Thermal Analysis and Thermodynamics

In Materials Science

Detlef Klimm

• Publisher: De Gruyter
• Year: 2022
• eBook ISBN: 9783110743845
• Edition: 1
• Topic: Tecnologia e ingegneria
• Subtopic: Chimica fisica e teoretica

This introduction to thermodynamics discusses typical phase diagrams features and presents the wide range of techniques such as Differential Scanning Calorimetry, Thermogravimetry and others. In the last part the author brings many examples for typical practical problems often solved by thermal analysis. As an instructive guideline for practitioners the work reveals the connection between experimental data and theoretical model and vice versa.

1 Thermodynamic basis

1.1 Specific heat capacity

1.1.1 Phenomenological description

One of the first reports on experiments, which we would now call “thermal analysis”, was given by Le Chatelier (1887),¹ who described the heating of different clay minerals. In his experiments, the sample was heated with constant electric power $\mathit{W}={\mathit{U}}_{\text{h}}·{\mathit{I}}_{\text{h}}$ ( ${\mathit{U}}_{\text{h}}$ and ${\mathit{I}}_{\text{h}}$ are the voltage and current of the heater) and sample temperature T was recorded by a thermocouple (see Section 1.3.1) at constant time increments. It turned out that the measured heating rate $\dot{\mathit{T}}=d\mathit{T}\mathrm{/}d\mathit{t}$ was not constant, because endothermal reactions in the sample (e. g., dehydration processes or phase transitions) resulted in temporally smaller $\dot{\mathit{T}}$. It will be described in Section 2.1 how such a type of heating (or cooling) experiments was developed further to the modern technique of differential thermal analysis (DTA).

The experimental setup of Le Chatelier corresponds to the scheme in Fig. 1.1. If during time t, the amount of heat energy

(1.1)$\begin{array}{rcl}\mathit{Q}& =& \mathit{W}·\mathit{t}\\ & =& {\mathit{U}}_{\text{h}}·{\mathit{I}}_{\text{h}}·\mathit{t}\end{array}$

is transferred to one mole of a sample, then its temperature increases under isochor (volume constant; $\mathrm{\Delta }\mathit{V}=0$) or the more typical isobar (pressure $\mathit{p}=\mathrm{const}.$; often, $\mathit{p}=1\text{bar}={10}^5\text{Pa}$) conditions by

(1.2)$\begin{array}{rcl}\mathrm{\Delta }{\mathit{T}}_{\mathit{V}}& =& {\displaystyle \frac{\mathrm{\Delta }\mathit{Q}}{{\mathit{c}}_{\mathit{V}}}}\mathrm{,}\end{array}$

(1.3)$\begin{array}{rcl}\mathrm{\Delta }{\mathit{T}}_{\mathit{p}}& =& {\displaystyle \frac{\mathrm{\Delta }\mathit{Q}}{{\mathit{c}}_{\mathit{p}}}}\mathrm{,}\end{array}$

where ${\mathit{c}}_{\mathit{V}}$ and ${\mathit{c}}_{\mathit{p}}$ are proportionality parameters called the specific heat capacities of the material under the given conditions, V or $\mathit{p}=\mathrm{const}$. Especially for technical purposes, the amount of substance is often given by the mass $\mathit{m}=\mathit{n}\mathit{M}$, where n is the number of moles, and M is the molar mass. The difference

(1.4)$\begin{array}{c}{\mathit{c}}_{\mathit{p}}-{\mathit{c}}_{\mathit{V}}={\displaystyle \frac{\mathit{T}}{\mathit{n}}}{\mathrm{\left(}{\displaystyle \frac{\partial \mathit{V}}{\partial \mathit{T}}}\mathrm{\right)}}_{\mathit{p}}{\mathrm{\left(}{\displaystyle \frac{\partial \mathit{p}}{\partial \mathit{T}}}\mathrm{\right)}}_{\mathit{V}}\end{array}$

is positive but usually small for condensed phases with small thermal expansion $\partial \mathit{V}\mathrm{/}\partial \mathit{T}$ (solids, liquids). For ideal gases, we have ${\mathit{c}}_{\mathit{p}}-{\mathit{c}}_{\mathit{V}}=\mathit{R}$ (gas constant). Table 1.1 reports some data from the literature (Regen and Brandes, 1979; Paufler, 1986).

Figure 1.1 The experimental setup used by Le Chatelier (1887) allows the measurement of the specific heat capacity using equation (1.3).

Table 1.1Specific heat capacities near room temperature for several substances. For gases, ideal data are scaled by the gas constant R. Data for solid phases are given in J/(mol K).

Substance	${\mathit{c}}_{\mathit{p}}$	${\mathit{c}}_{\mathit{V}}$
1-atomic gas	$\frac{5}{2}\mathit{R...}$

Table of contents

• Title Page
• Copyright
• Contents
• 1 Thermodynamic basis
• 2 Techniques
• 3 Applications
• Subject Index