure 3. For the TypeS-5 |ΔZmax| = 6, which is twice that for the TypeS-3.
This decrease in the ChProx of RF3 causes, starting with the GdF3-TbF3 system, the emergence of a new topological feature, MorphTr-1 (the peritectic phase reaction). The appearance of MorphTr-1 (Table 2) follows the critical |ΔZmax| [1].
The GdF3-DyF3 system (Figure 3) from the TypeS-5 (B-C) contains the limited t-Gd1-xDyxF3 and continuous β-Gd1-xDyxF3 ss [1]. The “window ΔT > 0” is marked with a red arrow.

3.4.2. NTE-II Materials in the TypeS-7 (A-B)

The TypeS-7 contains 16 systems (Table 5) with |ΔZmax| = 7 from RF3 of different SSGrs.
In the NdF3-PmF3 system, the first component is the last in the SSGr A, and the second component is the first component in the subsequent SSGr B. As a result, the NdF3-PmF3 system has |ΔZ| = 1, which refers to the QS. This system is borderline, similar to the GdF3-TbF3 system. The phase diagram of this system has not yet been studied.
The high |ΔZmax| makes β-ss limited, leaving continuous t-ss at high temperatures (Figure 4 and Table 2).

3.4.3. NTE-II Materials in the TypeS-9 (B-D)

The TypeS-9 consists of 16 systems with one component from the SSGr B (Table 6). In this TypeS, |ΔZmax| reaches 10. A large chemical difference in the Z values of the components is manifested in the difference in the structural types of the components. In the SSGr D, to which the second components of the TypeS-9 systems belong, the α-type appears at high temperatures.
MorphTr-2 of the second type, Liq (melt) →β- + α- (eutectic phase reaction), is also accompanied by a giant ΔV/Vform jump. In MorphTr-2, there is an increase in volume of the high-temperature α-modification by 16% (to the smaller value).
At |ΔZmax| = 10 in TypeS-9, the chemical interactions of the components lead to the simultaneous appearance of two topological signs of strong interactions: MorphTrs of two types.
In the phase diagram of the GdF3-ErF3 system (Figure 5), only one structural transformation, MorphTr-1 β-ss → t-ss (at heating), is associated with NTE-II. The peritectic MorphTr-1 that originated in the TypeS-5 (B-C) is supplemented by the eutectic MorphTr-2 in the GdF3-ErF3 system from the TypeS-9 (B-D). This MorphTr-2 is not related to NTE-II.
The chemical design with the ChCl highlights 50 systems (out of 105) of the four TypeSs in which the presence of NTE-II materials is possible. One or both components of these systems are selected from dimorphic RF3 from the SSG B(R = Pm, Sm, Eu, and Gd). They have the β-ss → t-ss PolTrs (at heating) associated with NTE-II. Only 11 of the 50 systems were studied. They are shown in bold in Table 3, Table 4, Table 5 and Table 6.

3.5. NTE-II Materials in the TypeS-8 (A-C) and TypeS-10 (A-D)

The remaining TypeS-8 (A-C) and TypeS-10 (A-D) implement Zav, corresponding to the Zs of R, which form fluorides from the SSGrB (from Pm to Gd). The first TypeS-8 has |ΔZmax| = 10 (similar to TypeS-9). The second has the highest |ΔZmax| = 14 for all TypeS. The phase diagrams at high |ΔZmax| become very complicated.

3.6. NTE-II and Kinetics of Phase Formation in RF3-R’F3 Systems

The features of NTE-II materials relate only to the equilibrium state. Structural transformations of the phases with NTE-II along the curves of their decay (formation) occur in the solid state. To achieve equilibrium, disinhibited changes in the phase composition are required.
The processes of ss ordering in the subsolidus and the formation of double compounds are usually inhibited. There are no such processes in the studied RF3-R’F3 systems [1].
“Liquid–solid” transitions are disinhibited. In the 34 studied systems, the thermal effects of crystallization (liquidus and solidus) were well separated by thermal analysis [1]. According to the kinetics of melt crystallization of the studied RF3-R’F3 systems during thermal analysis and the thermal effects of phase transformations, two-phase composite NTE-II materials, β-ss +t-ss, formed during phase reactions are in equilibrium with a high probability.
In this paper, 50 (out of 105) RF3-R’F3 systems in which these materials may form were selected using the principle of isovalent isomorphism.
Composite materials with NTE-II are also formed in MF2-RF3 systems with M = Ca, Sr, Ba; R = Gd-Lu, Y, and NaF-RF3 with R = Gd, Tb [1]. The LaF3-type structure has a high isomorphic capacity (up to 35% mol.) in relation to REE ions. When part of the R3+ cations is replaced with M2+ (Na+) cations (aliovalent isomorphism), berthollide phases with the t-type structure are formed [1,17,18]. When the temperature decreases, their decay occurs over the temperature range (the t- → β- PolTr with “window ΔT” > 0) with the formation of β-type phases [1]. The thermodynamic aspects of the phase transitions in the NTE-II berthollide phases are not included in the objectives of this study.
The t-type RF3 and R1-xR’xF3 considered in this report and berthollide phases based on RF3 can be obtained in the form of single crystals [1]. They are the best superionic conductors with fluorine-ion conductivity [19,20,21,22,23,24,25]. They are used as lasers [26,27] and as scintillators [28,29,30,31,32,33]. Nonstoichiometric crystals with the t-type structure have a low refractive index dispersion at the level of the initial RF3 [34].

Author Contributions

B.P.S. contributed to the conceptualization, methodology, investigation of the phase diagrams, analysis, interpretation, and writing of the published work. E.A.S. contributed to the original drafting, analysis, interpretation, and writing of the published work. All authors have read and agreed to the published version of the manuscript.

Funding

This work was performed within the State Assignment of FSRC “Crystallography and Photonics” RAS.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

The authors are grateful to P.V. Kostoglodov for useful discussion.

Conflicts of Interest

The authors declare no conflict of interest concerning this paper.

Abbreviations

PolTrPolymorphic transformation
NTENegative thermal expansion
NTE-IINegative thermal expansion based on a phase-transition-type mechanism
QSQuasi-system
ssSolid solution
ChProxChemical proximity
ChClChemical classification
TypeSType of a system
GrSsGroups of systems
REERare-earth element
VformVolume of one formula unit
SSGrStructural subgroup
MorphTrMorphotropic transformation

References

  1. Sobolev, B.P. The Rare Earth Trifluorides, Part 1: The High Temperature Chemistry of the Rare Earth Trifluorides; Institute of Crystallography: Moscow, Russia; Institut d’Estudis Catalans: Barcelona, Spain, 2000. [Google Scholar]
  2. Greis, O.; Haschke, J.M. Rare Earth Fluorides. In Handbook on the Physics and Chemistry of Rare Earths; Gscheidner, K.A., Eyring, L.R., Eds.; Elsevier (North Holland Publishing Co.): Amsterdam, The Netherlands, 1982; Volume 5, pp. 387–460. [Google Scholar]
  3. Spedding, F.H.; Daane, A.H. The Rare Earths; John Willey and Sons, Inc.: New York, NY, USA, 1961; 394p. [Google Scholar]
  4. Sobolev, B.P.; Garashina, L.S.; Fedorov, P.P.; Tkachenko, N.L.; Seiranian, K.B. Polymorphism and crystallographic properties of yttrium and rare earth trifluorides. Sov. Phys. Crystallogr. 1974, 18, 473–476. [Google Scholar]
  5. Greve, B.K.; Martin, K.L.; Lee, P.; Chupas, P.J.; Chapman, K.W.; Wilkinson, A.P. Pronounced Negative Thermal Expansion from a Simple Structure: Cubic ScF3. J. Am. Chem. Soc. 2010, 132, 15496–15498. [Google Scholar] [CrossRef]
  6. Kasatkin, L.; Gulina, N.; Platonova, V.; Tolstoy, P.; Murin, I. Strong negative thermal expansion in the hexagonal polymorph of ScF3. CrystEngComm 2018, 20, 2768. [Google Scholar] [CrossRef]
  7. Lazar, P.; Bučko, T.; Hafner, J. Negative thermal expansion of ScF3: Insights from density-functional molecular dynamics in the isothermal-isobaric ensemble. Phys. Rev. B 2015, 92, 224302. [Google Scholar] [CrossRef]
  8. Sobolev, B.P. Full quasi-system “from LaF3 to LuF3” as a combination of 14 binary systems of lanthanide trifluorides with maximal chemical proximity. J. Solid State Chem. 2022, 312, 123163. [Google Scholar] [CrossRef]
  9. Sobolev, B.P.; Sulyanova, E.A. Promethium trifluoride: Polymorphism and the structure of modifications on the model crystal 61(Ce0.5Gd0.5)F3. Part I. Structural and chemical modeling of “pseudo 61PmF3” in a short quasi-system “from CeF3 to GdF3”. CrystEngComm 2022, 24, 7602–7610. [Google Scholar] [CrossRef]
  10. Takenaka, K. Progress of Research in Negative Thermal Expansion Materials: Paradigm Shift in the Control of Thermal Expansion. Front. Chem. 2018, 6, 267. [Google Scholar] [CrossRef]
  11. Goldschmidt, V.M.; Barth, T.; Lunde, G. Geochemische Verteilungsgesetze der Elemente. Part V «Isomorphie Und Polymorphie Der Sesquioxyde. Die Lanthaniden-Kontraktion Und Ihre Konsequenzen; Jacob Dybwad, Kristiania: Oslo, Norway, 1925; Volume 5, pp. 1–59. [Google Scholar]
  12. Mansmann, M. Die Kristallstruktur von Lanthantrifluorid. Zeitschrift fur Krist. 1965, 122, 375–398. [Google Scholar] [CrossRef]
  13. Schlyter, K. On the crystal of fluorides of the tysonite (LaF3) type. Arkiv Kemi. 1953, 5, 73–82. [Google Scholar]
  14. Zalkin, A.; Templeton, D.H.; Hopkins, T.E. The Atomic Parameters in the Lanthanum Trifluoride Structure. Inorgan. Chem. 1966, 5, 1466–1468. [Google Scholar] [CrossRef]
  15. Greaves, C.; Fender, B.E.F. The structure of α-UO3 by neutron and electron diffraction. Acta Cryst. 1972, 28, 3609–3614. [Google Scholar] [CrossRef]
  16. Sobolev, B.P. High-temperature chemistry of Y, La and lanthanide trifluorides in RF3–R’F3 systems. Part 1. Chemical classification of systems. J. Solid State Chem. 2021, 298, 122079. [Google Scholar] [CrossRef]
  17. Bevan, D.J.M.; Greis, O. Fluorine-deficient tysonite-type solid solutions (Ca,Ln)F3-a and related superstructure phases Ca13Ln7F27. Rev. Chim. Miner. 1978, 15, 346–359. [Google Scholar]
  18. Fedorov, P.P. Berthollide Formation Conditions. Rus. J. Inorg. Chem. 2012, 57, 959–969. [Google Scholar] [CrossRef]
  19. Aalders, A.F.; Arts, A.F.M.; de Wijn, H.W. The fluorine motion in tysonite-structured solid solutions. Solid State Ionics 1985, 17, 241–250. [Google Scholar] [CrossRef]
  20. Chable, J.; Dieudonné, B.; Body, M.; Legein, C.; Crosnier-Lopez, M.-P.; Galven, C.; Mauvy, F.; Durand, E.; Fourcade, S.; Sheptyakov, D.; et al. Fluoride solid electrolytes: Investigation of the tysonite-type solid solutions La1−xBaxF3−x (x < 0.15). Dalton Trans. 2015, 44, 19625–19635. [Google Scholar] [CrossRef]
  21. Dieudonné, B.; Chable, J.; Mauvy, F.; Fourcade, S.; Durand, E.; Lebraud, E.; Leblanc, M.; Legein, C.; Body, M.; Maisonneuve, V.; et al. Exploring the Sm1–xCaxF3–x Tysonite Solid Solution as a Solid-State Electrolyte: Relationships between Structural Features and F- Ionic Conductivity. J. Phys. Chem. 2015, 119, 25170–25179. [Google Scholar] [CrossRef]
  22. Rongeat, C.; Reddy, M.A.; Witter, R.; Fichtner, M. Solid electrolytes for fluoride ion batteries: Ionic conductivity in polycrystalline tysonite-type fluorides. ACS Appl. Mater. Interfaces 2014, 6, 2103–2110. [Google Scholar] [CrossRef]
  23. Mori, K.; Morita, Y.; Saito, T.; Kamiyama, T.; Otomo, T.; Abe, T.; Fukunaga, T. Structural and Electrochemical Properties of Tysonite Ce0.95A0.05F2.95 (A = Mg, Ca, Sr, and Ba): Fast-Fluoride-Ion-Conducting Solid Electrolytes. J. Phys. Chem. C 2020, 124, 18452–18461. [Google Scholar] [CrossRef]
  24. Toma, O.; Rotella, H.; Dahab, H.; Maisonneuve, V.; Boulard, B. Tysonite-type solid state electrolyte for fluoride ion batteries: Highly dense thin film by PVD processing. J. Alloys Comp. 2021, 862, 158683. [Google Scholar] [CrossRef]
  25. Dieudonné, B.; Chable, J.; Body, M.; Legein, C.; Durand, E.; Mauvy, F.; Fourcade, S.; Leblanc, M.; Maisonneuve, V.; Demourgues, A. The key role of the composition and structural features in fluoride ion conductivity in tysonite Ce1-xSrxF3-x solid solutions. Dalton Trans. 2017, 46, 3761–3769. [Google Scholar] [CrossRef] [PubMed]
  26. Kaminskii, A.A.; Agamaljan, N.R.; Denisenko, G.A.; Sarkisov, S.E.; Fedorov, P.P. Spectroscopy and laser emission of disordered GdF3-CaF2:Nd3+ trigonal crystals. Phys. Stat. Sol. A 1982, 70, 397–406. [Google Scholar] [CrossRef]
  27. Kaminskii, A.A. Laser Crystals, Their Physics and Properties, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 1991; 457p. [Google Scholar]
  28. Moses, W.W.; Derenzo, S.E. CeF3—A new fast, heavy scintillator. IEEE Trans. Nucl. Sci. 1989, 36, 173–176. [Google Scholar] [CrossRef]
  29. Anderson, D.F. Properties of the high-density scintillator CeF3. IEEE Trans. Nucl. Sci. 1989, 36, 137–141. [Google Scholar] [CrossRef]
  30. Belli, P.; Bernabei, R.; Cerulli, R.; Dai, C.J.; Danevich, F.A.; Incicchittid, A.; Kobychev, V.V.; Ponkratenko, O.A.; Prosperi, D.; Tretyak, V.I.; et al. Performances of a CeF3 crystal scintillator and its application to the search for rare processes. Nucl. Instr. Meth. Phys. Res. 2003, 498, 352–361. [Google Scholar] [CrossRef]
  31. Gupta, S.K.; Mao, Y. Recent advances, challenges, and opportunities of inorganic nanoscintillators. Front. Optoelectron. 2020, 13, 156–187. [Google Scholar] [CrossRef]
  32. Nikl, M.; Yoshikawa, A.; Satonaga, T.; Kamada, K.; Sato, H.; Solovieva, N.; Beitlerova, A.; Fukuda, T. Scintillation characteristics of PrF3:Ce single crystal. Phys. Stat. Sol. A 2004, 201, R108–R110. [Google Scholar] [CrossRef]
  33. Feller, R.K.; Purdy, G.M.; Ortiz-Acosta, D.; Stange, S.; Li, A.; McKigney, E.A.; Esch, E.I.; Muenchausen, R.E.; Gilbertson, R.; Bacrania, M.; et al. Large-scale synthesis of CexLa1−xF3 nanocomposite scintillator materials. J. Mater. Chem. 2011, 21, 5716–5722. [Google Scholar] [CrossRef]
  34. Glushkova, T.M.; Kiselev, D.F.; Firsova, M.M.; Shtirkova, A.P.; Krivandina, E.A.; Zhmurova, Z.I. Refractometry of single crystals of solid solutions La1-xSrxF3-x (0< x < 0.15) with tysonite structure. Optichesk. Zhurn. 1997, 64, 31–33. (In Russian) [Google Scholar]
Ijms 24 14000 g001
Figure 1. The chemical design of 50 (out of 105) systems with the NTE-II materials (shown in color).
Figure 1. The chemical design of 50 (out of 105) systems with the NTE-II materials (shown in color).
Ijms 24 14000 g001
Ijms 24 14000 g002
Figure 2. The chemical design of Ttrans in the short QS “from PmF3 to GdF3(TbF3)”. Curve a-b-c-d-e, in the short “from PmF3 (point a) to GdF3 (Gd0.57Tb0.43F3, point e)” QS presents the dependence of Ttrans on Z.
Figure 2. The chemical design of Ttrans in the short QS “from PmF3 to GdF3(TbF3)”. Curve a-b-c-d-e, in the short “from PmF3 (point a) to GdF3 (Gd0.57Tb0.43F3, point e)” QS presents the dependence of Ttrans on Z.
Ijms 24 14000 g002
Ijms 24 14000 g003
Figure 3. The GdF3-DyF3 system of the TypeS-5 (B-C) with the β-ss →t-ssPolTr with NTE-II. ΔT > 0 is marked with a red arrow. The two-phase (t- + β-) region is highlighted in blue.
Figure 3. The GdF3-DyF3 system of the TypeS-5 (B-C) with the β-ss →t-ssPolTr with NTE-II. ΔT > 0 is marked with a red arrow. The two-phase (t- + β-) region is highlighted in blue.
Ijms 24 14000 g003
Ijms 24 14000 g004
Figure 4. The scheme of the CeF3-GdF3 system of the TypeS-7 (A-B) with NTE-II materials. The two-phase (t- + β-) region is highlighted in blue.
Figure 4. The scheme of the CeF3-GdF3 system of the TypeS-7 (A-B) with NTE-II materials. The two-phase (t- + β-) region is highlighted in blue.
Ijms 24 14000 g004
Ijms 24 14000 g005
Figure 5. The GdF3-ErF3 system from the TypeS-9 (B-D) with NTE-II materials. The two-phase (t- + β-) region is highlighted in blue.
Figure 5. The GdF3-ErF3 system from the TypeS-9 (B-D) with NTE-II materials. The two-phase (t- + β-) region is highlighted in blue.
Ijms 24 14000 g005
Table 1. The SSGrs A–D of RF3 in the ChCl [1,16].
Table 1. The SSGrs A–D of RF3 in the ChCl [1,16].
SSGrsRF3Structural Types of RF3Abbreviations
ALaF3, CeF3, PrF3, NdF3The high-temperature LaF3 t-type up to the meltt-
BDimorphic trifluorides:
PmF3, SmF3, EuF3, GdF3		(1) t-type up to the melt,
(2) The low temperature β-YF3 β-type		t-
β-
CTbF3, DyF3, HoF3β-type up to the meltβ-
DDimorphic trifluorides:
ErF3, TmF3, YbF3, LuF3		(1) α-YF3 α-type up to the melt,
(2) β-type		α-
β-
RF3 from the the SSGr B are highlighted in bold.
Table 2. Four TypeSs with components from the SSGr B with NTE-II materials.
Table 2. Four TypeSs with components from the SSGr B with NTE-II materials.
TypeS-N (B-X)
X = A, B, C, D		|ΔZ|max/|ΔZ|minSSGrTopological Signs of Phase DiagramsSystems with NTE-II
TypeS-3 (B-B’)3/1B = PmF3, SmF3, EuF3, GdF3Unlimited t-ss
and β-ss		6
TypeS-5 (B-C)6/1C = TbF3, DyF3, HoF3Unlimited β-ss
and limited t-ss +
MorphTr-1 (peritectic)		12
TypeS-7 (A-B)7/1A = LaF3, CeF3, PrF3, NdF3Unlimited t-ss +
limited β-ss		16
TypeS-9 (B-D)10/4D = ErF3, TmF3, YbF3, LuF3Limited t-ss +
unlimited β-ss
(MorphTr-1 + MorphTr-2)		16
RF3 from the the SSGr B are highlighted in bold.
Table 3. The TypeS-3 (B-B’) with the β-ss → t-ss PolTs and NTE-II.
Table 3. The TypeS-3 (B-B’) with the β-ss → t-ss PolTs and NTE-II.
No.B-B’|ΔZ|
1PmF3-SmF31
2SmF3-EuF31
3EuF3-GdF31
4PmF3-EuF32
5SmF3-GdF32
6PmF3-GdF33
Table 4. 12 systems of the TypeS-5 (B-C) with the β-ss → t-ss PolTrs and NTE-II.
Table 4. 12 systems of the TypeS-5 (B-C) with the β-ss → t-ss PolTrs and NTE-II.
No.B-C|ΔZ|No.B-C|ΔZ|
1 *GdF3-TbF317PmF3-TbF34
2EuF3-TbF328SmF3-DyF34
3GdF3-DyF329EuF3-HoF34
4SmF3-TbF3310PmF3-DyF35
5EuF3-DyF3311SmF3-HoF35
6GdF3-HoF3312PmF3-HoF36
* The studied systems are shown in bold.
Table 5. 16 systems of the TypeS-7 (A-B) with the β-ss → t-ss PolTrs and NTE-II.
Table 5. 16 systems of the TypeS-7 (A-B) with the β-ss → t-ss PolTrs and NTE-II.
No.A-B|ΔZ|No.A-B|ΔZ|
1NdF3-PmF319PrF3-EuF34
2PrF3-PmF3210 *NdF3-GdF34
3NdF3-SmF3211LaF3-SmF35
4CeF3-PmF3312CeF3-EuF35
5PrF3-SmF3313PrF3-GdF35
6NdF3-EuF3314LaF3-EuF36
7LaF3-PmF3415CeF3-GdF36
8CeF3-SmF3416LaF3-GdF37
* The studied systems are shown in bold.
Table 6. The TypeS-9 (B-D) from 16 systems with the β-ss → t-ss PolTr and NTE-II.
Table 6. The TypeS-9 (B-D) from 16 systems with the β-ss → t-ss PolTr and NTE-II.
No.B-D|ΔZ|No.B-D|ΔZ|
1 *GdF3-ErF349EuF3-YbF37
2EuF3-ErF3510GdF3-LuF37
3GdF3-TmF3511PmF3-TmF38
4SmF3-ErF3612SmF3-YbF38
5EuF3-TmF3613EuF3-LuF38
6GdF3-YbF3614PmF3-YbF39
7PmF3-ErF3715SmF3-LuF39
8SmF3-TmF3716PmF3-LuF310
* The studied systems are shown in bold.
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Sobolev, B.P.; Sulyanova, E.A. Two-Component Rare-Earth Fluoride Materials with Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in 50 RF3-R’F3 (R = La-Lu) Systems. Int. J. Mol. Sci. 2023, 24, 14000. https://doi.org/10.3390/ijms241814000

AMA Style

Sobolev BP, Sulyanova EA. Two-Component Rare-Earth Fluoride Materials with Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in 50 RF3-R’F3 (R = La-Lu) Systems. International Journal of Molecular Sciences. 2023; 24(18):14000. https://doi.org/10.3390/ijms241814000

Chicago/Turabian Style

Sobolev, Boris P., and Elena A. Sulyanova. 2023. "Two-Component Rare-Earth Fluoride Materials with Negative Thermal Expansion Based on a Phase Transition-Type Mechanism in 50 RF3-R’F3 (R = La-Lu) Systems" International Journal of Molecular Sciences 24, no. 18: 14000. https://doi.org/10.3390/ijms241814000

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop