Friday, January 18, 2019

First-order transitions and critical points in spin-crossover compounds

An interesting feature of spin-crossover compounds is that the transition from low-spin to high-spin with increasing temperature is usually a first-order phase transition. This is associated with hysteresis and the temperature range of the hysteresis varies significantly between compounds.
If there was no interaction between the transition metal ions the transition would be a smooth crossover. This is nicely illustrated in a figure taken from the paper below.

Abrupt versus Gradual Spin-Crossover in FeII(phen)2(NCS)2 and FeIII(dedtc)3 Compared by X-ray Absorption and Emission Spectroscopy and Quantum-Chemical Calculations 
Stefan Mebs, Beatrice Braun, Ramona Kositzki, Christian Limberg, and Michael Haumann


For the first compound, the transition is abrupt [much earlier work found a narrow hysteresis region of about 0.15 K]. For the second compound, the transition is a crossover.

The authors fit their data to an empirical equation that has a parameter n, describing the "interactions". You have to read the Supplementary Material to find the details. This equation cannot describe hysteresis.

 However, there is an elegant analytical theory going back to a paper by Wajnflasz and Pick from 1971. This is nicely summarised in the first section of a paper by Kamel Boukheddaden, Isidor Shteto, Benoit Hôo, and François Varret.
The system can be described by the Ising model

where the Ising spin denotes the high- and low-spin states. Delta is the energy difference between them and ln g the entropy difference.
The mean-field Hamiltonian for q nearest neighbours is

There are two independent dimensionless variables, d and r. Solving for the fraction of high-spin states (HS) versus temperature gives the graphs below for different values of d.
The vertical arrows show the hysteresis region for a specific value of d=2. 
As d increases the hysteresis region gets smaller. Above the critical value of d=r/2, the crossover temperature T0=Delta/ln g is larger than the mean-field critical temperature Tc= qJ, and the transition is no longer first-order but a crossover.
Using DFT-based quantum chemistry the authors calculate the change in vibrational frequencies and the associated entropy change for the SCO transition in a single molecule. The values for compound 1 and 2 are 0.68  and 0.21 meV/K respectively. The spin entropy changes are 0.21and 0.22 meV/K respectively. The total entropy changes are thus 0.89 and 0.43 meV/K respectively. The values of Delta are 175 and 125 meV, respectively. The corresponding crossover temperatures are 210 and 360 K, compared to the experimental values of 176 and 285 K.

If we assume that J is roughly the same for both compounds then the fact that the entropy change is half as big for compound 2, means r is twice as big. This naturally explains why the second compound has a smooth crossover, compared to the first, which is very close to the critical point.

Tuesday, January 15, 2019

Thinking skills for scientists (and engineers)

I keep coming back to the basic claim that the key ingredient of education is learning to think in particular ways. [n.b. In science, I am not at all playing up theory over experiment. You have to learn to think about what experiment to do and how to think about your results.].

In the past year, several people brought to my attention that MIT recently reviewed their engineering curricula. It is interesting that a key element is to teach students 11 ways of thinking. The list is worth reading and contemplating.

I have two minor comments. Although I affirm this as an admirable goal. I think the list is incredibly ambitious (even for MIT students) both in scope and content. But, maybe that is a good thing.
What do you think?

One of the 11 ways is Systems Thinking
Predicting emergence of the whole by examining inter-related entities in context, in the face of complexity and ambiguity, for homogeneous systems and systems that integrate multiple technologies.
Again, I love it. But, some would even argue you cannot predict emergence...

Wednesday, December 19, 2018

The relation between life changes, stress, and illness

I have often wondered about my personal experience and the anecdotal evidence that when you get stressed you seem more likely to get a cold or the flu. I finally found some research literature on the subject.
A helpful review is
Modern Approaches to Conceptualizing and Measuring Human Life Stress
Scott M. Monroe

A seminal paper from 50 years ago
The social readjustment rating scale 
TH Holmes, RH Rahe

The authors developed a quiz to estimate how your recent life circumstances and changes may be producing different levels of stress. They then correlated the stressful life circumstances to recent illness of the subjects.

It is worth occasionally doing the quiz. Here is one version.
Aside: One interesting aspect is that positive changes can create stress (e.g. starting a new job, getting married, having a baby, ...).

However, as discussed in detail by Monroe in his review all of this is more complicated than we might like. Measures of stress are subjective, subtle, personal, and hard to agree upon. For example, do you define the level of stress largely in terms of the environment or in terms of the response of the individual to the environment?
This is hardly surprising given that the subject is at the interface of medicine, psychology, and sociology.

Saturday, December 15, 2018

Metastability and first-order phase transitions

One of the simplest examples of a first-order phase transition is occurs in a ferromagnet at a temperature below the critical temperature and in an external magnetic field. The transition occurs when the field is varied so that it changes sign.

This can be described in terms of the following Landau free energy where H is the external field and r is negative.
One observes hysteresis as for non-zero H there is a metastable state.
The order parameter phi versus H is shown below

The boundaries of the region of metastability are defined by the field Hc given by
The above description is taken from a review article by Kurt Binder.
I have never seen this in a textbook.
Have you?
Any clear detailed presentations of this topic would be appreciated.



Monday, December 3, 2018

What should everyone know about science?

In a time when misunderstandings of science anti-science views are rising around the world, it is important that scientists do a better job of communicating to the broader public what science actually is, what it can do, and what it cannot do.

An interesting and important question is what it is that people should know and understand. There is a multitude of views on this (which is not necessarily a completely bad thing).

I only learned last week that in 1994, Phil Anderson had tackled this issue in a short article he wrote for The Daily Telegraph, a London-based newspaper. An interesting paper about Anderson's article just appeared. It nicely places the article in a broader context and gives a more recent perspective on the issues he raised.

Four Facts Everyone Ought to Know about Science:
The Two-Culture Concerns of Philip W. Anderson
Andrew Zhang and Andrew Zangwill

The four ``facts'' that Anderson chose were (as paraphrased by Zhang and Zangwill):

1. Science is not democratic.
2. Computers will not replace scientists.
3. Statistical methods are misused and often misunderstood.
4. Good science has aesthetic qualities.

This is a fascinating choice. 

One thing I learned was about Anderson's argument that Bayesian methods should have been used to rule out the significance of "discoveries" such as the 10 keV neutrino and the fifth force. In 1992 he wrote a Physics Today column on the subject.

Monday, November 26, 2018

A case for (and against) multi-dimensional measures

I am a vocal critic of the use of metrics to evaluate individuals, single scientific papers, journals, sub-fields, institutions, ....
However, my problem is really one of abuse. I don't think metrics are totally meaningless or useless. Rather, it is the mindless use of metrics, with a disregard for their limitations, that is a problem.

This post is not about metrics, jobs, and funding. I have probably already written too many posts on that. Rather, I want to give two examples where I have found some multi-dimensional metrics helpful, when considering issues relating to public policy and development, particularly in the Majority World.

The case is that of the HDI (Human Development Index). Prior to its introduction people tended to use GDP (Gross Domestic Product) as a measure of how a country was performing and where it ranked in the world. In contrast, the HDI is a composite metric, factoring in income per capita, life expectancy, and education. The map below gives a sense of how the HDI varies around the world.


There is a lot one can learn from just the map.  Sub-saharan Africa is the worst as a region. Even though India now has a middle class of several hundred million people, it is still comparable to some African countries.

Whenever I need to know something about a country, I look at the HDI. The fact that Australia often ranks in the top 3 tells me what a privileged environment I live in. Unfortunately, too many Australians really don't know or appreciate this.

I recently met a medical doctor from Niger [which I knew nothing about it]. He told me that Niger is ranked 182 out of 182 countries! This quickly gave me a sense of some of the challenges he faces.

Obviously, like any metric it has limitations. For example, some people prefer the IHDI (Inequality-adjusted HDI). The USA ranks 25th on the HDI.

The second example of a multi-dimensional metric concerns broader issues than human development, that is "human flourishing". This often means quite different things to different people. Last year there was a nice paper in PNAS that argues why this is important for both public policy, but also research in medicine and social sciences.

On the promotion of human flourishing 
Tyler J. VanderWeele

The abstract gives an excellent summary.
Many empirical studies throughout the social and biomedical sciences focus only on very narrow outcomes such as income, or a single specific disease state, or a measure of positive effect. Human well-being or flourishing, however, consists in a much broader range of states and outcomes, certainly including mental and physical health, but also encompassing happiness and life satisfaction, meaning and purpose, character and virtue, and close social relationships. The empirical literature from longitudinal, experimental, and quasi-experimental studies is reviewed in an attempt to identify major determinants of human flourishing, broadly conceived. Measures of human flourishing are proposed. Discussion is given to the implications of a broader conception of human flourishing, and of the research reviewed, for policy, and for future research in the biomedical and social sciences.
Broadly, when trying to describe and understand complex systems one should search for some measures of the properties of the system. Given the systems are complex one may need several measures. These will never be complete or perfect. But, provided one uses them with the appropriate caution this is a good thing.

Monday, November 19, 2018

How much background material do beginning graduate students need to master?

I am working with a graduate student beginning research and she has asked this important question. I don't think there is a simple universal answer.

Background material includes review articles of a field, details of an experimental technique or computer code, details of derivations, seminal articles on the topic, ....

At the UQ condensed matter theory group meeting, we had a brief discussion about the question.
Answers from students, both beginning and advanced, were helpful. It also underscored how important the question is because students really do struggle with this issue. One shared how he developed some mental health problems because at the beginning of his Ph.D. he was too obsessive about understanding all the details. The question and discussion underscored to me how we need to have more discussions of this nature.

Beginning research is a difficult transition for most graduate students. When they were undergraduates they often could understand all the details and work through all the derivations.
(They are unlike a significant fraction of undergraduates who just don't seem to realise that the details DO matter.)
However, the painful reality is that what was possible for a gifted and motivated undergraduate is simply not possible for most Ph.D. research.
Research fields are so vast and have so much foundational material a student simply does not have the time to check everything and understand everything in full.
The question is painfully relevant in Australia because Ph.D. students do not do coursework (or a Masters degree) and the government continues to reduce the number of years of funding.
Furthermore, the "publish or perish" culture puts pressure on students and advisors to be cranking out papers, which means there is pressure for students not to ``waste time'' on slow and deep learning of background material.

Like many things in life, I think answers to the question require some balance and need to allow for differences in personality, learning styles, personal goals, and nature of the research topic.

Here are some composite pictures to illustrate the extremes and the associated problems and potential.

Sanjay loves to understand and master details. He is also interested in the big foundational questions the research might address. When he reads an article he likes to work through all the details of the mathematical derivations. He would prefer to write his own computer code so he really knows what is going on. He has a large stack of papers on his desk, waiting to be read, consisting of many of the papers related to his research topic. After a year he is still learning background material. However, in his third year, he has a big breakthrough because he realises that one a key assumption/derivation in the field is wrong in certain cases. He not only corrects it but opens up a new avenue of research.

Priya just wants to get on with research and is not a detail oriented person. Following her advisors request she reads a few background articles superficially and dives into research. However, she does not really grasp the big picture or understand the limitations of the technique she is using. Consequently, she wastes a lot of time making mistakes, producing dubious results, and getting help for things she should have worked out for herself. However, this approach actually suits her learning style and she does eventually learn the essential things she needs to know and understand what is going on. Furthermore, because she has "dived in'' early, by the end of her Ph.D. she has produced several nice papers.

What do you think?
It would be good to hear from beginning graduate students, advanced graduate students, and faculty advisors.
What did you do? What do you wish you had done?